Three Dimensional Hydrodynamic Simulations of Multiphase Galactic Disks
  with Star Formation Feedback: II. Synthetic HI 21 cm Line Observations
  We use three-dimensional numerical hydrodynamic simulations of the turbulent,
multiphase atomic interstellar medium (ISM) to construct and analyze synthetic
HI 21 cm emission and absorption lines. Our analysis provides detailed tests of
21 cm observables as physical diagnostics of the atomic ISM. In particular, we
construct (1) the "observed" spin temperature, $T_{s,obs}(v_{ch})\equiv
T_B(v_{ch})/[1-e^{-{\tau}(v_{ch})}]$, and its optical-depth weighted mean
T_s,obs; (2) the absorption-corrected "observed" column density,
$N_{H,obs}\propto \int dv_{ch}
T_B(v_{ch}){\tau}(v_{ch})/[[1-e^{-{\tau}(v_{ch})}]$; and (3) the "observed"
fraction of cold neutral medium (CNM), $f_{c,obs}\equiv T_c/T_{s,obs}$ for T_c
the CNM temperature; we compare each observed parameter with true values
obtained from line-of-sight (LOS) averages in the simulation. Within individual
velocity channels, T_s,obs(v_ch) is within a factor 1.5 of the true value up to
${\tau}(v_{ch})\approx10$. As a consequence, N_H,obs and T_s,obs are
respectively within 5% and 12% of the true values for 90% and 99% of LOSs. The
optically thin approximation significantly underestimates N_H for ${\tau}>1$.
Provided that T_c is constrained, an accurate observational estimate of the CNM
mass fraction can be obtained down to 20%. We show that T_s,obs cannot be used
to distinguish the relative proportions of warm and thermally-unstable atomic
gas, although the presence of thermally-unstable gas can be discerned from 21
cm lines with 200K<$T_{s,obs}(v_{ch})$<1000K. Our mock observations
successfully reproduce and explain the observed distribution of the brightness
temperature, optical depth, and spin temperature in Roy et al. (2013a). The
threshold column density for CNM seen in observations is also reproduced by our
mock observations. We explain this observed threshold behavior in terms of
vertical equilibrium in the local Milky Way's ISM disk.
