The Size and Shape of the Milky Way Disk and Halo from M-type Brown
  Dwarfs in the BoRG Survey
  We have identified 274 M-type Brown Dwarfs in the Hubble Space Telescope's
Wide Field Camera 3 (WFC3) pure parallel fields from the Brightest of
Reionizing Galaxies (BoRG) survey for high redshift galaxies. These are
near-infrared observations with multiple lines-of-sight out of our Milky Way.
Using these observed M-type Brown Dwarfs we fitted a Galactic disk and halo
model with a Markov chain Monte Carlo (MCMC) analysis. This model worked best
with the scale length of the disk fixed at $h$ = 2.6 kpc. For the scale height
of the disk, we found $z_0 = 0.29^{+0.02}_{-0.019}$ kpc and for the central
number density $\rho_0 = 0.29^{+0.20}_{-0.13}$ \#/pc$^3$. For the halo we
derived a flattening parameter $\kappa$ = 0.45$\pm{0.04}$ and a power-law index
$p$ = 2.4$\pm{0.07}$. We found the fraction of M-type brown dwarfs in the local
density that belong to the halo to be $f_{h}$ = 0.0075$^{+0.0025}_{-0.0019}$.
We found no correlation between subtype of M-dwarf and any model parameters.
  The total number of M-type Brown Dwarfs in the disk and halo was determined
to be $58.2^{+9.81}_{-6.70} \times10^{9}$. We found an upper limit for the
fraction of M-type Brown Dwarfs in the halo of 7$^{+5}_{-4}$\%. The upper limit
for the total Galactic Disk mass in M-dwarfs is
$4.34^{+0.73}_{-0.5}\times10^{9}$ $M_{\odot}$, assuming all M-type Brown Dwarfs
have a mass of $80 M_J$.
