The Jeans condition and collapsing molecular cloud cores: Filaments or binaries?

The 1997 and 1998 studies by Truelove and colleagues introduced the Jeans c ondition as a necessary condition for avoiding artificial fragmentation dur ing protostellar collapse calculations. They found that when the Jeans cond ition was properly satisfied with their adaptive mesh refinement (AMR) code , an isothermal cloud with an initial Gaussian density profile collapsed to form a thin filament rather than the binary or quadruple protostar systems found in previous calculations. Using a completely different self-gravitat ional hydrodynamics code introduced by Boss & Myhill in 1992 (B&M), we pres ent here calculations that reproduce the filamentary solution first obtaine d by Truelove et al. in 1997. The filamentary solution only emerged with ve ry high spatial resolution with the B&M code, with effectively 12,500 radia l grid points (R-12500). Reproducing the filamentary collapse solution appe ars to be an excellent means for testing the reliability of self-gravitatio nal hydrodynamics codes, whether grid-based or particle-based. We then show that in the more physically realistic case of an identical initial cloud w ith nonisothermal heating (calculated in the Eddington approximation with c ode B&M), thermal retardation of the collapse permits the Gaussian cloud to fragment into a binary protostar system at the same maximum density where the isothermal collapse yields a thin filament. However, the binary clumps soon thereafter evolve into a central clump surrounded by spiral arms conta ining two more clumps. A roughly similar evolution is obtained using the AM R code with a barotropic equation of state--formation of a transient binary , followed by decay of the binary to form a central object surrounded by sp iral arms, though in this case the spiral arms do not form clumps. When the same barotropic equation of state is used with the B&M code, the agreement with the initial phases of the AMR calculation is quite good, showing that these two codes yield mutually consistent results. However, the B&M barotr opic result differs significantly from the B&M Eddington result at the same maximum density, demonstrating the importance of detailed radiative transf er effects. Finally, we confirm that even in the case of isothermal collaps e, an initially uniform density sphere can collapse and fragment into a bin ary system, in agreement with the 1998 results of Truelove et al. Fragmenta tion of molecular cloud cores thus appears to remain as a likely explanatio n of the formation of binary stars, but the sensitivity of these calculatio ns to the numerical resolution and to the thermodynamical treatment demonst rates the need for considerable caution in computing and interpreting three -dimensional protostellar collapse calculations.