The idea that non steady accretion during the embedded phase of protostar
evolution can produce the observed luminosity spread in the Herzsprung-Russell
diagram (HRD) of young clusters has recently been called into question.
Observations of Fu Ori, for instance, suggest an expansion of the star during
strong accretion events whereas the luminosity spread implies a contraction of
the accreting objects, decreasing their radiating surface. In this paper, we
present a global scenario based on calculations coupling episodic accretion
histories derived from numerical simulations of collapsing cloud prestellar
cores of various masses and subsequent protostar evolution. Our calculations
show that, assuming an initial protostar mass \mi \sim 1\,\mjup, typical of
the second Larson's core, both the luminosity spread in the HRD and the
inferred properties of Fu Ori events (mass, radius, accretion rate) can be
explained by this scenario, providing two conditions. First, there must be some
variation within the fraction of accretion energy absorbed by the protostar
during the accretion process. Second the range of this variation should
increase with increasing accretion burst intensity, and thus with the initial
core mass and final star mass. The numerical hydrodynamics simulations of
collapsing cloud prestellar cores indeed show that the intensity of the
accretion bursts correlates with the mass and initial angular momentum of the
prestellar core. Massive prestellar cores with high initial angular momentum
are found to produce intense bursts characteristic of Fu Ori like events. Our
results thus suggest a link between the burst intensities and the fraction of
accretion energy absorbed by the protostar, with some threshold in the
accretion rate, of the order of 10^{-5}\msolyr, delimitating the transition
from "cold" to "hot" accretion. [Abridged]Comment: 23 pages, 5 figures, ApJ accepte
