The Cauchy two-matrix model

We introduce a new class of two(multi)-matrix models of positive Hermitean matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The correlation functions are expressed entirely in terms of certain biorthogonal polynomials and solutions of appropriate Riemann-Hilbert problems, thus paving the way to a steepest descent analysis and universality results. The interpretation of the formal expansion of the partition function in terms of multicolored ribbon-graphs is provided and a connection to the O(1) model. A steepest descent analysis of the partition function reveals that the model is related to a trigonal curve (three-sheeted covering of the plane) much in the same way as the Hermitean matrix model is related to a hyperelliptic curve.Comment: 34 pages, 2 figures. V2: changes only to metadat

The Orthogonal Gaseous Kinematical Decoupling in the Sa Spiral NGC 2855

We present major and minor-axis kinematics of stars and ionized gas as well as narrow and broad-band surface photometry of the Sa spiral NGC 2855. In the nuclear regions of this unbarred and apparently undisturbed spiral galaxy the gas is rotating perpendicularly to the galaxy disk. We suggest that this kinematically-decoupled component is the signature of an acquisition process in the history of this galaxy.Comment: 7 pages, 4 PostScript figures. Accepted for pubblication in A&A. Figs. 1 and 3 at lower resolution. Data tables will be available at CD

Polar bulges and polar nuclear discs: the case of NGC 4698

The early-type spiral NGC 4698 is known to host a nuclear disc of gas and stars which is rotating perpendicularly with respect to the galaxy main disc. In addition, the bulge and main disc are characterised by a remarkable geometrical decoupling. Indeed they appear elongated orthogonally to each other. In this work the complex structure of the galaxy is investigated by a detailed photometric decomposition of optical and near-infrared images. The intrinsic shape of the bulge was constrained from its apparent ellipticity, its twist angle with respect to the major axis of the main disc, and the inclination of the main disc. The bulge is actually elongated perpendicular to the main disc and it is equally likely to be triaxial or axisymmetric. The central surface brightness, scalelength, inclination, and position angle of the nuclear disc were derived by assuming it is infinitesimally thin and exponential. Its size, orientation, and location do not depend on the observed passband. These findings support a scenario in which the nuclear disc is the end result of the acquisition of external gas by the pre-existing triaxial bulge on the principal plane perpendicular to its shortest axis and perpendicular to the galaxy main disc. The subsequent star formation either occurred homogeneously all over the extension of the nuclear disc or through an inside-out process that ended more than 5 Gyr ago.Comment: 6 pages, 3 figures. Accepted for publication in MNRAS Letter

The V_c-sigma_c relation in high and low surface brightness galaxies

We investigate the relation between the asymptotic circular velocity, V_c, and the central stellar velocity dispersion, sigma_c, in galaxies. We consider a new sample of high surface brightness spiral galaxies (HSB), low surface brightness spiral galaxies (LSB), and elliptical galaxies with HI-based V_c measurements. We find that: 1) elliptical galaxies with HI measurements fit well within the relation; 2) a linear law can reproduce the data as well as a power law (used in previous works) even for galaxies with sigma_c < 70 km/s; 3) LSB galaxies, considered for the first time with this respect, seem to behave differently, showing either larger V_c values or smaller sigma_c values.Comment: 2 pages, 2 figures, to appear in Proc. IAU Symp. 222, "The Interplay among Black Holes, Stars and ISM in Galactic Nuclei" eds. Th. Storchi Bergmann, L.C. Ho & H.R. Schmitt (Cambridge University Press

Ionized gas and stellar kinematics of seventeen nearby spiral galaxies

Ionized gas and stellar kinematics have been measured along the major axes of seventeen nearby spiral galaxies of intermediate to late morphological type. We discuss the properties of each sample galaxy distinguishing between those characterized by regular or peculiar kinematics. In most of the observed galaxies ionized gas rotates more rapidly than stars and have a lower velocity dispersion, as is to be expected if the gas is confined in the disc and supported by rotation while the stars are mostly supported by dynamical pressure. In a few objects, gas and stars show almost the same rotational velocity and low velocity dispersion, suggesting that their motion is dominated by rotation. Incorporating the spiral galaxies studied by Bertola et al. (1996), Corsini et al. (1999, 2003) and Vega Beltran et al. (2001) we have compiled a sample of 50 S0/a-Scd galaxies, for which the major-axis kinematics of the ionized gas and stars have been obtained with the same spatial (~1'') and spectral (~50km/s) resolution, and measured with the same analysis techniques. This allowed us to address the frequency of counterrotation in spiral galaxies. It turns out that less than 12% and less than 8% (at the 95% confidence level) of the sample galaxies host a counterrotating gaseous and stellar disc, respectively. The comparison with S0 galaxies suggests that the retrograde acquisition of small amounts of external gas gives rise to counterrotating gaseous discs only in gas-poor S0s, while in gas-rich spirals the newly acquired gas is swept away by the pre-existing gas. Counterrotating gaseous and stellar discs in spirals are formed only from the retrograde acquisition of large amounts of gas exceeding that of pre-existing gas, and subsequent star formation, respectively.Comment: 14 pages, 33 figures, A&A accepte

Spectra of random Hermitian matrices with a small-rank external source: supercritical and subcritical regimes

Random Hermitian matrices with a source term arise, for instance, in the study of non-intersecting Brownian walkers \cite{Adler:2009a, Daems:2007} and sample covariance matrices \cite{Baik:2005}. We consider the case when the $n\times n$ external source matrix has two distinct real eigenvalues: $a$ with multiplicity $r$ and zero with multiplicity $n-r$. The source is small in the sense that $r$ is finite or $r=\mathcal O(n^\gamma)$, for $0< \gamma<1$. For a Gaussian potential, P\'ech\'e \cite{Peche:2006} showed that for $|a|$ sufficiently small (the subcritical regime) the external source has no leading-order effect on the eigenvalues, while for $|a|$ sufficiently large (the supercritical regime) $r$ eigenvalues exit the bulk of the spectrum and behave as the eigenvalues of $r\times r$ Gaussian unitary ensemble (GUE). We establish the universality of these results for a general class of analytic potentials in the supercritical and subcritical regimes.Comment: 41 pages, 4 figure

Large N expansion of the 2-matrix model

We present a method, based on loop equations, to compute recursively all the terms in the large $N$ topological expansion of the free energy for the 2-hermitian matrix model. We illustrate the method by computing the first subleading term, i.e. the free energy of a statistical physics model on a discretized torus.Comment: 41 pages, 9 figures eps