  Radiation from accretion discs in cataclysmic variable stars (CVs) provides
fundamental information about the properties of these close binary systems and
about the physics of accretion in general. The detailed diagnostics of
accretion disc structure can be achieved by including in its description all
the relevant heating and cooling physical mechanism, in particular the
convective energy transport that, although dominant at temperatures less than
about 10 000 K, is usually not taken into account when calculating spectra of
accretion discs. We constructed a radiative transfer code coupled with a code
determining the disc's hydrostatic vertical structure. We have obtained for the
first time model spectra of cold, convective accretion discs. As expected,
these spectra are mostly flat in the optical wavelengths with no contribution
from the UV, which in quiescence must be emitted by the white dwarf. The disc
structures obtained with our radiative-transfer code compare well with the
solutions of equations used to describe the dwarf-nova outburst cycle according
to the thermal-viscous disc instability model thus allowing the two to be
combined. Our code allows calculating the spectral evolution of dwarf nova
stars through their whole outburst cycle, providing a new tool for testing
models of accretion discs in cataclysmic variables. We show that convection
plays an important role in determining the vertical disc structure and
substantially affects emitted spectra when, as often the case, it is effective
at optical depths tau ~ 1. The emergent spectrum is independent of the
parameters of the convection model.(Abstract shortened)
