See snippets about my research here.
I participated in the 4th Visualize This! challenge, a Canada-wide competition that “aims to celebrate the innovative ways visualization can help researchers explore datasets and answer important scientific questions”. It was hosted by Compute Canada regional partners and the Compute Canada Visualization Team (which I joined the following year). My submission, that won second place, explores the flow around an airfoil from a particularly large computational fluid dynamics simulation (performed by Joshua Brinkerhoff’s team at UBC Okanagan), in particular the separation of the laminar boundary layer from the airfoil and its transition to turbulence. My visualization was a demonstration of the VTK-m library (Visualization Toolkit–many cores), an open source C++ library for scientific visualization maintained by Kitware. I chose to experiment with this library because it was specifically designed for the GPU-accelerated HPC environment. This experiment was only partially successful, it turned out the library was not mature enough at the time to achieve my goals.
This is teaching material that I originally summarized for a lecture series I gave for senior physics undergrads in Budapest.
The Milky Way galaxy is surrounded by a large number (dozens known) of dwarf galaxies. Due to dynamical friction, such galaxies occasionally fall into the Milky Way; this causes them to be transformed from a nearly spherical shape to an elongated shape, eventually developing very long tails of stars in a phenomenon called tidal disruption. The tails of the disrupted dwarf galaxies contain stars streaming from that galaxy’s core out toward the Milky Way’s halo, and they can be observed as lines running across the night sky. These are called tidal streams. Their observation, however, is not a trivial matter. Since dwarf galaxies contain only very few stars to begin with (compared to the Milky Way), the number of stars in tidal streams is very small compared to the background. Thus, tidal streams are too faint certainly to observe with the naked eye, but telescopic data often requires careful analysis to reveal their presence. A census of tidal streams is important for the understanding of the history of the formation of the Milk Way galaxy, and by extension the assembly of galaxies in general.
We construct an algorithm based on an artificial neural network that accepts a sample with a variable number N of coordinates and returns the most likely geometrical parameters of the stream, and additional information (e.g. its relative amplitude and the detection probability). The figure above shows the predicted (recovered) values versus the true values of the three geometrical parameters, shown as density maps. Since the parameters are not uniformly distributed (their histograms are shown in the top panels), to normalize the results, we divided each pixel in the maps by the number of (true) values in its column.
Full details and source code here: https://meiron.org/code/?location=stream-detector
High performance computing (HPC for short) is an essential tool in astrophysics and I heavily use computer clusters for my research. The picture on the right is of the Laohu (老虎) (Tiger) cluster in Beijing, which I helped maintain. In its last configuration before it was shut down in Feb. 2020 it had 32 nodes equipped with 64 Nvidia Tesla K20 GPU accelerators. I have also been using GPU-equipped supercomputers in Germany, Hungary, and Canada. For code testing I usually use various desktop machines equipped with gaming GPUs (usually Nvidia’s GTX models), including the Silk Machines in Beijing that I helped build from scratch. In most of my papers from the last few years, supercomputers have been used to perform N-body simulations and analyze their results. For this paper however, I wrote a parallel GPU-accelerated code to Fourier transform (gravitational) waveforms perturbed by the gravity of a triple companion. It was beneficial to use both GPU and multi-node (MPI) acceleration in this case because we had to perform the same FFT operation on a very large number of waveforms, exploring the parameter space of the perturber.
In two papers with Bence Kocsis we studied relaxation of physical quantities in star clusters, specifically characterizing the relative importance of resonant relaxation vs. 2-body relaxation in these systems. Relaxation is the return of a perturbed system to equilibrium. This is very general: this return to equilibrium may occur in different ways and due to multiple processes, affecting different physical quantities. Therefore, the concept of relaxation time has had multiple quantitative definitions in the literature. In star clusters we have two processes driving relaxation: 2-body (collisional; nonresonant) and resonant relaxation. 2-body relaxation (which is what people traditionally mean when talking about relaxation in stellar systems) is so-named in analogy to molecules colliding in a gas. The traditional view is that a certain star happily moves in a straight line while occasionally a second star tugs it around in a way that statistically generates or maintains equilibrium.
Moving forward from this simplified 2-body view, we can break the gravitational field into two parts: a smooth time-independent component (mean field) and a fluctuating part on top of it. 2-body relaxation is due to temporal fluctuations in the gravitational field, in globular clusters it affects all conserved quantities (energy, angular momentum direction and magnitude). Resonant relaxation, on the other hand, is a result of spatial fluctuations in the mean field, and in globular clusters it affects only the angular momentum direction.
In the first paper (Meiron & Kocsis 2018), concentrating on nonresonant dynamics, we made an important distinction between the concepts of relaxation and mixing. Mixing is the tendency of a distribution of a quantity x of any subpopulation in the cluster to evolve toward the distribution in the whole cluster, or “forgetting the initial conditions”. It occurs on much longer timescales than the relaxation time of x (which in the context of star cluster means the diffusion time). Both relaxation and mixing are manifestations of 2-body encounters, but there are different associated time scales. We defined a quantity called mixedness that quantifies the extent to which the initial conditions of a particular orbit have been forgotten due to collisions.
In the second paper (Meiron & Kocsis 2019), we followed star clusters using N-body simulations and found that (vector-) resonant relaxation operates efficiently in clusters with N > 104 (i.e. virtually all globular clusters). Since the distribution of orbital planes relaxes much more rapidly than the distribution of the magnitude of angular momentum and the radial action, the relaxation process reaches an internal statistical equilibrium in the corresponding part of phase space while the whole cluster is generally out of equilibrium, in a state of quenched disorder.
In stellar dynamics, direct N-body codes are generally used due to their high accuracy in orbital integration. These codes consider all pairwise interactions and are thus very slow, while N-body methods used in cosmology (such as tree) are much faster per particle, but they are usually unsuitable for star clusters. The advantage of using a direct code is diminished when parts of the stellar system (or all of it) have very long relaxation times. This is the case in galactic nuclei, dwarf galaxies, and other astrophysical systems. The self-consistent field (SCF) method is a way to estimate the gravitational field through a series of smooth potential terms. Based on it, I wrote a collisionless N-body code called ETICS. This code is parallel (using MPI) and GPU-accelerated. It was a challenge to implement the SCF method on GPU efficiently. Special memory restrictions meant that algorithms designed for CPU, specifically to calculate spherical harmonics, would not work, and had to be devised from scratch using different recursion relations and order of loops.
As a follow-up project, I wrote GRAPite, a software layer that essentially transformed the φgrape N-body code into a hybrid of direct and SCF methods. This allows collisional dynamics to be followed accurately in parts of the stellar system where it is needed, allowing the rest of the system to be integrated much faster using SCF. The main challenge here was to wrap the hybridization mechanism in such a way that φgrape only had to be added a single line of code. A second issue was calculating the jerk in the SCF part of the code, which was done with divided differences.
In Meiron et al. (2017) we examined whether future gravitational wave (GW) detections may identify triple companions of merging binaries. Such a triple companion causes variations in the GW signal mostly due to the Doppler effect. The research was carried out by producing mock signals of merging compact objects in isolation, and then perturbing them by varying the light travel time to the observer in a way that imitates the motion of the binary around the center of mass of the triple system. The signal-to-noise ratio in the residual between the perturbed and unperturbed signals was computed (using the advanced LIGO noise curve) to determine whether the perturber is detectable. We found that the prospects for detecting a triple companion are the highest for low-mass compact object binaries. For example, for merging neutron star binaries, LIGO may detect a white dwarf or M-dwarf perturber if it is within a distance of 0.4 R⊙ from the binary and the system is within a distance of 100 Mpc.
In O’Leary et al. (2016) we performed N-body and Monte Carlo simulations of star clusters to investigate the formation of close pairs of stellar-mass black holes, which eventually merge to produce gravitational waves detectable by LIGO/Virgo and future instruments. We found that it is more likely for two high mass black holes to form a close pair due to dynamical interactions in the cluster. Therefore, it is most likely to detect black hole binaries with a mass close to twice that of the upper bound of stellar black hole masses, and a mass ratio close to unity. We showed that the enhancement of the rate, as a function of the total mass of the binary (as compared to random pairing), is proportional to the mass to the fourth power.
In this long term collaboration, we study several aspects of interactions of stars with gaseous disks in an AGN. We performed high resolution N-body simulations with an added source of friction (drag) representing the disk. We studied how the disk affects the tidal disruption event (TDE) rate of stars, as well as the formation of a stellar disk from captured stars. We found that the TDE rate may increase by a factor of ∼10 (compared to a galactic nucleus that does not contain a gaseous disk), but even if assuming that all material from the disrupted stars is accreted onto the supermassive black hole (SMBH), it is only a small contribution compared to mass accreted from the gaseous disk itself. The stellar disk around has a mass of ~0.7% of the SMBH mass, and its characteristic size is ~5% of the SMBH’s influence radius.
The figure on the right shows the spatial density distribution of the nuclear stellar cluster in our simulation, in particular the formation of a disk-like substructure due to the accretion disk. The thick black line represents the accretion radius (from Panamarev et al. 2018). There are several follow-up subprojects ongoing and planned to address shortcomings of the model we used. One important issue is that we have so far used single mass models. In future simulations, we plan to take a mass spectrum into account (including stellar evolution), which also means stars would have different radii and will thus be differently affected by the drag. Another very important caveat is that our disk has so far been static, i.e. not affected by the stars interacting with it. We are now working on hydrodynamical modeling of the disk, its response to the stars passing through it will be investigated in the next phase of this subproject.
My Ph. D. thesis (digital copy available on request) focused on stars around a supermassive black hole binary. The animation below shows the stability volume in velocity space for a star in the equatorial plane of such a supermassive black hole binary, or a planetoid in the equatorial plane of a binary star. Velocities inside the volume produce stable orbits while velocities outside it produce unstable ones. In the absence of the central object, the stability volume would look like a sphere – the only unstable orbits are ones with velocity magnitude larger than the local escape velocity. In the presence of a single object at the centre, a “loss cone” is carved, where orbits with low angular momentum produce radial orbits, which are said to be unstable because they lead to tidal disruption by the central object. In this velocity presentation, the loss cone appears as a cylinder. When the central object is itself a binary, the loss cone becomes much larger, because in addition to tidal disruption, the orbit can be dynamically unstable: in other words one of the black holes can kick the star out of the system. The fact that the binary supermassive black hole is rotating in a particular orientation breaks the symmetry: stellar orbits which are retrograde with respect to the central binary are more stable than prograde ones. This leads to the enlarged cylinder to also be distorted.