Neutral Gas Properties and Ly$\alpha$ Escape in Extreme Green Pea
  Galaxies
  Mechanisms regulating the escape of Ly$\alpha$ photons and ionizing radiation
remain poorly understood. To study these processes we analyze VLA 21cm
observations of one Green Pea (GP), J160810+352809 (hereafter J1608), and HST
COS spectra of 17 GP galaxies at $z<0.2$. All are highly ionized: J1608 has the
highest [O III] $\lambda5007$/[O II] $\lambda3727$ for star-forming galaxies in
SDSS, and the 17 GPs have [O III]/[O II] $\geq6.6$. We set an upper limit on
J1608's HI mass of $\log M_{HI}/M_\odot=8.4$, near or below average compared to
similar mass dwarf galaxies. In the COS sample, eight GPs show Ly$\alpha$
absorption components, six of which also have Ly$\alpha$ emission. The HI
column densities derived from Ly$\alpha$ absorption are high, $\log
N_{HI}/$cm$^{-2}=19-21$, well above the LyC optically thick limit. Using
low-ionization absorption lines, we measure covering fractions
($f_{\mbox{cov}}$) of $0.1-1$, and find that $f_{\mbox{cov}}$ strongly
anti-correlates with Ly$\alpha$ escape fraction. Low covering fractions may
facilitate Ly$\alpha$ and LyC escape through dense neutral regions. GPs with
$f_{\mbox{cov}}\sim1$ all have low neutral gas velocities, while GPs with lower
$f_{\mbox{cov}}=0.2-0.6$ have a larger range of velocities. Conventional
mechanical feedback may help establish low $f_{\mbox{cov}}$ in some cases,
whereas other processes may be important for GPs with low velocities. Finally,
we compare $f_{\mbox{cov}}$ with proposed indicators of LyC escape. Ionizing
photon escape likely depends on a combination of neutral gas geometry and
kinematics, complicating the use of emission-line diagnostics for identifying
LyC emitters.
