Stellar mass versus stellar velocity dispersion: which is better for linking galaxies to their dark matter halos?

It was recently suggested that, compared to its stellar mass (M*), the central stellar velocity dispersion (sigma*) of a galaxy might be a better indicator for its host dark matter halo mass. Here we test this hypothesis by estimating the dark matter halo mass for central alaxies in groups as function of M* and sigma*. For this we have estimated the redshift-space cross-correlation function (CCF) between the central galaxies at given M* and sigma* and a reference galaxy sample, from which we determine both the projected CCF, w_p(r_p), and the velocity dispersion profile (VDP) of satellites around the centrals. A halo mass is then obtained from the average velocity dispersion within the virial radius. At fixed M*, we find very weak or no correlation between halo mass and sigma*. In contrast, strong mass dependence is clearly seen even when sigma* is limited to a narrow range. Our results thus firmly demonstrate that the stellar mass of central galaxies is still a good (if not the best) indicator for dark matter halo mass, better than the stellar velocity dispersion. The dependence of galaxy clustering on sigma* fixed M*, as recently discovered by Wake et al. (2012), may be attributed to satellite galaxies, for which the tidal stripping occurring within halos has stronger effect on stellar mass than on central stellar velocity dispersion.Comment: 4 pages, 4 figures, accepted for publication in ApJ Letters, minor revisions in the tex

More on convexity and smoothness of operators

AbstractLet X and Y be Banach spaces and T:Y→X be a bounded operator. In this note, we show first some operator versions of the dual relation between q-convexity and p-smoothness of Banach spaces case. Making use of them, we prove then the main result of this note that the two notions of uniform q-convexity and uniform p-smoothness of an operator T introduced by J. Wenzel are actually equivalent to that the corresponding T-modulus δT of convexity and the T-modulus ρT of smoothness introduced by G. Pisier are of power type q and of power type p, respectively. This is also an operator version of a combination of a Hoffman's theorem and a Figiel–Pisier's theorem. As their application, we show finally that a recent theorem of J. Borwein, A.J. Guirao, P. Hajek and J. Vanderwerff about q-convexity of Banach spaces is again valid for q-convexity of operators

On the galactic spin of barred disk galaxies

We present a study of the connection between the galactic spin parameter $\lambda_{d}$ and the bar fraction in a volume-limited sample of 10,674 disk galaxies drawn from the Sloan Digital Sky Survey Data Release 7. The galaxies in our sample are visually classified into galaxies hosting long or short bars, and non-barred galaxies. We find that the spin distributions of these three classes are statistically different, with galaxies hosting long bars with the lowest $\lambda_{d}$ values, followed by non-barred galaxies, while galaxies with short bars present typically high spin parameters. The bar fraction presents its maximum at low to intermediate $\lambda_{d}$ values for the case of long bars, while the maximum for short bars is at high $\lambda_{d}$. This bi-modality is in good agreement with previous studies finding longer bars hosted by luminous, massive, red galaxies with low content of cold gas, while short bars are found in low luminosity, low mass, blue galaxies, usually gas rich. In addition, the rise and fall of the bar fraction as a function of $\lambda_{d}$, within the long-bar sample, shown in our results, can be explained as a result of two competing factors: the self-gravity of the disk that enhances bar instabilities, and the support by random motions instead of ordered rotational motion, that prevents the formation/growth of bars.Comment: 10 pages, 6 figures,1 table. Accepted for publication in Ap