Difference between revisions of "User:Tohline/Appendix/Ramblings/Photosphere"
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==Locating the Photosphere of Stably Accreting White | ==Locating the Photosphere of Stably Accreting Double White Dwarf Binaries== | ||
===Context=== | |||
At our regularly scheduled astrophysics group meeting on Monday, 2 May 2011, Juhan Frank and I started debating the answer to the following question: What should the photospheric radius be of the common envelope that surrounds a stably accreting, double white dwarf (DWD) binary? That is, does an accreting DWD binary that is destined to be an AM CVn system look like a single bloated star? The various mathematical relations that we think are relevant to this question were sketched on the whiteboard in room 218 Johnston Hall (CCT). Here is a photo of that whiteboard discussion and derivation. | |||
[[Image:May2011WhiteBoard.JPG|400px|center]]<br /> | |||
===More Careful Derivation=== | |||
As the accretion stream from the less massive white dwarf impacts the surface of the accretor supersonically, it will heat the accreted material to a temperature, | |||
<div align="center"> | |||
<math>T_{sh} \sim \frac{GM_a m_p}{kR_a}</math> , | |||
</div> | |||
where <math>M_a</math> and <math>R_a</math> are the mass and radius, respectively, of the accretor. | |||
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Revision as of 14:04, 6 May 2011
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Locating the Photosphere of Stably Accreting Double White Dwarf Binaries
Context
At our regularly scheduled astrophysics group meeting on Monday, 2 May 2011, Juhan Frank and I started debating the answer to the following question: What should the photospheric radius be of the common envelope that surrounds a stably accreting, double white dwarf (DWD) binary? That is, does an accreting DWD binary that is destined to be an AM CVn system look like a single bloated star? The various mathematical relations that we think are relevant to this question were sketched on the whiteboard in room 218 Johnston Hall (CCT). Here is a photo of that whiteboard discussion and derivation.
More Careful Derivation
As the accretion stream from the less massive white dwarf impacts the surface of the accretor supersonically, it will heat the accreted material to a temperature,
<math>T_{sh} \sim \frac{GM_a m_p}{kR_a}</math> ,
where <math>M_a</math> and <math>R_a</math> are the mass and radius, respectively, of the accretor.
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