We revisit our original papers on the burst mode of accretion by incorporating a detailed energy balance equation into a thin-disk model for the formation and evolution of circumstellar disks around low-mass protostars .
Our model includes the effect of radiative cooling , viscous and shock heating , and heating due to stellar and background irradiation .
Following the collapse from the prestellar phase allows us to model the early embedded phase of disk formation and evolution .
During this time , the disk is susceptible to fragmentation , depending upon the properties of the initial prestellar core .
Globally , we find that higher initial core angular momentum and mass content favors more fragmentation , but higher levels of background radiation can moderate the tendency to fragment .
A higher rate of mass infall onto the disk than that onto the star is a necessary but not sufficient condition for disk fragmentation .
More locally , both the Toomre Q -parameter needs to be below a critical value and the local cooling time needs to be shorter than a few times the local dynamical time .
Fragments that form during the early embedded phase tend to be driven into the inner disk regions , and likely trigger mass accretion and luminosity bursts that are similar in magnitude to FU-Orionis-type or EX-Lupi-like events .
Disk accretion is shown to be an intrinsically variable process , thanks to disk fragmentation , nonaxisymmetric structure , and the effect of gravitational torques .
The additional effect of a generic \alpha -type viscosity acts to reduce burst frequency and accretion variability , and is likely to not be viable for values of \alpha significantly greater than 0.01 .