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In the Latest Gravitational Wave Signal, a New Music Meets an Old Prediction

In the Latest Gravitational Wave Signal, a New Music Meets an Old Prediction

An image from a numerical simulation of a black-hole binary merger with asymmetric masses and orbital precession. Caption and image: N. Fischer, H. Pfeiffer, A. Buonanno (Max Planck Institute for Gravitational Physics), Simulating eXtreme Spacetimes (SXS) Collaboration

For the first time, two international experiments designed to observe and study gravitational waves – ripples in the spacetime continuum itself – have together detected the merger of two black holes of different masses. These experiments, called LIGO and Virgo, have detected black hole mergers before but the new one, dubbed GW190412, is noteworthy for many reasons.

Thanks to many features in the gravitational-wave signal, scientists were also able to extract several curious features of the black holes’ final moments themselves.

The LIGO and Virgo scientific collaborations announced their detection on April 18, 2020. The collision happened a little over two billion lightyears away, and the gravitational waves released by the collision arrived at Earth on April 12, 2019. Gravitational waves also travel at the speed of light, so if they journeyed across two billion lightyears, it means the black hole merger happened roughly two billion years ago (maybe a little less, considering the expansion of the universe). In this event, a black hole weighing about eight-times the mass of the Sun merged with a much more massive black hole that weighed 30-times as much as the Sun, to form a black hole weighing about 37-times as much as the Sun.

Gravitational waves are ripples in spacetime. Albert Einstein first predicted their existence in 1915, according to his general theory of relativity, which explains how gravity and spacetime are related. The US-based LIGO observatories first directly detected gravitational waves in 2015, and since then gravitational waves have well and truly become a part of popular imagination. In the last five years, more than a dozen gravitational-wave signals from many violent astronomical phenomena have been detected by LIGO and their European counterpart Virgo.

These detections have opened up an entirely new way to observe the universe. Today, the LIGO and Virgo observatories are new ‘telescopes’ designed to observe the cosmos just as other telescopes use light, neutrinos and cosmic rays as probes.

The Virgo (top), LIGO Hanford (bottom left) and LIGO Livingston (bottom right) observatories. Photos: Virgo and LIGO collaborations

A rich and complex signal

As black holes come closer to each other, they begin revolving around each other, their orbits slowly shrinking as they spiral closer and closer in. Eventually, they come so close that they collide and merge into one black hole. This motion of black holes induce ripples in the fabric of spacetime. During the inspiralling, the gravitational waves emitted are predominantly at twice the orbital frequency.

That is, the gravitational waves’ frequency is equal to twice the rate at which the black holes revolved around each other. But when the black holes have distinctly different masses, the general theory of relativity predicts that their inspiralling will generate a weaker signal at higher frequencies. So the next-strongest gravitational note produced by the black hole pair should be at one and half times (1.5x) the primary gravitational-wave frequency.

At any instant, the gravitational wave signal contains higher harmonics of the fundamental frequency – like notes from a guitar string, which has a fundamental frequency of vibration as well as several harmonics, which are integer multiples (2x, 3x, 4x, etc.) of the fundamental frequency. In the case of gravitational waves, the fundamental frequency is twice the orbital frequency of the binary black hole system.

In addition, as the black holes come closer and closer, they orbit each other faster, so the orbital frequency increases. As a result, the fundamental frequency of emission itself increases with time, building towards higher and higher pitches like the sound of a bird’s chirp.

An audio file simulating the waveform of a binary black hole merger with mass ratio 3.6:1. The audio is of a simulated waveform with frequency 25 times higher than GW190412. Credit: Florian Wicke and Frank Ohme (AEI Hannover, Germany)

The observed waves also suggested that the axis around which the black holes were spinning was rotating – a type of motion called precession, seen commonly with a spinning top.

Einstein’s general theory of relativity predicts that a rapidly spinning black hole will drag the spacetime around it. This ‘whirlpool’ effect will affect the rotation of the other black hole, as a result of which the spin axes of both black holes start to precess. In response to this, the orbital plane also undergoes precessional motion, creating modulations in the observed gravitational-wave signal.

Detecting the signature of precession in the observed signal is challenging, limited by the presence of noise in the detector. But LIGO and Virgo were still able to find weak evidence of precession in the gravitational-wave signals from GW190412.

Altogether, the gravitational waves emitted had a rich wave structure that LIGO and Virgo could study to elucidate various details of a black hole merger – including ones indicating that the predictions of a 105-year old theory still hold true.

Indian contribution

Various research institutes in India are part of the LIGO Science Collaboration: Chennai Mathematical Institute; Directorate of Construction, Services and Estate Management, Mumbai; International Centre for Theoretical Sciences (ICTS), Bengaluru; IISER Kolkata; IISER Pune; IIT Bombay; IIT Gandhinagar; IIT Hyderabad, IIT Madras; Institute of Plasma Research, Gandhinagar; Inter-University Centre for Astronomy and Astrophysics, Pune; Raja Ramanna Centre for Advanced Technology, Indore; and Tata Institute of Fundamental Research, Mumbai.

Since this is the first time we detected higher harmonics of gravitational waves, scientists needed to be absolutely sure. So the LIGO-Virgo collaboration used four different methods to independently confirm their presence in the wave structure. One of these methods was developed by scientists at IIT Gandhinagar and Chennai Mathematical Institute, led by Soumen Roy, a PhD scholar at IIT Gandhinagar. Apratim Ganguly, a researcher at ICTS, led another analysis that confirmed the consistency of the signal with the prediction of Einstein’s theory.

It turns out such mergers are not very rare in nature. If they were, LIGO and Virgo might not have spotted GW190412 given the maximum distances up to which these detectors can ‘see’ such mergers. We expect to observe many more of such events in the coming years, when LIGO and Virgo collect more data with better sensitivity.

These future observations could in turn help us better understand how pairs of black holes – called binaries – are formed. Nature hasn’t yet revealed to us the answer to this question. The simplest hypothesis is that these black holes that form binaries are the remains of massive stars. However, other scientists have argued that these black holes could have been produced in the very early universe, when dense clumps of primordial matter collapsed under their own gravity. To confirm one hypothesis over another, we need more data – which is where LIGO and Virgo, as well as other upcoming instruments, fit in.

A new astronomy

Until the 20th century, astronomers used only optical telescopes, which were and are capable of ‘seeing’ only the visible part of the electromagnetic spectrum. But in the last hundred years alone, we have become able to ‘see’ the universe in all the frequencies of the spectrum, from radio waves all the way up to gamma rays. And in the last few decades alone, we have developed instruments that help scientists understand events playing out in the far reaches of the cosmos by observing particles called cosmic rays and neutrinos coming from there.

The more ways in which we can ‘see’ the universe, the more we understand about it – not just independently but also by complementing, say, the findings of a neutrino detector with those of a gamma-ray telescope.

The astronomy using gravitational-wave observations has only just begun. In the next few years, LIGO and Virgo are expected to detect hundreds of gravitational-wave events. They will also be joined by the KAGRA detector from Japan and a third LIGO observatory to be built in India. The more detectors we have, the more our ability to probe the cosmos will be.

Indeed, scientists believe that upcoming observations will provide answers to some critical questions in modern physics, astrophysics and cosmology that have remained unanswered to this day. To quote Kip Thorne, one of the three founders of the LIGO observatories, “… we humans are embarking on a marvellous new quest: the quest to explore the warped side of the universe.”

P. Ajith is at the International Centre for Theoretical Sciences, Bengaluru. K.G. Arun is at the Chennai Mathematical Institute, Siruseri. Anand Sengupta is at IIT Gandhinagar. All three are physicists and members of the LIGO Scientific Collaboration. The views expressed here are their own.

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