  The mass assembly history of the Milky Way can inform both theory of galaxy
formation and the underlying cosmological model. Thus, observational
constraints on the properties of both its baryonic and dark matter contents are
sought. Here we show that hypervelocity stars (HVSs) can in principle provide
such constraints. We model the observed velocity distribution of HVSs, produced
by tidal break-up of stellar binaries caused by Sgr A*. Considering a Galactic
Centre (GC) binary population consistent with that inferred in more
observationally accessible regions, a fit to current HVS data with significance
level > 5\% can only be obtained if the escape velocity from the GC to 50 kpc
is $V_G < 850$ km/s, regardless of the enclosed mass distribution. When a NFW
matter density profile for the dark matter halo is assumed, haloes with $V_G <
850$ km/s are in agreement with predictions in the $\Lambda$CDM model and that
a subset of models around $M_{200} \sim 0.5-1.5 \times 10^{12}$ solar masses
and $r_s < 35$ kpc can also reproduce Galactic circular velocity data. HVS data
alone cannot currently exclude potentials with $V_G > 850$ km/s. Finally,
specific constraints on the halo mass from HVS data are highly dependent on the
assumed baryonic mass potentials. This first attempt to simultaneously
constrain GC and dark halo properties is primarily hampered by the paucity and
quality of data. It nevertheless demonstrates the potential of our method, that
may be fully realised with the ESA Gaia mission.
