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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 (β=0.0028--0.023). An increase in M_cl and/or βleads 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 βmay 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 β) are generally denser, hotter, larger, and more massive. On the other hand, protostellar disks formed from cloud cores of higher β(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 βbut 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-βcloud cores, but such massive disks are unstable and quickly fragment into binary/multiple systems.