Surface Photometry of Early-type Galaxies in the Hubble Deep Field

The detailed surface photometry of a sample of early-type galaxies in the Hubble Deep Field is presented as part of a long-term project aimed to settle strong observational constraints to the theories modelling the evolution of elliptical galaxies from the early stages. The sample has been extracted, in the V_606 band, from the catalog by Couch (1996). The analysis of the luminosity and geometrical profiles, carried out on 162 candidates obeying our provisional selection criteria, resulted in a list of 99 'bona fide' early-type galaxies, for which accurate total magnitudes and effective radii were computed. The comparison with the magnitudes given by Williams et al.(1996) indicates that the automated photometry tends to underestimate the total luminosity of the ellipticals. The luminosity profiles of most of galaxies in our sample follow fairly well the deVaucouleurs law (`Normal' profiles). However, a relevant fraction of galaxies, even following the deVaucouleurs law in the main body light distribution, exhibit in the inner region a flattening of the luminosity profile not attributable to the PSF (`Flat' profiles) or, in some cases, a complex (multi-nucleus) structure (`Merger' profiles). The average ellipticity of galaxies belonging to the `Flat' and `Merger' classes is found to be significantly higher than that of the `Normal' galaxies. Moreover, even taken into account the relevant uncertainty of the outer position angle profiles, the amount of isophotal twisting of HDF ellipticals turns out to be significantly larger with respect to that of the local samples.Comment: 22 pages, LaTeX with laa.sty and psfig.sty macros + 28 embedded postscript figures. To appear in Astronomy and Astrophysics Supp

The dependence on the monodromy data of the isomonodromic tau function

[Note: important Corrigendum now available at arXiv:1601.04790] The isomonodromic tau function defined by Jimbo-Miwa-Ueno vanishes on the Malgrange's divisor of generalized monodromy data for which a vector bundle is nontrivial, or, which is the same, a certain Riemann-Hilbert problem has no solution. In their original work, Jimbo, Miwa, Ueno did not derive the dependence on the (generalized) monodromy data (i.e. monodromy representation and Stokes' parameters). We fill the gap by providing a (simpler and more general) description in which all the parameters of the problem (monodromy-changing and monodromy-preserving) are dealt with at the same level. We thus provide variational formulae for the isomonodromic tau function with respect to the (generalized) monodromy data. The construction applies more generally: given any (sufficiently well-behaved) family of Riemann-Hilbert problems (RHP) where the jump matrices depend arbitrarily on deformation parameters, we can construct a one-form Omega (not necessarily closed) on the deformation space (Malgrange's differential), defined off Malgrange's divisor. We then introduce the notion of discrete Schlesinger transformation: it means that we allow the solution of the RHP to have poles (or zeros) at prescribed point(s). Even if Omega is not closed, its difference evaluated along the original solution and the transformed one, is shown to be the logarithmic differential (on the deformation space) of a function. As a function of the position of the points of the Schlesinger transformation, yields a natural generalization of Sato formula for the Baker-Akhiezer vector even in the absence of a tau function, and it realizes the solution of the RHP as such BA vector. Some exemples (Painleve' II and finite Toplitz/Hankel determinants) are provided.Comment: 34 pages, 7 figures. An important "Corrigendum" is now available as arXiv:1601.0479

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

Moment determinants as isomonodromic tau functions

We consider a wide class of determinants whose entries are moments of the so-called semiclassical functionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for the functionals. This shows that the vanishing of the tau-function for those systems is the obstruction to the solvability of a Riemann-Hilbert problem associated to certain classes of (multiple) orthogonal polynomials. The determinants include Haenkel, Toeplitz and shifted-Toeplitz determinants as well as determinants of bimoment functionals and the determinants arising in the study of multiple orthogonality. Some of these determinants appear also as partition functions of random matrix models, including an instance of a two-matrix model.Comment: 24 page

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