  Stars may be assembled in large growth spurts, however the evidence for this
hypothesis is circumstantial. Directly studying the accretion at the earliest
phases of stellar growth is challenging because young stars are deeply embedded
in optically thick envelopes, which have spectral energy distributions that
peak in the far-IR, where observations are difficult. In this paper, we
consider the feasibility of detecting accretion outbursts from these younger
stars by investigating the timescales for how the protostellar envelope
responds to changes in the emission properties of the central source. The
envelope heats up in response to an outburst, brightening at all wavelengths
and with the emission peak moving to shorter wavelengths. The timescale for
this change depends on the time for dust grains to heat and re-emit photons and
the time required for the energy to escape the inner, optically-thick portion
of the envelope. We find that the dust response time is much shorter than the
photon propagation time and thus the timescale over which the emission varies
is set by time delays imposed by geometry. These times are hours to days near
the peak of the spectral energy distribution and weeks to months in the sub-mm.
The ideal location to quickly detect continuum variability is therefore in the
mid- to far-IR, near the peak of the spectral energy distribution, where the
change in emission amplitude is largest. Searching for variability in sub-mm
continuum emission is also feasible, though with a longer time separation and a
weaker relationship between the amount of detected emission amplitude and
change in central source luminosity. Such observations would constrain
accretion histories of protostars and would help to trace the disk/envelope
instabilities that lead to stellar growth.
