Estimating the Mass Escaping Rates of Radius-valley-spanning Planets in the TOI-431 System via X-Ray and Ultraviolet Evaporation

Abstract The TOI-431 system has three close-in exoplanets, which gives an ideal lab to study gas escape. In this study, we measure the X-ray and ultraviolet luminosity for TOI-431 with XMM-Newton’s European Photon Imaging Camera-pn and Optical/UV Monitor Telescope data, then calculate the fluxes for the planets in the system. We find TOI-431 b’s <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>XUV</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">b</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>70</mml:mn> <mml:mo>,</mml:mo> <mml:msubsup> <mml:mn>286</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2611</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>12</mml:mn> <mml:mo>,</mml:mo> <mml:mn>060</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:mi>erg</mml:mi> <mml:mspace width="0.25em"/> <mml:msup> <mml:mi>cm</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mi mathvariant="normal">s</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> is 75 times TOI-431 d’s <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>F</mml:mi> <mml:mrow> <mml:mi>XUV</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mn>935</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>35</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>160</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:mi>erg</mml:mi> <mml:mspace width="0.25em"/> <mml:msup> <mml:mi>cm</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mi mathvariant="normal">s</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> . Adopting the energy limit method and hydrodynamic code ATES with a set of He/H ratios, we obtain mass-loss rates of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>10</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>51</mml:mn> <mml:mi>-0.02</mml:mi> <mml:mi>+0.07</mml:mi> </mml:msubsup> </mml:mrow> </mml:msup> </mml:math> g s −1 for TOI-431 b and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>9</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>14</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:mn>02</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:mn>07</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:msup> </mml:math> and 10 9.84 ∼9.94 g s −1 for TOI-431 d. We predict 2.93% ∼ 7.91% H i Ly α and 0.19% ∼ 10.65% He i triplet absorption depths for TOI-431 d; thus, its gas escaping is detectable in principle. For both TOI-431 b and d, we select similar planets from the New Generation Planetary Population Synthesis data. They show that, considering the mass-loss rates, TOI-431 b should be a naked solid planet, and TOI-431 d will likely maintain its gas envelope until the host star dies. According to the formation and evolution tracks, we find that TOI-431 b’s potential birthplace (0.1–2 au) should be further in than TOI-431 d’s (2–12 au). Our results are consistent with the interpretation of the radius valley being caused by atmospheric escape. The intrinsic reason may be their birthplace, which will determine how close they can migrate to the host star, then lose mass and result in the Fulton gap.