Towards determining the neutrino mass hierarchy: weak lensing and galaxy
  clustering forecasts with baryons and intrinsic alignments
  The capacity of Stage IV lensing surveys to measure the neutrino mass sum and
differentiate between the normal and inverted mass hierarchies depends on the
impact of nuisance parameters describing small-scale baryonic astrophysics and
intrinsic alignments. For a Euclid-like survey, we perform the first combined
weak lensing and galaxy clustering Fisher analysis with baryons, intrinsic
alignments, and massive neutrinos for both hierarchies. We use a matter power
spectrum generated from a halo model that captures the impact of baryonic
feedback and adiabatic contraction. For weak lensing, we find that baryons
cause severe degradation to forecasts of the neutrino mass sum, $\Sigma$,
approximately doubling $\sigma_{\Sigma}$. We show that including galaxy
clustering constraints from Euclid and BOSS, and cosmic microwave background
(CMB) Planck priors, can reduce this degradation to $\sigma_{\Sigma}$ to 9% and
16% for the normal and inverted hierarchies respectively. The combined
forecasts, $\sigma_{\Sigma_{\rm{NH}}}=0.034\, \rm{eV}$ and
$\sigma_{\Sigma_{\rm{IH}}}=0.034\, \rm{eV}$, preclude a meaningful distinction
of the hierarchies but could be improved upon with future CMB priors on $n_s$
and information from neutrinoless double beta decay to achieve a 2$\sigma$
distinction. The effect of intrinsic alignments on forecasts is shown to be
minimal, with $\sigma_{\Sigma}$ even experiencing mild improvements due to
information from the intrinsic alignment signal. We find that while adiabatic
contraction and intrinsic alignments will require careful calibration to
prevent significant biasing of $\Sigma$, there is less risk presented by
feedback from energetic events like AGN and supernovae.
