Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998apj...501l..77b&link_type=abstract
Astrophysical Journal Letters v.501, p.L77
Astronomy and Astrophysics
Astronomy
24
Stars: Binaries: General, Hydrodynamics, Ism: Clouds, Ism: Kinematics And Dynamics, Stars: Formation
Scientific paper
The collapse and fragmentation of molecular cloud cores into binary and multiple protostar systems is a demanding computational problem, in part because of the large range of length scales involved. Truelove et al. proposed that the computational cell size Delta x must be smaller than 1/4 of the Jeans length, lambda _{{J}} , if artificial (numerical) fragmentation is to be avoided. For a uniform Cartesian grid, Truelove et al.'s Jeans condition is equivalent to ensuring that the mass of a cell never exceeds ~1/64 of a Jeans mass. It is shown here that for a nonuniform spherical grid, artificial fragmentation can be avoided provided that the cell size of a cube with approximately the same volume as the spherical coordinate cell [ Delta x=( Delta xr Delta x_θ Delta x_φ)^{1/3} ] is less than lambda _{{J}} /4 (i.e., that the mass inside each cell is much less than a Jeans mass), even if one of the three cell lengths ( Delta xr, Delta x_θ, or Delta x_φ ) exceeds lambda _{{J}} /4. For a nonuniform grid, resolving a small fraction of a Jeans mass is less restrictive than resolving 1/4 of a Jeans length in each coordinate direction; resolving all three Jeans lengths is desirable but not necessary in order to avoid artificial fragmentation. The well-resolved collapse of an initially Gaussian-profile cloud is then followed with both isothermal and nonisothermal (Eddington approximation radiative transfer) thermodynamics and is shown to lead to fragmentation into a binary protostar system in both cases. The Jeans mass constraint appears to be a valuable indicator of physically realistic fragmentation.
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