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Register a new userDark halo response and the stellar initial mass function in early-type and late-type galaxies
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Aaron A. Dutton
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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.
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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 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.
We present an empirical method to measure the halo mass function (HMF) of galaxies. We determine the relation between the hi line-width from single-dish observations and the dark matter halo mass ($M_{200}$) inferred from rotation curve fits in the SPARC database, then we apply this relation to galaxies from the hi Parkes All Sky Survey (HIPASS) to derive the HMF. This empirical HMF is well fit by a Schecther function, and matches that expected in $Lambda$CDM over the range $10^{10.5} < M_{200} < 10^{12};mathrm{M}_{odot}$. More massive halos must be poor in neutral gas to maintain consistency with the power law predicted by $Lambda$CDM. We detect no discrepancy at low masses. The lowest halo mass probed by HIPASS, however, is just greater than the mass scale where the Local Group missing satellite problem sets in. The integrated mass density associated with the dark matter halos of hi-detected galaxies sums to $Omega_{rm m,gal} approx 0.03$ over the probed mass range.
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.
We extend our initial study of the connection between the UV colour of galaxies and both the inferred stellar mass-to-light ratio, $Upsilon_*$, and a mass-to-light ratio referenced to Salpeter initial mass function (IMF) models of the same age and metallicity, $Upsilon_*/Upsilon_{Sal}$, using new UV magnitude measurements for a much larger sample of early-type galaxies, ETGs, with dynamically determined mass-to-light ratios. We confirm the principal empirical finding of our first study, a strong correlation between the GALEX FUV-NUV colour and $Upsilon_*$. We show that this finding is not the result of spectral distortions limited to a single passband (eg. metallicity-dependent line-blanketing in the NUV band), or of the analysis methodology used to measure $Upsilon_*$, or of the inclusion or exclusion of the correction for stellar population effects as accounted for using $Upsilon_*/Upsilon_{Sal}$. The sense of the correlation is that galaxies with larger $Upsilon_*$, or larger $Upsilon_*/Upsilon_{Sal}$, are bluer in the UV. We conjecture that differences in the low mass end of the stellar initial mass function, IMF, are related to the nature of the extreme horizontal branch stars generally responsible for the UV flux in ETGs. If so, then UV color can be used to identify ETGs with particular IMF properties and to estimate $Upsilon_*$. We also demonstrate that UV colour can be used to decrease the scatter about the Fundamental Plane and Manifold, and to select peculiar galaxies for follow-up with which to further explore the cause of variations in $Upsilon_*$ and UV colour.
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