The SWELLS survey - V. A Salpeter stellar initial mass function in the bulges of massive spiral galaxies

Recent work has suggested that the stellar initial mass function (IMF) is not universal, but rather is correlated with galaxy stellar mass, stellar velocity dispersion, or morphological type. In this paper, we investigate variations of the IMF within individual galaxies. For this purpose, we use strong lensing and gas kinematics to measure independently the normalisation of the IMF of the bulge and disk components of a sample of 5 massive spiral galaxies with substantial bulge components taken from the SWELLS survey. We find that the stellar mass of the bulges are tightly constrained by the lensing and kinematic data. A comparison with masses based on stellar population synthesis models fitted to optical and near infrared photometry favors a Salpeter-like normalisation of the IMF. Conversely, the disk masses are less well constrained due to degeneracies with the dark matter halo, but are consistent with Milky Way type IMFs in agreement with previous studies. The disks are submaximal at 2.2 disk scale lengths, but due to the contribution of the bulges, the galaxies are baryon dominated at 2.2 disk scale lengths. Globally, our inferred IMF normalisation is consistent with that found for early-type galaxies of comparable stellar mass (> 10^11 M_sun). Our results suggest a non-universal IMF within the different components of spiral galaxies, adding to the well-known differences in stellar populations between disks and bulges.

Universal IMF vs dark halo response in early-type galaxies: breaking the degeneracy with the fundamental plane

We use the relations between aperture stellar velocity dispersion (sigma_ap), stellar mass (M_sps), and galaxy size (R_e) for a sample of sim 150,000 early-type galaxies from SDSS/DR7 to place constraints on the stellar initial mass function (IMF) and dark halo response to galaxy formation. We build LCDM based mass models that reproduce, by construction, the relations between galaxy size, light concentration and stellar mass, and use the spherical Jeans equations to predict sigma_ap. Given our model assumptions (including those in the stellar population synthesis models), we find that reproducing the median sigma_ap vs M_sps relation is not possible with {it both} a universal IMF and a universal dark halo response. Significant departures from a universal IMF and/or dark halo response are required, but there is a degeneracy between these two solutions. We show that this degeneracy can be broken using the strength of the correlation between residuals of the velocity-mass (Delta log sigma_ap) and size-mass (Delta log R_e) relations. The slope of this correlation, d_vr equiv Delta log sigma_ap/Delta log R_e, varies systematically with galaxy mass from d_vr simeq -0.45 at M_sps sim 10^{10}M_sun, to d_vr simeq -0.15 at M_sps sim 10^{11.6} M_sun. The virial fundamental plane (FP) has d_vr=-1/2, and thus we find the tilt of the observed FP is mass dependent. Reproducing this tilt requires {it both} a non-universal IMF and a non-universal halo response. Our best model has mass-follows-light at low masses (Msps < 10^{11.2}M_sun) and unmodified NFW haloes at M_sps sim 10^{11.5} M_sun. The stellar masses imply a mass dependent IMF which is lighter than Salpeter at low masses and heavier than Salpeter at high masses.

The SWELLS survey. II. Breaking the disk-halo degeneracy in the spiral galaxy gravitational lens SDSS J2141-0001

The degeneracy among the disk, bulge and halo contributions to galaxy rotation curves prevents an understanding of the distribution of baryons and dark matter in disk galaxies. In an attempt to break this degeneracy, we present an analysis of the spiral galaxy strong gravitational lens SDSS J2141-0001, discovered as part of the SLACS survey. We present new Hubble Space Telescope multicolor imaging, gas and stellar kinematics data derived from long-slit spectroscopy, and K-band LGS adaptive optics imaging, both from the Keck telescopes. We model the galaxy as a sum of concentric axisymmetric bulge, disk and halo components and infer the contribution of each component, using information from gravitational lensing and gas kinematics. This analysis yields a best-fitting total (disk plus bulge) stellar mass of log_{10}(Mstar/Msun) = 10.99(+0.11,-0.25). The photometric data combined with stellar population synthesis models yield log_{10}(Mstar/Msun) = 10.97pm0.07, and 11.21pm0.07 for the Chabrier and Salpeter IMFs, respectively. Accounting for the expected gas fraction of simeq 20% reduces the lensing plus kinematics stellar mass by 0.10pm0.05 dex, resulting in a Bayes factor of 11.9 in favor of a Chabrier IMF. The dark matter halo is roughly spherical, with minor to major axis ratio q_{halo}=0.91(+0.15,-0.13). The dark matter halo has a maximum circular velocity of V_{max}=276(+17,-18) km/s, and a central density parameter of log_{10}Delta_{V/2}=5.9(+0.9,-0.5). This is higher than predicted for uncontracted dark matter haloes in LCDM cosmologies, log_{10}Delta_{V/2}=5.2, suggesting that either the halo has contracted in response to galaxy formation, or that the halo has a higher than average concentration. At 2.2 disk scale lengths the dark matter fraction is f_{DM}=0.55(+0.20,-0.15), suggesting that SDSS J2141-0001 is sub-maximal.

Dark halo response and the stellar initial mass function in early-type and late-type galaxies

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.

On the Evolution of the Velocity-Mass-Size Relations of Disk-Dominated Galaxies over the Past 10 Billion Years

We study the evolution of the scaling relations between maximum circular velocity, stellar mass and optical half-light radius of star-forming disk-dominated galaxies in the context of LCDM-based galaxy formation models. Using data from the literature combined with new data from the DEEP2 and AEGIS surveys we show that there is a consistent observational and theoretical picture for the evolution of these scaling relations from zsim 2 to z=0. The evolution of the observed stellar scaling relations is weaker than that of the virial scaling relations of dark matter haloes, which can be reproduced, both qualitatively and quantitatively, with a simple, cosmologically-motivated model for disk evolution inside growing NFW dark matter haloes. In this model optical half-light radii are smaller, both at fixed stellar mass and maximum circular velocity, at higher redshifts. This model also predicts that the scaling relations between baryonic quantities evolve even more weakly than the corresponding stellar relations. We emphasize, though, that this weak evolution does not imply that individual galaxies evolve weakly. On the contrary, individual galaxies grow strongly in mass, size and velocity, but in such a way that they move largely along the scaling relations. Finally, recent observations have claimed surprisingly large sizes for a number of star-forming disk galaxies at z sim 2, which has caused some authors to suggest that high redshift disk galaxies have abnormally high spin parameters. However, we argue that the disk scale lengths in question have been systematically overestimated by a factor sim 2, and that there is an offset of a factor sim 1.4 between Halpha sizes and optical sizes. Taking these effects into account, there is no indication that star forming galaxies at high redshifts (zsim 2) have abnormally high spin parameters.

The Kinematic Connection Between Galaxies and Dark Matter Haloes

Using estimates of dark halo masses from satellite kinematics, weak gravitational lensing, and halo abundance matching, combined with the Tully-Fisher and Faber-Jackson relations, we derive the mean relation between the optical, V_opt, and virial, V_200, circular velocities of early- and late-type galaxies at redshift z~0. For late-type galaxies V_opt ~ V_200 over the velocity range V_opt=90-260 km/s, and is consistent with V_opt = V_maxh (the maximum circular velocity of NFW dark matter haloes in the concordance LCDM cosmology). However, for early-type galaxies V_opt e V_200, with the exception of early-type galaxies with V_opt simeq 350 km/s. This is inconsistent with early-type galaxies being, in general, globally isothermal. For low mass (V_opt < 250 km/s) early-types V_opt > V_maxh, indicating that baryons have modified the potential well, while high mass (V_opt > 400 km/s) early-types have V_opt < V_maxh. Folding in measurements of the black hole mass - velocity dispersion relation, our results imply that the supermassive black hole - halo mass relation has a logarithmic slope which varies from ~1.4 at halo masses of ~10^{12} Msun/h to ~0.65 at halo masses of 10^{13.5} Msun/h. The values of V_opt/V_200 we infer for the Milky Way and M31 are lower than the values currently favored by direct observations and dynamical models. This offset is due to the fact that the Milky Way and M31 have higher V_opt and lower V_200 compared to typical late-type galaxies of the same stellar masses. We show that current high resolution cosmological hydrodynamical simulations are unable to form galaxies which simultaneously reproduce both the V_opt/V_200 ratio and the V_opt-M_star (Tully-Fisher/Faber-Jackson) relation.

Confronting Scaling Relations of Spiral Galaxies with Hierarchical Models of Disk Formation

The scaling relations between rotation velocity, size and luminosity form a benchmark test for any theory of disk galaxy formation. We confront recent theoretical models of disk formation to a recent large compilation of such scaling relations. We stress the importance of achieving a fair comparison between models and observations.