Alex Nielsen Research areas

Research

My research interests overlap in both astrophysics and theoretical physics. We are now on the verge of observations that could radically alter our understanding of gravity and matter. Astronomical observations are entering an exciting new era with the arrival of gravitational wave observatories and for the first time we will be able to extract multimessenger information directly from regions of strong gravitational fields. Applying results from fundamental physics to astrophysical objects will be essential to understanding the structure of both black holes and neutron stars. Compact astrophysical objects also provide ideal probes of new physics due to their strong gravitational fields. The gravitational field in these cases can have important effects on matter both classically and quantum mechanically.

Research: Testing the nature of black holes

With the observation of merging black holes we are now able to test fundamental ideas about their nature. in particular we are not able to test horizon-scale effects. Even in Einstein's theory of general relativity these dynamical black holes are not described by the stationary Kerr solution because of distortions from the binary partner and strong gravitational wave emission. These systems therefore provide unique observational access to new physical effects that are normally highly suppressed in near-stationary black holes.

The standard paradigm for these black hole collisions is vacuum Einstein general relativity. Many theories that go beyond Einstein's theory predict new fields or new interactions. Most of these theories have so far only been studied in idealised static situations. However, the large amounts of energy that are released in the direct collision of two black hole horizons can excite new fields and interactions, leading to telltale sign of new physics in the gravitational wave signal. Along with LIGO colleagues, I have been developing methods to spot these telltale changes. First results have already been reported but we are constantly improving their accuracy and ability to discern different models. The improved tests will be applied to future LIGO observations.

For certain models, observations from dynamical events places far more stringent bounds than can be achieved observations restricted to static or near-static situations. A number of different tests have been employed by LIGO. I have been heavily involved in testing the consistency of the signal in different frequency regions, the inspiral-merger-ringdown test. Understanding which models are constrained by which tests is still in its infancy. This can be addressed by creating a library of known model waveforms and using these to ``test the tests'' that are currently employed by the LIGO collaboration. This will show which models are most constrained by which tests and may identify areas of parameter space that are currently under-constrained.

For particularly strong black hole merger signals, it is possible to detect independently the ringdown signal of the final black hole formed after merger. In this case one can directly extract parameters of the final black hole, its mass and spin. Using these values it is possible to test the Hawking area theorem and bound the amount of energy and angular momentum dispated by gravitational waves during the coalescence. We are currently studying just how loud the signal needs to be in order for these tests to be practical, but future observing runs are likely to provide at least a few events where this can be done.

To identify any new physics the devil is always in the detail. Possible mundane effects that mimic the signs of new physics must be clearly identified and eliminated. I am currently leading attempts to understand how noise features impact tests for new physics in merging black holes. Current techniques incorporate calibration uncertainties and noise estimates using broad spline fittings. I will develop new ways to study these effects using detector calibration measurements and accurate noise filtering. The best way to test susceptibility to noise artefacts is by software injection of known signals. The analysis can then be checked to see if it recovers the known signal. To do this reliably, injections should be performed over a wide range of data stretches with differing noise characteristics. Understanding these effects requires detailed knowledge of the noise properties and I will measure the influence of non-Gaussianties, including measurements of the skewness and kurtosis of actual noise residuals.

Research: Tests of gravity and gravitational waves

In addition to the sources of our gravitational wave observations and the strong horizon-scale physics of black holes, we are also using the very long distances traversed by the gravitational wave signals themselves to test the nature of weak gravity. Einstein's relativity predicts that gravitational waves should be composed of at most two polarisation states. Other theories with other fields predict more polarisation possibilities. This can be tested by looking at how the gravitational wave signals interact with our detectors, since different detectors will be affected in different ways. Such tests require multiple sensitive detectors and as progress continues on building a worldwide network of detectors this goal draw increasingly close.

We can also test how the gravitational wave signals are modified on their way to our detectors. Einstein's theory predicts that the waves could be lensed by passing close the large masses or redshifted by encountering time-varying gravitational fields due to collapsing matter such as the known Sachs-Wolfe effect from the CMB. It is also possible that gravitational waves interact differently to photons on their path to Earth and with EM counterparts to the gravitational wave observations this can be tested. With only a few observations these tests remain challenging, but with future runs promising a large number of events they become increasingly practical.

Research: Principal components

Gravitational wave signals depend on many parameters of the emitting source and its position relative to the detector. But the detectors are only sensitive to these parameters in certain combinations and some combinations more than others. To investigate which combinations of parameters are most relevant to searches requires a principal component analysis. This is particularly important for systems with spinning black holes because of the high degeneracy between the spin value and the mass ratio.

While gravitational waves depend on many physical parameters (up to 15) it turns out that there are only really 3 combinations that actual detections are sensitive to and in some parts of parameter space only two. The chirp mass, formed from the combination of the two masses involved in the body dominates the sensitivity and is an important concept for gravitational wave analysis. The second and third parameters are formed from a combination of the mass ratio and spins of the bodies. The third principal component depends also on other terms and is the most likely to show effects of as yet uncalculated, or unincluded effects such as tidal deformations, matter effects or corrections to Einstein relativity.

The plot below shows the variation of the second principal component, mu2, (the first is basically the chirp mass) as a function of the spin on the heavier object and the symmetric mass ratio, eta. This shows that the second most sensitive parameter is a combination of the spin and mass ratio.

Research: Spinning black holes

Isolated black holes are characterised by their mass and spin values. Searches for black holes with different masses has been routinely performed in previous LIGO runs but searches with different spins was considered challenging and unnecessary. We successfully employed aligned spin searches in the first and second Advanced LIGO observing runs. The detections made were largely compatible with black holes of low spin magnitudes. However, recent X-ray evidence from galactic black holes with accretion discs has indicated that other stellar-mass black holes are rapidly spinning, near the maximal limit for their spin. and these objects may be missed by searches that only consider their mass. The constrast between gravitational wave observations and X-ray observations suggest that either we are observing different populations with different formation channels, or that there are systematic effects in our observation methods that are not currently understood.

Searching for spinning signals requires ng that is not currently included in LIGO black hole searches is the effect of precession. Precession of the orbital plane is caused when the spins of the orbiting objects are misaligned with the orbital angular momentum. Including this effect in our searches would greatly increase the template bank that needs to be searched over, leading to computational cost both in terms of run time and data production of triggers. These can be mitigated by several methods that we are currently investigating including more efficient placement of templates and running on GPUs of Atlas at the AEI using the PyCBC toolkit

To search efficiently for black holes in gravitational wave data requires understanding how the signals change with the changing parameters of the sources. The plot below shows which parts of parameter space we are most sensitive to (the red parts) over a variety of different parameters. This is important for understanding selection bias in our searches and developing better waveforms and template banks to cover the "blind" spots.

Research: Parameter accuracy with spin and higher harmonics

Einstein's theory of general relativity makes a precise prediction for what the gravitational wave signal of a given source should look like. However, solving the equations exactly to obtain those predictions is practically impossible and so approximation methods must be employed. A frequently employed approximation in gravitational wave analysis is the post-Newtonian approximation, that expands the energy and flux of a binary orbit in powers of v/c, or similary powers of mass times frequency. Calculating higher order corrections in this scheme becomes a computationally complex problem and only a small number of terms have been calculated for near equal mass binaries.

When employing approximations it is essential to understand their range of validity and in particular what the impact might be of features that are neglected. In the case of gravitational waves, all as yet uncalculated higher post-Newtonian terms are implicitly neglected. We cannot investigate the effect of as yet uncalculated effects, because they haven't been calculated yet, but we can check to see what the leading effects are and how results change as we include more effects. This gives us an indication of where we need to calculate more accurate corrections.

The table below shows parameter estimations and correlations based on Fisher matrix calculations for an 11-10 solar mass, binary black hole system with maximal aligned spins. As can be seen in the eigth column, the higher order amplitude terms have the effect of reducing the degeneracy between the spin, chi, and the symmetric mass ratio, eta. This is important for parameter error estimations or multi-detector coincidence calculations based on Fisher matrices.

ALEX NIELSEN