17 mins read 14 Dec 2021

Double Pulsar System Strengthens Einstein’s Relativity

16-years of data, obtained from observing a double pulsar system first discovered by CSIRO’s Parkes radio telescope, has held up Einstein’s relativity once again - showcasing further evidence that General Relativity is a successful method of describing gravity in our Universe.

Artistic impression of the double pulsar system. The orbital motion of these extremely dense neutron stars causes a number of relativistic effects, including the creation of ripples in space-time known as gravitational waves. Credit: Michael Kramer/MPIfR.

Whenever I travel around our city, I am always fond of catching the train, and in particular, sitting right next to a window. It gives me the chance to look out to the world passing by, and I often find myself thinking about relativity.

I take out a pen from my backpack and raise it up in one hand and let it go dropping it into my other hand. What I consider is that from my perspective, sitting inside the train – the pen falls in a vertical line from one of my hands to the other. Then I consider what that must look like to someone sitting on the platform, watching me perform this simple experiment as the train rushes past. From their view, the pen does not fall in a straight line but follows a diagonal trajectory of greater length than the distance I observe.

When we arrive at some stations, like Sydney’s Central, I catch myself looking out at the big sandstone clocktower that rises above the historic building. And as the train pulls away and starts to accelerate down the track, I think about every time that clock ticks – I am moving further away from it, and so its signal takes just that little longer to get to me, a measure which is proportional to how fast the train is moving.

Remarkably, Einstein considered relativity in this manner – moving trains. He was able to formulate a whole new way to see the Universe (both through the Special Theory of Relativity, then the General Theory of Relativity) in a time well before the existence of computers, rockets, interplanetary space probes, and even pre-dating human’s confirmations that other galaxies were a distant island Universe of stars beyond the Milky Way.

Yet, in over 100 years of rigorous experiments, observations and heated science debates – both theories of relativity have stood the test of time, continually serving up evidence that Einstein was right, time and time again.

Now, Australian scientists (working as part of an international team) have added another piece of strong evidence to the relativity story, this time using 16-years of data and observation to fortify that Einstein’s gravity (as described in the General Theory of Relativity (GR)) is indeed how our Universe is governed.

To do so, astronomers used an interesting laboratory, one (and only one) that the Galaxy has provided us with – a system featuring not one, but two pulsars in a tightly configured orbit around their common centre of mass.

To make these exciting measurements, the team – led by Professor Michael Kramer from the Max-Planck-Institute for Radio Astronomy in Bonn, Germany, used 6 different radio telescopes located around the world to keep an eye on the double pulsar system known as PSR J0737-3039 A/B (with each letter representing each individual pulsar).

The new paper, which is published today in the journal Physical Review X, has added further conviction to Einstein’s theory of gravity. To do so, a number of new methods were introduced in studying the double pulsar system, improving the precision of previous results and revealing newly measured effects too.

Illustration of a pulsar. Credit: K. Gill.

Pulsars (a type of neutron star) are the remnant compact cores of massive stars (usually around 8 – 25 solar masses in their progenitor phase) that have since undergone a supernova event. When the massive star died, the core collapse processes created the pulsar, some of the conserving angular momentum and magnetic flux into the new compact remnant, allowing it to spin fast enough to generate powerful beams of radio light that are emitted from the star’s magnetic polar regions.

Pulsars themselves come in a few varieties, which include classical pulsars (which are newly formed, exhibit strong magnetic field strength and spin fairly fast), and a sub-class known as millisecond pulsars (MSP) – which spin hundreds of times per second but have relatively low strength magnetic fields. MSPs are the result of binary interactions, where the pulsar is re-spun up to high angular velocity after syphoning matter via accretion processes from the companion. The fastest on record spins at roughly 716 times per second, an extraordinary 24% the speed of light.

What makes pulsars (and neutron stars generally) special is that they’re tiny – about the size of a city, roughly 20-kilometres in diameter. But they pack a punch, containing an enormous mass, that can range between 1.4 and just over two times the mass of our Sun. That’s a lot of material packed into a small space. So great is the density, that a teaspoon of pulsar matter would weigh as much as all of humanity combined.

As astrophysical objects go, pulsars provide a valuable tool to test and probe theories, models and our understanding of the cosmos. With their regularity of pulses (which can rival the stability of terrestrial atomic clocks), highly sensitive precision timing experiments can be undertaken. Combine this with long-term observation cadence, and you’ve got yourself an excellent lab to test gravitational theories, the equations of state of matter under such extremities, and an ability to measure the mass and composition of these exotic objects.

The case of PSR J0737-3039 A/B is unique as it is extraordinary. It’s the only double pulsar system ever discovered (found in 2003 by Italian radio astronomer, Dr Marta Burgay using the Parkes radio telescope, which is owned and operated by Australia’s national science agency, CSIRO). That’s not to say these types of systems don’t exist, only that this is the first and only that we have so far observed. 

Tracing back the system’s evolution through time, it would have featured two massive stars, both of which underwent a supernova event and still remained bound (indicating a low-velocity natal kick model). Having survived not one, but two supernovae, the system produced two neutron stars that pulse – one (Pulsar A) a millisecond pulsar rotating with a 23-millisecond period, the other (Pulsar B) a classical pulsar, rotating with a period of 2.8 seconds.

The system follows a relatively eccentric orbit (e = 0.088) that lasts 2.45 hours, and as a result of this short period, both stars are slowly following a fatal in-spiral orbit, expected to merge in a cataclysmic event that should occur around 85 million years from now. As with other binary systems that feature in-spiralling massive objects, the system radiates gravitational waves – something that can be indirectly measured through the timing effects from each pulsar.

Dr Dick Manchester, a Fellow at Australia’s national science agency, CSIRO, and a member of the research team, explained how this result provides us with a more precise understanding of our Universe.

“The theory of general relativity describes how gravity works at large scales in the Universe, but it breaks down at the atomic scale where quantum mechanics reigns supreme,” Dr Manchester said.

“We needed to find ways of testing Einstein’s theory at an intermediate scale to see if it still holds true. Fortunately, just the right cosmic laboratory, known as the ‘double pulsar’, was found using the Parkes telescope in 2003.

“Our observations of the double pulsar over the past 16 years proved to be amazingly consistent with Einstein’s general theory of relativity, within 99.99 per cent to be precise,” he said.

Along with Dr Manchester, the team included other researchers from CSIRO, Swinburne University and the ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav). To produce these results, data from the Parkes radio telescope (which discovered PSR J0737-3039) was combined with observations from the Green Bank Telescope (USA), Nançay Radio Telescope (France), Effelsberg 100-m Radio Telescope (Germany), Lovell Radio Telescope (United Kingdom), and the Westerbork Synthesis Radio Telescope (Netherlands).

Science Check: Pulsars and Relativity

Artist rendition of when a pulsar’s signal passes through the gravitational field of a foreground object, in this case, a white dwarf, the space-time curvature (caused by the mass of the white dwarf) causes a delay in the pulsar signal arrival time. This is known as the Shapiro Delay. Credit: B. Saxton/NRAO/AUI/NSF.

Pulsars provide a superb opportunity to run relativity experiments, as they provide the right conditions – high mass, strong gravitational fields, rapid rotation, etc. combined with a signal that can be measured to high accuracy. These types of conditions would be impossible (and frankly, deadly) to try and recreate here on Earth – so these laboratories are at a good distance from us in which we can analyse their electromagnetic and gravitational radiation to further refine our understanding of science.

For example, the first indirect confirmation that gravitational waves existed (even though they were predicted by Einstein many decades prior) came in 1974, when Joseph Taylor (Jnr) and Russell Hulse used the Arecibo telescope (located in Peurto Rico) to measure the pulse signals from the Pulsar-Neutron star system PSR B1913+16. What they found was that the orbit of these two high-mass objects was decaying, astonishingly to a near-perfect match of what Einstein’s equations predicted. The distance between the two stars was shrinking, as the system emitted gravitational radiation.

Another relativistic effect that pulsars can highlight is called the Shapiro Delay. This extra time delay occurs when light travels past a massive object but experiences a delay due to time dilation. It was first observed by studying the arrival time of radar signal from spacecraft near Venus, as that signal traversed across the Solar system and near the Sun. The high mass of the Sun caused a slight, but measurable delay in the signal arrival time. In a similar fashion, many pulsars form part of a binary system – be that with other neutron stars, white dwarfs or in the case of PSR J0737-3039, another pulsar.

As the signal from the pulsar traverses along the line of sight that intersects with the binary companion, then its mass causes a measurable relativistic time dilation that can provide detailed information about the companion’s mass.

Another effect is the precession of the system’s orbital perihelion – that is, how the orbital axis slightly advances in the orbit of rotation. This was one of the earliest confirmations of Einstein’s theory, but rather than observing pulsars it was noted that Mercury follows this phenomenon, as it resides close to the Sun. Once again, thanks to their favourably stable and regular ticking, pulsars allow the opportunity to test this perihelion precession, confirming that GR is a solid theory in both the weak-field regime (like that found in the Solar system) and the strong field regime (like that found around orbiting compact remnants).

In this latest paper about PSR J0737-3039 A/B, astrophysicists have outlined some of the most precise measurements of relativistic parameters such as orbital decay due to gravitational radiation, Shapiro and Einstein delays, and the precession of the system’s perihelion.

Gravity Changing Over Time

Illustration of the effects of central mass on a superimposed on a flat, two-dimensional space-time grid. In reality, this grid is three dimensional and expressed as a function of time. Credit: CS Baird.

Gravity has always been one of the most elusive and intriguing phenomena to astronomers and scientists – because it is also the weakest of all four fundamental forces. However, whilst it is weakest, it also has the longest range and can act over great distances.

Prior to Einstein, gravity’s main quantification and description came from Isaac Newton though ancient Greek philosophers like Archimedes and scientists later on – like Galileo did discuss it in one form or another.

But it was Newton’s Theory of Gravitation from the 17th Century in which gravity could be described mathematically, tested against reality with strong supportive evidence. As the story goes, an apple fell from a tree – and the rest is history. At the time, the theory was further fortified when it was used to predict the existence of a whole new planet, beyond Uranus, due to how Uranus was orbiting the Sun. Soon thereafter, Neptune was discovered. But for all its firm predictions and results, Newton’s gravity also had holes in it – such as why Mercury’s orbit perihelion continued to advance.

Newton’s theory was superseded when Einstein came along in 1915 with GR, redefining our notion of gravity from the invisible rope-like force that connects two bodies across space, into the curvature of space-time itself, created by each body’s mass and their motion. This paradigm shift started to allow scientists to test all the holes that were present in Newton’s gravity, finding that experiments agreed more and more with GR. Not only was reality agreeing with this new theory, but it was also generating new ideas about phenomena and objects that would not be discovered for decades – gravitational waves, neutron stars, black holes, space-time frame-dragging, and even a way to describe the entire Universe’s cosmology.

But GR is not without its holes too. When considering everyday experiences (where regular velocities, masses and energies are considered), Newtonian physics still applies today. We can work out the orbits of planets and binary star systems, using Kepler’s formulation, Newton’s gravity and so on. When we start to get into more of the extremes (or relativistic side of things), then GR works a treat, on the macro scale.

But when we try and apply GR to the quantum scale, however, a great rift is formed. The laws of GR simply break down when considering quantum mechanics – and one of the greatest challenges (and an active area of research these days) is the marriage of both GR and quantum mechanics.

Additional to Einstein’s GR, there are also a number of other gravitational theories that exist – and are continually being put forward and tested by scientists today. However, none have stood (and successfully survived) the rigorous tests that GR has thus far.

Findings From The Double Pulsar

The first known double pulsar system was made by astronomers using the CSIRO Parkes radio telescope. Credit: J. Rowe.

Associate Professor Adam Deller from Swinburne University and the ARC Centre of Excellence for Gravitational Waves (OzGrav), another member of the research team, explained that the ticks from the pulsar ‘clocks’ had taken around 2,400 years to reach Earth.

“We modelled the precise arrival times of more than 20 billion of these clock ticks over 16 years,” Dr Deller said.

“That still wasn’t enough to tell us how far away the stars are, and we needed to know that to test general relativity.”

To determine the distance (calculated in this paper to be 2400 light-years give or take 200 light-years) was determined using an additional method known as Very Long Baseline Interferometry. This method utilises a network of telescopes spread across the globe (in this case it included telescopes dispersed across the USA, Hawaii and the Virgin Islands) to produce a more highly resolved signal using radio light. Then, by using the VLBI, the research team was able to measure a tiny wobble (on the order of 1.36 +/- 0.12 milliarcseconds, where a milliarcsecond is roughly the size of an Australian 10-cent coin sitting on top of Auckland’s Skytower, whilst being viewed from Perth) in the system’s position on an annual basis.

This method is known as parallax and takes advantage of Earth’s orbit of the Sun, allowing the opportunity to measure any variations in the location of nearby astrophysical objects, relative to the more distant background stars.

“One of the key tests of GR is the orbital period decay due to the emission of gravitational waves,” said Dr Deller. 

“But the orbital period decay we see from Earth is not the same as the true, "intrinsic" orbital period decay due to GR. It is modified by the relative motion and acceleration of the Double Pulsar relative to the Earth.  So we have to correct for that.  If we get the distance wrong, we get the correction wrong, and we'd think GR is wrong!”  

“We can estimate the distance using the pulsar timing alone, but the result is covariant with other parameters in the timing model.  Getting an independent measurement from VLBI helps both the precision and our peace of mind,” he added.

Other findings from this paper include determining the mass of each pulsar to a high degree of accuracy (Pulsar A = 1.338185 solar masses, and Pulsar B = 1.248868 solar masses), quantified the values of seven Post-Keplerian (PK) parameters (such as the Shapiro delay range and shape, the Einstein delay, Orbital deformation, the System’s frame-dragging component and of course gravitational wave emissions). These results now present the most PK parameters measured in any system.

This unique system also offers an opportunity to place limits on the equations of state of matter – which describes how physical matter behaves under different conditions. Within the internal layers of neutron stars – which have extraordinary density, gravity, pressure, temperature and internal energy – matter must be squeezed into extremely tight configurations, changing its properties. This new paper now places a constraint on this, by using the moment of inertia from Pulsar A – a value derived through understanding how the orientation of the orbit changes over time.

Additionally, one of the highlights of this paper is one of the most precise results achieved for the measurements of gravitational wave emissions (and validating GR) currently available, where a precession of 1.3 x 10-4  with a 95% confidence value has been reported.

“We're measuring the effects of GR in a system that is orbiting every 2.5 hours.  LIGO/Virgo do the same thing in a system that is orbiting dozens of times every second!” said Dr Deller. 

“So we test very different regimes - and alternate theories to GR predict different differences in these disparate regimes.  So it is complementary.  Basically, the pulsar timing is more precise (we have years and years of data) but the GW interferometers are looking at much bigger effects.”

The Double Pulsar System As A Lab

Artistic rendition of the double pulsar system, where one of the pulsar beams intersects with the secondary pulsar. Because of this alignment with our line of sight, sensitive timing experiments can be conducted to draw results from this system that helps test General Relativity. Credit: Michael Kramer/MPIfR.

Whilst the double pulsar system is unique to our breadth of observations of pulsars and neutron stars generally, it likely isn’t the only system of its type in the galaxy – a very likely outcome of the selection effects that we experience from both our position here in the Galaxy, and here at this time. There are very likely other double pulsar systems but their beams (either single or both) might not point at us, and as such, we don’t recognise them as a double pulsar system.

But we do have PSR J0737-3039, which provides an excellent laboratory to not only test GR applications and theories, but many other forms of astrophysics, such as binary evolution models, core-collapse supernovae events, and of course the equations of state of matter, through a better understanding of the mass, composition and structures of neutron stars.

When coupling a laboratory like PSR J0737-3039 with other studies such as the direct measurement of gravitational waves, captured through the sensitive yet giant interferometers placed around the world, or VLBI measurements, even better science, and refinement of GR becomes possible.

“We’ll be back in the future using new radio telescopes and new data analysis hoping to spot a weakness in general relativity that will lead us to an even better gravitational theory,” Dr Deller said.

It’s still rather remarkable that for over 100 years, and many thousands of verified experiments, Einstein’s relativity has stood strong the test of time. That he was able to see the Universe in a way that reshaped our collective understanding of its structure, behaviour and evolution.

I’m now very much looking forward to my next train ride.

The paper is available in the journal, Physics Review X