The quenching of star formation in accretion-driven clumpy turbulent tori of active galactic nuclei

Galactic gas-gas collisions involving a turbulent multiphase ISM share common ISM properties: dense extraplanar gas visible in CO, large linewidths (>= 50 km/s), strong mid-infrared H_2 line emission, low star formation activity, and strong radio continuum emission. Gas-gas collisions can occur in the form of ICM ram pressure stripping, galaxy head-on collisions, compression of the intragroup gas and/or galaxy ISM by an intruder galaxy which flies through the galaxy group at a high velocity, or external gas accretion on an existing gas torus in a galactic center. We suggest that the common theme of all these gas-gas interactions is adiabatic compression of the ISM leading to an increase of the turbulent velocity dispersion of the gas. The turbulent gas clouds are then overpressured and star formation is quenched. Within this scenario we developed a model for turbulent clumpy gas disks where the energy to drive turbulence is supplied by external infall or the gain of potential energy by radial gas accretion within the disk. The cloud size is determined by the size of a C-type shock propagating in dense molecular clouds with a low ionization fraction at a given velocity dispersion. We give expressions for the expected volume and area filling factors, mass, density, column density, and velocity dispersion of the clouds. The latter is based on scaling relations of intermittent turbulence whose open parameters are estimated for the CND in the Galactic Center. The properties of the model gas clouds and the external mass accretion rate necessary for the quenching of the star formation rate due to adiabatic compression are consistent with those derived from high-resolution H_2 line observations. Based on these findings, a scenario for the evolution of gas tori in galactic centers is proposed and the implications for star formation in the Galactic Center are discussed.Comment: 13 pages, 1 figure, accepted for publication by A&

Spectral Stability of the Neumann Laplacian

We prove the equivalence of Hardy- and Sobolev-type inequalities, certain uniform bounds on the heat kernel and some spectral regularity properties of the Neumann Laplacian associated with an arbitrary region of finite measure in Euclidean space. We also prove that if one perturbs the boundary of the region within a uniform H\"older category then the eigenvalues of the Neumann Laplacian change by a small and explicitly estimated amount. AMS subject classifications: 35P15, 35J25, 47A75, 47B25, 26D10, 46E35. Keywords: Neumann Laplacian, Sobolev inequalities, Hardy inequalities, spectral stability, H\"older continuity.Comment: 23 page

Dust Emissivity in the Far-Infrared

We have derived the dust emissivity in the Far-Infrared (FIR) using data available in the literature. We use two wavelength dependences derived from spectra of Galactic FIR emission (Reach et al. 1995). A value for the emissivity, normalised to the extinction efficiency in the V band, has been retrieved from maps of Galactic FIR emission, dust temperature and extinction (Schlegel et al. 1998). Our results are similar to other measurements in the Galaxy but only marginally consistent with the widely quoted values of Hildebrand (1983) derived on one reflection nebula. The discrepancy with measurements on other reflection nebulae (Casey 1991) is higher and suggests a different grain composition in these environments with respect to the diffuse interstellar medium. We measure dust masses for a sample of six spiral galaxies with FIR observations and obtain gas-to-dust ratios close to the Galactic value.Comment: 5 pages, 1 ps file, A&A letter accepte

Monte Carlo Predictions of Far-Infrared Emission from Spiral Galaxies

We present simulations of Far Infrared (FIR) emission by dust in spiral galaxies, based on the Monte Carlo radiative transfer code of Bianchi, Ferrara & Giovanardi (1996). The radiative transfer is carried out at several wavelength in the Ultraviolet, optical and Near Infrared, to cover the range of the stellar Spectral Energy Distribution (SED). Together with the images of the galactic model, a map of the energy absorbed by dust is produced. Using Galactic dust properties, the spatial distribution of dust temperature is derived under the assumption of thermal equilibrium. A correction is applied for non-equilibrium emission in the Mid Infrared. Images of dust emission can then be produced at any wavelength in the FIR. We show the application of the model to the spiral galaxy NGC 6946. The observed stellar SED is used as input and models are produced for different star-dust geometries. It is found that only optically thick dust disks can reproduce the observed amount of FIR radiation. However, it is not possible to reproduce the large FIR scalelength suggested by recent observation of spirals at 200 um, even when the scalelength of the dust disk is larger than that for stars. Optically thin models have ratios of optical/FIR scalelengths closer to the 200um observations, but with smaller absolute scalelengths than optically thick cases. The modelled temperature distributions are compatible with observations of the Galaxy and other spirals. We finally discuss the approximations of the model and the impact of a clumpy stellar and dust structure on the FIR simulations.Comment: 19 pages, 6 figures, accepted by A&

ISO observations of spirals: modelling the FIR emission

ISO observations at 200 micron have modified our view of the dust component in spiral galaxies. For a sample of seven resolved spirals we have retrieved a mean temperature of 20K, about 10K lower than previous estimates based on IRAS data at shorter wavelengths. Because of the steep dependence of far-infrared emission on the dust temperature, the dust masses inferred from ISO fluxes are a factor of 10 higher than those derived from IRAS data only, leading to gas-to-dust ratios close to the value observed in the Galaxy. The scale-length of the 200 micron emission is larger than for the IRAS 100 micron emission, with colder dust at larger distances from the galactic centre, as expected if the interstellar radiation field is the main source of dust heating. The 200 micron scale-length is also larger than the optical, for all the galaxies in the sample. This suggests that the dust distribution is more extended than that of the stars.A model of the dust heating is needed to derive the parameters of the dust distribution from the FIR emission. Therefore, we have adapted an existing radiative transfer code to deal with dust emission. Simulated maps of the temperature distribution within the dust disk and of the dust emission at any wavelength can be produced. The stellar spectral energy distribution is derived from observations in the ultraviolet, optical and near infrared. The parameters of the dust distribution (scale-lengths and optical depth) are chosen to reproduce the observed characteristics of the FIR emission, i.e. the shape of the spectrum, the flux and the spatial distribution. We describe the application of the model to one of the galaxies in the sample, NGC 6946.Comment: 6 pages, 5 figures. Contribution to the proceedings of the workshop "ISO Beyond Point Sources" held at VILSPA 14-17 September 199

SCUBA imaging of NGC 7331 dust ring

We present observations of the spiral galaxy NGC 7331 using the Sub-millimetre Common User Bolometer Array (SCUBA) on the James Clark Maxwell Telescope. We have detected a dust ring of 45 arcsec radius (3.3 kpc) at wavelengths of 450 and 850-micron. The dust ring is in good correspondence with other observations of the ring in the mid-infrared (MIR), CO and radio-continuum, suggesting that the observed dust is associated with the molecular gas and star formation. A B-K colour map shows an analogous ring structure with an asymmetry about the major axis, consistent with the extinction being produced by a dust ring. The derived temperature of the dust lies between 16 and 31 K and the gas-to-dust ratio between 150 and 570, depending on the assumed dust emission efficiency index (beta=1.5 or 2.).Comment: 5 pages, 6 figures, to be published in MNRA

Assessing Proof Reading Comprehension Using Summaries

In this paper, we explore the role of mathematical proof summaries as a tool for capturing students’ reading comprehension of a given proof. We present an interview study based on mathematicians’ pairwise evaluations of student-produced summaries of a proof demonstrating the uncountability of the open unit interval. We present a thematic analysis, exploring features of mathematicians’ pairwise decision-making and their priorities in evaluating summaries. We argue that the students’ proof summaries shared several properties with traditional modes of proof-writing and were frequently evaluated against similar conventions. We consider the consequences for research and practice with proof comprehension and conclude that proof summaries have the potential to form the basis of a new approach to assessment in this area

The effect of stellar-mass black holes on the structural evolution of massive star clusters

We present the results of realistic N-body modelling of massive star clusters in the Magellanic Clouds, aimed at investigating a dynamical origin for the radius-age trend observed in these systems. We find that stellar-mass black holes, formed in the supernova explosions of the most massive cluster stars, can constitute a dynamically important population. If a significant number of black holes are retained (here we assume complete retention), these objects rapidly form a dense core where interactions are common, resulting in the scattering of black holes into the cluster halo, and the ejection of black holes from the cluster. These two processes heat the stellar component, resulting in prolonged core expansion of a magnitude matching the observations. Significant core evolution is also observed in Magellanic Cloud clusters at early times. We find that this does not result from the action of black holes, but can be reproduced by the effects of mass-loss due to rapid stellar evolution in a primordially mass segregated cluster.Comment: Accepted for publication in MNRAS Letters; 2 figures, 1 tabl

Early-type Galaxies in the Cluster Abell 2390 at z=0.23

To examine the evolution of the early-type galaxy population in the rich cluster Abell 2390 at z=0.23 we have gained spectroscopic data of 51 elliptical and lenticular galaxies with MOSCA at the 3.5 m telescope on Calar Alto Observatory. This investigation spans both a broad range in luminosity (-19.3>M_B>-22.3) and uses a wide field of view of 10'x10', therefore the environmental dependence of different formation scenarios can be analysed in detail as a function of radius from the cluster centre. Here we present results on the surface brightness modelling of galaxies where morphological and structural information is available in the F814W filter aboard the Hubble Space Telescope (HST) and investigate for this subsample the evolution of the Fundamental Plane.Comment: 5 pages, 5 figures, to appear in "Carnegie Observatories Astrophysics Series, Vol. 3: Clusters of Galaxies: Probes of Cosmological Structure and Galaxy Evolution", ed. J. S. Mulchaey, A. Dressler, and A. Oemler (Pasadena: Carnegie Observatories, http://www.ociw.edu/ociw/symposia/series/symposium3/proceedings.html