Theory of Cluster Formation: Effects of Magnetic Fields
  Stars form predominantly in clusters inside dense clumps of molecular clouds
that are both turbulent and magnetized. The typical size and mass of the
cluster-forming clumps are $\sim 1$ pc and $\sim 10^2 - $ 10$^3$ M$_\odot$,
respectively. Here, we discuss some recent progress on numerical simulations of
clustered star formation in such parsec-scale dense clumps with emphasis on the
role of magnetic fields. The simulations have shown that magnetic fields tend
to slow down global gravitational collapse and thus star formation, especially
in the presence of protostellar outflow feedback. Even a relatively weak can
retard star formation significantly, because the field is amplified by
supersonic turbulence to an equipartition strength. However, in such a case,
the distorted field component dominates the uniform one. In contrast, if the
field is moderately strong, the uniform component remains dominant. Such a
difference in the magnetic structure is observed in simulated polarization maps
of dust thermal emission. Recent polarization measurements show that the field
lines in nearby cluster-forming clumps are spatially well-ordered, indicative
of a rather strong field. In such strongly-magnetized clumps, star formation
should proceed relatively slowly; it continues for at least several global
free-fall times of the parent dense clump ($t_{\rm ff}\sim $ a few $\times
10^5$ yr).
