DPhil Projects 2021: Theory

The impact of magnetic fields on gas accretion onto supermassive black holes and AGN feedback: the next frontier of galaxy formation cosmological simulations
Julien Devriendt & Adrianne Slyz

It is now well established that the main mechanism to fuel super massive black holes (SMBH) around which a sub-parsec sized accretion disk is spinning, is the magneto-rotational instability (Balbus & Hawley 1991). There also exists compelling observational evidence that SMBHs are ubiquitous and play an important role in regulating galaxy properties (mass, size, morphology) through extremely energetic AGN feedback events.

However, cosmological galaxy formation simulations, by and large, ignore the effect of magnetic fields. Presumably this failure reflects the fact that star formation and stellar feedback, and SMBH formation, accretion and feedback, take place on extremely small, sub-galactic scales, making it a tremendous challenge for simulations to model them with reasonable accuracy whilst resolving the galaxy larger scale environment at the same time. Building on previous work within our group (Beckmann, Devriendt, Slyz 2018 and Beckmann Slyz & Devriendt 2019) we propose to develop a fully magnetised implementation of SMBHs and AGN feedback in an explicit cosmological context.

The DPhil project will have several steps starting from revisiting the classic a Bondi-Hoyle-Lyttleton accretion model onto a point source to magnetize it, placing the black hole within an isolated galactic disk, adding AGN feedback to it before finally moving to the cosmological environment. The student will also be given the opportunity to develop their own model for galaxy synchrotron emission based on the post-processing of these galactic and cosmological MHD simulations, in a view to produce realistic mock observational data for the coming Square Kilometer Array instrument and its precursors (in interaction with the radio astronomy observational group at Oxford centred around Prof. Jarvis).

Although no prior knowledge of numerics is required to carry out the project, a strong taste for theoretical physics and the numerical implementation of physical problems is mandatory.

The impact of primordial magnetic fields on dwarf galaxies
A. Slyz and J. Devriendt

The smallest galaxies in the Universe, called dwarf galaxies, hold the key to many mysteries regarding the properties of the Universe. They are generally cast as responsible for forcing it to come out of the ‘Dark Ages’, making it transparent to ionising photons a second time, one billion years after the Big Bang, at the end of an epoch called ‘re-ionisation’. They also feature density profiles in tension with those predicted by the standard Lambda Cold Dark Matter model, being cored instead of cuspy at their centres. However, a largely unexplored area is the importance of dwarf galaxies for the study of primordial magnetic fields (PMFs). If they were generated before recombination, PMFs can act on the ionized baryons and drive density perturbations via the Lorentz force which then couple to the dark matter (DM) via gravity. For high values of PMF strengths (still compatible with current observational constraints) , this effect alters the number of objects of a given mass (mass function) in the dwarf galaxy regime. In comparison to the standard one predicted by inflation alone, the PMF modified mass function yields an increased number of dwarfs.

The goal of this DPhil project is to study a statistical sample of dwarf galaxies with different PMF modified initial conditions, explicitly taking into account magnetic fields and cosmic rays. Comparison to local dwarfs will provide constraints on primordial magnetic fields, helping to elucidate which theoretical magneto-genesis models are favoured. Realistic mock observational data for the coming Square Kilometer Array instrument and its precursors (in interaction with the radio astronomy observational group at Oxford centred around Prof. Jarvis) will also be generated..

Although no prior knowledge of numerics is required to carry out the project, a strong taste for theoretical physics and the numerical implementation of physical problems is

Black hole mergers in active galactic nuclei
Bence Kocsis

The recent discovery of gravitational waves opened new horizons for understanding the Universe and further developments are expected with new Earth and space-based instruments. The measurements have unveiled an abundant population of stellar mass black hole mergers in the Universe. The great challenge is to understand the possible astrophysical mechanisms that may lead to mergers. Existing theoretical models of the astrophysical origin of the observed sources are currently either highly incomplete or in tension with data (Barack+ 2018).

An interesting possibility is that stellar mass black hole mergers take place around supermassive black holes in the centers of galaxies. In these regions, the number density of stars and stellar black holes is up to a billion times higher than in the Solar neighborhood. Gas in the vicinity of a supermassive black hole collapses to a thin disk and rotates with nearly the speed of light, heats up, and releases a super-bright source of electromagnetic radiation. Such "quasars" often outshine all the stars of the host galaxy combined.
In this project, the student will work with Prof. Bence Kocsis to build a comprehensive model of quasars accounting for the cloud of stellar mass black holes which surround this region. The black holes twist and warp the disk gravitationally and represent a source of heat as their orbits pierce the disk. The gas in turn slows down the black holes, and causes them to settle into the disk, and catalyzes the formation of binaries, ultimately leading to mergers. We determine the rate of black hole mergers in these environments and examine the distinguishing features of electromagnetic and gravitational waves emitted by this source population.

Links to further reading:
Barack L. et al., 2019, Classical and Quantum Gravity, Volume 36, Issue 14, article id. 143001
Bartos, Kocsis, Haiman, Marka, 2017, ApJ, 835, 165 link:
Tagawa, Haiman, Kocsis, 2020, ApJ, 898, 25

Bence Hurt_IPAC_Caltech.jpg

An artist’s rendition of the two black holes orbiting each other in a gas disk that surrounds a supermassive black hole. (Credit: R. Hurt/IPAC/Caltech)

Caroline Terquem
Dissipation of tides in the convective envelope of stars

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 do 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. However, we have just developed a new description of the interaction between tides and convection that leads to the observed values of the circularisation period. 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.


Steven Balbus
Dynamical Behaviour of Black Hole Accretion Discs

It has been forty-seven years since the seminal paper of Shakura & Sunyaev (1973) laid down the foundations of turbulent accretion disc theory and twenty-five years since the establishment of the magnetorotational instability (MRI) as the fundamental physical basis for disc turbulence (Balbus & Hawley 1991). Yet, major features of disc behaviour remain poorly understood, especially time-dependent or transient behaviour around black holes. Discs spontaneously change their emission profile, and perhaps their gross physical state. In addition, there is a major class of black hole transients, so-called tidal disruption events (TDEs), in which a star passing near a massive (in excess of 106 M☉) black hole is pulled apart by the hole’s tidal forces, with some fraction of the star’s mass ultimately accreting into the hole. These objects are intrinsically time-dependent. While time-dependent disc theory following Newtonian gravity (Lynden-Bell & Pringle 1974) is by now well-established, the extension of this to Kerr black holes is very recent (Balbus 2017).

In this project we shall examine the theory of accretion around Kerr black holes, and apply this knowledge to better understand the expected accretion luminosity behaviour in different ambient conditions, the role of dynamical instabilities in discs, and observations of TDEs. The particular DPhil project is not expected to encompass all of these directions; rather it can in principle take many different paths (e.g., modelling, numerical simulations, mathematical analysis) depending upon the student’s interest and background. Key outstanding issues of astrophysical interests include addressing the stability of the inner accretion flow in both binaries and TDEs, obtaining reliable estimates for luminosity limits from primordial black holes, and investigating formation mechanisms for disc coronae.

References and Background Reading
Balbus, S. A. 2017, MNRAS, 471, 4832
Balbus, S. A., & Hawley, J. F. 1991, ApJ, 376, 214
Balbus, S. A., & Mummery, A. 2018, MNRAS, 481, 3348
Franck, J., King, A. ,& Raine, D. 2002, Accretion Power in Astrophysics (CUP: Cambridge)
Lightman, A.P. & Eardley, D,M. 1974, ApJ (Letters), 187, 1
Lynden-Bell, D., & Pringle, J. 1974, MNRAS, 168, 603
Mummery, A., & Balbus, S. A. 2019, MNRAS 489, 132
Page, D. N., & Thorne, K. S., 1974, ApJ, 191, 499
Shakura, N. I., & Sunyaev, R. A. 1973, A&A, 24, 337

John Magorrian
Beyond axisymmetry in models of galactic nuclei

The starting point for understanding the dynamical structure of galaxies or star clusters is the construction of an equilibrium model. These equilibria usually axisymmetric, but real galaxies can have interesting deviations from axisymmetry. Even galactic nuclei -- which are dynamically very old -- can have warps and lopsidedness. There are many dynamical mechanisms that have been proposed to explain such asymmetries, but few have been tested in any level of detail.The purpose of this project is to flesh out some of these scenarios and to test them against observations of real galaxies, the Milky Way and M31 in particular.

Mapping the Milky Way's ISM:
Most of the ongoing large-scale surveys of our Galaxy focus on its stellar content, but the gas and dust between the stars offer a complementary probe of Galactic structure and evolution. For example, interstellar gas can be traced through much of the Galactic plane from its line emission, such as HI or CO. Comparing the observed joint (longitude,velocity) distribution against that predicted by hydrodynamical models allows us to constrain the Galactic potential, as well as the three-dimensional distribution of the gas itself. Dust tends to occur where the gas is densest, but to map its three-dimensional distribution one has to rely on the "reddening" effect it has on stellar colours. We have developed a scheme that models the dust distribution as a Gaussian random field the values of which are constrained by these indirect reddening methods. These gas- and dust-mapping methods are still in their infancy and there is plenty of scope for a student interested in coupling Bayesian probability with some idealised models of astrophysical processes to develop them further.

Magnetised plasma turbulence: from laser lab to galaxy clusters.
Gianluca Gregori and Alexander Schekochihin (for this project, you may also apply for a DPhil in Atomic and Laser Physics)

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.

Background Reading:
1. P. Tzeferacos et al., “Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma,” Nature Comm. 9, 591 (2018)
2. A. F. A. Bott et al., “Time-resolved fast turbulent dynamo in a laser plasma,” preprint arXiv:2007.12837
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,” in preparation (2020)

Free-energy flows in turbulent astrophysical plasmas
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 are large spatial gradients of electric and magnetic fields and large gradients of the particle distribution functions with respect to velocities. This prompts two very intriguing 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 these days we can also measure density and magnetic fluctuations in galaxy clusters, 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 (we have done some preliminary work, so we know how to start off on this calculation, but obviously at some point we’ll be wading into unchartered waters). 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)
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)