General relativity: the Lense-Thirring effect highlighted in a binary pulsar

LUCAS GIERCZAK

By accurately tracing the path of a neutron star orbiting a white dwarf, astrophysicists have measured an extremely tenuous phenomenon predicted by Einstein’s theory.

According to Einstein’s theory of relativity, a rotating object distorts space-time in its vicinity. This phenomenon is called the “Lense – Thirring effect”. It was highlighted in a couple of stars composed of a white dwarf (in light blue on this artist’s view) and a pulsar (in purple), the latter’s trajectory being precisely measurable thanks to its periodic radio signals (in white).

© Mark Myers, ARC Center of Excellence for Gravitational Wave Discovery (OzGrav)
Trajectories of planets in the Solar System, deflection of light rays by massive objects, emission of gravitational waves during the fusion of two black holes, slowing down of time with the altitude measured by GPS satellites, slowing down of the periodic signal of binary pulsars …: The experimental confirmations of Albert Einstein’s theory of general relativity are already numerous. These phenomena are all indications that massive objects distort the space-time around them. But general relativity also predicts that the rapid rotation of a massive body on itself also distorts space-time, “dragging” it with it. Called “Lense – Thirring effect”, or frame dragging in English, this phenomenon is very difficult to measure. It was recently discovered by Vivek Krishnan, of Swinburne Technological University, Melbourne, Australia, and his colleagues, through the observation of a pulsar and a white dwarf couple.

The Lense – Thirring effect owes its name to the Austrian astrophysicists Josef Lense and Hans Thirring who, at the beginning of the 20th century, with the help of Albert Einstein, calculated the impact of this phenomenon on the main bodies of the Solar System. The deformation of space-time is all the more important that the mass in rotation is large and that this rotation is fast. One way to highlight this phenomenon is to observe with precision the movement of a celestial body which revolves around another body in rotation on itself. Einstein’s equations predict that due to the rotation of the main star, its satellite undergoes a “precession”, that is to say that its axis of revolution shifts over time. More precisely, this axis of revolution “rotates” in space around a fixed axis, drawing the surface of a cone.

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But the intensity of the Lense – Thirring effect is extremely weak. The two physicists, who had calculated the relativistic influence of the rotation of the Sun on the movement of the planets, had moreover concluded that it was impossible to measure this impact with the means of astronomical observation of the time. The intensity of this phenomenon decreases very quickly with the distance from the rotating object (it varies like the inverse of the cube of the distance). This effect is therefore difficult to measure.

It was not until a century later, thanks to improved measurement accuracy, that astrophysicists were able to demonstrate the Lense – Thirring effect for a satellite around the Earth. In 2011, Nasa’s Gravity Probe B satellite, equipped with four very precise gyroscopes intended to measure the angular position of the satellite over time in relation to distant stars considered to be fixed, measured an extremely weak precession of its orbit but according to Einstein’s theory: the axis of revolution of the satellite moves by less than 10-5 degrees per year. At this rate, it would make a complete revolution in approximately 40 million years.

At the same time, astrophysicists have tested the Lense – Thirring effect in contexts where it should be much greater, that is, when the mass of the rotating object is huge. They looked at PSR J1141-6545, a couple of stars formed by a white, massive and aged dwarf, and a young pulsar, that is to say a neutron star in rapid rotation on it- even that which emits beams of radio waves from its magnetic poles. The interest of pulsars is the regularity of their periodic signal (due to the rotation of the star), which allows extremely precise measurements. In this case, the pulsar has a period of about 400 milliseconds, and the two stars rotate around each other in less than five hours, at a distance not exceeding the radius of the Sun. In addition, the very dense and massive white dwarf (about a solar mass for a diameter smaller than that of the Earth) also turns very quickly on itself – in a few minutes. The Lense – Thirring effect it generates is therefore much stronger than of Earth: if we could send a satellite like Gravity Probe B in orbit around this star at the same altitude as around the Earth, the intensity of the effect measured would be a hundred million times higher.

It is therefore the relativistic effect of the rotation of the white dwarf that Vivek Krishnan and his colleagues measured, by analyzing the precession of the pulsar. For this, the researchers used the data collected for 20 years by the radio telescopes of the observatories of Parkes and Molonglo, in Australia. By analyzing the lag between the arrival of the radio signals emitted by the pulsar in the two telescopes, the astrophysicists reconstructed the trajectory of the neutron star with an accuracy of 30 kilometers and were therefore able to measure the variations of its orbit over the course time. Vivek Krishnan and his colleagues have shown that the almost circular pulsar orbit has shifted about 150 kilometers in twenty years, as predicted by theory. A variation due half to relativistic effects and to phenomena of classical celestial mechanics.

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