The half mass radius of MaNGA galaxies: Effect of IMF gradients

Gradients in the stellar populations (SP) of galaxies -- e.g., in age, metallicity, stellar Initial Mass Function (IMF) -- can result in gradients in the stellar mass to light ratio, $M_*/L$. Such gradients imply that the distribution of the stellar mass and light are different. For old SPs, e.g., in early-type galaxies at $z\sim 0$, the $M_*/L$ gradients are weak if driven by variations in age and metallicity, but significantly larger if driven by the IMF. A gradient which has larger $M_*/L$ in the center increases the estimated total stellar mass ($M_*$) and reduces the scale which contains half this mass ($R_{e,*}$), compared to when the gradient is ignored. For the IMF gradients inferred from fitting MILES simple SP models to the H$_\beta$, $\langle$Fe$\rangle$, [MgFe] and TiO$_{\rm 2SDSS}$ absorption lines measured in spatially resolved spectra of early-type galaxies in the MaNGA survey, the fractional change in $R_{e,*}$ can be significantly larger than that in $M_*$, especially when the light is more centrally concentrated. The $R_{e,*}-M_*$ correlation which results is offset by 0.3 dex to smaller sizes compared to when these gradients are ignored. Comparisons with `quiescent' galaxies at higher-$z$ must account for evolution in SP gradients (especially age and IMF) and the light profile before drawing conclusions about how $R_{e,*}$ and $M_*$ evolve. The implied merging between higher-$z$ and the present is less contrived if $R_{e,*}/R_e$ at $z\sim 0$ is closer to our IMF-driven gradient calibration than to unity.