Stellar Hydrostatic Equilibrium with Differential Rotation - sci.math

Message from discussion Stellar Hydrostatic Equilibrium with Differential Rotation

Steve Willner

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More options Jul 8, 2:58 am

Newsgroups: sci.astro, sci.physics, sci.math

From: will...@cfa.harvard.edu (Steve Willner)

Date: Mon, 7 Jul 2008 21:58:53 +0000 (UTC)

Local: Tues, Jul 8 2008 2:58 am

Subject: Re: Stellar Hydrostatic Equilibrium with Differential Rotation

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In article <Xns9AD2B538FAB62alsfaskldfjakls...@207.115.33.102>,
John Schutkeker <jschutke...@sbcglobal.net.nospam> writes:

> I added the centripetal force, rho*w^2*r, as a second body force term in
> equation (11) on that site, making that equation into

> dP/dr=rho(r)*w^2*r*sin(theta)-G*m(r)*rho(r)/r^2,
> where w is omega, the rotational frequency of the star, which is allowed to
> vary with the latitude on the star, as w=w(theta).

What you want to do is add the centrifugal force on the right side.
It looks to me, without checking a text, like you have it right if
you change sin(theta) to cos(theta). (Centrifugal force is zero at
the poles.)

I've seen this sort of thing in text books. Centrifugal force is
only important for rapidly-rotating stars. I vaguely remember having
seen comments to the effect that one really needs 3d, not just 2d,
models for those, but I don't know whether that's true or not. There
are certainly stellar models for rapid rotators in the literature.
While I suspect there is work yet to be done on the subject, it is
not as if no one has thought about it before. You should try an ADS
search if you haven't already.

> If I were to put in the compressible equation of state for a fluid,

As someone else mentioned, the ideal gas law is fine for all but the
most extreme stars. (The high temperature overcomes the high
density until degeneracy sets in.)

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Steve Willner Phone 617-495-7123 swill...@cfa.harvard.edu
Cambridge, MA 02138 USA
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