Wednesday, October 30, 2013

Galaxy Evolution and Gravitational Waves, Part I

Much has been said on previous blog posts here about how computer models of galaxy evolution, which are being refined and improved by the Hubble Space Telescope’s observations collectively known as CANDELS, contribute to our overall understanding of the universe. The numbers, types, shapes, sizes, and large-scale clustering properties of galaxies throughout cosmic history can at times be predicted with an astonishing accuracy. When predictions from computations of galaxy evolution do not line up well with observations, then, happily, we have a clue that something remains to be discovered. (A now classic example is the so-called missing satellite problem: simulations predict many more dwarf galaxies surrounding other galaxies than are actually observed. Are they as yet undiscovered, or is our understanding of dark matter structures – on which galaxy simulations rely – extremely flawed?)

The Arecibo Telscope in Arecibo, Puerto Rico. Russell Hulse and 
Joseph Taylor used this facility to make the first indirect
detection of gravitational waves in 1975. A direct detection
would help astronomers learn about how often galaxies merge
throughout the history of the universe.
A very nice spinoff of having a digital universe of growing, colliding, re-shaping, and color-changing galaxies is that these simulations can be used to make predictions in an entirely different area of physics: gravitational waves.

A gravitational wave is an oscillation in the fabric of spacetime itself, which, after its initial production, propagates away and has nothing further to do with the merging objects that made it. The wave travels through space on its own at the speed of light, stretching and bending everything in its path. (Not to worry, though: the stretching and bending is on a scale smaller than the nucleus of an atom, which is exactly why gravitational waves are difficult to detect!) The waves are emitted whenever a very massive object exhibits quadrupolar motion – which essentially means rotating motion with a lot of heaviness on the outer rim of whatever is rotating. (Thus, the rotating, spherical Sun produces no gravitational waves, whereas two stars orbiting one another closely do.) Ordinary binary stars are not dense enough and close enough together to produce any noticeable gravitational waves. It generally takes pairs of extremely dense objects – white dwarfs, neutron stars, and black holes – to inspiral very close to one another and merge with enough spherically asymmetric rotation for gravitational waves to come about. Generally, then, if a gravitational wave were detected here on Earth, that means it probably originated from a pair of extreme remnants of stars, whirling toward one another.

Gravitational waves have not been directly detected yet. However, there is indirect evidence that they exist. Hulse and Taylor won the Nobel Prize in Physics in 1993 for their discovery of a pulsar system using the Arecibo Observatory in Puerto Rico. (A pulsar is a rapidly rotating neutron star, emitting a very regular beam of radio pulses.) The pulsar had a companion (non-pulsating) neutron star and the two objects orbited each other closely. This was inferred by the sharp regularity of the pulses, after modeling the small changes in that regularity due to the otherwise invisible companion. However, the orbits did not fit the pattern that one would expect from ordinary, Newtonian gravity. The two objects had slightly decaying orbits, which indicated that energy was continually being dissipated. It turns out that the rate of energy loss was exactly that expected if the system were emitting gravitational waves. Look at how tiny the uncertainties are in Fig 1!

Figure 1: Deviations of the Hulse-Taylor pulsar system (black data
points) from Newtonian predictions (horizontal line). Thirty years later,
        the system continues to follow the predictions of general relativity. 
(From Weisberg and Taylor 2005.)
Here on earth, though, how does one go about directly detecting gravitational waves? The now “classic” method (I use quotation marks because this is a very new field of physics) uses laser interferometry. Facilities such as LIGO (Laser Interferometric Gravitational wave Observatory) in Washington state and Louisiana, as well as the Virgo observatory in Italy, use a very long laser beam to detect changes in length less than the radius of an atomic nucleus. (As a side note, astronomy today uses the term "observatory" somewhat loosely – apart from detecting length changes on earth due to astrophysical sources, the experiment doesn’t “see” anything in the sense that an optical telescope does.) Were a gravitational wave to pass the earth once these facilities are completely operating in 2017, the length measured by the laser interferometer would oscillate back and forth between 1 + 10-20 and 1 – 10-20 times its original length. The hard part of making such an observatory work is sorting out these vibrations from distant trains, from earthquakes on the other side of the world, from wind vibrations, and from a very long list of other irritating sources. A successful detection, however, would mean hundreds or thousands of these tiny oscillations a second, due to a gravitational wave tracing back to a particular pair of rapidly inspiraling pair of neutron stars (for instance).

However, detecting a particular merging pair of supermassive black holes with a laser interferometric observatory is not terribly likely, for the following reason. A supermassive black hole is one of the most exotic objects in the universe (by supermassive, astronomers mean anywhere from a million to about a billion solar masses worth of material in a single black hole. This can be a small but significant fraction of an entire galaxy, which typically weighs a hundred billion solar masses). Typically a supermassive black hole lies in the center of a galaxy. In fact, our own Milky Way galaxy very likely has one at its center: Saggitarius A, which is the equivalent mass of four million suns. But, given only one or two SMBHs per galaxy, and given the fact that mergers between supermassive black holes are rare (on the order of a million in the entire observable universe per year), one would have to look very far to find a pair (probably beyond a redshift of about 0.4). And chances are, it would be so far away that the merger’s gravitational waves would be too weak for us to detect. (As for merging white dwarfs and neutron stars, there are numerous sources nearby in our own galaxy, and so there will probably be plenty of gravitational wave sources to detect with LIGO and Virgo.)

Fortunately, more distant galaxies (far enough away that that we see them at about half the universe's age, due to the finite speed of light) merged more often. As a result, supermassive black hole mergers were also more common. This provides a way to detect gravitational waves from these mergers, which also happens to utilize pulsars. More about this in part two of this post.


  1. There are a few misleading statements about the LIGO/Virgo source population here. To be detected, a binary system needs to be orbiting with a frequency that the detector is sensitive to (tens to thousands of times per second for LIGO/Virgo). White dwarfs, being much larger than neutron stars or stellar-mass back holes, will collide with each other before they get to orbit that fast.

    LIGO/Virgo ends up being sensitive to binaries that contain neutron stars or stellar-mass black holes (up to about a hundred solar masses) only in the final seconds before merger, but the advanced versions will be capable of detecting binary systems in distant galaxies (~hundreds of megaparsecs) - which is fortunate, because we don't expect the actual mergers to happen very often in our own galaxy.

  2. Thanks for your comment. For brevity’s sake, and also for the sake of focusing on galaxy evolution, I didn’t get into the possibility of detecting individual merging pairs of black holes. As I’m sure you know, this is possible with pulsar timing arrays as well as with LIGO/Virgo. My point was that if I had to wager how merging pairs of *supermassive* black holes will first be detected, I would bet on the stochastic background over an individual detection. (Ordinary black holes are another story altogether.) But who knows what Nature will actually tell us. As for merging white dwarf pairs, I was giving an example of a GW source that’s outside the detection regime for pulsar timing arrays. What I didn’t say is that the ideal detector for such pairs, the LISA mission (Laser Interferometer Space Antenna) was sadly canceled due to funding limitations. Not wanting to open up this “can of worms”, I suppose I did make it sound like LIGO/Virgo would detect white dwarfs, which of course it’s not designed for.