Journal Article

On the fragmentation criteria of self-gravitating protoplanetary discs

Farzana Meru and Matthew R. Bate

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 410, issue 1, pages 559-572
Published in print January 2011 | ISSN: 0035-8711
Published online December 2010 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2010.17465.x
On the fragmentation criteria of self-gravitating protoplanetary discs

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We investigate the fragmentation criterion in massive self-gravitating discs. We present new analysis of the fragmentation conditions which we test by carrying out global three-dimensional numerical simulations. Whilst previous work has placed emphasis on the cooling time-scale in units of the orbital time-scale, β, we find that at a given radius the surface mass density (i.e. disc mass and profile) and star mass also play a crucial role in determining whether a disc fragments or not as well as where in the disc fragments form. We find that for shallow surface mass density profiles (p < 2, where Σ∝Rp), fragments form in the outer regions of the disc. However for steep surface mass density profiles (p > rsim 2), fragments form in the inner regions of a disc. In addition, we also find that the critical value of the cooling time-scale in units of the orbital time-scale, βcrit, found in previous simulations is only applicable to certain disc surface mass density profiles and for particular disc radii and is not a general rule for all discs. We find an empirical fragmentation criterion between the cooling time-scale in units of the orbital time-scale, β, the surface mass density, the star mass and the radius.

Keywords: accretion, accretion discs; gravitation; hydrodynamics; instabilities; planets and satellites: formation; protoplanetary discs

Journal Article.  9396 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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