The Game Is Afoot

Left: Chandra X-ray Telescope image of Cygnus X-1, the first black hole candidate discovered. Link.

In 1972, a bright X-ray source was discovered by the Uhuru satellite in the constellation Cygnus at the same location as a bright blue-white star with the highly memorable name HD226868. Ordinary blue stars don't produce a lot of X-rays, so astronomers quickly concluded there must be a companion object that doesn't give off much visible light. Careful observations of the dynamics of the blue star and variations in the X-ray luminosity show that the X-ray source, known today as Cygnus X-1, has a mass at least 6 times that of our Sun, but a physical size smaller than Earth.

Similarly, in 1989 a huge X-ray flare was detected in the vicinity of another star in Cygnus, known as V404 Cygni. Doppler effect measurements showed the X-ray source to be between 10 and 14 times the mass of the Sun. The star and the X-ray source orbit each other once every 6.5 days, which indicates a very close binary system – and a small size for the hidden companion. Both this and Cygnus X-1 are far too massive to be neutron stars – pulsars – which cannot grow beyond about 3 times the Sun's mass.

Right: Sagittarius A*, the bright X-ray source at the center of the Milky Way, with several star orbits mapped. Using data of the stars' motion, scientists have determined Sagittarius A* is 4 million times the mass of our Sun and smaller than the Solar system. Link.

A third example is an even brighter X-ray source at the center of our Milky Way galaxy, known euphoniously as Sagittarius A* ("A star" when spoken aloud). Using the motion of stars orbiting around Sagittarius A*, astronomers determined its mass to be approximately 4 million times the mass of our Sun. Unlike the previous two examples, the stars can actually be observed directly and their motion plotted; with the data collected, even Astronomy 101 students can calculate the mass of the X-ray source using Kepler's laws of motion. Another bonus from direct observation is that the size of Sagittarius A* can be no larger than the orbit of Uranus – about 20 times the distance from Earth to the Sun. In other words, whatever is at the center of our galaxy is far more massive than any star (which top out around 200-300 times the mass of the Sun, and stars that huge are incredibly luminous objects anyway), and is physically too small to be a cluster of stars. Objects similar to Sagittarius A* have been observed at the heart of nearly every galaxy.

All this is a tease, of course: everyone knows the scientific consensus is that these three X-ray sources, along with with many other objects, must be black holes. In this post, I will flesh out the observational evidence for black holes and attempt to separate what we understand about black holes from a lot of the more conjectural and controversial issues surrounding these mysterious objects.

What is a Black Hole?

Right: Trajectories near a black hole, showing how the event horizon “traps” particles. This figure is created for clarity, not for scientific accuracy – the paths are not precisely calculated. Link. Credit: Matthew Francis.

Black holes by their nature are difficult to observe, so the evidence for their existence is by necessity indirect. A good functional definition is as follows: a black hole is a compact object whose gravitational influence is so strong that anything coming too close cannot escape. According to Einstein's general theory of relativity, there will be a boundary called the event horizon which separates the “interior” of the black hole from the rest of space. Think about the effect of gravity on a particle: far from the black hole, the particle's trajectory won't be affected. Closer in, the particle gets deflected slightly by the gravitational influence; closer still, the particle may fall into some kind of orbit. If it gets very close, its path is so curved it will never again straighten out enough to escape – that's the event horizon.

A common misconception must now be addressed: black holes do not suck anything in. The combination of large mass and tiny size means a black hole's gravity is more intense than other objects, but gravity obeys the same rules whatever the object. If you replaced our Sun with a black hole of equal mass, Earth's orbit would not change! (Earth would freeze over, of course, since the Sun's light plays a major role in our planet's life, but the size and shape of our orbit would remain the same.) Similarly, the presence of a huge black hole at the center of our galaxy doesn't mean our Solar System will eventually fall in; if you removed that black hole entirely from the galaxy, our Solar System's path through the Milky Way would be unaffected – Sagittarius A* is simply too far away.

Left: Cross-section of a black hole, showing the event horizon and ergosphere. Credit: Matthew Francis.

The two properties that govern the size and shape of the event horizon and the strength of the gravitational attraction are the mass of the black hole and the amount of spin it has. The size of the event horizon is fairly easy to estimate: a black hole of equal mass to the Sun will have a radius of 3 kilometers; one with double the Sun's mass will be 6 kilometers in radius; etc. Rotation squashes the event horizon so that it's spheroidal in shape, and produces a strange region known as the ergosphere, where nothing can remain at rest.

From an observational point of view, we don't ever expect to "see" a black hole directly: it doesn't emit its own light, and light shining on it will be trapped within the event horizon. However, as a particle approaches the black hole, the gravitational pull will accelerate it to high speeds; if the particle is an electron or other charged particle, it will emit intense amounts of light -- including radio waves, X-rays, and gamma rays. Black holes can actually be very luminous, and that's how they are best identified.

Black holes may also give off particles through the process called Hawking radiation; close in to the event horizon, the energy is high enough that pairs of particles – matter and antimatter – can be produced. One particle falls into the black hole, while the other is free to escape. This process has not yet been detected in nature, and any light produced by particles falling on the black hole will overwhelm the Hawking radiation signal. However, it's an observable prediction, so scientists are keeping watch for it. If really tiny black holes exist, their Hawking radiation may be the best way to spot them.

One troubling aspect of black holes: the event horizon is a one-way wicket, so once something falls in, it is lost to the universe outside. Since the only things that characterize a black hole are mass, spin, and electric charge (though it's unlikely realistic black holes will ever have too much of that in excess), an electron and a positron will add the same amount of mass to a black hole even though one is matter and the other is antimatter. A photon will also increase the mass of a black hole, as its energy is converted to mass using Einstein's famous E = m c2 equation. We may be able to observe a particular type of particle crossing the event horizon, but the black hole seems to “forget” what went into it. This post is focusing on astronomical aspects of black holes, so there is no space to get into the full discussion of information loss in black holes (to which Stephen Hawking among others has devoted a lot of time and energy); suffice it to say that any resolution is beyond the reach of observational tests right now.

Black Holes in Astronomy

Right: Cartoon of a binary system consisting of a star and a black hole. The black hole is stripping gas from the star, distorting the star's shape. The gas forms a thin hot disc around the black hole, known as an accretion disc. Credit: Matthew Francis.

All this stuff is nice theory, but what about real observations? As I mentioned in the first part of this article, many black hole candidates observed have star companions, and this is the source of the matter that makes the black hole bright. The side of the star closer to the black hole feels a stronger gravitational force than the far side, so the star gets pulled out of shape, and some of the gas can be stripped off. Since the star is rotating and revolving around the black hole, the gas doesn't stream along a direct line; instead, it carries some of that spin with it, forming an accretion disc around the black hole. Some of the gas will go back to the star; some will fall into a more-or-less stable orbit around the black hole; and some will go into plunging spirals, radiating vigorously as the gas approaches the event horizon.

Now we must ask why astronomers think the objects Cygnus X-1, Sagittarius A*, and the like are black holes and not some other thing – especially since we aren't able to observe a black hole directly. As I pointed out before, the candidate objects are massive, relatively small, and produce no detectable light in the visible part of the spectrum. That rules out ordinary stars, whose relationship between mass and size is well-known, and which produce a lot of visible light – especially the really massive ones. They also are not particularly bright in X-ray or radio waves.

Two other candidates are the endpoints of star evolution: white dwarfs and neutron stars. White dwarfs are the cores of stars similar to our Sun after the nuclear fuel for fusion has been exhausted. They are compact – roughly Earth-sized – and kept from total gravitational collapse by degeneracy pressure from the electrons inside. Degeneracy pressure isn't like gas pressure, or even electrical repulsion; instead, it's a quantum-mechanical effect called the Pauli exclusion principle, which prevents two particles of the same type from occupying the same space. However, even degeneracy pressure has its limits: if the white dwarf has more than 1.4 times the Sun's mass, known as the Chandrasekhar limit, gravity will overcome it. When excess mass is added to a white dwarf through accretion, it explodes in a supernova. Cygnus X-1 and so forth are much more massive than 1.4 times the Sun.

Neutron stars are also supported by degeneracy pressure; the core of a star much more massive than our Sun collapses, crushing the atoms until they are a strange fluid with the density of an atomic nucleus. The degeneracy is from the nuclear particles: mostly neutrons, as the name suggests. Neutron stars are only about 10 kilometers in radius – about city-sized – so they are far more compact than white dwarfs. However, neutron stars also have an upper limit to their mass, often referred to as the Oppenheimer-Volkov limit, which is about 3 times the Sun's mass. (The co-discoverer of this limit is J. Robert Oppenheimer, most famous for his role in the Manhattan Project.) Again, the black hole candidates are too massive.

If the core of a star exceeds the Oppenheimer-Volkov limit at the end of its life, there is no force in any standard theory able to prevent it from collapsing completely into a black hole. (You may have read about quark stars, hypothetical neutron star-like objects composed of quarks. These also have an upper limit in mass, if they exist, and the physics governing them is essentially the same as neutron stars.) Black holes can be very massive – there's no upper limit, since gravity is the only force left. They can also grow by accretion or merging with other black holes, so if they form and grow in the right way, they could surely get as big as the supermassive objects at the centers of galaxies.

Black Holes and Their Discontents

So we are left with two options: Cygnus X-1, Sagittarius A*, and the other compact massive objects are black holes, or they are something involving new. Any alternative model must of course account for the observed characteristics: large mass with relatively small size, strong accretion producing X-ray emission, ability to grow to huge masses – or introduction of two new types of objects to account for both the stellar-mass black hold candidates and the supermassive galactic monsters. Black holes are relatively simple and convenient as an explanation: they require no new physical concepts, no new forces (or rather no new expressions of the fundamental forces of nature), but that alone isn't enough, especially in the absence of direct observation. Perhaps another explanation is out there.

One possible alternative was explained in part in an earlier post on this blog: "Maybe Black Holes Don't Really Exist" by George Chapline. The author presents two major objections to the black hole model, one theoretical and one observational. The observational objection is based on the strong jets of matter shooting out from the accretion discs around black holes: these are not yet fully understood, although partial explanations have been proposed. It's a challenging problem involving high temperature plasmas and strong magnetic fields, so failure to resolve it may not be a problem with black holes as much as it is a problem with understanding accretion phenomena.

The theoretical objection Chapline raises is that any object with an event horizon is incompatible with quantum mechanics. His reason is that there isn't a universal time associated with an event horizon, which is a true statement: the passage of time measured by an observer depends on their motion relative to the black hole. That's an inevitable consequence of relativity, but it doesn't just apply to black holes: the measurement of time on Earth is slightly different than the measurement of time by a satellite in orbit (a correction factor GPS and other communication satellites have to make). In fact, time is always measured relative to an observer, and two observers moving quickly relative to each other will not agree on how much time has passed. That's Einstein's relativity, and it is not controversial. Event horizons are also not controversial from a basic understanding of general relativity (and in fact the 18th century physicist Laplace predicted something very similar to them!); whether they exist in astrophysical objects is of course another question, since telling whether an event horizon is present is not an easy task.

Chapline is also correct that ordinary, non-relativistic quantum mechanics has a universal time: every particle described using the regular, low-energy version of quantum mechanics (the type most people have heard about, and which I wrote about on the Scientific American Guest Blog before) uses the same time. However, it's important to remember that the non-relativistic version of quantum mechanics is a useful approximation to the fully-relativistic version when energies are small, much as Newtonian physics is a useful approximation to relativistic mechanics when velocities are small compared to the speed of light. Quantum field theory, the relativistic version of quantum physics, doesn't require a universal time -- each particle carries its own time, so it is puzzling to insist on a universal time for a black hole. It's also telling that there are a huge number of physicists who work in general relativity and quantum physics, and none of them I know have raised this particular objection -- despite the fact that quantum field theory and gravity notoriously don't play well together.

All of these objections could be swept away if the alternative model to black holes was a convincing one: after all, emotional attachment and conventional wisdom make for poor science. However, the proposed replacement -- called a "crystal star", a "frozen star", or a "dark energy star" -- seems to be based on some rather speculative ideas. Some aspects of the crystal star idea aren't too far-fetched: the outer surface of the neutron star is believed to be a solid crust of atomic nuclei left over from the original star's core, so you could technically stand on it -- if you could withstand the intense temperatures and crushing gravity.

The crystal star idea seems to be an extension of the neutron star concept, where matter is even more highly compressed and dark energy -- the negative-pressure entity that causes the universe to accelerate -- prevents total collapse into a black hole. Chapline evokes quantum-gravitational effects to keep things from complete collapse, which is a bit dodgy as there is no complete quantum theory of gravity. (I don't wish to get into the entropy of black holes here, though I probably should to do full justice to Chapline's point of view.) However, in the understanding of most cosmologists, dark energy doesn't get trapped in the same way matter does: the more it is confined, the less pressure it exerts, and it only comes into its own when it has a lot of space. To its credit, the crystal star idea is a testable alternative to black holes, so I'll be interested to see how it may shape up.

Hints and Allegations

I have no doubt that any true quantum theory of gravity will have something to say about black holes, notably about whether information is truly lost when particles cross an event horizon. Similarly, I have glossed over the region of a black hole inside the event horizon, which includes the singularity: a place where, according to general relativity, all the mass is concentrated at infinite density. Infinities outside of mathematics are somewhat troubling and can lead to paradoxical conclusions, so quantum gravity holds out hopes of keeping things finite at the heart of a black hole. On the other hand, if event horizons are truly one-way gates, then we'll never know what actually lies inside them – no experiment will ever gain us access!

At the same time, there are testable aspects of the black hole model, and as our telescopes get better, we'll be able to answer more questions about their structure and history. With the discovery of huge numbers of black hole candidates in the early universe – the possible progenitors of supermassive black holes in galactic nuclei – we know that whether our model is complete or not, something very like black holes have shaped the structure of the universe we see and the galaxy we live in.

Notes: This post incorporates some edited material from my own blog. Many thanks to Arthur Kosowsky for discussion and Emma Rigby for help with accretion and active galactic nuclei.