Outcomes of Sub-Neptune Collisions

Abstract Observed high multiplicity planetary systems are often tightly packed. Numerical studies indicate that such systems are susceptible to dynamical instabilities. Dynamical instabilities in close-in tightly packed systems, similar to those found in abundance by Kepler, often lead to planet–planet collisions. For sub-Neptunes, the dominant type of observed exoplanets, the planetary mass is concentrated in a rocky core, but the volume is dominated by a low-density gaseous envelope. For these, using the traditional perfect merger assumption (also known as the “sticky-sphere” approximation) to resolve collisions is questionable. Using both N -body integration and smoothed-particle hydrodynamics, we have simulated sub-Neptune collisions for a wide range in realistic kinematic properties such as impact parameters ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>b</mml:mi> <mml:mo accent="false">′</mml:mo> </mml:math> ) and impact velocities ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>im</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) to study the possible outcomes in detail. We find that the majority of the collisions with kinematic properties similar to what is expected from dynamical instabilities in multiplanet systems may not lead to mergers of sub-Neptunes. Instead, both sub-Neptunes survive the encounter, often with significant atmosphere loss. When mergers do occur, they can involve significant mass loss and can sometimes lead to complete disruption of one or both planets. Sub-Neptunes merge or disrupt if <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>b</mml:mi> <mml:mo accent="false">′</mml:mo> <mml:mo>&lt;</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> , a critical value dependent on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>im</mml:mi> </mml:mrow> </mml:msub> </mml:math> / v esc , where v esc is the escape velocity from the surface of the hypothetical merged planet assuming perfect merger. For <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>im</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>esc</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≲</mml:mo> <mml:mn>2.5</mml:mn> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>im</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>esc</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> , and collisions with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>b</mml:mi> <mml:mo accent="false">′</mml:mo> <mml:mo>&lt;</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> typically leads to mergers. On the other hand, for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>im</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>esc</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≳</mml:mo> <mml:mn>2.5</mml:mn> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo>