  Gas mass remains one of the most difficult protoplanetary disk properties to
constrain. With much of the protoplanetary disk too cold for the main gas
constituent, H2, to emit, alternative tracers such as dust, CO, or the H2
isotopolog HD are used. However, relying on disk mass measurements from any
single tracer requires assumptions about the tracer's abundance relative to
\hh\ and the disk temperature structure. Using new Atacama Large
Millimeter/submillimeter Array (ALMA) observations from the Molecules with ALMA
at Planet-forming Scales (MAPS) ALMA Large Program as well as archival ALMA
observations, we construct a disk physical/chemical model of the protoplanetary
disk GM Aur. Our model is in good agreement with the spatially resolved CO
isotopolog emission from eleven rotational transitions with spatial resolution
ranging from 0.15'' to 0.46'' (24-73 au at 159 pc) and the spatially unresolved
HD J=1-0 detection from Herschel. Our best-fit model favors a cold
protoplanetary disk with a total gas mass of approximately 0.2 solar masses, a
factor of 10 reduction in CO gas inside roughly 100 au and a factor of 100
reduction outside of 100 au. Despite its large mass, the disk appears to be on
the whole gravitationally stable based on the derived Toomre Q parameter.
However, the region between 70 and 100 au, corresponding to one of the
millimeter dust rings, is close to being unstable based on the calculated
Toomre Q of <1.7. This paper is part of the MAPS special issue of the
Astrophysical Journal Supplement.
