The Demographics of Kepler's Earths and Super-Earths into the Habitable Zone

Abstract

Abstract Understanding the occurrence of Earth-sized planets in the habitable zone of Sun-like stars is essential to the search for Earth analogs. Yet a lack of reliable Kepler detections for such planets has forced many estimates to be derived from the close-in (2 &lt; P orb &lt; 100 days) population, whose radii may have evolved differently under the effect of atmospheric mass-loss mechanisms. In this work, we compute the intrinsic occurrence rates of close-in super-Earths (∼1–2 R ⊕ ) and sub-Neptunes (∼2–3.5 R ⊕ ) for FGK stars (0.56–1.63 M ⊙ ) as a function of orbital period and find evidence of two regimes: where super-Earths are more abundant at short orbital periods, and where sub-Neptunes are more abundant at longer orbital periods. We fit a parametric model in five equally populated stellar mass bins and find that the orbital period of transition between these two regimes scales with stellar mass, like <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>trans</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . These results suggest a population of former sub-Neptunes contaminating the population of gigayear-old close-in super-Earths, indicative of a population shaped by atmospheric loss. Using our model to constrain the long-period population of intrinsically rocky planets, we estimate an occurrence rate of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">Γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊕</mml:mo> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>15</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>%</mml:mo> </mml:math> for Earth-sized habitable zone planets, and predict that sub-Neptunes may be ∼ twice as common as super-Earths in the habitable zone (when normalized over the natural log-orbital period and radius range used). Finally, we discuss our results in the context of future missions searching for habitable zone planets.