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Vasileios Paschalidis

Department of Physics office: Jadwin Hall 229
Princeton University email: vp16@princeton.edu
Princeton NJ, 08544

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My research spans a range of topics in gravitational physics and theoretical astrophysics. The ultimate goal of my work is to understand strong field gravitation and solve long-standing astrophysical puzzles such as the nature of the progenitors of short gamma-ray bursts, the origin of X-shaped radio galaxies, the nature of the equation of state at and above the nuclear saturation densities, and the way through which planets may form around isolated pulsars, to name a few. I am interested in studying compact objects as multimessenger sources, i.e., as sources of gravitational wave, electromagnetic and neutrino signals. For this reason, compact object binaries, such as black hole-black hole (BHBH), neutron star-neutron star (NSNS), black hole-neutron star (BHNS) , and white dwarf-neutron star (WDNS) systems are a major theme of my research.

The era of gravitational wave astronomy and astrophysics has arrived! On Thursday, February 11, 2016, the LIGO-VIRGO Scientific collaboration announced to the world the first direct detection of a gravitational wave signal! The detection took place on September 14, 2015 at 09:50:45 UTC! What is more, the signal is very well matched by the inspiral and merger of two black holes with masses 36 and 29 times the mass of our Sun! This detection not only provides proof that binary black holes exist, but that compact (black) objects exist that can pack more than \(25M_\odot\) in a tiny volume! These are the heaviest stellar mass black holes ever observed. After the news were released, I launched a simulation of non-spinning BHs to simulate this system by solving the full non-linear Einstein equations in vacuum. A visualization of the (apparent) horizons of the two black holes and the cross polarization of the gravitational waves from this source can be view below
3D rendering of the cross polarization of gravitational waves generated by inspiral, merger ringdown of two BHs with mass ratio \(q=36/29\). The binary orbital angular momentum vector points toward the viewer. The quadrupole nature of the gravitational wave signal is clearly visible. The simulation predicts that the energy radiated in gravitational waves is equivalent to \(3M_\odot c^2\)! The time in the source frame is shown on the top right. The time is in units of ms. It is important to note here the crucial role of numerical simulations, such as this one shown here, in the discovery of the LIGO-VIRGO collaboration. Numerical relativity generated waveforms were paramount to increase the confidence level of the detection and to perform the parameter estimation leading to the determination of the masses of the BHs. Movie generated by the Illinois Relativity group REU team.

This detection is only the beginning. More gravitational waves (GWs) from these (and possibly unknown) sources will soon be detected by excuisite devices. These include the ground-based detectors, such as advanced LIGO, VIRGO and the near-future KAGRA, all targeting stellar mass compact binaries, Pulsar Timing Arrays such as NANOGrav, and the IPTA, targeting supermassive black hole binaries, and by future space based detectors such as eLISA, targeting massive black hole binaries and galactic compact binaries (see Fig. 1 for a more complete list of gravitational wave sources and detectors). Moreover, transient electromagnetic signatures arising from such sources will be detectable by current and future telescopes such as Fermi, PanSTARRS, JWST, and LSST. These observations in conjunction with careful theoretical modeling will provide unprecedented insights into the workings of the fabric of spacetime.
Fig. 1: The big picture of gravitational wave astronomy. Gravitational wave strain sensitivity curves for multiple current and future detectors and respective targeted sources. Source: Robert Cole's website.

Astrophysical general relativity

A common thread uniting the astrophysical problems I am interested in is the crucial role of relativistic gravitation and I have particular expertise in dynamical spacetime scenarios. For example, compact objects in binaries or isolation are a class of astrophysical systems for which relativistic gravitation is of paramount importance.

Mergers of NSNS and BHNS binaries are promising sources of gravitational waves. GWs from such binaries can potentially constrain the unknown equation of the state of the matter above the nuclear saturation density.

However, NSNS and BHNS binaries as true multimessenger systems, not only emit GWs, but can also power a host of electromagnetic signatures both prior to and following merger that will accompany the GWs. These binaries may ultimately also solve long standing astrophysical puzzles such as the nature of the progenitors of short gamma-ray bursts (sGRB), and the origin of r-process elements in the Universe. I am interested in solving these puzzles and have spent considerable effort trying to prove from a theoretical point of view that BHNS and NSNS are viable progenitors of sGRB engines.

I have just published a paper demonstrating for the first time in full general relativity that mergers of binary neutron stars can launch incipient jets and hence be the progenitors of the engines that power short gamma-ray bursts.

The following movie using data from my recent work, shows the generation of a collimated, mildly relativistic, Poynting-dominated outflow - an incipient jet - following the merger of two equal mass, magnetized neutron stars initially on a quasicircular orbit. Relativistic gravitation is used for all these simulations coupled to the equations of ideal magnetohydrodynamics. The remnant black hole has a dimensionless spin parameter of 0.75. You can read more about this work in my article arxiv.

Volume rendering of the binary neutron star rest-mass density. The white lines indicate the field lines corresponding to the magnetic field measured by a normal observer. Here, \(M\) is the total gravitational mass, \(1000M\simeq 15(M_{\rm NS}/1.625M_\odot)\rm ms\), where \(M_{\rm NS}\) is the rest-mass of the neutron star. Movie generated by the Illinois Relativity group REU team.

In a recent work of mine I discovered that a one-arm (m=1) instability can develop in the hypermassive neutron star that forms following a dynamical capture binary neutron star merger. The following movie demonstrates the last stages of the merger and the development of the one-arm instability.

Equatorial (log scale) rest-mass density contours of a dynamical capture merger of two equal-mass neutron stars each having a (gravitational) mass of \(M_{\rm NS}=1.35M_\odot\) and dimensionless spin \(J_{\rm NS}/M_{\rm NS}^2=0.025\) aligned with the orbital angular momentum. Following merger at \(t\approx 4.5\rm\ ms\) two vortices forming near the surface of the remnant with the tidal tails begin to inspiral toward the center. At \(t\approx 6.0\rm\ ms\) the vortices merge into a single central vortex, creating an underdense rotation axis. At \(t\approx 10\rm\ ms\) the one-arm instability grows, while the remnant undergows strong re-arrangement with m=3 azimuthal modes also excited, pushing the vortex off the center. The instability is fully developed by \(t\approx 15.0\rm\ ms\) and persists until the end of the simulation. The radius of the remnant is about 12km and sets the scale in the movie.

Due to this instability strong GWs are emitted, and if the remnant is long-lived and the instability persists, such GWs could be detectable by aLIGO at 10Mpc and by the future Einstein Telescope at 100Mpc. These GWs could potentially be powerful discriminators of the equation of state of the matter at super-nuclear densities. You can read more about this work in my article arXiv:1510.03432.

In a recent work I was able to demonstrate that BHNS mergers can also launch incipient jets. The key here was the seeding of the NS with a dipole magnetic field extending from the interior to the stellar exterior where I developed a method to mimic a force-free environment. Evolving exterior force-free magnetic fields with ideal magnetohydrodynamics codes is not possible, so only the magnetic pressure dominance was captured by my approach. The following movie shows the generation of a collimated, mildly relativistic, Poynting-dominated outflow - an incipient jet - following the merger of a black hole with a magnetized neutron star. Relativistic gravitation is used for all these simulations coupled to the equations of ideal magnetohydrodynamics. The black hole to neutron star mass ratio is 3:1 and the black hole initial dimensionless spin parameter is 0.75. You can read more about this work in my Letter ApJ, 806, L14 (2015).

Volume rendering of the neutron star rest-mass density. The black sphere designates the black hole (apparent) horizon, and the white lines are field lines corresponding to the magnetic field measured by a normal observer. Here, \(M\) is the total gravitational mass, \(1000M\simeq 25(M_{\rm NS}/1.4M_\odot)\rm ms\), where \(M_{\rm NS}\) is the rest-mass of the neutron star. Also, \(\rho_{\rm max}\simeq 10^{15}(M_{\rm NS}/1.4M_\odot)^{-2} \rm gr/cm^3 \). Movie generated by the Illinois Relativity group REU team.

A visualization of the accompanying gravitational waves generated during the inspiral and merger of the previous BHNS system is shown in the following movie

Volume rendering of the 2,2 mode of the gravitational wave strain corresponding to the cross polarization. Movie generated by the Illinois Relativity group REU team.

Apart from these quasicircular mergers, eccentric mergers of these compact binaries can take place in dense stellar systems, such as globular clusters. However, neutron stars in globular clusters tend to be rapidly spinning as they are typically observed as millisecond pulsars. This is because globular cluster favor the formation of low-mass X-ray binaries which are believed to be the progenitors of millisecond pulsars. In these mergers the spin of the neutron star can no longer be ignored. In my Letter ApJ., 807, L3 (2015), the effects of the neutron star spin in black hole-neutron star eccentric mergers were studied, finding that even moderately large neutron star spins can have a large impact on the amount of neutron-rich matter that escapes to infinity following tidal disruption of the neutron star by the black hole, and which will shine electromagnetically due to the decay of r-process elements.

Supermassive BHBH binaries emit not only copious amounts of detectable GWs, but also shine electromagnetically when surrounded by accretion disks (as is likely to be the case at the centers of distant active galactic nuclei which formed after galactic mergers) due to the binary-disk interaction. There is a world wide effort tagetted at observing such "binary black hole AGNs", and some exciting candidates already have been found. Such systems can drive spectacular galactic jets as is demonstrated in my articles Phys. Rev. D 89 , 064060 (2014), and Phys. Rev. D 90, 104030 (2014). A movie showing the generation of such jets can be viewed below.

Volume rendering of the rest-mass density of an accretion disk onto an equal-mass black hole binary with non-spinning black holes, and evolution of the magnetic fields. Helical twin jets are launched from the poles of the orbiting black holes and subsequently merge into one jet well above the black hole poles. Movie generated by the Illinois Relativity group REU team.

A movie of the previous system in equatorial and meridional 2D slices is shown below. It becomes clear that following merger the jet accelerates and become more strongly magnetized. The front that propagates changes the features of the jet from its foot to its head and this phenomenon may help observers identify past black hole - black hole mergers based on jet morphology alone.

Left: equatorial slice of the rest-mass density of the disk normalized to the maximum rest-mass density. The black hole (apparent) horizons can viewed as tiny black disks. Right: meridional slice of the ratio of magnetic pressure to rest-mass density. The arrows indicate the coordinate velocity of the fluid. Here, the total gravitational mass is \(M\simeq 1.5\times 10^8(M/10^8M_\odot)\rm km =500(M/10^8M_\odot)\rm min\). The inspiral is turned on after the disk has been relaxed at a binary orbital separation of \(5\times 10^{-5}(M/10^8M_\odot)\rm pc\), i.e., close to the so-called binary-disk decoupling radius. Movie generated by Roman Gold.

Moreover, BHBH-disk systems can potentially explain the origin of X-shaped radio galaxies because of spin-flip of the single black hole that forms following merger (work in progress), and their gravitational waves can even be used as standard sirens to determine the Hubble constant to very high precision, thus constraining cosmological dark energy models. A visualization of the gravitational waves from these sources (in the limit where the self-gravity of the disk can be ignored) can viewed in the following movie

Volume rendering of the 2,2 mode of the gravitational wave strain corresponding to the plus polarization. Movie generated by the Illinois Relativity group REU team.

Mergers of WDNS binaries are sources of low-frequency gravitational waves. The ultimate fate of massive WDNS mergers is currently unknown. These could lead either to the formation a Thorn-Zytkow-like object surrounded by an extended accretion disk or collapse to form a BH or even explode because of rapid nuclear burning. If the remnant neither collapses nor explodes, and the disk survives and fragments, such mergers may offer a plausible route to planet formation around pulsars. Due to the vast range of lengthscales and timescales involved in this problem, simulating these systems in full general relativity while resolving at the same time both the neutron star (which is necessary to ascertain if the remnant will collapse to a black hole) and the white dwarf, is prohibitive with current resources. However, with a careful modification of the equation of state to scale down the white dwarf branch while leaving the neutron star branch intact and maintaining all inequalities between timescales and lengthscales unchanged, one can study these mergers with current resources. Calling pseudo-white dwarfs these scaled down white dwarf models, and constructing a sequence of decreasing white dwarf compaction (\(M/R\)), one can obtain a good answer as to what happens to the neutron star core following merger. I have devised such an equation of state in my article Phys. Rev. D83, 064002 (2011). A movie showing the merger of a neutron star with a pseudo-white dwarf using hydrodynamic simulations in full general relativity can viewed below. So far, these simulations indicate that such mergers do not lead to the prompt formation of a black hole and that they are supported against gravitational collapse primarily due to the centrifugal support from differential rotation and not due to thermal pressure.

Equatorial slice of the rest-mass density of a hydrodynamic evolution of a neutron star with a pseudo-white dwarf in full general relativity (the small yellow disk is the neutron star). The color bar is in units of \(1/{\rm km}^2\), where \(10^{-3}/{\rm km}^2=1.35\times 10^{15}\rm gr/cm^3\). Here, the total mass \(M=2.38M_\odot\) and \(1000M\simeq 12\rm ms\), with the neutron star mass \(M_{\rm NS}=1.4M_\odot\). This simulation is the most computationally expensive I have ever run - it lasted for 9 months of wall time. You can read more about this work in my article Phys. Rev. D 84, 104032 (2011).

The initial data problem is an important problem one needs to solve to prepare the initial conditions for all these compact object (binary merger) simulations. This involves solving the elliptic Einstein constraints - a highly non-trivial task, especially when (quasi)equilibrium configurations are the desired solutions. In my articles Phys. Rev. D83, 064002 (2011) and Phys. Rev. D 84, 104032 (2011), I developed such an elliptic solver for corotating binaries. More recently, in my Letter ApJ., 807, L3 (2015) a method was developed for generating eccentric black hole-neutron star initial data treating rapidly spinning neutron stars. I am interested in the development of more sophisticated/efficient methods for generating generic initial data for relativistic computations.

Non-astrophysical relativistic gravitation

In addition to the above topics, I have recently grown a keen interest in the stability of black objects (black holes, black strings, black rings) in higher than 4 dimensions. Moreover, I have always been fascinated by the mathematical properties of the partial differential equations describing classical theories of gravitation, such as their classification (hyperbolic, parabolic, elliptic or mixed type), and the well-posedness of the initial value problem. While we know that general relativity admits a well-posed Cauchy problem, this is currently unknown for other competing theories of gravitation. Work of mine that falls in this category can be found in my articles Phys. Rev. D 75, 024026 (2007) and Phys. Rev. D 78, 024002 (2008). I have also done some mathematical work on f(R) theories of gravity in my article Class. Quantum Grav. 28 085006 (2011). Finally, formulating new tests capable of constraining these alternative gravity theories using the playground provided by compact objects is among my main interests.


I put considerable effort in designing computer models for compact objects in binaries or isolation, and spend time on smashing compact objects in the computer. The ultimate goal is to theoretically predict gravitational wave, electromagnetic, and neutrino signatures from these systems, so that ultimately we may better understand strong field gravitation and compact object physics.

To achieve this goal, I develop and use both (semi)analytic methods and state-of-the-art codes at supercomputer centers, to study the equations of relativistic gravitation. These codes are capable of solving the Einstein equations of general relativity coupled to Maxwell's equations of electromagnetism, the equations of relativistic (magneto)hydrodynamics for the motion of the matter, and those governing radiation transport.

An important theoretical product of my research was the development of a robust electromagnetic gauge condition, which I dubbed "Generalized Lorenz gauge". This new gauge allows for long-term and stable numerical integration of the equations of general relativistic ideal magnetohydrodynamics (GRMHD) using a vector potential formulation with mesh refinement techniques. You can read more about this work in my article Phys. Rev. D 85, 024013 (2012), where I carried out a mathematical analysis of electromagnetic gauge conditions and simulations were performed to show their effects, and in my Letter Phys. Rev. Lett. 109, 221102 (2012), where I proposed the new Generalized Lorenz gauge condition.

The Generalized Lorenz gauge is now an essential ingredient for the Illinois relativity group GRMHD code, of which I am a main co-developer and co-maintainer, and it has already been adopted by other groups. Recently, my collaborators and I (the lion's share credit for re-writing this code goes to Zach Etienne) embedded this code in the publicly available Einstein Toolkit, and this work has been published in Class. Quantum Grav. 32 (2015) 175009. More about this code can be found on the IllinoisGRMHD website. I am also interested in the development of highly accurate computational methods for general relativistic magnetohydrodynamics on structured and unstructured grids.


I have had the fortune to work with wonderful people and here is an incomplete list of my collaborators.