Modeling Nearly Spherical Pure-bulge Galaxies with a Stellar
  Mass-to-Light Ratio Gradient under the $\Lambda$CDM and MOND Paradigms: I.
  Methodology, Dynamical Stellar Mass, and Fundamental Mass Plane
  We carry out spherical Jeans modeling of nearly round pure-bulge galaxies
selected from the ATLAS$^{\rm 3D}$ sample. Our modeling allows for gradients in
the stellar mass-to-light ratio ($M_\star/L$) through analytic prescriptions
parameterized with a `gradient strength' $K$ introduced to accommodate any
viable gradient. We use a generalized Osipkov-Merritt model for the velocity
dispersion (VD) anisotropy. We produce Monte Carlo sets of models based on the
stellar VD profiles under both the $\Lambda$CDM and MOND paradigms. Here, we
describe the galaxy data, the empirical inputs, and the modeling procedures of
obtaining the Monte Carlo sets. We then present the projected dynamical stellar
mass, $M_{\rm \star e}$, within the effective radius $R_{\rm e}$, and the
fundamental mass plane (FMP) as a function of $K$. We find the scaling of the
$K$-dependent mass with respect to the ATLAS$^{\rm 3D}$ reported mass as:
$\log_{10} \left[M_{\star{\rm e}}(K)/M_{\star{\rm e}}^{\rm A3D} \right] = a' +
b' K$ with $a'=-0.019\pm 0.012$ and $b'=-0.18\pm 0.02$ ($\Lambda$CDM), or
$a'=-0.023\pm 0.014$ and $b'=-0.23\pm 0.03$ (MOND), for $0\le K < 1.5$. The FMP
has coefficients consistent with the virial expectation and only the zero-point
scales with $K$. The median value of $K$ for the ATLAS$^{\rm 3D}$ galaxies is
$\langle K\rangle =0.53^{+0.05}_{-0.04}$. We perform a similar analysis of the
much larger SDSS DR7 spectroscopic sample. In this case, only the VD within a
single aperture is available, so we impose the additional requirement that the
VD slope be similar to that in the ATLAS$^{\rm 3D}$ galaxies. Our analysis of
the SDSS galaxies suggests a positive correlation of $K$ with stellar mass.
