Extreme mass ratio inspirals - detection and source modelling

Overview

An extreme mass ratio inspiral (EMRI) is the inspiral of a compact object (e.g., a white dwarf, neutron star or black hole) into a supermassive black hole in the centre of a galaxy. These inspirals generate gravitational waves which we hope to detect with the future space based gravitational wave detector, LISA. The mass of the compact object is typically of the order of a few solar masses, while the mass of the central black hole (set by LISA's frequency sensitivity) is from a few hundred thousand to ten million solar masses. This extreme mass ratio ensures that the inspiralling object essentially acts as a test particle in the background spacetime of the central black hole. EMRI observations thus provide a meanse to probe the spacetime structure of astrophysically black holes with unprecendented precision.

There are various issues associated with modelling and detection of EMRIs that must be addressed before LISA is launched. I am actively involved with research into many of these issues, some of which are described below.

Population Synthesis

An important ingredient for estimating the number of EMRI events that LISA will detect is an estimate of the intrinsic rate at which supermassive black holes (SMBHs) are consuming compact objects in the Universe. This can be computed using numerical simulations. An important ingredient that is required for such simulations is an expression for the energy and angular momentum lost during very high eccentricity encounters with the central black hole. Most simulations to date have made use of the classic Peters and Mathews expression, which is strictly valid only for weak-field, Keplerian orbits. Using accurate computations, based on solution of the Teukolsky equation, it is possible to derive improved expressions for these energy and angular momentum losses, and hence for the inspiral timescale. These are described in the following paper

Gair, J R, Kennefick, D J and Larson, S L, 2005, Gravitational radiation timescales for extreme mass ratio inspirals, accepted for publication in Astrophys. J.. Available as gr-qc/0508275.

In the future, we hope to include these expressions in the numerical simulations of Marc Freitag, or Clovis Hopman and Tal Alexander to discover how much of an effect relativistic corrections have on the capture rate.

Source Modelling

Algorithms for detection of EMRIs with LISA rely heavily on matched filtering, i.e., computation of the overlap of a model waveform with the output of the detector. Therefore, for inspiral detection and for scoping out alternative detection algorithms, waveform templates are required. In principle, we know how to determine these exactly, since the extreme mass ratio means that black hole perturbation theory applies. However, fully accurate, 'self-force' waveforms are still some way off, and will be very slow to generate. The large parameter space of possible inspirals means that huge numbers of template waveforms are required for data analysis and there is therefore a requirement for the development of approximate, "kludge" waveforms which capture the key features of true waveforms, but which are much cheaper and easier to compute. One possible approach is to use "numerical kludge" (NK) waveforms. These are generated by computing exact geodesic orbits for the inspiralling objects, and combining these with as accurate as possible inspiral trajectories, and a weak-field gravitational wave emission formula. Using the weak-field quadrupole formula for GW emission, but a fully relativistic geodesic orbit as the source, allows the consturction of "semi-relativistic" waveforms and fluxes. Since these cpature the fully accurate dynamics of the source, they give better results (when compared to fully accurate Teukolsky results) than using a fully-consistent weak-field approximation. For Schwarzschild geodesic orbits, it is possible to compute the semi-relativistic fluxes analytically, and these are described in the following paper

Gair, J R, Kennefick, D J and Larson, S L, 2005, Semi-relativistic approximation to gravitational radiation from encounters with nonspinning black holes, Phys. Rev. D72 084009. Available as gr-qc/0508049.

The NK waveforms require a separate prescription for the inspiral trajectory. In Glampedakis, Hughes and Kennefick 2002, weak field flux expressions were combined with relativistically defined parameters to compute inspirals. However, these inspirals exhibited pathological behaviour in certain circumstances since they failed to enforce certain necessary conditions. It is possible to improve the inspirals in various ways - by enforcing the consistency conditions to hold, by adding higher order post-Newtonian terms in the fluxes and by including fits to Teukolsky based fluxes. Inclusion of these improvements generates inspirals that agree very closely with Teukolsky based calculations. These are described in the paper

Gair, J R and Glampedakis, K, 2005, Improved approximate inspirals of test-bodies into Kerr black holes, submitted to Phys. Rev. D. Available as gr-qc/0510129.

The other ingredient for NK waveform construction is a weak-field GW emission formula. There are various possibilities - the quadrupole formula, the quadrupole/octupole formula or the Press formula. Initial calculations used the pure-quadrupole formula, but better results may be obtained using the quadrupole/octupole formula (although the Press formula does not improve on this further). Using the quadrupole/octupole formula we find very good agreement with Teukolsky waveforms (> 90% overlap) except for very strong field orbits in rapidly rotating black hole spacetimes. These results are described in the paper

Babak, S, Fang, H, Gair, J R, Glampedakis, K and Hughes, S A, 2006, "Kludge" gravitational waveforms and fluxes for a test-body orbiting a Kerr black hole, in preparation.

Data Analysis Algorithms

The large parameter space of possible inspirals, and long duration of the signals means that the number of templates required to do fully-coherent matched filtering for EMRI signals is prohibitive and computationally impossible. Alternative algorithms are therefore required, of which I have been involved with exploring two.

Semi-coherent Matched Filtering

One option is to use a heirarchical algorithm - have an initial search using matched filtering on short (2-3 week) waveform segments, followed by a second stage that sums the power in the sequence of segments corresponding to possible inspirals. Assuming realistic computational resources, we find that such a search is possible and could detect as many as ~1000 events during the mission lifetime. These results are described in the paper

Gair, J R, Barack, L, Creighton, T, Cutler, C, Larson, S L, Phinney, E S and Vallisneri, M, 2004, Event rate estimates for LISA extreme mass ratio capture sources, Class. Quantum Grav. 21 S1595-S1606 Available as gr-qc/0405137.

Time-Frequency Methods

An alternative approach to data analysis is to use time-frequency methods. The basic idea is to construct a time-frequency spectrogram of the LISA data and then look for features in the spectrogram that might correspond to EMRIs. The simplest method is excess-power, i.e., to look for regions in which the power is unusually high. Exploring one-such algorithm we find that sources can be detected to about half the distance of the matched-filtering search, so in principle we could detect one tenth of the total sources in this way. These results are described in the two papers

Wen, L and Gair, J R, 2005, Detecting extreme mass ratio inspirals with LISA using time-frequency methods, Class. Quantum Grav. 22 S445-S452. Available as gr-qc/0502100.
Gair, J R and Wen, L, 2005, Detecting extreme mass ratio inspirals with LISA using time-frequency methods II: search characterization, Class. Quantum Grav. 22 S1359-S1371. Available as gr-qc/0506116.

The excess power approach has several drawbacks, including lack of parameter estimation and the inability to handle source confusion. We are therefore now exploring improved algorithms, such as the Hierarchical Algorithm for Clusters and Ridges (HACR).

Probing Black Hole Uniqueness

An exciting potential application of EMRI observations is as a probe of the structure of black hole spacetimes. The compact object acts as a test particle in the background spacetime of the central supermassive object, and the corresponding gravitational waveform thus encodes a map of the spacetime structure. While we believe that all supermassive compact objects in the Universe will be described by the Kerr metric, EMRI observations will allow us to test this belief, and quantify how different the spacetimes could possibly be within the accuracy of our observations.

Boson Star Inspirals

One proposed alternative to a black hole is a boson star. The fundamental difference between these objects is the absence of a horizon in the boson star case. An inspiral into a boson star would therefore look very much like an inspiral into a black hole, up until the point at which the inspiralling object should plunge into the black hole. In the case of a boson star, the gravitational wave emission would not cut off at this point, but would persist, with the compact object passing into and out of the boson star material. This behaviour provides a potential indicator for the presence of a boson star. This scenario is explored in the paper

Kesden, M, Gair, J R and Kamionkowski, M, 2005, Gravitational-Wave Signature of an Inspiral into a Supermassive Horizonless Object, Phys. Rev. D71 044015 Available as gr-qc/0411478.

"Bumpy" Black Holes

The black hole no hair theorem tells us that any stationary vacuum spacetime with a horizon must be described by the Kerr metric. We therefore expect all of the EMRI events that we observe to be inspirals into Kerr black holes. However, if the no hair theorem was violated, or the spacetime was non-vacuum (due to the presence of material outside the black hole), the inspiral would appear qualitatively different. In conjunction with Ilya Mandel, Hua Fang, Geoffrey Lovelace and Chao Li, I am currently investigating what differences might be apparent, and how these might be used to test the black hole no-hair theorem. As part of this investigation we are exploring the dynamics of geodesic orbits in a variety of perturbed black hole spacetimes. In general, the orbits in the perturbed spacetimes look very similar to orbits in Kerr spacetimes (including the existence of a third integral). However, we do find that ergodic orbits can exist (i.e., which lack a third integral) in certain regions of the perturbed spacetime. However, so far all of these ergodic orbits exist in spacetimes which also possess closed timelike curves, so the physical applicability of our perturbed spacetimes is not yet clear. More details will appear here as these become available.

Astrophysics with EMRIs

A year long observation of an EMRI with LISA will allow the determination of the source parameters with unprecendented accuracy. Preliminary estimates (Barack and Cutler, 2004) suggest that the mass and spin of the central black hole will be determined to an accuracy of one part in ten thousand. This compares to current estimates from electromagnetic observations which are at best within a factor of two. Such measurements can be used to address various problems in astrophysics. In collaboration with Marta Volonteri at the Institute of Astronomy in Cambridge, I am investigating how LISA obsevrations of EMRIs may be used to determine the black hole mass and spin functions, and hence distinguish between various scenarios for SMBH black hole evolution.

Useful References

Glampedakis, G, Hughes, S A and Kennefick, D J, 2002, Approximating the inspiral of test bodies into Kerr black holes, Phys. Rev. D66 064005.

Barack, L and Cutler, C, 2004, LISA Capture Sources: Approximate Waveforms, Signal-to-Noise Ratios, and Parameter Estimation Accuracy , Phys. Rev. D69 082005. Available as gr-qc/0506116.

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