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 above the nuclear saturation density.
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.
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.
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 the magnetic field lines. Here, \(M\) is the
total gravitational mass, \(100M\simeq 2.5(M_{\rm
NS}/1.4M_\odot)\rm ms\), where \(M_{\rm NS}\) is the
gravitational mass of the neutron star in
isolation. 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.
Methods
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.
Collaborators
I have had the fortune to work with wonderful people and here is an incomplete
list of my collaborators.
