CBCB (Compact Binary Coalescence... and Blues)

Last week, I told you about my work on gravitational waves that went into my PhD. My post-doc is still in the same field, but I'm looking for an entirely different type of wave than before. The continuous waves I studied before were weak, but long lasting. The work I do now is on waves from compact binary coalescences, CBCs. These are among the most powerful waves we expect to see, but last only seconds. All the detections LIGO and Virgo have made so far were from CBCs.

The name "Compact Binary Coalescence" is awfully jargony, so let me take it piece-by-piece:
Compact: A compact object is one with unusually high density. In this case it refers to either a neutron star, or a black hole. How high is the density? One teaspoon of neutron star material weighs 10 million tons, and black holes are even denser!
Binary: A binary system has two objects that orbit their common center of gravity. If one object is significantly bigger than the other, it might look like the small one orbits the big one, but even our Sun has a bit of wobble from the pull of the surrounding planets.
Coalescence: As the objects orbit, they radiate energy in the form of gravitational waves. That energy comes from their gravitational potential, which draws them closer together as it decreases. A closer orbit is also a faster one (think of Mercury), so the pair radiate stronger waves, which further speeds the process. Eventually, the two collide and coalesce into a single object.

I can show you what this type of orbit looks like thanks to the recently (but not yet officially) released LIGO Orrery:

This was inspired by the Kepler Orrery released a few years ago. It shows simulations of all the binary black hole detections LIGO and Virgo have made so far. Below the orbits, you can see a plot of the gravitational wave signal. Each peak of the wave corresponds to a half-orbit of the bodies. As the rate of revolution increases, so does the frequency of the wave.

The signal is divided into three parts
Inspiral: The majority of time is spent in this phase, as the orbit decays and the bodies spiral inward (good name, right?). The wave is sinusoidal with increasing frequency and amplitude.
Merger: When the bodies first collide, the new object is oblong, and takes some time to smooth out. This is the peak wave output.
Ringdown: There are tremendous forces involved in the collision, so the black hole that results from the merger needs to shake off the extra energy. You can't see it in the plots shown here, but immediately after the big burst are a couple more small waves.

I'm working with a group here in Annecy, France that's part of the European gravitational wave collaboration, Virgo. We look for these CBC signals in the data coming from the two LIGO detectors in the US, and the Virgo detector in Italy. The search technique I'm part of is called MBTA, which is not the Massachusetts Bay Transit Authority, but the Multi-Band Template Analysis. The goal is to identify signals as fast as possible, so we can send the coordinates to partner groups observing in the electromagnetic spectrum. This allowed us to show last year that gamma ray bursts are associated with neutron star mergers.

I have a lot to learn in this new pursuit, but everyone at my office and in town have been incredibly welcoming. I've been given an amazing opportunity to live an work in such a beautiful part of the world!

Doctoral Denouement

In September of this year, I successfully defended my thesis, and received my PhD! 

 

 

Photo credit to my wife Marika

In the time since, I've been packing up to head to Annecy, France to start a post-doctoral position with the Virgo gravitational wave group, but now I'm here! I haven't found a place to live yet, but I'm settled into my job, and since it has fixed hours (unlike grad school) there's a chance I'll be able to post here regularly again!

I thought a good return post would be to take you through my thesis, and show you why I deserve to dress as a crazy space-wizard (thanks to KC for that comparison). In theory, graduate theses from the University of Michigan get posted to their server DeepBlue, but they're being slow about it, so I put mine on Google. Here now is a summary of what I've been up to for the past 4 years...

Gravitational Waves

A little over 100 years ago, Albert Einstein came up with an idea called the General Theory of Relativity, which is currently our best description of gravity. The theory says that mass changes the shape of the space around it, influencing the motion of other bodies. The picture I like to think of is a bowling ball on a trampoline.

University of Michigan Physics Demo Lab

What Einstein discovered was that his equations allowed for ripples in the fabric of spacetime that would propagate outward from certain objects. These are called gravitational waves, and while there had been indirect evidence of their existence, they were not directly observed until 2015, when LIGO made the first detection of a passing wave produced by a pair of black holes.

Detecting Gravitational Waves

The effect of a passing gravitational wave is to change the distance between points in space. This is commonly demonstrated by imagining a wave passing through a ring of mass:

As the wave passes through the screen, distances are compressed along one dimension and stretched along the other. In reality, the degree of squeezing is far smaller than shown above, so to detect these waves, we need to measure distances with incredible precision. The solution is a laser interferometer, the LI in LIGO. Interferometers are typically L-shaped devices that measure the difference in the lengths of the two arms. The LIGO Scientific Collaboration has build two such detectors in the US, in Hanford, WA and Livingston, LA. The arms of each device are 4 km (2.5 mi) long, but the strongest waves detected only changed the length by less than the width of an atom.

Hanford Detector, Credit: LIGO Laboratory

Sources of Waves

There are 4 main types of gravitational wave that are predicted:

1. Compact Binary Coalescence
2. Burst
3. Stochastic
4. Continuous

The first type refers to pairs of black holes or neutron stars that spiral around each other and collide. All the detections made so far have come from this category, and it's the type I'll be looking for here in France (more on that in a later post). The second covers short-lived powerful waves which could result from a supernova. Stochastic waves are the sum total of all the gravitational waves hitting us, and could include effects from the Big Bang analogous to the cosmic microwave background. Finally, continuous waves are long-lasting waves from spinning neutron stars. These waves are significantly weaker than the CBCs and Bursts, but by adding up a signal over long periods, we hope to detect them.

Mock Data Challenge

The first search I was part of was a Mock Data Challenge, where fake signals were injected into real data, and the various analysis pipelines searched for them. Since continuous waves are yet to be detected, this is the best way to compare different techniques. I was part of a pipeline called PowerFlux, which emphasizes speed of computation. The main point of comparison is whether a particular injection is detected or not:

The most successful of the pipelines was Einstein@home, thanks to the computational resources they get from volunteers.

Advanced Detector Upgrades
Shortly before our first detection in 2015, upgrades to the detectors were completed, which greatly improved sensitivity. However, there were some isolated regions of high noise in the detector.

These sharp peaks are referred to as noise lines, and they are created by terrestrial sources. On the far left of the plot above is a large spike at 60 Hz due to the US power mains, and the four lines marked in red are called violin modes, the resonant frequencies of the cables that hold up the mirrors in the detector.

These lines are difficult to solve, since their sources are intrinsic to the function of the detector, but others can be solved if their source is removed. During the first observing run, there was a pervasive series of lines referred to as the half-hertz comb, appearing at 10.5 Hz, 11.5 Hz, 12.5 Hz, etc. Through extensive testing by people at the detector sites, it was discovered that this comb came from the GPS timing cards used in the equipment. The cards would indicate synchronization by blinking an LED on for a second and off for a second. This precisely-timed current draw was enough to interfere with the data collected. The cards have now been reprogrammed to stop blinking, but many lines remain. I investigated analysis techniques to mitigate the effect of these lines.

Barycentering Approximations
When making measurements, it's important to consider the frame of reference from which you make those measurements. Most physical laws only work in an inertial reference frame, meaning one that does not accelerate. Our detectors are on Earth though, which both rotates and revolves around the Sun. That means our measurements must be converted into an inertial frame, which requires knowing where the Earth is at any given moment.

This process is called barycentering, and there are accurate techniques for calculating all the necessary parameters. However, this process can be slow when it needs to be done for every point in the sky, so I developed more approximate routines that allowed us to get "good enough" measurements in a fraction of the time.

I couldn't have done this without the help of so many people – In times like these, it's important to remember that we don't move forward alone. It takes a team to make real progress.

Keeping the Beat

I haven't been posting here recently, since I've been busy with research, but the stuff I'm doing at the moment is a bit slow-moving, so I thought I'd stop in and give an update.  In February, I mentioned work I was doing on approximations to a piece of solar system dynamics code for LIGO.  I'm still working on it, and I wanted to talk about an interesting issue I just resolved.

The coordinates we use to specify a direction in the sky are called equatorial coordinates, given in right ascension and declination.  These correspond to taking the longitude and latitude at the spring equinox, and projecting them into space.  Since the coordinates are referenced to a specific position of the Earth, as the Earth moves the stars stay fixed in the coordinates, e.g. Procyon is always at 114.8° RA, 5.2° dec.  However, since this system assumes a fixed Earth, the planets and even the Sun will move around.  That means that as data is being collected from a source, the sun could cross the path and introduce the time delays I mentioned in the previous post.

Over a short time scale, say a week, the dominant frequency will be daily, due to Earth's rotation, but what kind of day?  The ones we're used to are called solar days, which correspond to the time it takes for the sun to return to the same position in the sky.  However, since the Earth is also moving around the sun, this is a bit longer than the time for the stars to return to their previous positions.  That period is called a sidereal day, and is about 4 minutes shorter than a solar day.

I tried fitting the parameters I need using these two frequencies, but comparing the fitted values to the data still showed some structure:

That plot of errors covers 1 week, so there's clearly something with a period of about a day, but not quite a solar or sidereal day.  That plot just shows a single point in the sky, but I also tried making a plot of the error over the whole sky, animated in time (a bit hypnotic, so don't stare too long):

I couldn't figure out what this other frequency could be, until my colleague Vladimir pointed out that it could be a beat frequency.

When two sinusoidal waves with slightly different frequencies are added, they result in a wave with a frequency related to the sum and the difference of the two original frequencies:

The blue curve is the sum of the red and green dashed curves.  Even though the red curve has a period much longer than the green, the resulting curve is only a little off from the original green.  Vladimir's suggestion was to add in the period of the moon, 27.3 days.  That resulted in this error curve:

It's significantly smaller, and there are no more sinusoidal wiggles!  These barycenter approximations I'm doing will likely be a chapter of my thesis, so I'm pleased to be making good progress.