Super-Earth Atmospheres: Self-Consistent Gas Accretion and Retention

Some recently discovered short-period Earth to Neptune sized exoplanets (super Earths) have low observed mean densities which can only be explained by voluminous gaseous atmospheres. Here, we study the conditions allowing the accretion and retention of such atmospheres. We self-consistently couple the nebular gas accretion onto rocky cores and the subsequent evolution of gas envelopes following the dispersal of the protoplanetary disk. Specifically, we address mass-loss due to both photo-evaporation and cooling of the planet. We find that planets shed their outer layers (dozens of percents in mass) following the disk's dispersal (even without photo-evaporation), and their atmospheres shrink in a few Myr to a thickness comparable to the radius of the underlying rocky core. At this stage, atmospheres containing less particles than the core (equivalently, lighter than a few % of the planet's mass) can be blown away by heat coming from the cooling core, while heavier atmospheres cool and contract on a timescale of Gyr at most. By relating the mass-loss timescale to the accretion time, we analytically identify a Goldilocks region in the mass-temperature plane in which low-density super Earths can be found: planets have to be massive and cold enough to accrete and retain their atmospheres, while not too massive or cold, such that they do not enter runaway accretion and become gas giants (Jupiters). We compare our results to the observed super-Earth population and find that low-density planets are indeed concentrated in the theoretically allowed region. Our analytical and intuitive model can be used to investigate possible super-Earth formation scenarios.Comment: Updated (refereed) versio

Magnetic field breakout from white dwarf crystallization dynamos

A convective dynamo operating during the crystallization of white dwarfs is one of the promising channels to produce their observed strong magnetic fields. Although the magnitude of the fields generated by crystallization dynamos is uncertain, their timing may serve as an orthogonal test of this channel's contribution. The carbon-oxygen cores of $M\approx 0.5-1.0\,{\rm M}_\odot$ white dwarfs begin to crystallize at an age $t_{\rm cryst}\propto M^{-5/3}$, but the magnetic field is initially trapped in the convection zone - deep inside the CO core. Only once a mass of $m_{\rm cryst}$ has crystallized, the convection zone approaches the white dwarf's helium layer, such that the magnetic diffusion time through the envelope shortens sufficiently for the field to break out to the surface, where it can be observed. This breakout time is longer than $t_{\rm cryst}$ by a few Gyr, scaling as $t_{\rm break}\propto t_{\rm cryst}f^{-1/2}$, where $f\equiv 1-m_{\rm cryst}/M$ depends on the white dwarf's initial C/O profile before crystallization. The first appearance of strong magnetic fields $B\gtrsim 1\textrm{ MG}$ in volume-limited samples approximately coincides with our numerically computed $t_{\rm break}(M)$ - potentially signalling crystallization dynamos as a dominant magnetization channel. However, some observed magnetic white dwarfs are slightly younger, challenging this scenario. The dependence of the breakout process on the white dwarf's C/O profile implies that magnetism may probe the CO phase diagram, as well as uncertainties during the core helium burning phase in the white dwarf's progenitor, such as the $^{12}{\rm C}(\alpha,\gamma)^{16}{\rm O}$ nuclear reaction.Comment: Matches published versio