Sculpting the Valley in the Radius Distribution of Small Exoplanets as a by-product of Planet Formation: The Core-Powered Mass-Loss Mechanism. (arXiv:1811.03202v1 [astro-ph.EP])

Sculpting the Valley in the Radius Distribution of Small Exoplanets as a by-product of Planet Formation: The Core-Powered Mass-Loss Mechanism. (arXiv:1811.03202v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Gupta_A/0/1/0/all/0/1">Akash Gupta</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Schlichting_H/0/1/0/all/0/1">Hilke E. Schlichting</a>

Recent observations revealed a bimodal radius distribution of small,
short-period exoplanets with a paucity in their occurrence, a radius `valley’,
around $1.5-2.0$ $R_oplus$. In this work, we investigate the effect of a
planet’s own cooling luminosity on its thermal evolution and atmospheric
mass-loss (core-powered mass-loss) and determine its observational consequences
for the radius distribution of small, close-in exoplanets. Using simple
analytical descriptions and numerical simulations, we demonstrate that
planetary evolution based on the core-powered mass-loss mechanism alone (i.e.,
without any photoevaporation) can produce the observed valley in the radius
distribution. Our results match the valley’s location, shape and slope in
planet radius-orbital period parameter space, and the relative magnitudes of
the planet occurrence rate above and below the valley. We find that the slope
of the valley is, to first order, dictated by the atmospheric mass-loss
timescale at the Bondi radius and given by $text{d log} R_p/ text{d log} P
simeq 1/(3(1-beta)) simeq -0.11$, where $M_c propto R_c^{beta}$ is the
mass-radius relation of the core. $beta simeq 4$ yields good agreement with
observations, attesting to the significance of internal compression for
planetary cores more massive than Earth. We further find that the location of
the valley scales with the uncompressed core density as $rho_{c*}^{-4/9}$ and
that the observed planet population must have predominantly rocky cores with
typical water-ice fractions of less than $sim 20%$. Furthermore, we show that
the relative magnitude of the planet occurrence rate above and below the valley
is sensitive to the details of the planet-mass distribution but that the
location of the valley is not.

Recent observations revealed a bimodal radius distribution of small,
short-period exoplanets with a paucity in their occurrence, a radius `valley’,
around $1.5-2.0$ $R_oplus$. In this work, we investigate the effect of a
planet’s own cooling luminosity on its thermal evolution and atmospheric
mass-loss (core-powered mass-loss) and determine its observational consequences
for the radius distribution of small, close-in exoplanets. Using simple
analytical descriptions and numerical simulations, we demonstrate that
planetary evolution based on the core-powered mass-loss mechanism alone (i.e.,
without any photoevaporation) can produce the observed valley in the radius
distribution. Our results match the valley’s location, shape and slope in
planet radius-orbital period parameter space, and the relative magnitudes of
the planet occurrence rate above and below the valley. We find that the slope
of the valley is, to first order, dictated by the atmospheric mass-loss
timescale at the Bondi radius and given by $text{d log} R_p/ text{d log} P
simeq 1/(3(1-beta)) simeq -0.11$, where $M_c propto R_c^{beta}$ is the
mass-radius relation of the core. $beta simeq 4$ yields good agreement with
observations, attesting to the significance of internal compression for
planetary cores more massive than Earth. We further find that the location of
the valley scales with the uncompressed core density as $rho_{c*}^{-4/9}$ and
that the observed planet population must have predominantly rocky cores with
typical water-ice fractions of less than $sim 20%$. Furthermore, we show that
the relative magnitude of the planet occurrence rate above and below the valley
is sensitive to the details of the planet-mass distribution but that the
location of the valley is not.

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