No Arabic abstract
We study the behaviour of the dynamical and stellar mass inside the effective radius (re) of early-type galaxies (ETGs). We use several samples of ETGs -ranging from 19 000 to 98 000 objects- from the ninth data release of the Sloan Digital Sky Survey. We consider Newtonian dynamics, different light profiles and different Initial Mass Functions (IMF) to calculate the dynamical and stellar mass. We assume that any difference between these two masses is due to dark matter and/or a non Universal IMF. The main results for galaxies in the redshift range 0.0024 < z < 0.3500 and in the dynamical mass range 9.5 < log(M) < 12.5 are: i) A significant part of the intrinsic dispersion of the distribution of dynamical vs. stellar mass is due to redshift. ii) The difference between dynamical and stellar mass increases as a function of dynamical mass and decreases as a function of redshift. iii) The difference between dynamical and stellar mass goes from approximately 0% to 70% of the dynamical mass depending on mass and redshift. iv) These differences could be due to dark matter or a non Universal IMF or a combination of both. v) The amount of dark matter inside ETGs would be equal to or less than the difference between dynamical and stellar mass depending on the impact of the IMF on the stellar mass estimation. vi) The previous results go in the same direction of some results of the Fundamental Plane (FP) found in the literature in the sense that they could be interpreted as an increase of dark matter along the FP and a dependence of the FP on redshift.
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.
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.
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.
The dramatic size evolution of early-type galaxies from z ~ 2 to 0 poses a new challenge in the theory of galaxy formation, which may not be explained by the standard picture. It is shown here that the size evolution can be explained if the non-baryonic cold dark matter is composed of compact objects having a mass scale of ~10^5 M_sun. This form of dark matter is consistent with or only weakly constrained by the currently available observations. The kinetic energy of the dark compact objects is transferred to stars by dynamical friction, and stars around the effective radius are pushed out to larger radii, resulting in a pure size evolution. This scenario has several good properties to explain the observations, including the ubiquitous nature of size evolution and faster disappearance of higher density galaxies.
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.