The mass-radius relation of intermediate-mass planets outlined by hydrodynamic escape and thermal evolution

We employ planetary evolution modeling to reproduce the MR distribution of the 198 so far detected planets with mass and radius measured to the <45% and <15% level, respectively, and less massive than 108Me. We simultaneously account for atmospheric escape, based on the results of hydrodynamic models, and thermal evolution, based on planetary structure evolution models. Since high-energy stellar radiation affects atmospheric evolution, we account for the entire range of possible stellar rotation histories. To set the planetary parameters at formation, we use analytical approximations based on formation models. Finally, we build a grid of synthetic planets with parameters reflecting those of the observed distribution. The predicted radius spread reproduces well the observed MR distribution, except for two distinct groups of outliers (~20% of the population). The first one consists of close-in Saturn-mass planets with Jupiter-like radii for which we underpredict the radius likely because it lacks additional heating similar to that responsible for inflation in hot Jupiters. The second group consists of warm sub-Neptunes, which should host massive primordial H-dominated atmospheres, but instead present high densities indicative of small gaseous envelopes. This suggests that their formation, internal structure, and evolution are different from that of atmospheric evolution through the escape of H-dominated envelopes accreted onto rocky cores. The observed characteristics of low-mass planets (<10-15Me) strongly depend on the impact of atmospheric escape, and thus on the evolution of the host star, while primordial parameters are less relevant. Instead, for more massive planets, the parameters at formation play the dominant role in shaping the final MR distribution.Comment: 14 pages + 8 pages Appendix, 8+4 Figures; Accepted for publication in A&

Planetary evolution with atmospheric photoevaporation II: Fitting the slope of the radius valley by combining boil-off and XUV-driven escape

The Kepler satellite has revealed a gap between sub-Neptunes and super-Earths that atmospheric escape models had predicted as an evaporation valley. We seek to contrast results from a simple XUV-driven energy-limited (ELIM) escape model against those from a direct hydrodynamic (HYDRO) model. Besides XUV-driven escape, the latter also includes the boil-off regime. We couple the two models to an internal structure model and follow the planets' temporal evolution over Gyr. To see the population-wide imprint of the two models, we first employ a rectangular grid in initial conditions. We then study the slope of the valley also for initial conditions derived from the Kepler planets. For the rectangular grid, we find that the power-law slope of the valley with respect to orbital period is -0.18 and -0.11 in the ELIM and HYDRO model, respectively. For the initial conditions derived from the Kepler planets, the results are similar (-0.16 and -0.10). While the slope found with the ELIM model is steeper than observed, the one of the HYDRO model is in excellent agreement with observations. The reason for the shallower slope is caused by the two regimes in which the ELIM model fails: First, puffy planets at low stellar irradiation. For them, boil-off dominates mass loss. However, boil-off is absent in the ELIM model, thus it underestimates escape relative to HYDRO. Second, massive compact planets at high XUV irradiation. For them, the ELIM approximation overestimates escape relative to the HYDRO case because of cooling by thermal conduction, neglected in the ELIM model. The two effects act together in concert to yield in the HYDRO model a shallower slope of the valley that agrees very well with observations. We conclude that an escape model that includes boil-off and a more realistic treatment of cooling mechanisms can reproduce one of the most important constraints, the valley slope.Comment: 20 pages, 11 figures, accepted to A&

The Transiting Multi-planet System HD15337: Two Nearly Equal-mass Planets Straddling the Radius Gap

We report the discovery of a super-Earth and a sub-Neptune transiting the star HD 15337 (TOI-402, TIC 120896927), a bright (V = 9) K1 dwarf observed by the Transiting Exoplanet Survey Satellite (TESS) in Sectors 3 and 4. We combine the TESS photometry with archival High Accuracy Radial velocity Planet Searcher spectra to confirm the planetary nature of the transit signals and derive the masses of the two transiting planets. With an orbital period of 4.8 days, a mass of ${7.51}_{-1.01}^{+1.09}\,{M}_{\oplus }$ and a radius of 1.64 ± 0.06 R ⊕, HD 15337 b joins the growing group of short-period super-Earths known to have a rocky terrestrial composition. The sub-Neptune HD 15337 c has an orbital period of 17.2 days, a mass of ${8.11}_{-1.69}^{+1.82}\,{{\rm{M}}}_{\oplus }$, and a radius of 2.39 ± 0.12 R ⊕, suggesting that the planet might be surrounded by a thick atmospheric envelope. The two planets have similar masses and lie on opposite sides of the radius gap, and are thus an excellent testbed for planet formation and evolution theories. Assuming that HD 15337 c hosts a hydrogen-dominated envelope, we employ a recently developed planet atmospheric evolution algorithm in a Bayesian framework to estimate the history of the high-energy (extreme ultraviolet and X-ray) emission of the host star. We find that at an age of 150 Myr, the star possessed on average between 3.7 and 127 times the high-energy luminosity of the current Sun

The Multiplanet System TOI-421: A Warm Neptune and a Super Puffy Mini-Neptune Transiting a G9 V Star in a Visual Binary

We report the discovery of a warm Neptune and a hot sub-Neptune transiting TOI-421 (BD-14 1137, TIC 94986319), a bright (V = 9.9) G9 dwarf star in a visual binary system observed by the Transiting Exoplanet Survey Satellite (TESS) space mission in Sectors 5 and 6. We performed ground-based follow-up observations—comprised of Las Cumbres Observatory Global Telescope transit photometry, NIRC2 adaptive optics imaging, and FIbre-fed Echellé Spectrograph, CORALIE, High Accuracy Radial velocity Planet Searcher, High Resolution Échelle Spectrometer, and Planet Finder Spectrograph high-precision Doppler measurements—and confirmed the planetary nature of the 16 day transiting candidate announced by the TESS team. We discovered an additional radial velocity signal with a period of five days induced by the presence of a second planet in the system, which we also found to transit its host star. We found that the inner mini-Neptune, TOI-421 b, has an orbital period of P_b = 5.19672 ± 0.00049 days, a mass of M_b = 7.17 ± 0.66 M⊕, and a radius of R_b = 2.68^(+0.19)_(-0.18) R⊕, whereas the outer warm Neptune, TOI-421 c, has a period of Pc = 16.06819 ± 0.00035 days, a mass of M_c = 16.42^(+1.06)_(-1.04) M⊕, a radius of R_c = 5.09^(+0.16)_(-0.15) R⊕ and a density of ρ_c = 0.685^(+0.080)_(-0.072) g cm⁻³. With its characteristics, the outer planet (ρ_c = 0.685^(+0.080)_(-0.072) g cm⁻³) is placed in the intriguing class of the super-puffy mini-Neptunes. TOI-421 b and TOI-421 c are found to be well-suited for atmospheric characterization. Our atmospheric simulations predict significant Lyα transit absorption, due to strong hydrogen escape in both planets, as well as the presence of detectable CH4 in the atmosphere of TOI-421 c if equilibrium chemistry is assumed

A critical assessment of the applicability of the energy-limited approximation for estimating exoplanetary mass-loss rates

Context: The energy-limited (EL) atmospheric escape approach is used to estimate mass-loss rates for a broad range of planets that host hydrogen-dominated atmospheres as well as for performing atmospheric evolution calculations. Aims: We aim to study the applicability range of the EL approximation. Methods: We revise the EL formalism and its assumptions. We also compare its results with those of hydrodynamic simulations, employing a grid covering planets with masses, radii, and equilibrium temperatures ranging between 1 $M_{\oplus}$ and 39 $M_{\oplus}$, 1 $R_{\oplus}$ and 10 $R_{\oplus}$, and 300 and 2000 K, respectively. Results: Within the grid boundaries, we find that the EL approximation gives a correct order of magnitude estimate for mass-loss rates for about 76% of the planets, but there can be departures from hydrodynamic simulations by up to three orders of magnitude in individual cases. Furthermore, we find that planets for which the mass-loss rates are correctly estimated by the EL approximation to within one order of magnitude have intermediate gravitational potentials as well as low-to-intermediate equilibrium temperatures and irradiation fluxes of extreme ultraviolet and X-ray radiation. However, for planets with low or high gravitational potentials, or high equilibrium temperatures and irradiation fluxes, the approximation fails in most cases. Conclusions: The EL approximation should not be used for planetary evolution calculations that require computing mass-loss rates for planets that cover a broad parameter space. In this case, it is very likely that the EL approximation would at times return mass-loss rates of up to several orders of magnitude above or below those predicted by hydrodynamic simulations. For planetary atmospheric evolution calculations, interpolation routines or approximations based on grids of hydrodynamic models should be used instead.Comment: 12 pages, 7 figures, Published in A&A in June 2021; Revised on 9.11.2021 to correct typo in equation