Planetary Giant Impacts

DiRAC resources used: COSMA8

A new understanding of the “canonical” model for Moon formation was provided by Kegerreis et al (2022). Our paper showed that a Moon-sized body can be immediately placed into orbit following the collision of a Mars-sized body, called Theia, with the proto-Earth.

Previous low resolution hydrodynamical simulations of this planetary collision had produced a disk of debris that would subsequently accrete to form the Moon over a timescale of years. Using the SWIFT simulation code, we were able to simulate this impact at a wide range of resolutions. Only when we included at least three million particles, which is more than previous studies had typically employed, did the initial clump of debris split into two after which the outer, Moon-sized, satellite was torqued onto a stable orbit. This moment of splitting is shown in the figure. At lower resolutions, the clump as a whole smashes back into Earth, leaving just a disk of orbiting debris.

The numerical resolution in our simulations allowed us to determine the radial variation of the provenance of material in the Moon-sized clump, with the outer layers containing at least as much proto-Earth as Theia material. Depending upon the extent of subsequent mixing within the satellite this radial variation could have a significant bearing upon the interpretation of isotope ratio measurements of lunar samples and Earth rocks. Immediately forming the Moon during a giant impact could lead to a thinner lunar magma ocean than when the Moon is entirely accreted from a diffuse disk. This would produce a thinner crust, which is what recent measurements show. Furthermore, there is more scope for imparting an orbital inclination to the Moon, relative to Earth’s equator, if it forms immediately.

Astrophysical Fluid Dynamics at Leeds

Dr Adrian Barker University of Leeds

Here are a few science hightlights since our project started on 1st April 2022.

Neutron stars are the strongest magnets in the Universe. Their extraordinary magnetic fields are formed during the supernova explosion and continue evolving when neutron star crust solidifies. Magnetic fields of neutron stars are so strong that they control how heat is transported within the crust forming complicated surface thermal patterns. In this project we investigate different initial magnetic field configurations and evaluate their impact on X-ray observations. We study in details the off-centred dipole configurations and check if the amount of dipole shift could be measured using spectral and timing observations. A figure is attached below from simulations by Andrei Igoshev on DIaL3.

The Earth’s magnetic field is known to reverse polarity on average a few times per million years.

Other planets with magnetic fields may well reverse polarity too, but our lack of understanding of the reversal mechanism has prevented us from answering the question of whether they actually do reverse.

A major problem is that the current numerical dynamo models which do reverse are strongly influenced by the inertial term in the equation of motion (Rossby number order 1), but this is term is actually small in planetary dynamos on the long reversal timescale. We are exploring whether reversing dynamo models are possible when the Rossby number is small (the situation in most planetary interiors), and whether large Peclet number convection (the Peclet number really is large in most planetary interiors) can provide the fluctuations necessary to get reversals. The answer is yes, we have a new class of dynamo models which do reverse at low Rossby number if the Peclet number is large enough.

The two images show the dipole moment as a function of magnetic diffusion time produced by Chris Jones. The left one at Prandtl number 30 has Peclet number 248. It fluctuates but does not change sign with time. The second image on the right has a larger Peclet number, 317, which is just above critical and does reverse the sign of the dipole moment.

Massive black holes in dwarf galaxies: from AGN feedback to multimessenger signatures

Contrary to the standard lore, there is mounting observational evidence that feedback from active galactic nuclei (AGN) may also play a role at the low-mass end of the galaxy population. We have explored this possibility with a series of high-resolution zoom-in simulations, varying the AGN prescription and supernova energetics.

We find that with the commonly employed Bondi model for black hole growth, black hole accretion in dwarfs is completely degenerate with the black hole seed mass. This motivated us to develop an alternative black hole accretion model that is directly tied to the gas availability in the immediate surroundings of the black hole and does not artificially suppress the growth of low-mass seeds. We also experimented with varying the boost parameter in the Bondi prescription. Both the supply-limited accretion model and the boosted Bondi set-ups lead to efficient accretion onto low-mass black hole seeds in our simulated dwarf system. In fact, there are sufficient amounts of gas to power brief, Eddington-limited accretion episodes in dwarf galaxies.

These episodes have a profound effect on the large-scale outflows, increasing outflow temperatures and velocities, which could be probed by future observations with JWST NIRSpec. The AGN-boosted outflows heat the circumgalactic medium and regulate star formation via maintenance-mode feedback, with the most significant impact at high redshifts, where supernova feedback alone cannot suppress cosmic inflows efficiently (see Fig. 1).

Fig. 1: Gas temperature projections of selected cosmological zoom-in simulations across a range of redshifts. Streamlines are also overplotted, with blue indicating inflows and red indicating outflows. The AGN runs can suppress the cosmic inflows at much higher redshifts and continuous AGN activity may keep the dwarf in a quenched state.

Finally, we investigated possible multi-messenger signatures of black hole mergers. The dwarf galaxy used for our zoom-ins lives in a relatively quiet environment, however, it experiences a high-redshift minor merger at z=4 that delivers significant amounts of fresh gas. For reasonable assumptions on the secondary black hole mass, we would expect this merger event to be observable by LISA with a signal-to-noise ratio greater than 10. Crucially, this merger event would also result in a bright EM counterpart, with the AGN X-ray luminosities for the majority of simulation set-ups explored peaking just after the merger at z=4, which may be observable by future X-ray missions such as AXIS or Lynx.

Project title: Modelling the multi-messenger signatures of massive black hole formation mechanisms with next-generation cosmological simulations

Project number: dp209

DiRAC resources used: CSD3 (Data Intensive Service, Cambridge) & COSMA (Memory Intensive Service, Durham)

IR-conformal dynamics in SU(2) gauge theories with adjoint fermions

Figure 1: The topological charge distribution of one of the new two-flavour configurations. This image was selected as the winner in the Particle and Nuclear Physics category of the DiRAC 2022 Research Image Competition.

Nearly-conformal gauge theories have been singled out as potential avenues for new physicics that can explain electroweak symmetry breaking in the standard model. Among them, SU(2) gauge theory with one or two adjoint fermions have shown good indications of being nearly conformal. Project dp208 has set out to probe closer to the continuum limit of these gauge theories than had been done in previous work, to observe whether previous tentative observations of near-conformality continue to hold.

We approach the continuum by increasing the value of the lattice inverse coupling β.

Figure 2: Fits of the Dirac mode number spectrum of the one-flavour theory, showing the mass anomalous dimension of the theory decreasing as the lattice coupling β is increased.

As we do this in the theory with Nf=1 fermion flavour, we see that the curcial quantity indicating near-conformality, the anomalous dimension, which has been measured both via the Dirac mode number (Figure 2) and via hyperscaling fits of spectral quantities, continues to decrease with increasing β. We also see that the previously observed trend—that the scalar is the lightest state in the spectrum, lighter than the pion that would be predicted to be the lightest state in chiral perturbation theory—persists (Figure 3), and is indeed enhanced at larger values of β.  Our results confirm the interesting properties of the model and at the same time highlight the need to perform further calculations in order to gain a clearer understanding of its large-distance behaviour. 

Figure 3: Mass spectrum of the one-flavour theory, showing the scalar remaining the lightest state observed at the new finer lattice spacings studied.

In the two-flavour theory, our early results were contaminated by finite-volume effects and poor plateaux, which are more severe than they were in our previous runs used for calibration. While computations on the largest volume are still ongoing, they have already produced a high-resolution view of topological charge density of one field configuration from this theory (Figure 1).

Einstein’s Universe: Using numerical relativity to unveil signatures of General Relativity in our cosmological observations

PI: Hayley J Macpherson

In cosmology we typically simplify the dynamics of the Universe via the assumption of a homogeneous and isotropic expansion of space-time. While such an assumption is extremely useful and necessary in most application, the dynamics are realistically more complicated. The existence of the large-scale structure of galaxies naturally results in an expansion of space-time which is dependent on both our physical location as well as which direction we observe on the sky. Theoretical descriptions of this complex expansion typically contain far too many degrees of freedom to be useful for observational constraints. These types of inhomogeneity can only be reliably studied in the context of general-relativistic simulations of cosmological structure formation.

In recent work, we explored these theoretical formalisms using numerical simulations which take into account the full complexity of the inhomogeneous expansion of space-time. Using simulations performed on DiRAC systems, we confirmed the simplified `quiet universe’ model as a good description for a realistic inhomogeneous space-time. From these models we were able to reduce the number of degrees of freedom by a factor of two, as well as identify the dominant anisotropic signatures we could hope to detect in future cosmological data.

Figure 1: Snapshots from a general-relativistic simulation of the cosmic web. Left panel shows the density distribution, normalised by the average value, lighter regions are higher density and are the regions where galaxies would reside, while darker regions represent voids. The right two panels show the shear scalar and electric Weyl curvature scalar, respectively, — both of which are exactly zero within usual simplifications in cosmology. These general-relativistic aspects of our universe are crucial for determining the validity of the `quiet universe’ models as well as predicting signatures of anisotropic expansion in cosmological data. Figure adapted from data used in Heinesen & Macpherson (2022).

Signatures of protoplanetary disc warps

Exoplanets form in cold discs of gas and dust around young stars. Our long-standing picture of these so-called protoplanetary discs is that all the planet-forming material orbits in a single plane (as with the planets in the Solar System). However, recent observations with the Hubble Space Telescope, the ESO VLT, and ALMA, have shown that many planet-forming discs are not coherently aligned, but are instead warped or twisted. A few discs show very large misalignments (which can even be greater than 90 degrees!), but smaller tilts and warps – of a few degrees – are more common. Such warps may be caused by the gravity of newly-formed planets, but because we can only observe a 2-D projection of these 3-D structures, our observations often struggle to distinguish between warps and other disc structures (such as spiral waves).

Fig.1: Simulated molecular line emission from a protoplanetary disc with a small warp. The background colour-scale shows the so-called “moment 1 map” of the 13CO 3-2 line, which traces the line-of-sight velocity of the gas (due to the Doppler shift): blue regions are moving towards us, while red regions are moving away from us. When viewed face-on the disc rotates in the plane of the sky, so any velocity along our line-of-sight traces out-of-plane motion (i.e., a warp). The smaller panels show the velocity profile of the emission line at each point in the disc. The line profiles are asymmetric, and these asymmetries provide a clear means of distinguishing a warp from other disc structures.

One way to break this degeneracy is to study the disc kinematics, as a warped disc moves quite differently to similar-looking co-planar structures. We used DiRAC’s Data Intensive at Leicester (DIaL) cluster to run sophisticated numerical simulations of warped discs, and study their observational appearance in detail. We used 3-D smoothed particle hydrodynamics to simulate the dynamics of disc with small warps, and these simulations were then taken as inputs to radiative transfer calculations. This allowed us to build up a detailed picture of how these discs appear to our telescopes, and understand which observable diagnostics probe the warp structure reliably. The most useful tracer is emission from cold gas molecules (such as CO), observed by ALMA, as Doppler shifts of these emission lines allow us to measure the disc kinematics directly. We showed that if discs are seen close to face-on then the CO kinematics can identify small warps clearly, but at higher inclinations these signatures become impossible to disentangle from the disc’s rotation. However, the amplitude of the inferred warp is strongly affected by the optical depth of the observed lines, so care is needed if we are to measure warp angles this way. We applied our models to several well-known discs, and found that in some cases disc warps may have been misinterpreted as other effects. Future observations are likely to discover many more such systems, and provide much-needed insight into the processes that shape young planetary systems.

These results were published in Characteristics of small protoplanetary disc warps in kinematic observations, A.K.Young et al., Monthly Notices of the Royal Astronomical Society, 513, 487 (2022). 

Cosmological constraints on decaying axion-like particles: a global analysis & Finite inflation in curved space

Axion-like particles (ALPs) are a candidate for dark matter, the elusive ‘missing mass’ of the universe, inferred by it’s gravitational presence in galaxies, clusters and cosmological structure formation. As a dark matter candidate, ALPs are preferred by theorists since they are a model independent generalisation of the standard model of particle physics, and are predicted by many beyond standard model extensions such as string theory. ALPs are preferred by experimentalists since data have not yet ruled them out (in a way that historical candidates such MACHOs and increasingly WIMPS have been in recent years). 

ALPs have characteristic properties, such as their mass, lifetime and possibly nonzero interaction rate with matter. This state-of-the-art analysis considers a class of ALPs which can have the capacity to occasionally decay into photons. This is interesting cosmologically, since for certain ranges of mass and lifetimes these would have effects on the expansion rate, element formation and large-scale structure evolution of the universe. Observations of the cosmos can therefore be combined with terrestrial experiments to rule out or confirm classes of ALP with (non-)detections informing our theories of fundamental physics and dark matter.

We find a lower bound on the ALP mass (>300keV) a little lower than around that of the electron (MeV), which can only be evaded if ALPs are stable on cosmological timescales. In order to achieve these strongest constraints, the team had to combine state-of-the-art calculations of the irreducible ALP freeze-in abundance, primordial element abundances (including photodisintegration through ALP decays), CMB spectral distortions and anisotropies, and constraints from supernovae and stellar cooling. In addition to these theoretical and observational innovations, the analysis also makes use of the global fitting framework GAMBIT, using state-of-the-art frequentist and Bayesian analyses. Future observations of CMB spectral distortions with a PIXIE-like mission are expected to improve this bound by two orders of magnitude, moving toward ruling out ALPs with masses of the proton and neutron (GeV).

The complexity of these calculations and the power of the data means that scouring the ALP parameter space requires high-performance computing, enabled by our DiRAC allocation. This analysis showcases the diversity of the datasets and sophistication tools the GAMBIT team has developed over the past decade, which we will continue to deploy over the next five years.

Finite inflation in curved space

The shape of the universe is one of the fundamental questions in cosmology. From their first lecture on Einstein’s theory applied to our Universe, students learn that the extended copernican principle demands the universe must come in one of three forms: closed, flat, or open (hyperspherical, Euclidean or saddle shaped), depending on the sign and degree of spatial curvature.

Since the release of Planck cosmic microwave background satellite data, there has been a debate in the literature as to the degree to which the current cosmological observations prefer closed, flat or open universes. Planck data alone has an moderate preference for closed universes (with betting odds of over 100:1). Alternative datasets, such as CMB lensing, Baryon acoustic oscillations and supernovae generally prefer flat universes. This discrepancy is termed ‘curvature tension’. Flat universers maintain that the Planck preference for closed universes is consistent with a statistical fluctuation, whilst proponents of the spherical Universe counter that the data analysis of all other datasets currently must assume a flat Universe. Future observations and more advanced data analyses will one day close this question, but in the meantime it is interesting to examine the impact that a closed universe has on other theories.

The standard model of the universe includes a primordial epoch of hyperinflation, where the universe begins in a rapidly accelerating phase. The theory of inflation explains the apparently acausal homogeneity of the CMB, the patterns of the microscopic anisotropies, and why the universe we see today is flat. An observation of spatial curvature today therefore has significant impact on many of the standard results in inflationary theory.

This paper represents a magnum opus lead by Lukas Hergt’s phd work. It’s careful and deep analysis, filled with informative and artistic figures represents the state-of-the-art in the theory and data analysis curved inflating Universes. Many results quantitatively shift when moving from flat to curved universes, as this figure shows. We can see that from an a priorir (grey) agnostic curvature prior Planck and BICEP data select for closed universes over flat ones, and in doing so prefer a higher value of the primordial inflationary parameter ns. Curvature therefore has non-trivial impact on other cosmological predictions. The paper considers a variety of inflationary and reheating models, and their non-trivial interaction with the shape of the universe.

Calculation of the scattering of two Goldstone bosons in the scalar resonance channel for an SU(2) gauge theory with two fundamental fermions.

Understanding the nature of the Standard Model Higgs boson is still an open problem. Extensions of the Standard Model in which its fields have a composite origin provide a compelling first-principle explanation of the existence of the Higgs boson and explain its mass in terms of spontaneous breaking of enlarged global symmetries of a novel strong interaction.  Among candidate realisations of Higgs compositeness are Sp(2N) gauge theories. The two simplest theories in this class are Sp(2), coinciding with SU(2), and Sp(4). Given the strong nature of the novel force, first-principle calculations allow to determine quantitative predictions that are used to test the experimental viability of these theories.

In our project, we performed the first calculation of the scattering of two Goldstone bosons in the scalar resonance channel for an SU(2) gauge theory with two fundamental fermions. The inevitable presence of a resonance in the scalar channel can affect the predictions for the LHC. Our work contributes to the understanding of the role of resonances in the phenomenology of the class of composite models characterised by the strong sector we are considering, irrespectively of its embedding.  Using the Lüscher quantization condition, we have been able to put non-perturbative constraints on the singlet scattering amplitude reported in Fig. 1 (left). This work represents the first study of the singlet channel in four-dimensional gauge theories beyond QCD.

Among the possible realisations of this idea, another particularly attractive is the one based on an Sp(4) gauge theory with two Dirac fermions in the fundamental representation and three in the antisymmetric representation because in addition, it admits bound states of mixed representation fermions—chimera baryons—that can be coupled to the QCD top quark, providing an explanation for its comparatively large mass. This mechanism is known as partial top compositeness. Our project has provided the first simulation of the Sp(4) model underlying partial top compositeness, simultaneously measuring both masses of mesons involving quarks in the same representation and of the chimera baryons. A first example of the resulting spectrum is reported in Fig. 1 (right).   

Lattice studies of 3d super-Yang–Mills and holography

DiRAC Project dp162/PPSP311, “Lattice studies of 3d super-Yang–Mills and holography”, is using the Cambridge icelake cluster to explore conjectured holographic dualities that relate supersymmetric quantum field theories to quantum gravity in a higher number of space-time dimensions. Such holographic dualities are widely employed in theoretical physics, and are beginning to benefit from first-principles lattice field theory studies. While holography is best understood in the limit of a large number of colours (N) with strong coupling, lattice field theory provides a powerful non-perturbative tool to explore the validity and applications of holography away from this limit.

The specific focus of this project is on maximally supersymmetric Yang–Mills (SYM) theory in three space-time dimensions, with gauge group U(N). Building on our prior work arXiv:2010.00026 that confirmed consistency between the low-temperature, large-volume behaviour of this field theory and the `D2′ phase of a homogeneous euclidean D2-brane black hole in the dual IIA supergravity, we are carrying out numerical lattice field theory computations to study the expected phase transition between this homogeneous D2 phase and a localized D0 phase as the volume decreases.

On the field-theory side, this corresponds to a `spatial deconfinement’ transition signalled by the Wilson lines that wrap around the spatial cycles of the lattice. The localized D0 black hole is dual to the small-volume spatially deconfined phase in which the Wilson line has a large magnitude |W|, relative to its maximum value |W|=1. The opposite regime of a large spatial volume with |W| vanishing in the large-N limit corresponds to the homogeneous D2 black hole we previously investigated.

The accompanying figure (from doi:10.22323/1.430.0221) presents preliminary results for the Wilson line magnitude |W|, demonstrating the behaviour described above. Here we work with fixed N=8 and 16^3 lattice volumes, which allows us to change the spatial volume by varying the temporal extent (dimensionless inverse temperature) r_beta. As described above, |W| increases as the spatial volume shrinks to enter the spatially deconfined D0 phase, while the smaller values of |W| for larger volumes in the spatially confined D2 phase would decrease even further for N>8. The four different data sets in the figure consider different values for certain tunable parameters in the SYM lattice action, as described in doi:10.22323/1.430.0221. Through ongoing analyses of the corresponding Wilson line susceptibilities, we will be able to carry out novel tests of holography based on our non-perturbative numerical lattice calculations.

The role of angular momentum in the formation of disk galaxies at high redshift

One of the key factors determining galaxies’ observable properties, such as their morphology and colour, is their angular momentum.

However, the origin of this angular momentum remains uncertain. Observations reveal that the spins of neighbouring galaxies are correlated one with another, a signal known as the intrinsic alignment signal. This suggests that part of this angular momentum should have a common cosmological origin to be elucidated. This effect has so far been studied statistically in large-volume simulations.

Figure 1: Mock images of a simulated galaxy three billion years after Big Bang. We modify how much angular momentum it will accrete, as labelled above. The same galaxy with increased angular momentum shows a more prominent disk structure and a larger spatial extent (as indicated by the white circle). Comparing different realisations of the same galaxy with different formation histories reveals the origin of its angluar momentum.

In addition, angular momentum is correlated with galaxy observables: for example, fast-rotating galaxies are more likely to display spiral structures or host more massive supermassive black holes. As of today, it remains to be confirmed that angular momentum is the underlying driver of these correlations rather than a consequence of another hidden one.

This DiRAC project aims at addressing these questions. To that end, we have performed a suite of cosmological zoom-in simulations using state-of-the-art physical models. We modified the initial conditions of seven galaxies so as to increase or decrease how much angular momentum they will accrete 3 billion years later (for the first three) and 6 billion years later (for the last four). This is achieved by modifying the initial conditions of the simulations (using the genetic modification technique, Roth et al. 2016; and in particular angular momentum modifications, Cadiou et al. 2021). We can thus make sure that there are no extra hidden parameters controlling the angular momentum.

In our first paper (Cadiou et al. 2022), we studied the first three galaxies with modified angular momentum 3 billion years after big bang. We find that this causes a change in the trajectory of their infalling satellites, which subsequently spin up or down the galaxy. We show how the resulting change in stellar angular momentum causes changes to the galaxy’s size and shape, as illustrated in Figure 1.

Future analysis of the four galaxies with modified angular momentum 6 billion years after big bang will allow us reveal whether similar mechanisms govern angular momentum acquisition in the late Universe. We will also concentrate future work on a detailed analysis of the gas trajectory from cosmological scales all the way to the center of the galaxy where stars form.