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Register a new userDark Matter Contraction and the Stellar Content of Massive Early-type Galaxies: Disfavoring Light Initial Mass Functions
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M. W. Auger
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We use stellar dynamics, strong lensing, stellar population synthesis models, and weak lensing shear measurements to constrain the dark matter (DM) profile and stellar mass in a sample of 53 massive early-type galaxies. We explore three DM halo models (unperturbed Navarro Frenk & White [NFW] halos and the adiabatic contraction models of Blumenthal and Gnedin) and impose a model for the relationship between the stellar and virial mass (i.e., a relationship for the star-formation efficiency as a function of halo mass). We show that, given our model assumptions, the data clearly prefer a Salpeter-like initial mass function (IMF) over a lighter IMF (e.g., Chabrier or Kroupa), irrespective of the choice of DM halo. In addition, we find that the data prefer at most a moderate amount of adiabatic contraction (Blumenthal adiabatic contraction is strongly disfavored) and are only consistent with no adiabatic contraction (i.e., a NFW halo) if a mass-dependent IMF is assumed, in the sense of a more massive normalization of the IMF for more massive halos.
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We present models for the dark and luminous mass structure of 12 strong lensing early-type galaxies (ETGs). We combine pixel-based modelling of multiband HST/ACS imaging with Jeans modelling of kinematics obtained from Keck/ESI spectra to disentangle the dark and luminous contributions to the mass. Assuming a gNFW profile for the dark matter halo and a spatially constant stellar-mass-to-light ratio $Upsilon_{star}$ for the baryonic mass, we infer distributions for $Upsilon_{star}$ consistent with IMFs that are heavier than the Milky Ways (with a global mean mismatch parameter relative to a Chabrier IMF $mu_{alpha c} = 1.80 pm 0.14$) and halo inner density slopes which span a large range but are generally cuspier than the dark-matter-only prediction ($mu_{gamma} = 2.01_{-0.22}^{+0.19}$). We investigate possible reasons for overestimating the halo slope, including the neglect of spatially varying stellar-mas-to-light ratios and/or stellar orbital anisotropy, and find that a quarter of the systems prefer radially declining stellar-mass-to-light ratio gradients, but that the overall effect on our inference on the halo slope is small. We suggest a coherent explanation of these results in the context of inside-out galaxy growth, and that the relative importance of different baryonic processes in shaping the dark halo may depend on halo environment.
The distribution of the radial trends of the mass-to-light ratios (M/L) within an assorted sample of early-type galaxies is discussed. Three classes of galaxies are identified according to their M/L gradients. Two such classes are characterized by the presence or by the absence of a radial gradient of the dark-matter (DM) distribution. A third class contains objects which are likely undergoing interaction; they exhibit steep M/L gradients which are possibly the result of a wrong assumption on their equilibrium conditions. Finally, a possible correlation between DM content and morphological types is briefly discussed.
We investigate the origin of the relations between stellar mass and optical circular velocity for early-type (ETG) and late-type (LTG) galaxies --- the Faber-Jackson (FJ) and Tully-Fisher (TF) relations. We combine measurements of dark halo masses (from satellite kinematics and weak lensing), and the distribution of baryons in galaxies (from a new compilation of galaxy scaling relations), with constraints on dark halo structure from cosmological simulations. The principle unknowns are the halo response to galaxy formation and the stellar initial mass function (IMF). The slopes of the TF and FJ relations are naturally reproduced for a wide range of halo response and IMFs. However, models with a universal IMF and universal halo response cannot simultaneously reproduce the zero points of both the TF and FJ relations. For a model with a universal Chabrier IMF, LTGs require halo expansion, while ETGs require halo contraction. A Salpeter IMF is permitted for high mass (sigma > 180 km/s) ETGs, but is inconsistent for intermediate masses, unless V_circ(R_e)/sigma_e > 1.6. If the IMF is universal and close to Chabrier, we speculate that the presence of a major merger may be responsible for the contraction in ETGs while clumpy accreting streams and/or feedback leads to expansion in LTGs. Alternatively, a recently proposed variation in the IMF disfavors halo contraction in both types of galaxies. Finally we show that our models naturally reproduce flat and featureless circular velocity profiles within the optical regions of galaxies without fine-tuning.
Dynamical studies of local ETGs and the Fundamental Plane point to a strong dependence of M/L ratio on luminosity (and stellar mass) with a relation of the form $M/L propto L^{gamma}$. The tilt $gamma$ may be caused by various factors, including stellar population properties, IMF, rotational support, luminosity profile non-homology and dark matter (DM) fraction. We evaluate the impact of all these factors using a large uniform dataset of local ETGs from Prugniel & Simien (1997). We take particular care in estimating the stellar masses, using a general star formation history, and comparing different population synthesis models. We find that the stellar M/L contributes little to the tilt. We estimate the total M/L using simple Jeans dynamical models, and find that adopting accurate luminosity profiles is important but does not remove the need for an additional tilt component, which we ascribe to DM. We survey trends of the DM fraction within one effective radius, finding it to be roughly constant for galaxies fainter than $M_B sim -20.5$, and increasing with luminosity for the brighter galaxies; we detect no significant differences among S0s and fast- and slow-rotating ellipticals. We construct simplified cosmological mass models and find general consistency, where the DM transition point is caused by a change in the relation between luminosity and effective radius. A more refined model with varying galaxy star formation efficiency suggests a transition from total mass profiles (including DM) of faint galaxies distributed similarly to the light, to near-isothermal profiles for the bright galaxies. These conclusions are sensitive to various systematic uncertainties which we investigate in detail, but are consistent with the results of dynamics studies at larger radii.
We determine an absolute calibration of the initial mass function (IMF) of early-type galaxies, by studying a sample of 56 gravitational lenses identified by the SLACS Survey. Under the assumption of standard Navarro, Frenk & White dark matter halos, a combination of lensing, dynamical, and stellar population synthesis models is used to disentangle the stellar and dark matter contribution for each lens. We define an IMF mismatch parameter alpha=M*(L+D)/M*(SPS) as the ratio of stellar mass inferred by a joint lensing and dynamical models (M*(L+D)) to the current stellar mass inferred from stellar populations synthesis models (M*(SPS)). We find that a Salpeter IMF provides stellar masses in agreement with those inferred by lensing and dynamical models (<log alpha>=0.00+-0.03+-0.02), while a Chabrier IMF underestimates them (<log alpha>=0.25+-0.03+-0.02). A tentative trend is found, in the sense that alpha appears to increase with galaxy velocity dispersion. Taken at face value, this result would imply a non universal IMF, perhaps dependent on metallicity, age, or abundance ratios of the stellar populations. Alternatively, the observed trend may imply non-universal dark matter halos with inner density slope increasing with velocity dispersion. While the degeneracy between the two interpretations cannot be broken without additional information, the data imply that massive early-type galaxies cannot have both a universal IMF and universal dark matter halos.
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