Evidence for violations of Cosmic Censorship in black-hole collisions in higher dimensions

Physics is the attempt to describe, predict and understand a vast range of phenomena in nature, — ranging from elementary particles to the entire Universe — in terms of mathematical expressions and equations. One of the most astonishing physical theories is Einstein’s general relativity (GR) that describes the gravitational interaction between all kinds of objects in terms of differential geometry and, ultimately, differential equations. One of most dreaded features in any kind of theory are so-called singularities, i.e. points where the physical system can no longer be described in terms of finite numbers. Famous examples include the big bang or the centre of black holes where curvature and mass-energy acquire infinite values. Singularities are dreaded because our physical theories lose their predictive power at these points. One of the most astonishing properties of GR is its prediction — the Hawking-Penrose singularity theorems — that seemingly innocent physical systems can form singularities; for example a sufficiently heavy star will end its life by collapsing to a black hole. In principle, this feature calls into question the predictive power of Einstein’s theory. The situation seems to be rescued, however, by Penrose’s Weak Cosmic Censorship Conjecture, which proposes that singularities formed in dynamical evolution must be hidden inside black-hole horizons. Through active investigation in over half a century, counter-examples to cosmic censorship in settings beyond astrophysics have been found, which can be regarded as a possibility to access the quantum regime of gravity, at least theoretically. They fall into two major categories: i) critical collapse, which involves fine tuning of initial data such that a zero-mass singularity is formed; ii) death by fragmentation, which results from elongated horizons becoming unstable and eventually pinching off in finite time.

Figure: Snapshots from the simulation of two black holes colliding at half the speed of light in 7 spacetime dimensions. The elongated horizons forming in this collision evolve into multiple generations of satellites connected by ever thinner string segment that ultimately pinch off, forming a naked singularity. The full animation is available on https://youtu.be/Ytqg9XX_4sM .

All these setups, however, have in common that the initial state is either arbitrarily improbable or already represents an inherently unstable configuration. One may thus wonder if the so-obtained singularities are a truly generic feature of the evolution in GR. In our work, we have explored a new and truly generic mechanism for violation of cosmic censorship: the collision of black holes in higher dimensions. The figure shows snapshots from such a simulation, performed with the GRChombo code, of two black holes approaching each other with half the speed of light in 7 spacetime dimensions (upper left). At time zero, they merge into a single peanut-shaped black hole (upper right) which then evolves into an increasingly elongated horizon (centre left). The resulting “neck” grows ever thinner (centre right) and develops local satellite bulges through a mechanism known as the Gregory-Laflamme instability (bottom left). This phenomenon repeats itself along the ever thinner string segments connecting the second-generation bulges (bottom right), leading to a cascade into ever thinner string segments that ultimately pinch off, leading to a so-called naked singularity, i.e. a singular point that is not veiled by a black-hole horizon. We observe this behaviour over a wide range of initial conditions in 6 and 7 spacetime dimensions, but never in 4 dimensions, where black-hole collisions ubiquitously obey Penrose’s Cosmic Censorship. It appears that the 4 spacetime dimensions we live in represent a particularly benign setup not only for GR, but also for those who exist in it.

Heating and Acceleration through Magnetic Reconnection in Space Plasma Turbulence

The nature of the processes responsible for the dissipation of energy in collisionless plasmas is an important open challenge in the field of space and astrophysical plasma physics. The solar wind is a prime example of a collisionless space plasma. Despite our efforts to measure these processes with spacecraft in the solar wind, we have not yet identified and quantified the relevant energy-transfer mechanisms successfully. Turbulence and magnetic reconnection are key candidates to explain the energy dissipation.

Using DiRAC’s high-performance-computing infrastructure, we design and analyse unprecedented three-dimensional particle-in-cell (PIC) simulations of anisotropic plasma turbulence under conditions like the plasma conditions in the solar wind (Agudelo Rueda et al., 2021). In our simulation domain, magnetic reconnection develops, which is a plasma process that transfers energy from the magnetic field to the plasma particles by re-structuring the field geometry. The high spatial resolution of our simulations allows us to study the energy transport and transfer between the electromagnetic fields and the plasma particles associated with reconnection events in great detail. Based on the moments of the kinetic Vlasov-Boltzmann equation, we evaluate proxy terms for the energy dissipation in these events.

We find that, in and around reconnection events, the thermal power density (heating) is greater than the kinetic power density (flow acceleration). The regions of intensified energy transfer extend along the direction of the background magnetic field, suggesting that a detailed three-dimensional analysis of the energy evolution is necessary (Agudelo Rueda et al., 2022). These results have major implications for our understanding of the geometry and distribution of the energy dissipation in turbulent space and astrophysical plasmas. In addition, our work informs the next generation of spacecraft analyses of the energy dissipation in the solar wind.

Sub-section of our simulation domain. Left: Kinetic power-density term (flow acceleration) for dissipation. Right: Thermal power-density term (heating) for dissipation. In the centres of the flux ropes, which form self-consistently in plasma turbulence, the energy transfer is enhanced. Heating occurs mostly along filamentary and elongated structures along the background magnetic field (vertical axis) and in the boundaries between the flux ropes. From Agudelo Rueda et al. (2022).


Agudelo Rueda, J. A., et al.: Three-dimensional magnetic reconnection in particle-in-cell simulations of anisotropic plasma turbulence, J. Plasma Phys. 87, 905870228, 2021, doi: 10.1017/S0022377821000404

Agudelo Rueda, J. A., et al.: Energy transport during 3D small-scale reconnection driven by anisotropic plasma turbulence, Astrophys. J., submitted, 2022

Numerical Simulations of Extreme Encounters of Stars with Supermassive Black Holes

Based on Norman, Nixon & Coughlin (2021, ApJ 923 184)

This research, led by undergraduate student Sarah Norman, presents numerical simulations of extreme encounters of stars with supermassive black holes. When a star gets sufficiently close to a supermassive black hole, the tidal field of the black hole can overwhelm the star’s self-gravity leading to the star being pulled apart into a thin stream of debris. Some of this debris falls back to the black hole over a period of order a year, powering a luminous flare that we can observe in distant galaxies. These events occur approximately every 10,000 years in each galaxy, and the number of observed events is expected to increase dramatically over the next few years due to new observing facilities, such as the Rubin Observatory, that will scan the sky every few days to find these energetic transients.

The numerical simulations presented in Norman et al. (2021), performed on DiRAC’s Data Intensive at Leicester (DIaL) cluster, explore several aspects of the physics of tidal disruption events including: (1) the pericentre distance of the stellar orbit, (2) the effects of heating due to shocks as the star is strongly compressed by the black hole’s gravitational field, and (3) the shape and time-dependence of the energy distribution of the stellar debris. We also varied the numerical resolution of the simulations, varying the SPH particle number from 250k to 128M, to determine the level of convergence of the simulation results. With these simulations we showed that simulating tidal disruptions with sufficiently small pericentre distance requires higher resolution than is typically employed in these calculations, with > 10 million particles required to accurately determine the orbital properties of the stellar debris. By comparing simulations that included and excluded the heating due to shocks we were able to show that this effect is only important for extreme encounters with small pericentre distances, and further, by comparing our simulations with detailed analytical calculations we were able to show that any shocks which do form are limited to Mach numbers of order unity. Finally, our results show that, while the shape of the energy distribution of the stellar debris is dependent on the original stellar orbit, the breadth of the energy distribution is essentially unchanged for the different orbits we simulated.

These simulations, and the analysis presented in Norman et al. (2021), has advanced our understanding of the physics of tidal disruption events, and the numerical parameters required to simulate them with high accuracy. Modelling observational data of these events can provide information on a number of important astrophysical topics including stellar dynamics in galaxy centres, supermassive black hole demographics, accretion physics and radiative processes. The next few years will see a substantial increase in the number of observed events and it is important that our theoretical and numerical calculations are robust enough to facilitate detailed comparisons in this area.

Kinematic signatures of gravitational instability

Young stars are born surrounded by cold discs or dust and gas. These discs act as a conduit for accretion of mass on to the central star, and also provide the raw material for planet formation. At early times these discs are thought to be sufficiently massive that they can be unstable to their own gravity. This gravitational instability initially leads to the formation of spiral density waves in the disc, and these spirals transport angular momentum very efficiently, increasing the disc accretion rate dramatically. In some cases the instability can also lead to fragmentation of the disc, leading directly to the formation of giant planets or brown dwarfs. Understanding gravitational instabilities is therefore crucial to understanding both star and planet formation. However, in the early stages of star formation discs are typically still enshrouded in their parent molecular clouds, making them difficult to observe, and measurements of the disc mass are plagued by systematic uncertainties (because the molecular hydrogen that comprises the bulk of the disc mass is largely invisible to our telescopes). Moreover, there are numerous other processes (such as disc-planet interactions) which can give rise to spiral structures in discs, and distinguishing these from the spirals caused by gravitational instabilities is challenging. It is therefore still not clear when, where, or even if, real discs become gravitationally unstable.

In recent years new observational facilities, especially the Atacama Large Millimetre/sub-millimetre Array (ALMA), have provided us with astonishing new high-resolution observations of discs around young stars. These discs have uncovered an unexpected wealth of structure in discs – gaps, rings, spirals, shadows – and have given us a huge array of new insights into the processes of star and planet formation. However, in the case of gravitational instabilities we have not been able to exploit these observations fully, because it was not clear what our telescopes should be looking for. By exploiting the power of DiRAC’s Data Intensive at Leicester (DIaL) cluster, we were able to perform a suite of 3-D Smoothed Particle Hydrodynamics simulations of gravitationally unstable discs, and then couple those simulations to radiative transfer calculations to generate synthetic observations of unstable discs. We found that the critical, unambiguous signature of gravitational instability lies not just in the existence of spirals, but rather in their kinematics, and that this signature is readily detectable in ALMA observations. Emission lines from carbon monoxide molecules provide the best probe of disc kinematics. In a “normal” (non-self-gravitating) disc the disc’s rotation results in a well-known “butterfly” pattern in the velocity structure, which is readily seen in ALMA’s so-called channel maps (essentially a series images of the CO emission at a particular velocities). Our DiRAC simulations showed that this is radically altered in self-gravitating discs, with the spiral density waves resulting in a characteristic “wiggle” in the channel maps (see Fig.1). This wiggle is a unique signature of the spirals generated by self-gravity, and represents the smoking gun of gravitational instability in discs around young stars. The race is now on to detect this signal in real observations, and these results will provide crucial new insight into the formation of stars and planets.

These results were published as Predicting the Kinematic Evidence of Gravitational Instability, C.Hall et al., The Astrophysical Journal, vol. 904, article 148 (2020).

Fig.1: Synthetic ALMA channel maps – “images” of the emission at a particular velocity – for the CO J=3-2 line from our simulated discs. The lower panels show the results for a disc without self-gravity, which shows the “butterfly” pattern resulting from Keplerian rotation. The upper panels show the corresponding channel maps for a gravitationally unstable disc: the spiral density waves manifest as very clear “GI-wiggles” in the channel maps. If detected in real discs, these wiggles would represent unambiguous evidence for gravitational instability.

Understanding the Galaxy-Halo Connection Using the Simba Simulation

Romeel Davé, PI

The Concordance Cosmological Model predicts the properties and distribution of dark matter halos with exceptional precision.  However, how these halos come to be populated with the diversity of galaxies that we observe remains unclear.  A curious recent observational result shows that at a given halo mass, quenched galaxies (i.e. those not forming stars currently) have lower stellar masses than star-forming galaxies.  Many models have attempted to explain this dichotomy, with mixed success.  In general, the difference is attributed to assembly bias, i.e. that halos hosting quenched galaxies assembled earlier and hence achieved a higher mass by today.  However, this does not pinpoint the physical origin of the dichotomy in star-forming properties; indeed, all models yield halo assembly bias yet can have qualitatively different predictions regarding the host galaxies!

In a paper published in Nature Astronomy (Cui et al., NatAs 2021, 5, 1069), Weiguang Cui and Romeel Davé showed that the Simba galaxy formation simulation quantitatively reproduces the observed trend.  This was a major success for Simba, which differs from other such simulations specifically by the mechanisms in which it quenches galaxies.  Taking advantage of the physical information provided by the simulation, we further explored the physics driving this dichotomy in galaxy properties.  We showed that Simba indeed produced halo assembly bias, but the key aspect that made it successful was the way that assembly bias interacted with Simba’s unique jet feedback model. 

In Simba, early halo assembly leads to increased cold gas accumulation at early epochs, resulting in longer sustained star formation and a bluer galaxy today.   Hence early-formed halos host star-forming galaxies.  Late-forming halos, meanwhile, accumulate less gas.  The key is that in Simba, galaxy quenching is driven by a low gas accretion rate onto the central black hole, which triggers radio jets and X-ray feedback that heat the surrounding gas.  Late-formed halos, having less gas, trigger jet and X-ray mode feedback earlier, shutting down the growth of stars and resulting in a galaxy with lower stellar mass by today.  Using Simba’s variant runs that switch off specific AGN feedback modes, we showed that without jet or X-ray feedback, we obtain the opposite trend to obsevrations, that at a given halo mass quenched galaxies are more massive!  Adding jets moved the results towards the observations, but only with both jet and X-ray feedback was Simba able to fully reproduce the observations.  This is a stunning success for Simba’s novel physics for black hole growth and feedback, and provides a springboard for using this observational relation to constrain models of black hole feedback.

Decays of an exotic 1-+ hybrid meson resonance in QCD

Using cutting-edge lattice Quantum Chromodynamics (QCD) methods, in a recent calculation [Phys. Rev. D103, 054502 (2021), arXiv:2009.10034] we demonstrated the presence of an exotic hybrid meson resonance for the first time. The results suggest that it is related to the  resonance observed by the COMPASS experiment at CERN.

Most observed hadrons (strongly bound clusters of quarks like protons and neutrons) can be explained in models as three-quark and quark-antiquark states. However, in recent years experiments have found a number of puzzling hadrons that do not appear to fit with this picture. One suggestion is that some are ‘hybrid’ mesons containing an excited gluonic field along with a quark and an antiquark. While hybrids have been studied in phenomenological models, this work was the first time a hybrid had been investigated from first principles in Quantum Chromodynamics, the fundamental theory of strongly-interacting matter, taking into account that it is a resonance, i.e. it can decay to lighter hadrons. We demonstrated the presence of a resonance containing light quarks with an exotic combination of spin , parity  and charge-conjugation , , that cannot arise from solely a quark-antiquark pair, and identified it as a hybrid meson. The calculation used unphysically heavy quarks; extrapolating to physical quark masses, the results are compatible with the  resonance observed by COMPASS in  and, interestingly, suggest that the dominant decay mode may actually be via , very relevant for ongoing and planned experiments.

Excited and exotic bottomonium spectroscopy from lattice QCD

In another study [JHEP 02 (2021) 214, arXiv:2008.02656], we computed the spectrum of bottomonium mesons containing a bottom quark and a bottom antiquark. Investigating a variety of  quantum numbers, many excited states were determined, as shown in the figure, including some with exotic quantum numbers ( ) that were identified as hybrid mesons. In models, hybrids can also arise with non-exotic quantum numbers and we observed states that could be identified as such hybrids, e.g. with  where experimental candidates exist. The pattern of hybrid mesons, highlighted in red and blue in the figure, suggests that the physics of bottomonium hybrids is similar to that of hybrid mesons and baryons with light, strange and charm quarks. These calculations neglected the unstable nature of the hybrids and further studies are required to understand these interesting states in more detail, like the investigation of the light hybrid meson resonance described above.

This work was made possible in part through the DiRAC Data Intensive Service hosted at the University of Cambridge.

Fundamental Physics from Strong Gravity

This project continues our work to characterise the behaviour of light fields in strong gravity environments, in particular focussing on the potential for gravitational wave signatures from dark matter, exotic compact objects and the possible formation of primordial black holes.

A key highlight this year was an investigation of superradiant clouds around black holes with spatially varying masses. Superradiance is a process by which light fields can extract energy from spinning black holes, leading to the build up of a “cloud” if the particle has a Compton wavelength comparable to the black hole’s Schwarzschild radius. One interesting possibility is that superradiance may occur for photons in a diffuse plasma, where they gain a small effective mass. We found either a constant asymptotic mass or a shell-like plasma structure is required for superradiant growth to occur. We studied thin disks and found a leakage of the superradiant cloud that suppresses its growth, concluding that thick disks are more likely to support superradiance.

Time evolution of the field’s energy density. We show snapshots at three different time steps: (1) when the field is in the transient phase (i.e. nonsuperradiant modes in the initial data are decaying into the BH or radiating away); (2) when the superradiant mode is just becoming dominant; and (3) when the cloud has been growing in the superradiant phase for some time. The values within the BH horizon are set to zero to mask the excision region. (See https://arxiv.org/abs/2201.08305 for more details.)

Proving a 40-year-old conjecture using lattice simulations

This project is focused on the study of field theories relevant for building holographic cosmological models. These models propose to use hypothetical theories dual to the unknown laws of gravity in the early universe and predict observable phenomena such as the cosmic microwave background (CMB). This allows to provide new models to consolidate current ones in observational cosmology, but also to constrain the existence of such dual theories.

Holographic cosmological models were shown [1,2] to describe well the CMB spectrum as measured by the Planck satellite. However, the observables from the dual theory were only computed in perturbation theory, which likely suffers from unphysical infrared divergences, limiting the predictivity of the model. It was conjectured in 1981 [3,4] that these divergences are just artefacts of perturbation theory, and do not exist in the full theory.

In this project we studied a specific class of field theories relevant for holographic models, scalar SU(N) theories in the adjoint representation and in a Euclidean three-dimensional space. We performed large-scale lattice simulations of the SU(2) and SU(4) theories on the DiRAC Data Intensive service in Cambridge University, and studied the phase diagram of the theory. We determined precisely the critical mass of the theory through finite-size scaling, in a completely non-perturbative manner. Through both frequentists and Bayesian hypothesis testing we found that our data strongly rejects the presence of infrared divergences in the critical mass, confirming the conjecture of Appelquist, Jackiw, Pisarski, and Templeton. Our result was published in the Physical Review Letters [5].

This important step sets the stage for using lattice simulations to understand the cosmological implications of holographic models, extending our knowledge of physics in the very early universe.

Figure 1 – Second-order phase transition in the dual SU(2) and SU(3) theories from the point of view of the Binder cumulant, which is the kurtosis of the magnetisation. The observed critical scaling with the simulation box size demonstrates the absence of infrared divergence as conjectured by Appelquist, Jackiw, Pisarski, and Templeton.


[1]: N. Afshordi, C. Corianò, L. D. Rose, E. Gould, and K. Skenderis, From Planck Data to Planck Era: Observational Tests of Holographic Cosmology, Phys.Rev.Lett. 118 (2017) 4, 041301.

[2]: N. Afshordi, E. Gould, and K. Skenderis, Constraining Holographic Cosmology Using Planck Data, Phys.Rev.D 95 (2017) 12, 123505.

[3]: R. Jackiw and S. Templeton, How Super-Renormalizable Interactions Cure Their Infrared Divergences, Phys.Rev.D 23 (1981), 2291.

[4]: T. Appelquist and R. D. Pisarski, High-Temperature Yang-Mills Theories and Three-Dimensional Quantum Chromodynamics, Phys.Rev.D 23 (1981), 2305.

[5]: G. Cossu, L. D. Debbio, A. Juttner, B. Kitching-Morley, J. K. L. Lee, A. Portelli, H. B. Rocha, and K. Skenderis, Nonperturbative Infrared Finiteness in Super-Renormalisable Scalar Quantum Field Theory, Phys.Rev.Lett. 126 (2021) 22, 221601.

Exoplanet Science at Imperial

Project – Exoplanet Demographics

In recent years, a bimodal distribution has been observed in the sizes of small, close-in exoplanets, often referred to as the ‘radius gap’. Currently there are two atmospheric evolution models which can provide explanations as to how the radius gap may arise, namely XUV photoevaporation and core-powered mass-loss. Both of these models propose that whilst larger planets that are further away from their host star can maintain an extended atmosphere, those that are smaller and closer may have their atmospheres removed due to irradiation from the host star. The models differ however, as to which part of the stellar spectrum is responsible for this atmospheric mass-loss. Photoevaporation relies primarily on the extreme ultra-violet and x-ray photons (XUV), whilst core-powered mass-loss requires the entire spectrum of stellar irradiation. In this work, this fact has been utilised to present a model comparison test to determine which of the models is the dominant in exoplanet evolution. DiRAC was implemented to model ~10^6 planets undergoing one of these two proposed mass-loss mechanisms. The radius gap that is then formed is analysed and compared to that which is observed in the Gaia Kepler Survey (GKS). The radius gap should vary differently with host stellar mass and incident flux received from the host star depending on the different models. With current data, we see that the measurements of the valley slope is consistent between the models and the GKS survey (see Figure). We have concluded that a future of survey of ~5000 planets with a wide range in stellar masses will be able to use this technique to determine which of these mass-loss mechanisms is dominant in exoplanet evolution.

Project – Stellar Variability

This project is concerned with modelling the spectra of stars commonly found to be the hosts of exoplanets. The objective is to provide reference UV spectra for a range of spectral types, magnetic fields and observational angles to estimate the stellar contamination of an exoplanet spectrum due to bright active regions (faculae). UV is of particular interest because of important atmospheric tracers having their signatures in this wavelength range. The more realistic non-LTE treatment has to be adopted for this work. Furthermore, the currently available 3D MHD models of stellar interiors allow for a detailed representation of the conditions in which the stellar spectrum is formed as opposed to 1D models reflecting only the average conditions in a stellar atmosphere. The figure shows the images of intensity at 187.5 nm for two MHD simulations of different magnetizations as seen from different inclination angles (required to model the movement of an active region across the stellar disk) and calculated in LTE and non-LTE regimes. The SSD magnetization represents the non-active surface of a solar-like star, while 300G magnetization represents a facular region. The bottom row of the figure shows the ratio of middle to top rows to highlight the correlation of non-LTE effects with the convective structure of the stellar atmosphere.

Collisional ionisation and recombination effects in partially ionised plasma

Project dp050 PI: A. Hillier, Research by G. Murtas

Plasmoid-mediated fast magnetic reconnection plays a fundamental role in driving explosive dynamics such as chromospheric jets (Shibata et al. 2007, Singh et al. 2012) and heating in the solar chromosphere, but relatively little is known about how it develops in chromospheric partially ionised plasmas (PIP). Partial ionisation can greatly alter the dynamics of the coalescence instability (Murtas et al. 2021), which promotes fast reconnection and forms a turbulent reconnecting current sheet through plasmoid interaction, but it is still unclear to what extent PIP effects influence this process.

Figure 1: Comparison of Jz between three PIP cases with different two-fluid coupling processes: elastic collisions only
(NIR, left), inclusion of ionisation and recombination (IR, centre) and inclusion of ionisation potential (IRIP, right). The
frames identify different steps of the coalescence instability. Panels (a), (b) and (c) show the initiation of the reconnection
process. In panels (d), (e) and (f) the evolution of coalescence is displayed at later stages. The final stage of coalescence
is shown in panels (g), (h), and (i) with the formation of the resulting plasmoid.

Using COSMA 7, we have investigated the development of plasmoid coalescence in PIP through 2.5D simulations of a two-fluid, ion-neutral hydrogen plasma. We have examined three different models for two-fluid interactions, where the two fluids are coupled by different processes: elastic collisions only (NIR), ionisation and recombination (IR), and ionisation, recombination and radiative losses (IRIP). The aim of this research is to understand to what extent the two-fluid coupling processes contribute in accelerating reconnection.

Figure 1 shows the time evolution of the coalescence through the current density for three fiducial cases corresponding to the three models for PIP. We have found that in general ionisation-recombination process slow down the coalescence. Unlike in the NIR model, ionisation and recombination stabilise current sheets and suppress non-linear dynamics, with turbulent reconnection occurring in limited cases: bursts of ionisation lead to the formation of thicker current sheets, even when radiative losses are included to cool the system. Therefore, the coalescence time scale is very sensitive to ionisation-recombination processes, who dominate the reconnection dynamics.

Our study demonstrates that ionisation and recombination rates are large enough to suppress the onset of fractal coalescence and small-scale dynamics, as they act on current sheets properties. However, multi-fluid physics is still capable to promote fast reconnection, hence explaining the short time scales of chromospheric explosive events. Further results were collected in a paper that has been recently submitted to Physics of Plasmas.