Occurrence Rates of Accreting Companions from a New Method for Computing Emission-line Survey Sensitivity: Application to the H<i>α</i> Giant Accreting Protoplanet Survey

Abstract A key scientific goal of exoplanet surveys is to characterize the underlying population of planets in the local galaxy. In particular, the properties of accreting proto planets can inform the rates and physical processes of planet formation. We develop a novel method to compute sensitivity to protoplanets in emission-line direct-imaging surveys, enabling estimates of protoplanet population properties under various planetary accretion and formation theories. In this work, we specialize to the case of H α and investigate three formation models governing the planetary-mass-to-mass-accretion-rate power law and two accretion models that describe the scaling between the total accretion luminosity and observable H α line luminosity. We apply our method to the results of the Magellan Giant Accreting Protoplanet Survey, to place the first constraints on accreting companion occurrence rates in systems with transitional circumstellar disks. We compute the posterior probability for transitional disk systems to host an accreting companion ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>−</mml:mo> <mml:mn>7</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>log</mml:mi> <mml:mi>M</mml:mi> <mml:mover accent="true"> <mml:mi>M</mml:mi> <mml:mo>̇</mml:mo> </mml:mover> <mml:mo>/</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi mathvariant="normal">J</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mi>yr</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≤</mml:mo> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:math> ) within 2″ (∼200 au). Using our two accretion models, we find consistent protoplanet rates, with median and 68% credible intervals of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.1</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.19</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.2</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.14</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.26</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> accreting companions per star, respectively. Our technique enables studying protoplanet populations under flexible assumptions about planet formation. This formalism provides the statistical underpinning necessary for protoplanet surveys to discriminate among formation and accretion theories for planets and brown dwarfs.