  The central compact objects are a newly-emerging class of young neutron stars
near the centre of supernova remnants. From X-ray timing and spectral
measurements, their magnetic fields are determined to be ~ 10^10-10^11 G, which
is significantly lower than that found on most pulsars. Using the latest
electrical and thermal conductivity calculations, we solve the induction
equation to determine the evolution of a buried crustal or core magnetic field.
We apply this model of a buried field to explain the youth and low observed
magnetic field of the central compact objects. We obtain constraints on their
birth magnetic field and depth of submergence (or accreted mass). Measurement
of a change in the observed magnetic field strength would discriminate between
the crustal and core fields and could yield uniquely the birth magnetic field
and submergence depth. If we consider the central compact objects as a single
neutron star viewed at different epochs, then we constrain the magnetic field
at birth to be ~ (6-9)x10^11 G. A buried magnetic field can also explain their
location in an underpopulated region of the spin period-period derivative plane
for pulsars.
