Searching for Hot Water World Candidates with CHEOPS: Supplementary Material for TOI-238 b and TOI-1685 b (atmospheric evolution tracks)

This distribution includes the supplementary data for sections 3.1.5 and 3.2.4 of Egger et al., 2025 (accepted for publication in A&A; https://arxiv.org/pdf/2502.07887), namely, the atmospheric evolution tracks of TOI-238 b and TOI-1685 b, assuming water steam atmospheres and in dependence on the observational parameters (masses and radii of the planets and ages of the systems within 1-sigma) and model assumptions (composition and luminosity of planetary core in the internal model, stellar rotator type, and heating efficiency coefficient in the evaporation model).

 

The distribution consists of two directories containing the results for the two planets. Each directory contains 18 subfolders corresponding to the specific combination of planetary core parameters employed by the internal structure model and stellar rotation. The subfolders are named as follows

 

    hist_silicates<<A>>pc_iron<<B>>pc_<<C>>rot_<<D>>

 

where <<A>> is the fraction of the silicates in the core in percent (30, 74, or 99),

           <<B>> is the fraction of the iron in the core in percent (70, 26, or 1),

           <<C>> is 'fast'/'slow' and indicates the type of the stellar rotator (see the original paper for details), and

           <<D>> is the luminosity of the planetary core (1e19, 1e21, or 1e23; kept constant throughout the evolution).

  

Each subfolder contains the set of "dat" (ASCII) files containing the evolutionary tracks and summary figures analogous to the individual panels of Fig. 8 of Egger et al., 2025 (note, that differently to Fig.8, these figures have individual colorbars reflecting the range of atmospheric mass fractions achieved for the specific combination of parameters). Each figure is duplicated in "eps" and "png" format and is named as follows

 

    hist_eta<<E>>_age<<F>>Myr_<<G>>_img.eps

 

where <<E>> is the value of the heating efficiency coefficient in percent (1, 5, 10, or 15)

           <<F>> is the adopted age of the system in [Myr]

                       (within 1-sigma estimate for the system, see Egger et al., 2025 for the references)

           <<G>> is the parameter plotted in the figure:

                        'FAT0' -- initial atmospheric mass fraction (as in Fig. 8),

                        'MPL0' -- initial mass of the planet, or

                        'AGE0' -- the age when (if) the atmospheric mass fraction reaches 50% 

  

The files containing the evolutionary tracks are named as follows

  

hist_fat_<<H>>_eta_<<I>>_alb_<<J>>_mpl_<<K>>_age_<<L>>Gyr.dat

 

where <<H>> is the present-day atmospheric mass fraction corresponding to the specific mass and radius

           <<I>> is the value of the heating efficiency coefficient (as a fraction: 0.01, 0.05, 0.1, 0.15)

           <<J>> is the albedo (always taken at 0.0)

           <<K>> is the adopted value of the present-day mass (within 1-sigma), in [Mearth]

           <<L>> is the adopted value of the present-day age in [Gyr]

  

Columns in the evolution tracks files are

    age            (.6e)    [year]       current age of the system (NOTE: the first row is present-day and it goes back in time to 10 Myr), 

    mpl            (.4f)    [Mearth]   mass of the planet, 

    rpl              (.4f)    [Rearth]    radius of the planet, 

    fat              (.4f)    []              current atmospheric mass fraction, 

    teq             (.4f)    [K]            equilibrium temperature (derived from stellar Lbol according to the stellar model), 

    mdot_euv  (.4e)    [g/s]         energy-limited escape rate corresponding to the extreme ultraviolet, 

    mdot_x      (.4e)    [g/s]         energy-limited escape rate corresponding to the X-ray, 

    mdot_cp    (.4e)    [g/s]         core-powered mass loss rate, 

    mdot         (.4e)    [g/s]         total atmospheric mass loss rate, 

    roc             (.4f)    [Rplanet]  Roche lobe of the planets (Rroche/Rpl)

 

For any questions/queries concerning this data set please contact Daria Kubyshkina:

    daria.kubyshkina@oeaw.ac.at

    kubyshkina.darya@gmail.com