Black Holes Eating Stars and Making Waves

By William E. East

One of the more graphic terms in black hole physics is "spaghettification."  It refers to the way that strongly varying gravitational forces can distort a round object into a shape most familiar from your dinner plate. This is a fate that can befall a star that has the misfortune to wander too close to a massive black hole. In this post, I want to tell you about some recent work I have done using computer simulations to explore how such stars get pulled and squashed as they fall into black holes. This work was done partly in order to understand whether we might soon be able to observe such events, in a nascent field of astronomy based on measuring gravitational waves.

Video clip: A star, like our Sun, falling into a black hole that's a million times as massive.  

(Simulation by William East. Visualization by Ralf Kaehler.)

Normally, a star's tendency to expand because of the pressure of the hot gas it is made of is held in check by the attraction of the star's gravity, which keeps the star together.  If the star passes near a black hole, however, things become very different.  The gravity of the black hole pulls surrounding objects, like the star, towards it. The closer the object is to the black hole, the stronger that gravitational pull is. This means that the different parts of the star feel different gravitational forces.  The part of the star facing the black hole will be pulled towards the black hole faster than the back of the star, which is farther away.  In the extreme case, the star will be stretched into a long, thin shape, a process known as “spaghettification.”  This relative difference in gravitational forces is known as a tidal force, because it is also what gives rise to ocean tides.    

I use computer models that keep track of all these opposing forces, and determine when the tidal forces from the black hole overwhelming the star’s ability to hold itself together by its own gravity. Material from stars that are “tidally disrupted” in this way can produce bright electromagnetic radiation - light - which we can observe with telescopes.  But for stars that fall into black holes, there is the possibility of producing another kind of radiation: gravitational waves.    

Image: A star being stretched lengthwise as it falls into a massive black hole.  

When black holes are perturbed, by, for example, a star falling into them, they act a little like bells. Like bells, black holes vibrate at specific frequencies, set by their mass and how much they are rotating. When you strike a bell, the energy in its vibrations are eventually carried away by vibrations in the air that we hear as sound.  Black holes behave similarly, but instead of emitting sound waves, they emit gravitational waves as they settle back down to a stationary state. This process, in keeping with our analogy, is known as “ringdown.”

As you might imagine, the strength of the gravitational waves produced by a star colliding with a black hole depends on how much the star is distorted before it collides.  If the star is pulled apart too much, it acts more like a series of gentle taps on the black hole bell, instead of one big wallop from the collision of a compact object.  My simulations help reveal how much the strength of the gravitational wave signal is affected by the tidal distortions of the star.

Image: The gravitational wave signal from various simulations of stars colliding with massive black holes.  This plot illustrates that the larger the star, relative to the size of the black hole, the weaker the resulting gravitational wave is, compared to if all the star's mass were concentrated at a single point.  This is because the larger stars are more strongly affected by tidal forces.

But what exactly is a gravitational wave?  While a sound wave is a traveling oscillation in the air, a gravitational wave is an oscillation in the fabric of spacetime itself. Einstein taught us that space acts sort of like a rubber sheet:  not only is space deformed by massive objects, it's capable of supporting propagating ripples. In the simulations, all these aspects of gravity - the pull of the black hole on the star, the star's own gravity, and the creation and propagation of these gravitational waves - all come from solving a single set of equations (named after their originator, Einstein).  

As a gravitational wave passes us, it stretches and squeezes space in alternating perpendicular directions.  For example, if a gravitational wave happened to pass through you while you were standing with out-stretched arms (perhaps in a gesture of greeting), the crest of the wave might stretch your arms out even farther, and at the same time, squeeze you head-to-toe. Then, when the trough of the wave passed through you, it would do the opposite.  You wouldn't notice these imperceptibly gentle changes since these waves would be quite weak by the time they reach us from their violent creation, vast distances away. However, one of the exciting things happening in physics today is the race to build instruments of such exquisite sensitivity so as to be able to directly detect, for the first time, these miniscule length changes due to gravitational waves.

One such gravitational wave detector, currently being upgraded to "advanced" sensitivity, is the Laser Interferometer Gravitational Wave Observatory (LIGO).  LIGO is a pair of instruments, one in Washington State, and one in Louisiana, that each use giant L-shaped configurations of lasers to measure amazingly tiny changes (on the order of 10-18 meters, or about 1000 times smaller than a proton radius!) in the distance between end stations in a tunnel, 4 kilometers apart. (There are several other similar instruments in Germany, Italy, and Japan.)  These observatories were mainly built to detect gravitational waves from mergers of pairs of neutron stars (incredibly dense stars described in a previous blog post "A Mad Ballerina Consumes Her Companion") or Sun-mass black holes.  My work suggests that gravitational waves from dense stars colliding with black holes hundreds of times our Sun's mass could be another possible source, but only if we're lucky enough that such an event happens nearby.

To detect the lower frequency ringdown of supermassive black holes (those with mass a million or more times that of our Sun, and that reside at the centers of galaxies) would require a space-based instrument.  A lot of effort has been put into designing and developing such an instrument, though the funding of such an expensive space laser is still uncertain.  However, with the possibility of gravitational wave observatories making their first detections in the near future, and thereby inaugurating a completely new type of astronomy, it is a very exciting time to be in gravitational physics.

More on stellar collisions with black holes:

Gravitational waves from the collision of tidally disrupted stars with massive black holes  (W. East, Aug 2014)