EDP Sciences logo
Subscriber Authentication Point
Search
Menu
Home All issues Volume 692 (December 2024) A&A, 692 (2024) A198 Full HTML
Open Access
Issue
A&A
Volume 692, December 2024
Article Number A198
Number of page(s) 14
Section Planets, planetary systems, and small bodies
DOI https://doi.org/10.1051/0004-6361/202451127
Published online 13 December 2024

© The Authors 2024

Licence Creative CommonsOpen 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.

This article is published in open access under the Subscribe to Open model. Subscribe to A&A to support open access publication.

1 Introduction

Demographic studies on mature exoplanets (Szabó & Kiss 2011; Fulton et al. 2017; Fulton & Petigura 2018; Van Eylen et al. 2018) suggest that early evolutionary processes like photoevaporation (Owen & Wu 2017) and core-powered mass loss (Ginzburg et al. 2018; Gupta & Schlichting 2019) significantly influence the structure and composition of low-mass planets, such as Neptunes and sub-Neptunes. Therefore, observing planets right after their formation is key to understanding these early evolutionary processes.

V1298 Tau, a 20–30 Myr old weak-lined T-Tauri star in the foreground of the Taurus-Auriga star-forming region (Oh et al. 2017; Luhman 2018), is particularly valuable for such studies. It has a temperature of ~5000 K, with a radius and mass of l.34±0.05 R⊙ and 1.1 ±0.05 M⊙, respectively, and it has a spectral type between K0-K1 (David et al. 2019a). It is a premain-sequence star, and shows rotational variability at the level of ~2% peak-to-peak and a rotational period of 2.86±0.01 days (David et al. 2019a; Feinstein et al. 2022; Sikora et al. 2023). Such rotational variability is typical of young pre-main-sequence stars (e.g. see David et al. 2016; Mann et al. 2016; Mann et al. 2022) and is due to the presence of spots and faculae on their photospheres. Feinstein et al. (2021) reproduced the optical photometric variability using a model with 20% spot coverage on the surface assuming a temperature contrast of 500 K between the photosphere and the spots.

V1298 Tau hosts four transiting planets, making it one of the youngest known transiting multi-planet systems. The inner three planets (V1298 Tau c, d, and b) are in a near 3:2:1 mean-motion resonance (David et al. 2019b; Feinstein et al. 2022; Sikora et al. 2023), suggesting possible migration within a gas disk (Terquem & Papaloizou 2018; Kajtazi et al. 2023). The mutual inclinations between the planets in this system are known to be low (Johnson et al. 2022), indicating planar orbital geometry for this system. The orbital period of the outermost planet, V1298 Tau e, remains unconfirmed but is under investigation (Damasso et al. 2023).

With a wealth of observations of exoplanet atmospheres, we have entered an era of understanding atmospheric processes, planet formation, and early evolution through comparative studies. There have been previous studies aimed at understanding the physical and chemical processes of mature transiting exoplanet atmospheres from a statistical point of view. For example, the dependence of thermal structure and opacity sources in the atmosphere on insolation (e.g, see Garhart et al. 2020; Baxter et al. 2020), emergence of clouds in the atmosphere (Sing et al. 2016; Fu et al. 2017; Keating et al. 2019), disequilibrium chemistry (Baxter et al. 2021; Fortney et al. 2020; Tsai et al. 2023; Baeyens et al. 2022), and the formation and composition of hazes (Gao et al. 2020; Brande et al. 2024) have been studied by comparing the atmospheres of different exoplanets. But, differences in the host stars can introduce biases due to uncertainty in their elemental abundances, activity levels, and evolution history. These challenges can be mitigated by performing comparative exoplanetology between multiple planets in the same system, since they share their host star. In this paper, we compare the atmospheric metallicity, chemistry, and potential evolution of two planets in the V1298 Tau system, V1298 Taub (0.9 RJ, 24.14 day period) and V1298 Tau c (0.5 RJ, 8.24 day period), by studying their atmospheres. Given its young age, this system also allows for atmospheric comparison with mature transiting exoplanets, as well as widely separated directly imaged planets of a similar age. A comparison between the known physical properties of planet b and c is shown in Table 1.

V1298 Tau c receives four times as much stellar irradiation as V1298 Tau b due to their orbital distance ratio of ~ 1:2. Stellar XUV flux is believed to play an important role in atmospheric chemistry (Venot & Agúndez 2015; Kawashima & Ikoma 2018; Shulyak et al. 2020; Tsai et al. 2023) as well as early evolution (Owen & Wu 2013; Owen & Wu 2017), which we aim to test with two planets in the same young system.

Measuring the masses of these young planets is challenging due to stellar activity induced jitter affecting radial velocity (RV) observations (Brems et al. 2019; Blunt et al. 2023). Initial RV studies (Suárez Mascareño et al. 2021) have reported Jovian masses (200±70, 400±100 M⊕) for the two outer V1298 Tau planets (b and e, respectively) and mass upper limits (70 and 100 M⊕) for the inner two (c and d, respectively). Follow-up RV observations of this system have challenged these mass measurements (Sikora et al. 2023; Finociety et al. 2023). Finociety et al. (2023) report an upper limit of ~50 M⊕ for planet c and d and an upper limit of ~150 M⊕ for planet b. Sikora et al. (2023) report a mass of 20± 10 M⊕ for planet c and upper limits of 36 and 160 M⊕ for planets d and b, respectively. The follow-up RV papers are consistent with Suárez Mascareño et al. (2021) for the mass of V1298 Tau e, but do not agree with the mass of planet b from Suárez Mascareño et al. (2021). Barat et al. (2024) estimate V1298 Tau b’s mass to be less than 23 M⊕ at a 3σ level of confidence from HST/WFC3 transmission spectra, and ruled out RV estimate from Suárez Mascareño et al. (2021) at a 5σ level of confidence. Ongoing transit timing variations (TTVs) studies (Livingston et al in prep) suggest that both V1298 Tau b and c are in the sub-Neptune mass regime.

In this paper, we compare the transmission spectra of V1298 Tau b and c. For planet b, we adopt the spectrum obtained in Barat et al. (2024). We analyze the primary transit observations of V1298 Tau c, observed using the same instrumental configuration as Barat et al. (2024), and present the transmission spectrum of planet c. We discuss the data reduction and light curve analysis for the visit of V1298 Tau c in Sect. 2, followed by the main results in Sect. 3. We discuss and interpret our findings in Sects. 4 and 5.

Table 1

Comparison of the physical properties of V1298 Tau b and c.

2 Data analysis and modeling

2.1 Observations

We observed one primary transit of V1298 Tau c (October 18, 2021) with eight HST orbits using the WFC3 instrument for Program GO 16462. The observations were taken with the G141 in bidirectional spatial scanning mode covering a range of 1.1– 1.7 µm. We used the 256 × 256 pixel subarray and SPARS2 5, NSAMP=5 readout mode, which resulted in 88.4 s exposures. We used a 0.23"/second scan rate, resulting in a 170 pixel long image in the spatial direction. The observations for V1298 Tau b had been taken using the same instrumental settings, with ten HST orbits (see Barat et al. (2024) for further details).

2.2 Data reduction and light curve analysis

We used a custom data reduction pipeline to analyze the raw HST spatially scanned images (Arcangeli et al. 2018; Arcangeli et al. 2019; Jacobs et al. 2022; Barat et al. 2024) for the V1298 Tau c visit. The same pipeline had been used to analyze the visit of planet b in Barat et al. (2024). We outline the data reduction methods we used in Appendix A.

The broadband-integrated white light curve for the visit of V1298 Tau c is shown in Fig. 1. It shows hook-like systematics for each orbit, which have been observed for similar HST observations (Berta et al. 2012; Deming et al. 2013; Ranjan et al. 2014). We also see that the orbital ramp is much larger in the first orbit compared to the rest of the orbits for this visit. This is a typical feature of HST visits where the first orbit shows larger systematics (Wakeford et al. 2016; Arcangeli et al. 2021). The light curves also show a long-term curvature, which is likely due to the rotational variability from active regions on the photosphere of this young star. This variability has been reported by Barat et al. (2024) and is well known for young pre-main- sequence stars that have large spot coverage and fast rotation rates (e.g. see David et al. 2016, 2019b; Mann et al. 2022). Such variability is known to affect multi-epoch transmission spectra (e.g, Désert et al. 2011b; Berta et al. 2012; Rackham et al. 2019).

These observations of planet c were planned using linear ephemeris from Feinstein et al. (2022), but this system is known to exhibit TTVs and the actual transit occurred ~2 hours prior to the predicted time from the linear ephemeris. Therefore, our observations covered only one pre-transit orbit and no exposures during ingress or egress. Typically, the first orbit of a visit for HST is known to exhibit large systematics, and it is common practice not to include it in time series analysis (e.g. see Berta et al. 2012; Ranjan et al. 2014; Jacobs et al. 2022; Barat et al. 2024). In the case of V1298 Tau b, there were three pre-transit orbits, and therefore the first orbit could be removed from the analysis. However, since we have only one pre-transit orbit for the visit of V1298 Tau c, we could not remove the first orbit while analyzing its light curve.

The white light curve of planet c has been modeled assuming a physically motivated charge-trapping model, RECTE (Zhou et al. 2017), to model the hook-like orbital ramps and a second-order polynomial function to model the baseline for the planet c visit. The RECTE model is known to fit the first orbit better compared to other known methods (e.g, Berta et al. 2012). The planet transit was modeled using batman (Kreidberg 2015), with orbital parameters taken from Sikora et al. (2023). This same approach had been used to fit the white light curve of planet b (Barat et al. 2024).

A linear limb darkening model was assumed for V1298 Tau. Barat et al. (2024) fit for the linear limb darkening coefficient for the visit of planet b. Since the planet c visit does not have any ingress or egress coverage, we have used the fit limb darkening for V1298 Tau from Barat et al. (2024) as a fixed parameter for the analysis of the planet c visit (Fig. F.2). V1298 Tau b and c have impact parameters (0.34−0.21+0.19$0.34_{ - 0.21}^{ + 0.19}$ and 0.46−0.24+0.13$0.46_{ - 0.24}^{ + 0.13}$ respectively) consistent within 1σ of each other (David et al. 2019b,a). Furthermore, Johnson et al. (2022) report a relatively low mutual inclination (0±19°), indicating a planar orbital geometry of the V1298 Tau system. Therefore, both planets would transit a similar part of the stellar photosphere, and are expected to to show similar limb darkening during their primary transits (further details of the light curve fitting methods are provided in Appendix B).

We obtained 17 spectroscopic light curves for the planet c visit by using 7-pixel bins. The same binning had been used for planet b in Barat et al. (2024). For the analysis of spectroscopic light curves of planet c, the semi-major axis was fixed from the white light curve fit of planet c. This approach had also been followed for the planet b visit. In the analysis of planet b (Barat et al. 2024), the common-mode method (using white light curve systematics models to correct the spectroscopic light curves) was applied to de-trend the spectroscopic light curves, assuming that the systematics were achromatic. However, the first orbit is known to exhibit wavelength-dependent systematics (Zhou et al. 2017, 2020), and therefore in the analysis of V1298 Tau c we could not use the common-mode technique for de-trending spectroscopic light curves. We used RECTE (Zhou et al. 2017) to model the hook-like orbital ramps and a second-order polynomial function to model the baseline of the spectroscopic light curves for the planet c visit. The parameters for the RECTE as well as the polynomial coefficients, were fit for each spectroscopic light curve. We tested different models for the baseline (linear, quadratic, and cubic). We found that the quadratic model fits the observed baseline the best (see Appendix C for further details on the baseline model). The limb darkening coefficients were fixed from Barat et al. (2024).

We derived the transmission spectrum of V1298 Tau c following the approach outlined in this section, and we present it in Fig. 2, along with the spectra of planet b, which has been adopted from Barat et al. (2024).

thumbnail Fig. 1

Transit light curve of V1298 Tau c observed using HST/WFC G141. Upper panel: raw white (1.12-1.65µm band) light curve for the transit of V1298 Tau c. Blue and green points show forward and reverse scanned exposures, respectively. The solid black lines show the best-fit transit model. We used a physically motivated charge trapping model, RECTE (Zhou et al. 2017, 2020) to fit the exponential ramps. The baseline was modeled using a quadratic function in time. See Appendix C for further discussion. The transit was modeled using batman (Kreidberg 2015). For details of light curve fitting, see Sect. 2. Lower panel: residuals from the fit to the white light curve observations.

2.3 Atmospheric models from ATMO

We interpreted the transmission spectrum of V1298 Tau c using the equilibrium chemistry ATMO retrieval framework (Tremblin et al. 2015; Drummond et al. 2016; Goyal et al. 2018). In this paper, for a consistent comparison with planet c, we also reanalyze the spectrum of V1298 Tau b adopted from Barat et al. (2024), using the same framework as was applied for planet c. ATMO has previously been used to analyze various exoplanet atmospheres (see for e.g Evans et al. 2018; Goyal et al. 2019; Carter et al. 2020). ATMO’s Python-based retrieval framework was applied and benchmarked in Lewis et al. (2020) and Rathcke et al. (2021) for HAT-P-41b and WASP-79b, respectively. This same retrieval framework was applied to V1298 Tau b and c in this work. This framework includes a Nested sampling Bayesian sampler DYNESTY (Speagle 2020) coupled to ATMO.

We modeled the planets using a 1D atmosphere with an isothermal T-P profile and calculated the molecular abundances, assuming chemical equilibrium. Atmospheric metallicity and C/O ratio were used as parameters to calculate the elemental abundances. For a given metallicity, in our model the C/O ratio is implemented by keeping the number of C atoms fixed, and adjusting the number of O atoms. We included a gray opacity source to model clouds. We included H2 -H2, H2-He collision- induced opacity in the retrieval, as well as H2O, CH4 , and CO high-temperature molecular opacity. These molecules were chosen as the HST bandpass includes absorption features from these molecules. We included planet mass as a free parameter in our retrieval setup for both planets b and c. We put similar uniform priors on the atmospheric metallicity (0.01–1000× solar), O/H ratio (0.01-100× solar), and degree of cloudiness (0.1-100× Rayleigh scattering cross-section at 350 nm) for both V1298 Tau b and c. We put uniform priors on the mass between 5 and 50 M⊕ for planet c (Finociety et al. 2023; Sikora et al. 2023) and between 5 and 25 M⊕ for planet b (Barat et al. 2024).

thumbnail Fig. 2

Transmission spectrum of V1298 Tau c (blue points) shown in comparison with its sibling planet V1298 Tau b (green points). The spectra have been derived by subtracting the median of the observed spectrum. The upper panel shows the spectra in terms of atmospheric scale height and the middle panel in terms of transit depth. We assumed Teq=979 K and 17 M⊕ for planet c and 685 K and 8 M⊕ for planet b to calculate the scale height for each planet. We assumed H/He-dominated primordial atmospheres and assumed a mean molecular weight of 2.33. The solid green and blue lines show the best-fit ATMO models from our retrievals for planet b and c with 8 and 17 M⊕, respectively (Sect. 3.2). The dashed lines show hazy atmospheric models for both planets simulated using the formalism presented in Kawashima & Ikoma (2018) (see Sect. 3.3). We show hazy atmospheric models with the same mass as the best-fit models and have been generated by rescaling the hazy atmospheric model grids described in Sect. 3.3. The lower panel shows the relative transmission spectrum (i.e., the ratio between transmission spectra) between V1298 Tau b and V1298 Tau c (see Sect. 3.4).

3 Results

3.1 The transmission spectrum of V1298 Tau c

We ran a free atmospheric chemistry retrieval using the opensource code PetitRadtrans (Mollière et al. 2019) on the transmission spectrum of planet c. We fixed the planet mass and temperature to 17 M⊕ and 950 K, respectively. These mass and temperature values for V1298 Tau c were taken from the best- fit models to the spectrum from ATMO models, described in Sect. 3.2. We included a gray cloud deck opacity in the free retrieval. The posterior distribution from this fit was uploaded to Zenodo. Our models find water vapor in the atmosphere of planet c, with a lower limit for the water volume mixing ratio (>10–5 at 3σ confidence level). We do not find any constraints on the methane abundance.

We tested the robustness of the water absorption feature indicated by the free retrieval. We compared the observed transmission spectrum of V1298 Tau c (Fig. 2) to a flat line using a Chi-square test. We found that models with atmospheric water absorption are slightly favored (2.5σ) by comparing the difference in chi-square values between a flat line and the best-fit model generated using median values of the fit parameters from the free retrieval.

We also tested the impact of fixing the planet mass and isothermal temperature, by including Gaussian priors at 950 K and 17 M⊕ with widths of 10 K and 1 M⊕. The retrieved posterior distributions and values for the water and methane abundance agree within 1σ with the ones derived from the fixed masstemperature retrievals. Thus, we conclude that with different sets of assumptions, our retrievals suggest the presence of water vapor in the atmosphere of planet c.

The transit depth uncertainties for planet c are larger by a factor of about 1.5 compared to the spectrum of planet b (Fig. 2), adopted from Barat et al. (2024). In Sect. 2.2, we discuss the differences in the light curve analysis between planet c and b. Since we cannot ignore the first orbit for the visit of planet c, unlike the case for the planet b visit, we cannot apply a common-mode correction to the spectroscopic light curves of planet c. Therefore, the higher uncertainty in the measured transit depth for V1298 Tau c is likely due to the modeling of each spectroscopic light curve independently using RECTE to model the charge trapping and second-order polynomial to model the baseline. The common-mode correction could correct for the curvature of the time-series baseline, allowing a linear baseline model, as is shown in the case of planet b (Barat et al. 2024).

3.2 Results from ATMO equilibrium chemistry retrievals

In this section, we summarize the results from the equilibrium chemistry atmospheric retrievals using ATMO for both planet b and c. The ATMO models are described in Sect. 2.3. Figure 2 shows the best-fit atmospheric models and the observed spectra for both planets. The retrieved parameters are enlisted in Table 2, with posterior distributions for planet c and b uploaded to Zenodo.

We included planet mass as a free parameter for both planets in our retrieval setup. We measure a mass (with a 1σ confidence interval) of 17−6+13$$17_{ - 6}^{ + 13}$$ M⊕ for planet c. The posterior distribution (uploaded to Zenodo) provides a 3σ mass upper limit of ~50 M⊕ for planet c. The measured mass of planet c from the spectrum is consistent with previous RV mass estimates for this planet: 20±10 M from Sikora et al. (2023) and <50 M⊕ at a 3σ level of confidence (Finociety et al. 2023). Our models find sub-solar or solar atmospheric metallicity for this planet: logZ/Z⊙=−0.16−0.9+1.1$$\log Z/{Z_ \odot } = - 0.16_{ - 0.9}^{ + 1.1}$$. Thus, within a 1σ confidence interval, the metallicity of planet c is between 0.1 and 10× solar. We do not find any constraint on the cloud deck opacity, the equilibrium temperature, or C/O ratio for planet c.

For planet b, we measured a mass of 8−2+4 M⊕$$8_{ - 2}^{ + 4}{{\rm{M}}_ \oplus }$$ from our free mass retrievals. The mass posterior distribution for planet b (uploaded to Zenodo) shows a 3σ upper limit at ~20 M⊕. The free mass retrieval posterior distribution from Barat et al. (2024), which used a different atmospheric model (PetitRadtrans) compared to the present study, found a mass (and a 1σ confidence interval) of 9−3+4 M⊕$$9_{ - 3}^{ + 4}$$ and a 3σ upper limit of 23 M⊕. The median value of mass found by Barat et al. (2024) is consistent with the present results within 1σ, and the updated mass upper limit is marginally lower.

The discrepancy arises because of the non-isothermal T-P profile with high interior temperature and vertical mixing to explain the non-detection of methane for this planet in Barat et al. (2024). However, our models assume isothermal atmospheres; as a result, retrievals favor higher isothermal temperatures (800– 900 K) compared to Barat et al. (2024) (600–700 K) to push the carbon chemistry into the methane-poor regime (Fortney et al. 2020). Therefore, we can conclude that, although the mass upper limits slightly differ between Barat et al. (2024) and this work, they can be considered consistent given the different model assumptions.

Our models retrieve a sub-solar atmospheric metallicity (logZ/Z⊙=−2−0.6+0.7$$\log {\rm{Z}}/{{\rm{Z}}_ \odot } = - 2_{ - 0.6}^{ + 0.7}$$) for planet b. This retrieved atmospheric metal- licity is consistent within 1σ with the metallicity reported in Barat et al. (2024). We found an upper limit to the cloud opacity for this planet: logκcld= –0.6. We do not find any constraints on the C/O ratio for planet b.

We tested the impact of keeping the planet mass as a free parameter in our retrievals. To assess this, we performed retrievals by fixing the mass of both planets. For V1298 Tau c, we chose two masses for this test: 10 and 50 M⊕, which are at two ends of the mass posterior distribution and which are also consistent with the mass upper limit from RV studies (Finociety et al. 2023). For planet b, we chose 10 and 23 M. Barat et al. (2024) have shown that the HST spectrum for V1298 Tau b could be explained with a 10 M model with a highly sub-solar metallicity and higher cloud opacity, as well as with a relatively clear solar metallicity atmosphere with a planet mass of 23 M⊕. We therefore chose these two scenarios for this test. The posterior distributions for these fixed mass retrievals were uploaded to Zenodo, with retrieved parameters provided in Table 2. The retrieved atmospheric metallicity from these fixed mass retrievals is consistent within 1σ with the free mass retrieval case for both planet b and c (Table 2). For planet c, we find that increasing the mass also leads to a small increase in the retrieved atmospheric metallicity, but in all three cases (free mass, 10 M⊕, and 50 M⊕) the retrieved metallicity lies in the range of 0.1-10×solar for a 1σ confidence interval. For planet b, the metallicity is sub-solar for all mass values; however, the metallicity increases for higher masses. Considering the 1σ confidence interval, in the three cases for this planet (free mass, 10 M⊕, and 23 M⊕), the atmospheric metallicity lies within 0.01-1× solar metallicity.

From the atmospheric retrievals on V1298 Tau b and c, we conclude that both these planets have masses in the Neptune or sub-Neptune regime. The RV mass for V1298 Tau b from Suárez Mascareño et al. (2021) is inconsistent with our measurement, but the planet c mass upper limit from RVs is consistent with our mass measurement for planet c. The mass measurements of both planet b and c from this work are consistent with follow-up RV studies (Finociety et al. 2023; Sikora et al. 2023). The mass we measure for planet b is consistent with previous analysis of its HST transmission spectrum (Barat et al. 2024). Furthermore, TTV analysis of this system (Livingston et al, in prep) also find masses of both these planets in the sub-Neptune mass regime. By testing the impact of including planet mass as a free parameter in our retrievals, we conclude that the atmosphere of V1298 Tau b appears to have a metallicity that is lower than or equivalent to the solar composition. For V1298 Tau c, the constraints on the atmospheric metallicity are not as precise compared to planet b; however, the posterior distribution for the metallicity peaks at the solar composition with a 1σ confidence interval between 0.1 and 10×solar. Therefore, it is possible that both these planets are young Neptunes or sub-Neptunes in terms of their mass. But their atmospheric metallicity is much lower (at least one order of magnitude) than what is typically found for known mature Neptune or sub-Neptune planets (e.g. see Bean et al. 2010; Désert et al. 2011a; Miller-Ricci Kempton et al. 2012; Morley et al. 2013; Kreidberg et al. 2014; Libby-Roberts et al. 2020; Bean et al. 2021).

Table 2

Derived parameters from atmospheric retrievals run using ATMO (see Sect. 3.2) for planet c and planet b.

3.3 Haze formation in the atmosphere of V1298 Tau b and c

Hazes have been found to be ubiquitous in exoplanet atmospheres (Pont et al. 2008; Désert et al. 2011a; Miller-Ricci Kempton et al. 2012; Morley et al. 2013; Kreidberg et al. 2014; Knutson et al. 2014; Libby-Roberts et al. 2020; Kempton et al. 2023). The temperature of V1298 Tau b and c is expected to be between 600 and 1000 K, which has been considered a sweet spot for haze formation (Brande et al. 2024). Furthermore, the host star is young and active, producing copious amounts of UV radiation, which is an important ingredient in haze formation (Kawashima & Ikoma 2018, 2019; Gao et al. 2020; Yu et al. 2021).

We simulated the transmission spectrum of V1298 Tau b and c, including hazes. We assumed a tholin-like composition for the hazes (Khare et al. 1984). The haze microphysics models were simulated using the models described in Kawashima & Ikoma (2018), following the approach of Kawashima & Ikoma (2019). First, using a photochemical model, the abundance of gaseous species was calculated. The XUV spectrum of V1298 Tau was adopted from Duvvuri et al. (2023). Haze production rates (or the efficiency of haze formation) are uncertain; therefore, we assumed a certain fraction of precursor molecules to be dissociated to form haze monomers. The haze precursor molecules are assumed to be CH4 , HCN, and C2H2 in our model. We derived vertical density and radius distributions of the haze particles following Kawashima & Ikoma (2018). We assumed a solar elemental abundance ratio and other parameters such as an eddy diffusion coefficient, monomer radius, internal density, and refractive index of haze particles similar to Kreidberg et al. (2022).

We assume 685 and 979 K to be the isothermal temperatures for these models of planet b and c, respectively (Table 1). Since the haze models are computationally expensive, we created models for two masses of planet b and c each. For planet b, we chose two masses: 10 Mθ (consistent within 1σ with the median of the ATMO retrieval mass posterior distribution for planet b) and 23 Mθ (3σ upper limit from Barat et al. 2024). For planet c, we chose 10 M⊕, and 20 M (consistent within 1σ with the median of the ATMO retrieval mass posterior distribution for planet c).

We chose 10 M⊕ for planet c because from ongoing TTV studies, it is likely that the mass of planet c is in the sub-Neptune regime (Livingston et., al in prep.).

In Fig. 2, we show the simulated transmission spectra assuming a 1 % haze production efficiency for masses of 8 and 17 M⊕ for planet b and c, respectively, for ease of comparison with the ATMO models. We have rescaled the planet c andb models computed with masses of 20 and 10 M⊕, respectively, to the 17 and 8M⊕ models, assuming that a small change in the planet mass will not significantly affect the haze models. The atmospheric signal (which is a relative measurement) is inversely proportional to the planet mass (Heng & Kitzmann 2017), through the scale height. Assuming this principle, we rescaled the haze grid models to different mass values. While significant haze formation can be ruled out for V1298 Tau b, high haze formation rates could explain the observed spectrum of V1298 Tau c.

The haze formation efficiency is an uncertain parameter in our models. Furthermore, the mass of the planets is also uncertain. So, to test the effects of this parameter on the hazy atmospheric models, we created a grid of models at different haze formation efficiencies and planet masses. In Fig. 3, we show the spectra of both planets with different haze formation efficiencies: 10–4 and 10–5 for planet b and 10–5 and 10–2 for planet c. For V1298 Tau b, irrespective of the mass, haze formation efficiencies as low as 10–4 can be ruled out as these do not reproduce the large water absorption feature. At 8 M⊕, a haze formation efficiency of 10–5 can potentially explain the water absorption feature for planet b, but introduces a strong slope in the continuum that is not seen in the observed spectrum. For V1298 Tau c, the haze formation rates cannot be constrained as haze formation efficiencies as low as 10–5 can explain the spectrum. However, for the 10 M⊕ for planet c, we can rule out low haze formation efficiencies (<10–5) at a 3.5σ level of confidence. Therefore, we conclude that V1298 Tau b has a haze formation efficiency lower than 10–5, whereas for V1298 Tau c the atmosphere is likely to have a higher haze formation than its sibling planet.

3.4 Relative transmission spectroscopy between planet b and c

In Fig. 2 (lower panel), we present the first relative transmission spectrum between two planets within the same system. By relative transmission spectrum, we mean the ratio of transit depths between two planets as a function of wavelength. In principle, the relative transmission spectrum is independent of the stellar radii and limb darkening effects, assuming that both planets share similar limb darkening; that is, they transit similar parts of the stellar disk. V1298 Tau b and c have impact parameters consistent with each other within 1σ (David et al. 2019b) and a relatively low mutual inclination (Johnson et al. 2022). Stellar inhomogeneities are known to contaminate transmission spectra (Désert et al. 2011a; Rackham et al. 2019), which has also been highlighted in recent JWST observations (May et al. 2023; Moran et al. 2023; Lim et al. 2023). A relative transmission spectrum between multiple planets in the same system is theoretically independent of stellar contamination, assuming similar stellar contamination across both transits. This enables a better relative comparison of abundances between the planets without precise information on the stellar properties, including metallicity, elemental abundance ratios, and limb darkening. However, in the case of V1298 Tau, an active star, changes in the stellar surface between observation epochs may still introduce contamination into the relative spectrum extracted at different times.

thumbnail Fig. 3

Comparison between observed HST transmission spectrum of V1298 Tau b (upper panel) and V1298 Tau c (lower panel) with haze grid models of different haze formation efficiency and planet mass. Upper panel: Solid lines represent models assuming 23 M⊕. Dashed lines represent models with 8 Mθ, which have been rescaled from the 10 M⊕ haze grid model of planet b. Blue and green represent haze formation efficiencies of 0.01% and 0.001%, respectively. Lower panel: Solid lines represent models assuming 17 M⊕ rescaled from the 20 Mθ haze grid model for planet c. Dashed lines represent models with 10 Mθ. Blue and green represent haze formation efficiencies of 1% and 0.001%, respectively.

4 Discussion

4.1 Relative orbital distances and stellar density

In multi-planet systems, it is possible to fix one planet’s semimajor axis based on another planet’s measured semi-major axis, since they are related to their orbital period ratio. However, due to known TTVs in this system, we have refrained from fixing the semi-major axis in this analysis. The semi-major axis ratio from independent fits to the white light curves of V1298 Tau b and c is 2.08 ±0.1 and agrees with the expected value from their known orbital periods. Assuming circular orbits, the semimajor axis can be used to estimate stellar density (Sandford & Kipping 2017). From the fits to our white light curves, we estimate the stellar density from the planet b and planet c transit light curve to be 0.70±0.01 gm/cm3 and 0.67±0.1 gm/cm3. These values align with the published stellar density for V1298 Tau (0.68±0.1 gm/cm3, David et al. (2019a)). The relatively low density of V1298 Tau compared to similar mass main-sequence stars indicates that it is inflated and currently undergoing an evolutionary phase, and is likely to end up as a sun-like star as it approaches the main sequence (David et al. 2019b).

4.2 Limb darkening of V1298 Tau

Modeling stellar limb darkening is crucial for deriving transmission spectra. Prior studies often used fixed limb darkening for main-sequence stars based on theoretical stellar structure models (e.g, see Sing et al. 2016). Barat et al. (2024) fit a linear limb darkening coefficient for V1298 Tau, revealing significantly higher limb darkening compared to theoretical models for a main-sequence star with a similar spectral type (K1). The limb darkening coefficients have been derived from fitting the transit light curves of V1298 Tau b observed using HST/WFC3 G141. These observations had both ingress and egress coverage and allowed precise constraints to be put on the linear limb darkening model. However, for simplicity we chose a linear limb darkening model, rather than other limb darkening models with more free parameters, since HST does not provide continuous time series. Higher limb darkening of pre-main-sequence stars compared to theoretical models for mature stars has previously been noted for β-Pictoris (Landman et al. 2024). The fit limb darkening coefficients and a theoretical linear limb darkening model is shown in Fig. F.2. This is the first direct measurement of limb darkening on a weak-lined T-Tauri star.

In Sect. 4.1, we highlighted that V1298 Tau’s density is lower than that of similar-mass main-sequence stars. Furthermore, it has a relatively high magnetic field strength on the order of 100– 300 Gauss (Finociety et al. 2023). High magnetic fields have been proposed as a potential cause of discrepancies between observed and theoretical limb darkening models (Kostogryz et al. 2024). Therefore, a combination of structural differences and higher magnetic fields compared to main-sequence stars could explain the differences we find with the main-sequence limb darkening model.

While leveraging light curves from multiple planets in the same system could potentially reduce limb darkening coefficient uncertainties, the absence of ingress or egress coverage in the light curves of planet c led us to fix the limb darkening coefficients to the values from Barat et al. (2024). A comparison of the transmission spectrum of planet c derived using fixed and free limb darkening is shown in Fig. F.1. For both cases, we assume a linear limb darkening law. For the free limb darkening case, we put uniform priors between 0 and 1 on the linear limb darkening coefficient. The transit depth uncertainties are higher by 5–10% for each spectroscopic bin in the latter case. Residuals in both cases are approximately 1.2 times the expected photon noise, indicating that stellar variability and instrumental systematics from the first orbit are likely to be the dominant sources of noise in our case. However, the median subtracted transit depths are consistent within 1σ for all spectroscopic bins (Fig. F.1). For the atmospheric retrievals, we used the transmission spectrum derived using the fixed limb darkening case. In Fig. F.1 we also show a transmission spectrum for planet c derived by fixing the linear limb darkening coefficient to the EXOCTK model shown in Fig. F.2. We find that the median subtracted transmission spectra for this scenario is consistent within 1σ for all spectroscopic bins with the fixed limb darkening case used for the analysis in this paper.

4.3 Comparative exoplanetology between V1298 Tau b and c

In Fig. 2, we show a comparison between the atmospheres of V1298 Tau b and c. Comparing the spectra in terms of the scale height of both planets (Fig. 2, upper panel) shows that these planets could host atmospheres of a similar nature. To compute the scale height, we used the best-fit mass from the ATMO posteriors for both planets (Table 2). V1298 Tau c has a smaller scale height (~ by a factor of 4) compared to V1298 Tau b. Atmospheric retrievals show that the masses of both these planets are likely to be in the Neptune or sub-Neptune regime (Sect. 3.2). These models also show that the atmospheric metallicities of both these planets are sub-solar to solar. Mature Neptune or sub-Neptune planets, are known to have hazy, metalrich (>100×solar) atmospheres (Bean et al. 2010; Désert et al. 2011a; Kempton et al. 2023; Madhusudhan et al. 2023; Libby- Roberts et al. 2020; Bean et al. 2021). Thus, V1298 Tau b and c, which are the two young Neptune or sub-Neptune progenitors, appear to have distinct atmospheres compared to their mature counterparts.

Efficient haze formation (>10–5) can be ruled out for V1298 Tau b (Fig. 3), given the large atmospheric absorption feature. However, for planet c atmospheric hazes, it can explain the observed spectrum. In the scenario in which the mass of planet c is around 17 M⊕, we cannot constrain the haze formation efficiency for planet c, but for lower masses (∼10 M⊕), very low haze formation efficiency (<10–5) can be ruled out. Therefore, planet c could have a higher haze formation efficiency than its sibling planet. Haze formation has been linked to the UV flux of the host star; a higher UV flux results in higher monomer production rates for organic hazes (Kawashima & Ikoma 2019). Higher atmospheric metallicity could also lead to higher haze formation. The higher haze formation in planet c compared to its sibling planet could be due to differences in the metallicity, temperature, and/or incident UV flux of the two planets.

4.4 Comparing the early evolution of V1298 Tau b and c

We ran evolutionary models for V1298 Tau b and c. These models start from the time of disk dispersal, and model the structural and thermal evolution, including atmospheric mass loss due to photoevaporation (Owen & Wu 2013). We terminated atmospheric mass loss at 100 Myr. We ran models assuming both a core-envelope interior structure as well as a gradually mixed interior. We used the evolutionary models presented in Vazan et al. (2022). A brief description of the models is provided in Appendix D. Figure 4 shows a possible mass and radius evolution tracks for these planets.

We set up the initial conditions of our models such that these models can match the mass and radius of the planets at the current age (23 Myr). For planet c, we assume 5.24 R⊕ and 17 M⊕ (median value of mass from ATMO retrieval). For planet b, we assume 9.95 R⊕ and show two models: a 10 M⊕ model that is consistent within 1σ with the median value from our ATMO retrievals for planet b, and a 23 M⊕ model that is the 3σ mass upper limit from Barat et al. (2024). We assume that the 10 M⊕ model should be similar to a 8 M⊕ model. For this calculation, we did not account for the uncertainty in the mass of the planets; therefore, the models should be considered as potential evolutionary tracks.

Based on these models, V1298 Tau c could have started out with ∼20 M⊕ with a 25% by mass H/He envelope. Currently, it hosts ∼10% by mass H/He in its envelope and after 100 Myr of evolution it ends up as a Neptune-mass planet with a <1% by mass H/He envelope. After 100 Myr, this planet enters a phase of gradual thermal contraction and ends up with a radius between 2.5-3R⊕ (typical for Neptunes and sub-Neptunes). However, for V1298 Tau b, atmospheric mass loss is not as dominant, because it is further away from the host star, thereby receiving ∼25% of the stellar flux compared to planet c. It starts off with ∼8.5 M⊕ and 23.5 M⊕ for the two models presented here, and loses less than 1 M⊕ in the course of its evolution. However, it is important to note here that Barat et al. (2024) report a high internal temperature (∼400 K) for V1298 Tau b from disequilibrium chemistry models of its atmosphere, which has not been considered in our evolution models. A higher-than-expected internal temperature for planet b could lead to a puffed-up atmosphere and enhanced atmospheric mass loss compared to our models.

The mass loss rates are strongly dependent on the current masses of the planets. In the scenario in which planet b and/or c has a mass lower than the estimates used for these calculations, the H/He mass fraction in its envelope would be higher, leading to higher mass loss rates. In extreme scenarios, these planets could be completely stripped of their primordial atmospheres.

While the final mass and radius depend on photoevaporation efficiency and the star’s activity level, from these models we can conclude that due to its proximity to the star, V1298 Tau c is likely to lose a larger fraction of its H/He envelope compared to planet b. Therefore, even if both planets have similar masses now, their early evolution could lead them to different mass-radius regimes as well as different ends of the radius valley.

Our models assume solar metallicity for the envelope opacity. However, the transmission spectrum of V1298 Tau c could also be explained using atmospheric hazes, unlike V1298 Tau b (Fig. 2). Young planets are expected to cool and contract over time (Kubyshkina et al. 2020; Linder et al. 2019). The presence of high altitude hazes can increase the atmospheric opacity, and therefore increase the cooling and contraction timescale (Lee & Chiang 2015), leading to higher photoevaporative mass loss. Thus, a hazy atmosphere of V1298 Tau c as opposed to a clear atmosphere of V1298 Tau b could also lead to slower cooling and higher mass loss rates for planet c.

thumbnail Fig. 4

Potential mass (upper panel) and radius (lower panel) evolutionary tracks for V1298 Tau c (black) and V1298 Tau b (red). M0 and R0 refer to the current mass and radius, respectively. For planet c, we assume 5.24 R⊕ and 17 M⊕ (median value from ATMO atmospheric retrieval) as the current radius and mass. For planet b, we assume 9.95 R⊕ as the current radius. We show models for two values for the current mass for planet b: 10 M⊕ (solid red line), which is consistent within 1σ with the mass measured from our ATMO retrievals (8-4 M æ), and 23 Mæ which is the 3σ upper limit from Barat et al. (2024). The left panels zoom in on the first 100 Myr and the right panels show the evolutionary tracks for 1 Gyr. The evolutionary models described in Appendix D calculate the mass and radius evolution due to cooling and atmospheric mass loss. We used evolutionary models described in Vazan et al. (2022). For further discussion, see Sect. 4.4. These evolutionary models represent one possible scenario for the early evolution of both these planets and do not take into account the planet mass uncertainty.

4.5 Comparing the atmospheres of V1298 Tau b and c with the exoplanet population

Figure 5 shows V1298 Tau b and c on the mass-metallicity and metallicity-orbital distance planes. The observed low atmospheric metallicity (solar or sub-solar) for these planets, deviates from the mass-metallicity trend predicted by coreaccretion models (Bodenheimer & Pollack 1986; Pollack et al. 1996) and reported for exoplanets (Welbanks et al. 2019; Thorn- gren & Fortney 2019). The atmospheric metallicities of planet b and c appear to be at least one order of magnitude lower than mature Neptunes and sub-Neptunes. This could potentially be explained by ongoing evolutionary processes that transform their current metal-poor atmospheres of V1298 Tau b and c into the metal-rich atmospheres, as found in known mature Neptune or sub-Neptune planets (Désert et al. 2011a; Miller-Ricci Kempton et al. 2012; Morley et al. 2013; Libby-Roberts et al. 2020; Bean et al. 2021; Kempton et al. 2023; Madhusudhan et al. 2023). One such possible mechanism has been suggested, whereby Neptunes and sub-Neptunes are naturally born with metallicity gradients in their envelope (Ormel et al. 2021). Atmospheric mass loss during the early evolutionary phase removes the upper layers of the atmosphere, revealing the inner metal-rich layers (Fortney et al. 2013; Vazan et al. 2022). Thus, this mechanism could reconcile the two Neptune or sub-Neptune progenitors, V1298 Tau b and c, with their mature counterparts.

We compared the V1298 Tau system with the ∼30 Myr old HR 8799 system (Marois et al. 2010) with four directly imaged planets (HR 8799 b, c, d, and e) with masses of 7−2+4,10−3+3,10−3+3$$7_{ - 2}^{ + 4},10_{ - 3}^{ + 3},10_{ - 3}^{ + 3}$$, and 10−4+7$$10_{ - 4}^{ + 7}$$ MJ, respectively (Marois et al. 2010; GRAVITY Collaboration 2019). Nasedkin et al. (2024), using ground-based spectra from the VLTI/GRAVITY program, report super-stellar(∼100 times stellar) atmospheric metallicities for these planets. Assuming a –0.65 dex metallicity for HR 8799 (Swastik et al. 2021), we converted the retrieved atmospheric metallicity into stellar units.

The HR 8799 planets exhibit a higher atmospheric metal- licity compared to the mass-metallicity trend (Thorngren & Fortney 2019) predicted by core-accretion formation, while V1298 Tau planets fall below this trend. HR 8799 is a system of widely separated massive gas giants, whereas V1298 Tau likely consists of compact, low-mass Neptune or sub-Neptune progenitors. Both systems likely host primordial atmospheres. The different mass regimes suggest that HR 8799 planets underwent runaway gas accretion (Pollack et al. 1996) or gravitational collapse (Boss 1997), unlike V1298 Tau planets. Formation theories of Neptune and sub-Neptunes suggest that these planets are born in situ within the water ice line in dusty or depleting disks to prevent runaway gas accretion (Lee et al. 2014; Lee & Chiang 2016). Wide-orbit gas giants likely formed beyond the ice lines, allowing for runaway accretion (Pollack et al. 1996) or gravitational instability (Boss 1997; Dodson-Robinson et al. 2009), but these mechanisms alone do not explain HR 8799’s high metallic- ity, necessitating the accretion of volatile-rich solids (Nasedkin et al. 2024). A formation location relative to ice lines could lead to differences in volatile enrichment, as beyond the ice line the disk contains volatile-rich solids, enhancing the metal content of primordial atmospheres (Öberg et al. 2011; Bitsch et al. 2019).

thumbnail Fig. 5

Comparison of the retrieved atmospheric metallicity of V1298 Tau b and c with those of mature exoplanets, with Solar System planets, and with young directly imaged planets orbiting HR 8799 (30 Myr old). The left panel shows these planets in the metallicity-orbital distance plane and the right panel shows the mass-metallicity distribution of these planets. The atmospheric metallicities of the two V1298 Tau b and c planets were derived from the ATMO retrievals (Table 2). The stars show metallicities for retrievals performed using 10 M⊕ for both planets and the squares for retrievals using 23 and 50 M⊕ for planet b and c, respectively. The metallicities of the HR 8799 system (blue circles) were obtained from Nasedkin et al. (2024). The gray points show metallicity constraints from pre-JWST observations (mostly driven by HST) taken from Wakeford & Dalba (2020) and the magenta points show metallicities derived from JWST observations (table uploaded to Zenodo). For planets that both appear in the sample of Wakeford & Dalba (2020) and have been observed with JWST, we plot the latter. For planets where metallicity was estimated from grids, we do not plot error bars. A comparison between the measured metallicities of the V1298 Tau and HR 8799 systems shows that these planets have very different atmospheric metal enrichment, indicative of differences in their formation mechanism, disk properties, and location. The dashed red line in the right panel shows a mass-metallicity relation derived in Thorngren & Fortney (2019). The V1298 Tau planets have metal-poor atmospheres by an order of magnitude compared to their mature counterparts and the observed mass-metallicity trend among exoplanets.

4.6 Formation and evolution of multi-planet systems

The masses of V1298 Tau b and c indicate that they are likely Neptune or sub-Neptune progenitors, which are in a near mean-motion resonance (1:2:3). Atmospheric retrievals suggest that both these planets could have relatively low-metallicity atmospheres. Population synthesis studies (Benz et al. 2014; Mordasini 2018) show that low-mass planets often form in multiplanet systems in mean motion resonance (Lambrechts et al. 2019). Emsenhuber et al. (2023) classify systems with multiple low-mass planets into two types: class I, comprising inner dry or rocky planets formed in situ with outer icy sub-Neptunes migrating inward, and class II, comprising multiple sub-Neptunes forming beyond the water ice line and migrating inward. In the first scenario, inner planets have metal-poor atmospheres, whereas in the second, all planets are metal-rich.

The relatively low atmospheric metallicity of V1298 Tau b and c suggests a formation similar to class I planets. However, these young planets’ atmospheric metallicity can evolve. In the pebble accretion scenario, a metallicity gradient forms in the protoplanet’s envelope (Bodenheimer et al. 2018; Ormel et al. 2021), with metal-rich layers hidden deep inside. Over time, atmospheric mass loss can strip volatile-poor upper layers, revealing deeper metal-rich atmospheric layers (Fortney et al. 2013; Vazan et al. 2022), aligning them with a mature sub-Neptune or super-Earth population. In this case, the V1298 Tau system could also have a formation similar to the class II systems.

If V1298 Tau c has a hazy atmosphere, it might be more metal-rich than the outer planet b, which does not fit either class I or class II systems. Class I systems have inner volatile-poor planets, while class II systems have planets with similar compositions. Due to its proximity to the star, V1298 Tau c is likely to lose more of its primordial envelope compared to V1298 Tau b Fig. 4. Thus, V1298 Tau b and c might have formed like class II systems, with volatiles hidden deep inside, but atmospheric mass loss caused planet c’s metallicity to evolve faster than planet b.

5 Conclusion

In this paper, we have performed the first comparative study of atmospheres of multiple planets in the same transiting multiplanet system. We have compared the transmission spectra of two exoplanets in the young (20–30 Myr old) V1298 Tau system: V1298 Tau b and c. The transmission spectrum of V1298 Tau c shows an absorption feature that we interpret as being due to water vapor (2.5σ), whereas the spectra of its sibling, V1298 Tau b (adopted from Barat et al. (2024)), show a clear atmosphere with a large scale height and a water absorption feature at a 5σ level of significance (Fig. 2). We measured the masses of both planets from the transmission spectra (8−2+4 M⊕$$8_{ - 2}^{ + 4}{{\rm{M}}_ \oplus }$$ for planet b and 17−6+13 M⊕$$17_{ - 6}^{ + 13}{{\rm{M}}_ \oplus }$$ for planet c), together with the chemical abundances using a Bayesian chemical equilibrium retrieval framework and the ATMO atmospheric model. The retrieved mass for planet c is consistent with previous RV estimates (Suárez Mascareño et al. 2021; Sikora et al. 2023; Finociety et al. 2023). Our mass determination from the atmospheric scale heights also agrees with ongoing TTV studies (Livingston et al, in prep). Our atmospheric models find sub-solar or solar atmospheric metallicities (logZ/Z⊙=−2.04−0.590.69$$\log Z/{Z_ \odot } = - 2.04_{ - 0.59}^{0.69}$$ for planet b and logZ/Z⊙=−0.16−0.941.15$\log Z/{Z_ \odot } = - 0.16_{ - 0.94}^{1.15}$, for planet c) for both these planets (Table 2), from free planet masses as well as fixed masses in the atmospheric retrievals. Compared to known mature Neptune or sub-Neptunes, which have been found to have metal-rich (>100×solar) and/or hazy atmospheres, the atmospheres of the two young Neptune or sub-Neptune progenitors (planet b and c) can be considered metal-poor by at least one order of magnitude. This hints at possible ongoing early evolutionary mechanisms that are expected to enhance the atmospheric metallicity of these planets, such that they are reconciled with their mature counterparts after evolution. Alternatively, the observed spectrum of V1298 Tau c could also be explained by atmospheric hazes. The large observed scale height of V1298 Tau b rules out a high haze formation efficiency (>10–5; Fig. 3) for this planet. Higher haze formation in planet c compared to planet b could be due to differences in the bulk composition, temperature-pressure profile, and incoming stellar UV flux, which are known to be important factors affecting haze formation in H/He-rich atmospheres (Kawashima & Ikoma 2018; Gao & Zhang 2020). In this scenario, the higher envelope opacity of planet c due to hazes could delay its cooling rate compared to planet b, which has a clearer atmosphere. Evolutionary models suggest that planet c could lose a large fraction of its current H/He envelope (~10% by mass) and end up with <1% by the end of its evolutionary phase. In contrast, our models applied to planet b, which receives 25% of the stellar flux received by planet c, do not predict significant mass loss and could end up retaining a substantial H/He envelope after 100 Myr of evolution.

Data availability

The data used used for this analysis are publicly available on the MAST archive. The data used for the figures are available upon request to the corresponding authors. Some of the supplementary figures are uploaded to Zenodo (https://zenodo.org/records/14044738).

Acknowledgements

J.M.D acknowledges support from the Amsterdam Academic Alliance (AAA) Program, and the European Research Council (ERC) European Union’s Horizon 2020 research and innovation program (grant agreement no. 679633; Exo-Atmos). This work is part of the research program VIDI New Frontiers in Exoplanetary Climatology with project number 614.001.601, which is (partly) financed by the Dutch Research Council (NWO). Y.K. acknowledges the support from JSPS KAKENHI Grant Numbers 21K13984, 22H05150, and 23H01224. We acknowledge publicly available open source softwares which have been used for this work: numpy, scipy, matplotlib, emcee, lmfit, pandas, ATMO, PetitRadtrans.

Appendix A Description of raw data reduction

We used the HST/WFC3 data reduction pipeline which has been presented in previous studies (Arcangeli et al. 2018; Arcangeli et al. 2019, 2021; Jacobs et al. 2022; Barat et al. 2024). We do not change anything in the pipeline for the analysis of this paper. We start our analysis from the ‘ima.fits’ files downloaded from MAST archive. During each exposure, the detector was read multiple times, without flushing out the accumulated charge (non-destructive reads). We create sub-exposures by subtracting consecutive non-destructive reads for each exposure which are reduced separately. This technique has been widely applied in past observations with HST. We apply a wavelength dependent flat-field correction and flag bad pixels with data quality DQ=4, 32, or 512 by calwf3. We applied a local median filter to identify cosmic rays and clip pixels which were more than five median deviations from the median. To account for the dispersion direction drift of the spectrum (Wakeford et al. 2016) we used the first exposure of a visit as a template and shifted the spectrum for an exposure along the dispersion direction to match the template. The maximum shift that we required was 0.1 pixels. We applied optimal extraction algorithm (Horne 1986) on each subexposure to maximize signal-to-noise ratio.

Appendix B Light curve fitting

HST WFC3 light curves often exhibit strong systematics, such as ‘hook-like’ ramps and visit-long slopes (Berta et al. 2012; Deming et al. 2013; Ranjan et al. 2014; Tsiaras et al. 2016; Wakeford et al. 2016). Common practice involves discarding the first orbit due to significantly larger systematics (see Fig. 1) compared to the rest of the visit (e.g. see, Wakeford et al. 2013; Arcangeli et al. 2018; Jacobs et al. 2022; Barat et al. 2024) from the light curve fitting. For the visit of planet b, the first orbit had been discarded (Barat et al. 2024). However, for the visit of planet c, we could not remove the first orbit of the visit from the analysis because the transit occurred two hours earlier than expected from the linear ephemeris (Feinstein et al. 2022) due to large TTVs and we could only secure one orbit prior to ingress.

The first-orbit systematics are strongly wavelength dependent (Zhou et al. 2020,2017). Therefore, the spectroscopic light curves of planet c could not be de-trended using a common-mode approach, which had been previously applied to similar observations of planet b (Barat et al. 2024). Therefore, to handle these systematics, we used the physically motivated RECTE chargetrapping model (Zhou et al. 2017), which fits the first orbit ramp better than other known methods (e.g, Berta et al. 2012). We fixed the mid-transit time using simultaneous TESS observations (Feinstein et al. 2022). V1298 Tau shows strong rotational variability, with an average amplitude of 2% and a rotational period of 2.83 days (David et al. 2019b). We modeled it with a second- order polynomial for the out-of-transit baseline (see Appendix C for more discussion on the baseline modeling). The planetary transit signal was modeled using batman (Kreidberg 2015).

For the white light curve (1.12-1.6 µm), we fitted for the RECTE parameters and the baseline polynomial coefficients, along with the planet’s transit depth and semi-major axis. Other orbital parameters were fixed to literature values (Feinstein et al. 2022; Sikora et al. 2023; David et al. 2019a). The RECTE parameters constitute 4 parameters: the number of initially filled fast/slow charge traps and the number of fast/slow charge traps that are filled in between orbits. Due to the lack of ingress and egress data, our limb darkening precision was impaired. However, by using the limb darkening parameter retrieved from the observations of planet b (Barat et al. 2024), we were able to significantly reduce the uncertainties on the transit spectrum (Fig. F.1). V1298 Tau b and c have impact parameters (0.34−0.21+0.19$0.34_{ - 0.21}^{ + 0.19}$ and 0.46−0.24+0.13$0.46_{ - 0.24}^{ + 0.13}$ respectively) consistent within 1σ of each other. Fur thermore, Johnson et al. (2022) report a relatively low mutual inclination (0±19°), indicating a planar orbital geometry of the V1298 Tau system. Therefore, both planets are likely to transit a similar part of the stellar photosphere with limb darkening during their primary transit. This highlights the advantage and uniqueness of studying multiple planets in the same system. For a discussion on the limb darkening of V1298 Tau see Sect. 4.2. We also independently measured the stellar density from the HST white light curves which is discussed in Sect. 4.1.

The fit was performed using emcee (Foreman-Mackey et al. 2013). The posterior distribution from these fits is shown in the figure uploaded to Zenodo and the best-fit transit model and residuals, are shown in Fig. 1 (upper panel).

Spectroscopic light curves were analyzed similarly by dividing the stellar spectra into 7-pixel bins, resulting in 17 channels (identical to V1298 Tau b). We fixed the semi-major axis from the white light curve fits and fit the RECTE parameters and baseline for each bin, and the transit depth. We fix the wavelength dependent limb darkening coefficients to values derived in Barat et al. (2024). The de-trended spectroscopic light curves and residuals are uploaded to Zenodo.

Appendix C Modeling the baseline

Young stars exhibit quasi-periodic flux modulation due to rotational variability (e.g. see David et al. 2019b; Mann et al. 2016; Mann et al. 2022). The transit of planet c analyzed in this work occurred near an inflection point of the stellar baseline, resulting in significant deviation from a linear function. We modeled the baseline using linear, quadratic, and cubic polynomial functions for all the spectroscopic channels. The transit depths from all three fits were consistent within 1σ, but quadratic and cubic polynomials were statistically favored over a linear baseline (figure uploaded to Zenodo).

Higher-order polynomials, however, introduce correlation between the transit depth and baseline, increasing uncertainties and scatter in the transmission spectrum. The Bayesian information criterion did not improve significantly with a cubic baseline compared to a quadratic one, and the cubic polynomial coefficients strongly correlated with the transit depths, likely adding noise. Therefore, we used a quadratic polynomial to model the baseline for the final transmission spectrum.

Appendix D Theoretical evolutionary models

The evolutionary models we used in the current study are described in Vazan et al. (2022). Our models started from the time of disk dispersal and calculate the thermal evolution and structural evolution. We considered both core-envelope as well as gradually mixed interior structures. We includeed atmospheric mass loss due to photoevaporation from the topmost layer of the planets using the formalism of Rogers & Owen (2021). The mass loss rates are estimated from an energy-limited model (Erkaev et al. 2007), assuming a fixed photoevaporation efficiency. Our models included core erosion and mixing with the envelope. We chose the initial conditions (mass and radius) such that they matched the current mass and radius for the planets. We assumed 17 M⊕ (peak of ATMO retrieval posterior distribution) for the current mass estimates of the V1298 Tau c. For planet b, we show two models: 10 M⊕ (consistent within 1σ to median mass retrieved from ATMO) and 23 M⊕ (3 σ mass upper limit from Barat et al. (2024)). We ran simulations with both core-envelope and gradually mixed interior models. Both interior structure models can explain the current mass/radius of the planets. Mass and radius (normalized at current value) evolution models for the V1298 Tau planets are shown in Fig. 4.

Appendix E Effect of stellar activity on transmission spectrum

We estimated the effect of stellar activity on the transmission spectrum of V1298 Tau c. We adopted the method outlined in Rackham et al. (2019), where we estimated a correction factor based on the spot coverage fraction and spot temperature contrast. We adopt a spot coverage fraction of 20% for V1298 Tau (Feinstein et al. 2021). We adopted an extreme spot contrast of 1000 K following spot contrasts derived for a sample of T Tauri stars (Koen 2016). A comparison between the observed and corrected transmission spectrum is provided in a figure uploaded to Zenodo. The observed and contamination corrected normalized spectra were consistent within 1σ for all spectroscopic channels.

Since V1298 Tau is a K-type star, its contamination function does not show molecular features like M-dwarfs (Barclay et al. 2021). Therefore, the main effect of the stellar correction is to change the level of the continuum in this case. However, the atmospheric features, which are relative to the continuum remain largely unaffected.

Appendix F Supplementary figures

thumbnail Fig. F.1

Comparison of the derived transmission spectrum of V1298 Tau c for a fixed and free limb darkening fit to the light curves (upper panel) and corresponding 1σ uncertainties for each each spectroscopic bin (lower panel). We fix the limb darkening to i) linear limb darkening coefficients derived from the primary transit of V1298 Tau b (Barat et al. 2024) shown in red ii) model limb darkening coefficients derived from EXOCTK (Sect. 4.2 and Fig. F.2) shown in orange. The transmission spectrum derived using free linear limb darkening coefficients for planet c is shown in blue. The median subtracted transmission spectra in all three cases are consistent within 1σ of each other for all channels. A comparison between the transit depth uncertainty for the free and fixed limb darkening cases shows that fixing the limb darkening reduces the transit depth uncertainty by 5-10% for each channel.
thumbnail Fig. F.2

Comparison between the fit linear limb darkening coefficients derived from the V1298 Tau b visit (Barat et al. 2024) and theoretical limb darkening model for a main sequence star of a similar spectral type. The theoretical models have been derived using EXOCTK (Bourque et al. 2021) for a star with similar spectral type as V1298 Tau (K1). We used photospheric temperature of 5000K, log g=4 and solar metallic- ity (Finociety et al. 2023) PHOENIX models to simulate the theoretical linear limb darkening coefficients in the HST/WFC3 G141 bandpass. To our knowledge, this is the first time that the limb darkening of a weak-lined T-Tauri star has been measured. The measured limb darkening appears significantly different compared to that of a main sequence star of the same spectral type. This discrepancy between with main- sequence models is could be due to different interior structure and high magnetic field of this young star (see Sect. 4.2). This figure highlights the importance of fitting for the limb darkening when analyzing transit light curves around such young stars.

References

  1. Arcangeli, J., Désert, J.-M., Line, M. R., et al. 2018, ApJ, 855, L30 [Google Scholar]
  2. Arcangeli, J., Désert, J.-M., Parmentier, V., et al. 2019, A&A, 625, A136 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  3. Arcangeli, J., Désert, J. M., Parmentier, V., Tsai, S. M., & Stevenson, K. B. 2021, A&A, 646, A94 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  4. Baeyens, R., Konings, T., Venot, O., Carone, L., & Decin, L. 2022, MNRAS, 512, 4877 [NASA ADS] [CrossRef] [Google Scholar]
  5. Barat, S., Désert, J.-M., Vazan, A., et al. 2024, Nat. Astron., submitted [arXiv:2312.16924] [Google Scholar]
  6. Barclay, T., Kostov, V. B., Colón, K. D., et al. 2021, AJ, 162, 300 [NASA ADS] [CrossRef] [Google Scholar]
  7. Baxter, C., Désert, J.-M., Parmentier, V., et al. 2020, A&A, 639, A36 [EDP Sciences] [Google Scholar]
  8. Baxter, C., Désert, J.-M., Tsai, S.-M., et al. 2021, A&A, 648, A127 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  9. Bean, J. L., Miller-Ricci Kempton, E., & Homeier, D. 2010, Nature, 468, 669 [NASA ADS] [CrossRef] [Google Scholar]
  10. Bean, J. L., Raymond, S. N., & Owen, J. E. 2021, J. Geophys. Res. Planets, 126, e06639 [NASA ADS] [CrossRef] [Google Scholar]
  11. Benz, W., Ida, S., Alibert, Y., Lin, D., & Mordasini, C. 2014, in Protostars and Planets VI, ed. H. Beuther, R. S. Klessen, C. P. Dullemond, & T. Henning (Tucson: University of Arizona Press), 691 [Google Scholar]
  12. Berta, Z. K., Charbonneau, D., Désert, J.-M., et al. 2012, ApJ, 747, 35 [NASA ADS] [CrossRef] [Google Scholar]
  13. Bitsch, B., Raymond, S. N., & Izidoro, A. 2019, A&A, 624, A109 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  14. Blunt, S., Carvalho, A., David, T. J., et al. 2023, AJ, 166, 62 [NASA ADS] [CrossRef] [Google Scholar]
  15. Bodenheimer, P., & Pollack, J. B. 1986, Icarus, 67, 391 [Google Scholar]
  16. Bodenheimer, P., Stevenson, D. J., Lissauer, J. J., & D’Angelo, G. 2018, ApJ, 868, 138 [NASA ADS] [CrossRef] [Google Scholar]
  17. Boss, A. P. 1997, Science, 276, 1836 [Google Scholar]
  18. Bourque, M., Espinoza, N., Filippazzo, J., et al. 2021, The Exoplanet Characterization Toolkit (ExoCTK) [Google Scholar]
  19. Brande, J., Crossfield, I. J. M., Kreidberg, L., et al. 2024, ApJ, 961, L23 [NASA ADS] [CrossRef] [Google Scholar]
  20. Brems, S. S., Kürster, M., Trifonov, T., Reffert, S., & Quirrenbach, A. 2019, A&A, 632, A37 [EDP Sciences] [Google Scholar]
  21. Carter, A. L., Nikolov, N., Sing, D. K., et al. 2020, MNRAS, 494, 5449 [NASA ADS] [CrossRef] [Google Scholar]
  22. Damasso, M., Scandariato, G., Nascimbeni, V., et al. 2023, A&A, 680, A8 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  23. David, T. J., Hillenbrand, L. A., Petigura, E. A., et al. 2016, Nature, 534, 658 [CrossRef] [Google Scholar]
  24. David, T. J., Cody, A. M., Hedges, C. L., et al. 2019a, AJ, 158, 79 [NASA ADS] [CrossRef] [Google Scholar]
  25. David, T. J., Petigura, E. A., Luger, R., et al. 2019b, ApJ, 885, L12 [Google Scholar]
  26. Deming, D., Wilkins, A., McCullough, P., et al. 2013, ApJ, 774, 95 [Google Scholar]
  27. Désert, J.-M., Bean, J., Miller-Ricci Kempton, E., et al. 2011a, ApJ, 731, L40 [Google Scholar]
  28. Désert, J.-M., Charbonneau, D., Demory, B.-O., et al. 2011b, ApJS, 197, 14 [Google Scholar]
  29. Dodson-Robinson, S. E., Veras, D., Ford, E. B., & Beichman, C. A. 2009, ApJ, 707, 79 [Google Scholar]
  30. Drummond, B., Tremblin, P., Baraffe, I., et al. 2016, A&A, 594, A69 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  31. Duvvuri, G. M., Cauley, P. W., Aguirre, F. C., et al. 2023, AJ, 166, 196 [NASA ADS] [CrossRef] [Google Scholar]
  32. Emsenhuber, A., Mordasini, C., & Burn, R. 2023, Euro. Phys. J. Plus, 138, 181 [NASA ADS] [CrossRef] [Google Scholar]
  33. Erkaev, N. V., Kulikov, Y. N., Lammer, H., et al. 2007, A&A, 472, 329 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  34. Evans, T. M., Sing, D. K., Goyal, J. M., et al. 2018, AJ, 156, 283 [NASA ADS] [CrossRef] [Google Scholar]
  35. Feinstein, A. D., Montet, B. T., Johnson, M. C., et al. 2021, AJ, 162, 213 [NASA ADS] [CrossRef] [Google Scholar]
  36. Feinstein, A. D., David, T. J., Montet, B. T., et al. 2022, ApJ, 925, L2 [NASA ADS] [CrossRef] [Google Scholar]
  37. Finociety, B., Donati, J. F., Cristofari, P. I., et al. 2023, MNRAS, 526, 4627 [NASA ADS] [CrossRef] [Google Scholar]
  38. Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306 [Google Scholar]
  39. Fortney, J. J., Mordasini, C., Nettelmann, N., et al. 2013, ApJ, 775, 80 [Google Scholar]
  40. Fortney, J. J., Visscher, C., Marley, M. S., et al. 2020, AJ, 160, 288 [NASA ADS] [CrossRef] [Google Scholar]
  41. Fu, G., Deming, D., Knutson, H., et al. 2017, ApJ, 847, L22 [NASA ADS] [CrossRef] [Google Scholar]
  42. Fulton, B. J., & Petigura, E. A. 2018, AJ, 156, 264 [Google Scholar]
  43. Fulton, B. J., Petigura, E. A., Howard, A. W., et al. 2017, AJ, 154, 109 [Google Scholar]
  44. Gao, P., & Zhang, X. 2020, ApJ, 890, 93 [Google Scholar]
  45. Gao, P., Thorngren, D. P., Lee, E. K. H., et al. 2020, Nat. Astron., 4, 951 [NASA ADS] [CrossRef] [Google Scholar]
  46. Garhart, E., Deming, D., Mandell, A., et al. 2020, AJ, 159, 137 [NASA ADS] [CrossRef] [Google Scholar]
  47. Ginzburg, S., Schlichting, H. E., & Sari, R. 2018, MNRAS, 476, 759 [Google Scholar]
  48. Goyal, J. M., Mayne, N., Sing, D. K., et al. 2018, MNRAS, 474, 5158 [Google Scholar]
  49. Goyal, J. M., Wakeford, H. R., Mayne, N. J., et al. 2019, MNRAS, 482, 4503 [NASA ADS] [CrossRef] [Google Scholar]
  50. GRAVITY Collaboration (Lacour, S., et al.) 2019, A&A, 623, L11 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  51. Gupta, A., & Schlichting, H. E. 2019, MNRAS, 487, 24 [Google Scholar]
  52. Heng, K., & Kitzmann, D. 2017, MNRAS, 470, 2972 [Google Scholar]
  53. Horne, K. 1986, PASP, 98, 609 [Google Scholar]
  54. Jacobs, B., Désert, J. M., Pino, L., et al. 2022, A&A, 668, L1 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  55. Johnson, M. C., David, T. J., Petigura, E. A., et al. 2022, AJ, 163, 247 [NASA ADS] [CrossRef] [Google Scholar]
  56. Kajtazi, K., Petit, A. C., & Johansen, A. 2023, A&A, 669, A44 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  57. Kawashima, Y., & Ikoma, M. 2018, ApJ, 853, 7 [NASA ADS] [CrossRef] [Google Scholar]
  58. Kawashima, Y., & Ikoma, M. 2019, ApJ, 877, 109 [NASA ADS] [CrossRef] [Google Scholar]
  59. Keating, D., Cowan, N. B., & Dang, L. 2019, Nat. Astron., 3, 1092 [NASA ADS] [CrossRef] [Google Scholar]
  60. Kempton, E. M. R., Zhang, M., Bean, J. L., et al. 2023, Nature, 620, 67 [NASA ADS] [CrossRef] [Google Scholar]
  61. Khare, B. N., Sagan, C., Arakawa, E. T., et al. 1984, Icarus, 60, 127 [CrossRef] [Google Scholar]
  62. Knutson, H. A., Benneke, B., Deming, D., & Homeier, D. 2014, Nature, 505, 66 [Google Scholar]
  63. Koen, C. 2016, MNRAS, 463, 4383 [NASA ADS] [CrossRef] [Google Scholar]
  64. Kostogryz, N. M., Shapiro, A. I., Witzke, V., et al. 2024, arXiv e-prints [arXiv:2403.00118] [Google Scholar]
  65. Kreidberg, L. 2015, PASP, 127, 1161 [Google Scholar]
  66. Kreidberg, L., Bean, J. L., Désert, J.-M., et al. 2014, Nature, 505, 69 [Google Scholar]
  67. Kreidberg, L., Mollière, P., Crossfield, I. J. M., et al. 2022, AJ, 164, 124 [CrossRef] [Google Scholar]
  68. Kubyshkina, D., Vidotto, A. A., Fossati, L., & Farrell, E. 2020, MNRAS, 499, 77 [Google Scholar]
  69. Lambrechts, M., Morbidelli, A., Jacobson, S. A., et al. 2019, A&A, 627, A83 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  70. Landman, R., Stolker, T., Snellen, I. A. G., et al. 2024, A&A, 682, A48 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  71. Lee, E. J., & Chiang, E. 2015, ApJ, 811, 41 [Google Scholar]
  72. Lee, E. J., & Chiang, E. 2016, ApJ, 817, 90 [Google Scholar]
  73. Lee, E. J., Chiang, E., & Ormel, C. W. 2014, ApJ, 797, 95 [Google Scholar]
  74. Lewis, N. K., Wakeford, H. R., MacDonald, R. J., et al. 2020, ApJ, 902, L19 [NASA ADS] [CrossRef] [Google Scholar]
  75. Libby-Roberts, J. E., Berta-Thompson, Z. K., Désert, J.-M., et al. 2020, AJ, 159, 57 [Google Scholar]
  76. Lim, O., Benneke, B., Doyon, R., et al. 2023, ApJ, 955, L22 [NASA ADS] [CrossRef] [Google Scholar]
  77. Linder, E. F., Mordasini, C., Mollière, P., et al. 2019, A&A, 623, A85 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  78. Luhman, K. L. 2018, AJ, 156, 271 [Google Scholar]
  79. Madhusudhan, N., Sarkar, S., Constantinou, S., et al. 2023, ApJ, 956, L13 [NASA ADS] [CrossRef] [Google Scholar]
  80. Mann, A. W., Newton, E. R., Rizzuto, A. C., et al. 2016, AJ, 152, 61 [Google Scholar]
  81. Mann, A. W., Wood, M. L., Schmidt, S. P., et al. 2022, AJ, 163, 156 [NASA ADS] [CrossRef] [Google Scholar]
  82. Marois, C., Zuckerman, B., Konopacky, Q. M., Macintosh, B., & Barman, T. 2010, Nature, 468, 1080 [NASA ADS] [CrossRef] [Google Scholar]
  83. May, E. M., MacDonald, R. J., Bennett, K. A., et al. 2023, ApJ, 959, L9 [CrossRef] [Google Scholar]
  84. Miller-Ricci Kempton, E., Zahnle, K., & Fortney, J. J. 2012, ApJ, 745, 3 [NASA ADS] [CrossRef] [Google Scholar]
  85. Mollière, P., Wardenier, J. P., van Boekel, R., et al. 2019, A&A, 627, A67 [Google Scholar]
  86. Moran, S. E., Stevenson, K. B., Sing, D. K., et al. 2023, ApJ, 948, L11 [NASA ADS] [CrossRef] [Google Scholar]
  87. Mordasini, C. 2018, in Handbook of Exoplanets, eds. H. J. Deeg, & J. A. Belmonte (Berlin: Springer), 143 [Google Scholar]
  88. Morley, C. V., Fortney, J. J., Kempton, E. M. R., et al. 2013, ApJ, 775, 33 [CrossRef] [Google Scholar]
  89. Nasedkin, E., Mollière, P., Lacour, S., et al. 2024, A&A, 687, A298 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  90. Öberg, K. I., Murray-Clay, R., & Bergin, E. A. 2011, ApJ, 743, L16 [Google Scholar]
  91. Oh, S., Price-Whelan, A. M., Hogg, D. W., Morton, T. D., & Spergel, D. N. 2017, VizieR Online Data Catalog: J/AJ/153/257 [Google Scholar]
  92. Ormel, C. W., Vazan, A., & Brouwers, M. G. 2021, A&A, 647, A175 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  93. Owen, J. E., & Wu, Y. 2013, ApJ, 775, 105 [Google Scholar]
  94. Owen, J. E., & Wu, Y. 2017, ApJ, 847, 29 [Google Scholar]
  95. Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124, 62 [NASA ADS] [CrossRef] [Google Scholar]
  96. Pont, F., Knutson, H., Gilliland, R. L., Moutou, C., & Charbonneau, D. 2008, MNRAS, 385, 109 [Google Scholar]
  97. Rackham, B. V., Apai, D., & Giampapa, M. S. 2019, AJ, 157, 96 [Google Scholar]
  98. Ranjan, S., Charbonneau, D., Désert, J.-M., et al. 2014, ApJ, 785, 148 [NASA ADS] [CrossRef] [Google Scholar]
  99. Rathcke, A. D., MacDonald, R. J., Barstow, J. K., et al. 2021, AJ, 162, 138 [NASA ADS] [CrossRef] [Google Scholar]
  100. Rogers, J. G., & Owen, J. E. 2021, MNRAS, 503, 1526 [NASA ADS] [CrossRef] [Google Scholar]
  101. Sandford, E., & Kipping, D. 2017, AJ, 154, 228 [NASA ADS] [CrossRef] [Google Scholar]
  102. Shulyak, D., Lara, L. M., Rengel, M., & Nèmec, N. E. 2020, A&A, 639, A48 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  103. Sikora, J., Rowe, J., Barat, S., et al. 2023, AJ, 165, 250 [NASA ADS] [CrossRef] [Google Scholar]
  104. Sing, D. K., Fortney, J. J., Nikolov, N., et al. 2016, Nature, 529, 59 [Google Scholar]
  105. Speagle, J. S. 2020, MNRAS, 493, 3132 [Google Scholar]
  106. Suárez Mascareño, A., Damasso, M., Lodieu, N., et al. 2021, Nat. Astron., submitted [arXiv:2111.09193] [Google Scholar]
  107. Swastik, C., Banyal, R. K., Narang, M., et al. 2021, AJ, 161, 114 [Google Scholar]
  108. Szabó, G. M., & Kiss, L. L. 2011, ApJ, 727, L44 [Google Scholar]
  109. Terquem, C., & Papaloizou, J. C. B. 2018, MNRAS, 482, 530 [Google Scholar]
  110. Thorngren, D., & Fortney, J. J. 2019, ApJ, 874, L31 [Google Scholar]
  111. Tremblin, P., Amundsen, D. S., Mourier, P., et al. 2015, ApJ, 804, L17 [CrossRef] [Google Scholar]
  112. Tsai, S.-M., Lee, E. K. H., Powell, D., et al. 2023, Nature, 617, 483 [CrossRef] [Google Scholar]
  113. Tsiaras, A., Waldmann, I. P., Rocchetto, M., et al. 2016, ApJ, 832, 202 [NASA ADS] [CrossRef] [Google Scholar]
  114. Van Eylen, V., Agentoft, C., Lundkvist, M. S., et al. 2018, MNRAS, 479, 4786 [Google Scholar]
  115. Vazan, A., Sari, R., & Kessel, R. 2022, ApJ, 926, 150 [NASA ADS] [CrossRef] [Google Scholar]
  116. Venot, O., & Agúndez, M. 2015, Exp. Astron., 40, 469 [NASA ADS] [CrossRef] [Google Scholar]
  117. Wakeford, H. R., & Dalba, P. A. 2020, Phil. Trans. R. Soc. London Ser. A, 378, 20200054 [Google Scholar]
  118. Wakeford, H. R., Sing, D. K., Deming, D., et al. 2013, MNRAS, 435, 3481 [NASA ADS] [CrossRef] [Google Scholar]
  119. Wakeford, H. R., Sing, D. K., Evans, T., Deming, D., & Mandell, A. 2016, ApJ, 819, 10 [NASA ADS] [CrossRef] [Google Scholar]
  120. Welbanks, L., Madhusudhan, N., Allard, N. F., et al. 2019, ApJ, 887, L20 [NASA ADS] [CrossRef] [Google Scholar]
  121. Yu, X., He, C., Zhang, X., et al. 2021, Nat. Astron., 5, 822 [NASA ADS] [CrossRef] [Google Scholar]
  122. Zhou, Y., Apai, D., Lew, B. W. P., & Schneider, G. 2017, AJ, 153, 243 [NASA ADS] [CrossRef] [Google Scholar]
  123. Zhou, G., Quinn, S. N., Irwin, J., et al. 2020, AJ, 161, 2 [NASA ADS] [CrossRef] [Google Scholar]

All Tables

Table 1

Comparison of the physical properties of V1298 Tau b and c.

In the text
Table 2

Derived parameters from atmospheric retrievals run using ATMO (see Sect. 3.2) for planet c and planet b.

In the text

All Figures

thumbnail Fig. 1

Transit light curve of V1298 Tau c observed using HST/WFC G141. Upper panel: raw white (1.12-1.65µm band) light curve for the transit of V1298 Tau c. Blue and green points show forward and reverse scanned exposures, respectively. The solid black lines show the best-fit transit model. We used a physically motivated charge trapping model, RECTE (Zhou et al. 2017, 2020) to fit the exponential ramps. The baseline was modeled using a quadratic function in time. See Appendix C for further discussion. The transit was modeled using batman (Kreidberg 2015). For details of light curve fitting, see Sect. 2. Lower panel: residuals from the fit to the white light curve observations.
In the text
thumbnail Fig. 2

Transmission spectrum of V1298 Tau c (blue points) shown in comparison with its sibling planet V1298 Tau b (green points). The spectra have been derived by subtracting the median of the observed spectrum. The upper panel shows the spectra in terms of atmospheric scale height and the middle panel in terms of transit depth. We assumed Teq=979 K and 17 M⊕ for planet c and 685 K and 8 M⊕ for planet b to calculate the scale height for each planet. We assumed H/He-dominated primordial atmospheres and assumed a mean molecular weight of 2.33. The solid green and blue lines show the best-fit ATMO models from our retrievals for planet b and c with 8 and 17 M⊕, respectively (Sect. 3.2). The dashed lines show hazy atmospheric models for both planets simulated using the formalism presented in Kawashima & Ikoma (2018) (see Sect. 3.3). We show hazy atmospheric models with the same mass as the best-fit models and have been generated by rescaling the hazy atmospheric model grids described in Sect. 3.3. The lower panel shows the relative transmission spectrum (i.e., the ratio between transmission spectra) between V1298 Tau b and V1298 Tau c (see Sect. 3.4).
In the text
thumbnail Fig. 3

Comparison between observed HST transmission spectrum of V1298 Tau b (upper panel) and V1298 Tau c (lower panel) with haze grid models of different haze formation efficiency and planet mass. Upper panel: Solid lines represent models assuming 23 M⊕. Dashed lines represent models with 8 Mθ, which have been rescaled from the 10 M⊕ haze grid model of planet b. Blue and green represent haze formation efficiencies of 0.01% and 0.001%, respectively. Lower panel: Solid lines represent models assuming 17 M⊕ rescaled from the 20 Mθ haze grid model for planet c. Dashed lines represent models with 10 Mθ. Blue and green represent haze formation efficiencies of 1% and 0.001%, respectively.
In the text
thumbnail Fig. 4

Potential mass (upper panel) and radius (lower panel) evolutionary tracks for V1298 Tau c (black) and V1298 Tau b (red). M0 and R0 refer to the current mass and radius, respectively. For planet c, we assume 5.24 R⊕ and 17 M⊕ (median value from ATMO atmospheric retrieval) as the current radius and mass. For planet b, we assume 9.95 R⊕ as the current radius. We show models for two values for the current mass for planet b: 10 M⊕ (solid red line), which is consistent within 1σ with the mass measured from our ATMO retrievals (8-4 M æ), and 23 Mæ which is the 3σ upper limit from Barat et al. (2024). The left panels zoom in on the first 100 Myr and the right panels show the evolutionary tracks for 1 Gyr. The evolutionary models described in Appendix D calculate the mass and radius evolution due to cooling and atmospheric mass loss. We used evolutionary models described in Vazan et al. (2022). For further discussion, see Sect. 4.4. These evolutionary models represent one possible scenario for the early evolution of both these planets and do not take into account the planet mass uncertainty.
In the text
thumbnail Fig. 5

Comparison of the retrieved atmospheric metallicity of V1298 Tau b and c with those of mature exoplanets, with Solar System planets, and with young directly imaged planets orbiting HR 8799 (30 Myr old). The left panel shows these planets in the metallicity-orbital distance plane and the right panel shows the mass-metallicity distribution of these planets. The atmospheric metallicities of the two V1298 Tau b and c planets were derived from the ATMO retrievals (Table 2). The stars show metallicities for retrievals performed using 10 M⊕ for both planets and the squares for retrievals using 23 and 50 M⊕ for planet b and c, respectively. The metallicities of the HR 8799 system (blue circles) were obtained from Nasedkin et al. (2024). The gray points show metallicity constraints from pre-JWST observations (mostly driven by HST) taken from Wakeford & Dalba (2020) and the magenta points show metallicities derived from JWST observations (table uploaded to Zenodo). For planets that both appear in the sample of Wakeford & Dalba (2020) and have been observed with JWST, we plot the latter. For planets where metallicity was estimated from grids, we do not plot error bars. A comparison between the measured metallicities of the V1298 Tau and HR 8799 systems shows that these planets have very different atmospheric metal enrichment, indicative of differences in their formation mechanism, disk properties, and location. The dashed red line in the right panel shows a mass-metallicity relation derived in Thorngren & Fortney (2019). The V1298 Tau planets have metal-poor atmospheres by an order of magnitude compared to their mature counterparts and the observed mass-metallicity trend among exoplanets.
In the text
thumbnail Fig. F.1

Comparison of the derived transmission spectrum of V1298 Tau c for a fixed and free limb darkening fit to the light curves (upper panel) and corresponding 1σ uncertainties for each each spectroscopic bin (lower panel). We fix the limb darkening to i) linear limb darkening coefficients derived from the primary transit of V1298 Tau b (Barat et al. 2024) shown in red ii) model limb darkening coefficients derived from EXOCTK (Sect. 4.2 and Fig. F.2) shown in orange. The transmission spectrum derived using free linear limb darkening coefficients for planet c is shown in blue. The median subtracted transmission spectra in all three cases are consistent within 1σ of each other for all channels. A comparison between the transit depth uncertainty for the free and fixed limb darkening cases shows that fixing the limb darkening reduces the transit depth uncertainty by 5-10% for each channel.
In the text
thumbnail Fig. F.2

Comparison between the fit linear limb darkening coefficients derived from the V1298 Tau b visit (Barat et al. 2024) and theoretical limb darkening model for a main sequence star of a similar spectral type. The theoretical models have been derived using EXOCTK (Bourque et al. 2021) for a star with similar spectral type as V1298 Tau (K1). We used photospheric temperature of 5000K, log g=4 and solar metallic- ity (Finociety et al. 2023) PHOENIX models to simulate the theoretical linear limb darkening coefficients in the HST/WFC3 G141 bandpass. To our knowledge, this is the first time that the limb darkening of a weak-lined T-Tauri star has been measured. The measured limb darkening appears significantly different compared to that of a main sequence star of the same spectral type. This discrepancy between with main- sequence models is could be due to different interior structure and high magnetic field of this young star (see Sect. 4.2). This figure highlights the importance of fitting for the limb darkening when analyzing transit light curves around such young stars.
In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.