arXiv subjects

Mohammed Khalil

Publications and source records attributed to Mohammed Khalil.

At least 19 recordsLinked to original sources

arXiv2024

Accurate waveforms for eccentric, aligned-spin binary black holes: The multipolar effective-one-body model SEOBNRv5EHM

The measurement of orbital eccentricity in gravitational-wave (GW) signals will provide unique insights into the astrophysical origin of binary systems, while ignoring eccentricity in waveform models could introduce significant biases in parameter estimation and tests of General Relativity. Upcoming LIGO-Virgo-KAGRA observing runs are expected to detect a subpopulation of eccentric signals, making it vital to develop accurate waveform models for eccentric orbits. Here, employing recent analytical results through the third post-Newtonian order, we develop SEOBNRv5EHM: a new time-domain, effective-one-body, multipolar waveform model for eccentric binary black holes with spins aligned (or antialigned) with the orbital angular momentum. Besides the dominant (2,2) mode, the model includes the (2,1), (3,3), (3,2), (4,4) and (4,3) modes. We validate the model's accuracy by computing its unfaithfulness against 99 (28 public and 71 private) eccentric numerical-relativity (NR) simulations, produced by the Simulating eXtreme Spacetimes Collaboration. Importantly, for NR waveforms with initial GW eccentricities below 0.5, the maximum (2,2)-mode unfaithfulness across the total mass range 20-200 $M_\odot$ is consistently below or close to $1 \%$, with a median value of $ \sim 0.02 \% $, reflecting an accuracy improvement of approximately an order of magnitude compared to the previous-generation SEOBNRv4EHM and the state-of-the-art TEOBResumS-Dal\'i eccentric model. In the quasi-circular-orbit limit, SEOBNRv5EHM is in excellent agreement with the highly accurate SEOBNRv5HM model. The accuracy, robustness, and speed of SEOBNRv5EHM make it suitable for data analysis and astrophysical studies. We demonstrate this by performing a set of recovery studies of synthetic NR-signal injections, and parameter-estimation analyses of the events GW150914 and GW190521, which we find to have no eccentricity signatures.

gr-qc↗

arXiv2024

Third post-Newtonian dynamics for eccentric orbits and aligned spins in the effective-one-body waveform model SEOBNRv5EHM

Accurate waveform models for coalescing binaries on eccentric orbits are crucial for avoiding biases in the analysis of eccentric gravitational-wave signals. The effective-one-body (EOB) formalism combines various analytical approximation methods with information derived from numerical-relativity simulations, and it has proven reliable in modeling the inspiral-merger-ringdown waveform of binaries on generic orbits. In this work, we derive new analytical results within the EOB formalism, specifically addressing eccentric, aligned-spin binaries. For the first time, we obtain EOB results for eccentric orbits that are accurate up to the third post-Newtonian (PN) order for the complete far-zone energy and angular-momentum fluxes, the radiation-reaction (RR) force, and waveform modes (including memory contributions). We obtain these results by deriving transformations from the harmonic to EOB coordinates and from the quasi-Keplerian to the Keplerian parametrization, that properly account for the spin-supplementary condition, post-adiabatic contributions, and the gauge freedom in the RR force. We employ these findings to build the inspiral part of the SEOBNRv5EHM waveform model, which includes the 3PN eccentricity contributions in the RR force and waveform modes using the Keplerian parametrization, and augments the EOB equations of motion with PN evolution equations for the Keplerian parameters. The new SEOBNR model achieves much better accuracy than its predecessor SEOBNRv4EHM and other eccentric models, even for eccentricities as high as $\lesssim 0.5$.

gr-qc↗

arXiv2024

Post-Newtonian observables for aligned-spin binaries to sixth order in spin from gravitational self-force and Compton amplitudes

Accurate modeling of compact binaries is essential for gravitational-wave detection and parameter estimation, with spin being an important effect to include in waveform models. In this paper, we derive new post-Newtonian (PN) results for the conservative aligned-spin dynamics at next-to-next-to-leading order for the spin$^3$ and spin$^4$ contributions, in addition to the next-to-leading order (NLO) spin$^5$ and spin$^6$ contributions. One approach we follow is the Tutti Frutti method, which relates PN and gravitational self-force results through the redshift and spin-precession invariants, by making use of the simple dependence of the scattering angle on the symmetric mass ratio. However, an ambiguity arises at the NLO spin$^5$ contribution, due to transcendental functions of the Kerr spin in the redshift; this is also the order at which Compton amplitudes calculations are affected by spurious poles. Therefore, we follow an additional approach to determine the NLO spin$^5$ and spin$^6$ dynamics: using on-shell Compton amplitudes obtained from black hole perturbation theory. The Compton amplitude used in this work is composed of the unambiguous tree-level far-zone part reported in [Phys. Rev. D 109, 084071 (2024)], as well as the full, non-interfering with the far-zone, $\ell=2$ partial wave contributions from the near zone, which are responsible for capturing Kerr finite-size effects. Other results in this paper include deriving the scattering angle of a spinning test body in a Kerr background from a parametrized worldline action, and computing the redshift and spin-precession invariants for eccentric orbits without an eccentricity expansion.

gr-qc↗

arXiv2024

ATHAR: A High-Quality and Diverse Dataset for Classical Arabic to English Translation

Classical Arabic represents a significant era that encompasses the golden age of Arab culture, philosophy, and scientific literature. With a broad consensus on the importance of translating these literatures to enrich knowledge dissemination across communities, the advent of large language models (LLMs) and translation systems offers promising tools to facilitate this goal. However, we have identified a scarcity of translation datasets in Classical Arabic, which are often limited in scope and topics, hindering the development of high-quality translation systems. In response, we present the ATHAR dataset, which comprises 66,000 high-quality classical Arabic to English translation samples that cover a wide array of topics including science, culture, and philosophy. Furthermore, we assess the performance of current state-of-the-art LLMs under various settings, concluding that there is a need for such datasets in current systems. Our findings highlight how models can benefit from fine-tuning or incorporating this dataset into their pretraining pipelines. The dataset is publicly available on the HuggingFace Data Hub: https://huggingface.co/datasets/mohamed-khalil/ATHAR.

cs.CL↗

arXiv2024

Testing eccentric corrections to the radiation-reaction force in the test-mass limit of effective-one-body models

In this work, we test an effective-one-body radiation-reaction force for eccentric planar orbits of a test mass in a Kerr background, which contains third-order post-Newtonian (PN) non-spinning and second-order PN spin contributions. We compare the analytical fluxes connected to two different resummations of this force, truncated at different PN orders in the eccentric sector, with the numerical fluxes computed through the use of frequency- and time-domain Teukolsky-equation codes. We find that the different PN truncations of the radiation-reaction force show the expected scaling in the weak gravitational-field regime, and we observe a fractional difference with the numerical fluxes that is $<5 \%$, for orbits characterized by eccentricity $0 \le e \le 0.7$, central black-hole spin $-0.99 M \le a \le 0.99 M$ and fixed orbital-averaged quantity $x=\langle M\Omega \rangle^{2/3} = 0.06$, corresponding to the mildly strong-field regime with semilatera recta $9 M<p<17 M$. Our analysis provides useful information for the development of spin-aligned eccentric models in the comparable-mass case.

gr-qc↗

arXiv2024

Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order

Upcoming observational runs of the LIGO-Virgo-KAGRA collaboration, and future gravitational-wave (GW) detectors on the ground and in space, require waveform models more accurate than currently available. High-precision waveform models can be developed by improving the analytical description of compact binary dynamics and completing it with numerical-relativity (NR) information. Here, we assess the accuracy of the recent results for the fourth post-Minkowskian (PM) conservative dynamics through comparisons with NR simulations for the circular-orbit binding energy and for the scattering angle. We obtain that the 4PM dynamics gives better agreement with NR than the 3PM dynamics, and that while the 4PM approximation gives comparable results to the third post-Newtonian (PN) approximation for bound orbits, it performs better for scattering encounters. Furthermore, we incorporate the 4PM results in effective-one-body (EOB) Hamiltonians, which improves the disagreement with NR over the 4PM-expanded Hamiltonian from $\sim 40\%$ to $\sim 10\%$, or $\sim 3\%$ depending on the EOB gauge, for an equal-mass binary, two GW cycles before merger. Finally, we derive a 4PN-EOB Hamiltonian for hyperbolic orbits, and compare its predictions for the scattering angle to NR, and to the scattering angle of a 4PN-EOB Hamiltonian computed for elliptic orbits.

gr-qc↗

arXiv2023

Spin effects in gravitational waveforms and fluxes for binaries on eccentric orbits to the third post-Newtonian order

Compact binaries can have non-negligible orbital eccentricities in the frequency band of ground-based gravitational-wave detectors, depending on their astrophysical formation channels. To accurately determine the parameters of such systems, waveform models need to incorporate eccentricity effects. In this paper, we consider an eccentric binary of spinning nonprecessing compact objects, and derive the energy and angular momentum fluxes at infinity, as well as the gravitational waveform modes to the third post-Newtonian order. The novel results of this paper include the next-to-leading order instantaneous spin-orbit and spin-spin contributions to the waveform modes, in addition to the hereditary (tail and memory) contributions to the modes and fluxes for eccentric orbits. The instantaneous contributions are derived for generic motion, while the hereditary contributions are computed in a small-eccentricity expansion, but we consider a resummation that makes them valid for large eccentricities. We employ a quasi-Keplerian parametrization of the motion using harmonic coordinates and the covariant spin-supplementary condition, which complements some results in the literature in other coordinates. Our results can be useful in improving the accuracy of waveform models for spinning binaries on eccentric orbits.

gr-qc↗

arXiv2023

Theoretical groundwork supporting the precessing-spin two-body dynamics of the effective-one-body waveform models SEOBNRv5

Waveform models are essential for gravitational-wave (GW) detection and parameter estimation of coalescing compact-object binaries. More accurate models are required for the increasing sensitivity of current and future GW detectors. The effective-one-body (EOB) formalism combines the post-Newtonian (PN) and small mass-ratio approximations with numerical-relativity results, and produces highly accurate inspiral-merger-ringdown waveforms. In this paper, we derive the analytical precessing-spin two-body dynamics for the SEOBNRv5 waveform model, which has been developed for the upcoming LIGO-Virgo-KAGRA observing run. We obtain an EOB Hamiltonian that reduces to the exact Kerr Hamiltonian in the test-mass limit. It includes the full 4PN precessing-spin information, and is valid for generic compact objects (i.e., for black holes or neutron stars). We also build an efficient and accurate EOB Hamiltonian that includes partial precessional effects, notably orbit-averaged in-plane spin effects for circular orbits, and derive 4PN-expanded precessing-spin equations of motion, consistent with such an EOB Hamiltonian. The results were used to build the computationally-efficient precessing-spin multipolar SEOBNRv5PHM waveform model.

gr-qc↗

arXiv2023

Laying the foundation of the effective-one-body waveform models SEOBNRv5: improved accuracy and efficiency for spinning non-precessing binary black holes

We present SEOBNRv5HM, a more accurate and faster inspiral-merger-ringdown gravitational waveform model for quasi-circular, spinning, nonprecessing binary black holes within the effective-one-body (EOB) formalism. Compared to its predecessor, SEOBNRv4HM, the waveform model i) incorporates recent high-order post- Newtonian results in the inspiral, with improved resummations, ii) includes the gravitational modes (l, |m|) = (3, 2), (4, 3), in addition to the (2, 2), (3, 3), (2, 1), (4, 4), (5, 5) modes already implemented in SEOBNRv4HM, iii) is calibrated to larger mass-ratios and spins using a catalog of 442 numerical-relativity (NR) simulations and 13 additional waveforms from black-hole perturbation theory, iv) incorporates information from second-order gravitational self-force (2GSF) in the nonspinning modes and radiation-reaction force. Computing the unfaithfulness against NR simulations, we find that for the dominant (2, 2) mode the maximum unfaithfulness in the total mass range $10-300 M_{\odot}$ is below $10^{-3}$ for 90% of the cases (38% for SEOBNRv4HM). When including all modes up to l = 5 we find 98% (49%) of the cases with unfaithfulness below $10^{-2} (10^{-3})$, while these numbers reduce to 88% (5%) when using SEOBNRv4HM. Furthermore, the model shows improved agreement with NR in other dynamical quantities (e.g., the angular momentum flux and binding energy), providing a powerful check of its physical robustness. We implemented the waveform model in a high-performance Python package (pySEOBNR), which leads to evaluation times faster than SEOBNRv4HM by a factor 10 to 50, depending on the configuration, and provides the flexibility to easily include spin-precession and eccentric effects, thus making it the starting point for a new generation of EOBNR waveform models (SEOBNRv5) to be employed for upcoming observing runs of the LIGO-Virgo-KAGRA detectors.

gr-qc↗

arXiv2023

SEOBNRv5PHM: Next generation of accurate and efficient multipolar precessing-spin effective-one-body waveforms for binary black holes

Spin precession is one of the key physical effects that could unveil the origin of the compact binaries detected by ground- and space-based gravitational-wave (GW) detectors, and shed light on their possible formation channels. Efficiently and accurately modeling the GW signals emitted by these systems is crucial to extract their properties. Here, we present SEOBNRv5PHM, a multipolar precessing-spin waveform model within the effective-one-body (EOB) formalism for the full signal (i.e. inspiral, merger and ringdown) of binary black holes (BBHs). In the non-precessing limit, the model reduces to SEOBNRv5HM, which is calibrated to $442$ numerical-relativity (NR) simulations, 13 waveforms from BH perturbation theory, and non-spinning energy flux from second-order gravitational self-force theory. We remark that SEOBNRv5PHM is not calibrated to precessing-spin NR waveforms from the Simulating eXtreme Spacetimes Collaboration. We validate SEOBNRv5PHM by computing the unfaithfulness against 1543 precessing-spin NR waveforms, and find that for 99.8% (84.4%) of the cases, the maximum value, in the total mass range 20-300 $M_\odot$, is below 3% (1%). These numbers reduce to 95.3% (60.8%) when using the previous version of the SEOBNR family, SEOBNRv4PHM, and to 78.2% (38.3%) when using the state-of-the-art frequency-domain multipolar precessing-spin phenomenological IMRPhenomXPHM model. Due to much better computational efficiency of SEOBNRv5PHM compared to SEOBNRv4PHM, we are also able to perform extensive Bayesian parameter estimation on synthetic signals and GW events observed by LIGO-Virgo detectors. We show that SEOBNRv5PHM can be used as a standard tool for inference analyses to extract astrophysical and cosmological information of large catalogues of BBHs.

gr-qc↗

arXiv2022

Effective-action model for dynamical scalarization beyond the adiabatic approximation

In certain scalar-field extensions to general relativity, scalar charges can develop on compact objects in an inspiraling binary -- an effect known as dynamical scalarization. This effect can be modeled using effective-field-theory methods applied to the binary within the post-Newtonian approximation. Past analytic investigations focused on the adiabatic (or quasi-stationary) case for quasi-circular orbits. In this work, we explore the full dynamical evolution around the phase transition to the scalarized regime. This allows for generic (eccentric) orbits and to quantify nonadiabatic (e.g., oscillatory) behavior during the phase transition. We also find that even in the circular-orbit case, the onset of scalarization can only be predicted reliably when taking the full dynamics into account, i.e., the adiabatic approximation is not appropriate. Our results pave the way for accurate post-Newtonian predictions for dynamical scalarization effects in gravitational waves from compact binaries.

gr-qc↗

arXiv2022

Spin contributions to the gravitational-waveform modes for spin-aligned binaries at the 3.5PN order

We complete the post-Newtonian (PN) prediction at the 3.5PN order for the spin contributions to the gravitational waveforms emitted by inspiraling compact binaries, in the case of quasi-circular, equatorial orbits, where both spins are aligned with the orbital angular momentum. Using results from the multipolar post-Minkowskian wave generation formalism, we extend previous works that derived the dynamics and gravitational-wave energy flux and phasing, by computing the full waveform decomposed in spin-weighted spherical harmonics. This new calculation requires the computation of multipolar moments of higher multipolar order, new quadratic-in-spin contributions to the hereditary tail terms entering at the 3.5PN order, as well as other non-linear interactions between moments. When specialized to the test-mass limit, our results are equivalent to those obtained in the literature for the waveform emitted by a test-mass in equatorial, circular orbits around a Kerr black hole. We also compute the factorized modes for use in effective-one-body waveform models, correcting the 2.5PN nonspinning and 3PN quadratic-in-spin terms in the (2,1) mode used in current models.

gr-qc↗

arXiv2022

Snowmass White Paper: Gravitational Waves and Scattering Amplitudes

We review recent progress and future prospects for harnessing powerful tools from theoretical high-energy physics, such as scattering amplitudes and effective field theory, to develop a precise and systematically improvable framework for calculating gravitational-wave signals from binary systems composed of black holes and/or neutron stars. This effort aims to provide state-of-the-art predictions that will enable high-precision measurements at future gravitational-wave detectors. In turn, applying the tools of quantum field theory in this new arena will uncover theoretical structures that can transform our understanding of basic phenomena and lead to new tools that will further the cycle of innovation. While still in a nascent stage, this research direction has already derived new analytic results in general relativity, and promises to advance the development of highly accurate waveform models for ever more sensitive detectors.

hep-th↗

arXiv2022

Effective-one-body multipolar waveforms for eccentric binary black holes with non-precessing spins

We construct an inspiral-merger-ringdown eccentric gravitational-wave (GW) model for binary black holes with non-precessing spins within the effective-one-body formalism. This waveform model, SEOBNRv4EHM, extends the accurate quasi-circular SEOBNRv4HM model to eccentric binaries by including recently computed eccentric corrections up to 2PN order in the gravitational waveform modes, notably the $(l,|m|)=(2,2),(2,1),(3,3),(4,4),(5,5)$ multipoles. The waveform model reproduces the zero eccentricity limit with an accuracy comparable to the underlying quasi-circular model, with the unfaithfulness of $\lesssim1\%$ against quasi-circular numerical-relativity (NR) simulations. When compared against 28 public eccentric NR simulations from the Simulating eXtreme Spacetimes catalog with initial orbital eccentricities up to $e\simeq0.3$ and dimensionless spin magnitudes up to $+0.7$, the model provides unfaithfulness $<1\%$, showing that both the $(2,|2|)$-modes and the higher-order modes are reliably described without calibration to NR datasets in the eccentric sector. The waveform model SEOBNRv4EHM is able to qualitatively reproduce the phenomenology of dynamical captures, and can be extended to include spin-precession effects. It can be employed for upcoming observing runs with the LIGO-Virgo-KAGRA detectors and used to re-analyze existing GW catalogs to infer the eccentricity parameters for binaries with $e\lesssim0.3$ (at 20 Hz or lower) and spins up to $\lesssim 0.9-0.95$. The latter is a promising region of the parameter space where some astrophysical formation scenarios of binaries predict mild eccentricity in the ground-based detectors' bandwidth. Assessing the accuracy and robustness of the eccentric waveform model SEOBNRv4EHM for larger eccentricities and spins will require comparisons with, and, likely, calibration to eccentric NR waveforms in a larger region of the parameter space.

gr-qc↗

arXiv2021

Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order

Accurate waveform models are crucial for gravitational-wave data analysis, and since spin has a significant effect on the binary dynamics, it is important to improve the spin description in these models. In this paper, we derive the spin-orbit (SO) coupling at the fifth-and-a-half post-Newtonian (5.5PN) order. The method we use splits the conservative dynamics into local and nonlocal-in-time parts, then relates the local-in-time part to gravitational self-force results by exploiting the simple mass-ratio dependence of the post-Minkowskian expansion of the scattering angle. We calculate the nonlocal contribution to the 5.5PN SO dynamics to eighth order in the small-eccentricity expansion for bound orbits, and to leading order in the large-eccentricity expansion for unbound orbits. For the local contribution, we obtain all the 5.5PN SO coefficients from first-order self-force results for the redshift and spin-precession invariants, except for one unknown that could be fixed in the future by second-order self-force results. However, by incorporating our 5.5PN results in the effective-one-body formalism and comparing its binding energy to numerical relativity, we find that the remaining unknown has a small effect on the SO dynamics, demonstrating an improvement in accuracy at that order.

gr-qc↗

arXiv2021

Radiation-reaction force and multipolar waveforms for eccentric, spin-aligned binaries in the effective-one-body formalism

While most binary inspirals are expected to have circularized before they enter the LIGO/Virgo frequency band, a small fraction of those binaries could have non-negligible orbital eccentricity depending on their formation channel. Hence, it is important to accurately model eccentricity effects in waveform models used to detect those binaries, infer their properties, and shed light on their astrophysical environment. We develop a multipolar effective-one-body (EOB) eccentric waveform model for compact binaries whose components have spins aligned or anti-aligned with the orbital angular momentum. The waveform model contains eccentricity effects in the radiation-reaction force and gravitational modes through second post-Newtonian (PN) order, including tail effects, and spin-orbit and spin-spin couplings. We recast the PN-expanded, eccentric radiation-reaction force and modes in factorized form so that the newly derived terms can be directly included in the state-of-the-art, quasi-circular--orbit EOB model currently used in LIGO/Virgo analyses (i.e., the SEOBNRv4HM model).

gr-qc↗

arXiv2020

The Field Substellar Mass Function Based on the Full-sky 20-pc Census of 525 L, T, and Y Dwarfs

We present final Spitzer trigonometric parallaxes for 361 L, T, and Y dwarfs. We combine these with prior studies to build a list of 525 known L, T, and Y dwarfs within 20 pc of the Sun, 38 of which are presented here for the first time. Using published photometry and spectroscopy as well as our own follow-up, we present an array of color-magnitude and color-color diagrams to further characterize census members, and we provide polynomial fits to the bulk trends. Using these characterizations, we assign each object a $T_{\rm eff}$ value and judge sample completeness over bins of $T_{\rm eff}$ and spectral type. Except for types $\ge$ T8 and $T_{\rm eff} <$ 600K, our census is statistically complete to the 20-pc limit. We compare our measured space densities to simulated density distributions and find that the best fit is a power law ($dN/dM \propto M^{-α}$) with $α= 0.6{\pm}0.1$. We find that the evolutionary models of Saumon & Marley correctly predict the observed magnitude of the space density spike seen at 1200K $< T_{\rm eff} <$ 1350K, believed to be caused by an increase in the cooling timescale across the L/T transition. Defining the low-mass terminus using this sample requires a more statistically robust and complete sample of dwarfs $\ge$Y0.5 and with $T_{\rm eff} <$ 400K. We conclude that such frigid objects must exist in substantial numbers, despite the fact that few have so far been identified, and we discuss possible reasons why they have largely eluded detection.

astro-ph.SR↗

arXiv2020

Gravitational spin-orbit and aligned spin$_1$-spin$_2$ couplings through third-subleading post-Newtonian orders

The study of scattering encounters continues to provide new insights into the general relativistic two-body problem. The local-in-time conservative dynamics of an aligned-spin binary, for both unbound and bound orbits, is fully encoded in the gauge-invariant scattering-angle function, which is most naturally expressed in a post-Minkowskian (PM) expansion, and which exhibits a remarkably simple dependence on the masses of the two bodies (in terms of appropriate geometric variables). This dependence links the PM and small-mass-ratio approximations, allowing gravitational self-force results to determine new post-Newtonian (PN) information to all orders in the mass ratio. In this paper, we exploit this interplay between relativistic scattering and self-force theory to obtain the third-subleading (4.5PN) spin-orbit dynamics for generic spins, and the third-subleading (5PN) spin$_1$-spin$_2$ dynamics for aligned spins. We further implement these novel PN results in an effective-one-body framework, and demonstrate the improvement in accuracy by comparing against numerical-relativity simulations.

gr-qc↗