Journal Article

3D perturbations in an isothermal self-similar flow

Yu-Qing Lou and Xue-Ning Bai

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 415, issue 1, pages 925-943
Published in print July 2011 | ISSN: 0035-8711
Published online July 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.18760.x
3D perturbations in an isothermal self-similar flow

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We explore three-dimensional (3D) isothermal perturbation structures in a non-linear dynamic background of self-gravitating isothermal radial flow with spherical symmetry. The overall flow then appears quasi-spherically symmetric. Here, the dynamic background radial flow describes a self-similar evolution with a central/final free-fall asymptotic solution and a far-away/initial flow but without involving the sonic critical line (SCL). As transients peter out, 3D perturbations can consistently emerge and evolve in a self-similar manner with angular variations separated out in terms of spherical harmonics and with xr/(at) as the independent self-similar variable where r, t and a are the radius, time and isothermal sound speed, respectively. Independent asymptotic perturbation solutions in large and small x regimes are derived analytically. Global 3D perturbation solutions are constructed numerically for sensible asymptotic solutions. The fifth-order perturbation equations have solutions of four curl-free modes and one vortex mode, with the former identified as multipole and antimultipole modes, P1 and P2 modes, respectively. Of the five solutions, four are of potential astrophysical interest and can be utilized for benchmarking numerical codes and simulation results. Our results show that perturbations may or may not grow in a free-fall manner, depending on initial perturbations in mass and velocity distribution. We also find that vortex mode can be converted to other modes during a collapse, and in the l= 1 case, mode conversion will serve to produce a gravitational dipole. For self-similar solutions characterized by envelope expansion with core collapse (EECC), global 3D isothermal perturbation configurations can also be constructed.

Keywords: hydrodynamics; stars: formation; stars: oscillations; supernovae: general; stars: winds, outflows; galaxies: clusters: general

Journal Article.  14479 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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