Cosmic lighthouses and continuous gravitational waves

The detection of gravitational waves revolutionised the way we study the Universe, allowing us to ‘listen’ to some of the most violent events in the Universe: collisions between black holes and neutron stars. We have seen more than 90 of these events since 2015. These sources produce a particular type of gravitational-wave, they are short in duration and we have a good understanding of what the signal should look like.  

But there are more types of gravitational waves and sources out there that are permeating across the Universe, each with its own unique signature and frequency.

You can describe gravitational-wave signals as follows: transient (short duration) OR persistent (long duration), and modelled OR unmodelled. The signals we have detected so far are transient and well modelled, but researchers are actively looking for other types of gravitational waves. An area where there is a lot of work, including by AUS-based researchers, is the search for continuous gravitational waves.

The hunt for continuous gravitational waves is an ongoing one, and as the name suggests, these signals are persistent and present as a dull roar, a continuous hum in the background noise. One possible source of these signals are from rapidly rotating neutron stars in accreting binary systems that have stellar companions similar in mass to our Sun.  

Neutron stars are one of the densest objects in the universe with a coffee mug of neutron star matter weighing as much as Mount Everest. When we consider a neutron star in an accreting system, they are in a binary with a low mass companion such as a regular star, like the Sun in the latter stages of its life, when it has ballooned up to enormous radii. There is also matter being transferred from the low mass star to the neutron star via an accretion disk. From this process we get a pile of matter on the neutron star to create small mountains, and by small I mean only a few centimetres in height. As the neutron star spins this mountain creates gravitational waves, thanks to the anistropic effect this tiny structure has, on a near perfect sphere, that have twice the spin frequency source.

But why did we expect to see gravitational waves from accreting neutron stars in the first place?

It is because these neutron stars are not spinning fast enough. Theory suggests that neutron stars can spin up to speeds of ~1000 times per second without breaking apart. However, pretty much all the neutron stars that are in accreting systems are spinning ~100-700 times per second. Something must be preventing these stars from spinning up; the culprit is thought to be gravitational waves.

When matter accretes onto the neutron star, the star itself spins up, and so the more matter that piles up on the neutron star, the faster it should spin due to the transfer of angular momentum. But we do not see neutron stars in these systems spinning much faster than 700 times per second. Something must transfer angular momentum away from the source: and here is where we think that a possible method is via the emission of gravitational waves from a rapidly rotating neutron star that is not perfectly round. 

The faster matter is transferred onto the neutron star, the more angular momentum it gains, and therefore the larger the gravitational waves produced to transfer away the angular momentum. We can tell if a source has a high accretion rate based on how bright the source is in X-ray emission: the brighter the source, the higher the accretion rate.

So what makes a promising continuous-wave candidate? Firstly, an accreting neutron star, and secondly, a very bright X-ray source.

Two of the most promising candidates under this hypothesis are low mass X-ray binary (LMXB) systems Scorpius X-1 (Sco X-1) and Cygnus X-2 (Cyg X-2); not to be confused with Cygnus X-1 which is a high mass X-ray binary that contains a black hole instead of a neutron star.

Sco X-1 and Cyg X-2 are two of the brightest sources in our sky, with Sco X-1 only second to our Sun. Not only are these sources expected to produce gravitational waves, their orbital properties such as the orbital period, and separation between the neutron star and its companion are well known. Tight constraints on the properties of these sources are needed to search for continuous gravitational waves since the frequency of the signal is modulated by the movement of the neutron star in its orbit. If there is little uncertainty in these orbital parameters then it is easier to find the frequency of the gravitational-wave signal.  

But we have a problem… we actually do not know how fast these sources are spinning.

The spin frequency of the neutron star is directly related to the frequency of the continuous gravitational waves it is expected to emit. If we have no constraint on this parameter, finding the gravitational-wave signal is very difficult. So, how do we find out how fast these sources are spinning? We can search for X-ray pulsations from these sources.

For accreting neutron stars, matter (in the form of a hot plasma) is channelled from the accretion disc and onto the neutron star via their magnetic fields, especially where the field lines are open, like at the magnetic poles. This creates hot spots on the neutron star's surface which emit X-rays as the neutron star spins, and if the X-ray emission crosses our line-of-sight, we will see this as periodic pulses of X-rays from the source, similar to flashes of light we see from a lighthouse. The detection of these X-ray pulsations immediately reveals to us the spin frequency of these sources.  

In my latest publication on work in collaboration with Dr Karl Wette (Australian National University), Assoc. Prof. Duncan Galloway (Monash University) and Dr Chris Messenger (University of Glasgow), I searched for X-ray pulsations Sco X-1 and Cyg X-2. Note, searches for X-ray pulsations and continuous gravitational waves have similar difficulties; we need to understand and account for the orbital motion of the neutron star in its binary system.  

To make these searches feasible we used a process involving a special technique that chops up the data into smaller segments, searches for a periodic increase in X-ray emission in each segment, and then stacked these segments to increase the power of any signal we detect. Given the neutron star is accelerating in its orbit as it goes around in an almost perfect circle, by chopping the segments of data up we can assume the acceleration of the object in the orbit is pretty much the same for small portions of the orbit, making our correction for the orbital motion less computationally expensive.

I reduced and processed over 1000 hours of X-ray data collected by the Rossi X-ray Timing Explorer instrument (vale 1995 - 2012). This instrument had the high timing resolution needed to detect pulses on the order of 1-10 milliseconds. The search required a total of ~500 hours of computational time on the OzSTAR supercomputer located at Swinburne University.

And here’s a fun fact about Sco X-1 - it is such an extremely bright source (more than 100,000 X-ray photon counts per second) that special modes and observations techniques needed to be used to collect the data using the RXTE, including recording data with the instrument pointing slightly offset the source!

Unfortunately, we did not find any clear evidence of pulsations from these LMXB sources, but there are a number of reasons why this could be: these sources could have very weak magnetic fields that would not be able to channel material to produce detectable X-ray pulsations, or the pulsations may not happen all the time which would be difficult to detect with current search methods.  

Unlike Cyg X-2, Sco X-1 is not a confirmed neutron star, so there is some possibility it could be a black hole, meaning that it would not produce X-ray pulsations - since black holes don’t actually have a physical surface, but rather an arbitrary boundary in space-time, known as the event horizon (from which no information could escape).

Our analysis does find the best limits so far on how bright these X-ray pulsations could be if they did occur. Our results seem to suggest that neutron stars cannot maintain mountains of matter under their immense gravity. Future work with better search techniques may be able to improve these limits.