On the reliability of the black hole mass and mass to light ratio determinations with Schwarzschild models

In this Letter, we investigate the claim of Valluri et al. (2003), namely that the use of Schwarzschild dynamical (orbit-based) models leads to an indeterminacy regarding the estimation of the free parameters like the central black hole mass and the stellar mass-to-light ratio of the galaxy under study. We examine this issue with semi-analytic two-integral models, which are not affected by the intrinsic degeneracy of three-integral systems. We however confirm the Valluri et al. result, and observe the so-called widening of the chi2 contours as the orbit library is expanded. We also show that, although two-dimensional data coverage help in constraining the orbital structure of the modelled galaxy, it does not in principle solve the indeterminacy issue, which mostly originates from the discretization of such an inverse problem. We show that adding regularization constraints stabilizes the confidence level contours on which the estimation of black hole mass and stellar mass-to-light ratio are based. We therefore propose to systematically use regularization as a tool to prevent the solution to depend on the orbit library. Regularization, however, introduces an unavoidable bias on the derived solutions. We hope that the present Letter will trigger some more research directed at a better understanding of the issues addressed here.Comment: 5 pages, 3 figures, accepted for publication in MNRAS Letter

Axisymmetric dynamical models for SAURON and OASIS observations of NGC3377

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Perfiles de gratitud, necesidades psicológicas y su relación con la resiliencia en estudiantes no tradicionales

The aim of this research was to identify gratitude profiles, basic psychological needs in relation with resilience of non-traditional students adults worker. This study was cross-sectional, descriptive, non-experimental in design and a cluster analysis was used. A total 114 students from a local university answered 3 instruments to evaluate these variables. This study reports 4 profiles and showed that only one significantly differs in resilience from the others, featuring high levels of gratitude and psychological needs. Profiles that are underperforming in the variables obtained lower resilience. One of them, equivalent to 10.5% of the students, also reports a lower need for autonomy. This study suggests that interventions must be focused on young students to strengthen their need for autonomy and resilience.El objetivo del estudio fue identificar perfiles de gratitud, necesidades psicológicas básicas y su relación con la resiliencia en estudiantes no tradicionales adultos-trabajadores. Se utilizó un diseño no experimental, transversal, descriptivo y un análisis de clústeres; 114 estudiantes universitarios respondieron tres instrumentos para evaluar las variables. Los resultados muestran 4 perfiles, sólo uno se diferencia significativamente en resiliencia, en ventaja de los otros, presentando altos niveles en gratitud y necesidades psicológicas. Los tres perfiles más desfavorecidos en las variables obtienen menor resiliencia. Uno de ellos, equivalente a un 10,5% de los estudiantes, presenta también baja necesidad de autonomía. Se concluye que las intervenciones deberían estar focalizadas en los estudiantes jóvenes, para fortalecer su necesidad de autonomía y resiliencia

Axisymmetric dynamical models for SAURON and OASIS observations of NGC 3377

We present a unique set of nested stellar kinematical maps of NGC 3377 obtained with the integral-field spectrographs OASIS and SAURON. We then construct general axisymmetric dynamical models for this galaxy, based on the Schwarzschild numerical orbit superposition technique applied to these complementary measurements. We show how these two datasets constrain the mass of the central massive object and the overall mass-to-light ratio of the galaxy by probing the inner and outer regions respectively. The simultaneous use of both datasets leads us to confirm the presence of a massive black hole with a mass of M_{BH} = 7_{-5}^{+4} 10^{7} M_\sun (99.7% confidence level), with a best-fit stellar mass-to-light ratio $\Upsilon_I = 2.1 \pm 0.2$ (for an assumed edge-on inclination).Comment: 15 pages, 14 figures. Accepted for publication in A&A (original fig. layout, letterpaper

Axisymmetric Three-Integral Models for Galaxies

We describe an improved, practical method for constructing galaxy models that match an arbitrary set of observational constraints, without prior assumptions about the phase-space distribution function (DF). Our method is an extension of Schwarzschild's orbit superposition technique. As in Schwarzschild's original implementation, we compute a representative library of orbits in a given potential. We then project each orbit onto the space of observables, consisting of position on the sky and line-of-sight velocity, while properly taking into account seeing convolution and pixel binning. We find the combination of orbits that produces a dynamical model that best fits the observed photometry and kinematics of the galaxy. A key new element of this work is the ability to predict and match to the data the full line-of-sight velocity profile shapes. A dark component (such as a black hole and/or a dark halo) can easily be included in the models. We have tested our method, by using it to reconstruct the properties of a two-integral model built with independent software. The test model is reproduced satisfactorily, either with the regular orbits, or with the two-integral components. This paper mainly deals with the technical aspects of the method, while applications to the galaxies M32 and NGC 4342 are described elsewhere (van der Marel et al., Cretton & van den Bosch). (abridged)Comment: minor changes, accepted for publication in the Astrophysical Journal Supplement

The velocity and mass distribution of clusters of galaxies from the CNOC1 cluster redshift survey

In the context of the CNOC1 cluster survey, redshifts were obtained for galaxies in 16 clusters. The resulting sample is ideally suited for an analysis of the internal velocity and mass distribution of clusters. Previous analyses of this dataset used the Jeans equation to model the projected velocity dispersion profile. However, the results of such an analysis always yield a strong degeneracy between the mass density profile and the velocity dispersion anisotropy profile. Here we analyze the full (R,v) dataset of galaxy positions and velocities in an attempt to break this degeneracy. We build an `ensemble cluster' from the individual clusters under the assumption that they form a homologous sequence. To interpret the data we study a one-parameter family of spherical models with different constant velocity dispersion anisotropy. The best-fit model is sought using a variety of statistics, including the overall likelihood of the dataset. Although the results of our analysis depend slightly on which statistic is used to judge the models, all statistics agree that the best-fit model is close to isotropic. This result derives primarily from the fact that the observed grand-total velocity histogram is close to Gaussian, which is not expected to be the case for a strongly anisotropic model. The best-fitting models have a mass-to-number-density ratio that is approximately independent of radius over the range constrained by the data. They also have a mass-density profile that is consistent with the dark matter halo profile advocated by Navarro, Frenk & White, in terms of both the profile shape and the characteristic scale length. This adds important new weight to the evidence that clusters do indeed follow this proposed universal mass density profile. [Abridged]Comment: 37 pages, LaTeX, with 11 PostScript figures. Accepted by the Astronomical Journal, to appear in the May 2000 issue. This replacement version contains an additional Appendix and one additional Figure with respect to the version submitted to astro-ph originall

Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research

This review discusses the current status of supermassive black hole research, as seen from a purely observational standpoint. Since the early '90s, rapid technological advances, most notably the launch of the Hubble Space Telescope, the commissioning of the VLBA and improvements in near-infrared speckle imaging techniques, have not only given us incontrovertible proof of the existence of supermassive black holes, but have unveiled fundamental connections between the mass of the central singularity and the global properties of the host galaxy. It is thanks to these observations that we are now, for the first time, in a position to understand the origin, evolution and cosmic relevance of these fascinating objects.Comment: Invited Review, 114 pages. Because of space requirements, this version contains low resolution figures. The full resolution version can be downloaded from http://www.physics.rutgers.edu/~lff/publications.htm