Collapse and Fragmentation of Molecular Cloud Cores. X. Magnetic Braking of Prolate and Oblate Cores

arXiv:0903.1810v1 [astro-ph.GA] 10 Mar 2009 Collapse and Fragmentation of Molecular Cloud Cores. X. Magnetic Braking of Prolate and Oblate Cores. Alan P. Boss Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Road, NW, Washington, DC 20015-1305 boss@dtm.ciw.edu ABSTRACT The collapse and fragmentation of initially prolate and oblate, magnetic molecular clouds is calculated in three dimensions with a gravitational, radiative hydrodynamics code. The code includes magnetic field effects in an approximate manner: magnetic pressure, tension, braking, and ambipolar diffusion are all modelled. The parameters varied for both the initially prolate and oblate clouds are the initial degree of central concentration of the radial density profile, the initial angular velocity, and the efficiency of magnetic braking (represented by a factor fmb = 10−4 or 10−3). The oblate cores all collapse to form rings that might be susceptible to fragmentation into multiple systems. The outcome of the collapse of the prolate cores depends strongly on the initial density profile. Prolate cores with central densities 20 times higher than their boundary densi- ties collapse and fragment into binary or quadruple systems, whereas cores with central densities 100 times higher collapse to form single protostars embedded in bars. The inclusion of magnetic braking is able to stifle protostellar fragmenta- tion in the latter set of models, as when identical models were calculated without magnetic braking (Boss 2002), those cores fragmented into binary protostars. These models demonstrate the importance of including magnetic fields in studies of protostellar collapse and fragmentation, and suggest that even when magnetic fields are included, fragmentation into binary and multiple systems remains as a possible outcome of protostellar collapse. Subject headings: hydrodynamics — ISM: clouds — ISM: kinematics and dy- namics — MHD — stars: formation – 2 – 1. Introduction Fragmentation during protostellar collapse is widely accepted to be the primary mecha- nism for the formation of binary and multiple star systems (e.g., Lafreni`ere et al. 2008; Chen et al. 2008). While it is clear that the overall form of the initial mass function for stars is directly tied to the initial conditions for protostellar collapse, i.e., the mass function of dense cloud cores (e.g., Dib et al. 2008; Swift & Williams 2008), fragmentation is necessary for producing binary star systems within these individual dense cores (Lafreni`ere et al. 2008; Chen et al. 2008). Three dimensional calculations of the collapse of centrally condensed, rotating cloud cores have been computed for quite some time (e.g., Boss 1993) and continue to attract theoretical attention (e.g., Saigo et al. 2008; Machida 2008; Commercon et al. 2008). These calculations neglected the effects of magnetic fields. However, observations of OH Zeeman splitting in dark cloud cores have shown that magnetic fields are often an important contributer to cloud support against collapse for densities in the range of 103 −104 cm−3 (Troland & Crutcher 2008). Given this observational constraint, it is clear that three dimen- sional hydrodynamical collapse calculations should include magnetic field effects as well as self-gravity and radiative transfer (e.g., Boss 1997, 1999, 2002, 2005, 2007). Magnetic fields are now being included in other three dimensional collapse models as well (e.g., Machida et al. 2004, 2005a,b, 2007, 2008; Kudoh et al. 2007; Price & Bate 2007, 2008). In particular, Price & Bate (2007) found that while magnetic pressure acts to resist fragmentation dur- ing collapse, magnetic tension can actually aid fragmentation, confirming the results found by Boss (2002). Machida et al. (2004, 2005a,b, 2007, 2008) generally found that binary fragmentation could still occur provided that the initial magnetic cloud core rotated fast enough. Magnetic braking is effective at reducing cloud rotation rates during the pre-collapse cloud phase, but has relatively little effect during the collapse phase, according to the two dimensional magnetohydrodynamics models of Basu & Mouschovias (1994, 1995a,b). How- ever, Hosking & Whitworth (2004) found that rotationally-driven fragmentation could be halted by magnetic braking during the collapse phase. Boss (2004) argued that the ther- modynamical treatment employed by Hosking & Whitworth (2004) could have been more important for stifling fragmentation than magnetic braking, but did not offer any models of magnetic braking to support this assertion. Price & Bate (2007) presented models of the collapse of magnetic cloud cores, finding that magnetic pressure was more important for inhibiting fragmentation than either magnetic tension or braking, contrary to the results presented by Hosking & Whitworth (2004) and Fromang et al. (2006), who found no evidence at all for the fragmentation of magnetic clouds. – 3 – Fromang et al. (2006) assumed ideal magnetohydrodyna

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