The Role of Convection in Determining the Ejection Efficiency of Common Envelope Interactions. (arXiv:1811.03161v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Wilson_E/0/1/0/all/0/1">E. C. Wilson</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Nordhaus_J/0/1/0/all/0/1">J. Nordhaus</a>
A widely used method for parameterizing the outcomes of common envelopes
(CEs) involves defining an ejection efficiency, $baralpha_{rm eff}$, that
represents the fraction of orbital energy used to unbind the envelope as the
orbit decays. Given $baralpha_{rm eff}$, a prediction for the post-CE
orbital separation is then possible with knowledge of the energy required to
unbind the primary’s envelope from its core. Unfortunately, placing
observational constraints on $baralpha_{rm eff}$ is challenging as it
requires knowledge of the primary’s structure at the onset of the common
envelope phase. Numerical simulations have also had difficulties reproducing
post-CE orbital configurations as they leave extended, but still bound,
envelopes. Using detailed stellar interior profiles, we calculate
$baralpha_{rm eff}$ values for a matrix of primary-companion mass pairs when
the primary is likely to incur a CE, i.e., at maximal extent in its evolution.
We find that the ejection efficiency is most sensitive to the properties of the
surface-contact convective region (SCCR). In this region, the convective
turnover times are short compared to orbital decay timescales, thereby allowing
the star to effectively radiate orbital energy and thus lower $baralpha_{rm
eff}$. The inclusion of convection in numerical simulations of CEs may resolve
the ejection problem without the need for additional energy sources as the
orbit must shrink substantially further before the requisite energy can be
tapped to drive ejection. Additionally, convection leads to predicted post-CE
orbital periods of less than a day, an observational result that has been
difficult to reproduce in population studies where $baralpha_{rm eff}$ is
taken to be constant. Finally, we provide a simple method to calculate
$baralpha_{rm eff}$ if the properties of the SCCR are known.
A widely used method for parameterizing the outcomes of common envelopes
(CEs) involves defining an ejection efficiency, $baralpha_{rm eff}$, that
represents the fraction of orbital energy used to unbind the envelope as the
orbit decays. Given $baralpha_{rm eff}$, a prediction for the post-CE
orbital separation is then possible with knowledge of the energy required to
unbind the primary’s envelope from its core. Unfortunately, placing
observational constraints on $baralpha_{rm eff}$ is challenging as it
requires knowledge of the primary’s structure at the onset of the common
envelope phase. Numerical simulations have also had difficulties reproducing
post-CE orbital configurations as they leave extended, but still bound,
envelopes. Using detailed stellar interior profiles, we calculate
$baralpha_{rm eff}$ values for a matrix of primary-companion mass pairs when
the primary is likely to incur a CE, i.e., at maximal extent in its evolution.
We find that the ejection efficiency is most sensitive to the properties of the
surface-contact convective region (SCCR). In this region, the convective
turnover times are short compared to orbital decay timescales, thereby allowing
the star to effectively radiate orbital energy and thus lower $baralpha_{rm
eff}$. The inclusion of convection in numerical simulations of CEs may resolve
the ejection problem without the need for additional energy sources as the
orbit must shrink substantially further before the requisite energy can be
tapped to drive ejection. Additionally, convection leads to predicted post-CE
orbital periods of less than a day, an observational result that has been
difficult to reproduce in population studies where $baralpha_{rm eff}$ is
taken to be constant. Finally, we provide a simple method to calculate
$baralpha_{rm eff}$ if the properties of the SCCR are known.
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