The galaxy-halo connection of disc galaxies over six orders of magnitude in stellar mass

Pavel E. Mancera Piña; Justin I. Read; Stacy Kim; Antonino Marasco; José A. Benavides; Marcin Glowacki; Gabriele Pezzulli; Claudia del P. Lagos

doi:10.1051/0004-6361/202554381

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Issue		A&A Volume 699, July 2025


Article Number		A311
Number of page(s)		29
Section		Extragalactic astronomy
DOI		https://doi.org/10.1051/0004-6361/202554381
Published online		18 July 2025

A&A, 699, A311 (2025)

The galaxy-halo connection of disc galaxies over six orders of magnitude in stellar mass

Pavel E. Mancera Piña¹^⋆, Justin I. Read², Stacy Kim³, Antonino Marasco⁴, José A. Benavides⁵, Marcin Glowacki⁶^,7, Gabriele Pezzulli⁸ and Claudia del P. Lagos⁹

¹ Leiden Observatory, Leiden University, P.O. Box 9513 2300 RA Leiden, The Netherlands
² Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK
³ Carnegie Theoretical Astrophysics Center, Carnegie Observatories, 813 Santa Barbara St, Pasadena, CA 91106, USA
⁴ INAF – Padova Astronomical Observatory, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy
⁵ Department of Physics and Astronomy, University of California, Riverside, 900 University Avenue, Riverside, CA 92521, USA
⁶ Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ, UK
⁷ Inter-University Institute for Data Intensive Astronomy, Department of Astronomy, University of Cape Town, Cape Town, South Africa
⁸ Kapteyn Astronomical Institute, University of Groningen, Landleven 12, 9747 AD Groningen, The Netherlands
⁹ International Centre for Radio Astronomy Research, Curtin University, Bentley, WA 6102, Australia

^⋆ Corresponding author: pavel@strw.leidenuniv.nl

Received: 5 March 2025
Accepted: 27 May 2025

Abstract

The relations between stellar (M_*), gas (M_gas), baryonic (M_bar = M_* + M_gas), and dark matter halo mass (M₂₀₀) provide unique constraints on galaxy formation and cosmology. The shape of the relations constrains how galaxies regulate their growth through gas accretion, star formation, and feedback, and their scatter probes the stochasticity of galaxy assembly, which depends on the underlying cosmological model. In this paper, we assemble a sample of 49 nearby gas-rich dwarf and massive disc galaxies with unmatched ancillary data. We obtain their gas kinematics and derive their dark matter properties through rotation curve decomposition. Our sample is representative of the regularly rotating gas-rich galaxy population and allowed us to study the galaxy-halo connection across nearly six orders of magnitude in M_*. We find that the M_gas − M₂₀₀ relation rises monotonically, with galaxies having around 4% of the average cosmological baryon fraction in cold gas. Contrastingly, the M_* − M₂₀₀ relation shows a more complex behaviour. A particularly interesting finding is that of a population of ‘baryon-deficient’ dwarfs (BDDs) with stellar masses ∼1 − 1.5 orders of magnitude lower than expected from current models. Yet, baryon-rich galaxies also exist, and we find a large spread in the baryon retention fraction across our galaxies. We compare our findings with semi-analytic (DarkLight) and hydrodynamical (TNG50, Simba) galaxy formation simulations. While the simulations broadly reproduce most observed features, they struggle to match the BDDs and do not capture the diversity in baryon fractions. Understanding these differences will shed new light on how feedback regulates galaxy formation. Finally, we study the dark matter halo concentration-mass relation. We find that below M₂₀₀ ∼ 10¹¹ M_⊙, the concentrations are systematically lower than expected from pure-dark matter simulations. We discuss whether these results stem from the influence of baryonic physics or the environment. Understanding this is crucial if gas-rich galaxies are to be used to test cosmological models.

Key words: galaxies: dwarf / galaxies: evolution / galaxies: formation / galaxies: halos / galaxies: kinematics and dynamics / galaxies: spiral

© The Authors 2025

Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1. Introduction

According to the current understanding of galaxy evolution, galaxies form in the centre of massive dark matter haloes. Cosmological accretion and mergers feed both dark matter and baryons, and together with stellar and active galactic nucleus feedback, they regulate galaxies through cosmic time (e.g. Press & Schechter 1974; Binney 1977; White & Rees 1978; Fall & Efstathiou 1980; Blumenthal et al. 1984; Dekel & Silk 1986; Frenk et al. 1988; Duffy et al. 2010; Lilly et al. 2013; Somerville & Davé 2015; Cimatti et al. 2019; Marasco et al. 2021). Despite the expected complexity in the above processes and the apparent stochasticity of some of them, they all result in the high degree of universality and regularity imprinted in the strong self-similarity observed in present-day galaxies. Examples of this are the existence of different scaling relations between various fundamental parameters such as mass (of dark matter and baryons), rotational speeds, angular momentum, star formation histories (SFHs), gas content, and sizes (e.g. Faber & Jackson 1976; Tully & Fisher 1977; Fall 1983; Kennicutt 1989; Courteau et al. 2007; van der Kruit & Freeman 2011; Cappellari et al. 2013; Cortese et al. 2016; Ponomareva et al. 2018; Catinella et al. 2018; Lelli et al. 2017; Posti et al. 2019a; Stone et al. 2021; Mancera Piña et al. 2021a; Geesink et al. 2025).

One of the most powerful tools for studying the dynamics of the galaxy-halo connection is mass modelling through rotation curve decomposition of high-resolution kinematics (see also e.g. Yasin et al. 2023; Yasin & Desmond 2024 for explorations with unresolved kinematics). With this technique, the observed kinematics of galaxies, typically traced with the neutral atomic hydrogen line (H I), are explained through a combination of the gravitational potentials provided by the observed baryons and a putative dark matter halo (e.g. Freeman 1970; Roberts & Rots 1973; Bosma 1978; van Albada & Sancisi 1986; Begeman 1987; Verheijen 1997; Bullock & Boylan-Kolchin 2017; Cimatti et al. 2019; Salucci 2019). Since one of the outcomes of rotation curve decomposition is the halo mass, this approach opens the possibility to investigate the stellar-, gas-, and baryonic-to-dark-matter mass fractions and to constrain how efficient galaxies have been at retaining their baryons, accreting gas, and forming stars through their evolution (e.g. Avila-Reese et al. 2008; Moster et al. 2010; Rodríguez-Puebla et al. 2015; Trujillo-Gomez et al. 2015; González-Samaniego et al. 2016; Chauhan et al. 2020; Girelli et al. 2020; Guo et al. 2020; Posti et al. 2019a; Korsaga et al. 2023; Dev et al. 2024; Lu et al. 2024).

The literature on the mass models of massive galaxies is extensive, and in recent years researchers have exploited high-quality samples using modern statistical techniques (e.g. Frank et al. 2016; Ren et al. 2019; Li et al. 2020; Zentner et al. 2022; Mancera Piña et al. 2022a). Among the most recent results are the findings that many of the most massive spiral galaxies have converted nearly all of their available baryons into stars (i.e. they have little to no ‘missing baryons’; e.g. Posti et al. 2019b; Di Teodoro et al. 2023) and that even sophisticated abundance-matching techniques and advanced cosmological hydrodynamical simulations struggle to reproduce galaxies with stellar masses (at fixed halo mass) as high as observed in nearby galaxies, arguably due to an overly efficient feedback implementation and/or wrong halo occupation fractions (e.g. Posti et al. 2019b,a; Marasco et al. 2020; Di Teodoro et al. 2023, and references therein).

Studying the low-mass regime (e.g. de Blok et al. 2001; Oh et al. 2015; Read et al. 2016a; Kaplinghat et al. 2020; Mancera Piña et al. 2022a; Bañares-Hernández et al. 2023; Roberts et al. 2024; Sylos Labini et al. 2025) is not straightforward, partially due to the difficulty of having dwarf galaxies with extended and high-resolution kinematics, near-infrared (NIR) photometry to trace the stellar mass (M_*), and accurate distance measurements. Yet, dwarfs are crucial for the study of dynamical scaling relations and can set strong and insightful constraints on galaxy formation and evolution theories given that their dynamical properties are susceptible to the underlying cosmological model, stellar feedback, their accretion histories and SFHs, and even the time at which reionisation took place (e.g. Di Cintio et al. 2014; Benítez-Llambay et al. 2015; Trujillo-Gomez et al. 2015; Oman et al. 2016; Read et al. 2016a, 2017; Robles et al. 2017; Fitts et al. 2018, 2019; Read et al. 2019; Agertz et al. 2020; Lazar et al. 2020; Nadler et al. 2020; Li et al. 2023; Danieli et al. 2023; Kim et al. 2024a; Koudmani et al. 2024; Oman et al. 2024; Muni et al. 2025). This makes the galaxy-halo connection in dwarfs a particularly powerful probe of both galaxy formation models and cosmology.

With this in mind, in this work, we build a curated sample of 49 nearby gas-rich dwarf and massive galaxies with archival high-resolution H I kinematics, NIR photometry, and accurate distance measurements. After obtaining robust kinematic models for our galaxies, we derived their mass models. This allowed us to infer our sample’s dark matter halo parameters and build a set of dynamical scaling laws to study the galaxy halo connection across six orders of magnitude in stellar mass with an unmatched quality sample. This work is organised as follows. We present our galaxy sample in Sect. 2. In Sect. 3, we build kinematic models for 22 of our dwarf galaxies, which we complement with literature models for the rest of our sample. The kinematic measurements are used in Sect. 4 to perform rotation curve decomposition. We present our resulting mass models in Sect. 5, together with the derived best-fitting dark matter halo parameters, mass-to-light ratios, and the gas scale heights of our sample. In Sect. 6, we study different scaling laws between baryonic and dark matter properties across six orders of magnitude in stellar mass, and we discuss the implications of our results. Finally, we summarise our main results in Sect. 7. Throughout this work, we adopt a Λ cold dark matter (CDM) cosmology with Ω_m = 0.3, Ω_Λ = 0.7 and H₀ = 70 km s⁻¹ Mpc⁻¹.

2. Data and sample

To obtain rotation curve decomposition as reliably as possible, it is necessary to perform mass modelling on a galaxy sample with the following characteristics: (i) high-resolution H I data to accurately trace the gas spatial distribution and kinematics; (ii) regular kinematic patterns of rotation to ease kinematic and dynamical modelling; (iii) kinematic models simultaneously obtaining the gas rotational velocity and velocity dispersion; (iv) inclination angles ≳35° (to avoid large uncertainties when deprojecting line-of-sight velocities) but lower than ∼80° (for which current kinematic modelling is not well suited); (v) deep NIR imaging to trace their stellar component robustly (e.g. McGaugh & Schombert 2014; Ponomareva et al. 2018; Marasco et al. 2025); and (vi) precise redshift-independent distances such as those coming from the tip of the red giant branch (TRGB) or Cepheids. Meeting all of these requirements is not straightforward. In this work, we have compiled a sample of nearby field dwarf and massive galaxies with those characteristics based on available public data. The following sections describe our galaxy sample and the gas and NIR imaging data we employed.

2.1. Massive galaxies

We select massive (M_* ≳ 10^9.5 M_⊙) galaxies following Mancera Piña et al. (2022a). Specifically, we start with a base sample of spiral galaxies with high-resolution H I data from Di Teodoro & Peek (2021). Of that initial sample, we keep only galaxies with regular kinematics, inclination angles 35° ≲i ≲ 80°, archival NIR photometry, available 2D bulge-disc decompositions (see below), available distances from standard candles (exclusively TRGB, Cepheids, or supernovae), and CO imaging (tracing molecular gas, H₂). Our selection cuts result in a sample of 16 massive spiral galaxies: NGC 0253, NGC 1313, NGC 2403, NGC 3198, NGC 3351, NGC 3621, NGC 3992, NGC 4535, NGC 4536, NGC 4559, NGC 4651, NGC 4725, NGC 4736, NGC 5005, and NGC 5055.

The H I surface densities are taken directly from Di Teodoro & Peek (2021), while the H₂ surface densities come from Mancera Piña et al. (2022a). Both H I and H₂ surface densities were derived from azimuthally averaged profiles of the total intensity maps and corrected by a factor of 1.36 to account for helium (the typical correction factor for our average M_*, see McGaugh et al. 2020), i.e. Σ_gas = 1.36 (Σ_HI + Σ_H₂). Obtaining robust constraints on the stellar surface densities (Σ_*) is particularly important for our massive galaxies since M_* dominates their baryonic budget. All our massive galaxies have (by selection) Spitzer (Werner et al. 2004) 3.6 μm surface brightness profiles. Their morphology can be complex, and careful 2D bulge-disc decomposition is necessary. Because of this, we rely upon the 2D bulge-disc¹ decomposition by Salo et al. (2015). The only three exceptions are NGC 2403, NGC 3198, and NGC 3621 (all discs without bulges, see Sect. 2.2.3 in Mancera Piña et al. 2022a), whose 3.6 μm surface brightness profiles are taken from Mancera Piña et al. (2022a).

The distances (TRGB or Cepheids) to all these galaxies are taken from the NASA/IPAC Extragalactic Database (NED) and the original references are Parodi et al. (2000), Saha et al. (2006), Rizzi et al. (2007), Takanashi et al. (2008), Dalcanton et al. (2009), Jacobs et al. (2009), Radburn-Smith et al. (2011), Foster et al. (2014), McQuinn et al. (2017), Sabbi et al. (2018). We note that these distances can differ from those reported in Di Teodoro & Peek (2021) and Mancera Piña et al. (2022a).

2.2. Dwarf galaxies

To assemble our dwarf sample, we first start with the sample from Iorio et al. (2017), who obtained kinematic models from a subset of galaxies from LITTLE THINGS (Local Irregulars That Trace Luminosity Extremes, The H I Nearby Galaxy Survey, Hunter et al. 2012). After selecting galaxies with inclinations 35° ≲i ≲ 80°, distances from standard candles, NIR photometry, and regular kinematics (see also Read et al. 2017), we end up with 11 dwarfs. The H I surface density profiles are taken from Iorio et al. (2017) and are azimuthally averaged radial profiles. Since molecular gas is expected to be dynamically negligible (e.g. Leroy et al. 2008, but see also Hunter et al. 2021), the gas surface densities are computed as Σ_gas = 1.33 Σ_HI. NIR (Spitzer 3.6 μm) surface brightness profiles are taken from Zhang et al. (2012) and Bouquin et al. (2018).

To expand this sample, we inspected different public H I surveys, namely: LVHIS (The Local Volume H I survey, Koribalski et al. 2018), THINGS (The H I Nearby Galaxy Survey, Walter et al. 2008), LITTLE THINGS, WHISP (Westerbork observations of neutral Hydrogen in Irregular and SPiral galaxies, van der Hulst et al. 2001), VLA-ANGST (Very Large Array – ACS Nearby Galaxy Survey Treasury, Ott et al. 2012) and HALOGAS (Hydrogen Accretion in LOcal GAlaxieS, Heald et al. 2011). To ensure a high-quality sample of dwarfs, we examine all the galaxies in the above surveys and select those with NIR images, TRGB/Cepheids distances, clear gradients in their velocity fields with rotational velocities ≲100 km/s, kinematic maps traced with at least five beams, and inclinations in the range 40° −80°. Our selection results in 22 galaxies. For these dwarfs, we derive Σ_gas = 1.33 Σ_HI from azimuthally averaged profiles.

For 16 out of these 22 dwarfs, Spitzer imaging at 3.6 μm is available. Our 3.6 μm surface brightness data come either from (the Sérsic parameters of) Salo et al. (2015), from the S4G survey (Bouquin et al. 2018), or, if the profiles are not publicly available, we download the 3.6 μm imaging from the NASA/IPAC Infrared Science Archive and derive azimuthally averaged surface brightness profiles following Marasco et al. (2019). For the remaining six galaxies (LVHIS 019, LVHIS 020, LVHIS 026, LVHIS 055, LVHIS 060, LVHIS 072), Kirby et al. (2008) and Young et al. (2014) provide H-band (1.65 μm) imaging; specifically, we use their Sérsic profiles fits. All our dwarf galaxies have distances derived from the TRGB or Cepheids methods and have been determined by Tully et al. (2006), Saha et al. (2006), Dalcanton et al. (2009), Jacobs et al. (2009), and Tully et al. (2013).

2.3. The final sample

From the above, we end up with a curated sample of 49 nearby, central, gas-rich galaxies. Since the galaxies come from different surveys and lie at different distances, they have a range of spectral and spatial resolutions. In the case of the former, it ranges between ∼1 and 5 km/s, and the latter between ∼0.1 and 2 kpc. These resolutions, coming from the most complete and dedicated publicly available H I surveys, are sufficient to provide robust kinematic and dynamic constraints (e.g. de Blok & Walter 2000; Verheijen 1997; Di Teodoro & Fraternali 2015; Oh et al. 2015; Lelli et al. 2016a; Read et al. 2016a; Iorio et al. 2017; Marasco et al. 2019). Despite coming from different surveys, we emphasise that our sample is homogenous: all galaxies have high-resolution H I (and CO for the massive ones) interferometric data, gas surface densities derived in the same way, distances from standard candles, and NIR photometry. Moreover, their kinematics were derived following similar approaches with the same fitting software (Sect. 3).

While our sample is driven by the data quality and is therefore not volume complete and has a complex selection function (similar to samples at higher masses in the literature; e.g. Lelli et al. 2016a; Ponomareva et al. 2016; Mancera Piña et al. 2021a), it is representative of the nearby dwarf galaxy population with regular kinematics and large gas reservoirs. To illustrate this, Fig. 1 presents an overview of our sample’s mass and kinematic properties. Specifically, the figure shows our sample in (i) the M_* − M_HI plane contrasted with the complete ALFALFA-SDSS sample of gas-rich galaxies (Durbala et al. 2020), (ii) the baryonic Tully-Fisher relation of Di Teodoro et al. (2023), and (iii) the stellar specific angular momentum vs mass (j_* − M_*) relation from Mancera Piña et al. (2021b). The stellar, gas, and baryonic masses of our galaxies are computed in Sect. 6, while V_circ is obtained in Sect. 3. The derivation of j_* follows Mancera Piña et al. (2021b). Fig. 1 highlights that our full sample has similar properties to the broad population of nearby star-forming galaxies across six orders of magnitude in M_*. Table A.1 lists the galaxy names (and SIMBAD link to check cross-IDs), their distance, characteristic outer circular speed V_circ, out, and average inclination.

Fig. 1.

Overview of our galaxy sample. We place our galaxies in different scaling relations. Top: Stellar mass vs. H I mass plane. The representative ALFALFA-SDSS sample (Durbala et al. 2020) is shown for comparison. Middle: Baryonic Tully-Fisher relation (BTFR; from Di Teodoro et al. 2023). Bottom: Stellar specific angular momentum vs. mass relation (j_* − M_*; from Mancera Piña et al. 2021b). In the top panel, the colour scale increases logarithmically with the density of the data counts. The shaded bands in the middle and top panels correspond to 1σ and 2σ from the best-fitting relations (black dashed lines).

3. Kinematic modelling

Gas kinematics can suffer from beam smearing if the size of the beam (PSF) is not negligible compared to the extent of the galaxies (e.g. Swaters 1999; Di Teodoro & Fraternali 2015; Iorio et al. 2017). This effect should be weak in our sample of massive galaxies because of the high spatial resolution, but ideally, it should be taken into account. For the dwarfs, with a smaller physical extent, correcting for beam smearing is imperative (Di Teodoro & Fraternali 2015; Iorio et al. 2017). In addition, determining the rotation velocity of the gas (V_rot) and its velocity dispersion (σ_{_HI}) self-consistently is crucial to estimating the circular speed of the galaxies and their thickness (see below). Considering this, one of the primary requisites when building our sample was to have (or to be able to derive) kinematic measurements free of beam smearing and with simultaneous determination of V_rot and σ_{_HI}.

In the case of our 16 massive galaxies, Di Teodoro & Peek (2021) derived their kinematic parameters using the software ^3DBarolo² (Di Teodoro & Fraternali 2015). ^3DBarolo implements a forward modelling approach that mitigates beam smearing while fitting simultaneously V_rot and σ_{_HI} (together with radial motions and geometric parameters if needed and if the spatial resolution is high). In practice, ^3DBarolo makes realisations of tilted-ring models (Rogstad et al. 1974) and, after convolution with the observational beam, compares them against the data using all the channel maps of the data cube. ^3DBarolo has been well-tested for a variety of data with different resolutions, emission lines, and redshifts (e.g. Di Teodoro et al. 2016; Iorio et al. 2017; Mancera Piña et al. 2019; Bacchini et al. 2020; Di Teodoro & Peek 2021; Rizzo et al. 2023; Mancera Piña et al. 2024; Deg et al. 2024; Rowland et al. 2024; Liu et al. 2025a).

From our sample of low-mass galaxies, 11 of them already have kinematic models derived using ^3DBarolo by Iorio et al. (2017)³, which we adopt⁴. We use ^3DBarolo to obtain the kinematic models for the remaining 22 galaxies, namely DDO 181, DDO 183, DDO 190, IC 2574, LVHIS 009, LVHIS 011, LVHIS 012, LVHIS 017, LVHIS 019, LVHIS 020, LVHIS 026, LVHIS 055, LVHIS 060, LVHIS 072, LVHIS 077, LVHIS 078, LVHIS 080, NGC 0925, NGC 2541, NGC 4190, NGC 7793, and UGC 1501. In the remaining part of this section, we describe the methodology used to derive the kinematic measurements.

As the first step for our kinematic modelling, we obtain initial estimates for the centre, position angle, and inclination of the H I discs. For this we use the software cannubi⁵ (see Fraternali et al. 2017; Mancera Piña et al. 2020; Roman-Oliveira et al. 2023), which uses a Markov Chain Monte Carlo (MCMC) forward modelling to find the centre, position angle, and inclination of a model H I map that better matches the observed data. Reassuringly, the results found by cannubi agree with the values found from photometry (Kirby et al. 2008; Zhang et al. 2012; Young et al. 2014; Koribalski et al. 2018) within a few degrees. Once the initial guesses for the geometrical parameters are estimated, we proceed to use ^3DBarolo to derive azimuthal models and obtain the best-fitting position angle, inclination, V_rot, and σ_{_HI}. We note that the position angle and inclination are only allowed to vary within 20 and 10 degrees from our input values (and generally, the resulting values move much less from the initial estimates), which is twice the typical uncertainty found by cannubi and our isophotal fitting. We performed our kinematic modelling following the next steps for each galaxy.

We set the ring separation for the tilted ring modelling (RADSEP within the ^3DBarolo environment). As a compromise between having a suitable rotation curve sampling but not oversampling the fit (having a strong correlation between the pixels), we chose RADSEP = 0.75 (b_maj b_min)^1/2, with b_maj and b_min the major and minor axes of the beam, respectively.
We built a mask. In practice, we first generated a preliminary mask using the SEARCH option in ^3DBarolo, which we then enlarged with a custom code by two or three pixels. This strategy avoids significant noise from being included, but it keeps faint H I emission, which is vital to tracing σ_{_HI} and V_rot in the outer discs.
We performed the first iteration of the kinematic modelling. We allowed ^3DBarolo to estimate the systemic velocity (V_sys) of the galaxies (based on the global H I spectrum) and their centre (based on the total H I map), which we found in good agreement with the results from cannubi. As free fitting parameters, we considered V_rot, σ_{_HI}, the position angle and the inclination. The last two parameters were regularised with smooth functions (typically straight lines or polynomials of degree one or two, see Di Teodoro & Fraternali 2015).
We inspected the first ^3DBarolo fit. We corroborated that V_sys is correct based on inspection of the position-velocity (PV) diagrams of the data and the model, which would be offset if V_sys is wrong. If needed, we manually adjusted V_sys, but this occurred only seldom. We fixed the value of V_sys.
We inspected whether ^3DBarolo finds evidence for a change (i.e. a warp) in position angle or inclination. At the same time, using the PV diagrams, we investigated if there are hints of radial motions (visible as gradients in the minor-axis PV; see Di Teodoro & Peek 2021).
We obtained a new kinematic model. If in the previous step we found evidence (from the visual inspection of the ^3DBarolo outputs) for warps in the position angle or inclination (or radial motions), we considered them as free parameters again together with V_rot and σ_{_HI}; otherwise (most of the time in practice), the only free parameters are V_rot and σ_{_HI}.
We performed a final check on the kinematic models (moment maps, channel maps, PV diagrams). If they could be improved, we repeated steps 4 to 6.

In this way, we fit our data cubes with ^3DBarolo. We obtain satisfactory models for all 22 galaxies, closely resembling the observations. Fig. 2 shows the kinematics (velocity field, PV slices for data and best-fitting model, and kinematic radial profiles, see below) for four representative galaxies; similar plots for the remaining galaxies can be found inFig. B.1.

Fig. 2.

Kinematics of four representative galaxies in our sample (see also Fig. B.1). (a): Velocity field (first moment map). We also show the kinematic (white circles) and average (black dashed lines) position angles as well as the beam (grey ellipse) of the observations. (b) and (c): Position-velocity slices along the average major (b) and minor (c, perpendicular to b) axes. The data are represented with a blue background and black contours (grey for negative values), while the best-fitting ^3DBarolo model is shown with red contours. Contours are plotted at 2ⁿ× the noise, with n = 1, 2, …, n. (d) Rotation curve, circular speed, and gas velocity dispersion. We emphasise that the velocity fields are shown for illustration purposes, but ^3DBarolo fits the entire data cube.

As expected by our sample selection, our dwarfs show ordered kinematics. On top of the velocity fields in Figs. 2 and B.1, we show the best-fitting (white circles) and average (black dashed line) kinematic position angle for our galaxies. As can be seen, most galaxies have constant position angles (so the white circles and the black dashed line overlap), with only a few showing compelling position angle warps (but still ordered rotation; e.g. DDO 181, LVHIS 009, LVHIS 077, NGC 2541, NGC 4190). The only galaxies with a warp in inclination are LVHIS 0012, LVHIS 078, NGC 0925, NGC 2541, and NGC 7793, albeit their effect is minor since the changes are of the order of 5° −10°. Three galaxies (LVHIS 019, LVHIS 055, and LVHIS 078) also show some evidence of radial motions (as seen in their X-shaped minor-axis PVs). However, the amplitudes of the radial velocities are negligible compared to the circularmotions.

The final step before going into the mass modelling is to compute the circular speed (V_circ) of the galaxies, i.e. correcting the observed V_rot for pressure-supported motions with the asymmetric drift correction (e.g. Binney & Tremaine 2008; Iorio et al. 2017; Cimatti et al. 2019; Mancera Piña et al. 2021b). For this, we follow the procedure detailed in Iorio et al. (2017) and refer the reader to that work (see their Sect. 4.3) for details. To show the effect that the asymmetric drift correction has on our data, we show in the right panels of Figs. 2 and B.1 the V_rot, σ_{_HI}, and V_circ profiles for the 22 galaxies with kinematics derived in this work. We make our kinematic profiles publicly available under this link. As shown below, these kinematic measurements can be used to test dynamical and gravity theories in the dwarf-galaxy regime. As mentioned before, we take the public kinematic measurements from the remaining galaxies from Iorio et al. (2017) and Di Teodoro & Peek (2021). With this, we have all the kinematic information for our entire sample, which is used in the following section during our rotation curve decomposition.

4. Building the mass models

The technique of obtaining mass models through rotation curve decomposition consists of reproducing the observed circular speed of galaxies considering the gravitational potential provided by baryons and dark matter, i.e.

$\begin{matrix} V_{circ}^{2} = Υ_{d} V_{d} | V_{d} | + Υ_{b} V_{b} | V_{b} | + V_{HI} | V_{HI} | + V_{H_{2}} | V_{H_{2}} | + V_{DM} | V_{DM} |, \end{matrix}$ $\begin{aligned} V_{\rm circ}^2 = \Upsilon _{\rm d} V_{\rm d}|V_{\rm d}| + \Upsilon _{\rm b} V_{\rm b}|V_{\rm b}| + V_{\rm HI}|V_{\rm HI}| + V_{\rm H_2}|V_{\rm {H_2}}| + V_{\rm DM}|V_{\rm DM}|\ , \end{aligned}$ (1)

where V_d, V_b, V_HI, V_H₂ and V_DM are the contributions provided by the stellar disc (up to its mass-to-light ratio), stellar bulge (up to its mass-to-light ratio), H I disc, H₂ disc and dark matter halo, respectively. The parameters Υ_d and Υ_b are the disc and bulge stellar mass-to-light ratios, normalising V_d, and V_b, respectively. Mass modelling assumes dynamical equilibrium (e.g. Binney & Tremaine 2008) such that the rotational motions trace the gravitational potential (for possible caveats see Downing & Oman 2023). Our mass modelling technique follows closely Mancera Piña et al. (2022a). In the following sections, we provide an overview of our main steps. We note that for galaxies without bulges (molecular gas), V_b (V_H₂) = 0.

4.1. The baryonic contribution

We determine V_d, V_b, and V_HI, and V_H₂ using the software GALPYNAMICS⁶, which computes numerically the gravitational potential of a given mass density profile. In our case, we determine the gravitational potential of the stellar disc and bulge (modulo Υ) and the gas components, together with their vertical distributions. GALPYNAMICS takes as input a continuous function for its numerical integration (see Cuddeford 1993; Iorio 2018; Mancera Piña et al. 2022a), so we fit the observed stellar and gas radial profiles with one of the following functional forms:

$\begin{matrix} Σ (R) = Σ_{0} e^{- R / R_{1}} {(1 + R / R_{2})}^{α}, \end{matrix}$ $\begin{aligned} \Sigma (R) = \Sigma _{0}\ e^{-R/\mathrm{R_{1}}} (1+R/\mathrm{R_{2}})^\alpha \ , \end{aligned}$ (2)

$\begin{matrix} Σ (R) = Σ_{e} exp {- b (n) [{(\frac{R}{R_{e}})}^{\frac{1}{n}} - 1]}, \end{matrix}$ $\begin{aligned} \Sigma (R) = \Sigma _{\rm e} \exp \left\{ -b(n) \left[ \left( \frac{R}{R_{\rm e}} \right)^{\frac{1}{n}} - 1 \right] \right\} \ , \end{aligned}$ (3)

$\begin{matrix} Σ (R) = Σ_{0, pex} e^{- R / R_{pex}} (1 + c_{1} R + c_{2} R^{2} + c_{3} R^{3} + \dots + c_{n} R^{n}) . \end{matrix}$ $\begin{aligned} \Sigma (R) = \Sigma _{\rm 0,pex}\ e^{-R/R_{\rm pex}}\ (1 + c_1 R + c_2 R^2 + c_3 R^3 +\ldots + c_n R^n)\ . \end{aligned}$ (4)

We used Eq. (2) (e.g. Oosterloo et al. 2007) to fit most of our H I profiles, as it mimics the typical behaviour of H I discs having a plateau or sink in their centre to then decay exponentially. Eq. (3) is the well-known Sérsic profile (Sersic 1968), which we use to fit most of the stellar surface profiles (for the massive galaxies Salo et al. (2015) provides directly the bulge⁷ and disc Sérsic parameters). Finally, Eq. (4) is a ‘poly-exponential’ disc, whose flexibility we use to fit the H₂ profiles as well as those H I and stellar profiles with more complex behaviour. For the galaxies from Di Teodoro & Peek (2021) and Iorio et al. (2017) we take the coefficients ([Σ₀, R₁, R₂, α], [Σ_e, n, R_e], and [Σ_0, pex, R_pex, c₁, c₂, c₃, c₄]) from Mancera Piña et al. (2022a). For the remaining 22 dwarfs, we fit the different free parameters using the MCMC fitting software emcee (Foreman-Mackey et al. 2013), adopting uniform priors.

Next, we specify the vertical distribution of the stellar and gas discs. For the former, we assume a sech² profile with a constant thickness $z_{d} / kpc = 0.196 {(R_{d} / kpc)}^{0.633}$ $z_{\mathrm{d}}/\rm{kpc} = 0.196\, (\mathit{R}_{\mathrm{d}}/\rm{kpc})^{0.633}$ (with R_d the scale length of Σ_*), as typically found in star-forming galaxies (Bershady et al. 2010). For the gas discs, which are known to flare with radius (e.g. Romeo 1992; Olling 1995; Kalberla & Dedes 2008; Marasco & Fraternali 2011; Yim et al. 2014; Patra 2020a; Jeffreson et al. 2022), we assume a Gaussian vertical profile and determine their flaring at the same time as deriving the mass models (see below) by exploiting the balance between the gravitational potential and the gas velocity dispersion in disc systems in vertical hydrostatic equilibrium (see Romeo 1992; Iorio 2018; Bacchini et al. 2019; Mancera Piña et al. 2022a).

The stellar mass-to-light ratios are the final ingredients to specify the baryonic contribution to the total V_circ. We treat Υ_d and Υ_b as free parameters but take advantage of well-known priors on NIR mass-to-light ratios, as we discuss in Sect. 4.3.

4.2. The dark matter contribution

To determine the gravitational contribution from the dark matter haloes, we parametrise their density with functional forms. The Navarro-Frenk-White (NFW, Navarro et al. 1997) profile is a commonly used halo profile. The NFW haloes have a density given by

$\begin{matrix} ρ_{NFW} (r) = \frac{4 ρ_{s}}{(r / r_{s}) {(1 + r / r_{s})}^{2}}, \end{matrix}$ $\begin{aligned} \rho _{\rm NFW}(r) = \dfrac{4\,\rho _{\rm s}}{(r/r_{\rm s})\,(1 + r/r_{\rm s})^2}\ , \end{aligned}$ (5)

with $r = \sqrt{R^{2} + z^{2}}$ $r\ =\ \sqrt{R^2+z^2}$ the spherical radius, r_s a scale radius (for an NFW, r_s = r₋₂, with r₋₂ the radius at which the log-slope of the profile equals −2), and ρ_s the volume density at r_s.

The enclosed mass of the profile is given by

$\begin{matrix} M_{NFW} (< r) = \frac{M_{200}}{ln (1 + c_{200}) - \frac{c_{200}}{1 + c_{200}}} \\ \times [ln (1 + \frac{r}{r_{s}}) - \frac{r}{r_{s}} {(1 + \frac{r}{r_{s}})}^{- 1}], \end{matrix}$ $\begin{aligned} M_{\rm NFW}({ < }r) = \dfrac{M_{200}}{\ln (1+c_{200}) - \dfrac{c_{200}}{1+c_{200}}} \nonumber \\ \times \, \left[\ln \left( 1 + \dfrac{r}{r_{\rm s}}\right) - \dfrac{r}{r_{\rm s}} \left( 1 + \dfrac{r}{r_{\rm s}}\right)^{-1} \right], \end{aligned}$ (6)

where M₂₀₀ is the halo mass within the radius R₂₀₀ (where the average density is 200 times the critical density of the universe, M₂₀₀/R₂₀₀³ = (4 π/3) 200 ρ_{crit(z = 0)}), and c₂₀₀ ≡ R₂₀₀/r₋₂ = R₂₀₀/r_s is the concentration parameter.

However, different studies suggest that galaxies (especially dwarfs) can have dark matter profiles that are cored (e.g. Moore 1994; Burkert 1995; de Blok et al. 2008; Oman et al. 2015; Bullock & Boylan-Kolchin 2017; Salucci 2019; Sales et al. 2022; Collins & Read 2022, but see also Roper et al. 2023) for which the cuspy NFW is not appropriate, and different profiles with flatter inner dark matter densities have been proposed (e.g. Begeman 1987; Burkert 1995; Read et al. 2016b; Freundlich et al. 2020; Lazar et al. 2020). In this work, we use the CORENFW profile (Read et al. 2016b,a), which gives extra freedom to the NFW profile to develop a core.

The CORENFW halo has the density profile

$\begin{matrix} ρ_{c o r e NFW} (r) = f^{n} ρ_{NFW} (r) + \frac{n f^{n - 1} (1 - f^{2})}{4 π r^{2} r_{c}} M_{NFW} (r) . \end{matrix}$ $\begin{aligned} \rho _{core {NFW}}(r) = f^n\, \rho _{\rm NFW}(r) + \dfrac{n\,f^{n-1}\,(1-f^2)}{4\,\pi \, r^2\, r_{\rm c}} M_{\rm NFW}(r)\ . \end{aligned}$ (7)

In this equation, ρ_NFW and M_NFW represent the density and mass for a NFW halo, f = tanh(r/r_c) is a function that generates a core of size r_c, and n is a parameter that regulates the cusp-core transition (n = 0 reduces to the NFW halo, while n = 1 produces a completely cored profile).

It follows then that the CORENFW has originally four free parameters M₂₀₀, c₂₀₀, n, and r_c. Based on simulations, Read et al. (2016b,a, 2017) proposed calibrations for n and r_c. For n, those authors propose n = tanh(κ t_SF/t_dyn), with κ = 0.04, t_SF the time whilst the galaxy has been forming stars (assumed to be 14 Gyr), and t_dyn the NFW dynamical time at r_s. For r_c, they propose r_c = η R_e, with η ≈ 1.75 and R_e the stellar half-light radius. However, this work treats n and r_c differently. To avoid relying entirely on the results from the simulations, we assume r_c = η R_e but treat η as a free parameter (with priors defined below). Moreover, we fix n = 1 to ensure that r_c is unambiguously defined and matches the inner radius where the coreNFW visually departs from the NFW. We note that fixing n = 1 does not preclude haloes from being cuspy: If the data prefer the NFW profile, then the fit can do so with r_c → 0. Therefore, the free parameters of our CORENFW haloes are M₂₀₀, c₂₀₀, and η. With Υ_d, Υ_b, and the vertical scale height of the gas discs, these parameters were later determined with our rotation curve decomposition. The next section explains the fitting procedure (Mancera Piña et al. 2022a).

4.3. Self-consistent mass models with gas disc flaring

The free parameters in our mass models (log(Υ_d), log(Υ_b), log(M₂₀₀), log(c₂₀₀), and log(η)) are found through a Bayesian Monte Carlo approach. Specifically, we use the software dynesty (Speagle 2020) to efficiently estimate their posterior distributions and evidence through nested sampling. This way, we can explore the full parameter space and build trial mass models to minimise Eq. (1). For the minimisation we use a likelihood of the form exp(−0.5χ²), with χ² = (V_circ − V_circ, mod)²/δ_{V_circ}². Here V_circ and V_circ, mod are the observed and model circular speed profiles, and δ_{V_circ} the uncertainty in V_circ.

The exploration of the parameter space follows a set of priors. For the sampling parameter log(Υ_d) we use Gaussian priors on Υ_d (so lognormal priors on log(Υ_d)). The priors are centred in the empirical luminosity–Υ_d relations described in Appendix C and are motivated by model Υ_d values obtained through SED fitting in some of our galaxies, following the procedure described in Marasco et al. (2025). Moreover, the priors also agree with stellar population models (SPMs) and dynamical estimates (e.g. McGaugh & Schombert 2014; Meidt et al. 2014; Querejeta et al. 2015; Marasco et al. 2025), as discussed in Appendix C. For Υ_b, SPMs in the NIR suggest Υ_b ≈ 1.2 − 1.6 Υ_d (Schombert et al. 2022). Therefore, we assumed the flat prior Υ_d < Υ_b < 2 Υ_d.

For the halo mass, we explore a flat prior bounded within 6 < log(M₂₀₀/M_⊙) < 14. In turn, for log(c₂₀₀) we use a Gaussian prior centred on the c₂₀₀ − M₂₀₀ relation of Diemer & Joyce (2019, hereafter DJ19), for which we assume a 1σ standard deviation (in log space) of 0.16 dex (Diemer & Kravtsov 2015). This prior is physically justified since the c₂₀₀ − M₂₀₀ relation is inherent to structure formation in the ΛCDM framework (e.g. Bullock et al. 2001; Ludlow et al. 2014; Correa et al. 2015). In particular, the relation from DJ19 is adequate for galaxies with masses such as those in our sample (DJ19; Wang et al. 2020). As discussed in Mancera Piña et al. (2022a), for some galaxies the data has enough sampling and accuracy to constrain log(c₂₀₀) even with a flat prior (typically recovering the c₂₀₀ − M₂₀₀ relation within some scatter), but for some cases the concentration remains unconstrained, which motivates us to use our Gaussian prior (a common practice; e.g. Posti et al. 2019b; Di Teodoro et al. 2023).

Finally, for η, we adopt the flat prior log(0.1)≤log(η)≤log(3.75). The lower bound is small enough to allow for the recovery of cuspy profiles if preferred by the data; the upper bound comes from considerations on supernovae energy, which is not strong enough to create cores larger than ∼3.75 R_e, * (Read et al. 2016b, 2017; Benítez-Llambay et al. 2019; Lazar et al. 2020) for realistic supernovae coupling efficiencies (∼1%; e.g. Read et al. 2016b; Bacchini et al. 2020). With this, all our priors and fitting parameters have been introduced.

Next, we detail how to self-consistently determine the gas disc thickness and the best-fitting dark matter halo. As introduced in Mancera Piña et al. (2022a), we achieve this through an iterative process based on GALPYNAMICS and our nested sampling Monte Carlo routine. The steps are as follows.

Assuming Υ_d = 1 and Υ_b = 1 (if a bulge is present), we use GALPYNAMICS (Sect. 4.1) to compute a preliminary gravitational potential for the stars (Φ_* = Φ_d + Φ_b) and its circular speed V_*. We assume the H I and H₂ (if a molecular gas disc is present) discs to be razor-thin and obtain a first estimate of Φ_HI, Φ_H₂, and their corresponding circular speeds.
With our initial circular speeds we fit Eq. (1) to obtain a preliminary (log(Υ_d), log(Υ_b), log(M₂₀₀), log(c₂₀₀), log(η)) set. With this, we update Φ_* and obtain Φ_DM and the corresponding V_* and V_DM.
With GALPYNAMICS and relying on the condition of vertical hydrostatic equilibrium, we computed the thickness of the gas disc taking into account Φ_DM, Φ_*, Φ_H₂, and the H I disc self-gravity⁸. This allowed us to obtain a new estimate of Φ_HI and V_HI for our flared H I disc.
GALPYNAMICS computes the H₂ taking into account Φ_DM, Φ_*, and Φ_HI (derived in the previous step), and the H₂ disc self-gravity.
Steps 3 and 4 are repeated iteratively until the changes in both scale heights at all radii are at least smaller than 15% (an appropriate threshold given the observational uncertainties, see Mancera Piña et al. 2022a) compared to the previous iteration. Once convergence is achieved, we obtain the thickness radial profile for H I and H₂. The thickness updates the gravitational potentials Φ_HI and Φ_H₂ and the corresponding circular speeds.
With the new total gravitational potential, our dynesty routine finds a new best-fitting (log(Υ_d), log(Υ_b), log(M₂₀₀), log(c₂₀₀), log(η)) set, updating the mass model and generating a new set of potentials Φ_*, Φ_gas, Φ_DM (and their corresponding circular speeds).
Steps 3 to 6 are repeated iteratively until all free parameters converge. In practice, we iterate until the changes in the parameters between the last and penultimate iterations are less than 3%. For most galaxies, three iterations are enough to reach convergence.

Following this iterative procedure, we simultaneously derive the scale height of the gas discs, the stellar mass-to-light ratios, and the dark matter halo parameters for our galaxy sample in a self-consistent way. In the following sections, we present the results of our mass models.

5. Mass models

5.1. Mass models

Examples of our resulting mass models for nine representative galaxies are shown in Fig. 3. The remaining mass models and all the corresponding corner plots of the posterior distributions are available at this link. In Appendix D, we discuss similarities and discrepancies between our mass models and literature values. Additionally, in Appendix E, we discuss the potential (negligible) effect of bars in our results.

Fig. 3.

Mass models of nine representative galaxies in our sample (similar plots for our full sample and the corresponding posterior distributions are available in this link). In each panel, the observed circular speed profiles are shown with dark red circular markers. The colour lines and bands represent the gravitational contribution from the stellar disc (orange), bulge (pink, if present), H I (blue), H₂ (green, if present) and dark matter (grey) to the total mass model (red) and their corresponding 1σ confidence bands.

We found satisfactory fits for all of our 49 galaxies. In particular, log(M₂₀₀), log(c₂₀₀), Υ_d and log(Υ_b) are always well constrained. We note that except for two galaxies (WLM and IC 2574) r_c < r_s. The posterior of log(η) is well-constrained for most galaxies but not all. For one-fifth of our sample, at the low-mass regime, η tends to go to the upper limit allowed by our priors, i.e. the data would prefer larger cores. At the high-mass end, some galaxies (but not all) prefer cuspy haloes, so η tends to go to the lower bound of the prior. We will further discuss the core size distribution of our sample in an upcoming paper (Mancera Piña et al. in prep); we note, however, that within our prior, η shows no strong degeneracies with M₂₀₀, c₂₀₀ or the mass-to-light ratios, so the results we present below are valid and robust. Similarly, thanks to our MC approach, the uncertainties in all the other parameters account for the behaviour of η since we marginalise over it.

There is a final aspect regarding our mass models to be considered. One of the main advantages of our sample is that all the galaxies have accurate distance measurements (D), which reduces the associated impact that distance uncertainties (δ_D) can have on the masses (∝D²) and radii (∝D). One possibility to incorporate the effect of δ_D is to include D as a (nuisance) free parameter in the fit (e.g. Li et al. 2020; Mancera Piña et al. 2022b). However, this approach is prohibitively time-consuming for us since, for each single trial D within our MC routine, the galactic potentials would need to be updated together with the scale height (see Sect. 4.3), which is computationally expensive for the thousands of iterations taken to explore the parameter space of our mass models. Instead, we perform the following exercise to examine the impact of δ_D. We obtain a new set of mass models considering D + δ_D and D − δ_D and look at their posterior distributions. Upon inspection, we find those posteriors are essentially indistinguishable from our fiducial posteriors (deriving assuming D), and the 50th, 16th, and 84th percentiles remain the same. Therefore, we conclude that thanks to our selection of galaxies with accurate distance measurements, we can ignore the impact of δ_D in our mass models since the dominant source for uncertainty is the kinematicmeasurements.

In Table G.1, we report our best-fitting (50th percentiles) parameters (log(M₂₀₀), log(c₂₀₀), log(η), log(Υ_d), and log(Υ_b)) and their corresponding uncertainties, which correspond to the absolute difference between the 50th percentiles (median) and the 16th, and 84th percentiles of our posterior distributions. In Sect. 6, we delve into our findings regarding the dark matter parameters for our galaxy sample. However, before that, in the following sections, we discuss two interesting by-products of our mass modelling, namely the resulting mass-to-light ratios and gas scale heights.

5.2. Stellar mass-to-light ratios

During our rotation curve decomposition, we fitted log(Υ_d) with wavelength-dependent priors determined by empirical luminosity–Υ_d relations informed by SED fitting and also supported by results from SPMs and dynamical models (see Appendix C). The prior for Υ_b was flat but bounded within Υ_d < Υ_b < 2 Υ_d, as suggested from SPMs.

Fig. 4 shows the Υ_d and Υ_b values obtained through our rotation curve decomposition as a function of their disc luminosity and distinguishing between galaxies with 3.6 μm and 1.65 μm data. The Gaussian priors imposed during our fit are also depicted. Focusing first on the galaxies with 3.6 μm photometry, we see that for $L_{d}^{3.6 μ m} ≳ 10^{10} L_{⊙}$ $L^{3.6\,{\upmu}\mathrm{m}}_{\mathrm{d}} \gtrsim 10^{10}\,L_\odot$ the Υ_d values can deviate from the centre of their prior and show a trend of less luminous galaxies having lower Υ_d, as reported in the literature (e.g. Marasco et al. 2025). Instead, galaxies of lower L^3.6 μm move little from the central value of their prior.

Fig. 4.

Our Υ_d (circles) and Υ_b (triangles) values as a function of disc luminosity (L_d). We distinguish between galaxies with photometry at 1.65 μm and 3.6 μm. The lines and bands represent the Gaussian priors adopted for Υ_d in our mass modelling (see Sect. 4 and Appendix C). The prior for Υ_b was flat within Υ_d < Υ_b < 2 Υ_d (not shown).

On the one hand, this tells us that the chosen priors do not disagree with the kinematics of the galaxies. On the other hand, the little scatter at low luminosities could also indicate little constraining power on Υ_d, a consequence of the dwarfs (unlike the massive spirals) being heavily dominated by the dark matter and gas components in their central parts (see Fig. 3). Mancera Piña et al. (2022a) showed that this is also the case when imposing $Υ_{d}^{3.6} / [M_{⊙} / L_{⊙}] = 0.5 \pm 0.1$ $\Upsilon_{\mathrm{d}}^{3.6}/[M_\odot/L_\odot] = 0.5\pm0.1$ as a prior, and argued that the uncertainties in their $Υ_{d}^{3.6}$ $\Upsilon_{\mathrm{d}}^{3.6}$ values for dwarfs were likely underestimated. This is true to some extent since the constraining power is not strong, but we emphasise that our $Υ_{d}^{3.6}$ $\Upsilon_{\mathrm{d}}^{3.6}$ and uncertainties are derived using a prior informed by SED fitting, ensuring they remain physically realistic. In Fig. 4, we also include the Υ_b values for the 12 galaxies in our sample with bulges. We can see a trend of galaxies with increasing disc luminosity having larger Υ_b. The values of the Υ_b/Υ_d ratio range between 1 and 1.75, with a mean (median) valueof 1.45 (1.48).

For the six galaxies with 1.65 μm photometry, their $Υ_{d}^{1.65}$ $\Upsilon_{\mathrm{d}}^{1.65}$ values are consistent within 1σ-pagination

with their prior. Kirby et al. (2008) studied the $Υ_{d}^{1.65}$ $\Upsilon_{\mathrm{d}}^{1.65}$ in a sample of low-mass galaxies (including some of our galaxies) and based on the observed B − H colour and the Υ_d–colour relation by Bell & de Jong (2001) estimated Υ_d = 0.9 ± 0.6. As also pointed out by Kirby et al. (2008), Bell et al. (2003) reports values in the range 0.7–1.3 for SDSS blue galaxies (somewhat more massive than ours) using g − r colours. Our dynamical estimates broadly agree with the lower bounds of the above studies, but we see no conspicuous dynamical evidence for $Υ_{d}^{1.65} ≳ 0.8 M_{⊙} / L_{⊙}$ $\Upsilon_{\mathrm{d}}^{1.65} \gtrsim 0.8\,M_\odot/L_\odot$ for galaxies with $L_{d}^{1.65 μ m} ≲ 10^{9} L_{⊙}$ $L^{1.65\,{\upmu}\mathrm{m}}_{\mathrm{d}} \lesssim 10^{9}\,L_\odot$ .

5.3. Gas scale heights

One of the most innovative aspects of our mass modelling, already introduced in Mancera Piña et al. (2022a), is that the gas scale height is derived simultaneously and consistently with the dark matter halo parameters. Studying the scale heights is vital to understanding the connection between the interstellar medium (ISM) kinematics and processes such as disc stability and star formation (see e.g. Romeo 1992; Romeo & Falstad 2013; Iorio 2018; Bacchini et al. 2019; Jeffreson et al. 2022; Bacchini et al. 2024). Furthermore, the gravitational potential of a thick disc is weaker in the mid-plane than that of a thin disc with the same mass (e.g. Binney 1977; Mancera Piña et al. 2022a), and so is their contribution to the circular speed, so incorporating gas flaring into the picture leads to a more robust determination of the halo parameters.

5.3.1. Scale heights

In Fig. 5, we show the H I scale heights for our sample (H₂ scale heights are less thick but otherwise exhibit a similar behaviour, see Mancera Piña et al. 2022a). To better compare the different profiles, we plot them in log-log scale, but linear versions of each scale height can be found as in this link, together with ASCII tables containing the scale heights.

Fig. 5.

Scale heights of the H I for our sample. The top panel colour-codes each galaxy depending on its halo mass, while the bottom panel uses the V_rot/σ_{_HI} ratio.

The interplay between the galactic gravitational potential and the gas pressure results in scale heights of increasing flare with increasing radii, as usually found in nearby galaxies (e.g. Kerr et al. 1957; Sancisi & Allen 1979; Olling 1996; Romeo 1992; Nakanishi & Sofue 2003; Yim et al. 2014; Marasco & Fraternali 2011; Bacchini et al. 2019; Elmegreen et al. 2025). This increase is typically from scales of ∼0.1 kpc in galaxy centres to 1 − 10 kpc in the outskirts. The one exception in our galaxy sample is LVHIS 055, which has a scale height that rises from the centre to R ∼ 2 kpc to bend downwards. As discussed by Bacchini et al. (2024), this happens for some gas-rich dwarfs (and some high-redshift galaxies) for which ρ_{_HI}(R, 0) in Eq. (8) bends down due to σ_{_HI}² decreasing faster with radius than the difference between Φ_tot evaluated in the midplane and above the midplane (i.e. gas pressure cannot counteract the gravity from the potential).

It has been attempted to find a universal profile for the gas flaring (e.g. Patra 2020b,a; Mancera Piña et al. 2022a). However, we conclude that the shapes remain too diverse to reconcile them with a universal profile (despite trying different normalisations, see Sect. 4.2 in Mancera Piña et al. 2022a). Nevertheless, some general trends can be appreciated. The top and bottom panels in Fig. 5 colour-code the scale heights depending on the galaxies’ halo mass and the rotation-to-dispersion ratio V_rot/σ_{_HI}, respectively. Here, V_rot/σ_{_HI} is computed as the ratio between the characteristic outer rotational speed (as in Table A.1 but for V_rot) and the median gas velocity dispersion.

Focusing on the top panel, we can see that, in absolute terms, dwarf galaxies usually have thicker H I discs than massive spiral galaxies; however, the scatter at a given halo mass remains significant, driven by different σ_{_HI}, mass-to-light ratios, and the presence of bulges in some of the massive spirals. The scatter is largely reduced when looking at the scale heights at fixed V_rot/σ_{_HI} ratio (bottom panel in Fig. 5). Evidently, galaxies with lower V_rot/σ_{_HI} values have thicker H I scale heights. This trend is consistent with the expectations (e.g. Appendix A in Bacchini et al. 2019) since V_rot correlates with the galactic potential (pushing the scale heights towards the midplane) and σ_{_HI} with the gas pressure (counteracting the effect of gravity). These results are also in qualitative agreement with Randriamampandry et al. (2021), who reported that gas-rich galaxies typically have thicker H I layers within their optical discs.

The scale heights here derived (and which we make publicly available) are relevant due to their impact on mass models (see the following section). Moreover, they can be used to study the processes driving star formation and turbulence in the ISM (e.g. Bacchini et al. 2019, 2020). Additionally, they can also set constraints to discriminate between baryonic physics implementations in hydrodynamical simulations (e.g. Gensior et al. 2024).

5.3.2. Dynamical impact on the mass models

We finish this section by touching briefly upon the gas flaring’s effect on our mass models. As discussed in Mancera Piña et al. (2022a), the flaring has a negligible dynamical effect (i.e. the mass models with the flaring are almost identical to those using razor-thin discs) for massive galaxies. There is a tendency for the flaring to allow higher halo masses (the flaring lowers the gravitational potential of the gas in the mid-plane, leaving more room for the dark matter), but usually the change (∼0.1 dex) is within the uncertainties.

The above holds truth for our sample. However, as in Mancera Piña et al. (2022a), we note that the dynamical effect of the flaring can severely impact the smallest and most gas-rich galaxies. Specifically, there is a trend of increasing differences in the recovery of halo mass for decreasing halo mass, stellar mass, and V_rot/σ_{_HI}. The impact becomes noticeable for M₂₀₀ ≲ 10¹⁰ M_⊙, M_* ≲ 10⁷ M_⊙, and V_rot/σ_{_HI} ≲ 3. We refrain from doing a more in-depth quantification since a larger sample at those regimes is needed, but we raise caution on using the razor-thin approximation for such low-mass galaxies.

For example, we highlight our sample’s four most extreme cases. For the galaxies DDO 181, DDO 183, DDO 210, and CVn I dwA, the halo masses considering the gas flaring compared to the razor-thin case increase by a factor of 1.4, 1.4, 1.6, and 6.8, respectively. These four galaxies are also those with the lowest V_circ in our entire sample ( $V_{circ} ≲ 30 km / s$ $V_{\mathrm{circ}} \lesssim 30\ \rm{km/s}$ ) and are among the six galaxies with the lowest stellar mass and rotation-to-dispersion ratios (M_* < 10⁷ M_⊙ and V_rot/σ_{_HI} ≲ 3). These results highlight the importance of considering the effects of gas disc thickness and flaring when deriving the mass models of the smallest gas-rich dwarf galaxies. Upcoming surveys should consider such effects to provide robust measurements of dark matter halo properties at the above scales.

6. Galaxy-halo connection

Here we use the results of our rotation curve decomposition to study different dynamical scaling relations. These scaling relations rely on the best-fitting dark matter halo parameters and the baryonic content of the galaxies. We estimate M_* and M_gas by integrating the functional forms fitted to the observed mass surface density profiles in Sect. 4.1 up to R₂₀₀. We do this to be fully consistent with our M₂₀₀ estimate, but we emphasise that the integration limit has negligible impact on the integrated masses since Σ → 0 shortly after the extent of our deep data. Finally, the baryonic mass is simply M_bar = M_* + M_gas. The associated uncertainties in M_* and M_gas come from the 16th and 84th percentiles of Monte Carlo realisations that propagate the error from the distance, mass surface density profiles (typically of the order of 10%), and, in the case of M_*, from Υ_d and Υ_b. The uncertainty in M_bar also comes from Monte Carlo sampling propagating the errors in M_* and M_gas.

We looked into the (cold) baryon retention fraction relative to the cosmological baryon f_{bar, cosmic}⁹, i.e.:

$\begin{matrix} {\tilde{f}}_{i} = \frac{M_{i}}{f_{bar, cosmic} M_{200}}, \end{matrix}$ $\begin{aligned} \tilde{f}_{i} = \dfrac{M_i}{f_{\rm bar, cosmic}\,M_{200}}\ , \end{aligned}$ (9)

with i as the stellar, gas, or baryonic component of the galaxies. These quantities are of significant astrophysical relevance, as they allow some quantification of the fraction of baryons retained during galaxy formation and the amount converted into stars or ejected beyond the ISM (e.g. Avila-Reese et al. 2008; González-Samaniego et al. 2014; Cimatti et al. 2019; Pezzulli & Cantalupo 2019; Posti et al. 2019a). As before, the uncertainties in ${\tilde{f}}_{i}$ $\tilde{f}_{i}$ are obtained through Monte Carlo realisations considering the distribution of the parameters involved in each calculation. Table G.2 lists M_*, M_gas, M_bar, f_gas = M_gas/M_bar, ${\tilde{f}}_{*}$ $\tilde{f}_{\mathrm{\ast}}$ , ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ , and ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ for our sample.

We contrasted our results with theoretical expectations from models and cosmological hydrodynamical simulations. Our goal is not to perform an in-depth comparison or to discuss the various physics implementations among the different models and simulations (see Wright et al. 2024 for a detailed study) but rather to see general trends and obtain an overview of the similarities and discrepancies between our data and state-of-the-art implementations of galaxy formation models. We looked at two cosmological hydrodynamical simulations, TNG50 (Nelson et al. 2019) and Simba (Davé et al. 2019). TNG50 generates galaxies within a 51.7 Mpc³ volume with a baryon and dark matter particle resolution of 8.5 × 10⁴ M_⊙ and 4.5 × 10⁵ M_⊙, respectively. In the case of Simba, we focused on the high-resolution full-physics run with a box length of 25 Mpc, which has a dark matter and baryon particle resolution of 1.2 × 10⁷ M_⊙ and 2 × 10⁶ M_⊙, respectively. We made the following selection cuts to select simulated TNG50 and Simba galaxies with properties similar to those of our sample. First, we chose central (i.e. not satellites) systems. Next, we required f_gas ≥ 0.01 to avoid gas-depleted galaxies. Further, we imposed κ_rot > 0.45 (with κ_rot being the fraction of kinetic energy invested in ordered rotation in the stars, as introduced by Sales et al. 2012). While κ_rot ≳ 0.7 is often adopted to select disc galaxies, it primarily works at the high-mass regime: simulated dwarfs (even gas-rich and rotating) have only very seldom κ_rot ≳ 0.7. We find instead that κ_rot > 0.45 results in simulated galaxies that match well our observed data in the M_* − f_gas plane, so we adopted this as our threshold. The selection cuts result in 327 galaxies from Simba and 2292 from TNG50.

Regarding models, we first considered as a reference the one by Moster et al. (2010), which uses abundance-matching. Although the Moster et al. (2010) relation was initially derived for galaxies with log(M_*/M_⊙) > 9 and log(M₂₀₀/M_⊙) > 11, we compared it against our entire stellar and halo mass range, so this caveat should be kept in mind. In addition, we considered DarkLight (Kim et al. 2024a), a semi-empirical dwarf galaxy formation model calibrated such that the halo assembly histories match the relation between peak halo velocity and star formation rate in real galaxies (Read et al. 2017) and in the high-resolution zoom-in EDGE cosmological simulation (Agertz et al. 2020). DarkLight is particularly important for our purposes since it focuses on the low-mass regime, which is inaccessible to simulations due to their resolution limits. Furthermore, DarkLight galaxies are simulated in a void, which resembles the environment of our field galaxies more than a more crowded environment. From the full DarkLight model, we chose those systems classified as blue and star-forming (see Kim et al. 2024a), resulting in 461 dwarfs.

The stellar, gas, and dark matter masses in TNG50 and Simba come directly by summing the particle masses associated with each halo (see Nelson et al. 2019; Davé et al. 2019). This approach is qualitatively similar to our approach of integrating the fitted functional forms describing Σ_* and Σ_gas out to R₂₀₀; in fact, as we show in the upcoming sections, there is an overall good agreement in the stellar and gas masses of data and simulations. In the case of DarkLight, the stellar masses come from mapping the growth history of the haloes into SFHs so that the empirical relation between SFR and halo circular velocity is reproduced (see Kim et al. 2024a for details). As for c₂₀₀ (available for TNG50 and DarkLight), the estimates come from NFW fits to the density profile of the haloes and computing c₂₀₀ = R₂₀₀/r_s.

6.1. Stellar-to-halo mass relation

The first dynamical scaling law we inspect is the stellar-to-halo mass relation (SHMR), which we complement with the $log ({\tilde{f}}_{*}) - log (M_{200})$ $\log(\tilde{f}_{\mathrm{\ast}})-\log(M_{200})$ and $log ({\tilde{f}}_{*}) - log (M_{*})$ $\log(\tilde{f}_{\mathrm{\ast}})-\log(M_\ast)$ planes. These three planes are shown in the top panels Fig. 6, where galaxies are colour-coded by their logarithmic gas-to-stellar mass ratios log(M_gas/M_*). The colour scheme reflects that, unlike spirals, dwarf galaxies are gas-dominated. More importantly, we find that at fixed M₂₀₀ gas-poor galaxies tend to show higher M_* (and therefore $\tilde{f_{*}}$ $\tilde{f_\ast}$ ), at least down to M₂₀₀ ≈ 10¹¹ M_⊙, where the trend becomes less apparent (see also Geha et al. 2006; Romeo et al. 2020). Interestingly, Scholz-Díaz et al. (2024) has reported a trend at fixed halo mass (for M₂₀₀ ≳ 3 × 10¹⁰ M_⊙) of galaxies with older ages having higher M_*. Since stellar population ages correlate with stellar mass (e.g. Gallazzi et al. 2005) in a similar fashion as M_gas/M_* anticorrelates (i.e. gas-poor galaxies usually have older stellar ages), both trends are likely connected and evidence of the coupling between baryons and dark matter.

Fig. 6.

Relations between stellar and halo mass in our galaxy sample. The left panels show M_* vs. M₂₀₀, while the middle and right panels show ${\tilde{f}}_{*}$ $\tilde{f}_{\ast}$ as a function of M₂₀₀ and M_*, respectively. The observations are colour-coded by the log(M_gas/M_*) ratio. All panels highlight the cosmological baryon fraction f_{bar, cosmic}. In the bottom panels, we contrast our observations against the abundance-matching model of Moster et al. (2010), the semi-empirical DarkLight model (light green, Kim et al. 2024a) and the TNG50 (cyan, Nelson et al. 2019) and Simba (orange, Davé et al. 2019) cosmological hydrodynamical simulations. The bottom panels highlight a population of observed baryon-deficient dwarfs (BDDs, squares enclosing circles), characterised by having stellar masses more than one order of magnitude below abundance-matching expectations (plum region).

Regarding the shape of the SHMR, the data generally show the expected behaviour of more massive haloes hosting galaxies of higher M_* (and a bend at high halo masses), although the scatter is significant at any given stellar or halo mass, as shown in the top middle and right panels of Fig. 6. From the $log ({\tilde{f}}_{*}) - log (M_{*})$ $\log(\tilde{f}_{\mathrm{\ast}})-\log(M_\ast)$ plane, we can see that $\tilde{f_{*}}$ $\tilde{f_\ast}$ appears to grow nearly monotonically with M_*, with those spiral galaxies with the highest M_* having baryon fractions that approach and even surpass the line of the cosmological baryon fraction (i.e. they have virtually no ‘missing baryons’), as also reported by Posti et al. (2019b), Posti & Fall (2021), and Di Teodoro et al. (2023).

The $log ({\tilde{f}}_{*}) - log (M_{200})$ $\log(\tilde{f}_{\mathrm{\ast}})-\log(M_{200})$ plane instead shows a more complex distribution. From log(M₂₀₀/M_⊙)∼13 to log(M₂₀₀/M_⊙)∼12, there appears to be an anticorrelation until star-forming galaxies reach their peak of maximum $\tilde{f_{*}}$ $\tilde{f_\ast}$ . At lower mass scales, galaxies show significant scatter (between ∼0.001 − 60% of f_{bar, cosmic}), perhaps with hints of an anticorrelation with M₂₀₀ in the range 9 ≲ log(M₂₀₀/M_⊙)≲12. The scatter is large enough that below M₂₀₀ ∼ 10¹² M_⊙ haloes of lower M₂₀₀ can host stellar components of larger M_* than more massive haloes.

The $log ({\tilde{f}}_{*}) - log (M_{200})$ $\log(\tilde{f}_{\mathrm{\ast}})-\log(M_{200})$ and $log ({\tilde{f}}_{*}) - log (M_{*})$ $\log(\tilde{f}_{\mathrm{\ast}})-\log(M_\ast)$ planes also show a handful of ‘baryon-deficient’ dwarf galaxies (BDDs) with halo masses log(M₂₀₀/M_⊙)∼10.5 − 12 but stellar masses as low as log(M_*/M_⊙)∼7 − 9. Below, we discuss this finding further, and show that this population also has low ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ and ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ . In general, our results suggest that the galaxy-halo connection is more intricate than expected, likely driven by the stochasticity of star formation (particularly important in low-mass galaxies).

We contrast our galaxies against the models and simulations described above. The comparison is shown in the bottom panels of Fig. 6. First, we can see that the SHMR from abundance matching broadly follows the observations. However, it is clear that its scatter ( $σ_{log (M_{*})} \approx 0.15 dex$ $\sigma_{\log(M_\ast)} \approx 0.15\,\rm{dex}$ , Moster et al. 2010) in log(M_*) at fixed halo mass is way too narrow compared to the data, and it cannot match the M_* ∼ 10^10.5 M_⊙ galaxies with no missing baryons (see also Posti et al. 2019b; Di Teodoro et al. 2023), or the M_* ∼ 10^6.5 − 10^8.5 M_⊙ galaxies with low and high $\tilde{f_{*}}$ $\tilde{f_\ast}$ , which appear to follow a trend almost perpendicular to the one from abundance matching. In fact, we identify a population of BDDs (squares in the bottom panels of Fig. 6) with M_* more than one order of magnitude below (plum-coloured regions) the predictions from abundance-matching. We delve into this galaxy population a few paragraphs below.

Next, we turn our attention to more sophisticated simulations. Fig. 6 shows that, generally, TNG50 produces simulated galaxies with higher ${\tilde{f}}_{*}$ $\tilde{f}_{\mathrm{\ast}}$ than Simba. As discussed in Wright et al. (2024), this is likely due to the different feedback implementations. In TNG50, outflows driven by supernovae do not leave R₂₀₀, allowing for (i) gas accretion to continue and (ii) a more enriched CGM that is easier to cool and can be recycled into the ISM (see e.g. Pezzulli et al. 2017; Cimatti et al. 2019). In contrast, the outflows in Simba are stronger at R₂₀₀ scales, favouring a more depleted CGM and generating significantly lower inflow rates at ISM scales. Our analysis reveals that both TNG50 and Simba manage to match the overall behaviour of the data in the three observational planes, but they fall short of reproducing the observed scatter, despite their different feedback implementations and their larger volumes compared to the observational data set. Neither TNG50 nor Simba appears to produce systems with ${\tilde{f}}_{*} \approx 1$ $\tilde{f}_{\mathrm{\ast}}\approx 1$ , suggesting that these simulated galaxies might be too dark matter dominated. Marasco et al. (2020) has suggested that advanced cosmological hydrodynamical simulations produce massive galaxies that are too dark matter dominated, in agreement with our observations (see also Glowacki et al. 2020 for indications of similar behaviour in the low-mass regime). As we discuss below, the simulations also appear to struggle to reproduce the BDDs.

Below M₂₀₀ ≈ 2 × 10¹⁰ M_⊙ and down to M₂₀₀ ≈ 3 × 10⁹ M_⊙ DarkLight provides the best comparison. As real galaxies, DarkLight blue dwarfs preferentially lie above the relation from Moster et al. (2010) and show significant scatter, although arguably not enough within 2 × 10¹⁰ ≲ M₂₀₀/M_⊙ ≲ 2 × 10¹¹. This, however, can also be related to selection effects since the overall low-mass population traced by abundance matching could be quiescent (but see Boylan-Kolchin et al. 2012 for discrepancies also with quenched dwarfs), as red DarkLight dwarfs (not shown, see Kim et al. 2024a). While the low-mass end of the DarkLight model should be treated with caution, it is interesting to note the hinted tail towards higher ${\tilde{f}}_{*}$ $\tilde{f}_{\mathrm{\ast}}$ values in the direction of our observations. Overall, the different simulations/models seem to be able to reproduce some of the observed features in the three planes of Fig. 6, but none of them can match them all.

We now focus on the population of BDDs (which are dwarfs in terms of their M_*) revealed by our analysis, which have stellar (halo) masses a factor ∼20 − 60 lower (higher) than expected. As discussed in detail in Appendix F, we find it unlikely that these BDDs are spurious (arising from problems with our observations or models). However, we remain cautious since the uncertainties in M₂₀₀ for the BDDs are relatively large, driven mainly by the fact that in some of the galaxies the flattening of the rotation curves becomes evident only at the edge of our data. To have a better assessment of the confidence level at which the BDDs are atypical, we look into the maximum circular speed of the halo V_DM, max, which is easier to measure than M₂₀₀ (for details see Appendix F). We find that the BDDs also have high V_DM, max for their M_*. Out of the five galaxies highlighted in Fig. 6, three (DDO 190, LVHIS 080, and UGC 8508) have a V_DM, max lower than simulated TNG50 and DarkLight galaxies at a 2 σ level, and the remaining two (LVHIS 017 and LVHIS 072, both at M₂₀₀ ∼ 10^11.5 M_⊙ and V_DM,max ∼ 120 km/s) at a level ≳3 σ. Therefore, although the uncertainties of the BDDs in the SHMR are relatively large (see Fig. 7 below), we find statistical differences compared to simulated galaxies.

Clearly, enlarging our galaxy sample will be crucial to definitively establishing the existence of this baryon-deficient population¹⁰. Nevertheless, we highlight an additional argument that lends support to our findings: determinations from weak lensing show a similar feature in the SHMR, as we show in Fig. 7. The figure shows our SHMR compared against a set of weak lensing measurements. Specifically, we show at high masses the relation from the KiDS+GAMMA surveys by Dvornik et al. (2020), and at intermediate masses those from central galaxies in the Dark Energy Survey by Thornton et al. (2024) and the VOICE survey by Luo et al. (2022). There is a reasonable agreement between those estimates and ours. In particular, one of the measurements from the Dark Energy Survey and one from VOICE lie close to our BDDs. Although observational uncertainties cannot be neglected, the agreement between these independent estimations suggests that the baryon-deficient population is authentic. The fact that among the VOICE measurements, the one consistent with the dip is that from blue galaxies (see Luo et al. 2022 for details) may point to a morphology-dependent effect in which the dip is driven by blue, gas-rich galaxies such as those in our sample. This is hard to establish with the current data, but potentially, it could explain the deviations from abundance matching if the model galaxies are more gas-poor and red than our observations. Still, this would require a biased selection function not only in the VOICE data but also in DES, which did not note any bias in preferentially selecting blue galaxies.

Fig. 7.

Zoom-in SHMR for our galaxy sample contrasted against estimates from weak lensing (Dvornik et al. 2020; Luo et al. 2022; Thornton et al. 2024). For the lensing data, vertical error bars represent the width of the M_* bin of each measurement. The independent results from weak lensing and rotation curve decomposition suggest the existence of a population of BDDs. Note the smaller mass span compared to Fig. 6.

Finally, we come back to the models and simulations. The Moster et al. (2010) abundance matching relation (or similar empirical models; e.g. Behroozi et al. 2019) does not produce this baryon-poor population. If selection effects drive the observed feature (but see the previous discussion), it could be that the mismatch with abundance matching is due to the model being biased towards red and quenched galaxies. However, this would indicate a problem in the pairing between haloes and galaxies in abundance matching since most observed central galaxies within our M_* range are not quenched systems (Geha et al. 2012).

The BDDs do not have clear counterparts in TNG50 or Simba, despite their relatively large cosmological volumes and having selected simulated galaxies with rotational support and matching our observed gas fractions. As shown in Fig. 6 Simba produces a few galaxies in a position consistent with our BDDs in the SHMR (we also note the relative scarcity of Simba galaxies with M₂₀₀ ∼ 2 × 10¹¹ M_⊙ and M_* ∼ 10⁹ M_⊙, as in our data). However, while encouraging, there is an essential difference between these Simba galaxies and the observations. The gas fractions of the simulated galaxies are about two times larger than for real galaxies. This makes the simulated galaxies stand out in terms of their $\tilde{f_{*}}$ $\tilde{f_\ast}$ , but be ‘normal’ when looking at their ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ and ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ ; instead, as we show below (see Figs. 8 and 9), our BDDs have low $\tilde{f_{*}}$ $\tilde{f_\ast}$ , ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ and ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ . A caveat in this comparison is the Simba resolution (systems with M_* ≈ 10⁸ M_⊙ are resolved with only ∼50 particles), which could complicate the quantification of gas fractions at low masses. Understanding the different features in our SHMR and the origin of BDDs will be key to further deciphering how feedback regulates galaxy formation at such mass scales.

Fig. 8.

Relations between the cold gas and halo mass in our sample. The left panel shows M_gas vs. M₂₀₀, while the middle and right panels show ${\tilde{f}}_{gas}$ $\tilde{f}_\mathrm{{gas}}$ as a function of M₂₀₀ and M_gas, respectively. The observations are colour-coded by the M_gas/M_* ratio. The plum dashed curve represents a gas mass equal to 4% of f_{bar, cosmic}, a median trend for our sample. All panels highlight the cosmological baryon fraction f_{bar, cosmic}. TNG50 (cyan) and Simba (orange) galaxies are also included. The bottom panels highlight with squares those galaxies with M_* lower than abundance-matching expectations by more than an order of magnitude.

6.2. Gas-to-halo mass relation

Next, we focus on the connection between haloes and the cold ISM. For simplicity, we refer to the cold ISM (i.e. H I and H₂) as the total gas since the mass contribution from hotter gas phases to the ISM is thought to be small within our halo mass regime (e.g. Papastergis et al. 2012; Cimatti et al. 2019; Dev et al. 2024). We remind the reader that for our dwarf sample, M_gas is given by the H I mass corrected for helium and neglecting any potential contribution from H₂, expected to be minor. In contrast, the M_gas measurements of the massive spirals include both H I and H₂. The comparison with theoretical models is limited to TNG50 and Simba since the abundance matching relation was valid only for stars (but see also e.g. Calette et al. 2018, 2021), and the addition to the gas component in DarkLight is work in progress. For both TNG50 and Simba, we include H I and H₂. This should not introduce strong biases when comparing against our dwarfs (assumed to have no molecular gas) since the H₂ content in the simulated dwarfs is subdominant compared to H I.

Fig. 8 shows the relations between M₂₀₀, M_gas, and ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ . As in the previous figure, the top panels display our measurements, while the bottom panels include the simulated galaxies. First, we notice that the log(M_gas)−log(M₂₀₀) relation is much shallower than the SHMR (see also Chauhan et al. 2020). Moreover, while the low-mass end shows scatter, the global relation appears to be parallel to the dashed line, indicating f_{bar, cosmic}; that is, the gas content of star-forming galaxies is consistent with being a constant fraction of f_{bar, cosmic} across our observed halo mass range¹¹. We can also see that the BDDs discussed in the previous section have a behaviour similar to the other galaxies, but they have an overly massive halo for their M_gas (or vice-versa).

As expected from the above, the $log ({\tilde{f}}_{gas}) - log (M_{200})$ $\log(\tilde{f}_{\mathrm{gas}})-\log(M_{200})$ plane shows no correlation, as also noticed by Korsaga et al. (2023). Our $log ({\tilde{f}}_{gas})$ $\log(\tilde{f}_{\mathrm{gas}})$ has a median value of −1.4, indicating that across 9 ≲ log(M₂₀₀/M_⊙)≲13, M_gas is about 4% of f_{bar, cosmic} (or 0.005 of M₂₀₀), within a factor of around 4 (0.55 dex). To illustrate this, we add to the log(M_gas)−log(M₂₀₀) plots the curve (plum colour) of 4% of f_{bar, cosmic}. Lastly, in the right panels of Fig. 8, we see no compelling correlation between ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ and M_gas, a very different picture from the stellar content. At fixed halo and gas mass, the scatter in ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ has been suggested to be driven by the specific angular momentum of the galaxies and their offset from the star-formation main sequence (see e.g. Stevens et al. 2019; Chauhan et al. 2020; Romeo et al. 2020; Mancera Piña et al. 2021a; Saraf et al. 2024).

Regarding the TNG50 and Simba galaxies, they tend to scatter towards higher ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ values but also appear to lie parallel to lines of fixed baryon fraction. There are some indications of curvature for Simba and TNG50 in the $log ({\tilde{f}}_{gas}) - log (M_{200})$ $\log(\tilde{f}_{\mathrm{gas}})-\log(M_{200})$ and $log ({\tilde{f}}_{gas}) - log (M_{gas})$ $\log(\tilde{f}_{\mathrm{gas}})-\log(M_{\mathrm{gas}})$ plane, respectively, but both their median distributions are broadly consistent with the observations down to the halo mass range in common. We note that while Simba and TNG50 overlap in the high ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ galaxies, TNG50 produces more galaxies with lower ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ values, and it has a scatter that resembles more closely the observed one (which likely goes beyond the fact that the simulated volume for TNG50 is larger that for Simba) although does not fully match our lowest ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ values. Interestingly, there are a few Simba galaxies with ${\tilde{f}}_{gas} \approx f_{bar, cosmic}$ $\tilde{f}_{\mathrm{gas}} \approx f_{\mathrm{bar,cosmic}}$ as a few of our dwarfs (see also Sect. 6.3).

Generally, the results shown in this subsection highlight the high degree of self-regulation and self-similarity in the cold ISM of star-forming galaxies across four orders of magnitude in halo mass (see also Romeo et al. 2020; Korsaga et al. 2023). Similar to the SHMR, the gas-to-halo mass relation encodes important physical information that can provide insightful constraints to models and simulations.

6.3. Baryonic-to-halo mass relation

We then combine the information on our galaxies’ stellar and gas content to study their baryon-to-halo mass relation. From a physical viewpoint, this relation should be more fundamental and complete than the SHMR and the gas-to-halo mass relation, and it will give a fairer comparison between massive galaxies (dominated by the stars) and dwarfs (dominated by the gas).

In Fig. 9 we present the scaling relations involving M_bar, ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ , and M₂₀₀. Unlike in Figs. 6 and 8, galaxies in Fig. 9 are colour coded by their gas fraction f_gas = M_gas/M_bar. Above M₂₀₀ ∼ 10¹⁰ M_⊙, our data suggests a monotonic relation with M_bar increasing for larger M₂₀₀. However, the scatter at M_bar ∼ 10⁸ − 10⁹ M_⊙ is large, in part driven by the BDDs discussed above. At lower halo masses, our few data points scatter around, suggesting a wide baryon retention fraction in dwarfs with M₂₀₀ ≤ 10¹⁰ M_⊙. There is no clear correlation between M₂₀₀ and ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ (middle panels in Fig. 9). This changes when looking at ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ as a function of M_bar, where a positive correlation can be seen. As expected from the previous sections, the trend is weaker than for the ${\tilde{f}}_{*} - M_{*}$ $\tilde{f}_{\mathrm{\ast}}-M_\ast$ relation but stronger than the gas counterpart. The ${\tilde{f}}_{bar} - M_{bar}$ $\tilde{f}_{\mathrm{bar}}-M_{\mathrm{bar}}$ plane also suggests that, at fixed M_bar, gas-rich galaxies tend to have retained more baryons than gas-poor ones.

Fig. 9.

Relations between baryonic and halo mass in our sample. The left panels show M_bar vs. M₂₀₀, while the middle and right panels show ${\tilde{f}}_{bar}$ $\tilde{f}_\mathrm{{bar}}$ as a function of M₂₀₀ and M_bar, respectively. The observations are colour-coded by the M_gas/M_bar ratio. All panels highlight the cosmological baryon fraction f_{bar, cosmic}. The bottom panels also include comparisons with TNG50 (cyan) and Simba (orange) galaxies. The bottom panels highlight with squares those galaxies with M_* lower than abundance-matching expectations by more than an order of magnitude.

The bottom panels of Fig. 9 include the TNG50 and Simba data. Given their resolution, we can only compare down to M₂₀₀ > 10¹⁰ M_⊙. While Simba produces more galaxies with ${\tilde{f}}_{bar} \approx f_{bar, cosmic}$ $\tilde{f}_{\mathrm{bar}} \approx f_{\mathrm{bar,cosmic}}$ , the physics implementation of TNG50 shows a broader spread in ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ . Both TNG50 and Simba align with our main trends on average. Nevertheless, they do not match the massive spirals with ${\tilde{f}}_{bar} \approx f_{bar, cosmic}$ $\tilde{f}_{\mathrm{bar}} \approx f_{\mathrm{bar,cosmic}}$ neither the baryon-poor galaxies with $log ({\tilde{f}}_{bar}) < - 1.2$ $\log(\tilde{f}_{\mathrm{bar}}) < -1.2$ . Once large-volume cosmological hydrodynamical simulations manage to reach our lowest M₂₀₀ and M_bar values with enough resolution (e.g. Munshi et al. 2021; Gutcke et al. 2022), it will be interesting to test if the trends and diversity in ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ can be reproduced.

Our analysis shows that dwarf and massive disc galaxies can have a large spread (up to a significant percentage of the cosmological average) in their baryon fractions. Our results represent a substantial addition to the growing evidence of a population of gas-rich low-mass galaxies with large scatter in their baryon fractions, from baryon-poor to baryon-rich cases (e.g. Di Teodoro et al. 2019; Mancera Piña et al. 2019; Kong et al. 2022; Maccagni et al. 2024; Mancera Piña et al. 2024; Šiljeg et al. 2024). The improvement in simulations mentioned above should be paired with enlarging the samples of dwarfs with high-quality data and reducing the observational uncertainties. This will clarify whether broader feedback implementations (e.g. Silk 2017; Bradford et al. 2018; Mina et al. 2021; Azartash-Namin et al. 2024) in simulations are necessary or if a deeper understanding of stochasticity in galaxy evolution is needed–ideas hinted at in our data (see also Kaplinghat et al. 2020), as shown in Figs. 6–9.

6.4. Concentration–mass relation

An anticorrelation between halo mass and concentration arises naturally in N-body simulations in the CDM framework (Avila-Reese et al. 2001; Bullock et al. 2001; Wechsler et al. 2002; Dutton & Macciò 2014; Ludlow et al. 2014; Correa et al. 2015; Diemer & Kravtsov 2015; Wang et al. 2020). The scatter of the relation is, in principle, dictated by the differentassembly histories of the haloes (Navarro et al. 1997; Wechsler et al. 2002), such that haloes that assemble earlier tend to have higher concentrations. Theoretically, the c₂₀₀ − M₂₀₀ relation (not only its scatter, but also its median value) can be influenced by baryonic physics (e.g. Di Cintio et al. 2014; Dutton et al. 2016; Lazar et al. 2020; Anbajagane et al. 2022). In principle, the environment could also play a role, although there is still no consensus on systematic variations of the concentrations across most galaxy environments (Lemson & Kauffmann 1999; Macciò et al. 2007; Lee et al. 2017; Hellwing et al. 2021). All this makes the concentration-mass relation another insightful probe of the galaxy-halo connection.

Despite having imposed the log(c₂₀₀)−log(M₂₀₀) relation from DJ19 as a Gaussian prior during our mass modelling, its generous standard deviation (σ = 0.16 dex, see Diemer & Kravtsov 2015) gives room for the data to deviate from the relation if that provides a better fit. We analyse this in Fig. 10, where we show the c₂₀₀ − M₂₀₀ plane for our galaxy sample compared to the DJ19 relation and its 1σ and 2σ confidence bands. While all our concentration parameters are consistent within 2σ with the prior, we still see indications of substructure or ‘wiggles’ in the relation. Below M₂₀₀ ∼ 10¹⁰ M_⊙, the haloes appear to scatter around the mean relation. Between 10¹⁰ ≲ M₂₀₀/M_⊙ ≲ 10¹¹, the galaxies instead systematically lie below the DJ19 relation. Systems with halo masses within 10¹¹ ≲ M₂₀₀/M_⊙ ≲ 10¹² show large scatter, with some haloes under- and over-concentrated at a 2 σ level. Finally, galaxies with M₂₀₀ ≳ 10¹² M_⊙ tend to be below the relation. We note that the first and last halo mass bins remain more uncertain, given the low number of galaxies within them. In this section, we speculate whether halo assembly, feedback, or environment are the drivers for the scatter and substructure in our c₂₀₀ − M₂₀₀ relation.

Fig. 10.

Concentration–mass relation for our galaxy sample (pink markers, squares highlight BDDs). The blue dashed line shows the theoretical relation by DJ19 (imposed as a prior), and the bands show their 1σ and 2σ confidence bands. The 1σ (84th percentiles) distributions of DarkLight (green) and TNG50 (turquoise) simulated galaxies are also included for comparison.

First, we consider the possibility that the observed diversity in the c₂₀₀ − M₂₀₀ relation is a consequence of different halo assembly histories. While there is no direct way to test this scenario, we deem it unlikely that all the features arise from halo growth histories. This is because Sorini et al. (2025) has found that simulated TNG50 galaxies (which we further discuss below) follow typical concentration-mass relations in the dark-matter-only run (but see also Kong et al. 2022) and only present deviations when hydrodynamical effects are considered.

Indeed, as discussed by Lovell et al. (2018), Anbajagane et al. (2022), Mancera Piña et al. (2022a), Sorini et al. (2025), and references therein, the oscillations or wiggles are thought to result from the interplay between baryonic physics and the dark matter halo. In this context, the concentration parameters in our second and fourth mass bins could be low due to halo expansion driven by stellar and black hole feedback, respectively. At 10¹¹ ≲ M₂₀₀/M_⊙ ≲ 10¹², a competition between feedback and adiabatic contraction (for the latter, see Gnedin et al. 2004; Schulz et al. 2010; Di Cintio et al. 2014; Dutton et al. 2016; Lazar et al. 2020) could drive the large scatter (although dark matter physics may also play a role, see Kaplinghat et al. 2020; Kong & Yu 2025). At the low-mass end, feedback might not be strong enough to systematically lower the concentration parameters¹², but it is hard to establish this with our sample size.

To further explore the above ideas, we add to Fig. 10 the TNG50 and DarkLight samples (values for c₂₀₀ are not yet available for Simba, poor fits from DarkLight have been discarded). Specifically, we bin the simulated galaxies from TNG50 and DarkLight in 100 and 20 bins of equal galaxy counts, respectively, and show the 1σ distributions, assumed to be the 16th − 84th percentile range. We highlight a few relevant implications found from this comparison.

The first regards the distribution of TNG50 in Fig. 10. While it shows some overlap with the data and DarkLight, the TNG50 c₂₀₀ distribution for log(M₂₀₀/M_⊙)≳10.5 is systematically shifted towards high values (see also Sorini et al. 2025) and does not reproduce the entire observed distribution. Therefore, as previous studies (Lovell et al. 2018; Heinze et al. 2024; Li et al. 2024), our analysis indicates an enhanced adiabatic contraction in TNG50, which our data suggest is overly efficient. TNG50 has also been reported to be inefficient at lowering the central dark matter densities (Lovell et al. 2018), and indeed, our data support this idea given the lower c₂₀₀ parameters seen in real galaxies.

The comparison with DarkLight is also insightful. Below halo masses log(M₂₀₀/M_⊙)∼10.6, DarkLight galaxies fall systematically below the DJ19 relation. Two considerations should be taken into account for these simulated galaxies. The first one is that DarkLight systems were simulated in a void, and the second one is that the current version of DarkLight does not include feedback-driven halo expansion. This is interesting for different reasons. The lower c₂₀₀ parameters with respect to DJ19 are likely reflecting the low-density environment in which the galaxies formed. In fact, theoretical studies have found tentative evidence for haloes in low-density environments having lower c₂₀₀ than their high-density environment counterparts (Macciò et al. 2007; Lee et al. 2017; Hellwing et al. 2021).

If environmental effects are at play, it could have important implications for our understanding of galaxy formation¹³, and we will further explore this possibility in future work by creating DarkLight realisations in different environments. In this context, some of the low concentrations in our galaxy sample could be due to their environment since, by selection, they tend to inhabit environments of relatively low density (they are central, relatively unperturbed, and with gas reservoirs). Still, a handful of our galaxies have c₂₀₀ parameters lower than those in DarkLight, specially for log(M₂₀₀/M_⊙)≳10.5. As discussed above, the culprit behind these differences could be feedback-driven halo expansion, which is not yet implemented in DarkLight but might be at play in our galaxies – most of which exhibit cored dark matter distributions.

7. Conclusions

In this work, we have studied the galaxy-halo connection for nearby disc galaxies through several dynamic scaling relations that connect baryons and dark matter. To do so, we assembled a sample of 49 galaxies (Fig. 1) with unmatched data quality spanning six orders of magnitude in stellar mass (M_*). Of our total sample, 27 galaxies have kinematic models derived with the software ^3DBarolo (Di Teodoro & Fraternali 2015) by Di Teodoro & Peek (2021) and Iorio et al. (2017). For the remaining 22 (dwarf) galaxies, we built robust kinematic models using ^3DBarolo (Fig. 2). Our work significantly enlarges the sample of dwarf galaxies with high-quality kinematics (which we make publicly available). These observations can be used as strong constraints to test galaxy formation models and their implementation in simulations.

Using a novel and sophisticated technique, we obtained mass models for our galaxies through rotation curve decomposition (Fig. 3). The free parameters of our mass model are mass-to-light ratios for the stellar disc (Υ_d) and bulge (Υ_b) and those describing the halo (assumed to be a CORENFW, see Read et al. 2016b), namely halo mass (M₂₀₀), concentration (c₂₀₀), and the parameter η which regulates the size of the dark matter core (r_c = η R_e, with R_e the half-light radius of the stellar component).

Our rotation curve decomposition exploits the condition of vertical hydrostatic equilibrium to self-consistently derive the mass models and the vertical scale heights of the gas discs (Fig. 5). The scale heights are flared and show a moderate correlation with halo mass (the scale heights of galaxies with low-mass haloes are usually thicker) and a strong correlation with V_rot/σ_{_HI} (galaxies with higher V_rot/σ_{_HI} have thinner gas discs). For galaxies with V_circ < 300 km/s, M_* < 10⁷ M_⊙, and V_rot/σ_{_HI} ≲ 3 the flaring has a major dynamical effect on the rotation curve decomposition (Sect. 5.3.2.)

Using our homogeneous sample, we built different scaling laws connecting baryons and dark matter. We also compared the location of our galaxies with simulated systems from abundance matching calibrations (Moster et al. 2010), the DarkLight model (Kim et al. 2024a), and the TNG50 (Nelson et al. 2019) and Simba (Davé et al. 2019) cosmological hydrodynamical simulations. Our main findings are summarised as follows.

The relation between M_*, M₂₀₀, and their ratio normalised to the average cosmological baryon fraction (i.e. ${\tilde{f}}_{*} = M_{*} / (f_{bar, cosmic} \times M_{200})$ $\tilde{f}_{\mathrm{\ast}} = M_\ast/(f_{\mathrm{bar,cosmic}}\times M_{200})$ ) is complex, deviates from abundance matching, and implies a wide variety of M_*/M₂₀₀ ratios at a given M_* or M₂₀₀ (Fig. 6).
We find tentative evidence for the existence of a population of baryon-deficient dwarf galaxies (BDDs) with stellar and baryonic masses ∼1.5 orders of magnitude below expectations. Observational uncertainties remain important, but our findings appear to be supported by recent weak lensing measurements (Fig. 7). Galaxies from the Simba simulation show hints of a population of BDDs similar to what we observe, but the simulated systems are too gas-rich to be consistent with our observations. Overall, our results imply a broad range in the baryon retention efficiency, which is not fully reproduced by the simulated galaxies.
The cold gas mass (M_gas) correlates more simply with M₂₀₀ (Fig. 8). The M_gas − M₂₀₀ relation is well described by a curve parallel to the cosmological baryon fraction but with 4% (within a factor of three to four) of its normalisation. Consequently, ${\tilde{f}}_{gas}$ $\tilde{f}_{\mathrm{gas}}$ shows no clear correlations with M₂₀₀ or M_gas.
The baryonic mass (M_bar = M_* + M_gas) correlates with M₂₀₀ (Fig. 9). The fraction ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ shows a large scatter and correlates weakly with M_bar and does not clearly vary as a function of M₂₀₀. Remarkably, galaxies with ${\tilde{f}}_{bar}$ $\tilde{f}_{\mathrm{bar}}$ being a significant fraction of the average cosmological baryon fraction are present at low and high halo masses. Again, theoretical models reproduce the main trends but fall short of explaining the wide diversity in the baryon fractions.
We imposed the c₂₀₀ − M₂₀₀ relation from dark-matter only cosmological simulations (Diemer & Joyce 2019) as a Gaussian prior in our mass models. Yet, the resulting c₂₀₀ − M₂₀₀ relation shows substructure (Fig. 10). In particular, below log(M₂₀₀/M_⊙)≈11, galaxies have a significantly lower c₂₀₀ than expected. We discussed possible explanations for this and argued that the culprits might be the low-density environment and stellar feedback. We also find that TNG50 galaxies have concentration parameters that are too high compared to our data, which is a symptom of over-efficient adiabatic contraction.

Overall, our results show strong correlations in the galaxy-halo connection and a wide range in the baryon retention fraction and halo structure of nearby disc galaxies. While observational uncertainties are discussed and should be considered, our results hint at the need for more diverse implementations of feedback and galaxy evolution stochasticity in galaxy formation models.

¹

For simplicity, for some of the galaxies (see Salo et al. 2015; Mancera Piña et al. 2022a), we ignore a small bar component (accounting for less than 5 − 10% of the flux). We expect their dynamical contribution to be small given their low mass, and we corroborate that this is the case in Appendix E (see first Sect. 5).

²

v1.7, https://editeodoro.github.io/Bbarolo/

³

We note that Oh et al. (2015) derived kinematic models for some galaxies in our sample but using a less sophisticated method, upon which Iorio et al. (2017) improved. See Iorio et al. (2017) for details.

⁴

For DDO 133, Iorio et al. (2017) adopted a distance of 6.1 Mpc following Hunter et al. (2012), which was derived from the galaxy’s recessional velocity. We instead adopted a TRGB distance of 5.11 Mpc.

⁵

https://www.filippofraternali.com/cannubi

⁶

https://gitlab.com/iogiul/galpynamics/

⁷

We note that we assume our bulges to be spherical and to have a projected 2D radial density that follows the given Sérsic profiles.

⁸

In practice, solving numerically the equation

$\begin{matrix} ρ_{_{HI}} (R, z) = ρ_{_{HI}} (R, 0) exp [- \frac{Φ_{tot} (R, z) - Φ_{tot} (R, 0)}{σ_{_{HI}}^{2} (R)}], \end{matrix}$ $\begin{aligned} \rho _{\rm _{HI}}(R,z) = \rho _{\rm _{HI}}(R,0)\exp \left[ - \dfrac{\Phi _{\rm tot}(R,z) - \Phi _{\rm tot}(R,0)}{\sigma _{\rm _{HI}}^2(R)} \right]\ , \end{aligned}$ (8)

with ρ_{_HI}(R, z) and Φ_tot(R, z) the gas volume density and total galactic potential evaluated at a given vertical distance z from the midplane. For details see Iorio (2018), Bacchini et al. (2019), Mancera Piña et al. (2022a), Bacchini et al. (2024).

⁹

f_{bar, cosmic} ≡ Ω_b/Ω_m ≈ 0.16 is the average cosmological baryon fraction; e.g. Komatsu et al. (2011), Planck Collaboration VI (2020).

¹⁰

See also Forbes & Gannon (2024) for hints of a gas-poor population with overly massive haloes (based on globular cluster counts) given their stellar mass.

¹¹

At M₂₀₀ ≳ 10¹² M_⊙, where AGN feedback is expected to become strong, some models and semi-empirical studies suggest a flattening on the log(M_gas)−log(M₂₀₀), which we perhaps start to see evidence of in our data. For a dedicated study and discussion on this high-mass end, see Chauhan et al. (2020), Spinelli et al. (2020), Saraf et al. (2024) and references therein.

¹²

Note that the dwarf with high c₂₀₀ at log(M₂₀₀/M_⊙)≈9.8 is WLM, whose concentration remains somewhat ambiguous since it has r_s < r_c, see also Read et al. (2016a).

¹³

We also note that this can have repercussions for the formation mechanisms of isolated gas-rich ultra-diffuse galaxies, which appear to have concentration parameters much lower than expected in the CDM model (Mancera Piña et al. 2019; Sengupta et al. 2019; Mancera Piña et al. 2022b; Shi et al. 2021; Kong et al. 2022; Mancera Piña et al. 2024; Afruni et al. 2025).

¹⁴

We chose the above works because they more closely resemble our analysis, but some of our galaxies have also been studied elsewhere (e.g. Begeman 1987; de Blok et al. 2008; Randriamampandry & Carignan 2014; Oh et al. 2015; Frank et al. 2016).

¹⁵

More sophisticated methods to account for bar effects (e.g. Randriamampandry et al. 2018; Liu et al. 2025b) exist, but their implementation is beyond our current scope.

Acknowledgments

We want to thank the anonymous referee for their careful and constructive review, which helped strengthen our study. We thank Filippo Fraternali for stimulating comments regarding our results and Vladimir Avila-Reese and Haibo Yu for their valuable comments on our manuscript. We also thank Marijn Franx, Andrés Bañares-Hernández, Jorge Martin Camalich, and Anton Rudakovskyi for helpful discussions, and Giuliano Iorio for his assistance regarding GALPYNAMICS. PEMP acknowledges the support from the Dutch Research Council (NWO) through the Veni grant VI.Veni.222.364. JAB is grateful for partial financial support from NSF-CAREER-1945310 and NSF-AST-2107993 grants and data storage resources of the HPCC, which were funded by grants from NSF (MRI-2215705, MRI-1429826) and NIH (1S10OD016290-01A1). MG is supported by the UK STFC Grant ST/Y001117/1. MG acknowledges support from the Inter-University Institute for Data Intensive Astronomy (IDIA). IDIA is a partnership of the University of Cape Town, the University of Pretoria and the University of the Western Cape. For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission. We acknowledge the use of the ilifu cloud computing facility - www.ilifu.ac.za, a partnership between the University of Cape Town, the University of the Western Cape, Stellenbosch University, Sol Plaatje University, the Cape Peninsula University of Technology and the South African Radio Astronomy Observatory. The ilifu facility is supported by contributions from the Inter-University Institute for Data Intensive Astronomy (IDIA - a partnership between the University of Cape Town, the University of Pretoria and the University of the Western Cape), the Computational Biology division at UCT and the Data Intensive Research Initiative of South Africa (DIRISA). We have used the services from SIMBAD, NED, and ADS extensively, as well the tool TOPCAT (Taylor 2005) and the Python packages NumPy (Oliphant 2007), Matplotlib (Hunter 2007), SciPy (Virtanen et al. 2020), spectral_cube (Ginsburg et al. 2019), pandas (McKinney et al. 2010), Astropy (Astropy Collaboration 2018), and COLOSSUS (Diemer 2018), for which we are thankful.

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Appendix A: Galaxy sample

Table A.1 lists the galaxies in our sample.

Table A.1.

Galaxy sample used in this work.

Appendix B: Kinematics of our remaining galaxy sample

In this work, we derived kinematic models for 22 dwarf galaxies. Figs. 2 and B.1 present the main kinematic information (velocity fields, position velocity diagrams, and kinematic radial profiles).

Fig. B.1.

Kinematic models for our galaxy sample. This figure continues on the next page and is complemented by Fig. 2. Panels, markers, and symbols are as in Fig. 2

Fig. B.1.

Continuation.

Fig. B.1.

Continuation.

Appendix C: Priors on luminosity−Υ_d relations

During our mass modelling, we have assumed a set of priors for the disc mass-to-light ratios (Υ_d). The priors are particularly important for dwarf galaxies, where the gravitational contribution from the stars is small compared to the gas and, especially, the dark matter. Our dwarfs have photometry in the 3.6 μm and 1.65 μm bands.

In practice, we fit log(Υ_d) by assuming Gaussian priors on Υ_d. We determine the centre and standard deviation of the Gaussians from an empirical relation between NIR luminosities and Υ, motivated by the work by Marasco et al. (2025). Those authors performed careful SED fitting (using up to 10 photometric bands, ranging from far-UV to mid-IR) with the software Bagpipes (Carnall et al. 2018) on galaxies from the SPARC database (Lelli et al. 2016a); they adopted the 2016 version of the Bruzual & Charlot (2003) SPs models, a Kroupa (2002) IMF, and the dust attenuation model from Charlot & Fall (2000). Marasco et al. (2025) found that the M_* (and Υ^{3.6 μm}) values derived with their method are in excellent agreement with those estimated from dynamics (rotation curve decomposition) by Posti et al. (2019b). Moreover their Υ^{3.6 μm} estimates match well the expectations from SPMs (e.g. McGaugh & Schombert 2014; Meidt et al. 2014; Querejeta et al. 2015).

As shown in Fig. C.1, there is a clear trend in the data from Marasco et al. (2025) of increasing Υ^{3.6 μm} with increasing 3.6 μm disc luminosity (red markers, from Spitzer data). In addition to this, a trend for H−band (1.662 μm) can also be seen (green markers, from 2MASS data), albeit with a somewhat larger scatter, likely driven by the lower 2MASS data quality compared to Spitzer (see Marasco et al. 2025 for details). We exploit these correlations (assuming that our 1.65 μm data follows the 1.662 μm from Marasco et al. 2025) and fit them with exponential profiles as a function of the disc luminosity (L_d):

$\begin{matrix} Υ_{d} = A e^{B log (L_{d} / L_{⊙})} + C . \end{matrix}$ $\begin{aligned} \Upsilon _{\rm d} = A\, e^{B\, \log (L_{\rm d}/L_\odot )} + C\ . \end{aligned}$ (C.1)

Our best-fitting values for the 3.6 μm data are A = 0.016, B = 0.303, and C = 0.105. In turn, for the 1.65 μm data the best-fitting coefficients are A = 0.034, B = 0.277, and C = 0.200. The exponential functions (evaluated at a given L_d) set the centre of our Gaussian priors. Based on the scatter around the best-fitting relations, we assign an uncertainty (i.e. the standard deviation of our Gaussian priors) of 0.1 M_⊙/L_⊙ and 0.15 M_⊙/L_⊙ for the 3.6 μm and 1.65 μm data, respectively. These uncertainties (represented with confidence bands in Fig. C.1) agree well with typically quoted values in the literature (e.g. Lelli et al. 2016b; Kirby et al. 2008 and references therein). Finally, we truncate the Gaussian priors to avoid Υ_d < 0.05, which has no repercussions for our results but ensures that only physically motivated values are sampled during our Nested Sampling routine. We emphasise that our fits are not associated with any particular star formation history framework. They are purely empirical descriptions that are useful as they approximate well the L_d − Υ_d relations apparent from the analysis by Marasco et al. (2025). We remind the reader that out of our 49 galaxies, 43 have photometry in the 3.6 μm band and six in 1.65 μm.

Fig. C.1.

Relations between disc luminosity and disc mass-to-light ratio exploited to set our mass models priors. Data (from Marasco et al. 2025) are shown with red (3.6 μm) and green (1.65 μm) markers. Our best-fitting exponential functions and the adopted uncertainties are shown with colour lines and bands. These exponential fits are imposed as priors during our mass models in Sec. 4.

Appendix D: Comparison of mass models with previous works

In this Appendix, we compare the dark matter parameters found in this work for some of our galaxies against values previously reported in the literature. Specifically, we compare against 11 galaxies from Read et al. (2017), six from Posti et al. (2019b), six form Li et al. (2020), and 26 from Mancera Piña et al. (2022a). Before delving into the comparison, we list the main differences with respect to these works¹⁴.

First, we highlight significant differences in the data. The differences between us and Read et al. (2017) and Mancera Piña et al. (2022a) are minor since we use the same rotation curves and stellar and gas surface density profiles. This is not the case for Posti et al. (2019b) and Li et al. (2020). Those works rely on the simple bulge-disc decomposition from Lelli et al. (2016a), while we instead use the 2D bulge-disc decomposition modelling from Salo et al. (2015). Additionally, their rotation curves come from a collection of different studies with somewhat different methodologies (Lelli et al. 2016a), while our measurements come from accurate kinematic modelling using the same software and techniques. Our massive galaxies also include H₂ surface densities, unlike Posti et al. (2019b) or Li et al. (2020).

There are also important differences in the methodology. The most obvious one is the halo profiles. Posti et al. (2019b) fitted NFW haloes, while Read et al. (2017), Li et al. (2020), Mancera Piña et al. (2022a), and us used CORENFW profiles. However, Read et al. (2017), Li et al. (2020), and Mancera Piña et al. (2022a) fixed n and η to the calibrations from CORENFW, while we fixed n = 1 and treated η as a free parameter. Second, different priors in halo mass were used. Li et al. (2020) imposed a prior centred in the abundance-matching SHMR from Moster et al. (2010), while we and the other three works used a flat prior. Third, different priors in the concentration parameter were assumed. Read et al. (2017) used a flat prior (resulting in some concentrations being very high, see below). Posti et al. (2019b), Li et al. (2020), and Mancera Piña et al. (2022a) used all a Gaussian prior centred in the c₂₀₀ − M₂₀₀ relation from Dutton & Macciò (2014). Instead, we used the DJ19 relation, which relies on more sophisticated techniques and is more appropriate for our halo mass range. Fourth, there were differences in the stellar mass-to-light ratios. Read et al. (2017) did not fit Υ_d, and instead used M_* values from Zhang et al. (2012) based on SED fitting. Posti et al. (2019b), Li et al. (2020), and Mancera Piña et al. (2022a) used a Gaussian prior across their full mass regime centred at $Υ_{d}^{3.6} = 0.5$ $\Upsilon_{\mathrm{d}}^{3.6} = 0.5$ , and assumed $Υ_{b}^{3.6} \approx 1.4 Υ_{d}^{3.6}$ $\Upsilon_{\mathrm{b}}^{3.6} \approx 1.4\,\Upsilon_{\mathrm{d}}^{3.6}$ . We instead used the empirical priors defined in Appendix C. Another difference is that only our work and Mancera Piña et al. (2022a) considered the gas scale heights when deriving the mass models (see Sec. 5.3.2). Last, small differences could also arise from slightly different adopted distances and fitting methods (MCMC in the previous works vs. MC nested sampling in this paper).

Fig. D.1.

Comparison between halo masses and concentrations derived in this work and previous determinations.

Fig. D.1 shows the comparison of halo masses and concentration parameters between this paper and the above studies. The halo masses are in reasonably good agreement. However, there is a slight but systematic offset of our halo masses being slightly higher than the literature values. The concentration parameters show more scatter, mainly driven by the high values from Read et al. (2017), but are usually consistent with our work within 3 σ. Most of the time, our concentrations are lower, somewhat expectedly given that the concentration-mass relation from DJ19 has a lower normalisation than that of Dutton & Macciò (2014). Considering the numerous differences highlighted above, the agreement with literature values for the subset of galaxies in common is reasonable.

Appendix E: The impact of potential bars in our mass models

As discussed in the main text, we have selected galaxies whose NIR photometry indicates only a weak presence of a bar-like structure, or no bar at all. Yet, while small, and even though we account for radial motions during our kinematic models, it is possible that the bars introduce non-circular motions that could affect our kinematic measurements (e.g. Kim et al. 2024b; Liu et al. 2025b and references therein) and therefore our mass models.

To test the potential impact of bars in our results, we have performed the following exercise¹⁵. First, we selected our galaxies with log(M_*/M_⊙)≳8.3; observations indicate that below this mass threshold bars are relatively rare (Díaz-García et al. 2016; Erwin 2018). We do this regardless of whether or not the available bulge-disc decomposition indicates the presence of a bar (i.e. even for ‘pure discs’), testing an extreme scenario. Second, we estimate the extent of a putative bar (r_bar) following Erwin (2019), who provide NIR r_bar estimates as a function of R_eff. Thirdly, we find which of our selected galaxies have rotation curve data at radii R < r_bar (we note that the maximum bar torque always occurs inside r_bar, see Kim et al. 2012), and we mask the data with R < r_bar and re-derive our mass models. We find that the mass models derived with the masked data are in excellent agreement with our fiducial values, with the differences being usually smaller than 0.5 σ and always smaller than 1.5 σ. Therefore, we conclude that thanks to our selection cuts and our accounting for potential radial motions in the kinematics, our mass models are robust against the presence of small bars.

Appendix F: Could the baryon-deficient dwarfs result from observational or modelling errors?

As discussed in Sec. 6, our analysis revealed a population of baryon-deficient dwarfs (BDDs) with 20 − 60 times less (more) stellar (dark matter halo) mass than expected from theoretical models (see Figs. 6–9). In this Appendix, we investigate the possibility that the feature arises artificially by an overestimation of M₂₀₀. We note that an underestimation of M_* by ∼1 − 1.5 orders of magnitude is extremely improbable according to our dynamical modelling and in general with Υ values from SED fitting and SPMs (e.g. Schombert et al. 2022; Marasco et al. 2025). Instead, we consider three potential reasons for a halo mass overestimation (we note in advance that these factors do not explain the observations).

The first explanation could be that the M₂₀₀ values are overestimated due to observational errors. For instance, if our inclinations were underestimated, V_circ would be biased high, and so would M₂₀₀. However, the BDDs are DDO 190, LVHIS 017, LVHIS 072, LVHIS 080, and UGC 8508 (and note from Fig. 6 that more galaxies are on the verge of surpassing our threshold), which are seen at high inclinations (i ∼ 70°, except for DDO 190 with i = 41°) and therefore there is little room for a significant change lowering V_circ. We also checked that their M₂₀₀ are robust to reasonable changes in the deprojection of the highly inclined surface density profiles (for which the correction is larger). Moreover, there are other galaxies with i ∼ 70° that are not baryon-deficient as well as systems of lower inclination close to our baryon-deficient threshold. Since by selection all the distances to our galaxies are well constrained, we do not find it likely that observational errors are the culprit.

A second explanation we explore is that those galaxies may have suffered from strong adiabatic contraction (e.g. Blumenthal et al. 1986; Dutton et al. 2016) so that our fit interprets a central density excess as an overly massive halo. However, adiabatic contraction could elevate the concentration parameters but does not bias the recovery of halo masses (Lazar et al. 2020; Li et al. 2022). Moreover, the gap galaxies do not have high c₂₀₀ values for their mass (if anything the opposite, see Fig. 10), so it is unlikely that adiabatic contraction is playing a significant role.

The third possibility could be that our M₂₀₀ values are biased by the large extrapolation between R₂₀₀ (between tens and a couple of hundred kiloparsecs) and the radial extent of our rotation curves (a few kiloparsecs for dwarfs, tens of kiloparsecs for massive galaxies). To test this, we use another proxy for M₂₀₀, namely the maximum circular speed of the halo V_DM, max. This reduces the impact of any extrapolation (and mergers or environmental processes) since V_DM, max typically occurs at a radius within or close to the radial coverage of our rotation curves. To measure V_DM, max, we sample the posterior distributions of our best-fitting mass models and extract the maximum circular speed of the halo. Fig. F.1 shows M_*, M_gas, and M_bar as a function of V_DM, max. Symbols and colours are as in Fig. 6. Reassuringly, the same observed features and diversity in M_*, M_gas, and M_bar at fixed M₂₀₀ can be seen at fixed V_DM, max. This indicates that the baryon fractions studied in Sec. 6 are robust, and our M₂₀₀ estimates are not significantly affected by the extrapolation between the extent of our rotation curves and R₂₀₀.

From all of the above, we consider it highly unlikely that the baryon-deficient population is spurious. Moreover, additional and independent weak-lensing measurements appear to agree with our results (see Sec. 6 and Fig. 7).

Fig. F.1.

Stellar (left), gas (middle), and baryonic (right) mass of our galaxies as a function of the maximum circular speed of their host dark matter haloes. Symbols and colours are as in Fig. 6.

Appendix G: Halo best-fitting parameters and baryonic budget

Table G.1 lists the best-fitting dark matter halo parameters obtained through our mass modelling (Sec. 4). Table G.2 provides the information on the baryonic content of our galaxy sample (Sec. 6).

Table G.1.

Best-fitting mass model parameters

Table G.2.

Baryonic budget of our dwarf galaxy sample.

All Tables

Table A.1.

Galaxy sample used in this work.

In the text

Table G.1.

Best-fitting mass model parameters

In the text

Table G.2.

Baryonic budget of our dwarf galaxy sample.

In the text

All Figures

Fig. 1.

Overview of our galaxy sample. We place our galaxies in different scaling relations. Top: Stellar mass vs. H I mass plane. The representative ALFALFA-SDSS sample (Durbala et al. 2020) is shown for comparison. Middle: Baryonic Tully-Fisher relation (BTFR; from Di Teodoro et al. 2023). Bottom: Stellar specific angular momentum vs. mass relation (j_* − M_*; from Mancera Piña et al. 2021b). In the top panel, the colour scale increases logarithmically with the density of the data counts. The shaded bands in the middle and top panels correspond to 1σ and 2σ from the best-fitting relations (black dashed lines).

In the text

Fig. 2.

Kinematics of four representative galaxies in our sample (see also Fig. B.1). (a): Velocity field (first moment map). We also show the kinematic (white circles) and average (black dashed lines) position angles as well as the beam (grey ellipse) of the observations. (b) and (c): Position-velocity slices along the average major (b) and minor (c, perpendicular to b) axes. The data are represented with a blue background and black contours (grey for negative values), while the best-fitting ^3DBarolo model is shown with red contours. Contours are plotted at 2ⁿ× the noise, with n = 1, 2, …, n. (d) Rotation curve, circular speed, and gas velocity dispersion. We emphasise that the velocity fields are shown for illustration purposes, but ^3DBarolo fits the entire data cube.

In the text

Fig. 3.

Mass models of nine representative galaxies in our sample (similar plots for our full sample and the corresponding posterior distributions are available in this link). In each panel, the observed circular speed profiles are shown with dark red circular markers. The colour lines and bands represent the gravitational contribution from the stellar disc (orange), bulge (pink, if present), H I (blue), H₂ (green, if present) and dark matter (grey) to the total mass model (red) and their corresponding 1σ confidence bands.

In the text

	Fig. 4. Our Υ_d (circles) and Υ_b (triangles) values as a function of disc luminosity (L_d). We distinguish between galaxies with photometry at 1.65 μm and 3.6 μm. The lines and bands represent the Gaussian priors adopted for Υ_d in our mass modelling (see Sect. 4 and Appendix C). The prior for Υ_b was flat within Υ_d < Υ_b < 2 Υ_d (not shown).
In the text

	Fig. 5. Scale heights of the H I for our sample. The top panel colour-codes each galaxy depending on its halo mass, while the bottom panel uses the V_rot/σ_{_HI} ratio.
In the text

Fig. 6.

Relations between stellar and halo mass in our galaxy sample. The left panels show M_* vs. M₂₀₀, while the middle and right panels show ${\tilde{f}}_{*}$ $\tilde{f}_{\ast}$ as a function of M₂₀₀ and M_*, respectively. The observations are colour-coded by the log(M_gas/M_*) ratio. All panels highlight the cosmological baryon fraction f_{bar, cosmic}. In the bottom panels, we contrast our observations against the abundance-matching model of Moster et al. (2010), the semi-empirical DarkLight model (light green, Kim et al. 2024a) and the TNG50 (cyan, Nelson et al. 2019) and Simba (orange, Davé et al. 2019) cosmological hydrodynamical simulations. The bottom panels highlight a population of observed baryon-deficient dwarfs (BDDs, squares enclosing circles), characterised by having stellar masses more than one order of magnitude below abundance-matching expectations (plum region).

In the text

Fig. 7.

Zoom-in SHMR for our galaxy sample contrasted against estimates from weak lensing (Dvornik et al. 2020; Luo et al. 2022; Thornton et al. 2024). For the lensing data, vertical error bars represent the width of the M_* bin of each measurement. The independent results from weak lensing and rotation curve decomposition suggest the existence of a population of BDDs. Note the smaller mass span compared to Fig. 6.

In the text

Fig. 8.

Relations between the cold gas and halo mass in our sample. The left panel shows M_gas vs. M₂₀₀, while the middle and right panels show ${\tilde{f}}_{gas}$ $\tilde{f}_\mathrm{{gas}}$ as a function of M₂₀₀ and M_gas, respectively. The observations are colour-coded by the M_gas/M_* ratio. The plum dashed curve represents a gas mass equal to 4% of f_{bar, cosmic}, a median trend for our sample. All panels highlight the cosmological baryon fraction f_{bar, cosmic}. TNG50 (cyan) and Simba (orange) galaxies are also included. The bottom panels highlight with squares those galaxies with M_* lower than abundance-matching expectations by more than an order of magnitude.

In the text

Fig. 9.

Relations between baryonic and halo mass in our sample. The left panels show M_bar vs. M₂₀₀, while the middle and right panels show ${\tilde{f}}_{bar}$ $\tilde{f}_\mathrm{{bar}}$ as a function of M₂₀₀ and M_bar, respectively. The observations are colour-coded by the M_gas/M_bar ratio. All panels highlight the cosmological baryon fraction f_{bar, cosmic}. The bottom panels also include comparisons with TNG50 (cyan) and Simba (orange) galaxies. The bottom panels highlight with squares those galaxies with M_* lower than abundance-matching expectations by more than an order of magnitude.

In the text

	Fig. 10. Concentration–mass relation for our galaxy sample (pink markers, squares highlight BDDs). The blue dashed line shows the theoretical relation by DJ19 (imposed as a prior), and the bands show their 1σ and 2σ confidence bands. The 1σ (84th percentiles) distributions of DarkLight (green) and TNG50 (turquoise) simulated galaxies are also included for comparison.
In the text

	Fig. B.1. Kinematic models for our galaxy sample. This figure continues on the next page and is complemented by Fig. 2. Panels, markers, and symbols are as in Fig. 2
In the text

	Fig. B.1. Continuation.
In the text

	Fig. B.1. Continuation.
In the text

	Fig. C.1. Relations between disc luminosity and disc mass-to-light ratio exploited to set our mass models priors. Data (from Marasco et al. 2025) are shown with red (3.6 μm) and green (1.65 μm) markers. Our best-fitting exponential functions and the adopted uncertainties are shown with colour lines and bands. These exponential fits are imposed as priors during our mass models in Sec. 4.
In the text

	Fig. D.1. Comparison between halo masses and concentrations derived in this work and previous determinations.
In the text

	Fig. F.1. Stellar (left), gas (middle), and baryonic (right) mass of our galaxies as a function of the maximum circular speed of their host dark matter haloes. Symbols and colours are as in Fig. 6.
In the text

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The galaxy-halo connection of disc galaxies over six orders of magnitude in stellar mass

1. Introduction

2. Data and sample

2.1. Massive galaxies

2.2. Dwarf galaxies

2.3. The final sample

3. Kinematic modelling

4. Building the mass models

4.1. The baryonic contribution

4.2. The dark matter contribution

4.3. Self-consistent mass models with gas disc flaring

5. Mass models

5.1. Mass models

5.2. Stellar mass-to-light ratios

5.3. Gas scale heights

5.3.1. Scale heights

5.3.2. Dynamical impact on the mass models

6. Galaxy-halo connection

6.1. Stellar-to-halo mass relation

6.2. Gas-to-halo mass relation

6.3. Baryonic-to-halo mass relation

6.4. Concentration–mass relation

7. Conclusions

Acknowledgments

References

Appendix A: Galaxy sample

Appendix B: Kinematics of our remaining galaxy sample

Appendix C: Priors on luminosity−Υd relations

Appendix D: Comparison of mass models with previous works

Appendix E: The impact of potential bars in our mass models

Appendix F: Could the baryon-deficient dwarfs result from observational or modelling errors?

Appendix G: Halo best-fitting parameters and baryonic budget

All Tables

All Figures

Appendix C: Priors on luminosity−Υ_d relations