# Eclipses of continuous gravitational waves as a probe of stellar structure

Understanding how stars work is a fundamental problem in astrophysics. We can’t open up a star to investigate its inner workings, which makes it difficult to test our models. Over the years, we have developed several ways to sneak a peek into what must be happening inside stars, such as by measuring solar neutrinos, or using asteroseismology to measure how sounds travels through a star. In this paper, we propose a new way to examine the hearts of stars using gravitational waves.

Gravitational waves interact very weakly with stuff. Whereas light gets blocked by material (meaning that we can’t see deeper than a star’s photosphere), gravitational waves will happily travel through pretty much anything. This property means that gravitational waves are hard to detect, but it also means that there’ll happily pass through an entire star. While the material that makes up a star will not affect the passing of a gravitational wave, its gravity will. The mass of a star can lead to gravitational lensing and a slight deflecting, magnification and delaying of a passing gravitational wave. If we can measure this lensing, we can reconstruct the mass of star, and potentially map out its internal structure.

Two types of eclipse: the eclipse of a distant gravitational wave (GW) source by the Sun, and gravitational waves from an accreting millisecond pulsar (MSP) eclipsed by its companion. Either scenario could enable us to see gravitational waves passing through a star. Figure 2 of Marchant et al. (2020).

We proposed looking at gravitational waves for eclipsing sources—where a gravitational wave source is behind a star. As the alignment of the Earth (and our detectors), the star and the source changes, the gravitational wave will travel through different parts of the star, and we will see a different amount of lensing, allowing us to measure the mass of the star at different radii. This sounds neat, but how often will we be lucky enough to see an eclipsing source?

To date, we have only seen gravitational waves from compact binary coalescences (the inspiral and merger of two black holes or neutron stars). These are not a good source for eclipses. The chances that they travel through a star is small (as space is pretty empty) [bonus note]. Furthermore, we might not even be able to work out that this happened. The signal is relatively short, so we can’t compare the signal before and during an eclipse. Another type of gravitational wave signal would be much better: a continuous gravitational wave signal.

Probability of observing at least one eclipsing source amongst a number of observed sources. Compact binary coalescences (CBCs, shown in purple) are the most rare, continuous gravitational waves (CGWs) eclipsed by the Sun (red) or by a companion (red) are more common. Here we assume companions are stars about a tenth the mass of the neutron star. The number of neutron stars with binary companions is estimated using the COSMIC population synthesis code. Results are shown for eclipses where the gravitational waves get within distance $b$ of the centre of the star. Figure 1 of Marchant et al. (2020).

Continuous gravitational waves are produced by rotating neutron stars. They are pretty much perfect for searching for eclipses. As you might guess from their name, continuous gravitational waves are always there. They happily hum away, sticking to pretty much the same note (they’d get pretty annoying to listen to). Therefore, we can measure them before, during and after an eclipse, and identify any changes due to the gravitational lensing. Furthermore, we’d expect that many neutron stars would be in close binaries, and therefore would be eclipsed by their partner. This would happen each time they orbit, potentially giving us lots of juicy information on these stars. All we need to do is measure the continuous gravitational wave…

The effect of the gravitational lensing by a star is small. We performed detailed calculations for our Sun (using MESA), and found that for the effects to be measurable you would need an extremely loud signal. A signal-to-noise ratio would need to be hundreds during the eclipse for measurement precision to be good enough to notice the imprint of lensing. To map out how things changed as the eclipse progressed, you’d need signal-to-noise ratios many times higher than this. As an eclipse by the Sun is only a small fraction of the time, we’re going to need some really loud signals (at least signal-to-noise ratios of 2500) to see these effects. We will need the next generation of gravitational wave detectors.

We are currently thinking about the next generation of gravitational wave detectors [bonus note]. The leading ideas are successors to LIGO and Virgo: detectors which cover a large range of frequencies to detect many different types of source. These will be expensive (billions of dollars, euros or pounds), and need international collaboration to finance. However, I also like the idea of smaller detectors designed to do one thing really well. Potentially these could be financed by a single national lab. I think eclipsing continuous waves are the perfect source for this—instead of needing a detector sensitive over a wide frequency range, we just need to be sensitive over a really narrow range. We will be able to detect continuous waves before we are able to see the impact of eclipses. Therefore, we’ll know exactly what frequency to tune for. We’ll also know exactly when we need to observe. I think it would be really awesome to have a tunable narrowband detector, which could measure the eclipse of one source, and then be tuned for the next one, and the next. By combining many observations, we could really build up a detailed picture of the Sun. I think this would be an exciting experiment—instrumentalists, put your thinking hats on!

Let’s reach for(the centres of) the stars.

arXiv: 1912.04268 [astro-ph.SR]
Journal: Physical Review D; 101(2):024039(15); 2020
Data release: Eclipses of continuous gravitational waves as a probe of stellar structure
CIERA story: Using gravitational waves to see inside stars
Why does the sun really shine? The Sun is a miasma of incandescent plasma

### Bonus notes

#### Silver lining

Since signals from compact binary coalescences are so unlikely to be eclipsed by a star, we don’t have to worry that our measurements of the source property are being messed up by this type of gravitational lensing distorting the signal. Which is nice.

#### Prospects with LISA

If you were wondering if we could see these types of eclipses with the space-based gravitational wave observatory LISA, the answer is sadly no. LISA observes lower frequency gravitational waves. Lower frequency means longer wavelength, so long in fact that the wavelength is larger than the size of the Sun! Since the size of the Sun is so small compared to the gravitational wave, it doesn’t leave a same imprint: the wave effectively skips over the gravitational potential.

# First low frequency all-sky search for continuous gravitational wave signals

It is the time of year for applying for academic jobs and so I have been polishing up my CV. In doing so I spotted that I had missed the publication of one of the LIGO Scientific–Virgo Collaboration papers. In my defence, it was published the week of 8–14 February, which saw the publication of one or two other papers [bonus note]. The paper I was missing is on a search for continuous gravitational waves.

Continuous gravitational waves are near constant hums. Unlike the chirps of coalescing binaries, continuous signals are always on. We think that they could be generated by rotating neutron stars, assuming that they are not perfectly smooth. This is the first search to look for continuous waves from anywhere on the sky with frequencies below 50 Hz. The gravitational-wave frequency is twice the rotational frequency of the neutron star, so this is the first time we’ve looked for neutron stars spinning slower than 25 times per second (which is still pretty fast, I’d certainly feel more than a little queasy). The search uses data from the second and fourth Virgo Science Runs (VSR2 and VSR4): the detector didn’t behave as well in VSR3, which is why that data isn’t used.

The frequency of a rotating neutron star isn’t quite constant for two reasons. First, as the Earth orbits around the Sun it’ll move towards and away from the source. This leads to the signal being Doppler shifted. For a given position on the sky, this can be corrected for, and this is done in the search. Second, the neutron star will slow down (a process known as spin-down) because it looses energy and angular momentum. There are various processes that could slow a neutron star, emitting gravitational waves is one, some form of internal sloshing around is another which could also cause things to speed up, or perhaps some braking from its magnetic field. We’re not too sure exactly how quickly spin down will happen, so we search over a range of possible values from $-1.0\times10^{-10}~\mathrm{Hz\,s^{-1}}$ to $+1.5\times10^{-11}~\mathrm{Hz\,s^{-1}}$.

The particular search technique used is called FrequencyHough. This chops the detector output into different chunks of time. In each we calculate how much power is at each frequency. We then look for a pattern, where we can spot a signal across different times, allowing for some change from spin-down. Recognising the track of a signal with a consistent frequency evolution is done using a Hough transform, a technique from image processing that is good at spotting lines.

The search didn’t find any signals. This is not too surprising. Therefore, we did the usual thing of setting some upper limits. The plot below shows 90% confidence limits (that is where we’d expect to detect 9/10 signals) on the signal amplitude at different frequencies.

90% confidence upper limits on the gravitational-wave strain at different frequencies. Each dot is for a different 1 Hz band. Some bands are noisy and feature instrumental artefacts which have to be excluded from the analysis, these are noted as the filled (magenta) circles. In this case, the upper limit only applies to the part of the band away from the disturbance. Figure 12 of Aasi et al. (2016).

Given that the paper only reports a non-detection, it is rather lengthy. The opening sections do give a nice introduction to continuous waves and how we hunt for them, so this might be a good paper is you’re new to the area but want to learn some of the details. Be warned that it does use $\jmath = \sqrt{-1}$ for some reason. After the introduction, it does get technical, so it’s probably only for insomniacs. However, if you like a good conspiracy and think we might be hiding something, the appendices go through all the details of removing instrumental noise and checking outliers found by the search.

In summary, this was the first low-frequency search for continuous gravitational waves. We didn’t find anything in the best data from the initial detector era, but the advanced detectors will be much more sensitive to this frequency range. Slowly rotating neutron stars can’t hide forever.

arXiv: 1510.03621 [astro-ph.IM]
Journal: Physical Review D; 93(4):042007(25); 2016
Science summary: First search for low frequency continuous gravitational waves emitted by unseen neutron stars
Greatest regret:
I didn’t convince the authors to avoid using “air quotes” around jargon.

### Bonus note

#### Better late than never

I feel less guilty about writing a late blog post about this paper as I know that it has been a long time in the making. As a collaboration, we are careful in reviewing our results; this can sometimes lead to delays in announcing results, but hopefully means that we get the right answer. This paper took over three years to review, a process which included over 85 telecons!

# Comprehensive all-sky search for periodic gravitational waves in the sixth science run LIGO data

The most recent, and most sensitive, all-sky search for continuous gravitational waves shows no signs of a detection. These signals from rotating neutron stars remain elusive. New data from the advanced detectors may change this, but we will have to wait a while to find out. This at least gives us time to try to figure out what to do with a detection, should one be made.

### New years and new limits

The start of the new academic year is a good time to make resolutions—much better than wet and windy January. I’m trying to be tidier and neater in my organisation. Amid cleaning up my desk, which is covered in about an inch of papers, I uncovered this recent Collaboration paper, which I had lost track of.

The paper is the latest in the continuous stream of non-detections of continuous gravitational waves. These signals could come from rotating neutron stars which are deformed or excited in some way, and the hope that from such an observation we could learn something about the structure of neutron stars.

The search uses old data from initial LIGO’s sixth science run. Searches for continuous waves require lots of computational power, so they can take longer than even our analyses of binary neutron star coalescences. This is a semi-coherent search, like the recent search of the Orion spur—somewhere between an incoherent search, which looks for signal power of any form in the detectors, and a fully coherent search, which looks for signals which exactly match the way a template wave evolves [bonus note]. The big difference compared to the Orion spur search, is that this one looks at the entire sky. This makes it less sensitive in those narrow directions, but means we are not excluding the possibility of sources from other locations.

Artist’s impression of the local part of the Milky Way. The yellow cones mark the extent of the Orion Spur spotlight search, and the pink circle shows the equivalent sensitivity of this all-sky search. Green stars indicate known pulsars. Original image: NASA/JPL-Caltech/ESO/R. Hurt.

The search identified 16 outliers, but an examination of all of these showed they could be explained either as an injected signal or as detector noise. Since no signals were found, we can instead place some upper limits on the strength of signals.

The plot below translates the calculated upper limits (above which there would have been a ~75%–95% chance of us detected the signal) into the size of neutron star deformations. Each curve shows the limits on detectable signals at different distance, depending upon their frequency and the rate of change of their frequency. The dotted lines show limits on ellipticity $\varepsilon$, a measure of how bumpy the neutron star is. Larger deformations mean quicker changes of frequency and produce louder signals, therefore they can can be detected further away.

Range of the PowerFlux search for rotating neutron stars assuming that spin-down is entirely due to gravitational waves. The solid lines show the upper limits as a function of the gravitational-wave frequency and its rate of change; the dashed lines are the corresponding limits on ellipticity, and the dotted line marks the maximum searched spin-down. Figure 6 of Abbott et al. (2016).

Neutron stars are something like giant atomic nuclei. Figuring the properties of the strange matter that makes up neutron stars is an extremely difficult problem. We’ll never be able to recreate such exotic matter in the laboratory. Gravitational waves give us a rare means of gathering experimental data on how this matter behaves. However, exactly how we convert a measurement of a signal into constraints on the behaviour of the matter is still uncertain. I think that making a detection might only be the first step in understanding the sources of continuous gravitational waves.

arXiv: 1605.03233 [gr-qc]
Journal: Physical Review D; 94(4):042002(14); 2016
To attempt to grow a beard. Beard stroking helps you think, right?

### Bonus note

#### The semi-coherent search

As the first step of this search, the PowerFlux algorithm looks for power that changes in frequency as expected for a rotating neutron star: it factors in Doppler shifting due to the motion of the Earth and a plausible spin down (slowing of the rotation) of the neutron star. As a follow up, the Loosely Coherent algorithm is used, which checks for signals which match short stretches of similar templates. Any candidates to make it through all stages of refinement are then examined in more detail. This search strategy is described in detail for the S5 all-sky search.

# Search of the Orion spur for continuous gravitational waves using a loosely coherent algorithm on data from LIGO interferometers

A cloudy bank holiday Monday is a good time to catch up on blogging. Following the splurge of GW150914 papers, I’ve rather fallen behind. Published back in February, this paper is a search for continuous-wave signals: the almost-constant hum produced by rapidly rotating neutron stars.

Continuous-wave searches are extremely computationally expensive. The searches take a while to do, which can lead to a delay before results are published [bonus note]. This is the result of a search using data from LIGO’s sixth science run (March–October 2010).

To detect a continuous wave, you need to sift the data to find a signal that present through all the data. Rotating neutron stars produce a gravitational-wave signal with a frequency twice their orbital frequency. This frequency is almost constant, but could change as the observation goes on because (i) the neutron star slows down as energy is lost (from gravitational waves, magnetic fields or some form of internal sloshing around); (ii) there is some Doppler shifting because of the Earth’s orbit around the Sun, and, possibly, (iii) the there could be some Doppler shifting because the neutron star is orbiting another object. How do you check for something that is always there?

There are two basic strategies for spotting continuous waves. First, we could look for excess power in a particular frequency bin. If we measure something in addition to what we expect from the detector noise, this could be a signal. Looking at the power is simple, and so not too expensive. However, we’re not using any information about what a real signal should look like, and so it must be really loud for us to be sure that it’s not just noise. Second, we could coherently search for signals using templates for the expected signals. This is much more work, but gives much better sensitivity. Is there a way to compromise between the two strategies to balance cost and sensitivity?

This paper reposts results of a loosely coherent search. Instead of checking how well the data match particular frequencies and frequency evolutions, we average over a family of similar signals. This is less sensitive, as we get a bit more wiggle room in what would be identified as a candidate, but it is also less expensive than checking against a huge number of templates.

We could only detect continuous waves from nearby sources: neutron stars in our own Galaxy. (Perhaps 0.01% of the distance of GW150914). It therefore makes sense to check nearby locations which could be home to neutron stars. This search narrows its range to two directions in the Orion spur, our local band with a high concentration of stars. By focussing in on these spotlight regions, we increase the sensitivity of the search for a given computational cost. This search could possibly dig out signals from twice as far away as if we were considering all possible directions.

Artist’s impression of the local part of the Milky Way. The Orion spur connects the Perseus and Sagittarius arms. The yellow cones mark the extent of the search (the pink circle shows the equivalent all-sky sensitivity). Green stars indicate known pulsars. Original image: NASA/JPL-Caltech/ESO/R. Hurt.

The search found 70 interesting candidates. Follow-up study showed that most were due to instrumental effects. There were three interesting candidates left after these checks, none significant enough to be a detection, but still worth looking at in detail. A full coherent analysis was done for these three candidates. This showed that they were probably caused by noise. We have no detections

arXiv: 1510.03474 [gr-qc]
Journal: Physical Review D; 93(4):042006(14); 2016
Science summary: Scouting our Galactic neighborhood
Other bank holiday activities:
Scrabble

Bank holiday family Scrabble game. When thinking about your next turn, you could try seeing if your letters match a particular word (a coherent search which would get you the best score, but take ages), or just if your letters jumble together to make something word-like (an incoherent search, that is quick, but may result in lots of things that aren’t really words).

### Bonus note

#### Niceness

The Continuous Wave teams are polite enough to wait until we’re finished searching for transient gravitational-wave signals (which are more time sensitive) before taking up the LIGO computing clusters. They won’t have any proper results from O1 just yet.

# Searches for continuous gravitational waves from nine young supernova remnants

The LIGO Scientific Collaboration is busy analysing the data we’re currently taking with Advanced LIGO at the moment. However, the Collaboration is still publishing results from initial LIGO too. The most recent paper is a search for continuous waves—signals that are an almost constant hum throughout the observations. (I expect they’d be quite annoying for the detectors). Searching for continuous waves takes a lot of computing power (you can help by signing up for Einstein@Home), and is not particularly urgent since the sources don’t do much, hence it can take a while for results to appear.

### Supernova remnants

Massive stars end their lives with an explosion, a supernova. Their core collapses down and their outer layers are blasted off. The aftermath of the explosion can be beautiful, with the thrown-off debris forming a bubble expanding out into the interstellar medium (the diffuse gas, plasma and dust between stars). This structure is known as a supernova remnant.

The youngest known supernova remnant, G1.9+0.3 (it’s just 150 years old), observed in X-ray and optical light. The ejected material forms a shock wave as it pushes the interstellar material out of the way. Credit: NASA/CXC/NCSU/DSS/Borkowski et al.

At the centre of the supernova remnant may be what is left following the collapse of the core of the star. Depending upon the mass of the star, this could be a black hole or a neutron star (or it could be nothing). We’re interested in the case it is a neutron star.

### Neutron stars

Neutron stars are incredibly dense. One teaspoon’s worth would have about as much mass as 300 million elephants. Neutron stars are like giant atomic nuclei. We’re not sure how matter behaves in such extreme conditions as they are impossible to replicate here on Earth.

If a neutron star rotates rapidly (we know many do) and has an uneven or if there are waves in the the neutron star that moves lots of material around (like Rossby waves on Earth), then it can emit continuous gravitational waves. Measuring these gravitational waves would tell you about how bumpy the neutron star is or how big the waves are, and therefore something about what the neutron star is made from.

Neutron stars are most likely to emit loud gravitational waves when they are young. This is for two reasons. First, the supernova explosion is likely to give the neutron star a big whack, this could ruffle up its surface and set off lots of waves, giving rise to the sort of bumps and wobbles that emit gravitational waves. As the neutron star ages, things can quiet down, the neutron star relaxes, bumps smooth out and waves dissipate. This leaves us with smaller gravitational waves. Second, gravitational waves carry away energy, slowing the rotation of the neutron star. This also means that the signal gets quieter (and harder) to detect as the  neutron star ages.

Since young neutron stars are the best potential sources, this study looked at nine young supernova remnants in the hopes of finding continuous gravitational waves. Searching for gravitational waves from particular sources is less computationally expensive than searching the entire sky. The search included Cassiopeia A, which had been previously searched in LIGO’s fifth science run, and G1.9+0.3, which is only 150 years old, as discovered by Dave Green. The positions of the searched supernova remnants are shown in the map of the Galaxy below.

The nine young supernova remnants searched for continuous gravitational waves. The yellow dot marks the position of the Solar System. The green markers show the supernova remnants, which are close to the Galactic plane. Two possible positions for Vela Jr (G266.2−1.2) were used, since we are uncertain of its distance. Original image: NASA/JPL-Caltech/ESO/R. Hurt.

### Gravitational-wave limits

No gravitational waves were found. The search checks how well template waveforms match up with the data. We tested that this works by injecting some fake signals into the data.  Since we didn’t detect anything, we can place upper limits on how loud any gravitational waves could be. These limits were double-checked by injecting some more fake signals at the limit, to see if we could detect them. We quoted 95% upper limits, that is where we expect that if a signal was present we could see it 95% of the time. The results actually have a small safety margin built in, so the injected signals were typically found 96%–97% of the time. In any case, we are fairly sure that there aren’t gravitational waves at or above the upper limits.

These upper limits are starting to tell us interesting things about the size of neutron-star bumps and waves. Hopefully, with data from Advanced LIGO and Advanced Virgo, we’ll actually be able to make a detection. Then we’ll not only be able to say that these bumps and waves are smaller than a particular size, but they are this size. Then we might be able to figure out the recipe for making the stuff of neutron stars (I think it might be more interesting than just flour and water).

arXiv: 1412.5942 [astro-ph.HE]
Journal: Astrophysical Journal; 813(1):39(16); 2015
Science summary: Searching for the youngest neutron stars in the Galaxy
Favourite supernova remnant:
Cassiopeia A

# Directed search for gravitational waves from Scorpius X-1 with initial LIGO

new paper from the LIGO Scientific Collaboration has snuck out. It was actually published back in March but I didn’t notice it, nearly risking my New Year’s resolution. This is another paper on continuous waves from rotating neutron stars, so it’s a little outside my area of expertise. However, there is an official science summary written by people who do know what they’re talking about.

The paper looks at detecting gravitational waves from a spinning neutron star. We didn’t find any. However, we have slightly improved our limit for how loud they need to be before we would have detected them, which is nice.

Neutron stars can rotate rapidly. They can be spun up if they accrete material from a disc orbiting them. If they neutron star has an asymmetry, if it has a little bump, as it rotates it emits gravitational waves. The gravitational waves carry away angular momentum, which should spin down the neutron star. This becomes more effective as the angular velocity increases. At some point you expect that the spin-up effect from accretion balances the spin-down effect of gravitational waves and you are left with a neutron star spinning at pretty constant velocity. We have some evidence that this might happen, as low-mass X-ray binaries seem to have their spins clustered in a small range of frequencies. Assuming we do have this balance, we are looking for a continuous gravitational wave with constant frequency, a rather dull humming.

Scorpius X-1 is the brightest X-ray source in the sky. It contains a neutron star, so it’s a good place to check for gravitational waves from neutron stars. In this case, we’re using data from initial LIGO’s fifth science run (4 November 2005–1 October 2007). This has been done before, but this paper implements some new techniques. I expect that the idea is to test things out ahead of getting data with Advanced LIGO.

Swift X-ray Telescope image of Scorpius X-1 and the X-ray nova J1745-26 (a stellar-mass black hole), along with the scale of moon, as they would appear in the field of view from Earth. Credit: NASA/Goddard Space Flight Center/S. Immler and H. Krimm.

A limit of 10 days’ worth of data is used, as this should be safely within the time taken for the rotational frequency to fluctuate by a noticeable amount due to variation in the amount of accretion. In human terms, that would be the time between lunch and dinner, where your energy levels change because of how much you’ve eaten. They picked data from 21–31 August 2007, as their favourite (it has the best noise performance over the frequency range of interest), and used two other segments to double-check their findings. We’d be able to use more data if we knew how the spin wandered with time.

We already know a lot about Scorpius X-1 from electromagnetic observations (like where it is and its orbital parameters). We don’t know its spin frequency, but we might have an idea about the orientation of its spin if this coincides with radio jets. The paper considers two cases: one where we don’t know anything about the spin orientation, and one where we use information from the jets. The results are similar in both cases.

As the neutron star orbits in its binary system, it moves back and forth which Doppler shifts the gravitational waves. This adds a little interest to the hum, spreading it out over a range of frequencies. The search looks for gravitational waves over this type of frequency range, which they refer to as sidebands.

There are a few events where it looks like there is something, but after carefully checking, these look like they are entirely consistent with noise. I guess this isn’t too surprising. Since they didn’t detect anything, they can only impose an upper limit. This is stronger than the previous upper limit, but only by a factor of about 1.4. This might not sound too great, but the previous analysis used a year of data, whereas this only used 10 days. This method therefore saves a lot on computational time.

The result of the paper is quite nice, but not too exciting. If it were a biscuit, it’d probably be a rich tea. It’s nice to have, but it’s not a custard cream.

arXiv: 1412.5942 [astro-ph.HE]
Journal: Physical Review D; 91(6):062008(20); 2015
Science summary: Combing Initial LIGO Data for the Potentially Strong Continuous Wave Emitter Scorpius X-1
Biscuit rating:
Rich tea

# Narrow-band search of continuous gravitational-wave signals from Crab and Vela pulsars in Virgo VSR4 data

## Collaboration papers

I’ve been a member of the LIGO Scientific Collaboration for just over a year now. It turns out that designing, building and operating a network of gravitational-wave detectors is rather tricky, maybe even harder than completing Super Mario Bros. 3, so it takes a lot of work. There are over 900 collaboration members, all working on different aspects of the project. Since so much of the research is inter-related, certain papers (such as those that use data from the instruments) written by collaboration members have to include the name of everyone who works (at least half the time) on LIGO-related things. After a year in the collaboration, I have now levelled up to be included in the full author list (if there was an initiation ritual, I’ve suppressed the memory). This is weird: papers appear with my name on that I’ve not actually done any work for. It seems sort of like having to bring cake into your office on your birthday: you do have to share your (delicious) cupcakes with everyone else, but in return you get cake even when your birthday is nowhere near. Perhaps all those motivational posters where right about the value of teamwork? I do feel a little guilty about all the extra trees that will die because of people printing out these papers.

My New Year’s resolution was to write a post about every paper I have published. I am going to try to do the LIGO papers too. This should at least make sure that I actually read them all. There are official science summaries written by the people who did actually do the work, which may be better if you actually want an accurate explanation. My first collaboration paper is a joint publication of the LIGO and Virgo collaborations (even more sharing).

## Searching for gravitational waves from pulsars

Neutron stars are formed from the cores of dead stars. When a star’s nuclear fuel starts to run out, their core collapses. The most massive form black holes, the lightest (like our Sun) form white dwarfs, and the ones in the middle form neutron stars. These are really dense, they have about the same mass as our entire Sun (perhaps twice the Sun’s mass), but are just a few kilometres across. Pulsars are a type of neutron star, they emit a beam of radiation that sweeps across the sky as they rotate, sort of like a light-house. If one of these beams hits the Earth, we see a radio pulse. The pulses come regularly, so you can work out how fast the pulsar is spinning (and do some other cool things too).

The mandatory cartoon of a pulsar that everyone uses. The top part shows the pulsar and its beams rotating, and the bottom part shows the signal measured on Earth. We not really sure where the beams come from, it’ll be something to do with magnetic fields. Credit: M. Kramer

Because pulsars rotate really quickly, if they have a little bump on their surface, they can emit (potentially detectable) gravitational waves. This paper searches for these signals from the Crab and Vela pulsars. We know where these pulsars are, and how quickly they are rotating, so it’s possible to do a targeted search for gravitational waves (only checking the data for signals that are close to what we expect). Importantly, some wiggle room in the frequency is allowed just in case different parts of the pulsar slosh around at slightly different rates and so the gravitational-wave frequency doesn’t perfectly match what we’d expect from the frequency of pulses; the search is done in a narrow band of frequencies around the expected one. The data used is from Virgo’s fourth science run (VSR4). That was taken back in 2011 (around the time that Captain America was released). The search technique is new (Astone et al., 2014), it’s the first one that incorporates this searching in a narrow band of frequencies; I think the point was to test their search technique on real data before the advanced detectors start producing new data.

Composite image of Hubble (red) optical observations and Chandra (blue) X-ray observations of the Crab pulsar. The pulsar has a mass of 1.4 solar masses and rotates every 30 ms. Credit: Hester et al.

The pulsars emit gravitational waves continuously, they just keep humming as they rotate. The frequency will slow gradually as the pulsar loses energy. As the Earth rotates, the humming gets louder and quieter because the sensitivity of gravitational-wave detectors depends upon where the source is in the sky. Putting this all together gives you a good template for what the signal should look like, and you can see how well it fits the data. It’s kind of like trying to find the right jigsaw piece by searching for the one that interlocks best with those around it. Of course, there is a lot of noise in our detectors, so it’s like if the jigsaw was actually made out of jelly: you could get many pieces to fit if you squeeze them the right way, but then people wouldn’t believe that you’ve actually found the right one. Some detection statistics (which I don’t particularly like, but probably give a sensible answer) are used to quantify how likely it is that they’ve found a piece that fits (that there is a signal). The whole pipeline is tested by analysing some injected signals (artificial signals made to see if things work made both by adding signals digitally to the data and by actually jiggling the mirrors of the interferometer). It seems to do OK here.

Turning to the actual data, they very carefully show that they don’t think they’ve detected anything for either Vela or Crab. Of course, all the cool kids don’t detect gravitational waves, so that’s not too surprising.

This paper doesn’t claim a detection of gravitational waves, but it doesn’t stink like Zoidberg.

Having not detected anything, you can place an upper limit of the amplitude of any waves that are emitted (because if they were larger, you would’ve detected them). This amplitude can then be compared with what’s expected from the spin-down limit: the amplitude that would be required to explain the slowing of the pulsar. We know how the pulsars are slowing, but not why; it could be because of energy being lost to magnetic fields (the energy for the beams has to come from somewhere), it could be through energy lost as gravitational waves, it could be because of some internal damping, it could all be gnomes. The spin-down limit assumes that it’s all because of gravitational waves, you couldn’t have bigger amplitude waves than this unless something else (that would have to be gnomes) was pumping energy into the pulsar to keep it spinning. The upper limit for the Vela pulsar is about the same as the spin-down limit, so we’ve not learnt anything new. For the Crab pulsar, the upper limit is about half the spin-down limit, which is something, but not really exciting. Hopefully, doing the same sort of searches with data from the advanced detectors will be more interesting.

In conclusion, the contents of this paper are well described by its title:

• Narrow-band search: It uses a new search technique that is not restricted to the frequency assumed from timing pulses
• of continuous gravitational-wave signals: It’s looking for signals from rotating neutron stars (that just keep going) and so are always in the data
• from Crab and Vela pulsars: It considers two particular sources, so we know where in parameter space to look for signals
• in Virgo VSR4 data: It uses real data, but from the first generation detectors, so it’s not surprising it doesn’t see anything

It’s probably less fun that eating a jigsaw-shaped jelly, but it might be more useful in the future.

arXiv: 1410.8310 [gr-qc]
Journal: Physical Review D; 91(2):022004(15); 2015
Science summary: An Extended Search for Gravitational Waves from the Crab and Vela Pulsars
Percentage of paper that is author list: ~30%