Close-in Sub-Neptunes Reveal the Past Rotation History of Their Host Stars: Atmospheric Evolution of Planets in the HD 3167 and K2-32 Planetary Systems

Planet atmospheric escape induced by high-energy stellar irradiation is a key phenomenon shaping the structure and evolution of planetary atmospheres. Therefore, the present-day properties of a planetary atmosphere are intimately connected with the amount of stellar flux received by a planet during its lifetime, thus with the evolutionary path of its host star. Using a recently developed analytic approximation based on hydrodynamic simulations for atmospheric escape rates, we track within a Bayesian framework the evolution of a planet as a function of stellar flux evolution history, constrained by the measured planetary radius. We find that the ideal objects for this type of study are close-in sub-Neptune-like planets, as they are highly affected by atmospheric escape, and yet retain a significant fraction of their primordial hydrogen-dominated atmospheres. Furthermore, we apply this analysis to the HD 3167 and K2-32 planetary systems. For HD 3167, we find that the most probable irradiation level at 150 Myr was between 40 and 130 times solar, corresponding to a rotation period of days. For K2-32, we find a surprisingly low irradiation level ranging between half and four times solar at 150 Myr. Finally, we show that for multi-planet systems, our framework enables one to constrain poorly known properties of individual planets.

[1]  H. Lammer,et al.  Overcoming the Limitations of the Energy-limited Approximation for Planet Atmospheric Escape , 2018, The Astrophysical Journal.

[2]  H. Lammer,et al.  Grid of upper atmosphere models for 1–40 M⊕ planets: application to CoRoT-7 b and HD 219134 b,c , 2018, Astronomy & Astrophysics.

[3]  D. Lai,et al.  Photoevaporation and high-eccentricity migration created the sub-Jovian desert , 2018, Monthly Notices of the Royal Astronomical Society.

[4]  D. Huber,et al.  Revised Radii of Kepler Stars and Planets Using Gaia Data Release 2 , 2018, The Astrophysical Journal.

[5]  Clea F. Schumer,et al.  275 Candidates and 149 Validated Planets Orbiting Bright Stars in K2 Campaigns 0–10 , 2018, 1802.05277.

[6]  D. Stevenson,et al.  On the Role of Dissolved Gases in the Atmosphere Retention of Low-mass Low-density Planets , 2018, 1802.04296.

[7]  F. Timmes,et al.  Modules for Experiments in Stellar Astrophysics ( ): Convective Boundaries, Element Diffusion, and Massive Star Explosions , 2017, 1710.08424.

[8]  Marshall C. Johnson,et al.  The Transiting Multi-planet System HD 3167: A 5.7 M⊕ Super-Earth and an 8.3 M⊕ Mini-Neptune , 2017, 1706.02532.

[9]  R. P. Butler,et al.  Three’s Company: An Additional Non-transiting Super-Earth in the Bright HD 3167 System, and Masses for All Three Planets , 2017, 1706.01892.

[10]  Christoph Mordasini,et al.  Compositional Imprints in Density–Distance–Time: A Rocky Composition for Close-in Low-mass Exoplanets from the Location of the Valley of Evaporation , 2017, 1706.00251.

[11]  James E. Owen,et al.  The Evaporation Valley in the Kepler Planets , 2017, 1705.10810.

[12]  Erik A. Petigura,et al.  Four Sub-Saturns with Dissimilar Densities: Windows into Planetary Cores and Envelopes , 2017, 1702.00013.

[13]  H. Lammer,et al.  Aeronomical constraints to the minimum mass and maximum radius of hot low-mass planets , 2016, 1612.05624.

[14]  S. Hadden,et al.  Kepler Planet Masses and Eccentricities from TTV Analysis , 2016, 1611.03516.

[15]  Nate B. Lust,et al.  ON CORRELATED-NOISE ANALYSES APPLIED TO EXOPLANET LIGHT CURVES , 2016, 1610.01336.

[16]  Michael C. Liu,et al.  197 CANDIDATES AND 104 VALIDATED PLANETS IN K2's FIRST FIVE FIELDS , 2016, 1607.05263.

[17]  Christoph Baranec,et al.  TWO SMALL PLANETS TRANSITING HD 3167 , 2016, 1607.05248.

[18]  M. R. Haas,et al.  FALSE POSITIVE PROBABILITIES FOR ALL KEPLER OBJECTS OF INTEREST: 1284 NEWLY VALIDATED PLANETS AND 428 LIKELY FALSE POSITIVES , 2016, 1605.02825.

[19]  Fei Dai,et al.  DOPPLER MONITORING OF FIVE K2 TRANSITING PLANETARY SYSTEMS , 2016, 1604.01413.

[20]  Howard Isaacson,et al.  TWO TRANSITING LOW DENSITY SUB-SATURNS FROM K2 , 2015, 1511.04497.

[21]  H. Lammer,et al.  THE EVOLUTION OF STELLAR ROTATION AND THE HYDROGEN ATMOSPHERES OF HABITABLE-ZONE TERRESTRIAL PLANETS , 2015, 1511.03647.

[22]  Xavier Bonfils,et al.  A giant comet-like cloud of hydrogen escaping the warm Neptune-mass exoplanet GJ 436b , 2015, Nature.

[23]  H. Rauer,et al.  A DEFINITION FOR GIANT PLANETS BASED ON THE MASS–DENSITY RELATIONSHIP , 2015, 1506.05097.

[24]  H. Lammer,et al.  The Extreme Ultraviolet and X-Ray Sun in Time: High-Energy Evolutionary Tracks of a Solar-Like Star , 2015, 1504.04546.

[25]  E. Dorfi,et al.  Hydrodynamic simulations of captured protoatmospheres around Earth-like planets , 2015, 1505.06859.

[26]  M. Gudel,et al.  Stellar winds on the main-sequence - II. The evolution of rotation and winds , 2015, 1503.07494.

[27]  S. Ida,et al.  Water contents of Earth-mass planets around M dwarfs , 2015 .

[28]  Christoph Mordasini,et al.  PLANETARY POPULATION SYNTHESIS COUPLED WITH ATMOSPHERIC ESCAPE: A STATISTICAL VIEW OF EVAPORATION , 2014, 1409.2879.

[29]  J. Fortney,et al.  UNDERSTANDING THE MASS–RADIUS RELATION FOR SUB-NEPTUNES: RADIUS AS A PROXY FOR COMPOSITION , 2013, 1311.0329.

[30]  T. Hirano,et al.  CHARACTERIZATION OF THE KOI-94 SYSTEM WITH TRANSIT TIMING VARIATION ANALYSIS: IMPLICATION FOR THE PLANET–PLANET ECLIPSE , 2013, 1310.5771.

[31]  P. Giommi,et al.  The PLATO 2.0 mission , 2013, 1310.0696.

[32]  J. Fortney,et al.  THE ROLE OF CORE MASS IN CONTROLLING EVAPORATION: THE KEPLER RADIUS DISTRIBUTION AND THE KEPLER-36 DENSITY DICHOTOMY , 2013, 1305.0269.

[33]  Howard Isaacson,et al.  THE MASS OF KOI-94d AND A RELATION FOR PLANET RADIUS, MASS, AND INCIDENT FLUX , 2013, 1303.2150.

[34]  P. J. Wheatley,et al.  Temporal variations in the evaporating atmosphere of the exoplanet HD 189733b , 2012, 1206.6274.

[35]  Nicholas J. Wright,et al.  THE STELLAR-ACTIVITY–ROTATION RELATIONSHIP AND THE EVOLUTION OF STELLAR DYNAMOS , 2011, 1109.4634.

[36]  I. Ribas,et al.  Estimation of the XUV radiation onto close planets and their evaporation , 2011, 1105.0550.

[37]  R. G. West,et al.  METALS IN THE EXOSPHERE OF THE HIGHLY IRRADIATED PLANET WASP-12b , 2010, 1005.3656.

[38]  L. Hillenbrand,et al.  Improved Age Estimation for Solar-Type Dwarfs Using Activity-Rotation Diagnostics , 2008, 0807.1686.

[39]  M. Mayor,et al.  An extended upper atmosphere around the extrasolar planet HD209458b , 2003, Nature.

[40]  Leon Golub,et al.  Relations among stellar X-ray emission observed from Einstein, stellar rotation and bolometric luminosity , 1981 .

[41]  N. Pizzolato,et al.  The stellar activity-rotation relationship revisited: Dependence of saturated and non-saturated X-ray emission regimes on stellar mass for late-type dwarfs ? , 2003 .

[42]  J. Jeans,et al.  The dynamical theory of gases , 1925 .

[43]  G. B..  The Dynamical Theory of Gases , 1916, Nature.