Ilya Mandel - Research Projects
I am interested in all aspects of the rapidly growing field of gravitational-wave
astrophysics. Gravitational waves that will be measured by ground-based and space-based
detectors provide a unique way to explore the universe --- to observe in detail a variety
of astrophysical and relativistic phenomena. Gravitational waves (GWs) are an integral
part of Einstein's theory of general relativity, and were one of the earliest predictions
after its formulation. There exists a significant body of indirect evidence for GWs, most
famously in the observations of the Hulse-Taylor binary pulsar, which loses orbital energy
at a rate that matches the expected value from GW emission. GWs have yet to be observed
directly, however, making this a very exciting and challenging time in the development of
the field of GW astronomy.
The first generation of ground-based interferometric GW detectors is already in operation.
The Laser Interferometer Gravitational-Wave Observatory (LIGO)
has finished a full year of data taking at the designed
sensitivity. In 2014-2015 Advanced LIGO detectors are expected to begin operating at
sensitivities ~ 10-15 times greater than Initial LIGO. These detectors will be able to
detect GWs from inspirals, mergers, and ringdowns associated with coalescences of compact
binary systems composed of neutron stars (NSs) or black holes (BHs). Although estimates
of the rates of such coalescences cover a rather wide range, Advanced LIGO may be able to
detect tens to hundreds of these events per year. A proposed space-based detector, the
Laser Interferometer Space Antenna (LISA), will
complement the
ground-based detectors by being sensitive to waves at a lower frequency than ground-based
detectors, with a peak sensitivity at a few mHz vs. ~ 150 Hz for LIGO. LISA will thus be
able to detect Galactic white-dwarf (WD) binaries, massive black-hole (MBH) binary
inspirals, and inspirals of stellar-mass compact objects into MBHs. In this era, when
detections will become routine, GW astrophysics will be able to illuminate many of the
mysteries of the most energetic phenomena in the universe. However, to take full
advantage of the wealth of information that will be available, it is incumbent to begin
preparations for source analysis, data analysis, and astrophysical investigation today.
I am working in some of the following projects toward the goal of ensuring that we
are adequately prepared to engage in GW astrophysics:
- Rate predictions for compact-binary coalescences I am finalizing a summary of
the existing literature on compact-binary coalescences that could be detected by LIGO
(these are coalescences involving neutron stars, stellar-mass black holes, and possibly
intermediate-mass black holes). I am engaged in improving rate predictions for
compact-binary coalescences and extrapolating them to elliptical galaxies. Conversely, I
would like to develop a framework for converting observed upper limits or rates for
compact-binary sources into constraints on the complex multi-dimensional space of
astrophysical parameters.
- Parameter estimation for compact binaries We need to be able to accurately
extract source parameters, such as masses and spins, in order to extract astrophysical
information from observed GWs. Markov Chain Monte Carlo (MCMC) is a particularly
promising method for determining the parameters of a compact-binary coalescence signal.
With colleagues from Northwestern University and elsewhere, we have implemented an MCMC
search that allows us to estimate the maximum-likelihood parameters and to determine the
parameter-estimation accuracy via the posterior probability-density function. Current and
planned work includes improving the sampling of the MCMC, comparing the
parameter-estimation accuracy predicted by the MCMC with Fisher matrix results, and
systematically studying (near-)degeneracies in the parameter space.
- Intermediate-mass black holes There is a growing, but still uncertain, body of
evidence that a population of intermediate-mass black holes (IMBHs) may exist in globular
clusters. If so, gravitational waves from intermediate-mass-ratio inspirals (IMRIs) of
stellar-mass compact objects into IMBHs could be detected by Advanced LIGO, and IMRIs of
IMBHs into massive black holes in galactic centers could be detected by LISA. I have
worked on predicting the possible rates of such events. Meanwhile, my current work on
IMRI gravitational waveforms suggests that neither perturbative expansions in the mass
ratio nor post-Newtonian expansions in the velocity will be faithful approximations of the
true IMRI waveforms. Further work is needed to develop hybrid waveforms usable for IMRI
detection and to understand statistical and systematic errors in IMRI parameter
estimation.
- Online LISA data analysis Some of the most exciting paybacks of LISA could
come from simultaneous GW and electromagnetic observations of the same source. In order
to provide pointing information for telescopes, it will be necessary to perform rapid
online searches on LISA data. One possibility includes time-frequency approaches, which
we have shown to work during Mock LISA Data Challenges. I am continuing efforts to
improve the quality of LISA data analysis via time-frequency spectrograms with an eye to
applying them to online searches. We will also consider other possibilities, such as
searching for extreme-mass-ratio inspirals with simpler phenomenological waveforms.
- Testing General Relativity Because of the large number of cycles they spend in
the strong-gravity regime, intermediate- and extreme-mass-ratio inspirals can serve as
exquisite probes of the spacetime of the massive body involved. For instance, they can be
used to test whether the central body is a Kerr black hole by measuring higher-order mass
multipole moments. We had considered orbits in non-Kerr spacetimes to look for observable
deviations from Kerr, such as the onset of chaos. We will extend this work to inspirals
driven by gravitational radiation. Future work will involve testing whether the
differences in GW generation in alternative theories of gravity can be used to test
GR.
Last edited December 29, 2008.