General-relativistic MHD simulation of an accreting neutron star

3D general-relativistic MHD simulation of an accreting neutron star    

Relativistic Astroplasmas

Numerical Simulations for High-Energy Astrophysics

I'm an assistant professor in the School of Maths at Trinity College Dublin. I work in theoretical and computational relativistic astrophysics, in particular the dynamics of plasmas and magnetic fields around black holes and neutron stars, which I study using global numerical simulations and occasional pencil-and-paper models. I'm also exploring a new interest in fusion energy research, mediated by developing a code for time-dependent MHD simulations of stellarator plasmas.

You can check out my papers through your favourite article database:


Killing Horizon album Our project has acquired its own official soundtrack: the Michigan-based electronic-music collective Satyrasis are using our visualisation of a black-hole plasma simulation as the cover of their new album Killing Horizon. I can confirm that its eerie sci-fi vibes create the perfect atmosphere for astrophysics research, and that it's all-around some of the best hypersurface-themed music you'll come across.


I've worked on a range of topics, including collisionless plasmas around black holes, black-hole jets, neutron-star accretion and jet production, pulsar magnetospheres, magnetar giant flares, the solar sunspot problem, and the effects of modified-gravity theories on cosmological structure formation. While I maintain interests in most of these, I'm currently most active in the following few areas.

Positron density: GR collisionless plasma simulation

aps april meeting

Black-hole plasma kinetics

I've been studying how rotating black holes drive relativistic jets via the Blandford-Znajek mechanism, using a new tool — particle-based general-relativistic collisionless plasma simulations. With these we can directly model how gravitationally induced electric fields supply the jet with pair plasma, see where particle acceleration occurs, and follow "negative energy" particles as they extract black-hole energy through a kind of Penrose process. These studies are relevant to all jet-launching black-hole systems (AGN, long and short GRBs, X-ray binaries etc.), but should be particularly interesting in the context of observations of Sgr A* and M87 by the Event Horizon Telescope and GRAVITY.


First-Principles Plasma Simulations of Black-Hole Jet Launching
K. Parfrey, A. Philippov, and B. Cerutti, 2019
PRL, ADS, arXiv, Physics Viewpoint

Multidimensional Simulations of Ergospheric Pair Discharges around Black Holes
Crinquand, Cerutti, Philippov, Parfrey, Dubus, 2020
PRL, ADS, arXiv

For a less technical description, check out press releases from Berkeley Lab and the Flatiron Institute, or news stories from Nature, Physics Today, Physics World, LiveScience, Ars Technica, Vice Motherboard, New Scientist, and

Accreting Neutron Stars

Accreting pulsars

A focus of my current research is general-relativistic simulations of accretion onto magnetized, rotating neutron stars. This process is central to understanding a wide range of interesting astrophysical systems, including accreting and transitional millisecond pulsars, jet-launching neutron stars, and pulsing ultra-luminous X-ray sources, and may be involved in producing short gamma-ray bursts from neutron star mergers. The physics is also directly applicable to important topics in non-relativistic astrophysics, such as star-disc magnetic interactions in protoplanetary systems.

Hi-Res Movies YouTube Movies

See for example:
General-relativistic Simulations of Four States of Accretion onto Millisecond Pulsars
Kyle Parfrey and Alexander Tchekhovskoy, 2017
ApJ Letters, ADS, arXiv

Jets from turbulence-supported magnetic fields

Black-hole jets with MRI-generated magnetic fields

The canonical model of relativistic jets from black holes requires a large-scale ordered magnetic field. Many systems, including long GRBs and jetted TDEs, do not appear to contain the magnetic flux required by the jet power. We have advanced an alternative scenario, in which jets are produced using the magnetic field generated and sustained by the accretion flow's MRI turbulence. General-relativistic simulations of the combined black-hole–disc magnetosphere show runaway field-line inflation, magnetic reconnection in thin current layers, and the ejection of discrete bubbles of Poynting-flux-dominated plasma. The dissipation of magnetic energy in these coronal reconnection events is a potential source of black holes' observed high-energy emission.


Black hole jets without large-scale net magnetic flux
K. Parfrey, D. Giannios, and A. Beloborodov, 2015
MNRAS Letters, ADS, arXiv

Movies and Animations

The movies are in .mp4 format, encoded with the H.264 codec. You can download the files, or play them in most web browsers. Feel free to use them in your own presentations, with a reference to the relevant paper.

Collisionless black-hole magnetospheres and jets

Particle-in-cell simulations of jet launching by Kerr black holes, from Parfrey, Philippov, and Cerutti (2019). We start from vacuum, and inject plasma in cells where the parallel electric field exceeds a "pair-creation" threshold. The simulations are axisymmetric (evolving in the r-θ poloidal plane only, i.e. azimuthal derivatives are zero), and the movies show the number densities of electrons (left side) and positrons (right side). The boundaries of the ergosphere (peanut shape) and the horizon (black disk) are drawn in white. The black hole is nearly extremal, with a spin parameter of a = 0.999. Here's what you find when plasma isn't supplied freely (non-negligible threshold):

This movie corresponds to the low plasma supply scenario; you can also see a more detailed movie with magnetic field lines. If you instead use a smaller pair-creation threshold on the parallel electric field, the system transitions to a different steady state — see the movie for the high plasma supply case.

Accreting neutron stars: GRMHD simulations

Accreting pulsar movie key Rotating neutron stars interacting with accretion flows, from Parfrey and Tchekhovskoy (2017). The accreting plasma is initially contained within an equilibrium torus, which becomes unstable due to the MRI. Four different states are reached, depending on the relative magnitudes of the stellar magnetic dipole moment and the mass accretion rate: a crushed or opened magnetosphere, magnetically channelled accretion, the classic propeller, and exclusion from the light cylinder by the pulsar wind. Here we use the same torus in every run (i.e. the large-scale accretion rate is fixed) and vary the stellar field strength. Also important in these axisymmetric simulations is whether the torus's magnetic field is initially parallel or anti-parallel to the star's closed-zone field where they meet at the equator. The light cylinder is at 20 gravitational radii, five times the stellar radius, in all cases.

dipole moment star-torus B orientation state reached
movie 1.25 anti-parallel crushing / opening
movie 5 anti-parallel channelled accretion
movie 10 anti-parallel channelled accretion
movie 10 parallel channelled accretion
movie 20 anti-parallel propeller
movie 80 anti-parallel propeller and exclusion
movie 160 anti-parallel exclusion from light cylinder

Accreting neutron stars: relativistic force-free simulations

Accreting pulsar with force-free electrodynamicsHere we take a more idealized approach to the accreting-pulsar problem, and solve only for the electromagnetic fields; see Parfrey, Beloborodov, and Spitkovsky (2017). We specify a disc region (in purple in the movies) where we evolve E and B subject to the current that would be supplied by a disc, whose velocity and conductivity fields we set using an alpha-disc model. Outside the disc, we evolve the electromagnetic fields using a resistive version of relativistic force-free electrodynamics. See the fiducial run (labelled R1 in the paper) and a variation where the disc has a magnetic Prandtl number of 100 (i.e. alpha-viscosity much larger than magnetic diffusivity). The colour in the movie shows the toroidal magnetic field; gold is positive, blue is negative. The green bar indicates the corotation radius, and the light cylinder is the vertical grey line. Note that the opening of the stellar field by the star-disc interaction is fairly efficient in both cases. This kind of field-opening increases the power of the pulsar's electromagnetic wind, which may be the source of relativistic jets from neutron stars.

Black-hole jets and X-ray coronae from turbulence-supported magnetic fields

BH jets from small-scale fields: prograde simulation General-relativistic force-free simulations of black-hole coronae, from Parfrey, Giannios, and Beloborodov (2015). We start with a sequence of magnetic loops, two gravitional radii wide and of alternating direction, frozen into a nearly ideal disc. In these idealized simulations the disc is thin. The loops are sheared by Keplerian rotation, and dragged towards the rotating black hole (a = 0.98) with a radial velocity of c/200. The ergosphere boundary is in green, and the green bar denotes the ISCO radius. The toroidal magnetic field is shown with gold (positive) and blue (negative).

With small magnetic loops, a significant Blandford-Znajek-type jet is not produced when the accretion flow is prograde, but each magnetic structure produces a jet phase when you have retrograde accretion. For larger loops, above a critical scale, jets are produced by prograde flows as well. Notice the frequent plasmoid-dominated magnetic reconnection above the disc, which may cause the particle acceleration and heating behind black holes' X-ray coronae.


School of Mathematics
Hamilton Building
Trinity College Dublin, the University of Dublin
Dublin 2, Ireland

kyle at maths dot tcd dot ie