Unlocking the secrets of the Universe

Albert Einstein predicted the possibility more than a century ago, however the measurement of such a cosmic event by the Laser Interferometer Gravitational-Wave Observatory (LIGO) in the United States and Italy’s Virgo detector has sent an understandable ripple of excitement through the global scientific community. 

“Einstein always said that it’s very unlikely that these gravitational waves will ever be detected because they’re so tiny, so it was quite high risk but it paid off eventually,” says Associate Professor Renate Meyer from the Department of Statistics, who has been part of a huge collaborative effort spearheaded by LIGO. 

“My contribution was more on the theoretical side at the beginning,”she says of the initial work using Markov Chain Monte Carlo techniques to create prototype algorithms and develop the computational techniques that are now used to estimate the parameters of gravitational waves.

Over the years, around fifty data scientists in the parameter estimation group have played a crucial role in extracting the parameters from the gravitational wave signal. Being part of a global collaboration that includes some 1,500 scientists and engineers worldwide, Renate says that she is “in awe” of the engineers who have built the incredibly sensitive L-shaped detectors in the states of Washington and Louisiana. 

Using huge mirrors, the four kilometer-long LIGO interferometers can measure the distance to Proxima Centauri with an accuracy that’s smaller than the width of a human hair. However their initial failure to detect any waves led to a hardware upgrade and an Advanced LIGO with much increased sensitivity. 

The first breakthrough came in late 2015 with the detection of waves from the collision of two black holes that took place nearly 1.3 billion years ago. In addition to being able to estimate the parameters of the coalescing black hole merger waveform, the statistical techniques provided the means to infer important characteristics such as the individual masses of the black holes and the final mass, the distance to the Earth and the energy radiated in gravitational waves.

Renate’s involvement in the ground-breaking project dates back to 1998 and a chance conversation about the challenges of identifying gravitational waves with physics lecturer Nelson Christensen. Now a Professor of Physics at Carleton College in Minnesota, and a member of the LIGO Scientific Collaboration, Nelson and Renate have collaborated ever since and co-wrote a paper (published by the Royal Statistical Society in April 2016) entitled ‘Gravitational waves: A statistical autopsy of a black hole merger’.

Describing the discovery as ‘a landmark moment for science’, they also presciently observed; “This is only the beginning of the story of gravitational waves. Soon, the Virgo detector (near Pisa, Italy) will be operating in concert with LIGO, and with more than two detectors, located in different parts of the world, it will be possible to estimate the sky location of future events even more accurately.”

Sixteen months later, in August 2017, that possibility became reality when a gravitational signal code-named GW170817 helped to pinpoint the location of the neutron star merger within a cluster of 50-100 galaxies – and enabled electromagnetic telescopes at 70 observatories to witness the moment. “What is so exciting about it is that these Markov Chain Monte Carlo techniques have been used and they’re now put to good use for all these exciting discoveries,” says Renate.

It had always been theorised that gravitational waves traveled at the speed of light, and that theory was confirmed by the measurement of light-emitting gamma rays which arrived almost simultaneously. Describing it as a “rich event”, Renate says that observations from different telescopes of the kilonova (the afterglow that followed the initial gamma ray burst) have also enabled physicists to analyse what happens to the inner core of neutron stars when they merge.

“It has enormous consequences for fundamental physics. They have much better estimates of the expansion rate and the age of the universe now, and they know that these neutron stars produce heavy elements such as gold and platinum. It’s immensely important.” 

Looking ahead, Renate is working on the development of more robust models for ‘noise characterisation’ that will further increase the accuracy of gravitational wave parameter estimates. “It’s one new research direction where maybe in the future we could make an impact and it might have a direct impact on the accuracy of the credible interval for the parameters of the gravitational wave forms.”

In particular, she’s extremely excited about LISA – the Laser Interferometer Space Antenna project being developed by the European Space Agency. Expected to be operational by 2034, LISA will consist of a constellation of three Pathfinder spacecraft arranged in an equilateral triangle with sides 2.5 million kilometres long. Flying along an Earth-like orbit, the distance between the satellites will be precisely monitored to detect a passing gravitational wave. 

With the advancement of new technology comes new challenges for statisticians. While space-based interferometers are no longer subject to the underlying noise on Earth, Renate says that data analysis will face other problems associated with ‘source confusion’ in space. “We’ve got all these waves coming in from various sources at the same time, so it’s a big problem filtering out signals from different sources.”

As always, the work starts with a rough algorithm prototype. If something works, she says you need to make it faster which might require transferring from one programming language, like R, to a faster one such as C++. The work conducted by PhD students and collaborators involves simulations using parallel computers that make the process faster, and Renate is grateful to the New Zealand eScience Infrastructure (NeSI) for their high performance computing facilities and for the technical support from the University’s Centre for eResearch.

“One of our challenges is to make them fast enough so that they can be used in real time so you don’t have to wait for a day or so to get results back, so very computer intensive.”

To facilitate collaboration, and demonstrate the feasibility of LISA data analysis, LISA organised global data analysis challenges which involve hypothetical observations with signals embedded in the noise for groups to analyse and try to extract the signal from the noise. “So groups were challenging each other and seeing how their particular algorithms work out.”

The addition of Japan’s KAGRA detector in 2019 and a third LIGO detector in India in 2023 will also ensure that the analysis of all the data will provide ample opportunities for statisticians to make significant contributions within the field of astrostatistics.

From a statistical viewpoint, the research essentially involves time series analysis which is transferable to other disciplines. For instance, Renate has been analysing asthma attacks in children as well as the recurrence of tumours in cancer patients. “If a person has recurrent events we need to model the dependence structure between these events in order to estimate the time until a certain event reoccurs. We need to look at the dependence in these events.”

Likewise, the same noise characterisation methods that were developed and applied to LIGO will be also used in future research to analyse temperature data gathered in New Zealand since 1907 to help determine the potential effects of climate change. “We’re trying to use our methods and see whether we can either validate the temperature increase that other statisticians have obtained, or maybe we’ll get a different estimate. We’ll see.” 

Current research is being funded from various sources including a two-year post-doctoral fellowship from the University of Auckland and three years of funding for a theoretical time series project from the German Research Foundation (DFG).

However Renate is especially proud of an initial Marsden Fund grant in 2002 for two PhD students, one of whom went on to conduct post-doctoral work at the California Institute of Technology jet-propulsion lab and the other who completed their post-doctoral at Germany’s prestigious Max Plank Institute. “I quite enjoy seeing the careers of my PhD students flourish. A lot of them have gone on to good positions overseas.” 

What’s more, her present PhDs are now basking in the reflected glory of the 2017 Nobel Prize for Physics which was jointly awarded to Professor of Physics, Emeritus Rainer Weiss who is best-known for devising the laser interferometric technique for gravitational wave measurements – AND who supervised the PhD of Renate’s original collaborator, Nelson Christensen. 

Having co-supervised four students with Nelson on various aspects of gravitational wave parameter estimation, Renate says “it’s quite exciting for my PhDs because they now have a direct line to a Nobel Prize winner in Physics, that’s quite cool.”