Tidal Imprints of a Dark Sub-Halo on the Outskirts of the Milky Way II.
  Perturber Azimuth
  We extend our analysis of the observed disturbances on the outskirts of the
HI disk of the Milky Way. We employ the additional constraints of the phase of
the modes of the observed HI image and asymmetry in the radial velocity field
to derive the azimuth of the perturber inferred to be responsible for the
disturbances in the HI disk. We carry out a modal analysis of the phase of the
disturbances in the HI image and in SPH simulations of a Milky Way-like galaxy
tidally interacting with dark perturbers, the relative offset of which we
utilize to derive the perturber azimuth. To make a direct connection with
observations, we express our results in sun-centered coordinates, predicting
that the perturber responsible for the observed disturbances is between $-50
\la l \la -10$. We show explicitly that the phase of the disturbances in the
outskirts of simulated galaxies at the time that best fits the Fourier
amplitudes, our primary metric for the azimuth determination, is relatively
insensitive to the equation of state. Our calculations here represent our
continuing efforts to develop the "Tidal Analysis" method of Chakrabarti \&
Blitz (2009; CB09). CB09 employed SPH simulations to examine tidal interactions
between perturbing dark sub-halos and the Milky Way. They found that the
amplitudes of the Fourier modes of the observed planar disturbances are
best-fit by a perturbing dark sub-halo with mass one-hundredth that of the
Milky Way, and a pericentric approach distance of $\sim 5-10~\rm kpc$. The
overarching goal of this work is to attempt to outline an alternate procedure
to optical studies for characterizing and potentially discovering dwarf
galaxies -- whereby one can approximately infer the azimuthal location of a
perturber, its mass and pericentric distance (CB09) from analysis of its tidal
gravitational imprints on the HI disk of the primary galaxy.
