r-modes

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.

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