  The prompt emission of low-luminosity gamma-ray bursts (llGRBs) indicates
that these events originate from a relativistic shock breakout. In this case we
can estimate, based on the properties of the prompt emission, the energy
distribution of the ejecta. We develop a general formalism to estimate the
afterglow produced by synchrotron emission from the forward shock resulting
from the interaction of this ejecta with the circum-burst matter. We assess
whether this emission can produce the observed radio and X-ray afterglows of
the available sample of 4 llGRBs. All 4 radio afterglows can be explained
within this model, providing further support for shock breakouts being the
origin of llGRBs. We find that in one of the llGRBs (GRB 031203) the predicted
X-ray emission, using the same parameters that fit the radio, can explain the
observed one. In another one (GRB 980425) the observed X-rays can be explained
if we allow for a slight modification of the simplest model. For the last two
cases (GRBs 060218 and 100316D), we find that, as is the case for previous
attempts to model these afterglows, the simplest model that fits the radio
emission underpredicts the observed X-ray afterglows. Using general arguments,
we show that the most natural location of the X-ray source is, like the radio
source, within the ejecta-external medium interaction layer but that emission
is due to a different population of electrons or to a different emission
process.
