H$\alpha$ Distances to the Leading Arm of the Magellanic Stream
  The Leading Arm is a tidal feature that is in front of the Magellanic Clouds
on their orbit through the Galaxy's halo. Many physical properties of the
Leading Arm, such as its mass and size, are poorly constrained because it has
few distance measurements. While H$\alpha$ measurements have been used to
estimate the distances to halo clouds, many studies have been unsuccessful in
detecting H$\alpha$ from the Leading Arm. In this study, we explore a group of
H I clouds which lie $75^{\circ} - 90^{\circ}$ from the Magellanic Clouds.
Through ultraviolet and 21-cm radio spectroscopy, this region, dubbed the
Leading Arm Extension, was found to have chemical and kinematic similarities to
the Leading Arm. Using the Wisconsin H$\alpha$ Mapper, we detect H$\alpha$
emission in four out of seven of our targets. Assuming that this region is
predominantly photoionized, we use a radiation model that incorporates the
contributions of the Galaxy, Magellanic Clouds, and the extragalactic
background at $\rm z = 0$ to derive a heliocentric distance of
$d_{\odot}\ge13.4~kpc$. We also use this model to rederive H$\alpha$ distances
of $d_{\odot} \geq 5.0$ kpc and $d_{\odot} \geq 22.9~kpc$ to two clouds in the
literature that might also be associated with the Leading Arm. Using these new
measurements, and others in the literature, we provide a general trend of the
variation of Leading Arm heliocentric distance as a function of Magellanic
Stream longitude, and explore its implications for the origin and closest point
of approach of the Leading Arm.
