Oort Cloud Formation and Evolution in Star Clusters

Abstract It is unknown whether an Oort cloud reaches its maximum mass within its star’s birth cluster or millions of years later. Complicating the Oort cloud evolution process is the fact that comets can be stripped from orbit due to perturbations from passing stars. We explore how a star’s cluster escape time ( t esc ) and the time its Oort cloud reaches maximum mass ( t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) affect the Oort cloud’s ability to survive via N -body simulations. In a 14 M ⊙ pc –3 cluster, we identify 50 stars of 1 M ⊙ with a range of t esc to host Oort clouds, each with 1000 comets at t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msub> </mml:math> . For each host, we consider Oort clouds that reach maximum mass 0, 50, and 250 Myr after the cluster’s formation. Each Oort cloud’s evolution is simulated in the cluster from t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msub> </mml:math> to t esc . Only a fraction of comets tend to remain in orbit, with this amount depending on t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msub> </mml:math> and t esc . We observe that 12%, 22%, and 32% of Oort clouds with a t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msub> </mml:math> of 0, 50, and 250 Myr retain &gt;50% of their comets at t esc , respectively. We find that the fraction of comets stripped has the relationship <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">log</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msub> <mml:mrow> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:mfrac> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">esc</mml:mi> </mml:mrow> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo form="prefix" movablelimits="true">max</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Myr</mml:mi> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> , where m = 0.32 ± 0.04, indicating that the longer the Oort cloud remains in the cluster, the more comets are stripped, with this fraction increasing logarithmically at approximately the same rate for each t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msub> </mml:math> .