Mixed Correlation Functions of the Two-Matrix Model

We compute the correlation functions mixing the powers of two non-commuting random matrices within the same trace. The angular part of the integration was partially known in the literature: we pursue the calculation and carry out the eigenvalue integration reducing the problem to the construction of the associated biorthogonal polynomials. The generating function of these correlations becomes then a determinant involving the recursion coefficients of the biorthogonal polynomials.Comment: 16 page

The Supernova Impostor Impostor SN 1961V: Spitzer Shows That Zwicky Was Right (Again)

SN 1961V, one of Zwicky's defining Type V supernovae (SN), was a peculiar transient in NGC 1058 that has variously been categorized as either a true core collapse SN leaving a black hole (BH) or neutron star (NS) remnant, or an eruption of a luminous blue variable (LBV) star. The former case is suggested by its association with a decaying non-thermal radio source, while the latter is suggested by its peculiar transient light curve and its low initial expansion velocities. The crucial difference is that the star survives a transient eruption but not an SN. All stars identified as possible survivors are significantly fainter, L_opt ~ 10^5 Lsun, than the L_opt ~ 3 10^6 Lsun progenitor star at optical wavelengths. While this can be explained by dust absorption in a shell of material ejected during the transient, the survivor must then be present as a L_IR ~ 3 10^6 Lsun mid-infrared source. Using archival Spitzer observations of the region, we show that such a luminous mid-IR source is not present. The brightest source of dust emission is only L_IR ~ 10^5 Lsun and does not correspond to the previously identified candidates for the surviving star. The dust cannot be made sufficiently distant and cold to avoid detection unless the ejection energy, mass and velocity scales are those of a SN or greater. We conclude that SN 1961V was a peculiar, but real, supernova. Its peculiarities are probably due to enhanced mass loss just prior to the SN, followed by the interactions of the SN blast wave with this ejecta. This adds to the evidence that there is a population of SN progenitors that have major mass loss episodes shortly before core collapse. The progenitor is a low metallicity, ~1/3 solar, high mass, M_ZAMS > 80 Msun, star, which means either that BH formation can be accompanied by an SN or that surprisingly high mass stars can form a NS.Comment: 26 pages, 7 figures, submitted to Ap

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

Mixed correlation function and spectral curve for the 2-matrix model

We compute the mixed correlation function in a way which involves only the orthogonal polynomials with degrees close to $n$, (in some sense like the Christoffel Darboux theorem for non-mixed correlation functions). We also derive new representations for the differential systems satisfied by the biorthogonal polynomials, and we find new formulae for the spectral curve. In particular we prove the conjecture of M. Bertola, claiming that the spectral curve is the same curve which appears in the loop equations.Comment: latex, 1 figure, 55 page

Price, Wage and Employment Response to Shocks: Evidence from the WDN Survey

This paper analyses information from survey data collected in the framework of the Eurosystem's Wage Dynamics Network (WDN) on patterns of firm-level adjustment to shocks. We document that the relative intensity and the character of price vs. cost and wage vs. employment adjustments in response to cost-push shocks depend - in theoretically sensible ways - on the intensity of competition in firms' product markets, on the importance of collective wage bargaining and on other structural and institutional features of firms and of their environment. Focusing on the pass-through of cost shocks to prices, our results suggest that the pass-through is lower in highly competitive firms. Furthermore, a high degree of employment protection and collective wage agreements tend to make this pass-through stronger.Wage bargaining, Labour-market institutions, Survey data, European Union.

The Circumnuclear Ring of Ionized Gas in NGC3593

We present the results of narrow-band Halpha+NII imaging of the early-type spiral NGC3593 in combination with a study of the flux radial profiles of the NII (lambda: 654.80, 658.34 nm), Halpha, and SII (lambda: 671.65, 673.08 nm) emission lines along its major axis. The galaxy is known to contain two counterrotating stellar discs of different size and luminosity. We find that the Halpha emission mainly derives from a small central region of 57 arcsec x 25 arcsec. It consists of a filamentary pattern with a central ring. This has a diameter of about 17 arcsec (~ 0.6/h kpc) and it contributes about half of the total Halpha flux. The ring is interpreted as the result of the interaction between the acquired retrograde gas which later formed the smaller counterrotating stellar disc and the pre-existing prograde gas of the galaxy.Comment: Accepted for pubblication in Astronomy and Astrophysics; one latex file (corsini.tex), and 2 encapsulated postscript figures (corsini_fig1.ps,corsini_fig2.ps). To be compiled with aa.cls latex2e macro style (pslatex option): 6 pages after latex compilatio

Loop equations for the semiclassical 2-matrix model with hard edges

The 2-matrix models can be defined in a setting more general than polynomial potentials, namely, the semiclassical matrix model. In this case, the potentials are such that their derivatives are rational functions, and the integration paths for eigenvalues are arbitrary homology classes of paths for which the integral is convergent. This choice includes in particular the case where the integration path has fixed endpoints, called hard edges. The hard edges induce boundary contributions in the loop equations. The purpose of this article is to give the loop equations in that semicassical setting.Comment: Latex, 20 page

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

The bulge-disk orthogonal decoupling in galaxies: NGC 4698 and NGC 4672

We report the case of the geometrical and kinematical decoupling between the bulge and the disk of the Sa galaxy NGC 4698. The R-band isophotal map of this spiral shows that the bulge structure is elongated perpendicularly to the major axis of the disk. At the same time a central stellar velocity gradient is found along the major axis of the bulge. We also present the Sa NGC 4672 as good candidate of a spiral hosting a bulge and a disk orthogonally decoupled with respect to one other. This decoupling of the two fundamental components of a visible galaxy suggests that the disk could represent a second event in the history of early-type spirals.Comment: 4 pages, 3 figures (LaTeX, cupconf.sty). To appear in "The Formation of Bulges" C. M. Carollo, H. C. Ferguson, R. F. G. Wyse (eds.), Cambridge University Pres