Spinning Neutron Star-White Dwarf Binary drags spacetime along with it

As massive objects in space spin, they drag the very fabric of space along with them, a study 20 years in the making uses this phenomenon to investigate a distant binary star system.

Frame dragging —the swirling of spacetime by a massive object as predicted by Einstein’s theory of General Relativity — has been used to investigate the formation of a distant binary star system. The study also opens up the prospect of exciting future applications for the churning of spacetime in answering some of the most pressing questions in astrophysics.

One of the most important aspects of Einstein’s theories of special and general relativity was the idea that space and time are united and can no longer be considered a static stage on which the events of the universe simply play out. One of the consequences of this revelation is the idea that spacetime is a dynamic entity that can be affected by matter and that, as a consequence, a massive object drags local-spacetime along with it when it rotates. This churning of the very fabric of the universe — referred to as ‘frame-dragging’ or more formally ‘the Lense-Thirring effect’ — has previously been measured around Earth with the aid of satellites, but now an international team of astronomers have used this phenomenon as an investigative tool in its own right.

The team, including scientists from the Max Planck Institute, Bonn, Germany, have detected the swirling of the space-time around a neutron star-white dwarf binary, using it to measure the rotational speed of the white dwarf and determine the system’s unusual origins. The team’s research is published in the journal Science.

Video sequence, showing the pulsar- white dwarf binary system PSR J1141–6545. Copyright: Mark Myers, ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav).

For twenty years the researchers have monitored a binary star system containing the neutron star — the pulsar PSR J1141–6545 — and a relatively massive white dwarf star. The pulsar-white dwarf system — found in the constellation Musca (the Fly) close to the Southern Cross constellation — completes an orbit in under five hours with the radio pulsar emitting radio waves along its magnetic poles.

“We see that the orbit of this system is tumbling in space, inferring that if Einstein’s theory is right, part of the reason for this is due to the white dwarf dragging the space-time in its vicinity around with it,” says Dr Vivek Venkataraman Krishnan, the first author of the paper and a scientist at the Max Planck Institute for Radio Astronomy, who performed the data analysis and parts of the observations of PSR J1141–6545 when he was a PhD student at the Swinburne University of Technology in Australia. “We use this observation to estimate the rotation period of the white dwarf — finding it should be about a minute or so.”

Venkataraman Krishnan points out, white dwarfs do not usually rotate this fast unless something ‘spins them up.’ This means that ordinarily frame-dragging effects would not be observable in such systems, making the discovery of such an effect in this system a pleasant and extremely useful surprise.

What came first, the white dwarf or the neutron star?

“In this case, the pulsar’s progenitor star transferred some mass to the white dwarf before it exploded into a supernova to form the pulsar. This mass transfer spun the white dwarf up to such fast speeds,” Venkataraman Krishnan says. “ Our measurement of the white dwarf spin period has proved the unique way that this binary system came to be.”

The binary star system containing the pulsar PSR J1141–6545 and a relatively massive white dwarf companion.

Thus, the speed of the rotation of the white dwarf shows it must have formed and received a significant amount of mass from a progenitor star before this donor star underwent the supernova explosion that transformed it into a neutron star. Something that sets it apart from other similar binary systems.

“This binary has undergone a special evolution — which is now proven by this paper,” Venkataraman Krishnan adds. “Systems like PSR J1141–6545 where the pulsar is younger than the white-dwarf are quite rare. In fact, this is the only one that we know that has such a short orbit so that we can detect relativistic effects in the system.”

Frame dragging as a measurement tool

The standard procedure to measure the rotational speed of a star is to analyse the Doppler shift in the characteristic spectral pattern the star emits. This method wasn’t possible with this system, as PSR J1141–6545’s white dwarf companion is too faint to carry out such a study. Hence the team turned to a prediction that emerged from Einstein’s theory of general relativity over 100 years ago.

As mentioned above, general relativity revolutionised both the way we think about space and time and the effect that mass and energy have on spacetime and vice versa. Perhaps physicist John Wheller explained this aspect of general relativity — also known as the geometric theory of gravity — best when he said: “Matter tells space how to curve, space tells matter how to move.”

This idea is most often visualised as a ball placed on a stretched rubber sheet or a trampoline. The dent created is analogous to the curvature created by massive objects such as planets, stars and black holes. As is the case with the rubber sheet, the greater the mass the more extreme the curvature. So, just as a bowling ball creates a larger dent than an apple, a black hole creates a more extreme curvature than a star like the Sun.

Where this analogy falters is in the fact that the rubber sheet is 2 dimensional and spacetime is intrinsically 4 dimensional, and also when considering what happens when the massive object in question is rotating.

To tackle this later aspect, three years after the publication of general relativity in 1915, Josef Lense and Hans Thirring — supported by Einstein — calculated the effect of a massive rotating body in our Solar System using general relativity. In particular, they modelled how the dragging of space-time caused by the rotation of the Sun influences the movement of planets, concluding that these effects were impossibly small to measure.

Venkataraman Krishnan has another useful analogy to describe the effects of frame-dragging. He explains: “Place a small ball in a bowl of honey. Add a drop of food colouring near the ball. Now, spin the ball quickly and notice that the honey turns with it. The honey that is closer to the ball is pulled around more than the honey that is farther away from the ball. Notice also that the food colouring, or anything else floating in the honey, is pulled around, as well.

“In this analogy, the spinning ball is the spinning star. The honey is space-time that is dragged along with a strength that reduces as you move away from the star. The food colouring is any other objects in the vicinity — in the case of the system we studied, the pulsar — that are dragged along as well.”

The problem remains though, how to measure these effects that are predicted to be extremely weak?

Fortunately, since 1918 when Lense and Thirring first proposed frame dragging as a phenomenon, technology has progressed to such an extent that even the slight effect caused by the Earth’s rotation can be accurately measured. For example, Gravity Probe B used a set of four precision gyroscopes to measure frame-dragging around Earth, whilst the laser-ranging satellites LAGEOS 1 & 2 and LARES measure the resultant slow precession of the orbital plane of the satellites in the direction of Earth’s rotation — known as ‘the Lense-Thirring precession’(remember the swirling food colouring)—and confirm it to an accuracy of 2%, in agreement with general relativity’s predictions.

“While frame-dragging has already been observed even with the rotation of the earth with satellites such as LARES and Gravity Probe B, this is the first time that this has been measured in a binary star system. This is because the effect is very subtle.”

A finding twenty years in the making

Whilst it would be impossible to send satellites such as the Gravity Probe B to PSR J1141–6545, as it is several thousand light-years away from Earth, precise measurements are possible to collect thanks to the radio signals blasted out by the pulsar. These radio signals allow astronomers to monitor changes in the pulsar’s motion in a way that is analogous to the laser-ranging measurements of the LARES and LAGEOS-1 & 2 satellites.

Artist concept of Gravity Probe B orbiting the Earth to measure space-time, a four-dimensional description of the universe including height, width, length, and time. (NASA)

“With the help of atomic clocks, we were able to perform highly accurate measurements of the arrival times of the pulsar signals at the Parkes and UTMOST radio telescopes,” Venkataraman Krishnan explains. “We could track the pulsar in its orbit with an average ranging precision of 30 km per measurement, over a period of almost twenty years. This led to a precise determination of the size and orientation of the orbit.”

For the binary system studied, Venkataraman Krishnan says, the frame-dragging could amount to a maximum tumbling of the orbital plane of 1.7 seconds of arc per year for this system — or about 0.0004 degrees per year. This is an effect that is roughly a million times weaker than would be experienced by a body at a LAGEOS-1-like orbit. Despite this, over the twenty years that the team has been studying PSR J1141–6545, even this minimal effect was enough to cause precession of the pulsar’s path of about 150 km.

By analysing this measurement and accounting for the frame-dragging effect, the researchers were able to determine the rotational period of the white dwarf — estimating it to be roughly 100 seconds. This confirms the idea that, before the supernova explosion that formed the pulsar occurred approximately 1.5 million years ago, a significant mass transfer from the progenitor of the pulsar to the white dwarf took place.

“Given that this system is a few hundred quadrillion kilometres away, it is mind-boggling that we could measure this, that too in a system that it was initially not expected to be detected.”

The method established and used by the team in this study should also prove useful for astronomers in the future. “The Lense Thirring effect can be used as a tool to understand the properties of the rotating star that causes it,” Venkataraman Krishnan says. “In the future, the same techniques can be applied to short-period double neutron star systems — a binary system with two neutron stars — such as the double pulsar PSR J0737–3039A.”

Venkataraman Krishnan hopes that the method employed by the could reveal neutron stars’ hidden secrets (NASA)

For Venkataraman Krishnan, the prospect of answering long-standing questions in astrophysics using this method is an exciting one, in particular, deducing the properties and origins of neutron stars. “Detecting evidence of Lense Thirring precession can be used to estimate the Moment of Inertia of the neutron star, and hence its radius,” he tells me. “Since the mass of the stars in this system is well known, it directly leads to an understanding of the internal composition of neutron stars — which even after more than 50 years of observation, we do not yet have a handle on.”

The density of matter inside neutron star far exceeds what can be achieved in a lab — so there is a wealth of new physics to be learnt by using this technique to double neutron star systems, Venkataraman Krishnan points out. “Based on our simulations, we think this can be done for the double pulsar system in the next 5 years or so.

“What I am more broadly interested in is to use pulsar observations to understand fundamental truths about the universe. Observing pulsars help us answer questions like is general relativity still the best explanation for gravity?” He concludes.