arXiv subjects

Dalia Chakrabarty

Publications and source records attributed to Dalia Chakrabarty.

At least 37 records · Page 2Linked to original sources

arXiv2014

Bayesian Density Estimation via Multiple Sequential Inversions of 2-D Images with Application in Electron Microscopy

We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the convolution of the density function with the unknown microscopy correction function that we also learn from the data. We invoke a novel design of experiment, involving imaging at multiple values of the parameter that controls the sub-surface depth from which information about the density structure is carried, to result in the image. Real-life material density functions are characterised by high density contrasts and typically are highly discontinuous, implying that they exhibit correlation structures that do not vary smoothly. In the absence of training data, modelling such correlation structures of real material density functions is not possible. So we discretise the material sample and treat values of the density function at chosen locations inside it as independent and distribution-free parameters. Resolution of the available image dictates the discretisation length of the model; three models pertaining to distinct resolution classes are developed. We develop priors on the material density, such that these priors adapt to the sparsity inherent in the density function. The likelihood is defined in terms of the distance between the convolution of the unknown functions and the image data. The posterior probability density of the unknowns given the data is expressed using the developed priors on the density and priors on the microscopy correction function as elicitated from the Microscopy literature. We achieve posterior samples using an adaptive Metropolis-within-Gibbs inference scheme. The method is applied to learn the material density of a 3-D sample of a real nano-structure and of simulated alloy samples.

stat.AP↗

arXiv2014

Inverse Bayesian Estimation of Gravitational Mass Density in Galaxies from Missing Kinematic Data

In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with situations in which training data is not available. Then we cannot model the unknown functional relationship between data and the unknown model function (or parameter vector) with a Gaussian Process of appropriate dimensionality. A Bayesian method based on state space modelling is advanced instead. Within this framework, the likelihood is expressed in terms of the probability density function ($pdf$) of the state space variable and the sought model parameter vector is embedded within the domain of this $pdf$. As the measurable vector lives only inside an identified sub-volume of the system state space, the $pdf$ of the state space variable is projected onto the space of the measurables, and it is in terms of the projected state space density that the likelihood is written; the final form of the likelihood is achieved after convolution with the distribution of measurement errors. Application motivated vague priors are invoked and the posterior probability density of the model parameter vectors, given the data is computed. Inference is performed by taking posterior samples with adaptive MCMC. The method is illustrated on synthetic as well as real galactic data.

stat.AP↗

arXiv2009

Non-parametric Deprojection of Surface Brightness Profiles of Galaxies in Generalised Geometries

We present a new Bayesian non-parametric deprojection algorithm DOPING (Deprojection of Observed Photometry using and INverse Gambit), that is designed to extract 3-D luminosity density distributions $ρ$ from observed surface brightness maps $I$, in generalised geometries, while taking into account changes in intrinsic shape with radius, using a penalised likelihood approach and an MCMC optimiser. We provide the most likely solution to the integral equation that represents deprojection of the measured $I$ to $ρ$. In order to keep the solution modular, we choose to express $ρ$ as a function of the line-of-sight (LOS) coordinate $z$. We calculate the extent of the system along the ${\bf z}$-axis, for a given point on the image that lies within an identified isophotal annulus. The extent along the LOS is binned and density is held a constant over each such $z$-bin. The code begins with a seed density and at the beginning of an iterative step, the trial $ρ$ is updated. Comparison of the projection of the current choice of $ρ$ and the observed $I$ defines the likelihood function (which is supplemented by Laplacian regularisation), the maximal region of which is sought by the optimiser (Metropolis Hastings). The algorithm is successfully tested on a set of test galaxies, the morphology of which ranges from an elliptical galaxy with varying eccentricity to an infinitesimally thin disk galaxy marked by an abruptly varying eccentricity profile. Applications are made to faint dwarf elliptical galaxy Ic~3019 and another dwarf elliptical that is characterised by a central spheroidal nuclear component superimposed upon a more extended flattened component. The result of deprojection of the X-ray image of triaxial cluster A1413 is also presented.

astro-ph.IM↗

arXiv2009

Comparing X-ray and Dynamical Mass Profiles in the Early-Type Galaxy NGC 4636

We present the results of an X-ray mass analysis of the early-type galaxy NGC 4636, using Chandra data. We have compared the X-ray mass density profile with that derived from a dynamical analysis of the system's globular clusters (GCs). Given the observed interaction between the central active galactic nucleus and the X-ray emitting gas in NGC 4636, we would expect to see a discrepancy in the masses recovered by the two methods. Such a discrepancy exists within the central ~10kpc, which we interpret as the result of non-thermal pressure support or a local inflow. However, over the radial range ~10-30kpc, the mass profiles agree within the 1-sigma errors, indicating that even in this highly disturbed system, agreement can be sought at an acceptable level of significance over intermediate radii, with both methods also indicating the need for a dark matter halo. However, at radii larger than 30kpc, the X-ray mass exceeds the dynamical mass, by a factor of 4-5 at the largest disagreement. A Fully Bayesian Significance Test finds no statistical reason to reject our assumption of velocity isotropy, and an analysis of X-ray mass profiles in different directions from the galaxy centre suggests that local disturbances at large radius are not the cause of the discrepancy. We instead attribute the discrepancy to the paucity of GC kinematics at large radius, coupled with not knowing the overall state of the gas at the radius where we are reaching the group regime (>30kpc), or a combination of the two.

astro-ph.CO↗

arXiv2009

Warps and Bars from the External Tidal Torques of Tumbling Dark Halos

The dark matter halos in $Λ$CDM cosmological simulations are triaxial and highly flattened. In many cases, these triaxial equilibria are also tumbling slowly, typically about their short axes, with periods of order a Hubble time. Halos may therefore exert a slowly changing external torque on spiral galaxies that can affect their dynamical evolution in interesting ways. We examine the effect of the external torques exerted by a tumbling quadrupolar tidal field on the evolution of spiral galaxies using N-body simulations with realistic, disk galaxy models. We measure the amplitude of the external quadrupole moments of dark halos in cosmological simulations and use these to force disk galaxy models in a series of N-body experiments for a range of pattern speeds. We find that the torques are strong enough to induce long lived transient warps in disks similar to those observed in real spirals and also induce the bar instability at later times in some galaxy models that are otherwise stable for long periods of time in isolation. We also observe forced spiral structure near the edge of the disk where normally self-gravity is too weak to be responsible for such structure. This overlooked influence of dark halos may well be responsible for many of the peculiar aspects of disk galaxy dynamics.

astro-ph.GA↗

arXiv2009

CHASSIS - Inverse Modelling of Relaxed Dynamical Systems

The state of a non-relativistic gravitational dynamical system is known at any time $t$ if the dynamical rule, i.e. Newton's equations of motion, can be solved; this requires specification of the gravitational potential. The evolution of a bunch of phase space coordinates ${\bf w}$ is deterministic, though generally non-linear. We discuss the novel Bayesian non-parametric algorithm CHASSIS that gives phase space $pdf$ $f({\bf w})$ and potential $Φ({\bf x})$ of a relaxed gravitational system. CHASSIS is undemanding in terms of input requirements in that it is viable given incomplete, single-component velocity information of system members. Here ${\bf x}$ is the 3-D spatial coordinate and ${\bf w}={\bf x+v}$ where ${\bf v}$ is the 3-D velocity vector. CHASSIS works with a 2-integral $f=f(E, L)$ where energy $E=Φ+ v^2/2, \: v^2 = \sum_{i=1}^{3}{v_i^2}$ and the angular momentum is $L = |{\bf r}\times{\bf v}|$, where ${\bf r}$ is the spherical spatial vector. Also, we assume spherical symmetry. CHASSIS obtains the $f(\cdot)$ from which the kinematic data is most likely to have been drawn, in the best choice for $Φ(\cdot)$, using an MCMC optimiser (Metropolis-Hastings). The likelihood function ${\cal{L}}$ is defined in terms of the projections of $f(\cdot)$ into the space of observables and the maximum in ${\cal{L}}$ is sought by the optimiser.

math.ST↗

arXiv2009

Total mass distributions of Sersic galaxies from photometry $&$ cent\ ral velocity dispersion

We develop a novel way of finding total mass density profiles in Sersic ellipticals, to about 3 times the major axis effective radius, using no other information other than what is typically available for distant galaxies, namely the observed surface brightness distribution and the central velocity dispersion $σ_0$. The luminosity density profile of the observed galaxy is extracted by deprojecting the measured brightness distribution and scaling it by a fiduciary, step-function shaped, $raw$ mass-to-light ratio profile ($M/L$). The resulting raw, discontinuous, total, 3-D mass density profile is then smoothed according to a proposed smoothing prescription. The parameters of this raw $M/L$ are characterised by implementing the observables in a model-based study. The complete characterisation of the formalism is provided as a function of the measurements of the brightness distribution and $σ_0$. The formalism, thus specified, is demonstrated to yield the mass density profiles of a suite of test galaxies and is successfully applied to extract the gravitational mass distribution in NGC 3379 and NGC 4499, out to about 3 effective radii.

astro-ph.IM↗

arXiv2008

Cluster Geometry & Inclinations from Deprojection Uncertainties

{The determination of cluster masses is a complex problem that would be aided by information about the cluster shape and orientation (along the line-of-sight).} {It is in this context, that we have developed a scheme for identifying the intrinsic morphology and inclination of a cluster, by looking for the signature of the true cluster characteristics in the inter-comparison of the different deprojected emissivity profiles (that all project to the same X-ray brightness distribution) and by using SZe data when available.} {We deproject the cluster X-ray surface brightness profile under the assumptions of four different geometry and inclination configurations for the observed system; these 4 configurations correspond to four extreme geometry+inclination scenarios. The deprojection in question is performed by the non-parametric algorithm DOPING. The formalism is tested with model systems and then is applied to a sample of 24 clusters. While the shape determination is possible by implementing the X-ray brightness alone, the estimation of the inclination is usually markedly improved by the usage of SZe data that is available for the considered sample.}{We spot 8 prolate systems, 1 oblate and 15 of the clusters in our sample as triaxial. In fact, for systems identified as triaxial, we are able to discern how the three semi-axes lengths compare with each other. This, when compounded by the information about the line-of-sight extent, allows us to constrain the inclination quite tightly and offers the two intrinsic axial ratios of the triaxial systems.}{}

astro-ph↗

arXiv2008

Quantifying Chaos in Models of the Solar Neighbourhood

{} {To quantify the amount of chaos that exists in the local phase space.} {A sample of orbits from four different models of the Solar neighbourhood phase space are analysed by a new chaos identification (and quantification) technique. While three of the used models bear the signature of the perturbation due to both the Galactic bar and the spiral pattern, the last of the models is a bar only one. We explore the models by inter-comparing the corresponding values of chaos strength that is induced at the various energy levels .}{(1) We find that of all the viable models that have been demonstrated to successfully reproduce the local phase space structure, i.e. those that include the bar as well as the spiral, bear strong chaoticity, though the model that implies the highest degree of chaos is the one in which overlap of the major resonances of the bar and the spiral occurs. The bar only model is found to display regularity. (2) We advance chaos to be primarily responsible for the splitting of the Hyades-Pleiades mode (the larger mode) of the local velocity distribution}{}

astro-ph↗

arXiv2008

The Distribution of Dark Matter in the Halo of the early-type galaxy NGC 4636

We present the density structure of dark matter in the outer parts (to about 7 effective radii) of the elliptical galaxy NGC 4636, from the radial velocities of 174 globular clusters, using the non-parametric, Bayesian algorithm CHASSIS. We find the galaxy to be rich in dark matter, with $R$-band mass-to-light ($M/L$) ratios rising to about 30, at nearly 4$R_e$; the $K$-band $M/L$ at about 3$R_e$ is found to be nearly 10. The result does not depend on applying the method to the red and blue globular clusters separately. This estimate of $M/L$ is higher than the previous analysis from the same kinematic data. We also find that the dark matter distribution is highly concentrated towards the inner halo.

astro-ph↗

arXiv2008

Local Phase Space - Shaped by Chaos?

We attempt to understand the state of the local phase space by comparing simulated 2-D velocity distributions to the distribution that is constructed for the solar neighbourhood, from measurements of stellar radial and transverse velocities. The joint perurbation of the central bar in the Galaxy and the spiral pattern is found to be a must, in order to produce successful models of the local phase space. The existence of chaos is found to be an important ingredient in the formation of the observed phase space structure.

astro-ph↗

arXiv2008

DOPING: a New Non-parametric Deprojection Scheme

We present a new non-parametric deprojection algorithm DOPING (Deprojection of Observed Photometry using and INverse Gambit), that is designed to extract the three dimensional luminosity density distribution $ρ$, from the observed surface brightness profile of an astrophysical system such as a galaxy or a galaxy cluster, in a generalised geometry, while taking into account changes in the intrinsic shape of the system. The observable is the 2-D surface brightness distribution of the system. While the deprojection schemes presented hitherto have always worked within the limits of an assumed intrinsic geometry, in DOPING, geometry and inclination can be provided as inputs. The $ρ$ that is most likely to project to the observed brightness data is sought; the maximisation of the likelihood is performed with the Metropolis algorithm. Unless the likelihood function is maximised, $ρ$ is tweaked in shape and amplitude, while maintaining positivity, but otherwise the luminosity distribution is allowed to be completely free-form. Tests and applications of the algorithm are discussed.

astro-ph↗

arXiv2007

Phase Space Structure in the Solar Neighbourhood

We examine the idea that dynamical parameters can be estimated by identifying locations in the solar neighbourhood where simulated velocity distributions match the observed local distribution. Here, the dynamical influence of both the Galactic bar and the outer spiral pattern are taken into account. The Milky Way disc is stirred by analytical potentials that are chosen to represent the two perturbations, the ratio of pattern speeds of which is explored, rather than held constant. The velocity structure of the final configuration is presented as heliocentric velocity distributions at different locations. These model velocity distributions are compared to the observed distribution in terms of a goodness-of-fit parameter that has been formulated here. We monitor the spatial distribution of the maximal value of this parameter, in order to constrain the solar position from a model. Efficiency of a model is based on a study of this distribution as well as on other independent dynamical considerations. We reject the bar only and spiral only models and arrive at the following bar parameters from the bar+spiral simulations: bar pattern speed of 57.4^{+2.8}_{-3.3} km/s/kpc and a bar angle in [0^\circ$, 30^\circ$]. However, extracting information in this way is no longer viable when the dynamical influence of the spiral pattern does not succumb to that of the bar. Orbital analysis indicates that even though the basic bimodality in the local velocity distribution can be attributed to scattering off the Outer Lindblad Resonance of the bar, it is the interaction of irregular orbits and orbits of other resonant families, that is responsible for the other moving groups; it is realised that such interaction increases with the warmth of the background disk.

astro-ph↗

arXiv2007

Mass Modelling with Minimum Kinematic Information

Mass modelling of early-type systems is a thorny issue. In this paper, we present a new mass modelling formalism for ellipticals that invokes no observations other than the central velocity dispersion ($σ_0$) and photometry. The essence of the method lies in choosing a local mass-to-light ratio ($M/L$) profile for a galaxy, with which the deprojected luminosity density distribution (along the major axis coordinate $x$) is scaled. The resulting discontinuous mass density profile is then smoothed, according to a laid out prescription; the local $M/L$ profile that stems from this smoothed mass density, is found to be significantly different from the raw $M/L$ distribution. A suite of model galaxies (both Sersic and cored in nature) is used for extensive experimentation in order to characterise this raw $M/L$ profile and in each case, the mass density recovered from this mass modelling technique is compared to the known mass distribution. We opt to work with a raw $M/L$ profile that is a simple two-stepped function of $x$, with a low inner and higher outer value of $M/L-Υ_{in}$ and $Υ_{out}$, respectively. The only constraint that we have on this profile is in the centre of the galaxy, via $σ_0$. This value of $σ_0$ is implemented in the virial theorem to obtain an estimate of the central $M/L$ ratio of the galaxy. The fallibility of the virial mass estimate is taken care of, by allowing for a range in the values of $Υ_{in}$ that can be used for a given galaxy model. Moreover, our experiments indicate that $Υ_{out}$ is uniquely known, for a given $Υ_{in}$; for cored galaxies, this functional form is found uniquely dependant on the core radius. The jump radius of the raw $M/L$ profile is chosen to be thrice the effective radius of the galaxy.

astro-ph↗

arXiv2006

An Inverse Look at the Center of M15

The observed radial and transverse velocities of individual stars in M15 are implemented as inputs to a fully non-parametric code (CHASSIS) in order to estimate the equilibrium stellar distribution function and the three-dimensional mass density profile. In particular, the paper explores the possibility of the existence of a central black hole in M15 via several runs that utilize the radial velocity data set which offers kinematic measurements closer to the centre of the cluster than the proper motion data. These runs are distinguished from each other in the choice of the initial seed for the cluster characteristics; however, the profiles identified by the algorithm at the end of each run concur with each other, within error bars, thus confirming the robustness of CHASSIS. The recovered density profiles are noted to exhibit unequivocal flattening, inner to about 0.0525pc. Also, the enclosed mass profile is very close to being a power-law function of radius inside 0.1pc and is not horizontal. Simplistically speaking, these trends negate the possibility of the central mass to be concentrated in a black hole, the lower bound on the radius of the sphere of influence of which would be $\gtrsim$0.041pc, had it existed. However, proper analysis suggests that the mass enclosed within the inner 0.01pc could be in the form of a black hole of mass $\sim{10^3}$M$_{\odot}$, under two different scenarios, which are discussed. The line-of-sight velocity dispersion is visually found to be very similar to the observed dispersion profile. The enclosed mass and velocity dispersion profiles calculated from runs done with the proper motion data are found to be consistent with the profiles obtained with the radial velocity data.

astro-ph↗

arXiv2004

An Inverse Problem Approach to Cluster Dynamics

We propose a new non-parametric algorithm that can be implemented to study and characterize stellar clusters. The scheme attempts to simultaneously recover the stellar distribution function and the cluster potential by using projected radii and velocity information about the cluster members. The pair of these functions that is most consistent with the input data is detected by the Metropolis algorithm. In this work, the cluster characteristics recovered by CHASSIS are calibrated against the N-body realizations of two clusters, namely Hyades and Arches. The cluster mass and line-of-sight projected velocity dispersion profiles are correctly reproduced by the algorithm when the cluster obeys the assumption used in the code, namely isotropy in phase space. The results recovered by the code are shown to be insensitive to the choice of the initial parameters. The results are also not influenced by increasing the number of input data points as long as this number exceeds a minimum value which is moderately low for an input data set that obeys the assumptions of isotropy and sphericity.

astro-ph↗

arXiv2004

Patterns in the Outer Parts of Galactic Disks

This paper describes test particle simulations of the response of the outer parts of Galactic disks to barring and spiral structure. Simulations are conducted for cold Mestel disks and warm quasi-exponential disks with completely flat rotation curves, subjected to pure quadrupoles and logarithmic spirals. Even though the starting velocity distributions are smooth, the end-points of the bar simulations show bimodality and multi-peaked structures at locations near the outer Lindblad resonance (OLR), although spirality can make this smoother. The growth of a bar may cause the disk isophotes to become boxy at the OLR, as stars accummulate particularly along the minor axis. The growth of a bar is also accompanied by substantial heating of the disk stars near the OLR. For the growth of a $10^{10} M_{\rm \odot}$ bar, the radial velocity dispersion is typically quadrupled for initially cold disks (initial \sigmau $\sim 10$ \kms), and typically doubled for disks with final \sigmau $\sim 45$ \kms. Simulations performed of the growth and dissolution of bars give very similar results, demonstrating that the heat once given to disk stars is very difficult to remove.

astro-ph↗

arXiv2002

Magnetically warped discs in close binaries

We demonstrate that measurable vertical structure can be excited in the accretion disc of a close binary system by a dipolar magnetic field centred on the secondary star. We present the first high resolution hydrodynamic simulations to show the initial development of a uniform warp in a tidally truncated accretion disc. The warp precesses retrogradely with respect to the inertial frame. The amplitude depends on the phase of the warp with respect to the binary frame. A warped disc is the best available explanation for negative superhumps.

astro-ph↗