Central Mass Concentration and Bar Dissolution in Nearby Spiral Galaxies

We use data from the BIMA Survey of Nearby Galaxies (SONG) to investigate the relationship between ellipticity and central mass concentration in barred spirals. Existing simulations predict that bar ellipticity decreases as inflowing mass driven by the bar accumulates in the central regions, ultimately destroying the bar. Using the ratio of the bulge mass to the mass within the bar radius as an estimate of the central mass concentration, we obtain dynamical mass estimates from SONG CO 1-0 rotation curve data. We find an inverse correlation between bar ellipticity and central mass concentration, consistent with simulations of bar dissolution.Comment: 10 pages, 2 figures and 2 tables, accepted for publication in the Astrophysical Journa

Extension of formal conjugations between diffeomorphisms

We study the formal conjugacy properties of germs of complex analytic diffeomorphisms defined in the neighborhood of the origin of ${\mathbb C}^{n}$. More precisely, we are interested on the nature of formal conjugations along the fixed points set. We prove that there are formally conjugated local diffeomorphisms $\phi, \eta$ such that every formal conjugation $\hat{\sigma}$ (i.e. $\eta \circ \hat{\sigma} = \hat{\sigma} \circ \phi$) does not extend to the fixed points set $Fix (\phi)$ of $\phi$, meaning that it is not transversally formal (or semi-convergent) along $Fix (\phi)$. We focus on unfoldings of 1-dimensional tangent to the identity diffeomorphisms. We identify the geometrical configurations preventing formal conjugations to extend to the fixed points set: roughly speaking, either the unperturbed fiber is singular or generic fibers contain multiple fixed points.Comment: 34 page

Hyperasymptotic solutions for certain partial differential equations

We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalisation is based on the method of Borel summability, which allows us to find integral representations of solutions for such PDEs.Comment: 17 page

A Connection between Star Formation in Nuclear Rings and their Host Galaxies

We present results from a photometric H-alpha survey of 22 nuclear rings, aiming to provide insight into their star formation properties, including age distribution, dynamical timescales, star formation rates, and galactic bar influence. We find a clear relationship between the position angles and ellipticities of the rings and those of their host galaxies, which indicates the rings are in the same plane as the disk and circular. We use population synthesis models to estimate ages of each H-alpha emitting HII region, which range from 1 Myr to 10 Myrs throughout the rings. We find that approximately half of the rings contain azimuthal age gradients that encompass at least 25% of the ring, although there is no apparent relationship between the presence or absence of age gradients and the morphology of the rings or their host galaxies. NGC1343, NGC1530, and NGC4321 show clear bipolar age gradients, where the youngest HII regions are located near the two contact points of the bar and ring. We speculate in these cases that the gradients are related to an increased mass inflow rate and/or an overall higher gas density in the ring, which would allow for massive star formation to occur on short timescales, after which the galactic rotation would transport the HII regions around the ring as they age. Two-thirds of the barred galaxies show correlation between the locations of the youngest HII region(s) in the ring and the location of the contact points, which is consistent with predictions from numerical modeling.Comment: 23 pages, 10 figures (7 color), 23 tables, accepted for publication in ApJS (Feb 08); NASA-GSFC, IAC, University of Maryland, STSc

Boundary Limitation of Wavenumbers in Taylor-Vortex Flow

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig

Regularization of Linear Ill-posed Problems by the Augmented Lagrangian Method and Variational Inequalities

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a standard source condition. Using the method of variational inequalities, we extend these results in this paper to convergence rates of lower order, both for the case of an a priori parameter choice and an a posteriori choice based on Morozov's discrepancy principle. In addition, our approach allows the derivation of convergence rates with respect to distance measures different from the Bregman distance. As a particular application, we consider sparsity promoting regularization, where we derive a range of convergence rates with respect to the norm under the assumption of restricted injectivity in conjunction with generalized source conditions of H\"older type

Molecular Gas, Dust and Star Formation in the Barred Spiral NGC 5383

We present multi-wavelength (interferometer and single-dish CO J=1-0, Halpha, broadband optical and near-infrared) observations of the classic barred spiral NGC 5383. We compare the observed central gas and dust morphology to the predictions of recent hydrodynamic simulations. In the nuclear region, our observations reveal three peaks lying along a S-shaped gas and dust distribution. In contrast, the model predicts a circumnuclear ring, not the observed S-shaped distribution; moreover, the predicted surface density contrast between the central gas accumulation and the bar dust lanes is an order of magnitude larger than observed. The discrepancies are not due to unexplored model parameter space or a nuclear bar but are probably due to the vigorous (7 solar masses per year) star formation activity in the center. As is common in similar bars, the star formation rate in the bar between the bar ends and the central region is low (~0.5 solar masses per yr), despite the high gas column density in the bar dust lanes; this is generally attributed to shear and shocks. We note a tendency for the HII regions to be associated with the spurs feeding the main bar dust lanes, but these are located on the leading side of the bar. We propose that stars form in the spurs, which provide a high column density but low shear environment. HII regions can therefore be found even on the leading side of the bar because the ionizing stars pass ballistically through the dust laneComment: Accepted for publication in The Astrophysical Journal, 33 pages (includes 10 figures

Resonances in a spring-pendulum: algorithms for equivariant singularity theory

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.

Corotation: its influence on the chemical abundance pattern of the Galaxy

A simple theory for the chemical enrichment of the Galaxy which takes into account the effects of spiral arms on heavy elements output was developed. In the framework of the model with the corotation close to the position of the Sun in the Galaxy the observed abundance features are explained.Comment: LaTeX, 6 pages, 5 jpg figures, uses aastex.sty, submitted to ApJ Let

Gas flows in galaxies: the relative importance of mergers and bars

Galaxy-galaxy interactions and large scale galaxy bars are usually considered as the two main mechanisms for driving gas to the centres of galaxies. By using large samples of galaxy pairs and visually classified bars from the Sloan Digital Sky Survey (SDSS), we compare the relative efficiency of gas inflows from these two processes. We use two indicators of gas inflow: star formation rate (SFR) and gas phase metallicity, which are both measured relative to control samples. Whereas the metallicity of galaxy pairs is suppressed relative to its control sample of isolated galaxies, galaxies with bars are metal-rich for their stellar mass by 0.06 dex over all stellar masses. The SFRs of both the close galaxy pairs and the barred galaxies are enhanced by ~60%, but in the bars the enhancement is only seen at stellar masses M* >10^10 M_solar. Taking into account the relative frequency of bars and pairs, we estimate that at least three times more central star formation is triggered by bars than by interactions.Comment: Proceedings of "Tracing the Ancestry of Galaxies on the Land of our Ancestors", Eds Carignan, Freeman & Combe