Talks

Non-abelian Hodge theory is a profound three-way equivalence between topological, smooth and holomorphic objects, i.e. representations of the fundamental group, flat connections and Higgs bundles. It is natural to explore a group-theoretic or multiplicative version — an enterprise that has been untaken by Soibelman, Kontsevich, Mochizuki and others. In this talk, we will review the current landscape of multiplicative non-abelian Hodge theory and discuss some outstanding questions.

Magnetic fields play a key role in shaping the dynamics and observational phenomenology of binary neutron star (BNS) mergers. In this talk, I will present results from general relativistic magnetohydrodynamic (GRMHD) simulations performed with the code GR-Athena++, exploring how different initial magnetic field configurations affect the evolution of BNS mergers. We investigated magnetic field amplification, primarily driven by the Kelvin-Helmholtz instability, the post-merger remnant and disk structure, and the characteristics of the ejected material. I will discuss how these processes impact potential electromagnetic counterparts and their detectability. Finally, I will highlight recent advancements in our numerical methods that improve the modeling of magnetized neutron star mergers, paving the way for more accurate predictions of multimessenger signals from these extreme events.

Numerical simulations are essential to understand the complex physics accompanying the merger of binary systems of neutron stars. However, these simulations become computationally challenging when they have to model the merger remnants on timescales over which secular phenomena, such as the launching of magneti- cally driven outflows, develop. To tackle these challenges, we have recently developed a hybrid approach that combines, via a hand-off transition, a fully general-relativistic code (FIL) with a more efficient code mak- ing use of the conformally flat approximation (BHAC+). We here report important additional developments of BHAC+ consisting of the inclusion of gravitational-wave radiation-reaction contributions and of higher-order formulations of the equations of general-relativistic magnetohydrodynamics. Both improvements have allowed us to explore scenarios that would have been computationally prohibitive otherwise. More specifically, we have investigated the impact of the magnetic-field strength on the long-term (i.e., ∼ 200 ms) and high-resolution (i.e., 150 m) evolutions of the “magnetar” resulting from the merger of two neutron stars with a realistic equa- tion of state. In this way, and for sufficiently large magnetic fields, we observe the loss of differential rotation and the generation of magnetic flares in the outer layers of the remnant. These flares, driven mostly by the Parker instability, are responsible for intense and collimated Poynting flux outbursts and low-latitude emissions. This novel phenomenology offers the possibility of seeking corresponding signatures from the observations of short gamma-ray bursts and hence revealing the existence of a long-lived strongly magnetized remnant.

Supermassive black hole mergers represent a spectacular cosmic event with immense energy implications, emitting gravitational waves equivalent to the total light output of stars in the entire Universe within a brief timespan. These mergers play a crucial role in shaping the overall mass distribution of supermassive black holes across the cosmos. However, capturing visual evidence of these mergers remains elusive due to uncertainties surrounding the type of light emissions accompanying gravitational waves during these events. To address this challenge, novel General Relativistic Magnetohydrodynamics (GRMHD) simulations are being conducted to gain detailed insights into the astrophysical environments surrounding supermassive black hole binaries as they progress towards merger. By employing sophisticated computational techniques capable of accurately capturing the intricate dynamics of accretion within circumbinary disks and the relativistic flow of magnetized matter around each black hole, these simulations reveal the behavior of gas flows near binary systems, particularly when both black holes exhibit spin. These simulated scenarios provide critical data for predicting the electromagnetic and gravitational wave signatures produced by supermassive binary black holes, guiding future observational strategies utilizing advanced missions like LISA and other upcoming astronomical facilities. Ongoing initiatives are focused on refining computational tools to deepen our understanding of supermassive black hole behavior within binary systems and its interactions.

In this talk, I will explore key open questions in our understanding of neutron star mergers and their multi-messenger emission, highlighting recent progress made by our group. I will then introduce some of the first applications of AthenaK to compact binary mergers and outline our plans for its future development.

With the ongoing transition toward exascale computing to tackle a range of open questions via numerical simulations, the development of GPU-optimized codes has become essential. In this talk, I will highlight the key features of AsterX, a novel open-source, modular, GPU-accelerated general relativistic magnetohydrodynamic (GRMHD) code for fully dynamical spacetimes in 3D Cartesian coordinates. Built for exascale applications, AsterX integrates with CarpetX, the new driver for the Einstein Toolkit, leveraging AMReX for block-structured adaptive mesh refinement (AMR). The code employs the flux-conservative Valencia formulation for GRMHD, and uses high-resolution shock capturing schemes to ensure accurate hydrodynamic modeling. Alongside discussions on the ongoing code development, I will also present the results of comprehensive 1D, 2D, and 3D GRMHD tests conducted on OLCF's Frontier supercomputer, highlighting AsterX's performance gains through subcycling in time and demonstrating its scaling efficiency across thousands of nodes.

In certain scenarios, the accreted angular momentum of plasma onto a black hole could be low; however, how the accretion dynamics depends on the angular momentum content of the plasma is still not fully understood. We present three-dimensional, general relativistic magnetohydrodynamic simulations of low angular momentum accretion flows around rapidly spinning black holes (with spin $a = +0.9$). The initial condition is a Fishbone-Moncrief (FM) torus threaded by a large amount of poloidal magnetic flux, where the angular velocity is a fraction $f$ of the standard value. For $f = 0$, the accretion flow becomes magnetically arrested and launches relativistic jets but only for a very short duration. After that, free-falling plasma breaks through the magnetic barrier, loading the jet with mass and destroying the jet-disk structure. Meanwhile, magnetic flux is lost via giant, asymmetrical magnetic bubbles that float away from the black hole. The accretion then exits the magnetically arrested state. For $f = 0.1$, the dimensionless magnetic flux threading the black hole oscillates quasi-periodically. The jet-disk structure shows concurrent revival and destruction while the gas efficiency at the event horizon changes accordingly. For $f \geq 0.3$, we find that the dynamical behavior of the system starts to approach that of a standard accreting FM torus. Our results thus suggest that the accreted angular momentum is an important parameter that governs the maintenance of a magnetically arrested flow and launching of relativistic jets around black holes.

It has been proposed recently that Inverse Compton scattering of soft photons by pairs acceleration in reconnecting current sheets that form during MAD states, can be the source of the TeV emission detected in M87. In this talk I’ll argue that synchrotron emission by ions accelerated in the current sheet is expected to be the dominant source of the GeV emission observed. The analysis is based on 3D, radiative PIC simulations of magnetic reconnection in pair-ion plasma, under conditions anticipated in M87 during MAD states.