Stars form in dense cores of molecular clouds that are observed to be significantly magnetized. In the simplest case of a laminar (non-turbulent) core with the magnetic field aligned with the rotation axis, both analytic considerations and numerical
simulations have shown that the formation of a large, $10^2au$-scale, rotationally supported protostellar disk is suppressed by magnetic braking in the ideal MHD limit for a realistic level of core magnetization. This theoretical difficulty in forming protostellar disks is termed magnetic braking catastrophe. A possible resolution to this problem, proposed by citeauthor{HennebelleCiardi2009} and citeauthor{Joos+2012}, is that misalignment between the magnetic field and rotation axis may weaken the magnetic braking enough to enable disk formation. We evaluate this possibility quantitatively through numerical simulations. We confirm the basic result of citeauthor{Joos+2012} that the misalignment is indeed conducive to disk formation. In relatively weakly magnetized cores with dimensionless mass-to-flux ratio $gtrsim 5$, it enabled the formation of rotationally supported disks that would otherwise be suppressed if the magnetic field and rotation axis are aligned. For more strongly magnetized cores, disk formation remains suppressed, however, even for the maximum tilt angle of $90degree$. If dense cores are as strongly magnetized as indicated by OH Zeeman observations (with a mean dimensionless mass-to-flux ratio $sim 2$), it would be difficult for the misalignment alone to enable disk formation in the majority of them. We conclude that, while beneficial to disk formation, especially for the relatively weak field case, the misalignment does not completely solve the problem of catastrophic magnetic braking in general.
(Abridged) We investigate massive star formation in turbulent, magnetized, parsec-scale clumps of molecular clouds including protostellar outflow feedback using Enzo-based MHD simulations with accreting sink particles and effective resolution $2048^3
$. We find that, in the absence of regulation by magnetic fields and outflow feedback, massive stars form readily in a turbulent, moderately condensed clump of $sim 1,600$ solar masses, along with a cluster of hundreds of lower mass stars. The massive stars are fed at high rates by (1) transient dense filaments produced by large-scale turbulent compression at early times, and (2) by the clump-wide global collapse resulting from turbulence decay at late times. In both cases, the bulk of the massive stars mass is supplied from outside a 0.1 pc-sized core that surrounds the star. In our simulation, the massive star is clump-fed rather than core-fed. The need for large-scale feeding makes the massive star formation prone to regulation by outflow feedback, which directly opposes the feeding processes. The outflows reduce the mass accretion rates onto the massive stars by breaking up the dense filaments that feed the massive star formation at early times, and by collectively slowing down the global collapse that fuel the massive star formation at late times. The latter is aided by a moderate magnetic field of strength in the observed range. We conclude that the massive star formation in our simulated turbulent, magnetized, parsec-scale clump is outflow-regulated and clump-fed (ORCF for short). An important implication is that the formation of low-mass stars in a dense clump can affect the formation of massive stars in the same clump, through their outflow feedback on the clump dynamics.
