  The galactic halo likely grew over time in part by assembling smaller
galaxies, the so-called building blocks. We investigate if the properties of
these building blocks are reflected in the halo white dwarf (WD) population in
the Solar neighborhood. Furthermore, we compute the halo WD luminosity
functions (WDLFs) for four major building blocks of five cosmologically
motivated stellar haloes. We couple the SeBa binary population synthesis model
to the Munich-Groningen semi-analytic galaxy formation model, applied to the
high-resolution Aquarius dark matter simulations. Although the semi-analytic
model assumes an instantaneous recycling approximation, we model the evolution
of zero-age main sequence stars to WDs, taking age and metallicity variations
of the population into account. Although the majority of halo stars is old and
metal-poor and therefore the WDs in the different building blocks have similar
properties (including present-day luminosity), we find in our models that the
WDs originating from building blocks that have young and/or metal-rich stars
can be distinguished from WDs that were born in other building blocks. In
practice however, it will be hard to prove that these WDs really originate from
different building blocks, as the variations in the halo WD population due to
binary WD mergers result in similar effects. The five joined stellar halo WD
populations that we modelled result in WDLFs that are very similar to each
other. We find that simple models with a Kroupa or Salpeter initial mass
function (IMF) fit the observed luminosity function slightly better, since the
Chabrier IMF is more top-heavy, although this result is dependent on our choice
of the stellar halo mass density in the Solar neighborhood.
