Detecting neutral hydrogen in emission at redshift z ~ 1
  We use a large N-body simulation to examine the detectability of HI in
emission at redshift z ~ 1, and the constraints imposed by current observations
on the neutral hydrogen mass function of galaxies at this epoch. We consider
three different models for populating dark matter halos with HI, designed to
encompass uncertainties at this redshift. These models are consistent with
recent observations of the detection of HI in emission at z ~ 0.8. Whilst
detection of 21 cm emission from individual halos requires extremely long
integrations with existing radio interferometers, such as the Giant Meter Radio
Telescope (GMRT), we show that the stacked 21 cm signal from a large number of
halos can be easily detected. However, the stacking procedure requires accurate
redshifts of galaxies. We show that radio observations of the field of the
DEEP2 spectroscopic galaxy redshift survey should allow detection of the HI
mass function at the 5-12 sigma level in the mass range 10^(11.4) M_sun/h <
M_halo < 10^(12.5)M_sun/h, with a moderate amount of observation time. Assuming
a larger noise level that corresponds to an upper bound for the expected noise
for the GMRT, the detection significance for the HI mass function is still at
the 1.7-3 sigma level. We find that optically undetected satellite galaxies
enhance the HI emission profile of the parent halo, leading to broader wings as
well as a higher peak signal in the stacked profile of a large number of halos.
We show that it is in principle possible to discern the contribution of
undetected satellites to the total HI signal, even though cosmic variance
limitation make this challenging for some of our models.
