Estimate the Mass Escaping Rates of Radius-valley-spanning Planets in TOI-431 System via XUV Evaporation

TOI-431 system has 3 close-in exoplanets, which gives an ideal lab to study gas escape. In this 8 study, we measure the XUV luminosity for TOI-431 with XMM-Newton/EPIC-pn and OM data, 9 then calculate the fluxes for the planets in the system. We find that, TOI-431 b’s FXUV,b = 70285.63+12059.89 −2610.93 erg cm−2 s −1 is 75 times of TOI-431 d FXUV,d = 934.48+160.35 −34.71 erg cm−2 s −1 10 . Adopt11 ing the energy limit method and hydrodynamic code AT ES with a set of He/H ratios, we obtain the mass-loss rates of 1010.5061+0.0688 −0.0164 g/s for TOI-431 b, 109.1379+0.0688 −0.0164 and 109.84∼9.94 12 g/s for TOI-431 d. 13 We predict the 2.93 ∼ 7.91% H I Lyα and 0.19 ∼ 10.65% He I triplet absorption depths for TOI-431 14 d, thus its gas escaping is detectable in principle. For both TOI-431 b and d, we select similar planets 15 from the New Generation Planetary Population Synthesis (NGPPS) data. Then show that considering 16 the mass-loss rates, TOI-431 b should be a naked solid planet, and TOI-431 d will likely maintain its 17 gas envelope until the host star dies. According to the formation and evolution tracks, we find that 18 TOI-431 b’s potential birthplace (0.1-2 AU) should be inner than TOI-431 d (2-12 AU). Our results 19 are consistent with the interpretation of the radius valley being caused by atmospheric escape. The 20 intrinsic reason may be their birthplace, which will determine how close they can migrate to the host 21 star, then lose mass and result in the Fulton gap.