We use three-dimensional numerical hydrodynamic simulations of the turbulent , multiphase atomic interstellar medium ( ISM ) to construct and analyze synthetic H i 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 } ) \sim 10 .
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 } } can not 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 200 { K } \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } T _ { s, { obs } } ( v _ { % ch } ) \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 1000 { K } .
Our mock observations successfully reproduce and explain the observed distribution of the brightness temperature , optical depth , and spin temperature in Roy et al .
( 52 ) .
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 .