The Warm Gas in the MW: A Kinematical Model
  We develop a kinematical model for the Milky Way Si IV-bearing gas to
determine its density distribution and kinematics. This model is constrained by
a column density line shape sample extracted from the {\it HST}/COS archival
data, which contains 186 AGN sight lines. We find that the Si IV ion density
distribution is dominated by an extended disk along the $z$-direction (above or
below the midplane), i.e., $n(z)=n_0\exp(-(z/z_0)^{0.82})$, where $z_0$ is the
scale height of $6.3_{-1.5}^{+1.6}$ kpc (northern hemisphere) and
$3.6_{-0.9}^{+1.0}$ kpc (southern hemisphere). The density distribution of the
disk in the radial direction shows a sharp edge at $15-20$ kpc given by,
$n(r_{\rm XY})=n_0\exp(-(r_{\rm XY}/r_0)^{3.36})$, where $r_0 \approx
12.5\pm0.6$ kpc. The difference of density distributions over $r_{\rm XY}$ and
$z$ directions indicates that the warm gas traced by \ion{Si}{4} is mainly
associated with disk processes (e.g., feedback or cycling gas) rather than
accretion. We estimate the mass of the warm gas (within 50 kpc) is $\log (M(50
{\rm kpc})/M_\odot)\approx8.1$ (assuming $Z\approx0.5Z_\odot$), and a $3\sigma$
upper limit of $\log (M(250 {\rm kpc})/M_\odot)\approx9.1$ (excluding the
Magellanic system). Kinematically, the warm gas disk is nearly co-rotating with
the stellar disk at $v_{\rm rot}=215\pm3\rm~km~s^{-1}$, which lags the midplane
rotation by about $8\rm~km~s^{-1}~kpc^{-1}$ (within 5 kpc). Meanwhile, we note
that the warm gas in the northern hemisphere has significant accretion with
$v_{\rm acc}$ of $69\pm 7\rm ~km~s^{-1}$ at 10 kpc (an accretion rate of
$-0.60_{-0.13}^{+0.11}~M_\odot\rm~yr^{-1}$), while in the southern hemisphere,
there is no measurable accretion, with an upper limit of
$0.4~M_\odot\rm~yr^{-1}$.
