  The Spitzer Space Telescope has identified a population of ultra-luminous
infrared galaxies (ULIRGs) at z ~ 2 that may play an important role in the
evolution of massive galaxies. We measure the stellar masses of two populations
of Spitzer-selected ULIRGs, both of which have extremely red R-[24] colors
(dust-obscured galaxies, or DOGs) and compare our results with sub-millimeter
selected galaxies (SMGs). One set of 39 DOGs has a local maximum in their
mid-IR spectral energy distribution (SED) at rest-frame 1.6um associated with
stellar emission ("bump DOGs"), while the other set of 51 DOGs has a power-law
dominated mid-IR SED with spectral features typical of obscured AGN ("power-law
DOGs"). We use stellar population synthesis models applied self-consistently to
broad-band photometry in the rest-frame ultra-violet, optical, and
near-infrared of each of these populations and test a variety of stellar
population synthesis codes, star-formation histories (SFHs), and initial mass
functions (IMFs). Assuming a simple stellar population SFH and a Chabrier IMF,
we find that the median and inner quartile stellar masses of SMGs, bump DOGs
and power-law DOGs are given by log(M_*/M_sun) = 10.42_-0.36^+0.42,
10.62_-0.32^+0.36, and 10.71_-0.34^+0.40, respectively. Implementing more
complicated SFHs with multiple age components increases these mass estimates by
up to 0.5 dex. Our stellar mass estimates are consistent with physical
mechanisms for the origin of z~2 ULIRGs that result in high star-formation
rates for a given stellar mass. Such mechanisms are usually driven by a major
merger of two gas-rich systems, rather than smooth accretion of gas and small
satellites.
