The distribution of HI velocity profiles in a $\Lambda$CDM universe
  We model the distribution of the observed profiles of 21 cm line emission
from neutral hydrogen (HI) in central galaxies selected from a statistically
representative mock catalog of the local Universe in the Lambda-cold dark
matter framework. The distribution of these HI velocity profiles (specifically,
their widths $W_{50}$) has been observationally constrained, but has not been
systematically studied theoretically. Our model profiles derive from rotation
curves of realistically baryonified haloes in an N-body simulation, including
the quasi-adiabatic relaxation of the dark matter profile of each halo in
response to its baryons. We study the predicted $W_{50}$ distribution using a
realistic pipeline applied to noisy profiles extracted from our
luminosity-complete mock catalog with an ALFALFA-like survey geometry and
redshift selection. Our default mock is in good agreement with observed ALFALFA
results for $W_{50}\gtrsim700$ km/s, being incomplete at lower widths due to
the intrinsic threshold of $M_r\leq-19$. Variations around the default model
show that the velocity width function at $W_{50}\gtrsim300$ km/s is most
sensitive to a possible correlation between galaxy inclination and host
concentration, followed by the physics of quasi-adiabatic relaxation. We also
study the excess kurtosis of noiseless velocity profiles, obtaining a
distribution which tightly correlates with $W_{50}$, with a shape and scatter
that depend on the properties of the turbulent HI disk. Our results open the
door towards using the shapes of HI velocity profiles as a novel statistical
probe of the baryon-dark matter connection.
