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Register a new user$M_*/L$ gradients driven by IMF variation: Large impact on dynamical stellar mass estimates
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Mariangela Bernardi
Publication date
2017
fields
Physics
and research's language is
English
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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.
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Spatially resolved kinematics of nearby galaxies has shown that the ratio of dynamical- to stellar population-based estimates of the mass of a galaxy ($M_*^{rm JAM}/M_*$) correlates with $sigma_e$, if $M_*$ is estimated using the same IMF for all galaxies and the stellar M/L ratio within each galaxy is constant. This correlation may indicate that, in fact, the IMF is more dwarf-rich for galaxies with large $sigma$. We use this correlation to estimate a dynamical or IMF-corrected stellar mass, $M_*^{rm alpha_{JAM}}$, from $M_{*}$ and $sigma_e$ for a sample of $6 times 10^5$ SDSS galaxies for which spatially resolved kinematics is not available. We also compute the `virial mass estimate $k(n,R),R_e,sigma_R^2/G$, where $n$ is the Sersic index, in the SDSS and ATLAS$^{rm 3D}$ samples. We show that an $n$-dependent correction must be applied to the $k(n,R)$ values provided by Prugniel & Simien (1997). Our analysis also shows that the shape of the velocity dispersion profile in the ATLAS$^{rm 3D}$ sample varies weakly with $n$: $(sigma_R/sigma_e) = (R/R_e)^{-gamma(n)}$. The resulting stellar mass functions, based on $M_*^{rm alpha_{JAM}}$ and the recalibrated virial mass, are in good agreement. If the $M_*^{rm alpha_{JAM}}/M_* - sigma_e$ correlation is indeed due to the IMF, and stellar M/L gradients can be ignored, then our $phi(M_*^{rm alpha_{JAM}})$ is an estimate of the stellar mass function in which $sigma_e$-dependent variations in the IMF across the population have been accounted for. Using a Fundamental Plane based observational proxy for $sigma_e$ produces comparable results. By demonstrating that cheaper proxies are sufficiently accurate, our analysis should enable a more reliable census of the mass in stars for large galaxy samples, at a fraction of the cost. Our results are provided in tabular form.
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We investigate the evolution of stellar population gradients from $z=2$ to $z=0$ in massive galaxies at large radii ($r > 2R_{mathrm{eff}}$) using ten cosmological zoom simulations of halos with $6 times 10^{12} M_{odot} < M_{mathrm{halo}} < 2 times 10^{13}M_{odot}$. The simulations follow metal cooling and enrichment from SNII, SNIa and AGB winds. We explore the differential impact of an empirical model for galactic winds that reproduces the mass-metallicity relation and its evolution with redshift. At larger radii the galaxies, for both models, become more dominated by stars accreted from satellite galaxies in major and minor mergers. In the wind model, fewer stars are accreted, but they are significantly more metal poor resulting in steep global metallicity ($langle abla Z_{mathrm{stars}} rangle= -0.35$ dex/dex) and color (e.g. $langle abla g-r rangle = -0.13$ dex/dex) gradients in agreement with observations. In contrast, colour and metallicity gradients of the models without winds are inconsistent with observations. Age gradients are in general mildly positive at $z=0$ ($langle abla Age_{mathrm{stars}} rangle= 0.04$ dex/dex) with significant differences between the models at higher redshift. We demonstrate that for the wind model, stellar accretion is steepening existing in-situ metallicity gradients by about 0.2 dex by the present day and helps to match observed gradients of massive early-type galaxies at large radii. Colour and metallicity gradients are significantly steeper for systems which have accreted stars in minor mergers, while galaxies with major mergers have relatively flat gradients, confirming previous results. This study highlights the importance of stellar accretion for stellar population properties of massive galaxies at large radii, which can provide important constraints for formation models.
Mass-to-light versus colour relations (MLCRs), derived from stellar population synthesis models, are widely used to estimate galaxy stellar masses (M$_*$) yet a detailed investigation of their inherent biases and limitations is still lacking. We quantify several potential sources of uncertainty, using optical and near-infrared (NIR) photometry for a representative sample of nearby galaxies from the Virgo cluster. Our method for combining multi-band photometry with MLCRs yields robust stellar masses, while errors in M$_*$ decrease as more bands are simultaneously considered. The prior assumptions in ones stellar population modelling dominate the error budget, creating a colour-dependent bias of up to 0.6 dex if NIR fluxes are used (0.3 dex otherwise). This matches the systematic errors associated with the method of spectral energy distribution (SED) fitting, indicating that MLCRs do not suffer from much additional bias. Moreover, MLCRs and SED fitting yield similar degrees of random error ($sim$0.1-0.14 dex) when applied to mock galaxies and, on average, equivalent masses for real galaxies with M$_* sim$ 10$^{8-11}$ M$_{odot}$. The use of integrated photometry introduces additional uncertainty in M$_*$ measurements, at the level of 0.05-0.07 dex. We argue that using MLCRs, instead of time-consuming SED fits, is justified in cases with complex model parameter spaces (involving, for instance, multi-parameter star formation histories) and/or for large datasets. Spatially-resolved methods for measuring M$_*$ should be applied for small sample sizes and/or when accuracies less than 0.1 dex are required. An Appendix provides our MLCR transformations for ten colour permutations of the $grizH$ filter set.
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