# 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 for transient gravitational waves in coincidence with short-duration radio transients during 2007–2013

Gravitational waves give us a new way of observing the Universe. This raises the possibility of multimessenger astronomy, where we study the same system using different methods: gravitational waves, light or neutrinos. Each messenger carries different information, so by using them together we can build up a more complete picture of what’s going on. This paper looks for gravitational waves that coincide with radio bursts. None are found, but we now have a template for how to search in the future.

On a dark night, there are two things which almost everyone will have done: wondered at the beauty of the starry sky and wondered exactly what was it that just went bump… Astronomers do both. Transient astronomy is about figuring out what are the things which go bang in the night—not the things which make suspicious noises, but objects which appear (and usually disappear) suddenly in the sky.

Most processes in astrophysics take a looooong time (our Sun is four-and-a-half billion years old and is just approaching middle age). Therefore, when something happens suddenly, flaring perhaps over just a few seconds, you know that something drastic must be happening! We think that most transients must be tied up with a violent event such as an explosion. However, because transients are so short, it can difficult to figure out exactly where they come from (both because they might have faded by the time you look, and because there’s little information to learn from a blip in the first place).

Radio transients are bursts of radio emission of uncertain origin. We’ve managed to figure out that some come from microwave ovens, but the rest do seem to come from space. This paper looks at two types: rotating radio transients (RRATs) and fast radio bursts (FRBs). RRATs look like the signals from pulsars, except that they don’t have the characteristic period pattern of pulsars. It may be that RRATs come from dying pulsars, flickering before they finally switch off, or it may be that they come from neutron stars which are not normally pulsars, but have been excited by a fracturing of their crust (a starquake). FRBs last a few milliseconds, they could be generated when two neutron stars merge and collapse to form a black hole, or perhaps from a highly-magnetised neutron star. Normally, when astronomers start talking about magnetic fields, it means that we really don’t know what’s going on [bonus note]. That is the case here. We don’t know what causes radio transients, but we are excited to try figuring it out.

This paper searches old LIGO, Virgo and GEO data for any gravitational-wave signals that coincide with observed radio transients. We use a catalogue of RRATs and FRBs from the Green Bank Telescope and the Parkes Observatory, and search around these times. We use a burst search, which doesn’t restrict itself to any particular form of gravitational-wave; however, the search was tuned for damped sinusoids and sine–Gaussians (generic wibbles), cosmic strings (which may give an indication of how uncertain we are of where radio transients could come from), and coalescences of binary neutron stars or neutron star–black hole binaries. Hopefully the search covers all plausible options. Discovering a gravitational wave coincident with a radio transient would give us much welcomed information about the source, and perhaps pin down their origin.

Search results for gravitational waves coincident with radio transients. The probabilities for each time containing just noise (blue) match the expected background distribution (dashed). This is consistent with a non-detection.

The search discovered nothing. Results match what we would expect from just noise in the detectors. This is not too surprising since we are using data from the first-generation detectors. We’ll be repeating the analysis with the upgraded detectors, which can find signals from larger distances. If we are lucky, multimessenger astronomy will allow us to figure out exactly what needs to go bump to create a radio transient.

arXiv: 1605.01707 [astro-ph.HE]
Journal: Physical Review D; 93(12):122008(14); 2016
Science summary: Searching for gravitational wave bursts in coincidence with short duration radio bursts
Favourite thing that goes bump in the night: Heffalumps and Woozles [probably not the cause of radio transients]

### Bonus note

#### Magnetism and astrophysics

Magnetic fields complicate calculations. They make things more difficult to model and are therefore often left out. However, we know that magnetic fields are everywhere and that they do play important roles in many situations. Therefore, they are often invoked as an explanation of why models can’t explain what’s going on. I learnt early in my PhD that you could ask “What about magnetic fields?” at the end of almost any astrophysics seminar (it might not work for some observational talks, but then you could usually ask “What about dust?” instead). Handy if ever you fall asleep…

# 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.

# All-sky search for long-duration gravitational wave transients with LIGO

It’s now about 7 weeks since the announcement, and the madness is starting to subside. Although, that doesn’t mean things aren’t busy—we’re now enjoying completely new forms of craziness. In mid March we had our LIGO–Virgo Collaboration Meeting. This was part celebration, part talking about finishing our O1 analysis and part thinking ahead to O2, which is shockingly close. It was fun, there was cake.

Celebratory cake from the March LIGO–Virgo Meeting. It was delicious and had a fruity (strawberry?) filling. The image is February 11th’s Astronomy Picture of the Day. There was a second cake without a picture, that was equally delicious, but the queue was shorter.

All the business means that I’ve fallen behind with my posts, and I’ve rather neglected the final paper published the week starting 8 February. This is perhaps rather apt as this paper has the misfortune to be the first non-detection published in the post-detection world. It is also about a neglected class of signals.

### Long-duration transients

We look for several types of signals with LIGO (and hopefully soon Virgo and KAGRA):

• Compact binary coalescences (like two merging black holes), for which we have templates for the signal. High mass systems might only last a fraction of a second within the detector’s frequency range, but low mass systems could last for a minute (which is a huge pain for us to analyse).
• Continuous waves from rotating neutron stars which are almost constant throughout our observations.
• Bursts, which are transient signals where we don’t have a good model. The classic burst source is from a supernova explosion.

We have some effective search pipelines for finding short bursts—signals of about a second or less. Coherent Waveburst, which was the first code to spot GW150914 is perhaps the best known example. This paper looks at finding longer burst signals, a few seconds to a few hundred seconds in length.

There aren’t too many well studied models for these long bursts. Most of the potential sources are related to the collapse of massive stars. There can be a large amount of matter moving around quickly in these situations, which is what you want for gravitational waves.

Massive stars may end their life in a core collapse supernova. Having used up its nuclear fuel, the star no longer has the energy to keep itself fluffy, and its core collapses under its own gravity. The collapse leads to an explosion as material condenses to form a neutron star, blasting off the outer layers of the star. Gravitational waves could be generated by the sloshing of the outer layers as some is shot outwards and some falls back, hitting the surface of the new neutron star. The new neutron star itself will start life puffed up and perhaps rapidly spinning, and can generate gravitational waves at it settles down to a stable state—a similar thing could happen if an older neutron star is disturbed by a glitch (where we think the crust readjusts itself in something like an earthquake, but more cataclysmic), or if a neutron star accretes a large blob of material.

For the most massive stars, the core continues to collapse through being a neutron star to become a black hole. The collapse would just produce a short burst, so it’s not what we’re looking for here. However, once we have a black hole, we might build a disc out of material swirling into the black hole (perhaps remnants of the outer parts of the star, or maybe from a companion star). The disc may be clumpy, perhaps because of eddies or magnetic fields (the usual suspects when astrophysicists don’t know exactly what’s going on), and they rapidly inspiralling blobs could emit a gravitational wave signal.

The potential sources don’t involve as much mass as a compact binary coalescence, so these signals wouldn’t be as loud. Therefore we couldn’t see them quite as far way, but they could give us some insight into these messy processes.

### The search

The paper looks at results using old LIGO data from the fifth and sixth science runs (S5 and S6). Virgo was running at this time, but the data wasn’t included as it vastly increases the computational cost while only increasing the search sensitivity by a few percent (although it would have helped with locating a source if there were one). The data is analysed with the Stochastic Transient Analysis Multi-detector Pipeline (STAMP); we’ll be doing a similar thing with O1 data too.

STAMP searches for signals by building a spectrogram: a plot of how much power there is at a particular gravitational wave frequency at a particular time. If there is just noise, you wouldn’t expect the power at one frequency and time to be correlated with that at another frequency and time. Therefore, the search looks for clusters, grouping together times or frequencies closer to one another where there is more power then you might expect.

The analysis is cunning, as it coherently analysis data from both detectors together when constructing the spectrogram, folding in the extra distance a gravitational wave must travel between the detectors for a given sky position.

The significance of events is calculated is a similar way to how we search for binary black holes. The pipeline ranks candidates using a detection statistic, a signal-to-noise ratio for the cluster of interesting time–frequency pixels $\mathrm{SNR}_\Gamma$ (something like the amount of power measured divided by the amount you’d expect randomly). We work out how frequently you’d expect a particular value of $\mathrm{SNR}_\Gamma$ by analysing time-shifted data: where we’ve shifted the data from one of the detectors in time relative to data from the other so that we know there can’t be the same signal found in both.

The distribution of $\mathrm{SNR}_\Gamma$ is shown below from the search (dots) and from the noise background (lines). You can see that things are entirely consistent with our expectations for just noise. The most significant event has a false alarm probability of 54%, so you’re better off betting it’s just noise. There are no detections here.

False alarm rate (FAR) distribution of triggers from S5 (black circles) and S6 (red triangles) as a function of the
signal-to-noise ratio. The background S5 and S6 noise distributions are shown by the solid black and dashed red lines respectively. An idealised Gaussian noise background is shown in cyan. There are no triggers significantly above the expected background level. Fig. 5 from Abbott et al. (2016).

Since the detectors are now much more sensitive, perhaps there’s something lurking in our new data. I still think this in unlikely since we can’t see sources from a significant distance, but I guess we’ll have to wait for the results of the analysis.

arXiv: 1511.04398 [gr-qc]
Journal: Physical Review D; 93(4):042005(19); 2016
Science summary: Stuck in the middle: an all-sky search for gravitational waves of intermediate duration
Favourite (neglected) middle child:
Lisa Simpson

Sunset over the Grand Canyon. One of the perks of academia is the travel. A group of us from Birmingham went on a small adventure after the LIGO–Virgo Meeting. This is another reason why I’ve not been updating my blog.

# 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