DPhil Projects 2020: Theory

Modelling the most extreme high redshift galaxies: from star formation rates to supermassive black hole growth.
Julien Devriendt & Adrianne Slyz

Extreme galaxies are routinely detected with star formation rates in excess of 1000 solar masses per year at high redshift (z>2). These galaxies are also thought to host the most massive supermassive blackholes (SMBH) in the Universe, at a time when their energy input into the circum-galactic medium (so called Active Galactic Nuclei (AGN) feedback) is the largest.
However, these objects have proven notoriously challenging to model, as they are very rare and hence necessitate running very large volume cosmological simulations whilst still resolving the interstellar medium (ISM) of the galaxy and the central region surrounding their SMBH.
To overcome these difficulties, this DPhil project proposes to extract a sample of rare objects from a gigaparsec cube dark matter only simulation and resimulate them with resolution fine enough to resolve the giant molecular clouds that form in their ISM. Analysing these zoom simulations, the student will focus on understanding what physical conditions are necessary to reach the extreme star formation rates observed in these galaxies and feed their central SMBH engine. In particular, they will focus on disentangling the contribution of AGN feedback and star formation to their luminosties and assess their role in driving the evolution of these galaxies.

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.


Black hole disks embedded in globular clusters.
Bence Kocsis

The recent discovery of gravitational waves opened new horizons for understanding the Universe and further developments are expected in the near future 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).
One possibility is that the observed black hole mergers are generated in dense stellar systems. In these systems, black holes become the most massive objects and sink to the center of the cluster and undergo frequent dynamical encounters. These encounters lead to the formation of black hole binaries, whose separation decreases during subsequent encounters until eventually the binary merges due to gravitational wave emission. Recent developments showed that the black hole subclusters do not necessarily decouple and evaporate at short time scales and that globular clusters can retain black holes up to a Hubble time (Morscher+ 2015),
A common simplification in globular cluster models is the assumption of spherical symmetry. This approximation is motivated by the approximately spherical appearance of these systems. However, observations show deviations from spherical symmetry both spatially and in velocity space (e.g. Van de Ven+ 2006, Bianchini+ 2018, Zocchi+ 2019). The geometry of the embedded black hole population in these systems may be even more anisotropic. This possibility is supported by the recent finding that the most massive objects dynamically settle to a disk-like configuration (Szolgyen & Kocsis 2018, Szolgyen, Meiron, Kocsis 2019).
In this project, the student will work with Prof. Bence Kocsis and examine the consequences of black hole disks embedded in globular clusters using direct N-body simulation methods and analytical techniques. The student will determine if such subsystems may be long-lived, how it affects the evolution of the cluster, the formation and evolution of binaries, and examine the implications for electromagnetic and gravitational wave observatories.

Links to further reading:
Barack L. et al., 2019, Classical and Quantum Gravity, Volume 36, Issue 14, article id. 143001, arxiv:1806.05195
Bianchini P. et al. 2018, MNRAS, 481, 2125, arXiv:1806.02580
Morscher M. et al.. 2015, Astrophysical Journal 800, 9, arxiv:1409.0866
Samsing J, 2017, Physical Review D, Volume 97, Issue 10, id.103014, arxiv:1711.07452
Szolgyen A, Kocsis B., 2018, PRL, 121, 101101, arxiv:1803.07090
Szolgyen A, Meiron Y, Kocsis B., 2019, arXiv:1903.11610
van de Ven G. et al,, 2006, A&A 445, 513, arXiv:astro-ph/0509228
Zocchi A., Gieles M., Hénault-Brunet V., 2019, MNRAS, 482, 4713, arXiv:1806.02157

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, diffusion and acceleration of particles by turbulence [3,4]. 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.

Background Reading:
1. G. Gregori et al., “The generation and amplification of intergalactic magnetic fields in analogue laboratory experiments with high power lasers,” Phys. Reports 601, 1 (2015) 2. P. Tzeferacos et al., “Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma,” Nature Comm. 9, 591 (2018) 3. A. F. A. Bott et al., “Proton imaging of stochastic magnetic fields,” J. Plasma Phys. 83, 905830614 (2017) 4. L. E. Chen et al., “Stochastic transport of high-energy particles through a turbulent plasma,” arXiv:1808.04430

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)

Universal equilibria, phase-space structure of collisionless plasma systems, and turbulence in non-Maxwellian astrophysical plasmas
Alexander Schekochihin

We know from statistical physics and kinetic theory that an ideal gas or plasma will strive towards a Maxwellian equilibrium and achieve it on time scales associated with inter-particle collisions. However, in many astrophysical plasma systems, e.g., the solar wind, the interstellar and intergalactic media, these time scales are very long and relaxation to some form of collisionless equilibrium appears to occur. Both ion and electron distribution functions that are measured in situ by spacecraft in the solar wind, while non-Maxwellian, appear to take certain forms that can be generically parametrised and might not be sensitive to initial conditions (i.e., to the way the wind is launched at the corona) in a detailed way. Both the MMS spacecraft flotilla currently probing the Earth’s magnetotail and the Parker Solar Probe that is en route to the outer corona and has sent first data in 2019 are giving us unprecedented amount of information about particle distribution functions. The distribution functions in extrasolar plasmas are difficult to measure, but there are credible efforts underway to observe them in, for example, galaxy clusters. This project will be preoccupied with the underlying questions that are made urgent by these new observational developments: In the absence of collisions, are there universal equilibria, or classes of equilibria, independent of initial conditions, that a plasma will want to converge to? Do collisionless plasmas have an "effective collisionality", caused by collective interactions between particles and fields? These are old questions [1,2], but they have stayed open because of the difficulty of nonlinear theory and impossibility of kinetic numerical simulations capable of sufficient resolution. The latter impediment to progress, while somewhat obviated by the arrival of “kinetic observations”, is also being lifted as both computers and numerical methods get more powerful, while the nonlinear theory of phase-space plasma turbulence, with which the problem of collisionless relaxation is intimately intertwined, has recently been advanced in a new direction [3,4]. It is, therefore, a good time to revisit the old theories of collisionless relaxation and attempt new ones. A related topic is the nature and structure of turbulence in plasmas that are not close to the Maxwellian equilibrium: a seemingly simple but conceptually fascinating question is what is the counterpart to the energy cascade in such systems (indeed, what is the cascaded invariant) [5]. Depending on the student's inclinations, s/he will be able to take a numerical or analytical route, or, more likely, a mixture of the two. Some opportunities for getting engaged with the space data analysis may also be on offer.

Background Reading:
1. B. B. Kadomtsev & O. P. Pogutse, “Collisionless relaxation in systems with Coulomb interactions,” Phys. Rev. Lett. 25, 1155 (1970)
2. T. H. Dupree, “Theory of phase space density granulation in plasma,” Phys. Fluids 14, 334 (1972)
3. A. A. Schekochihin et al., “Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence,” J. Plasma Phys. 82, 905820212 (2016)
4. T. Adkins & A. A. Schekochihin, “A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space,” J. Plasma Phys. 84, 905840107 (2018)
5. M. W. Kunz, A. A. Schekochihin, C. H. K. Chen, I. G. Abel and S. C. Cowley, “Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas,” J. Plasma Phys. 81, 325810501 (2015)