Periodic Reporting for period 1 - GR-PLUTO (General Relativistic numerical models of accretion disks and magnetic reconnection with the PLUTO code)
Reporting period: 2022-11-01 to 2024-10-31
In the last few years, the scientific research on astrophysical black holes (BHs) has produced some historical discoveries, such as the detection of gravitational waves and the imaging of supermassive black holes with their accretion disk at the center of galaxies, including our own Milky Way.
One of the main ingredients that made these achievements possible is the theoretical understanding of how magnetic fields shape the dynamics of the gas around black holes.
Matter in such extreme gravitational fields assumes the form of hot plasma, i.e. a state where charged particles such protons and electrons are not bound within atoms and travel much more freely under the influence of electromagnetic fields.
A primary example of physical process that can take place in plasmas is magnetic reconnection, i.e. the rearrangement of the magnetic field's own structure, which converts magnetic energy into kinetic and thermal energy.
One of the main consequences of reconnection is the acceleration of particles to velocities close to the speed of light, which then produces high-energy non-thermal radiation that we can observe from accreting black holes.
Since astrophysical plasmas are generally non-collisional, the coupling of particles and magnetic fields leads to kinetic instabilities and dissipation of magnetic energy at spatial scales much smaller than the size of a black hole.
Particle-In-Cell (PIC) simulations are a chief instrument for the investigation of plasma dynamics at small scales, but they are generally too computationally expensive to model black holes and their accretion disks.
General relativistic magnetohydrodynamic (GRMHD), on the other hand, offers a more suitable framework to describe the behavior of accretion disks around black holes, doing so by treating particles and electromagnetic fields as a single magnetized fluid.
GRMHD models can be extended to include magnetic dissipation, but they generally consider a constant electric conductivity, which generally lead to results that are not in agreement with first principles PIC models.
The goal of the GR-PLUTO project is to perform the first numerical study on reconnection in relativistic disks using an effective non-constant resistivity, which will go beyond standard fluid models by introducing a new non-collisional effect in the way that magnetic fields are dissipated.
This approach will test our current knowledge of relativistic magnetic reconnection and provide more consistent estimates for the rate at which particles can be accelerated and the general structure of the magnetized accretion flow around a black hole.
Since the required simulations will have a high computational cost, a significant part of the project is devoted to the development a numerical tool for the modeling of GRMHD flows that combines the benefits of highly accurate numerical schemes with energy-efficient computational methods.
To this end the freely-distributed astrophysical code PLUTO is extended (in collaboration with the PLUTO development team at the physics department of the University of Turin) to include the effects of General Relativity, complementing it with high-order integration schemes and GPU-accelerated routines.
One of the main ingredients that made these achievements possible is the theoretical understanding of how magnetic fields shape the dynamics of the gas around black holes.
Matter in such extreme gravitational fields assumes the form of hot plasma, i.e. a state where charged particles such protons and electrons are not bound within atoms and travel much more freely under the influence of electromagnetic fields.
A primary example of physical process that can take place in plasmas is magnetic reconnection, i.e. the rearrangement of the magnetic field's own structure, which converts magnetic energy into kinetic and thermal energy.
One of the main consequences of reconnection is the acceleration of particles to velocities close to the speed of light, which then produces high-energy non-thermal radiation that we can observe from accreting black holes.
Since astrophysical plasmas are generally non-collisional, the coupling of particles and magnetic fields leads to kinetic instabilities and dissipation of magnetic energy at spatial scales much smaller than the size of a black hole.
Particle-In-Cell (PIC) simulations are a chief instrument for the investigation of plasma dynamics at small scales, but they are generally too computationally expensive to model black holes and their accretion disks.
General relativistic magnetohydrodynamic (GRMHD), on the other hand, offers a more suitable framework to describe the behavior of accretion disks around black holes, doing so by treating particles and electromagnetic fields as a single magnetized fluid.
GRMHD models can be extended to include magnetic dissipation, but they generally consider a constant electric conductivity, which generally lead to results that are not in agreement with first principles PIC models.
The goal of the GR-PLUTO project is to perform the first numerical study on reconnection in relativistic disks using an effective non-constant resistivity, which will go beyond standard fluid models by introducing a new non-collisional effect in the way that magnetic fields are dissipated.
This approach will test our current knowledge of relativistic magnetic reconnection and provide more consistent estimates for the rate at which particles can be accelerated and the general structure of the magnetized accretion flow around a black hole.
Since the required simulations will have a high computational cost, a significant part of the project is devoted to the development a numerical tool for the modeling of GRMHD flows that combines the benefits of highly accurate numerical schemes with energy-efficient computational methods.
To this end the freely-distributed astrophysical code PLUTO is extended (in collaboration with the PLUTO development team at the physics department of the University of Turin) to include the effects of General Relativity, complementing it with high-order integration schemes and GPU-accelerated routines.
WP1: Development of the gPLUTO code and its resistive GRMHD module
Along with my collaborators at the Physics department of UniTo I first contributed to the development of high-order schemes that significantly increase the computational efficiency of the original version of the PLUTO code. In a first work led by a PhD student I co-supervised (Vittoria Berta), we implemented high-accuracy algorithms for the integration of classical and relativistic ideal magnetohydrodynamics (MHD; Berta et al. 2024, Journal of Computational Physics), leading to an overall increase in effective resolution for a typical astrophysical simulation by at least a factor two. We then extended these results to the relativistic resistive regime (Mignone et al. 2024, MNRAS), which in general requires specific strategies to integrate the stiff differential equations governing the electric field evolution.
During the same period, the PLUTO code has been completely rewritten in C++ and modified to be efficiently run on GPU-accelerated clusters, in collaboration with NVIDIA experts from CINECA. This new version of the code, named "gPLUTO", has been thoroughly tested on pre-exascale EuroHPC machines such as Leonardo (CINECA) and Marenostrum (BSC-CNS), demonstrating an increase in performance with respect to the legacy code of at least one order of magnitude (Rossazza, Mignone, Bugli et al. 2025, submitted to IEEE-TPDS). In a similar fashion, I collaborated with Luca Del Zanna to accelerate the GRMHD code ECHO on GPUs, reaching a similar performance improvement but with a code written in Fortran (Del Zanna et al. 2024, Fluids).
In the meantime, I developed the resistive GRMHD module using first the legacy RMHD module of PLUTO to introduce the standard 3+1 covariant formalism in the code. This allows one to model not only plasma dynamics around a compact object such as a black hole, but also adopt more specific metrics that can be used to model expanding/contracting boxes or the dynamics of a quark-gluon plasma. Later on I ported this module to the GPU-accelerated code gPLUTO, in order to fully exploit its latest developments in term of computational efficiency (Bugli et al. 2025b, to be submitted in A&A).
WP2: Relativistic magnetic reconnection and astrophysical outflows
In collaboration with a master student I co-supervised at the Physics Department of UniTo (Edoardo Lopresti), I adapted a recently proposed prescription for a kinetic formulation of the magnetic diffusivity for the resistive relativistic MHD framework. I then led a collaboration with Benôit Cerutti (renown expert of kinetic models and magnetic reconnection) from the "Institut de Planétologie et d'Astrophysique de Grenoble" (IPAG) to validate our prescription against first-principles Particle-In-Cell (PIC) simulations (Bugli et al. 2025, A&A). On top of obtaining an exceptional agreement between our fluid models with effective resistivity and the PIC simulations in terms of dynamics of the reconnecting current sheet, thanks to hybrid RMHD-PIC models we verified that charged particles are also accelerated in a very similar fashion when a more realistic magnetic dissipation is taken into account (Lopresti, Bugli et al. 2025, to be submitted in A&A). We are also currently testing the fundamental properties of relativistic magnetic reconnection performing 3D high-order RMHD models, which show how the onset of plasma instabilities along the current sheet can qualitatively affect the properties of magnetic dissipation (Berta, Bugli et al. 2025, to be submitted in A&A).
In connection to large-scale astrophysical simulations of relativistic plasmas, I contributed to one of the first systematic studies of gamma-ray burst jets with a finite conductivity, showcasing the qualitative impact of magnetic dissipation on the jet's dynamics and the morphology of the current sheets where particle acceleration by magnetic reconnection can occur (Mattia, Del Zanna, Bugli et al. 2023, A&A). I further explored the impact of magnetic fields in connection to the formation of compact objects during the onset of extreme core-collapse supernovae, highlighting their central role in determining the expected neutrino signals (Bendahman et al. 2023, JCAP) and the associated formation of new heavy elements during the explosive nucleosynthesis (Reichert, Bugli et al. 2024, MNRAS). Finally, I am currently leading a code comparison project focused on highly magnetized core-collapse simulations, where together with other 4 independent research groups I demonstrate how different codes can qualitatively reproduce the same dynamics for the explosion and the magnetic fields, although presenting quantitative deviations in the evolution of key diagnostics such as explosion energy and ejecta collimation (Bugli et al. 2025c, to be submitted in A&A).
Along with my collaborators at the Physics department of UniTo I first contributed to the development of high-order schemes that significantly increase the computational efficiency of the original version of the PLUTO code. In a first work led by a PhD student I co-supervised (Vittoria Berta), we implemented high-accuracy algorithms for the integration of classical and relativistic ideal magnetohydrodynamics (MHD; Berta et al. 2024, Journal of Computational Physics), leading to an overall increase in effective resolution for a typical astrophysical simulation by at least a factor two. We then extended these results to the relativistic resistive regime (Mignone et al. 2024, MNRAS), which in general requires specific strategies to integrate the stiff differential equations governing the electric field evolution.
During the same period, the PLUTO code has been completely rewritten in C++ and modified to be efficiently run on GPU-accelerated clusters, in collaboration with NVIDIA experts from CINECA. This new version of the code, named "gPLUTO", has been thoroughly tested on pre-exascale EuroHPC machines such as Leonardo (CINECA) and Marenostrum (BSC-CNS), demonstrating an increase in performance with respect to the legacy code of at least one order of magnitude (Rossazza, Mignone, Bugli et al. 2025, submitted to IEEE-TPDS). In a similar fashion, I collaborated with Luca Del Zanna to accelerate the GRMHD code ECHO on GPUs, reaching a similar performance improvement but with a code written in Fortran (Del Zanna et al. 2024, Fluids).
In the meantime, I developed the resistive GRMHD module using first the legacy RMHD module of PLUTO to introduce the standard 3+1 covariant formalism in the code. This allows one to model not only plasma dynamics around a compact object such as a black hole, but also adopt more specific metrics that can be used to model expanding/contracting boxes or the dynamics of a quark-gluon plasma. Later on I ported this module to the GPU-accelerated code gPLUTO, in order to fully exploit its latest developments in term of computational efficiency (Bugli et al. 2025b, to be submitted in A&A).
WP2: Relativistic magnetic reconnection and astrophysical outflows
In collaboration with a master student I co-supervised at the Physics Department of UniTo (Edoardo Lopresti), I adapted a recently proposed prescription for a kinetic formulation of the magnetic diffusivity for the resistive relativistic MHD framework. I then led a collaboration with Benôit Cerutti (renown expert of kinetic models and magnetic reconnection) from the "Institut de Planétologie et d'Astrophysique de Grenoble" (IPAG) to validate our prescription against first-principles Particle-In-Cell (PIC) simulations (Bugli et al. 2025, A&A). On top of obtaining an exceptional agreement between our fluid models with effective resistivity and the PIC simulations in terms of dynamics of the reconnecting current sheet, thanks to hybrid RMHD-PIC models we verified that charged particles are also accelerated in a very similar fashion when a more realistic magnetic dissipation is taken into account (Lopresti, Bugli et al. 2025, to be submitted in A&A). We are also currently testing the fundamental properties of relativistic magnetic reconnection performing 3D high-order RMHD models, which show how the onset of plasma instabilities along the current sheet can qualitatively affect the properties of magnetic dissipation (Berta, Bugli et al. 2025, to be submitted in A&A).
In connection to large-scale astrophysical simulations of relativistic plasmas, I contributed to one of the first systematic studies of gamma-ray burst jets with a finite conductivity, showcasing the qualitative impact of magnetic dissipation on the jet's dynamics and the morphology of the current sheets where particle acceleration by magnetic reconnection can occur (Mattia, Del Zanna, Bugli et al. 2023, A&A). I further explored the impact of magnetic fields in connection to the formation of compact objects during the onset of extreme core-collapse supernovae, highlighting their central role in determining the expected neutrino signals (Bendahman et al. 2023, JCAP) and the associated formation of new heavy elements during the explosive nucleosynthesis (Reichert, Bugli et al. 2024, MNRAS). Finally, I am currently leading a code comparison project focused on highly magnetized core-collapse simulations, where together with other 4 independent research groups I demonstrate how different codes can qualitatively reproduce the same dynamics for the explosion and the magnetic fields, although presenting quantitative deviations in the evolution of key diagnostics such as explosion energy and ejecta collimation (Bugli et al. 2025c, to be submitted in A&A).
The development of the gPLUTO code and its new resistive GRMHD module (soon available to the scientific community) will enable a more realistic and accurate modeling of accretion flows around compact objects, ranging from X-ray binaries and gamma-ray bursts, to active galactic nuclei and accreting supermassive black holes.
The unprecedented accuracy of the code (which is constantly maintained by myself and the core development group at UniTo) will be coupled with a novel prescription for magnetic dissipation that can, for the first time, quantitatively capture the dynamics of magnetic reconnection and particle acceleration within the relativistic MHD framework. This is a crucial step towards a realistic modeling of the high-energy electromagnetic emission of extreme astrophysical sources where magnetic reconnection plays a central role in accelerating charged particles that can then radiate the system's energy away.
The technical achievements of WP1, combined to the physical insights obtained in WP2, pave the way towards a more effective tackling of the large scale-separation affecting numerical models of accreting compact objects and, thus, a more direct connection between the compact central engine and the associated electromagnetic emission.
The unprecedented accuracy of the code (which is constantly maintained by myself and the core development group at UniTo) will be coupled with a novel prescription for magnetic dissipation that can, for the first time, quantitatively capture the dynamics of magnetic reconnection and particle acceleration within the relativistic MHD framework. This is a crucial step towards a realistic modeling of the high-energy electromagnetic emission of extreme astrophysical sources where magnetic reconnection plays a central role in accelerating charged particles that can then radiate the system's energy away.
The technical achievements of WP1, combined to the physical insights obtained in WP2, pave the way towards a more effective tackling of the large scale-separation affecting numerical models of accreting compact objects and, thus, a more direct connection between the compact central engine and the associated electromagnetic emission.