  Protostars grow in mass by accreting material through their discs, and this
accretion is initially their main source of luminosity. The resulting radiative
feedback heats the environments of young protostars, and may thereby suppress
further fragmentation and star formation. There is growing evidence that the
accretion of material onto protostars is episodic rather than continuous; most
of it happens in short bursts that last up to a few hundred years, whereas the
intervals between these outbursts of accretion could be thousands of years. We
have developed a model to include the effects of episodic accretion in
simulations of star formation. Episodic accretion results in episodic radiative
feedback, which heats and temporarily stabilises the disc, suppressing the
growth of gravitational instabilities. However, once an outburst has been
terminated, the luminosity of the protostar is low, and the disc cools rapidly.
Provided that there is enough time between successive outbursts, the disc may
become gravitationally unstable and fragment. The model suggests that episodic
accretion may allow disc fragmentation if (i) the time between successive
outbursts is longer than the dynamical timescale for the growth of
gravitational instabilities (a few kyr), and (ii) the quiescent accretion rate
onto the protostar is sufficiently low (at most a few times 1e-7 Msun/yr). We
also find that after a few protostars form in the disc, their own episodic
accretion events shorten the intervals between successive outbursts, and sup-
press further fragmentation, thus limiting the number of objects forming in the
disc. We conclude that episodic accretion moderates the effect of radiative
feedback from young protostars on their environments, and, under certain
conditions, allows the formation of low-mass stars, brown dwarfs, and
planetary-mass objects by fragmentation of protostellar discs.
