  The evolution of white dwarfs (WDs) depends crucially on thermal processes.
The plasma in their core can produce neutrinos which escape from the star, thus
contributing to the energy loss. While in absence of a magnetic field the main
cooling mechanism is plasmon decay at high temperature and photon surface
emission at low temperature, a large magnetic field in the core hiding beneath
the surface even of ordinary WDs, and undetectable to spectropolarimetric
measurements, can potentially leave an imprint in the cooling. In this paper,
we revisit the contribution to WD cooling stemming from neutrino pair
synchrotron radiation and the effects of the magnetic field on plasmon decay.
Our key finding is that even if observations limit the magnetic field strength
at the stellar surface, magnetic fields in the interior of WDs -- with or
without a surface magnetic field -- can be strong enough to modify the cooling
rate, with neutrino pair synchrotron emission being the most important
contribution. This effect may not only be relevant for the quantification and
interpretation of cooling anomalies, but also suggests that the internal
magnetic fields of WDs should be smaller than $\sim 6\times 10^{11}\,\rm G$,
slightly improving bounds coming from a stability requirement. While our
simplified treatment of the WD structure implies that further studies are
needed to reduce the systematic uncertainties, the estimates based on comparing
the emissivities illustrate the potential of neutrino emission as a diagnostic
tool to study the interior of WDs.
