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.
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