Galaxy disc scaling relations: A tight linear galaxy -- halo connection
  challenges abundance matching
  In $\Lambda$CDM cosmology, to first order, galaxies form out of the cooling
of baryons within the virial radius of their dark matter halo. The fractions of
mass and angular momentum retained in the baryonic and stellar components of
disc galaxies put strong constraints on our understanding of galaxy formation.
In this work, we derive the fraction of angular momentum retained in the
stellar component of spirals, $f_j$, the global star formation efficiency
$f_M$, and the ratio of the asymptotic circular velocity ($V_{\rm flat}$) to
the virial velocity $f_V$, and their scatter, by fitting simultaneously the
observed stellar mass-velocity (Tully-Fisher), size-mass, and mass-angular
momentum (Fall) relations. We compare the goodness of fit of three models: (i)
where the logarithm of $f_j$, $f_M$, and $f_V$ vary linearly with the logarithm
of the observable $V_{\rm flat}$; (ii) where these values vary as a double
power law; and (iii) where these values also vary as a double power law but
with a prior imposed on $f_M$ such that it follows the expectations from widely
used abundance matching models. We conclude that the scatter in these fractions
is particularly small ($\sim 0.07$ dex) and that the linear model is by far
statistically preferred to that with abundance matching priors. This indicates
that the fundamental galaxy formation parameters are small-scatter single-slope
monotonic functions of mass, instead of being complicated non-monotonic
functions. This incidentally confirms that the most massive spiral galaxies
should have turned nearly all the baryons associated with their haloes into
stars. We call this the failed feedback problem.
