  Using the Pan-STARRS1 survey, we derive limiting magnitude, spatial
completeness and density maps that we use to probe the three dimensional
structure and estimate the stellar mass of the so-called Monoceros Ring. The
Monoceros Ring is an enormous and complex stellar sub-structure in the outer
Milky Way disk. It is most visible across the large Galactic Anticenter region,
120 < l < 240 degrees, -30 < b < +40 degrees. We estimate its stellar mass
density profile along every line of sight in 2 X 2 degree pixels over the
entire 30,000 square degree Pan-STARRS1 survey using the previously developed
MATCH software. By parsing this distribution into a radially smooth component
and the Monoceros Ring, we obtain its mass and distance from the Sun along each
relevant line of sight. The Monoceros Ring is significantly closer to us in the
South (6 kpc) than in the North (9 kpc). We also create 2D cross sections
parallel to the Galactic plane that show 135 degrees of the Monoceros Ring in
the South and 170 degrees of the Monoceros Ring in the North. We show that the
Northern and Southern structures are also roughly concentric circles,
suggesting that they may be a wave rippling from a common origin. Excluding the
Galactic plane, we observe an excess stellar mass of 4 million solar masses
across 120 < l < 240 degrees. If we interpolate across the Galactic plane, we
estimate that this region contains 8 million solar masses. If we assume
(somewhat boldly) that the Monoceros Ring is a set of two Galactocentric rings,
its total stellar mass is 60 million solar masses. Finally, if we assume that
it is a set of two circles centered at a point 4 kpc from the Galactic center
in the anti-central direction, as our data suggests, we estimate its stellar
mass to be 40 million solar masses.
