14 mins read 05 Jun 2023

The Milky Way’s Cosmic Clocks - Pulsars

Astrophysics changed forever in 1967, with the discovery of a new type of object - pulsars. Since then, we’ve used these cosmic clocks to probe some of our most fundamental sciences. This article is the first in a multi-article, deep-dive series about pulsars, gravitational waves and radio astronomy. To start, we take a look at how pulsars are changing astronomy, and what discoveries, lay ahead.

A rapidly rotating, highly magnetised neutron star emits beams or radio waves from its magnetic poles - this is a pulsar. Astronomers analyse pulsar signals to determine their internal structure. Credit: NASA Goddard Space Flight Centre.

When we look up and see the brightest stars in our night sky, it’s always humbling to remember that nearly all humans have also gazed upwards at the bright points of light and reflected upon them. We share this deep connection with our ancestors, who have also known about most of the brightest stars for thousands of years - since the time of ancient civilisations. As time advanced, our technology became better and we now peer into the furthest reaches of the Universe, across the electromagnetic spectrum - discovering new types of objects as our knowledge expands. But not all our knowledge of space comes from the time of the ancients. One such object, which is relatively speaking only 'new', was discovered in 1967 by Dame Prof. Jocelyn Bell Burnell. It is the pulsar

Since their discovery, roughly 55 years ago, these exotic stellar remnants have been used in a variety of different experiments, helping us learn more about how matter, space, time, and radiation behave under extreme conditions. In that time, thousands of papers, many of which have been peer-reviewed have been written and submitted to publication across science journals, describing their properties, their emission processes, how their signals are affected as they travel across our Galaxy, and so much more. It seems the unexpected discovery of these astrophysical lighthouses, has spawned entire knowledge branches of science and discovery. But what are pulsars, and what can we use them for?

Nature’s Cosmic Clocks - Pulsars

The complex nature of the magnetic fields of pulsars. As the pulsar rotates, beams of energy from the magnetic poles sweep past the Earth and we see it pulse. In most models, we assume the pulsar has a dipole (i.e., a north-south axis) but for some pulsars, like this example, we find it is asymmetrical and misaligned. Credit: NASA Goddard Space Flight Centre.

Pulsars are born from violent beginnings. Their origin begins when massive stars (usually about 8 - 25 solar masses) reach the end of their lives and undergo a powerful supernova. During this event, most of the progenitor star is thrown outwards into space, but the inner part of the star - the core - collapses in on itself. This forces protons and neutrons together, creating neutron matter and unleashing an extraordinary amount of neutrinos. What’s left behind is known as a neutron star - an extremely dense object with approx. 1.2 - 2 times the mass of the Sun, squeezed into a space no bigger than a small town (~ 20 kilometres in diameter). A single teaspoon of material from a neutron star would weigh as much as all of humanity combined. 

As the radius of the core is reduced in the collapsing phase, the angular velocity increases - very much like an ice skater who pulls their arms in during a pirouette - causing the neutron star to spin rapidly on its axis. These objects also contain some of the most powerful magnetic fields in the Universe, usually ranging from billions to trillions of times the strength of a regular fridge magnet (the most powerful are a sub-class known as magnetars). 

Because of these two properties - the rapid rotation, and the powerful magnetic field - these neutron stars emit radiation from their magnetic poles, in the form of radio waves. We’re not really certain of what causes the emission process, but some modelling suggests electrons being ripped off the surface of the neutron star and being accelerated to relativistic speeds. This causes an electron cascade which results in the coherently beamed emissions of radio waves from the magnetic poles out into space. Here’s where things get interesting. 

The magnetic poles are not aligned with the rotational axis, and are instead offset, so as the neutron star rotates, its beams of radio waves sweep around as they are emitted into space. When one of these beams intersects with Earth’s line of sight, our radio telescopes (like the Parkes radio telescope, also known as Murriyang) detect these emissions. 

Pulse. Pulse. Pulse. This is why we call them pulsars - rapidly rotating neutron stars that are highly magnetised and emitting radio frequency pulses. So far we’ve discovered about 3,300 pulsars so far, but there are many radio telescopes continually searching the skies for new candidates. 

When we observe pulsars, we’re able to derive two main parameters. The first is we are able to measure the frequency of pulses in a single second and derive how fast the pulsar’s rotational spin period (P) is. We find most are spinning with periods that range from seconds to milliseconds. We also observe that with each rotation, pulsars slow down a little, and can measure this value (known as P-Dot) very precisely. An interesting story starts to emerge when we plot these values of the pulsar population against each other - showing us not only where different sub-categories of the pulsar population reside in terms of their properties, but also of their evolution. 

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.

One interesting aspect of this P/P-Dot diagram is a small sub-population of pulsars, located in the lower left. These appear to have weaker magnetic fields, are spinning much faster, and also have smaller P-Dot values. Many of them also appear to be in a binary configuration with a companion stellar object. 

These are known as millisecond pulsars (MSPs) and have characteristic ages that are in the billions of years. They’re also extremely stable, unlike younger pulsars which tend to glitch as they settle down. All of this points to an evolutionary tale - one that involves the pulsar accreting matter from its companion, causing it to spin up to millisecond rotational periods. 

This is not a quick process and can take billions of years. To start with, the first star in the binary configuration (the more massive primary) needs to live out its life, and undergo a supernova event that creates the pulsar. The second star (the less massive secondary) then needs time to burn through its nuclear time, expanding into a red giant and reaching the point where its material can overflow onto the pulsar, causing it to spin up. This secondary process can take billions of years. Not to mention, the binary configuration must also survive the initial violent supernova - which in some cases is known to give the neutron star a ‘kick’, completely disrupting the pair, and leaving only an isolated neutron star or pulsar. 

There are also cases in which two massive stars (8+ times the mass of the Sun) in a binary can each undergo a supernova event, and still not disrupt the binary, leaving behind two neutron stars. In some of these cases, one can be a pulsar, which allows us to precisely time the parameters of the binary system and learn lots of science. In a single case, there is even a double pulsar binary system, which has provided an enriching amount of data for relativity studies. 

Due to the reliably stable, periodic ticking of these cosmic clocks, pulsars have opened up a new look at analysing astrophysical phenomena, helping us search for and probe some of the most extreme conditions presented across our Universe - such as gravitational waves.

The Galactic-scale Detector

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. Credit: Rami Mandow.

Astronomers have found pulsars located across the Milky Way Galaxy and even detected them in our neighbouring satellite galaxies, the Small and Large Magellanic Clouds. Beyond this, extra-galactic pulsars are much harder to come by - they would most certainly exist, but their signals would be too hard to detect across such vast distances. 

When we plot the distribution of the Milky Way’s Galactic pulsars, we find that most of them predominately reside in the Galactic Plane - which is expected, given that pulsars form as a result of stellar supernovae, and most stellar objects reside in this plane. That’s not to say we don’t find them at high Galactic latitudes - these pulsars are very likely to have travelled to their off-plane locations over billions of years as a result of the natal kick they received during supernova events. The distribution of pulsars across the Galaxy (including above and below the Galactic plane) opens up the opportunity to use pulsars, and in particular, millisecond pulsars in a configuration known as a pulsar timing array or PTA. 

PTAs are a pulsar astronomer’s way of building a detector as big as the Galaxy itself. Not physically of course. As noted, millisecond pulsars are extremely stable, clock-like rotators, which can be measured over the long term for any anomalies. As we know the P-dot (slow-down rate) of these objects, we can also predict what their period will be into the future - which makes for interesting science, when comparing the predicted value vs. the observed value. 

As these cosmic clocks tick away any anomalies in their signal could be further investigated to determine if it might be caused by intrinsic properties of the millisecond pulsar (such as magnetospheric events), a product of the signal propagation through the interstellar medium, or potentially something more exciting.

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.

There are several PTA teams around the world that are monitoring sets of millisecond pulsars for a range of science objectives. The four main teams include the Parkes Pulsar Timing Array (PPTA) project, the North American Nanohertz Observatory for Gravitational Waves group (NANOGrav), the European Pulsar Timing Array (EPTA) project, and the Indian Pulsar Timing Array (InPTA) group. Additionally, there are emerging PTAs, such as the Chinese Pulsar Timing Array (CPTA) project and the South African-based MeerTIME project. Each project uses one or more radio telescopes (of a variety of sizes) to observe millisecond pulsars across a range of radio frequencies. In Australia, the Parkes radio telescope is used. Collectively, the main PTA members (PPTA, NANOGrav, EPTA, InPTA) work under the umbrella international collaboration known as the International Pulsar Timing Array (IPTA) project. 

The Galactic-scale detector can be analogised as a giant interferometer with many arms - similar to the LIGO/VIRGO/KAGRA interferometers that use lasers in tunnels that stretch for kilometres. Instead of mirrors for test masses, PTAs use millisecond pulsars, and instead of lasers, they utilise the beams of pulses that travel between the pulsar and the Earth. As these millisecond pulsars are stable, any variation observed in the timing of their periodic signals could be indicative of unmodelled phenomena, which can lead to really interesting science. 

Each of these PTAs monitors at least 20+ millisecond pulsars at a regular cadence, pointing in a variety of directions across the Galaxy to account for any effects of Earth’s atmosphere, the interstellar medium, individual pulsar noise, orbital variations in binary systems, and so on.

Science and Applications of Pulsar Timing Arrays

The stochastic background of gravitational waves across the Universe contains the signature of inspiral supermassive black hole binaries. Pulsar timing arrays are designed to tune into the frequency of this background. Credit: Mingarelli et al. 2022./Science.

Astronomers can utilise PTAs for a number of different science objectives, and applications - which can include studying individual millisecond pulsar binary systems, the population of millisecond pulsars, or a configuration of millisecond pulsars observed by the PTA. The main goal, however, is to use them to detect low-frequency (nanohertz regime) gravitational waves. 

Gravitational waves are distortions of space-time that are created by accelerating masses (due to changes in their quadrupole moment in time), radiating away from sources at the speed of light. Whilst all accelerating masses produce gravitational waves, it is only the largest masses (such as those found in binary systems featuring neutron stars or black holes) that can be detected by our current technologies. Gravitational waves also exhibit along a spectrum (similar to the electromagnetic spectrum) based on the frequency of the observed waves, which is a result of the masses that produce them. 

The first indirect evidence of gravitational waves came from a pulsar-neutron star binary system, in which precision timing of the pulsar’s signal revealed that the distance between the two objects was shrinking as they orbited each other. Einstein’s General Relativity predicted this (accurately), which could be explained if the system was radiating gravitational waves. 

Direct evidence finally arrived in 2015, when the LIGO instruments confirmed the first observational evidence of a gravitational wave signal. These were generated by stellar-mass compact binaries, with wave periods on the order of seconds and minutes. 

PTAs are looking for a much lower frequency of gravitational waves, one that is generated by masses many billions of times that of the Sun. These are the supermassive black hole binaries that inspiral as entire galaxies merge and collide. The wave periods of these events is on the order of decades - which is why no terrestrial-based interferometer would be able to make these detections. 

As these gravitational waves pass by the millisecond pulsars and/or the Earth, they create a small variation in the distance between each pulsar and the observatory, which manifests in a tiny change that is detected in the timed signal. By having a number of different millisecond pulsars observed, astronomers exploit a spatial correlation metric that forms part of the PTA, as a function of the angular sky separation of each system. This is the true signature of a nanohertz-regime gravitational wave background, and this correlation is called the Hellings-Downs Correlation. 

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.

As yet, PTA projects have not made any detections of these types of gravitational waves, but there is some evidence to suggest that we might be getting close to this. Caution must still be applied, as this common signal can also be easily confused. However, when a PTA makes a clear detection of the Hellings-Downs correlation, and this can be verified - then the results can be confirmed. 

The confirmation of a nanohertz frequency gravitational wave will start to provide estimations on the number of supermassive black hole binaries (and we could compare this to observations made through the electromagnetic spectrum), the density of power of the background noise, as a function of frequency, and the different frequencies at which all these gravitational waves are resonating in. A wealth of information that can teach us about the cosmological history of galaxy mergers across our Universe’s past. Additionally, supermassive black hole binaries might not be the only sources of these types of gravitational waves - they could also reveal information about cosmological phase transitions, cosmic strings, and even primordial gravitational waves from inflation - allowing scientists to probe very early epochs in the Universe’s history. 

It has also been suggested that PTAs can contribute to real-world applications, such as using them to develop Galactic GPS - a potential solution for positioning, navigation and timing as humans start to explore regions of the Solar System, where our terrestrial-based GPS network is null and void. 

But pulsar observations are not limited to PTAs and searching for these low-frequency gravitational waves. The ongoing observations of these systems can be used for relativistic studies such as precisely measuring orbital decay, Shapiro and Einstein delay and precession of perihelion and finding evidence of frame-dragging. Pulsar have been used to find the first exoplanets outside our Solar System, with a handful more discovered since. Some millisecond pulsars also devour and ablate their companions (known as spider pulsars) and studying these systems reveals interesting science of what happens when an object, like a companion star, strays too close to a pulsar - being subjected to its powerful winds and radiation. 

The propagation of pulsar signals (especially when comparing multiple pulsars, like a PTA set) through the interstellar medium has also allowed astronomers to measure the magnetic field of the Milky Way Galaxy, based on the electron column density along the signal line of sight. Closer to home, a similar analysis can be conducted on pulsar signals that travel through the Solar System and are subjected to the solar wind. Even variations in Earth’s ionosphere (which can be affected by solar activity) can be measured using signals from pulsars as they travel through our atmosphere and to our radio observatories. 

In the next instalment of this series, we'll be looking into the low-frequency gravitational wave background - what this is, how it forms part of a larger spectrum, and what happens when we finally detect it.


Video credit: NASA