The Evolution of Stellar Rotation and the Hydrogen Atmospheres of Habitable-Zone Terrestrial Planets

Abstract

Terrestrial planets formed within gaseous protoplanetary disks can accumulate significant hydrogen envelopes. The evolution of such an atmosphere due to XUV driven evaporation depends on the activity evolution of the host star, which itself depends sensitively on its rotational evolution, and therefore on its initial rotation rate. In this Letter, we derive an easily applicable method for calculating planetary atmosphere evaporation that combines models for a hydrostatic lower atmosphere and a hydrodynamic upper atmosphere. We show that the initial rotation rate of the central star is of critical importance for the evolution of planetary atmospheres and can determine if a planet keeps or loses its primordial hydrogen envelope. Our results highlight the need for a detailed treatment of stellar activity evolution when studying the evolution of planetary atmospheres.

Rocky Worlds Limited to ∼1.8 Earth Radii by Atmospheric Escape during a Star’s Extreme UV Saturation

“…During hydrodynamic escape, a high altitude portion of an atmosphere is heated by XUV flux and flows hydrodynamically outward (Johnstone et al 2015;Mordasini et al 2012). …”

“…For young, Sun-like stars, this XUV flux can be orders of magnitude larger than the modern Sun (Johnstone et al 2015;Lammer et al 2014). A saturated XUV flux can last for ~100 Myr Lammer et al 2012;Ribas et al 2005).…”

DYNAMICAL ACCRETION OF PRIMORDIAL ATMOSPHERES AROUND PLANETS WITH MASSES BETWEEN 0.1 AND 5 M⊕ IN THE HABITABLE ZONE

“…More massive cores are able to keep a significant fraction of their nebula-accreted atmosphere, and the final amount of atmosphere depends on the efficiency of atmospheric escape processes. Hydrodynamic atmospheric escape caused by the high soft X-ray and extreme ultraviolet (XUV) radiation of the young host star can remove on the order of about 10 25 g of atmosphere gas (Erkaev et al 2013;Lammer et al 2014;Johnstone et al 2015) in the habitable zone of a solar-like star.…”

“…The values were calculated by Johnstone et al (2015), who combined a static lower atmosphere model with a hydrodynamic upper atmosphere model to derive scaling laws for the mass loss rate as a function of planetary mass, atmospheric mass, and input stellar XUV flux. Using the stellar XUV evolutionary tracks derived by Tu et al (2015), they calculated the amount of atmosphere lost by hydrogen atmospheres with a range of planetary masses and initial atmospheric masses.…”

“…More planet mass-radius measurements by satellites like CHEOPS (Broeg et al 2013) will produce more accurate data that can be used to constrain the transition between rocky planets and planets with extended gaseous envelopes. As demonstrated in Figure 6 and Table 2, cores of about Earth mass can easily capture a large amount of primordial envelope from the nebula that is unlikely to be lost by thermal escape after the dissipation of the disk (Lammer et al 2014;Johnstone et al 2015).…”