Collapse and fragmentation of molecular cloud cores. VI. Slowly rotating magnetic clouds

Fragmentation during gravitational collapse has been reasonably successful at explaining the formation of binary and multiple stars, yet nearly all, f ragmentation calculations have ignored the effects of magnetic, fields. The previous paper in this series attempted to remedy this oversight by includ ing magnetic held effects in fully three-dimensional models of cloud collap se. These models allowed for magnetic held loss by ambipolar diffusion and showed that fragmentation is likely to occur during the resulting collapse of initially prolate, rapidly rotating, magnetically supported cloud cores. The main effect of the magnetic held was simply to delay the onset of the collapse phase. These calculations have now been extended to include the co llapse of slowly rotating, magnetic clouds, including clouds that rotate so slowly that binary fragmentation does not occur. The new models show that a cloud initially in either solid-body or differential rotation can fragmen t into a binary protostar, provided that its ratio of rotational to gravita tional energy (beta(i)) exceeds about 0.01. Because the clouds with beta(i) < 0.01 fragment in the absence of magnetic fields, evidently magnetic fiel ds can stifle fragmentation as well as delay collapse. The numerical models satisfy the Jeans conditions for physically realistic fragmentation, and a relatively high spatial resolution calculation indicates convergence to th e binary fragmentation solution for rapidly rotating clouds. Because the cr itical value of beta(i) for fragmentation falls close to the median of the observed distribution of rotational energies for dense molecular cloud core s, the results imply that roughly half of all cloud cores should form binar y stars, a prediction that is consistent with the observed frequency of bin ary stars.