Workshop on Kinetic Models of Relativistic Plasmas

Hamilton Mathematics Institute Trinity College Dublin

Many interesting astrophysical plasmas are in the collisionless regime, where the assumptions underpinning the fluid approximation aren't satisfied and more demanding kinetic methods may be required. This workshop at Trinity College Dublin's Hamilton Mathematics Institute aims to bring together researchers working on theory and computation in the continuum, particle-based, and magnetohydrodynamic approaches. 


Talks will be held from Tuesday February 28th to Thursday March 2nd, 2023. A significant fraction of the time will be reserved for discussion. Additional informal discussions will take place on the Monday and Friday. There is no registration fee.



Luciano Rezzolla (Frankfurt & TCD)

Kyle Parfrey (TCD)


  • Alejandro Cruz Osorio
  • Alisa Galishnikova
  • Ammar Hakim
  • Andrei Beloborodov
  • Andrew Chael
  • Benjamin Crinquand
  • Benoit Cerutti
  • Charles Gammie
  • Christoph Köhn
  • Ileyk EL MELLAH
  • Joonas Nättilä
  • Kenichi Nishikawa
  • Kyle Parfrey
  • Lorenzo Sironi
  • Luca Comisso
  • Luciano Rezzolla
  • Martin Pohl
  • Monika Moscibrodzka
  • Oliver Porth
  • Sergio Servidio
  • Yosuke Mizuno
    • 9:25 AM 9:40 AM
      Welcome & Practical Information 15m
    • 9:40 AM 10:20 AM
      Nonideal Fluid Models of Accretion 40m

      The numerical accretion models that are used to interpret EHT observations of low accretion rate black holes are almost exclusively ideal fluid models. Kinetic models of the same accretion flows, by contrast, can capture effects not present in an ideal fluid, but they are much more computationally expensive and must make approximations of their own. This motivates interest in nonideal fluid models that use a closure to incorporate some kinetic effects but are nontheless computationally inexpensive enough to be useful for interpreting observations. I will describe a nonideal fluid model, its numerical implementation, lessons learned, and early results.

      Speaker: Charles Gammie
    • 10:20 AM 11:00 AM
      Coffee 40m
    • 11:00 AM 11:40 AM
      Temperature properties in two-temperature accretion flows onto a black hole 40m

      In the accretion flows around low-luminosity active galactic nuclei such as M87, electrons and ions are not in thermal equilibrium. Therefore, the electron temperature, which is important for the thermal synchrotron radiation at EHT frequencies of 230 GHz, is not independently determined. Simplified assumptions about the electron thermodynamics are normally employed in GRMHD simulations of accretion flows onto a black hole. To counter this, we have developed a self-consistent approach to study two-temperature accretion flows around a black hole. We have compared radiative properties between the commonly used parametrized ion-to-electron temperature ratio prescription R−beta model and electron-heating prescriptions obtained from two-temperature GRMHD simulations and found a good match between them. We have also investigated magnetized and radiatively cooled two-temperature accretion flows around a Kerr black hole. The inclusion of the radiative cooling impacts the thermodynamical properties of both the ions and electrons which are important for radiative images.

      Speaker: Yosuke Mizuno (Tsung-Dao Lee Institute, Shanghai Jiao Tong University)
    • 11:40 AM 12:20 PM
      Hot spots around Sgr A*: model constraints from ALMA polarimetric observations 40m

      I will report on the polarized light curves of the Galactic Center supermassive black hole Sagittarius A, obtained at millimeter wavelength with the Atacama Large Millimeter/submillimeter Array. The observations took place as a part of the Event Horizon Telescope campaign. We compare the observations taken during the low variability source state on 2017 Apr. 6 and 7 with those taken immediately after the X-ray flare on 2017 Apr. 11. For the latter case, we observe rotation of the electric vector position angle with a timescale of ∼70 min. We interpret this rotation as a signature of the equatorial clockwise orbital motion of a hot spot embedded in a magnetic field dominated by a dynamically important vertical component. We postulate that Sgr A is surrounded by a magnetically arrested disk in which the observed hot spots are exhausts of reconnection events. I will highlight possibilities to use these new findings to learn more about collisionless plasma in advection dominated accretion flows.

      Speaker: Monika Moscibrodzka
    • 12:20 PM 2:00 PM
      Lunch 1h 40m
    • 2:00 PM 2:40 PM
      On the use of callibrated resistivity models in global GRMHD simulations 40m

      In this contribution, I will discuss the prospects for using PIC calibrated resistivity models in global GRMHD fluid simulations. Using relativistic PIC simulations of plasmoid dominated reconnecting current sheet with and without guide field, we have recently investigated the statistical properties of the non-ideal electric field at the X-points. There are interesting differences between the cases with and without guidefield. While the non-ideal field in the zero guidefield case can be expressed solely by means of bulk flow quantities (two-fluid or single fluid with further assumptions), the case with moderate guidefield requires a modeling of the pressure tensor. I will show how these findings can be used to formulate an effective non-uniform resistivity model. I will further discuss the potential pitfalls of this approach which might necessitate more sophisticated models of the anisotropic pressure tensor in the X-points.

      Speaker: Oliver Porth
    • 2:40 PM 3:20 PM
      The Black Hole-Jet Connection in M87: Insights from Radiative Simulations 40m

      The Event Horizon Telescope (EHT) has produced images of both total intensity and polarized radiation from plasma around the supermassive black hole in M87 on event horizon scales.
      In a large library of simulated images from general relativistic magnetohydrodynamic (GRMHD) simulations, the models most consistent with Event Horizon Telescope (EHT) polarized images of M87 are all magnetically arrested accretion disks (MADs).In MAD systems, near-horizon magnetic fields are coherent and dynamically important; they limit accretion and launch powerful jets via the Blandford-Znajek (BZ) mechanism. The EHT results also suggest that the radiative efficiency in M87's accretion flow is on the order of 1%, suggesting that radiative cooling plays a strong role in determining the temperature of the emitting electrons and affects image morphology at all wavelengths. By including radiative feedback and electron-ion thermodynamics self-consistently in simulations of MADs, we are able to produce images of M87 that are consistent with VLBI observations from EHT images of the black hole shadow at 1 mm to images of the jet at cm wavelengths. While the jet is most prominent at longer wavelengths, most of the observed emission in MAD models originates from a relatively thin equatorial region. In these simulations, the darkest region in the observed image -- the black hole's "inner shadow" -- approaches the lensed outline of event horizon in the equatorial plane.Measurements of the relative size, shape, and position of the inner shadow and black hole photon ring can break degeneracies in measurements of the black hole mass and spin using submillimeter VLBI images. If time permits, I will briefly discuss a new method in development for simulations that link GRMHD with Force-Free electrodynamics in the jet region, enabling simulations to run without artificial density floors in magnetically dominated regions.

      Speaker: Andrew Chael (Princeton University)
    • 3:20 PM 3:50 PM
      Coffee 30m
    • 3:50 PM 4:30 PM
      Multiwavelength emission of M87 jet using self-consistent electron-to-proton temperature 40m

      The mechanism of non-thermal particle acceleration in turbulent plasma
      is the magnetic reconnection that occurs when plasmoids interact with others. In this talk, I will discuss the new results from Particle In Cell (PIC) simulations and the implications for the astrophysical plasma. In particular, the non-thermal particle population and electron temperature in relativistic jets.

      Speaker: Alejandro Cruz Osorio
    • 4:30 PM 5:00 PM
      Discussion 30m
    • 9:00 AM 9:40 AM
      General relativistic radiative PIC simulations of black hole magnetospheres 40m

      Spinning black holes have long been suspected to be involved in some of the most extreme astrophysical phenomena such as, e.g., active galactic nuclei, tidal disruption events, gamma-ray bursts, and microquasars. The activity of black holes is often associated with the creation and the launching of a relativistic magnetized plasma jet accompanied by efficient particle acceleration and non-thermal radiation. Horizon-scale observations of supermassive black holes reveal that these processes occur in the closest vicinity to the black-hole event horizon: the magnetosphere, the inner parts of the accretion flow and the jet. Yet, the underlying physical mechanisms are still poorly understood because they result from a complex interplay between general relativity, electrodynamics and plasma physics. I will review our current efforts to model black hole magnetospheres from first principles with the help of general relativistic radiative particle-in-cell simulations. These numerical methods can capture plasma processes at a microscopic kinetic level where particle acceleration takes place, and therefore, they may hold the key to bridge the gap between theoretical models and horizon-scale observations of black holes.

      Speaker: Benoit Cerutti (CNRS & Univ. Grenoble Alpes)
    • 9:40 AM 10:20 AM
      Plasma relations from kinetic modelling of special-relativistic turbulence 40m

      The small scales properties of astrophysical plasmas near accreting compact objects are still poorly understood. For instance, in modern general-relativistic magnetohydrodynamic simulations, the relation between the temperature of electrons and protons is prescribed in terms of simplified phenomenological models where the electron temperature is related to the proton temperature in terms of the ratio between the plasma and magnetic pressures (beta). We present a very comprehensive campaign of 2D kinetic Particle-In-Cell (PIC) simulations of special-relativistic turbulence to investigate systematically the microphysical properties of the plasma in the relativistic regime. Using a realistic mass ratio between particle species, we analyze how the index of the electron energy distributions, the efficiency of nonthermal particle production, and the temperature ratio vary over a wide range of values of plasma beta and magnetization. For each of these quantities, we provide two-dimensional fitting functions that describe their behavior in the relevant space of parameters, thus connecting the microphysical properties of the plasma to the macroscopic ones. Our results can find application in a wide range of astrophysical scenarios, including the accretion and the jet emission onto supermassive black holes, such as M87 and Sgr A.

      Speaker: Sergio Servidio (University of Calabria)
    • 10:20 AM 11:00 AM
      Coffee 40m
    • 11:00 AM 11:40 AM
      GRPIC Simulations of Jet Formation 40m

      We developed a 3D GRPIC code using the algorithm and implementation of the Kerr–Schild metric for the simulation of charged particles in a region surrounding a spinning black hole (BH). We test the overall model by using a ‘toy’ black hole and accretion disk system in a uniform magnetic field to produce bipolar jets. We aim to refine this code by implementing advanced simulation techniques including, initial, boundary conditions and other essential methods.

      We have investigated the temporal evolution of an axisymmetric magnetosphere around a rapidly rotating stellar-mass BH by applying a two-dimensional particle-in-cell simulation scheme. Adopting homogeneous pair production and assuming that the mass accretion rate is much less than the Eddington limit, we found that the BH's rotational energy is preferentially extracted from the middle latitudes and that this outward energy flux exhibits an enhancement that lasts approximately 160 dynamical timescales. It is demonstrated that the magnetohydrodynamic approximations cannot be justified in such a magnetically dominated magnetosphere because Ohm’s law loses its validity and the charge-separated electron–positron plasmas are highly nonneutral. An implication is given regarding the collimation of relativistic jets.

      In the second report with our 2D axisymmetric GRPIC simulation, assuming a stellar-mass BH
      solving full equations, we found that the created pairs fail to screen the electric field along the magnetic field, provided that the mass accretion rate is much smaller compared to the Eddington limit. Magnetic islands are created by reconnection near the equator and migrate toward the event horizon, expelling magnetic flux tubes from the BH vicinity during a large fraction of time. When the magnetic islands stick to the horizon due to redshift and virtually vanish, a strong magnetic field penetrates the horizon, enabling efficient extraction of energy from the BH. During this flaring phase, a BH gap appears around the inner light surface with a strong meridional return current toward the equator within the ergosphere. If the mass accretion rate is 0.025 percent of the Eddington limit, the BH’s spin-down luminosity becomes 16-19 times greater than its analytical estimate during the flares, although its long-term average is only 6 percent of it. We demonstrate that the extracted energy flux concentrates along the magnetic field lines threading the horizon in the middle latitudes. It is implied that this meridional concentration of the Poynting flux may result in the formation of limb-brightened jets from low-accreting BH systems.

      In future using a general relativistic Particle-in-Cell simulation, we have planned to demonstrate that the rotational energy of a rapidly rotating BH is preferentially extracted along the magnetic field lines threading the event horizon in the middle latitudes. We will show that the jets exhibit limb-brightened structures in a wide range of viewing angles.

      Speaker: Kenichi Nishikawa (Alabama A&M University)
    • 11:40 AM 12:20 PM
      Flares from black-hole magnetospheres 40m

      A variety of astrophysical phenomena can only be explained as being powered by black holes. In particular, accreting supermassive black holes are responsible for launching relativistic plasma jets and for accelerating ultra-energetic particles. Recent years have seen several observational breakthroughs in the understanding of these objects. The Event Horizon Telescope (EHT) collaboration has been able to image the shadow of the supermassive black hole M87*, probing the magnetic structure almost down to the event horizon. Very high-energy gamma-ray flares from radio galaxies are detected at very short time scales, hinting at a magnetospheric origin. However, a first-principles understanding of these observations is still lacking.

      In this talk, I will present recent progress in capturing the key signatures of these black-hole flares. I will present first-principles kinetic simualations of a flaring black-hole, displaying a reconnecting equatorial current sheet. I will show polarized images of the nonthermal radiation emitted during the flare, in order to predict features of future polarized EHT observations. I will also talk about a novel strategy designed to alleviate the numerical challenges inherent to global kinetic 3D simulations of black-holes magnetospheres.

      Speaker: Benjamin Crinquand (Princeton University)
    • 12:20 PM 2:00 PM
      Lunch 1h 40m
    • 2:00 PM 2:40 PM
      Non-thermal flares and hot spots around Sagittarius A* - A plasmoid origin 40m

      The EHT observations have highlighted the major role played by large scale magnetic fields around accreting supermassive black holes (BHs), in agreement with the polarimetric results from their stellar-mass siblings. The magnetic field not only funnels an electromagnetic jet but it also accelerate particles when it reconnects and it sometimes even regulates the accretion. The GRAVITY collaboration followed during a NIR flare a centroid shift consistent with a synchrotron-emitting hot spot on a face-on orbit around Sgr A*. Several aspects challenge our understanding though: its super-Keplerian speed, a non-zero velocity along the line-of-sight, the incompleteness of the orbit and a shift of almost 10 gravitational radii between the alleged orbit center and the center of mass deduced from the S2 orbit.

      In this talk, I will present 3D global GR-PIC simulations of particle acceleration in the magnetosphere of a spinning BH. I will show that magnetic loops advected into the BH ergosphere are prone to open and feed a current sheet in the sheath of the jet. In this highly magnetized region, magnetic field lines reconnect in the relativistic regime and leptons are accelerated up to Lorentz factors of a few 100 to a few 1,000. At the Y-ring at the basis of the jet’s sheath, a few gravitational radii above the disk, plasmoids form and co-rotate with the footpoint of the outermost closed magnetic field line, hence the apparent super-Keplerian motion. They later detach due to the tearing instability and further propagate along a coiled trajectory on the sheath of the jet. We compute the evolution of the synchrotron emission from these plasmoids and compare it to typical Sgr A* flares.

      Speaker: Ileyk El Mellah
    • 2:40 PM 3:20 PM
      Relativistic Continuum Kinetic Algorithms, and a Path Towards a Novel Magnetised Kinetic Model for Relativistic Applications 40m

      I will present our recent work on developing advanced discontinuous Galerkin algorithms for the special/general relativistic kinetic equations. These algorithms are based on directly discretizing the Vlasov equation as a PDE in phase-space, rather than using particles. I will show how one can carefully initialize initial equilibrium distribution functions and compute moments in a consistent manner. Recently we have developed a reduced 4D set of kinetic equations for making kinetic simulations of strongly magnetized plasmas more feasible. Though initially developed and implemented in the non-relativistic regime, the extensions to relativistic kinetics is straightforward, at least when the distribution function is separable, a situation commonly encountered in extreme astrophysical systems.

      Speaker: Ammar Hakim
    • 3:20 PM 3:50 PM
      Coffee 30m
    • 3:50 PM 4:30 PM
      Collisionless Black Hole Accretion 40m

      The accretion flows around the black holes in Sgr A, M87, and other systems are strongly magnetized and collisionless. This, in fact, makes the usually employed general relativistic (GR) magnetohydrodynamic (MHD) method formally inapplicable. Thus, addressing the BH accretion problem, in principle, requires a fully kinetic approach. In this talk, I will show a study of axisymmetric accretion of collisionless plasma around the black holes from first principles using GR particle-in-cell simulations (GRPIC). By doing so, I carry out a side-by-side comparison of global dynamics in GRMHD simulations and GRPIC for the same black hole accretion problem. Magnetic reconnection, which is believed to be responsible for particle acceleration and subsequent flares, is accurately captured in the kinetic approach. I directly examine the production of non-thermal particles due to magnetic reconnection. I will also discuss the implications of our results for modeling event-horizon scale observations of Sgr A and M87 by GRAVITY and the Event Horizon Telescope.

      Speaker: Alisa Galishnikova (Princeton University)
    • 4:30 PM 5:00 PM
      Discussion 30m
    • 9:00 AM 9:40 AM
      Alfven-wave Turbulence vs. Reconnecting Turbulence 40m

      Relativistic turbulence can energize and illuminate magnetized plasmas around magnetars, neutron star mergers, jets, and accretion flows. In some cases, the turbulence can be naturally powered by "ringing" and "twisting" motions of the local magnetic field lines - magnetic shear waves. In other cases, the turbulence is triggered by rapid reconfiguration of the magnetosphere - magnetic reconnection events. Both cases are efficient at transferring the local magnetic energy into the kinetic energy of the plasma. In my talk, I will give an overview of the possible astrophysical sources that can house such turbulent magnetospheres. I will also present our latest efforts in modeling these turbulent energy-transfer processes with fully-kinetic 3D plasma simulations. Lastly, I will remark on their radiative properties and how to distinguish these various forms of turbulence from each other.

      Speaker: Joonas Nättilä
    • 9:40 AM 10:20 AM
      Particle Acceleration in 'Reconnecting' Turbulence 40m

      Turbulence and magnetic reconnection are ubiquitous in astrophysical environments, and they are often invoked to explain the origin of non-thermal particles inferred to occur in a variety of astrophysical sources. Yet, the mechanisms responsible for accelerating particles to ultra-relativistic energies are still poorly understood. Recent fully-kinetic particle-in-cell simulations suggest that turbulence and magnetic reconnection operate in synergy, with reconnection being responsible for particle injection from the thermal pool and stochastic scattering off turbulent fluctuations leading to extended non-thermal power-law tails. The acceleration mechanisms, as well as the resulting particle distributions, depend on particle species. We find that the ion energy spectrum is harder than the electron one, and both distributions get harder for higher plasma magnetization. The energization of electrons is accompanied by a significant energy-dependent pitch-angle anisotropy, with most electrons moving parallel to the local magnetic field, while ions stay roughly isotropic. Parallel electric fields associated with magnetic reconnection are responsible for the initial energy gain of electrons, whereas perpendicular electric fields control the overall energization of ions. These findings have important implications for the origin of non-thermal particles in black hole accretion flows and jets.

      Speaker: Luca Comisso (Columbia University)
    • 10:20 AM 11:00 AM
      Coffee 40m
    • 11:00 AM 11:40 AM
      3D particle-in-cell simulations of particle acceleration in instabilities created by relativistic jets in a cold, ambient plasma 40m

      Astrophysical jets, associated with the activity of central black holes in active galactic nuclei or occurring in Gamma-ray bursts, are a source of ultra-relativistic particles. However, we still miss details on how particles are accelerated to such high energies in astrophysical environments. We will present how the interaction of a jet with a toroidal magnetic field injected within a cold, ambient plasma develops Weibel instabilities, mushroom instabilities and kinetic Kelvin-Helmholtz instabilities and how these in turn modify the magnetic field and thus create electric field sufficiently large to accelerate particles to higher energies. We here consider magnetized electron-positron and electron-ion pairs carrying an initial toroidal magnetic field. For the first time, we perform 3D particle-in-cell simulations allowing us to not only monitor the temporal evolution of fields and instabilities, but also the positions and energies of individual jet and ambient plasma particles. We will present the evolution of the electromagnetic field and its spatial distribution as well as the densities and energies of jet and ambient particles. Finally, we will compare results with simulations results of unmagnetized jets and discuss them with respect to polarimetric observations.

      Speaker: Christoph Köhn
    • 11:40 AM 12:20 PM
      Monster electromagnetic waves and shocks in the magnetospheres of neutron stars 40m

      Magnetars are believed to excite ultrastrong electromagnetic waves of low frequencies. Physics of these magnetospheric waves will be discussed. Their propagation and damping involves formation of monster radiative shocks, extreme plasma heating, and production of X-rays. The results can help understand the observed activity of magnetars, including X-ray bursts and fast radio bursts.

      Speaker: Andrei M. Beloborodov
    • 12:20 PM 2:00 PM
      Lunch 1h 40m
    • 2:00 PM 2:40 PM
      Electron pre-acceleration at oblique collisionless shocks 40m

      We discuss nonthermal electron acceleration mechanisms at quasi-perpendicular shocks, for which substantial progress has been made in recent
      years. Thermal electrons have gyroradii many orders of magnitude smaller than the finite width of a shock, thus need to be pre-accelerated before they can cross it and be accelerated by diffusive shock acceleration. One region where pre-acceleration may occur is the inner foreshock, which upstream electrons must pass through before any potential downstream crossing. We report on large scale particle-in-cell simulations that generate a single shock with parameters motivated from supernova remnants. Within the foreshock, reflected electrons excite the oblique whistler instability and produce electromagnetic whistler waves that quickly evolve into non-linear structures. Although these non-linear structures do not in general interact with co-spatial upstream electrons, they resonate with electrons that have been reflected at the shock. We show that they can scatter, or even trap, reflected electrons, confining around 0.8% of the total upstream electron population to the region close to the shock where they can undergo substantial pre-acceleration. This acceleration process is similar to, yet approximately 3 times more efficient than, stochastic shock drift acceleration. We shall also comment on the role of pre-existing turbulence in the upstream medium and on particular aspects of shocks associated with neutron-star mergers.

      Speaker: Martin Pohl
    • 2:40 PM 3:20 PM
      Reconnection-Powered Emission in Black Hole Jets and Coronae 40m


      Speaker: Lorenzo Sironi
    • 3:20 PM 3:50 PM
      Coffee 30m
    • 3:50 PM 4:30 PM
      Discussion 40m