Evidence for two spatially separated UV continuum emitting regions in
  the Cloverleaf broad absorption line quasar
  Testing the standard Shakura-Sunyaev model of accretion is a challenging task
because the central region of quasars where accretion takes place is unresolved
with telescopes. The analysis of microlensing in gravitationally lensed quasars
is one of the few techniques that can test this model, yielding to the
measurement of the size and of temperature profile of the accretion disc. We
present spectroscopic observations of the gravitationally lensed broad
absorption line quasar H1413+117, which reveal partial microlensing of the
continuum emission that appears to originate from two separated regions: a
microlensed region, corresponding to the compact accretion disc; and a
non-microlensed region, more extended and contributing to at least 30\% of the
total UV-continuum flux. Because this extended continuum is occulted by the
broad absorption line clouds, it is not associated with the host galaxy, but
rather with light scattered in the neighbourhood of the central engine. We
measure the amplitude of microlensing of the compact continuum over the
rest-frame wavelength range 1000-7000 \AA. Following a Bayesian scheme, we
confront our measurements to microlensing simulations of an accretion disc with
a temperature varying as $T \propto R^{-1/\nu}$. We find a most likely source
half-light radius of $R_{1/2} = 0.61 \times 10^{16}\,$cm (i.e., 0.002\,pc) at
0.18\,$\mu$m, and a most-likely index of $\nu=0.4$. The standard disc
($\nu=4/3$) model is not ruled out by our data, and is found within the 95\%
confidence interval associated with our measurements. We demonstrate that, for
H1413+117, the existence of an extended continuum in addition to the disc
emission only has a small impact on the inferred disc parameters, and is
unlikely to solve the tension between the microlensing source size and standard
disc sizes, as previously reported in the literature.
