Dimension-Independent MCMC Sampling for Inverse Problems with Non-Gaussian Priors

The computational complexity of MCMC methods for the exploration of complex probability measures is a challenging and important problem. A challenge of particular importance arises in Bayesian inverse problems where the target distribution may be supported on an infinite dimensional space. In practice this involves the approximation of measures defined on sequences of spaces of increasing dimension. Motivated by an elliptic inverse problem with non-Gaussian prior, we study the design of proposal chains for the Metropolis-Hastings algorithm with dimension independent performance. Dimension-independent bounds on the Monte-Carlo error of MCMC sampling for Gaussian prior measures have already been established. In this paper we provide a simple recipe to obtain these bounds for non-Gaussian prior measures. To illustrate the theory we consider an elliptic inverse problem arising in groundwater flow. We explicitly construct an efficient Metropolis-Hastings proposal based on local proposals, and we provide numerical evidence which supports the theory.Comment: 26 pages, 7 figure

From the Circumnuclear Disk in the Galactic Center to thick, obscuring tori of AGNs

We compare three different models of clumpy gas disk and show that the Circumnuclear Disk (CND) in the Galactic Center and a putative, geometrically thick, obscuring torus are best explained by a collisional model consisting of quasi-stable, self-gravitating clouds. Kinetic energy of clouds is gained by mass inflow and dissipated in cloud collisions. The collisions give rise to a viscosity in a spatially averaged gas dynamical picture, which connects them to angular momentum transport and mass inflow. It is found that CND and torus share the same gas physics in our description, where the mass of clouds is 20 - 50 M_sun and their density is close to the limit of disruption by tidal shear. We show that the difference between a transparent CND and an obscuring torus is the gas mass and the velocity dispersion of the clouds. A change in gas supply and the dissipation of kinetic energy can turn a torus into a CND-like structure and vice versa. Any massive torus will naturally lead to sufficiently high mass accretion rates to feed a luminous AGN. For a geometrically thick torus to obscure the view to the center even super-Eddington accretions rates with respect to the central black hole are required.Comment: 9 pages, no figures. Accepted for publication in A&

Impact of microphysics on the growth of one-dimensional breath figures

Droplet patterns condensing on solid substrates (breath figures) tend to evolve into a self-similar regime, characterized by a bimodal droplet size distribution. The distributions comprise a bell-shaped peak of monodisperse large droplets, and a broad range of smaller droplets. The size distribution of the latter follows a scaling law characterized by a non-trivial polydispersity exponent. We present here a numerical model for three-dimensional droplets on a one-dimensional substrate (fiber) that accounts for droplet nucleation, growth and merging. The polydispersity exponent retrieved using this model is not universal. Rather it depends on the thickness of the fiber and on details of the droplet interaction leading to merging. In addition, its values consistently differ from the theoretical prediction by Blackman (Phys. Rev. Lett., 2000). Possible causes of this discrepancy are pointed out

Pre-peak ram pressure stripping in the Virgo cluster spiral galaxy NGC 4501

VIVA HI observations of the Virgo spiral galaxy NGC 4501 are presented. The HI disk is sharply truncated to the southwest, well within the stellar disk. A region of low surface-density gas, which is more extended than the main HI disk, is discovered northeast of the galaxy center. These data are compared to existing 6cm polarized radio continuum emission, Halpha, and optical broad band images. We observe a coincidence between the western HI and polarized emission edges, on the one hand, and a faint Halpha emission ridge, on the other. The polarized emission maxima are located within the gaps between the spiral arms and the faint Halpha ridge. Based on the comparison of these observations with a sample of dynamical simulations with different values for maximum ram pressure and different inclination angles between the disk and the orbital plane,we conclude that ram pressure stripping can account for the main observed characteristics. NGC 4501 is stripped nearly edge-on, is heading southwest, and is ~200-300 Myr before peak ram pressure, i.e. its closest approach to M87. The southwestern ridge of enhanced gas surface density and enhanced polarized radio-continuum emission is due to ram pressure compression. It is argued that the faint western Halpha emission ridge is induced by nearly edge-on ram pressure stripping. NGC 4501 represents an especially clear example of early stage ram pressure stripping of a large cluster-spiral galaxy.Comment: 22 pages, 25 figures, accepted for publication in A&

The Minispiral in the Galactic Center revisited

We present the results of a re-examination of a [Ne II] line emission data cube (\lambda 12.8 \mu m) and discuss the kinematic structure of the inner \sim 3 \times 4 pc of the Galaxy. The quality of [Ne II] as a tracer of ionized gas is examined by comparing it to radio data. A three dimensional representation of the data cube allows us to disentangle features which are projected onto the same location on the sky. A model of gas streams in different planes is fitted to the data. We find that most of the material is located in a main plane which itself is defined by the inner edge of the Circum-Nuclear Disk in the Galactic Center. Finally, we present a possible three dimensional model of the gas streams.Comment: 12 pages, 18 figures; submitted to New Astronomy; higher resolution version and two animations available via anonymous ftp ftp://ftp.ita.uni-heidelberg.de/pub/ITA/wjd/Minispira

Ram pressure stripping of the multiphase ISM in the Virgo cluster spiral galaxy NGC 4438

Ram pressure stripping of the multiphase ISM is studied in the perturbed Virgo cluster spiral galaxy NGC 4438. This galaxy underwent a tidal interaction ~100 Myr ago and is now strongly affected by ram pressure stripping. Deep VLA radio continuum observations at 6 and 20 cm are presented. We detect prominent extraplanar emission to the west of the galactic center, which extends twice as far as the other tracers of extraplanar material. The spectral index of the extraplanar emission does not steepen with increasing distance from the galaxy. This implies in situ re-acceleration of relativistic electrons. The comparison with multiwavelength observations shows that the magnetic field and the warm ionized interstellar medium traced by Halpha emission are closely linked. The kinematics of the northern extraplanar Halpha emission, which is ascribed to star formation, follow those of the extraplanar CO emission. In the western and southern extraplanar regions, the Halpha measured velocities are greater than those of the CO lines. We suggest that the ionized gas of this region is excited by ram pressure. The spatial and velocity offsets are consistent with a scenario where the diffuse ionized gas is more efficiently pushed by ram pressure stripping than the neutral gas. We suggest that the recently found radio-deficient regions compared to 24 mum emission are due to this difference in stripping efficiency.Comment: 8 pages, 6 figures, A&A, accepted for publicatio

Ram-pressure stripped molecular gas in the Virgo spiral galaxy NGC 4522

IRAM 30m 12CO(1-0) and 12CO(2-1) HERA observations are presented for the ram-pressure stripped Virgo spiral galaxy NGC 4522. The CO emission is detected in the galactic disk and the extraplanar gas. The extraplanar CO emission follows the morphology of the atomic gas closely but is less extended. The CO maxima do not appear to correspond to regions where there is peak massive star formation as probed by Halpha emission. The presence of molecular gas is a necessary but not sufficient condition for star formation. Compared to the disk gas, the molecular fraction of the extraplanar gas is 30% lower and the star formation efficiency of the extraplanar gas is about 3 times lower. The comparison with an existing dynamical model extended by a recipe for distinguishing between atomic and molecular gas shows that a significant part of the gas is stripped in the form of overdense arm-like structures. It is argued that the molecular fraction depends on the square root of the total large-scale density. Based on the combination of the CO/Halpha and an analytical model, the total gas density is estimated to be about 4 times lower than that of the galactic disk. Molecules and stars form within this dense gas according to the same laws as in the galactic disk, i.e. they mainly depend on the total large-scale gas density. Star formation proceeds where the local large-scale gas density is highest. Given the complex 3D morphology this does not correspond to the peaks in the surface density. In the absence of a confining gravitational potential, the stripped gas arms will most probably disperse; i.e. the density of the gas will decrease and star formation will cease.Comment: 11 pages, 15 figures, A&A accepted for publicatio

Hot gas in Mach cones around Virgo Cluster spiral galaxies

The detailed comparison between observations and simulations of ram pressure stripped spiral galaxies in the Virgo cluster has led to a three dimensional view of the galaxy orbits within the hot intracluster medium. The 3D velocities and Mach numbers derived from simulations can be used to derive simple Mach cone geometries for Virgo spiral galaxies. We search for indications of hot gas within Mach cones in X-ray observations of selected Virgo Cluster spiral galaxies (NGC 4569, NGC 4388, and NGC 4501). We find extraplanar diffuse X-ray emission in all galaxies. Based on the 3D velocity vectors from dynamical modelling a simple Mach cone is fitted to the triangular shape of NGC 4569's diffuse X-ray emission. Assuming that all extraplanar diffuse X-ray emission has to be located inside the Mach cone, we also fit Mach cones to NGC 4388's and NGC 4501's extraplanar X-ray emission. For NGC 4569 it is hard to reconcile the derived Mach cone opening angle with a Mach number based on the sound speed alone. Instead, a Mach number involving the Alfv\'enic speed seems to be more appropriate, yielding a magnetic field strength of $\sim 3$-6 $\mu$G for a intracluster medium density of $n \sim 10^{-4}$ cm$^{-3}$. Whereas the temperature of the hot component of NGC 4569's X-ray halo (0.5 keV) is at the high end but typical for a galactic outflow, the temperature of the hot gas tails of NGC 4388 and NGC 4501 are significantly hotter (0.7-0.9 keV). In NGC 4569 we find direct evidence for a Mach cone which is filled with hot gas from a galactic superwind. We suggest that the high gas temperatures in the X-ray tails of NGC 4388 and NGC 4501 are due to the mixing of the stripped ISM into the hot intracluster medium of the Virgo cluster.Comment: 11 pages, 10 figures, 5 tables. Accepted for publication in Astronomy and Astrophysic

The influence of the cluster environment on the large-scale radio continuum emission of 8 Virgo cluster spirals

The influence of the environment on the polarized and total power radio continuum emission of cluster spiral galaxies is investigated. We present deep scaled array VLA 20 and 6 cm observations including polarization of 8 Virgo spiral galaxies. These data are combined with existing optical, HI, and Halpha data. Ram pressure compression leads to sharp edges of the total power distribution at one side of the galactic disk. These edges coincide with HI edges. In edge-on galaxies the extraplanar radio emission can extend further than the HI emission. In the same galaxies asymmetric gradients in the degree of polarization give additional information on the ram pressure wind direction. The local total power emission is not sensitive to the effects of ram pressure. The radio continuum spectrum might flatten in the compressed region only for very strong ram pressure. This implies that neither the local star formation rate nor the turbulent small-scale magnetic field are significantly affected by ram pressure. Ram pressure compression occurs mainly on large scales (>=1 kpc) and is primarily detectable in polarized radio continuum emission.Comment: 16 pages, 10 figures, accepted for publication in A&