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Sourav Chatterjee

Publications and source records attributed to Sourav Chatterjee.

At least 73 records · Page 4Linked to original sources
arXiv2022

Globular Cluster UVIT legacy Survey (GlobUleS) III. Omega Centauri in Far-Ultraviolet

We present the first comprehensive study of the most massive globular cluster Omega Centauri in the far-ultraviolet (FUV) extending from the center to ~ 28% of the tidal radius using the Ultraviolet Imaging Telescope aboard AstroSat. A comparison of the FUV-optical color-magnitude diagrams with available canonical models reveals that the horizontal branch (HB) stars bluer than the knee (hHBs) and the white dwarfs (WDs) are fainter in the FUV by ~ 0.5 mag than model predictions. They are also fainter than their counterparts in M13, another massive cluster. We simulated HB with at least five subpopulations, including three He-rich populations with a substantial He enrichment of Y up to 0.43 dex, to reproduce the observed FUV distribution. We find the He-rich younger subpopulations to be radially more segregated than the He-normal older ones, suggesting an in-situ enrichment from older generations. The Omega Cen hHBs span the same effective temperature range as their M13 counterparts, but some have smaller radii and lower luminosities. This may suggest that a fraction of Omega Cen hHBs are less massive than those of M13, similar to the result derived from earlier spectroscopic studies of outer extreme HB stars. The WDs in Omega Cen and M13 have similar luminosity-radius-effective temperature parameters, and 0.44 - 0.46 M$_\odot$ He-core WD model tracks evolving from progenitors with Y = 0.4 dex are found to fit the majority of these. This study provides constraints on the formation models of Omega Cen based on the estimated range in age, [Fe/H] and Y (in particular), for the HB stars.

astro-ph.SR↗
arXiv2022

The Yang-Mills heat flow with random distributional initial data

We construct local solutions to the Yang-Mills heat flow (in the DeTurck gauge) for a certain class of random distributional initial data, which includes the 3D Gaussian free field. The main idea, which goes back to work of Bourgain as well as work of Da Prato-Debussche, is to decompose the solution into a rougher linear part and a smoother nonlinear part, and to control the latter by probabilistic arguments. In a companion work, we use the main results of this paper to propose a way towards the construction of 3D Yang-Mills measures.

math.PR↗
arXiv2022

Polarization correction towards satellite-based QKD without an active feedback

Quantum key distribution (QKD) is a cryptographic protocol to enable two parties to share a secure key string, which can be used in one-time pad cryptosystem. There has been an ongoing surge of interest in implementing long-haul photonic-implementation of QKD protocols. However, the endeavour is challenging in many aspects. In particular, one of the major challenges is the polarization degree of freedom of single-photons getting affected while transmission through optical fibres, or atmospheric turbulence. Conventionally, an active feedback-based mechanism is employed to achieve real-time polarization tracking. In this work, we propose an alternative approach where we first perform a state tomography to reconstruct the output density matrix. We then evaluate the optimal measurement bases at Bob's end that leads to the maximum (anti-)correlation in the measurement outcomes of both parties. As a proof-of-principle demonstration, we implement an in-lab BBM92 protocol -- a particular variant of a QKD protocol using quantum entanglement as a resource -- to exemplify the performance of our technique. We experimentally generate polarization-entangled photon pairs having $94\%$ fidelity with $\ketψ_1 = 1/\sqrt{2}\,(\ket{HV}+\ket{VH})$ state and a concurrence of $0.92$. By considering a representative 1 ns coincidence window span, we are able to achieve a quantum-bit-error-rate (QBER) of $\approx 5\%$, and a key rate of $\approx 35$ Kbps. The protocol performance is independent of local polarization rotations through optical fibres. We also develop an algorithmic approach to optimize the trade-off between the key rate and QBER. Our approach obviates the need for active polarization tracking. Our method is also applicable to entanglement-based QKD demonstrations using partially mixed as well as non-maximally entangled states, and extends to single-photon implementations over fibre channels.

quant-ph↗
arXiv2022

Local KPZ behavior under arbitrary scaling limits

One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a scaling limit, so that the limit is nontrivial, is not known in a rigorous sense. To understand KPZ growth without being hindered by this issue, this article introduces a notion of "local KPZ behavior", which roughly means that the instantaneous growth of the surface at a point decomposes into the sum of a Laplacian term, a gradient squared term, a noise term that behaves like white noise, and a remainder term that is negligible compared to the other three terms and their sum. The main result is that for a general class of surfaces, which contains the model of directed polymers in a random environment as a special case, local KPZ behavior occurs under arbitrary scaling limits, in any dimension.

math.PR↗
arXiv2022

Compact Object Modeling in the Globular Cluster 47 Tucanae

The globular cluster 47~Tucanae (47~Tuc) is one of the most massive star clusters in the Milky Way and is exceptionally rich in exotic stellar populations. For several decades it has been a favorite target of observers, and yet it is computationally very challenging to model because of its large number of stars ($N\gtrsim 10^6$) and high density. Here we present detailed and self-consistent 47~Tuc models computed with the \texttt{Cluster Monte Carlo} code (\texttt{CMC}). The models include all relevant dynamical interactions coupled to stellar and binary evolution, and reproduce various observations, including the surface brightness and velocity dispersion profiles, pulsar accelerations, and numbers of compact objects. We show that the present properties of 47~Tuc are best reproduced by adopting an initial stellar mass function that is both bottom-heavy and top-light relative to standard assumptions \citep[as in, e.g.,][]{Kroupa2001}, and an initial Elson profile \citep{Elson1987} that is overfilling the cluster's tidal radius. We include new prescriptions in \texttt{CMC} for the formation of binaries through giant star collisions and tidal captures, and we show that these mechanisms play a crucial role in the formation of neutron star binaries and millisecond pulsars in 47~Tuc; our best-fit model contains $\sim 50$ millisecond pulsars, $70\%$ of which are formed through giant collisions and tidal captures. Our models also suggest that 47~Tuc presently contains up to $\sim 200$ stellar-mass black holes, $\sim 5$ binary black holes, $\sim 15$ low-mass X-ray binaries, and $\sim 300$ cataclysmic variables.

astro-ph.HE↗
arXiv2022

MOSPAT: AutoML based Model Selection and Parameter Tuning for Time Series Anomaly Detection

Organizations leverage anomaly and changepoint detection algorithms to detect changes in user behavior or service availability and performance. Many off-the-shelf detection algorithms, though effective, cannot readily be used in large organizations where thousands of users monitor millions of use cases and metrics with varied time series characteristics and anomaly patterns. The selection of algorithm and parameters needs to be precise for each use case: manual tuning does not scale, and automated tuning requires ground truth, which is rarely available. In this paper, we explore MOSPAT, an end-to-end automated machine learning based approach for model and parameter selection, combined with a generative model to produce labeled data. Our scalable end-to-end system allows individual users in large organizations to tailor time-series monitoring to their specific use case and data characteristics, without expert knowledge of anomaly detection algorithms or laborious manual labeling. Our extensive experiments on real and synthetic data demonstrate that this method consistently outperforms using any single algorithm.

cs.LG↗
arXiv2022

Existence of stationary ballistic deposition on the infinite lattice

Ballistic deposition is one of the many models of interface growth that are believed to be in the KPZ universality class, but have so far proved to be largely intractable mathematically. In this model, blocks of size one fall independently as Poisson processes at each site on the $d$-dimensional lattice, and either attach themselves to the column growing at that site, or to the side of an adjacent column, whichever comes first. It is not hard to see that if we subtract off the height of the column at the origin from the heights of the other columns, the resulting interface process is Markovian. The main result of this article is that this Markov process has at least one invariant probability measure. We conjecture that the invariant measure is not unique, and provide some partial evidence.

math.PR↗
arXiv2022

A random walk on the Rado graph

The Rado graph, also known as the random graph $G(\infty, p)$, is a classical limit object for finite graphs. We study natural ball walks as a way of understanding the geometry of this graph. For the walk started at $i$, we show that order $\log_2^*i$ steps are sufficient, and for infinitely many $i$, necessary for convergence to stationarity. The proof involves an application of Hardy's inequality for trees.

math.PR↗
arXiv2022

Superconcentration in surface growth

Height functions of growing random surfaces are often conjectured to be superconcentrated, meaning that their variances grow sublinearly in time. This article introduces a new concept, called subroughness, meaning that there exist two distinct points such that the expected squared difference between the heights at these points grows sublinearly in time. The main result of the paper is that superconcentration is equivalent to subroughness in a class of growing random surfaces. The result is applied to establish superconcentration in a variant of the restricted solid-on-solid (RSOS) model and in a variant of the ballistic deposition model, and give new proofs of superconcentration in directed last-passage percolation and directed polymers.

math.PR↗
arXiv2022

Globular Clusters UVIT Legacy Survey (GlobULeS) I. FUV-optical Color-Magnitude Diagrams for Eight Globular Clusters

We present the first results of eight Globular Clusters (GCs) from the AstroSat/UVIT Legacy Survey program GlobULeS based on the observations carried out in two FUV filters (F148W and F169M). The FUV-optical and FUV-FUV color-magnitude diagrams (CMDs) of GCs with the proper motion membership were constructed by combining the UVIT data with HST UV Globular Cluster Survey (HUGS) data for inner regions and Gaia Early Data Release (EDR3) for regions outside the HST's field. We detect sources as faint as F148W $\sim$ 23.5~mag which are classified based on their locations in CMDs by overlaying stellar evolutionary models. The CMDs of 8 GCs are combined with the previous UVIT studies of 3 GCs to create stacked FUV-optical CMDs to highlight the features/peculiarities found in the different evolutionary sequences. The FUV (F148W) detected stellar populations of 11 GCs comprises 2,816 Horizontal Branch (HB) stars (190 Extreme HB candidates), 46 post-HB (pHB), 221 Blue Straggler Stars (BSS), and 107 White Dwarf (WD) candidates. We note that the blue HB color extension obtained from F148W$-$G color and the number of FUV detected EHB candidates are strongly correlated with the maximum internal Helium (He) variation within each GC, suggesting that the FUV-optical plane is the most sensitive to He abundance variations in the HB. We discuss the potential science cases that will be addressed using these catalogues including HB morphologies, BSSs, pHB, and, WD stars.

astro-ph.GA↗
arXiv2022

Matrix completion with data-dependent missingness probabilities

The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and nuclear norm minimization. Most of the past works on this subject assume that there is a single number $p$ such that each entry of the matrix is available independently with probability $p$ and missing otherwise. This assumption may not be realistic for many applications. In this work, we replace it with the assumption that the probability that an entry is available is an unknown function $f$ of the entry itself. For example, if the entry is the rating given to a movie by a viewer, then it seems plausible that high value entries have greater probability of being available than low value entries. We propose two new estimators, based on singular value thresholding and nuclear norm minimization, to recover the matrix under this assumption. The estimators involve no tuning parameters, and are shown to be consistent under a low rank assumption. We also provide a consistent estimator of the unknown function $f$.

math.ST↗
arXiv2022

Gaia May Detect Hundreds of Well-characterised Stellar Black Holes

Detection of black holes (BHs) with detached luminous companions (LCs) can be instrumental in connecting the BH properties with their progenitors' since the latter can be inferred from the observable properties of the LC. Past studies showed the promise of Gaia astrometry in detecting BH-LC binaries. We build upon these studies by: 1) initialising the zero-age binary properties based on realistic, metallicity-dependent star-formation history in the Milky Way (MW), 2) evolving these binaries to current epoch to generate realistic MW populations of BH-LC binaries, 3) distributing these binaries in the MW preserving the complex age-metallicity-Galactic position correlations, 4) accounting for extinction and reddening using three-dimensional dust maps, 5) examining the extended Gaia mission's ability to resolve BH-LC binaries. We restrict ourselves to detached BH-LC binaries with orbital period <10 yr such that Gaia can observe at least one full orbit. We find: 1) the extended Gaia mission can astrometrically resolve 30-300 detached BH-LC binaries depending on our assumptions of supernova physics and astrometric detection threshold; 2) Gaia's astrometry alone can indicate BH candidates for 10-100 BH-LC binaries by constraining the dark primary mass >3 Msun; 3) distributions of observables including orbital periods, eccentricities, and component masses are sensitive to the adopted binary evolution model, hence can directly inform binary evolution models. Finally, we comment on the potential to further characterise these BH binaries through radial velocity measurements and observation of X-ray counterparts.

astro-ph.GA↗
arXiv2021

Convergence of deterministic growth models

We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are characterized as the unique (viscosity solutions) of first- or second-order partial differential equations depending on whether the growth models are scaled hyperbolically or parabolically. The results greatly simplify and extend a recent work by the first author to more general surface growth models. The proofs are based on the methodology developed by Barles and the second author to prove convergence of approximation schemes.

math.PR↗
arXiv2021

Gravitational Wave observatories may be able to detect hyperbolic encounters of Black Holes

Gravitational Wave (GW) astronomy promises to observe different kinds of astrophysical sources. Here we explore the possibility of detection of GWs from hyperbolic interactions of compact stars with ground-based interferometric detectors. It is believed that a bound compact cluster, such as a globular cluster, can be a primary environment for these interactions. We estimate the detection rates for such events by considering local geometry within the cluster, accounting for scattering probability of compact stars at finite distances, and assuming realistic cluster properties guided by available numerical models, their formation times, and evolution of stars inside them. We find that, even in the conservative limit, it may be possible to detect such black hole encounters in the next few years by the present network of observatories with the ongoing sensitivity upgrades and one to few events per year with the next generation observatories. In practice, actual detection rates can significantly surpass the estimated average rates, since the chances of finding outliers in a very large population can be high. Such observations (or, no observation) may provide crucial constraints to estimate the number of isolated compact stars in the universe. These detections will be exciting discoveries on their own and will be complimentary to observations of binary mergers bringing us one step closer to address a fundamental question, how many black holes are there in the observable universe.

gr-qc↗
arXiv2021

Weighing the Darkness II: Astrometric Measurement of Partial Orbits with Gaia

Over the course of several years, stars trace helical trajectories as they traverse across the sky due to the combined effects of proper motion and parallax. It is well known that the gravitational pull of an unseen companion can cause deviations to these tracks. Several studies have pointed out that the astrometric mission Gaia will be able to identify a slew of new exoplanets, stellar binaries, and compact object companions with orbital periods as short as tens of days to as long as Gaia's lifetime. Here, we use mock astrometric observations to demonstrate that Gaia can identify and characterize black hole companions to luminous stars with orbital periods longer than Gaia's lifetime. Such astrometric binaries have orbital periods too long to exhibit complete orbits, and instead are identified through curvature in their characteristic helical paths. By simultaneously measuring the radius of this curvature and the orbital velocity, constraints can be placed on the underlying orbit. We quantify the precision with which Gaia can measure orbital accelerations and apply that to model predictions for the population of black holes orbiting stars in the stellar neighborhood. Although orbital degeneracies imply that many of the accelerations induced by hidden black holes could also be explained by faint low-mass stars, we discuss how the nature of certain putative black hole companions can be confirmed with high confidence using Gaia data alone.

astro-ph.SR↗
arXiv2021

Modeling Dense Star Clusters in the Milky Way and Beyond with the Cluster Monte Carlo Code

We describe the public release of the Cluster Monte Carlo Code (CMC) a parallel, star-by-star $N$-body code for modeling dense star clusters. CMC treats collisional stellar dynamics using Hénon's method, where the cumulative effect of many two-body encounters is statistically reproduced as a single effective encounter between nearest-neighbor particles on a relaxation timescale. The star-by-star approach allows for the inclusion of additional physics, including strong gravitational three- and four-body encounters, two-body tidal and gravitational-wave captures, mass loss in arbitrary galactic tidal fields, and stellar evolution for both single and binary stars. The public release of CMC is pinned directly to the COSMIC population synthesis code, allowing dynamical star cluster simulations and population synthesis studies to be performed using identical assumptions about the stellar physics and initial conditions. As a demonstration, we present two examples of star cluster modeling: first, we perform the largest ($N = 10^8$) star-by-star $N$-body simulation of a Plummer sphere evolving to core collapse, reproducing the expected self-similar density profile over more than 15 orders of magnitude; second, we generate realistic models for typical globular clusters, and we show that their dynamical evolution can produce significant numbers of black hole mergers with masses greater than those produced from isolated binary evolution (such as GW190521, a recently reported merger with component masses in the pulsational pair-instability mass gap).

astro-ph.GA↗
arXiv2021

Universality of deterministic KPZ

Consider a deterministically growing surface of any dimension, where the growth at a point is an arbitrary nonlinear function of the heights at that point and its neighboring points. Assuming that this nonlinear function is monotone, invariant under the symmetries of the lattice, equivariant under constant shifts, and twice continuously differentiable, it is shown that any such growing surface approaches a solution of the deterministic KPZ equation in a suitable space-time scaling limit.

math.PR↗