16 mins read 20 Jun 2023

Humanity's Galactic-Scale Detectors: Pulsar Timing Arrays

Nanohertz-frequency gravitational waves have wave periods that last decades, which makes building any dedicated terrestrial-based detectors impossible. Astronomers have figured out a way to get around this - by using pulsars located across the Galaxy, simulating a Galactic-scale gravitational wave detector. In part three of this series, we dive into what Pulsar Timing Arrays are, some of the challenges they face, and how they can improve their sensitivity.

Credit: NR Fuller / Science.

Massive stars tend to live bright and die young, spending most of their existence giving off enormous amounts of energy, illuminating the Galaxy. Even more spectacular is when these massive stars die, in violent supernovae events which can be seen at great distances across the Universe. It is in this spectacular show of light and raw energy that new elementary particles – like some of the stuff humans are made of – are generated. What’s even more exciting is that some kinds of supernovae (the types that involve the core of the progenitor massive star collapsing in on itself under the pressure of gravity), leave behind a special, exotic and mind-boggling object – a neutron star.

Neutron stars were theorised back in the 1930s, but confirmation of their discovery came in 1967 when (then PhD student) Dame Professor Jocelyn Bell-Burnell discovered pulsars using an instrument she helped build in Cambridge. In a nutshell, pulsars are neutron stars that spin rapidly and have powerful magnetic fields. It is because of these two conditions that radio wavelength emissions are generated from the magnetic poles of these neutron stars and are beamed out into space. When one (or in some cases both) of these beams intersects with Earth’s line of sight, astronomers register it as a pulse - and hence why this particular flavour of neutron stars are called pulsars

Approximately 3,300 pulsars have since been found, making up the majority of the overall neutron star population - though there are other, non-radio-pulsing, thermally-detected neutron stars that also make up part of the known population of these compact remnants. Most pulsars are located in the Milky Way Galaxy, including several which belong to the Galaxy’s Globular Clusters. There’s even a handful that are found in both the Small and Large Magellanic clouds. It is expected that pulsars are also found in other galaxies, but their signals are likely too weak to be detected by current radio telescopes across vast intergalactic distances. 

The Milky Way’s population of pulsars is also expected to be much higher, but due to observational biases, selection biases and beaming biases (where pulsar beams just don’t point at Earth), scientists don’t see them all through EM observations.

Pulsar’s are analogous to cosmic lighthouses - when their beams intersect with Earth, we see a pulse. Their fast rotational periods and stability make them excellent for timing experiments. Credit: Shutterstock.

What makes pulsars unique is their rotational periods (usually lasting from about ten seconds down to millisecond periods), and ongoing stability - making them some of nature’s most accurate cosmic clocks. Using large radio telescopes around the world, pulsar astronomers have been able to learn a great deal of detail about these objects, including many of their properties to a high degree of precision. 

Pulsars exhibit two main fundamental properties. The first is the observed sequences of pulses they intrinsically emit (and which our radio telescopes detect) - representing the neutron star’s rotation period (P), and the second is the observed small increase of the rotation period over time - known as P-Dot (or period derivative). This slowing down of the pulsar’s rotation is due to a number of reasons, such as the neutron star continually losing energy in the form of magnetic dipole radiation, as well as emissions of electromagnetic radiation. Additionally, as the interiors of hot, young pulsars cool and turn into a state of matter that behaves as a fluid without its friction and viscosity – this change of state also gradually affects the rotation period.

When plotting the known pulsar population as a function of P vs. P-Dot (as in the diagram above), an interesting picture emerges of the sub-populations of pulsars, and a story of their evolution starts to become apparent. Using these two main properties, astronomers can derive a suite of assumed information about these objects, such as their characteristic ages and magnetic fields. These derived values help describe the evolution of neutron stars and are marked as the diagonal lines on the P/P-dot diagram.

The P/P-Dot diagram showing the total pulsar population as a function of their rotation periods and slow-down rates. In this plot, we see emerging sub-populations. Millisecond pulsars are found in the cluster in the lower left corner. Credit: Rami Mandow.

For example, evidence has been found that can directly associate supernova remnants with some young pulsars (centre of the P/P-dot diagram), which adds further context that neutron stars (and pulsars) are formed during violent supernovae events. In the upper right of the diagram, a sub-population also exhibits powerful characterised magnetic fields. These are known as magnetars (SGRs/AXPs) and contain the most powerful magnetic fields in the Universe, approx. a trillion times more powerful than the average fridge magnet.  

We now understand that pulsars are born towards the centre of the diagram, and slowly move across to the right and then down as they age. At one point, due to the loss of energy, a pulsar’s magnetic field and rotational period will fall below a threshold in which the beamed radio emissions will no longer be able to be generated, and so, the pulsar simply becomes a cooling neutron star. Whilst these objects can still be detected in high-energy bands like X-rays, they have fallen into the ‘death valley’, the slightly shaded region of the diagram, in which for many of these objects we no longer detect pulses. In recent times there have been a few objects that have been found in this region, though the debate is still ongoing as to how these should be classified.  

The P/P-dot diagram does reveal something additionally interesting, however. In the bottom left, there appears a cluster of a much older class of pulsars, mostly in binary systems (sometimes in globular clusters), rotating hundreds of times per second on their axis and yet having both a low period derivative, as well as a weakly derived magnetic field. 

These are known as millisecond pulsars, which as the name suggests, have millisecond period rotations. Unlike their younger cousins, observational data collected since their discovery in 1982 on millisecond pulsars (MSPs) indicates they are extremely stable rotators, having settled into these conditions over the billions of years of their evolution. They’re also called recycled pulsars because originally, they too were once classical pulsars that slowed down enough to stop producing radio emissions, and simply became thermally cooling neutron stars in the death valley. However, they’ve roared back into emitting radio pulses because they have been re-spun up to higher angular velocities, through the accretion of material from their binary companions over periods spanning billions of years. This spinning up is the mechanism that restarts their pulse emissions, making them once again detectable to radio telescopes on Earth. 

Pulsar Timing Arrays

Pulsars located in all directions - as their signal travels to Earth, any distortions in space-time created by gravitational waves will slightly change the signal regularity. Credit: DJ Champion.

This stability of MSPs makes them the perfect tools to use in precision timing experiments - in particular, in building a Galactic-scale detector known as the Pulsar Timing Array (PTA). These experiments are, as the name suggests, an array of pulsars being monitored by astronomers over the long term.

There are several global PTA teams that have been observing pulsars, with some of their data sets spanning back decades. The four main teams include the Parkes Pulsar Timing Array (PPTA) in Australia, the European Pulsar Timing Array (EPTA), the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), and the Indian Pulsar Timing Array (InPTA). Additionally, there are several emerging PTA teams in China, South Africa and Argentina. Collectively, the four main teams of the PTAs operate under a larger, global collaborative network of approximately 300 scientists known as the International Pulsar Timing Array (IPTA) project.

In PTA experiments, astronomers measure the time of arrival of signals from MSPs and compare this to an expected time of arrival which has previously been modelled. What they’re looking for are any residuals (discrepancies) between the model and the observation. Fluctuating residuals from an individual MSP system could potentially represent a number of interesting science cases to be explored including learning about the individual pulsar’s magnetosphere, its binary companion (including any planets), or the interstellar medium between the pulsar and Earth. They can also be used to learn more about how matter behaves under extreme conditions within neutron stars and use these cosmic clocks as laboratories of General Relativity – seizing the opportunity to test theories and frameworks in conditions that can never be recreated on Earth.

PTAs however also have a core science objective – with global teams hunting for the yet-to-be-discovered nanohertz-frequency gravitational wave background (GWB), which is expected to be generated by a number of sources. The loudest signal of this background is thought to be produced by the inspiral and mergers of supermassive black holes in the hearts of galaxies as they have collided together across the history of the Universe.

The Hellings-Downs correlation (simulated) on pulsar timing residuals, of pulsars that have angular separation across the sky (shown in radians). This is the expected signal correlation between pulsars generated by a stochastic background of gravitational waves. Credit: Verbiest et al. 2021.

So how do astronomers use pulsars to find this signal? In accordance with General Relativity, should a gravitational wave pass between the MSP and the Earth, then it will induce a tiny variation in the baseline distance between these two bodies which will manifest as a tiny change in the timing of the arrival of the MSP’s signal. From Earth’s (or more accurately, the PTA’s) perspective, each of these baselines leads out to a different MSP located in a different part of the sky (and Galaxy), giving scientists uniform coverage in all directions to search for these gravitational waves.

There could be a suite of reasons as to why this would be observed for a single pulsar system, but as PTAs are observing a suite of pulsars at a regular cadence – what they are truly searching for is the spatially correlated signal amongst all MSP’s timing residuals. In other words, a correlated signal that is affecting all MSP-Earth baselines. This is the true smoking gun signature of a GWB detection and is known as the Hellings-Downs (HD) correlation

Fighting the Noise

Simulations of the turbulent, interstellar medium. Credit: Federrath et al. 2021.

Unfortunately, it’s not as straightforward and simple as this, as pulsars (in general) are complex objects which are, in many ways, not yet fully understood. Our best understanding of each pulsar comes from continually observing and collecting data on them to produce a mathematical model of everything we know about them (such as their spin period, their period derivative, their motion in space, their binary orbital periods, relativistic effects, etc.). This is known as the timing model. The parameters of a timing model are used to make the predictions to a pulsar’s signal time of arrivals (ToAs) that are used to measure observations against to determine timing residuals.

The emitted radio light from pulsars has to travel across great distances through the Milky Way’s interstellar medium (ISM) which has components that are ionised. This inhomogeneous, turbulent and magnetised medium can affect the radiation in a number of ways. The most prominent is a dispersion effect caused by the ionised ISM, which leads to pulses at higher frequencies arriving earlier than the same pulse of lower frequencies – and so the pulsar signal needs to be ‘de-dispersed’ as part of the process to remove any frequency-dependent delays. Dispersion is not the only effect the ionised ISM has on the pulsar’s signal – it can also lead to scintillation, scattering and broadening of the pulse.

Pulsar signals are also very weak (even much fainter than the thermal noise of the large radio telescope collecting the data), and so many pulses need to be folded at the known rotation period and integrated to produce a high signal-to-noise pulse profile. This can involve averaging hundreds or thousands of individual pulses to create this average profile (which is remarkably stable over the long term). Given that MSPs rotate hundreds of times per second on their axis and have stabilised, this makes them ideal to use in these types of experiments instead of younger pulsars.

Radio telescopes and observatories are also located on the Earth's surface, which is a continually moving frame (spinning on its axis, slightly shifting to account for the Earth-Moon barycentre, orbiting around the Sun, etc.) which makes the baselines that connect each PTA to the MSP not very effective. To correct for this, pulsar signals are instead transformed to be measured at the Solar System Barycentre, as the inertial frame of reference.

The Solar System Barycentre lies just outside the Sun’s radius, thanks to (mostly) Jupiter’s high mass and its distance. Other planets, like Saturn, also contribute to this, but to a smaller degree. Pulsar timing measurements are transformed to be measured from the Solar System Barycentre, which in itself is dynamic as the planets orbit the Sun. Credit: T. Klein/NANOGrav.

These observatories are also built where humans are, which results in the introduction of radio frequency interference (RFI) that also needs to be accounted for (usually by zapping the frequency channel that is affected by it). Some observatories have been built in government-assigned radio quiet zones, which help reduce terrestrial-based RFI, but this doesn’t rule out some interference generated by the growing number of satellites that broadcast their signals into the beams of radio telescopes.

Once all of these considerations are taken into account, the timing model can be continually improved, and better residuals can be calculated. If the predicted model matches that of the observation, then the residuals would be zero – but this is never the case. Residuals often display non-zero values as a result of modelled and unmodelled phenomena, known as noise, which can be categorised into two main branches.

The first is known as white noise and includes both modelled radiometer noise (produced by thermal electron fluctuations of the instrument in addition to the sky background of Galactic synchrotron-radiating electrons) and unmodelled jitter of the pulsar – which is induced by individual profile shape variations that are intrinsic to the pulsar and observed from epoch to epoch. White noise tends to dominate at the shorter timescales of observing.

The second is known as red noise, which dominates at longer timescales. Red noise can be both temporally correlated and uncorrelated amongst the pulsars. An important source of red noise is the unique spin noise of each pulsar, which are a result of its rotational instabilities, internal structural shifts or magnetospheric reconfigurations – is present even for the most stable MSPs. Spin noise is considered uncorrelated (as each pulsar is different) and achromatic as it is not dependent on frequency. Another red noise source is the dispersion measure variations across all observed pulsars – which is chromatic in nature, as dispersion is a frequency-dependent effect. Instrumental noise, such as errors in the clocks that measure the signal times of arrival is another source of red noise.

The weak GWB signal is itself is a correlated and achromatic red noise process (i.e., it is observed across all MSPs in a PTA but is not frequency dependent) and in order to isolate and decouple this from other noise sources, a number of mitigation strategies must be implemented by PTAs to improve the sensitivity of the array, helping make the first detection of this much-sought-after signal.

Improving PTA Sensitivity

The Galactic distribution of the Milky Way pulsars (incl. pulsars found in the Magellanic Clouds). Most of the pulsars reside in the Galactic plane, but a number are located at higher Galactic latitudes. Different sub-populations are shown. To improve sensitivity, PTAs are required to continually add new pulsars into their observing programs. Credit: Rami Mandow.

Given the many different contributions that bury the elusive stochastic GWB signal within the overall observed red noise, PTAs have developed a number of mitigation strategies to deal with noise in their data sets, characterising this and accounting for it in their overall analysis of their pulsar timing data.

For example, to combat white noise such as instrumental thermal noise, receivers can be cooled down using cryogenic fluids like liquid helium. Increasing observation integration times for each pulsar also assists in combatting the jitter noise they intrinsically produce. Additionally, observing with a wider bandwidth and selecting bright MSPs that have short duty cycles is ideal. 

When it comes to the observed red noise that is present in pulsar timing data sets, mitigation strategies can include better quantification of the intrinsic spin noise per pulsar (by observing them for longer timespans), utilising better Solar System ephemeris models (used for barycentric frame corrections), ensuring any localised observatory clock errors are accounted for, as are the variations of dispersion measure for each of the MSPs.

There are also a number of strategies that PTAs can employ to improve their sensitivity to the GWB signal - strategies that have been undertaken by all of the global PTA teams as part of their search for this signal over the last few decades. 

One method is to increase the number of MSPs that PTAs observe as part of their observing program. This assists with the smoking-gun confirmation of the GWB - the Hellings-Downs correlation - by increasing the number of pulsar pairs in which varying angular sky separation that the quadrupolar spatial metric can be measured against. Having these MSPs spread across greater separations across the sky also assists, instead of focusing only on MSPs that reside in the Galactic plane. Additionally, having more MSPs helps to decouple the GWB signal from the red noise observed in PTA data sets. This is a strategy that is employed by the International Pulsar Timing Array project - which takes the data and MSPs from all the regional PTAs (which have their own set of MSPs due to their localised sky coverage) and combines these to increase the number of pulsar pairs used to make the GWB detection. 

However, having more MSPs alone won’t increase the sensitivity to the GWB. PTAs must also observe MSPs for longer timespans as the lowest frequencies of the GWB power spectrum fall below the white noise of the pulsars. As enough observing time passes (on the scale of years), the power spectrum of the GWB overcomes the white noise at all frequencies. 

There are also some challenges that PTAs face with these mitigation strategies - such as the competitiveness and finite telescope time for multiple projects (not just PTA science) limiting the availability to observe more MSPs. Hence why PTAs continually survey the sky looking for new MSPs, and then time these for approximately one year to determine if these are considered ‘good quality’ to use in PTA experiments, then either adding them in (if extra time is made available in observing programs) or replacing not-so-good MSPs - though, this is rarer, as these MSPs have already accumulated a large timespan of data that a new MSP will require years to reach).

Next week is our final instalment of this series, where we will be covering the convergence of all of these topics discussed so far and how they add to new scientific knowledge.