Subject: Re: Looking for analytical solutions of solar wind equations

Date: 31 Jul 1997 00:54:18 GMT

From: fcrary@rintintin.Colorado.EDU (Frank Crary)

Organization: University of Colorado, Boulder

To: gherbert

Newsgroups: sci.space.science, sci.physics.research, sci.physics.plasma, sci.physics

References: In article <Pine.OSF.3.95.970730092649.19226A-100000@osf1.mpae.gwdg.de>,
Uwe Lauth <lauth@osf1.mpae.gwdg.de> wrote:
>Has anyone already done an analytical solution of the solar wind
>equations? I know the numerical solutions from Pizzo and Gosling
>[Geophys. Res. L. 21 (1994) 2063-2066].
>But what I need are formulas.

I'd suggest Kivelson and Russell's _Introduction_of_Space_Physics_
(I might have the title wrong, but that's close.) It's got the
equations, and the Parker wind solution, and references to other
solar wind solutions. There are a fair number of solutions, but
they are all approximate. The Parker wind, the earliest and least
complicated, assumes a non-rotating and un-magnetized Sun, and
an isothermal solar wind. That gives an analytic solution. Similar
solutions also exist for an adiabatic solar wind temperature, and
for solar winds with an assumed, approximate heating term. Well,
almost... They yield an equation that can be solved numerically,
and once solved, can be used to give analytic forms for the
solar wind's density, temperature, etc. as a function of distance.
(I.e. you numerically solve for temperature and density at the
sonic point, and once that is known, everything else is analytic.)
There are also solutions for a rotating and magnetized Sun, but they
are only valid in the Sun's equatorial plane. A general solution
for a rotating and/or magnetized Sun (i.e. one valid for all latitudes)
does not exist. (In fact, I once spent some time trying to find one,
and got far enough to convince myself that no analytic solution
exists.) In addition, the analytic solutions all assume azimuthal
symmetry and very simplified solar magnetic fields (which, at best,
is highly unrealistic...) The lack of analytic solutions to a
realistic case is one of the main reasons people do numerical
simulations.

Frank Crary
CU Boulder