$M_*/L$ gradients driven by IMF variation: Large impact on dynamical stellar mass estimates

Within a galaxy the stellar mass-to-light ratio $\Upsilon_*$ is not constant. Spatially resolved kinematics of nearby early-type galaxies suggest that allowing for a variable initial mass function (IMF) returns significantly larger $\Upsilon_*$ gradients than if the IMF is held fixed. If $\Upsilon_*$ is greater in the central regions, then ignoring the IMF-driven gradient can overestimate $M_*^{\rm dyn}$ by as much as a factor of two for the most massive galaxies, though stellar population estimates $M_*^{\rm SP}$ are also affected. Large $\Upsilon_*$-gradients have four main consequences: First, $M_*^{\rm dyn}$ cannot be estimated independently of stellar population synthesis models. Second, if there is a lower limit to $\Upsilon_*$ and gradients are unknown, then requiring $M_*^{\rm dyn}=M_*^{\rm SP}$ constrains them. Third, if gradients are stronger in more massive galaxies, then $M_*^{\rm dyn}$ and $M_*^{\rm SP}$ can be brought into agreement, not by shifting $M_*^{\rm SP}$ upwards by invoking constant bottom-heavy IMFs, as advocated by a number of recent studies, but by revising $M_*^{\rm dyn}$ estimates in the literature downwards. Fourth, accounting for $\Upsilon_*$ gradients changes the high-mass slope of the stellar mass function $\phi(M_*^{\rm dyn})$, and reduces the associated stellar mass density. These conclusions potentially impact estimates of the need for feedback and adiabatic contraction, so our results highlight the importance of measuring $\Upsilon_*$ gradients in larger samples.