all sky

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!

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.

Limits on detectable signals and ellipticities

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
Other new academic year resolution: 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.