23rd Jul, 2018

Tezpur University

Question

Asked 22nd Jul, 2018

Spherical waves are ubiquitous in astrophysical environments. Can someone provide some useful references on spherical wave analysis in spherical gravito-magnetized fluids?

Thanks. I am interested in the stability of spherical plasma systems, such as spherical molecular clouds, stars, etc. May I get more helps?

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What kind of system are you examining? Have you looked into how the magnetic field is treated in the solar corona and the solar p-modes? We investigated magnetic fields in white dwarf stars https://ui.adsabs.harvard.edu/#abs/1989ApJ...336..403J/abstract and much literature is devoted to the interaction of nonracial oscillations and magnetic fields in stars.

Thanks, anyway. I am rather interested in spherical wave analyses with and without approximations. The physical model may spherical stars, dust molecular clouds, etc.

The only approximation we make is linear wave theory. The system is very important. Waves inside stars tend to adiabatic because the material is optically thick. Waves in optically thin matter, such as the solar corona, have different characteristics. Waves in interstellar dust clouds aren't spherical when the cloud isn't self-gravitating. Although spherically symmetric waves were the first variable stars to be observed (radial oscillators such as Cepheids, RR Lyrae stars, and Mira stars), nonradial oscillations are far more common throughout the H-R diagram. Nonlinear calculations of Cepheids and RR Lyrae stars are easy to find in the literature (Christy and Cox are among the authors.)

J. P. Cox, Theory of Stellar Oscillations, is a good place to start. It's a little old but thorough in theory and observations. Additional references are difficult to provide without knowing your application. Cox is good for stars, but other systems have different approaches.

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Question

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- Asked 19th Dec, 2013

- James Dwyer

Newtonian analytical studies of spiral galaxy rotation have most often considered the gravitational force imparted to a test body (whose rotational velocity is measured) to be determined by the summation of all mass contained within its orbit, diminished by the inverse-square of its radial distance.

This extends, to planar disk mass distributions, shell theorem's justification for treating discrete spherical masses as though their mass was concentrated at a central point - thereby allowing the application of the inverse-square, two body point-mass law of universal gravitation. Obviously however, a spiral galaxy is not a spherically symmetrical distribution of mass.

"If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies. In the limit, as the component point masses become "infinitely small", this entails integrating the force (in vector form, see below) over the extents of the two bodies.

"In this way it can be shown that an object with a spherically-symmetric distribution of mass exerts the same gravitational attraction on external bodies as if all the object's mass were concentrated at a point at its centre. (This is not generally true for non-spherically-symmetrical bodies.)"

This would seem to indicate that solutions to a representative distribution of point masses should be obtained, then combined by vector summation to determine a more representative result. This may be necessary because the inverse-square force contributed by millions of discrete masses, each with individual separation distances much less than the subject's radial distance from the galactic center, would exceed the force estimation using a single separation distance term.

Also see http://en.wikipedia.org/wiki/Shell_theorem - for points outside the 'shell'.

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