arXiv subjects

Felix M. Heinze

Publications and source records attributed to Felix M. Heinze.

6 recordsLinked to original sources

arXiv2026

A Fully Analytic Expression for the 2PN N-Body Hamiltonian

We present a complete analytic expression for the $N$-body Hamiltonian of nonspinning point particles at second post-Newtonian (2PN) order in the Arnowitt-Deser-Misner (ADM) gauge. Recent work reduced the general $N$-body Hamiltonian to a form containing a single unresolved integral term, which prevented a fully explicit closed-form representation. Here, we evaluate this integral analytically and thereby obtain a fully explicit closed-form expression for the general 2PN $N$-body Hamiltonian. We outline the main steps of the derivation and validate the analytic expression through direct numerical comparisons with the original integral representation.

gr-qc↗

arXiv2026

The N-Body 2PN Hamiltonian and Numerical Integration of the Equations of Motion

To date, the second-order post-Newtonian (2PN) Hamiltonian has been known in closed analytic form only for systems of up to three point masses. In this paper, we present an analytic expression for the general $N$-body 2PN Hamiltonian in the ADM gauge up to a single integral term that, to our knowledge, has no known closed-form analytic solution. We show that the integrals appearing in the 2PN Hamiltonian can be evaluated numerically to machine precision, allowing for cross-validation against analytical results and enabling the full numerical computation of the $N$-body 2PN Hamiltonian. Furthermore, we demonstrate the practical feasibility of the numerical integration of the equations of motion for $N$ bodies at 2PN order using different methods and discuss several strategies for improving computational efficiency.

gr-qc↗

arXiv2026

Exploring the Dynamics of General Relativistic Binary-Single and Binary-Binary Encounters of Black Holes

In this exploratory study, we demonstrate the capability of the numerical-relativity code BAM to simulate fully relativistic black-hole binary-single and binary-binary encounters. While previous work has demonstrated the general capability of numerical-relativity frameworks to evolve spacetimes with $N$ black holes, detailed explorations of such encounters remain limited. We focus on scenarios involving initially non-spinning, equal-mass black holes that result in a variety of dynamical outcomes, including flybys, delayed or accelerated eccentric mergers, exchanges, and more complex interactions. Our results show that we can reliably simulate scattering experiments involving three and four black holes, which exhibit interesting dynamics and gravitational-wave signals. The dynamics of these systems show noticeable differences compared to analogous systems in post-Newtonian approximations up to 2.5PN. A key result is that the gravitational waveforms exhibit remarkable features that could potentially make them distinguishable from regular binary mergers.

gr-qc↗

arXiv2024

Detecting low-mass haloes with strong gravitational lensing II: constraints on the density profiles of two detected subhaloes

Strong gravitational lensing can detect the presence of low-mass haloes and subhaloes through their effect on the surface brightness of lensed arcs. We carry out an extended analysis of the density profiles and mass distributions of two detected subhaloes, intending to determine if their properties are consistent with the predictions of the cold dark matter (CDM) model. We analyse two gravitational lensing systems in which the presence of two low-mass subhaloes has been previously reported: SDSSJ0946+1006 and JVASB1938+66. We model these detections assuming four different models for their density profiles and compare our results with predictions from the IllustrisTNG50-1 simulation. We find that the detected subhaloes are well-modelled by steep inner density slopes, close to or steeper than isothermal. The NFW profile thus needs extremely high concentrations to reproduce the observed properties, which are outliers of the CDM predictions. We also find a characteristic radius within which the best-fitting density profiles predict the same enclosed mass. We conclude that the lens modelling can constrain this quantity more robustly than the inner slope. We find that the diversity of subhalo profiles in TNG50, consistent with tidally stripping and baryonic effects, is able to match the observed steep inner slopes, somewhat alleviating the tension reported by previous works even if the detections are not well fit by the typical subhalo. However, while we find simulated analogues of the detection in B1938+666, the stellar content required by simulations to explain the central density of the detection in J0946+1006 is in tension with the upper limit in luminosity estimated from the observations. New detections will increase our statistical sample and help us reveal more about the density profiles of these objects and the dark matter content of the Universe.

astro-ph.CO↗

arXiv2023

Gravitational lenses in hydrodynamical simulations

The gravitational lensing signal produced by a galaxy or a galaxy cluster is determined by its total matter distribution, providing us with a way to directly constrain their dark matter content. State-of-the-art numerical simulations successfully reproduce many observed properties of galaxies and can be used as a source of mock observations and predictions. Many gravitational lensing studies aim at constraining the nature of dark matter, discriminating between cold dark matter and alternative models. However, many past results are based on the comparison to simulations that did not include baryonic physics. Here we show that the presence of baryons can significantly alter the predictions: we look at the structural properties (profiles and shapes) of elliptical galaxies and at the inner density slope of subhaloes. Our results demonstrate that future simulations must model the interplay between baryons and alternative dark matter, to generate realistic predictions that could significantly modify the current constraints.

astro-ph.CO↗

arXiv2023

Not All Subhaloes Are Created Equal: Modelling the Diversity of Subhalo Density Profiles in TNG50

In this work, we analyse the density profiles of subhaloes with masses $M_\mathrm{sh} \geq 1.4 \times 10^8$ M$_\odot$ in the TNG50 simulation, with the aim of including baryonic effects. We evaluate the performance of frequently used models, such as the standard NFW, the Einasto, and a smoothly truncated version of the NFW profile. We find that these models do not perform well for the majority of subhaloes, with the NFW profile giving the worst fit in most cases. This is primarily due to mismatches in the inner and outer logarithmic slopes, which are significantly steeper for a large number of subhaloes in the presence of baryons. To address this issue, we propose new three-parameter models and show that they significantly improve the goodness of fit independently of the subhalo's specific properties. Our best-performing model is a modified version of the NFW profile with an inner log-slope of -2 and a variable truncation that is sharper and steeper than the slope transition in the standard NFW profile. Additionally, we investigate how both the parameter values of the best density profile model and the average density profiles vary with subhalo mass, $V_\mathrm{max}$, distance from the host halo centre, baryon content and infall time, and we also present explicit scaling relations for the mean parameters of the individual profiles. The newly proposed fit and the scaling relations are useful to predict the properties of realistic subhaloes in the mass range $10^8$ M$_\odot$ $\leq M_\mathrm{sh} \leq$ $10^{13}$ M$_\odot$ that can be influenced by the presence of baryons.

astro-ph.GA↗