arXiv subjects

Fazlu Rahman

Publications and source records attributed to Fazlu Rahman.

7 recordsLinked to original sources

arXiv2026

Understanding the non-Gaussian nature of Galactic foreground emissions towards small scales

We present a unified, multi-scale study of non-Gaussianity of Galactic foreground emissions using Minkowski Functionals and generalized skewness-kurtosis parameters, focusing on the characterization of small-scale non-Gaussianity and its underlying physical origin. We find that all foreground components studied exhibit a remarkably universal non-Gaussian nature dominated by excess kurtosis, whose shape remains stable across angular scales despite large differences in emission physics. Focusing on thermal dust, we perform a detailed comparison between observed maps (GNILC and Planck 545 GHz) and dust model realizations (PySM and filament-based models) to assess the performance of state-of-the-art models in reproducing the observed non-Gaussian properties. At the global level, GNILC and PySM display closely matched kurtosis behavior over the angular scales where the GNILC reconstruction is reliable, while the filament-based model produces substantially weaker skewness and kurtosis signals. For PySM, however, a patch-based analysis reveals statistically significant regional variations, indicating that while the model reproduces the overall non-Gaussian amplitude and scale dependence, it does not fully capture the spatial variability of the observed kurtosis signal. Using simple PDF-based toy models, we demonstrate that the universal kurtosis signature arises from the combination of heavy-tailed one-point statistics and steep large-scale spatial correlations, while its detailed amplitude and scale dependence depend on the underlying foreground physics. These results identify excess kurtosis as a robust statistical fingerprint of Galactic foregrounds and provide a practical framework for validating small-scale foreground models for future CMB analyses.

astro-ph.CO↗

arXiv2025

Local patch analysis of ACT DR6 convergence map using morphological statistics

We carry out a comprehensive hierarchical multi-scale morphological analysis to search for anomalous behaviour in the large scale matter distribution using convergence map provided by the Atacama Cosmology Telescope (ACT) Data Release 6. We use a suite of morphological statistics consisting of Minkowski functionals, contour Minkowski tensor and Betti numbers for the analysis, and compute their deviations from the ensemble expectations and median values obtained from isotropic $\Lambda$CDM simulations provided by ACT. To assess the statistical significance of these deviations, we devise a general methodology based on the persistence of the deviations across threshold ranges and spatial resolutions, while taking into account correlations among the statistics. From the analysis of the full dataset, and hemispherical regions, we find consistency with isotropic $\Lambda$CDM simulations provided by ACT. Since deviations in smaller sky regions tend to get washed out when averaged over larger regions, we further analyze smaller sky patches. This localized analysis reveals some patches that exhibit statistically significant deviations which we refer to as 'anomalous'. We find that near the CMB cold spot, both the positive and negative density fluctuations are anomalous, at 99% CL and 95% CL respectively. This region also encompasses an anomalous southern spot previously identified in Planck CMB temperature data. We also carry out a comparison of anomalous patches identified here for ACT data with a previous analysis of the convergence map from Planck. We do not find common patches between the two datasets, which suggest that the anomalous behavior of the Planck data arises from noise in the map. Further investigation of the atypical patches using large scale structure surveys is warranted to determine their physical origin.

astro-ph.CO↗

arXiv2023

Minkowski Functionals for composite smooth random fields

Minkowski functionals quantify the morphology of smooth random fields. They are widely used to probe statistical properties of cosmological fields. Analytic formulae for ensemble expectations of Minkowski functionals are well known for Gaussian and mildly non-Gaussian fields. In this paper we extend the formulae to composite fields which are sums of two fields and explicitly derive the expressions for the sum of uncorrelated mildly non-Gaussian and Gaussian fields. These formulae are applicable to observed data which is usually a sum of the true signal and one or more secondary fields that can be either noise, or some residual contaminating signal. Our formulae provide explicit quantification of the effect of the secondary field on the morphology and statistical nature of the true signal. As examples, we apply the formulae to determine how the presence of Gaussian noise can bias the morphological properties and statistical nature of Gaussian and non-Gaussian CMB temperature maps.

astro-ph.CO↗

arXiv2022

Statistical properties of Galactic synchrotron temperature and polarization maps -- a multi-frequency comparison

Understanding the statistical properties of synchrotron emission from our Galaxy is valuable from the perspective of observations targeting signals of cosmological origin, as well as for understanding physical processes in our Galaxy. In this work, we extend the analysis of arXiv:2104.00419v2 to -- (a) all-sky observed maps of total foreground emissions at different frequencies provided by WMAP, Planck and Stockert-Villa, (b) component separated synchrotron temperature maps provided by WMAP, Planck and BeyondPlanck, and (c) component separated polarization maps provided by WMAP and Planck. The tools we use are Minkowski functionals and tensors. Our main goals are twofold. First, we determine the variation of morphological properties of the total foreground maps with observing frequency and compare with simulations. This elucidates how the morphology varies due to the relative dominance of different foreground components at different frequencies. Next, we analyze the nature of non-Gaussianity and statistical isotropy of synchrotron fluctuations on smaller scales using various component separated synchrotron temperature and polarization maps. We find that all maps exhibit kurtosis non-Gaussianity, in agreement with the Haslam map. This result can be an important input for the modelling of small-scale synchrotron fluctuations for component separation pipelines. This also suggests that residual synchrotron contamination in CMB will manifest as kurtosis. Studying different component separated maps, we find that BeyondPlanck and WMAP MCMC-e agree well with Haslam at all scales. The other maps show differences of varying statistical significance. Our analysis suggests a combination of residual AME and/or free-free emissions and point sources as contributing to these differences, and underscores the need for further improvement of the pipelines.

astro-ph.CO↗

arXiv2022

Analysis of the structural complexity of Crab Nebula observed at radio frequency using a multifractal approach

The Crab Nebula is an astrophysical system that exhibits complex morphological patterns at different observing frequencies. We carry out a systematic investigation of the structural complexity of the nebula using publicly available imaging data at radio frequency. For the analysis, we use the well-known multifractal detrended fluctuation analysis in two dimensions. We find that radio data exhibit long-range correlations, as expected from the underlying physics of the supernova explosion and evolution. The correlations follow a power-law scaling with length scales. The structural complexity is found to be multifractal in nature, as evidenced by the dependence of the generalized Hurst exponent on the order of the moments of the detrended fluctuation function. By repeating the analysis on shuffled data, we further probe the origin of the multifractality in the radio imaging data. For the radio data, we find that the probability density function is close to a Gaussian form. Hence, the multifractal behavior is due to the differing nature of long-range correlations of the large and small detrended fluctuation field values. We investigate the multifractal parameters across different partitions of the radio image and find that the structures across the image are highly heterogeneous, making the Crab Nebula a structurally complex astrophysical system. Our analysis thus provides a fresh perspective on the morphology of the Crab Nebula from a complexity science viewpoint.

nlin.AO↗

arXiv2021

The nature of non-Gaussianity and statistical isotropy of the 408 MHz Haslam synchrotron map

Accurate component separation of full-sky maps in the radio and microwave frequencies, such as the cosmic microwave background (CMB), relies on a thorough understanding of the statistical properties of the Galactic foreground emissions. Using scalar Minkowski functionals and their tensorial generalization known as Minkowski tensors, we analyze the statistical properties of one of the major foreground components, namely the Galactic synchrotron given by the full sky 408 MHz Haslam map. We focus on understanding the nature of non-Gaussianity and statistical isotropy of the cooler regions of the map as a function of angular scale. We find that the overall level of the non-Gaussian deviations does decrease as more high emission regions are masked and as we go down to smaller scales, in agreement with the results obtained in earlier works. However, they remain significantly high, of order 3.3$\sigma$, at the smallest angular scales relevant for the Haslam map. We carry out a detailed examination of the non-Gaussian nature using the generalized skewness and kurtosis cumulants that arise in the perturbative expansion of Minkowski functionals for weakly non-Gaussian fields. We find that the leading sources of non-Gaussianity are the kurtosis terms which are considerably larger than the skewness terms at all angular scales. Further, for the cooler regions of the Haslam map, we find that the non-Gaussian deviations of the Minkowski functionals can be well explained by the perturbative expansion up to second-order (up to kurtosis terms), with first-order terms being sub-dominant. Lastly, we test the statistical isotropy of the Haslam map and find that it becomes increasingly more isotropic at smaller scales.

astro-ph.CO↗

arXiv2018

Aspects of Black Hole Physics and Formation of Super-massive Black Holes from Ultra-light Dark Bosons

First, we verify that the physical parameters estimated for the four directly detected gravitational wave (GW) events involving coalescence of binary black holes (BHs) indeed uphold the second law of BH thermodynamics, strengthening further the case for BH physics. Non-spherical gravitational collapse leading to BH formation may entail very high GW luminosities during the final phase of implosion, reaching non-negligible fraction of Dyson luminosity $\sim c^5/G $. Most galaxies harbor supermassive black holes (SMBHs) in their nuclear regions. Several bright quasars detected at redshifts $\gtrsim$ 6 are powered by accreting SMBHs of mass $\gtrsim 10^9 M_\odot$ when the universe was only $\sim 10^9$ yrs old. We posit that creation of SMBHs occurs due to collapse (on dynamical time scales $\sim 10^8$ yrs) of ultra-light bosonic dark matter (DM) particles that have undergone Bose-Einstein condensation. Furthermore, oscillations in DM Bose-Einstein condensates (BECs) triggered by tidal forces in interacting galaxies can lead to bursts of star formation in the galactic nuclei because of frequent collisions of gas clouds due to changing gravitational field. We buttress our proposal by first employing simple but tangible physical arguments, and then by making use of Gross-Pitaevskii equation to study the formation of rotating SMBHs having mass $\gtrsim 10^9 M_\odot$. We also make simple estimates of GW amplitude as well as luminosity ensuing from the time varying configuration of BECs, constituted by the ultra-light dark bosons, and remark on the possibility of detecting such GWs using Pulsar Timing Arrays.

gr-qc↗