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Detecting Gravitational Waves Using Pulsars

Updated: Jul 5, 2022

In 1915, Albert Einstein published his paper on the general theory of relativity [1], which changed the field of physics and astrophysics forever. It gave a completely new definition of already established notions of gravity, space, and time. Einstein was able to prove in full mathematical detail that time is relative and can vary from one observer to another. He explained that the phenomena we experience as gravity, is just the product of an object with mass bending the fabric of space around it, and he called this fabric ‘Spacetime’.

Albert Einstein by Ferdinand Schmutzer and an artist's illustration of two black holes merging and creating ripples in spacetime known as gravitational waves. (Image credit: LIGO/T. Pyle)


With the help of the mathematics provided by Einstein [2], it was theorized that gravitational interactions between two very massive objects like Blackholes (BH) or neutron stars may cause a ripple in spacetime like a wave that can travel at the speed of light. This phenomenon is called a gravitational wave (GW) and it gives definitive proof of Einstein’s general theory of relativity. Currently, the best tool we have to detect GWs is the LIGO detector.

Virgo Observatory. Credit: The Virgo Collaboration/CCO 1.0 and a schematic of its working by Leah Tiscione.


The Laser Interferometer Gravitational-Wave Observatory (LIGO) is made up of two separate detectors, one is LIGO Hanford in south-eastern Washington State in an arid shrub-steppe region crisscrossed by hundreds of layers of ancient lava flows, and the second one is LIGO Livingston, ‘3002 Km’ away in a vast, humid, loblolly pine forest east of Baton Rouge, Louisiana. The basic structure of the LIGO detector is made up of two long arms ‘4 Km’ in length at a right angle to each other, with mirrors on the far end and a photodiode light detector at their junction. An extremely powerful and precise laser is fired at the mirrors and as they bounce back, the light is detected by the detector. The light beams are kept out of phase with each other such that, when they meet again in the middle, their light waves subtract, and no light is detected at the photodiode. If a gravitational wave passes through the earth, it will literally stretch or squeeze space and effectively alter the arm-lengths of LIGO. This change would cause the beams of light to be reflected and reach the junction at a slightly different time and no longer be in the phase required to cancel each other out. In such a case, the light diode would detect a pulse of light, signaling the detection of a GW. [3]


To be able to achieve this, LIGO needs to be extremely sensitive and precisely calibrated. LIGO has a detecting range frequency of a 'few hundred Hz' to a 'few thousand Hz' which means it can detect GWs created by BHs of around the range of '100 - 1000 solar masses'. It is believed that very ancient black holes in the center of the very early galaxies of the universe are speculated to be around a 'million solar masses' [4]. When these BHs interact with each other, the GWs created, are speculated to be in the ‘nano-hertz region (10^-9 Hz)’ [5], which would mean that their wavelength could be as large as the entire galaxies! The arms of LIGO aren’t that long and the detectors aren’t as sensitive to detect GWs of such proportions. To detect them, we need a mechanism of detectors as big as the GW itself. One solution to this problem could be using Pulsars to detect GWs.

Artist illustration of a Pulsar by Kevin Gill and an artist’s rendition of the different parts of a pulsar. Image Credit: Astronomy Magazine


When a massive star 8 - 15 times the mass of our Sun dies, in other words, it gets debleated of all its nuclear fusion material in its core, there is no nuclear energy available to counter the force of gravity, and the star collapses in on itself. This rapid collapse causes the star to explode in a spectacular burst of light. This is called a type-II supernova. The enormous pressure in the star’s core causes the electrons in atoms at the core to get captured by the protons, turning them into neutrons that keep getting accumulated at the core of the dying star. If the star was massive enough (around ‘27 solar masses’), this could lead to the formation of a black hole, but otherwise, it would lead to a neutron star, which is a very dense ball of tightly packed neutrons of around ‘5 - 20 Km’ in radius but with the mass of around 1 - 3 times that of the Sun. [6]


The angular momentum of the star gets conserved when the star collapses, because of which, the neutron star spins at a very high rate. Neutrons stars are some of the strongest magnets in the universe and the strong magnetic field of neutron stars causes beams of electromagnetic radiation to emit from their magnetic poles. Since the magnetic poles and the axis of its rotation do not align, the spin of the neutron star makes the beam of light act as if it’s a light source from a lighthouse. If the direction of the beam of light being emitted aligns with that of Earth, we can detect this signal, and to us, the neutron star would seem to be pulsing at very regular intervals. This gave it the name pulsars. They are one of the most consistent periodically spinning objects in the Universe. So accurate in fact, that the pulses which are detected are used by researchers as one of the most accurate clocks in the universe. [7]


We talked to Neel Kolhe, a research student who has completed his Master's in Astrophysics through St. Xavier’s College, Mumbai, and worked on detecting gravitational waves using pulsar timing arrays (PTAs) for his thesis. In an interview with him, Neel explained, how GWs are created by some extreme gravitational interactions, how GWs created through different interactions differ from each other, and the tools available to us to detect such gravitational waves. In his study, he used a special kind of pulsars called the millisecond pulsars, which have a rotational speed of ‘one rotation per millisecond’, with a very stable frequency and showing the least glitchy behaviour.


Neel said, “As they (pulsars) are very very accurate clocks, we can use them to detect gravitational waves because gravitational waves are stretching and squeezing space and time. If a gravitational wave is passing by a millisecond pulsar, its pulse’s time of arrival to a telescope will either be delayed or it might reach us faster, and this change in the time of arrival of pulses can be characterized as a gravitational wave being detected and that is what we expect to do with pulsar timing arrays.”


So, what are pulsar timing arrays?


The Indian pulsar timing array operated from the National Centre for Radio Astrophysics (NCRA) in Pune, uses the Giant Meter-wave Radio Telescope (GMRT) to keep track of a set of pulsars spread all across the galaxy, with the observation cycle of 20 - 40 days every single year. They time these pulsars to keep a check of their rotational frequency, time of arrival, and the characteristics of the pulses. Since the GWs can have a wavelength on a scale of light-years, it may take months to detect just one wave. What they expect to detect in the near future are not really waves from individual binaries, but the gravitational wave background. There can be millions of neutron stars or BH binaries all over the universe, all emitting GWs.


Neel said, “These GWs are reaching us in an incoherent and uncorrelated background. So, all these GWs overlapping on each other will make like a ‘noise floor’, like a baseline GW background which could be detected every year”.

SPDO/TDP/DRAO/Swinburne Astronomy Productions - SKA Project Development Office and Swinburne Astronomy Productions, and an illustration of the NANOGrav project observing pulsars in an effort to detect gravitational waves - ripples in the fabric of space. The project is seeking a low-level gravitational wave background signal that is thought to be present throughout the universe. credit: NANOGrav / T. Klein


The same way we have the Cosmic Microwave Background, we have a Gravitational-wave Background. By the end of this decade, we can expect the Square Kilometre Array (SKA) to come online, which is a radio telescope with a surface area of ‘one square km’ and is going to join the pulsar timing array effort. Once a GW background is obtained and characterized, we can detect individual binaries of supermassive BHs. Once we start detecting GWs using this method, we can expect to find GW created by all kinds of Interactions with all kinds of binary orbits.


It started as a theory presented in 1916 by Albert Einstein, who himself remained skeptical about the physical existence of GW for most of his life. But now with the help of technological advances and tools available, we are getting get actual physical proof of the existence of gravitational waves.


Acknowledgments


Thank you very much to Neel Kolhe, for providing your valuable insights into this topic and agreeing and taking some time out for the interview podcast. You can check out Neel Kolhe’s work at:

Evidence for profile changes in PSR J1713+0747 using the uGMRT. https://arxiv.org/abs/2107.04607



References


[1] Einstein, Albert (1915), " Grundgedanken der allgemeinen Relativitätstheorie und Anwendung dieser Theorie in der Astronomie"(Fundamental Ideas of the General Theory of Relativity and the Application of this Theory in Astronomy), Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin: 315


[2] Einstein, Albert (1915), "Die Feldgleichungen der Gravitation" (The Field Equations of Gravitation),Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin: 844–847


[3] Christensen, N., LIGO Scientific Collaboration and Virgo Collaboration, 2010. LIGO S6 detector characterization studies. Classical and Quantum Gravity, 27(19), p.194010.


[4] "Black Hole | COSMOS". astronomy.swin.edu.au. Retrieved August 29, 2020.


[5] Shannon, R.M., Ravi, V., Coles, W.A., Hobbs, G., Keith, M.J., Manchester, R.N., Wyithe, J.S.B., Bailes, M., Bhat, N.D.R., Burke-Spolaor, S. and Khoo, J., 2013. Gravitational-wave limits from pulsar timing constrain supermassive black hole evolution. Science, 342(6156), pp.334-337.


[6] Kalogera, V. and Baym, G., 1996. The maximum mass of a neutron star. The Astrophysical Journal Letters, 470(1), p.L61.


[7] Taylor, J.H., 1991. Millisecond pulsars: Nature's most stable clocks. Proceedings of the IEEE, 79(7), pp.1054-1062.


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