Embedded protostellar disks around (sub-)solar protostars. I. Disk
  structure and evolution
  We perform a comparative numerical hydrodynamics study of embedded
protostellar disks formed as a result of the gravitational collapse of cloud
cores of distinct mass (M_cl=0.2--1.7 M_sun) and ratio of rotational to
gravitational energy (\beta=0.0028--0.023). An increase in M_cl and/or \beta
leads to the formation of protostellar disks that are more susceptible to
gravitational instability. Disk fragmentation occurs in most models but its
effect is often limited to the very early stage, with the fragments being
either dispersed or driven onto the forming star during tens of orbital
periods. Only cloud cores with high enough M_cl or \beta may eventually form
wide-separation binary/multiple systems with low mass ratios and brown dwarf or
sub-solar mass companions. It is feasible that such systems may eventually
break up, giving birth to rogue brown dwarfs. Protostellar disks of {\it equal}
age formed from cloud cores of greater mass (but equal \beta) are generally
denser, hotter, larger, and more massive. On the other hand, protostellar disks
formed from cloud cores of higher \beta (but equal M_cl) are generally thinner
and colder but larger and more massive. In all models, the difference between
the irradiation temperature and midplane temperature \triangle T is small,
except for the innermost regions of young disks, dense fragments, and disk's
outer edge where \triangle T is negative and may reach a factor of two or even
more. Gravitationally unstable, embedded disks show radial pulsations, the
amplitude of which increases along the line of increasing M_cl and \beta but
tends to diminish as the envelope clears. We find that single stars with a
disk-to-star mass ratio of order unity can be formed only from high-\beta cloud
cores, but such massive disks are unstable and quickly fragment into
binary/multiple systems.
