HALOGAS Observations of NGC 4559: Anomalous and Extra-planar HI and its
  Relation to Star Formation
  We use new deep 21 cm HI observations of the moderately inclined galaxy NGC
4559 in the HALOGAS survey to investigate the properties of extra-planar gas.
We use TiRiFiC to construct simulated data cubes to match the HI observations.
We find that a thick disk component of scale height $\sim\,2\,\mathrm{kpc}$,
characterized by a negative vertical gradient in its rotation velocity (lag) of
$\sim13 \pm 5$ km s$^{-1}$ kpc$^{-1}$ is an adequate fit to extra-planar gas
features. The tilted ring models also present evidence for a decrease in the
magnitude of the lag outside of $R_{25}$, and a radial inflow of $\sim 10$ km
s$^{-1}$. We extracted lagging extra-planar gas through Gaussian velocity
profile fitting. From both the 3D models and and extraction analyses we
conclude that $\sim10-20\%$ of the total {\HI} mass is extra-planar. Most of
the extra-planar gas is spatially coincident with regions of star formation in
spiral arms, as traced by H$\alpha$ and GALEX FUV images, so it is likely due
to star formation processes driving a galactic fountain. We also find the
signature of a filament of a kinematically "forbidden" HI, containing $\sim
1.4\times 10^{6}$ M$_{\odot}$ of HI, and discuss its potential relationship to
a nearby HI hole. We discover a previously undetected dwarf galaxy in HI
located $\sim 0.4^{\circ}$ ($\sim 58$ kpc) from the center of NGC 4559,
containing $\sim 4\times10^{5}$ M$_{\odot}$. This dwarf has counterpart sources
in SDSS with spectra typical of HII regions, and we conclude it is two merging
blue compact dwarf galaxies.
