arXiv subjects

Alaa Ibrahim

Publications and source records attributed to Alaa Ibrahim.

9 recordsLinked to original sources

arXiv2025

Machine Learning Identification of Gravitationally Microlensed Gamma-Ray Bursts

Gravitational microlensing of gamma-ray bursts (GRBs) provides a unique opportunity to probe compact dark matter and small-scale structures in the Universe. However, identifying such microlensed GRBs within large data sets is a significant challenge. In this study, we develop a machine learning (ML) approach to distinguish lensed GRBs from their nonlensed counterparts, using simulated light curves. A comprehensive data set is generated, comprising labeled light curves for both categories. Features are extracted using the Cesium package, capturing critical temporal properties of the light curves. Multiple ML models are trained on the extracted features, with Random Forest achieving the best performance, delivering an accuracy of 86% and an F1 score of 0.86 (0.87) for the nonlensed (lensed) class. This approach successfully demonstrates the potential of ML for identifying gravitational lensing in GRBs, paving the way for future observational applications.

astro-ph.HE↗

arXiv2025

Positivity Proofs for Linear Recurrences with Several Dominant Eigenvalues

Deciding the positivity of a sequence defined by a linear recurrence and initial conditions is, in general, a hard problem. When the coefficients of the recurrences are constants, decidability has only been proven up to order 5. The difficulty arises when the characteristic polynomial of the recurrence has several roots of maximal modulus, called dominant roots of the recurrence. We study the positivity problem for recurrences with polynomial coefficients, focusing on sequences of Poincar\'e type, which are perturbations of constant-coefficient recurrences. The dominant eigenvalues of a recurrence in this class are the dominant roots of the associated constant-coefficient recurrence. Previously, we have proved the decidability of positivity for recurrences having a unique, simple, dominant eigenvalue, under a genericity assumption. The associated algorithm proves positivity by constructing a positive cone contracted by the recurrence operator. We extend this cone-based approach to a larger class of recurrences, where a contracted cone may no longer exist. The main idea is to construct a sequence of cones. Each cone in this sequence is mapped by the recurrence operator to the next. This construction can be applied to prove positivity by induction. For recurrences with several simple dominant eigenvalues, we provide a condition that ensures that these successive inclusions hold. Additionally, we demonstrate the applicability of our method through examples, including recurrences with a double dominant eigenvalue.

cs.SC↗

arXiv2024

Positivity Proofs for Linear Recurrences through Contracted Cones

Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only for order up to~5. We consider a large class of linear recurrences of arbitrary order, with polynomial coefficients, for which an algorithm decides positivity for initial conditions outside of a hyperplane. The underlying algorithm constructs a cone, contracted by the recurrence operator, that allows a proof of positivity by induction. The existence and construction of such cones relies on the extension of the classical Perron-Frobenius theory to matrices leaving a cone invariant.

cs.SC↗

arXiv2023

Selection of Compton-thick AGN from a hard photometric sample using XMM-Newton observations

We present a selection technique to detect Compton-thick (CT) active galactic nuclei (AGNs) in the 3XMM/SDSS-DR7 cross-correlation. A subsample of 3481 X-ray sources that are detected in the hard band (2-8 keV) and have photometric redshifts constitute our parent sample. We first applied an automated spectral-fitting procedure to select highly absorbed sources (N_H > 10^23 cm^-2). We found 184 highly absorbed candidates. Then, we performed the Bayesian Monte Carlo Markov chains (MCMCs) selection technique to find CT AGNs. We also tested the MCMC selection technique by applying Monte Carlo simulations. We found that the method is accurate at 90 percent independently of the nature of the underlying source. Our sample contains 52 bona fide CT AGNs. The CT AGNs were selected to have a range > 0.75 of probability of being CT when either fitting with the two models Torus and MYTorus. About 75 percent of CT AGNs in our sample had probabilities > 90 percent. From the spectral analysis, we significantly found an anticorrelation between the equivalent width of the neutral Fe K_{\alpha} line and the X-ray luminosity at 2-10 keV, the so-called X-ray Baldwin effect.

astro-ph.GA↗

arXiv2023

Positivity certificates for linear recurrences

We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a precisely defined genericity condition. For positive sequences, the algorithm produces a certificate of positivity that is a data-structure for a proof by induction. This induction works by showing that an explicitly computed cone is contracted by the iteration of the recurrence.

cs.SC↗

arXiv2022

Fermi-GBM Observation of GRB 090717034: $\chi^2$ Test Confirms Evidence of Gravitational Lensing by a Supermassive Black Hole with Million Solar Mass

Gravitational lensing of gamma-ray bursts (GRBs) can provide an opportunity to probe the massive compact objects in the universe at different redshifts. We have discovered two consecutive pulses in the light curve of GRB 090717034, with the same temporal profile and different count rate, separated by a time interval, which is identified as gravitationally lensed candidate in Fermi/GBM GRB catalogue \citep{Kalantari}. Here, we use the $\chi^2$ method to investigate the similarity of the temporal profile variability of the two pulses as a gravitationally lensed candidate GRB. We find the magnification factor and the time delay between two pulses to correspond to minimising the $\chi^2$ function. Then, we perform a Monte Carlo simulation on a sample of mock lensed GRBs and compare the $\chi^2$ of the lensed GRB candidate with the simulation, which confirms this candidate with $1\sigma$ confidence level. Assuming that GRB 090717034 is lensed by a point-like object, the redshifted lens mass is about $M_L(1+z)=(4.220\pm 6.615) \times 10^6 M_{\odot}$. The lens of this GRB is a candidate for a super-massive black hole along the line of sight to the GRB.

astro-ph.HE↗

arXiv2021

Imprints of Gravitational Millilensing on the Light Curve of GRBs

In this work, we search for signatures of gravitational millilensing in Gamma-ray bursts (GRB) in which the source-lens-observer geometry produces two images that manifest in the GRB light curve as superimposed peaks with identical temporal variability (or echoes), separated by the time delay between the two images. According to the sensitivity of our detection method, we consider millilensing events due to point mass lenses in the range of $10^5 - 10^7 M_{\odot}$ at lens redshift about half that of the GRB, with a time delay in the order of $10$ seconds. Current GRB observatories are capable of resolving and constraining this lensing scenario if the above conditions are met. We investigated the Fermi/GBM GRB archive from the year 2008 to 2020 using the autocorrelation technique and we found one millilensed GRB candidate out of 2137 GRBs searched, which we use to estimate the optical depth of millilensed GRBs by performing a Monte-Carlo simulation to find the efficiency of our detection method. Considering a point-mass model for the gravitational lens, where the lens is a supermassive black hole, we show that the density parameter of black holes ($\Omega_{BH}$) with mass $\approx10^6 M_\odot$ is about $0.007 \pm 0.004$. Our result is one order of magnitude larger compared to consist with previous work in a lower mass range ($10^2 - 10^3 M_{\odot}$), which gave a density parameter $\Omega_{BH} \approx 5\times 10^{-4}$, and recent work in the mass range of $10^2 - 10^7 M_{\odot}$ that reported $\Omega_{BH} \approx 4.6\times 10^{-4}$. The mass fraction of black holes in this mass range to the total mass of the universe would be $f\approx \Omega_{BH}/\Omega_M=0.027 \pm 0.016$.

astro-ph.CO↗

arXiv2004

The Pulsed Spectra of Two Extraordinary Pulsars

We report on X-ray monitoring of two isolated pulsars within the same RXTE field of view. PSR J1811-1925 in the young supernova remnant G11.2-0.3 has a nearly sinusoidal pulse profile with a hard pulsed spectrum (photon index \~1.2). The pulsar is a highly efficient (~ 1% of spin-down energy) emitter of 2-50 keV pulsed X-rays despite having a fairly typical B ~ 2e12 G magnetic field. PSR J1809-1943/XTE J1810-197 is a newly discovered slow (P=5.54 s), apparently isolated X-ray pulsar which increased in flux by a factor of ~100 in 2003 January. Nine months of monitoring observations have shown a decrease in pulsed flux of ~ 30% without a significant change in its apparently thermal spectrum (kT ~0.7 keV) or pulse profile. During this time, the spin-down torque has fluctuated by a factor of ~ 2. Both the torque and the flux have remained steady for the last 3 months, at levels consistent with a magnetar interpretation.

astro-ph↗

arXiv1998

X-ray Spectroscopy of Bursts from SGR 1806-20 with RXTE

We report on new RXTE X-ray spectral analysis of bursts from SGR 1806-20, the most prolific SGR source known. Previous studies of bursts from this source revealed a remarkable lack of spectral variability both in single bursts as well as from burst to burst. We present here some of the first evidence for significant spectral evolution within SGR bursts. We find that optically thin thermal bremsstrahlung (OTTB) spectra including photoelectric absorption provide the best fits to most bursts, however, other models (power law, Band GRB) can also produce statistically acceptable fits. We confirm the existence of a rolloff in the photon number spectrum below 5 keV.

astro-ph↗