Dynamical instabilities in accretion discs

Supervisors: Steven Balbus and Bence Kocsis

It has been almost fifty years since the seminal paper of Shakura & Sunyaev (1973) established the basis of turbulent accretion disc theory and some thirty years since the establishment of the magnetorotational instability (MRI) as the fundamental cause for disc turbulence (Balbus & Hawley 1991).    Yet, major features of disc activity remain poorly understood, especially transient behaviour.    Discs can spontaneously change their emission profile, and perhaps their gross physical state. This may occur over a wide variety of time scales, depending on the mass and the nature of the disk's central body.  

For example, little is well-understood about the “state changes” in black hole discs, which involve the appearance of distinct nonthermal hard X-ray components together with jets and outflows from an initially quiescent thermally emitting system.    Another class of black transients, so-called tidal disruption events, in which a star passing near a massive black hole is pulled apart by the hole’s tidal forces with some fraction of the star’s mass ultimately binding to, and accreting into, the hole. 

A black hole and its accretion disk


It has been established from first principles that there is an instability associated with the mutual roles of small-scale viscosity and resistivity in black hole accretion discs (Potter & Balbus 2017).   In most of the disc, the viscosity is much smaller than the resistivity, but the reverse is true in the inner disc region (Balbus & Henri 2008).    The transitional region, where the two are comparable, is unstable in a complex manner that has yet to be fully understood.   This behavior can be studied at some level by mathematical analysis, but requires a full numerical simulation of MHD turbulent flow.   Technical support will  be available from Prof James Stone at the Institute for Advanced Study, a leading numerical astrophysicist.   We will use the Athena ++ code for this calculation.   The initial effort is envisaged to focus on the role of viscosity and ohmic resistance, the two dissipation processes associated with MHD turbulence.  There has long been good numerical evidence that the behaviour of the large scale turbulence is sensitive to whether the viscosity or resistivity is larger (Fromang et al. 2007).    When the viscosity is larger, the turbulence is more vigorous and better correlated, but the ensuing heating is generally associated with making the viscosity itself yet larger and the resistance smaller.  The goal of this project is to determine under what conditions this instability saturates, and what the nonlinear resolution state of this instability is.   The hope is that the nonlinear behaviour will prove to be connected with the observed X-ray state changes, and we shall pursue this possibility vigorously.   The problem is, just on its own, one of fundamental interest to the physics turbulence community, in and of itself.    


References and Background Reading

Balbus, S. A., & Hawley, J. F. 1991, ApJ, 376, 214

Balbus, S. A. & Henri, P. 2008, ApJ, 674, 408

Fromang, S., Papaloizou, J. E., Lesur G., & Heinemann, T.  2007, A&A, 476, 1123

Lynden-Bell, D., & Pringle, J. 1974, MNRAS, 168, 603

Potter, W. J.  & Balbus, S. A. 2014, MNRAS 441, 681

Potter, W. J.  & Balbus, S. A. 2017, MNRAS 472, 3021

McClintock, J. E., & Remillard, R. A. 2006, in Compact X-ray Sources, eds. W. Lewin &

                   M. Van der Klis, Cambridge Astrophysics Series, No 39 (Cambridge UK: Cambridge

                   Univ. Press), p 157

Shakura, N. I., & Sunyaev, R. A. 1973, A&A, 24, 337

Free-energy flows in turbulent astrophysical plasmas

Supervisors: Michael Barnes and Alexander Schekochihin

In magnetised astrophysical plasmas, there is a turbulent cascade of electromagnetic fluctuations carrying free energy from large to small scales. The energy is typically extracted from large-scale sources (e.g., in the solar wind, the violent activity in the Sun's corona; in accretion discs, the Keplerian shear flow; in galaxy clusters, outbursts from active galactic nuclei) and deposited into heat---the internal energy of ions and electrons. In order for this dissipation of energy to happen, the energy must reach small scales---in weakly collisional plasmas, these are small scales in the 6D kinetic phase space, i.e., what emerges is large spatial gradients of electric and magnetic fields and large gradients of the particle distribution functions with respect to velocities. This prompts two fundamental questions: (1) how does the energy flow through the 6D phase space and what therefore is the structure of the fluctuations in this space: their spectra, phase-space correlation functions etc. (these fluctuations are best observed in the solar wind, but we can measure density and magnetic fluctuations even in extragalactic plasmas, via X-ray and radio observations); (2) when turbulent fluctuations are dissipated into particle heat, how is their energy partitioned between various species of particles that populate the plasma: electrons, bulk ions, minority ions, fast non-thermal particles (e.g., cosmic rays). The latter question is particularly important for extragalactic plasmas because all we can observe is radiation from the particles and knowing where the internal energy of each species came from is key to constructing and verifying theories both of turbulence and of macroscale dynamics and thermodynamics. This project has an analytical and a numerical dimension (which of these will dominate depends on the student's inclinations). Analytically, we will work out a theory of phase space cascade at spatial scales between the ion and electron Larmor scales. Numerically, we will simulate this cascade using "gyrokinetic" equations---an approach in which we average over the Larmor motion and calculate the distribution function of "Larmor rings of charge" rather than particles (this reduces the dimension of phase space to 5D, making theory more tractable and numerics more affordable).

Background reading:

1. A. A. Schekochihin et al., "Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas," Astrophys. J. Suppl. 182, 310 (2009)

2. A. A. Schekochihin et al., "Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence," J. Plasma Phys. 82, 905820212 (2016) (2019 IoP Payne-Gaposchkin Prize)

3. Y. Kawazura, M. Barnes, and A. A. Schekochihin, "Thermal disequilibration of ions and electrons by collisionless plasma turbulence," PNAS 116, 771 (2019)

4. R. Meyrand, A. Kanekar, W. Dorland, and A. A. Schekochihin, "Fluidization of collisionless plasma turbulence," PNAS 116, 1185 (2019)

5. A. A. Schekochihin, Y. Kawazura, and M. A. Barnes, "Constraints on ion vs. electron heating by plasma turbulence at low beta," J. Plasma Phys. 85, 905850303 (2019)

6. R. Meyrand, J. Squire,  A. A. Schekochihin, and W. Dorland, "On the violation of the zeroth law of turbulence in space plasmas," J. Plasma Phys. 87, 535870301 (2021)

Magnetic-field amplification by the fluctuation dynamo in astrophysical plasmas

Supervisors: Archie Bott and Alexander Shekochihin

Understanding cosmic magnetism is a long-standing problem in astrophysics. Astronomical observations of various astrophysical environments – for example, those of our own galaxy by the MeerKAT telescope [1] or of more distant galaxy clusters [2] – reveal the presence of finely structured magnetic fields of sufficient strength to affect the dynamics of such systems. A possible mechanism for explaining the presence and characteristics of these magnetic fields is the so-called fluctuation dynamo, whereby stochastic or turbulent motions of the plasma in which these magnetic fields are embedded amplify and maintain them [3]. The fluctuation dynamo has mostly been studied using simplified magnetohydrodynamic (MHD) plasma models whose key transport properties (viz., resistivity and viscosity) do not depend on macroscopic plasma properties such as density, temperature, and the magnetic field. However, the plasma often found in the astrophysical systems of interest is often weakly collisional, and current theories for the transport properties of such plasma typically do predict a dependence on macroscopic plasma properties. It is an outstanding question whether `anomalous’ transport properties can explain why certain predictions of the simplified theory of the fluctuation dynamo are at odds with astronomical observations (for example, that the energy-containing scale of the magnetic field is macroscopic). In this project, a student would explore how more realistic models of transport properties affect the fluctuation dynamo using both theory and numerical simulations, and then attempt to identify key differences with simplified dynamo theories that could be detected in astronomical observations.

Key reading:

  1. I. Heywood et al., Nature 573, 235 (2019).
  2. C. L. Carilli & G.B. Taylor, Annu. Rev. Astron. Astrophys. 40, 319 (2002).
  3. F. Rincon, J. Plasma Phys. 85, 205850401 (2019).  
  4. A. A. Schekochihin et al., Astrophys. J. 612, 276 (2004).
  5. A. K. Galishnikova, M.W. Kunz, A.A. Schekochihin, arXiv:2201.07757 (2022).
  6. A. A. Schekochihin, S. C. Cowley, Phys. Plasmas 13, 056501 (2006).
  7. A. F. A. Bott et al., Proc. Nat. Acad Sci. 118, e2015729118 (2021).


Magnetised plasma turbulence: from laser lab to galaxy clusters

Supervisors: Gianluca Gregori, Archie Bott, and Alexander Schekochihin

There are a number of possibilities within this project to design, take part in, and theorise about laboratory experiments employing laser-produced plasmas to model astrophysical phenomena and basic, fundamental physical processes in turbulent plasmas. Recent examples of our work in this field include turbulent generation of magnetic fields ("dynamo") [1,2], supersonic turbulence mimicking star-forming molecular clouds [3], diffusion and acceleration of particles by turbulence [4,5], suppression of thermal conduction in galaxy-cluster-like plasmas [6]. Our group has access to several laser facilities (including the National Ignition Facility, the largest laser system in the world). Students will also have access to a laser laboratory on campus, where initial experiments can be fielded. Depending on the student's inclinations, it is also possible to pursue a project focused on theory and/or numerical modelling of plasma phenomena in astrophysical and laboratory-astrophysical environments.


1. P. Tzeferacos et al., "Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma," Nature Comm. 9, 591 (2018) (2019 APS Dawson Prize)

2. A. F. A. Bott et al., "Time-resolved fast turbulent dynamo in a laser plasma," PNAS 118, e2015729118 (2021) (2020 EPS PhD Award in Plasma Physics)

3. T. G. White et al.,"Supersonic plasma turbulence in the laboratory," Nature Comm. 10, 1758 (2019)

4. A. F. A. Bott et al., "Proton imaging of stochastic magnetic fields," J. Plasma Phys. 83, 905830614 (2017)

5. L. E. Chen et al., "Transport of high-energy charged particles through spatially intermittent turbulent magnetic fields," Astrophys. J. 892, 114 (2020)

6. J. Meinecke et al., "Strong suppression of heat conduction in a laboratory analogue of galaxy-cluster turbulent plasma," Science Adv. 8, eabj6799 (2022)

Microphysics of gamma-ray bursts

Supervisors: Gianluca Gregori, Archie Bott, and Alexander Schekochihin

Gamma-ray bursts (GRBs) are among the most energetic events in the Universe. They occur at cosmological distances and are the result of the collapse of massive stars or neutron stars mergers, with emission of relativistic “fireballs" of electron-positron pairs. From astrophysical observations, a wealth of information has been gleaned about the mechanism that leads to such strong emission of radiation, with leading models predicting that this is due to the disruption of the beam as it blasts through the surrounding plasma. This produces shocks and hydromagnetic turbulence that generate synchrotron emission, potentially accelerating to ultra-high energies the protons which are observed on Earth as cosmic rays. However, there is no direct evidence of the generation of either magnetic fields or cosmic rays by GRBs. Estimates are often based on crude energy equipartition arguments or idealized numerical simulations that struggle to capture the extreme plasma conditions. We propose to address this lacuna by conducting laboratory experiments at large laser and accelerator facilities to mimic the jet propagation through its surrounding plasma. Such experiments will enable in situ measurement of the plasma properties, with exquisite details that cannot be achieved elsewhere. The experiments also complement numerical simulations by providing long measurement times extending into the non-linear regime where numerical simulations are not possible today. The proposed experiments will study fundamental physics processes, unveil the microphysics of GRBs, and provide a new window in high energy astrophysics using novel Earth-based laboratory tools.

Background Reading:

1. C. D. Arrowsmith et al., "Generating untradense pair beams using 400 GeV/c protons," Phys. Rev. Res. 3, 023103 (2021)

Black hole discs in dense stellar systems

Supervisor: Bence Kocsis

The recent discovery of gravitational waves opened new horizons for understanding the Universe. The measurements have unveiled an abundant population of stellar mass black hole mergers. The great challenge is to understand the possible astrophysical mechanisms that may lead to mergers. The existing theoretical models of their astrophysical origin are currently either highly incomplete or in tension with data (Barack+ 2019).

An interesting possibility is that the observed black hole mergers are generated in dense stellar systems such as globular clusters or galactic nuclei harboring a supermassive black hole with or without a gaseous accretion disk. In these systems, stellar mass black holes sink to the center of the cluster and undergo frequent dynamical encounters, forming binaries, which may eventually merge and produce gravitational wave emission.

In this project, the student will work with Prof. Bence Kocsis to build a comprehensive dynamical model of dense stellar systems with a population of stellar mass black holes. The black holes are expected to settle to a flattened disk-like structure which gets twisted and warped due to the fluctuating anisotropy of the otherwise spherical surrounding star cluster. We will use a combination of analytic and numerical methods including statistical mechanics, kinetic theory, and N-body simulations to determine if such subsystems may be long-lived, how it affects the evolution of the cluster, study the formation and evolution of binaries, and examine the implications for electromagnetic and gravitational wave observatories.

Black holes distorting the background starlight due to gravitational lensing


Abbott R. et al., 2021, ApJL 913, 7 (https://iopscience.iop.org/article/10.3847/2041-8213/abe949)

Barack L. et al., 2019, Classical and Quantum Gravity, Volume 36, Issue 14, article id. 143001 (https://arxiv.org/abs/1806.05195)

Samsing et al. 2022, 603, 7900, 237 

Szolgyen A. & Kocsis B. 2018, PRL, 121, 101011 (https://arxiv.org/abs/1803.07090)

The response of stellar discs to perturbations

Supervisor: John Magorrian

The starting point for understanding the dynamical structure of self-gravitating stellar discs is usually the construction of an axisymmetrized equilibrium model.  Real stellar discs are never axisymmetric though and so the next step is to apply the methods of perturbation theory to calculate both the qualitative and quantitive response of such models to the various types of noise experienced by real discs.  Most investigations to date have focused on the frequency-dependent response of the disc, but this project will adopt an explicitly time-dependent approach, which also makes comparison with $N$-body models more straightforward.  Its goals are to investigate various ways of treating (i) orbital resonances and (ii) 3d structure applied to either the stellar kinematics of the solar neighbourhood in our own Galactic disc or to the eccentric disc around the supermassive black hole in M31.

Particle acceleration in outflows from supermassive black holes

Supervisor: James Matthews

Supermassive black holes are thought to lie at the centre of virtually every galaxy, and many of them are "active", in the sense that they accrete matter from their surroundings and give of prodigous amounts of radiation. These Active Galactic Nuclei (AGN) are fascinating and astrophysically important objects.  Remarkably, the accretion process also expels outflowing material, a process that can transport huge amounts of energy and momentum to vast distances, allowing the AGN to influence physical proceedings far from its gravitational sphere of influence. These outflows are split into two broad classes -- narrow beams of relativistic material called "jets", and slower, wider-angle flows called "winds". Both winds and jets are important in influencing their surroundings, but also seem to be intimately connected to the underlying AGN accretion disc. Additionally, the outflowing material dissipates its energy in shocks and turbulence which can accelerate particles to high energy, producing radio gamma-ray emission as well as other messengers like neutrinos and cosmic rays. Understanding the details of this energy dissipation process, the particle acceleration physics, and the connection between observable quantities and the underlying physics is an important goal of modern high-energy astrophysics.

Oxford takes a prominent role in a range of international projects relevant for particle acceleration in AGN outflows, with prominent examples being the Cherenkov Telescope Array (CTA), a next-generation ground-based gamma-ray observatory, and MeerKAT, a powerful radio telescope which acts as a precursor for the Square Kilometre Array. As a result, this is an exciting time to be working on the topic, and the project may involve collaboration with Profs. Rob Fender and Garret Cotter to exploit synergies with other research groups.

A simulated jet from an active galactic nucleus

Movies available here.

The exact direction of the DPhil project will be flexible, but the main aim of the project is to provide the theoretical insight and numerical modelling needed to maximise the science output from the next generation of instruments. In particular, we will use hydrodynamic simulations combined with particle acceleration physics to predict observational signatures from AGN outflows and study the link between particle acceleration and observational signatures. An important part of the project will be the development of a new particle module (or adapting an existing one) so that we can predict radio and gamma-ray spectra and images from numerical simulations. There are various astrophysical applications for this tool. One possibility is to model nonthermal emission from AGN wind shocks, produced as winds from the accretion disc propagate into the surrounding galaxy. Another is to conduct simulations of AGN jets on large scales, with the aim of predicting combined observational signatures for the next generation of gamma-ray and radio telescopes. This DPhil project may also involve working on ultrahigh energy cosmic rays, and the theory of particle acceleration at shocks, and interested students may want to take a look at my other project on cosmic ray origins.


Contrasting simulations and observations: what can we learn about galaxy evolution

Supervisors: Dimitra Rigopoulou, Nirajan Thatte, Julien Devriendt

Cosmological simulations, like the New Horizon suite, can now achieve spatial resolutions of ~50 pc at redshifts z > 1, comparable to that achieved by the latest generation of mm/sub-mm telescopes (such as ALMA), and soon to be achieved by the ELT+HARMONI at near-infrared wavelengths. This provides a unique opportunity to test predictions of galaxy evolution models by comparing “mock observations” of simulated galaxy properties with ALMA and (in the near future) ELT+HARMONI observations. 

Our method uses cosmological simulations that forward propagate primordial density fluctuations consistent with observations of the cosmic microwave background, creating individual galaxies at high spatial resolution, whose kinematic, morphology and dynamical properties are consistent with observed ensemble properties of the population at the corresponding redshift. As the input physics (e.g. star formation laws) for the simulation is well understood, the resulting objects provide dynamically stable mock galaxies consistent with physical laws and cosmological evolution models at the appropriate redshift. We have developed a method for post-processing these mock galaxies, computing gas emission line intensities using CLOUDY radiative transfer computations in each cell, to get realistic model galaxy observations with self-consistent kinematics and dynamics.

Stars and gas density snapshots from the New Horizon simulation


We are looking for a motivated D.Phil student who has a keen interest in state-of-the-art numerical simulations, and is eager to work at comparing simulations with observations to test models of galaxy evolution. We are particularly interested in establishing the role of minor mergers in galaxy evolution and in particular their influence on the location of galaxies on the `main sequence’. Our focus is, at first instance, on z~2 galaxies however, we are keen to explore the kinematics of galaxies at higher redshifts.

The successful candidate will gain expertise in radiative transfer, cosmological simulations, data reduction and analysis. The project work involves working with astronomical data sets, both real and simulated.

Further Reading:

On the viability of determining galaxy properties from observations: I. Star formation rates and kinematics

K. Grisdale, L. Hogan, D. Rigopoulou, et al., 2022, MNRAS, 513, 3906

Integral field spectroscopy of main sequence luminous infrared galaxies at cosmic noon

L. Hogan, D. Rigopoulou, G. Magdis, et al., 2021, MNRAS, 503, 5329

HARMONI: The ELT’s first light near infrared and visible integral field spectrograph

N. Thatte, M. Tecza, H. Schnetler, et al., 2021, The Messenger, 182, 7


Nuclear and globular star clusters: the missing link between supermassive black holes and their host galaxies?

Supervisors: Adrianne Slyz and Julien Devriendt

Nuclear star clusters (NSC) are ubiquitously observed at the centre of sufficiently resolved galaxies. In dwarfs, they tend to replace the supermassive black hole (SMBH) detected in most massive galaxies. However, in galaxies like our own Milky Way (see picture), they happily co-exist with SMBHs of a similar mass. NSCs are the densest star clusters in the Universe with dynamic masses ranging from 106 to 108 solar masses enclosed in a radius no larger than 5pc. This places them firmly at the bright end of the globular cluster luminosity function (see e.g. the recent review by Neumayer et al, 2020, ARA&A, arXiv: 2001.03626). There exists clear evidence that their physical properties correlate with those of their host galaxies, which makes them key ingredients for our understanding galaxy formation and evolution. 

Although they were first detected in the early 1970s, the formation mechanism of NSCs is still debated. Crudely speaking, the formation channels put forward can be divided into two main categories: the ones which invoke an inward migration of star clusters through dynamical friction, and those that argue in favour of in-situ star formation triggered by high gas densities present in the galaxy nucleus.

The nuclear star cluster of the Milky Way seen with adaptive optics in the infrared with the NaCo instrument on the VLT.


However, regardless of their mode of formation, if NSCs truly are ubiquitous, those that form in early dwarf galaxies, before the re-ionization epoch, could still be present in the halo of the present-day galaxy which results from the merger of these dwarfs. This provides a hypothesis for the formation of globular clusters (GC) as the remains of NSCs which have been stripped of their gas content, preventing them from being rejuvenated by new star formation.

Moreover, given the extreme environment in which NSCs are located, and the well documented co-existence of NSCs and SMBHs in the nucleus of quite a large fraction of galaxies, it is quite natural to speculate that the formation and evolution of these two components are tightly linked. For instance, early collisions of stars within a dense NSC could easily provide seed black holes which could further grow from tearing apart other stars of the NCS.

Arguably the main reason why little progress has been made on these issues is that the direct modelling of NSCs and GCs (not to mention SMBHs) is difficult because their behaviour is collisional (as opposed to the collisionless approach used to numerically simulate dark matter and ordinarily distributed stars in cosmological simulations of galaxy formation and evolution). This means that direct N-body codes must be used to properly track the dynamical evolution of these star clusters (example N-Body6 (Aarseth 2003)). However, such calculations are currently out of reach of even the most powerful super-computers, especially for massive NSCs (see  e.g. DiCintio et al (2021) for a recent review of alternative techniques). 

Therefore, the DPhil project consists of exploring the issue by developing a sub-grid, semi-analytic model of NSC, GC and SMBH co-evolution based on direct N-body simulations, including their potential disruption. This model will be grafted onto the well-developed sink particle technique (see e.g. Beckmann et al 2019) already employed in the RAMSES code (Teyssier, 2002) to describe  the evolution of SMBHs in high-resolution cosmological zoom simulations of individual galaxies.  The student will target the formation and evolution of a Milky Way galaxy analogue, with a view to address the fundamental questions of when and how NSCs and GCs form. They will also study their interplay with the SMBH and possibly the entire galaxy depending on time and resources. This project will be done in collaboration with the group of Prof. T. Kimm at Yonsei University.     

Interaction between tides and convection in stars and giant planets

Supervisor: Caroline Terquem

A large proportion of stars are found in binary systems.  When the distance between the two stars in such systems is small enough, oscillations are excited in each of the stars by the tidal potential of its companion.  These tidal waves are dissipated in the convective regions of the stars.  Such dissipation of energy leads to circularisation of the orbits.  Observations show that close orbits are circular whereas wider orbits have eccentricities.  The period at which the transition occurs for a type of stars is called the 'circularisation period'.  Until now,  theoretical studies, which have relied on mixing length theory to model convection, have predicted circularisation periods significantly smaller than the observed ones. We have developed  a new description of the interaction between tides and convection that yields the observed values of the circularisation period. This new formalism is also able to account for the rate of tidal energy dissipation which is needed in giant planets to explain the orbital evolution of their satellites, and which had been a puzzle for the last 50 years.  There is a large number of problems that should be revisited using this new description, and this is the aim of the project.  These studies can be applied to a variety of systems, including binary systems with two stars, or with one star and a giant planet, or with a giant planet and a satellite. The project will use analytical and numerical tools.