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What We Know about Black Holes

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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.

Matthew Francis About the Author: About the author: Matthew Francis is a theoretical physicist (meaning he theoretically does physics), freelance science writer, and seeker of weirdness throughout the cosmos. He blogs at Galileo's Pendulum and tweets at @DrMRFrancis; his opinions are his own. Follow on Twitter @DrMRFrancis.

The views expressed are those of the author and are not necessarily those of Scientific American.






Comments 11 Comments

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  1. 1. rloldershaw 11:53 am 09/2/2011

    Hi Matthew,

    Do you know of any reasonably straightforward algebraic equations that give the radius of a Kerr ring singularity as a function of its mass, energy and/or angular momentum.

    Every discussion notes the ring singularity, but I can never find a quick and simple way to approximate its size.

    Thanks for any help.

    If you go to …www3.amherst.edu/~rloldershaw you can find my email address, and you can respond by email if you prefer.

    Rob O
    Fractal Cosmology

    Link to this
  2. 2. matthewfrancis 12:14 pm 09/2/2011

    Rob: That’s a really good question, and one for which there isn’t a simple answer. The short version is that the ring doesn’t have a size — it’s a true singularity. Why it’s a ring rather than a point requires delving a bit into the mathematics of the Kerr geometry. Let me see if I can put together a relatively straightforward explanation, and I’ll post it on my own blog later on.

    Link to this
  3. 3. matthewfrancis 3:17 pm 09/2/2011

    OK, this may help. Let me know if you want more a more technical discussion than this! http://galileospendulum.org/2011/09/02/some-further-notes-on-black-holes/

    Link to this
  4. 4. Wilhelmus de Wilde 12:24 pm 09/3/2011

    I just don’t believe in the idea “singulairity”

    keep on thinking free

    Wilhelmus

    Link to this
  5. 5. christinaak 4:51 pm 09/8/2011

    since nothing is known about the physics within the event horizon of a black hole it does not seem reasonable to assume that black holes have electric charge. in fact, it is likely that the electromagnetic force does not operate at all within black holes (probably breaking down at the event horizon). also it is not likely that hawking radiation exists, and it is virtually certain that black holes do not evaporate. in addition, general relativity is a classic theory of gravity and not a quantum theory of gravity, which means any assumptions about black hole structure based on general relativity are wrong. this means there are no singularities and that there exists a structure within the event horizon that possesses volume, and that is probably composed of an enormous quantity of discrete quantum units of space-time. the very least that can be said is that next to nothing is currently understood about black holes by the orthodox scientific community. christina anne knight

    Link to this
  6. 6. johnthetraveller 10:58 am 09/9/2011

    “a black hole is a compact object whose gravitational influence is so strong that anything coming too close cannot escape”
    But gravity waves escape! So the above statement is not strictly true?
    If gravity is transmitted by a particle, then that particle must escape, presumably having no mass?

    Link to this
  7. 7. ktperera 8:42 pm 09/9/2011

    Einstein Quote:
    “My equations may predict blak holes, but nature is the final arbiter of its reality.”
    What he is hinting at is that all seemingly beautiful equations are subject to natural limitations.
    The truth is that no forces of nature can be limitless. There cannot be extreme unlimited conditions of nature that can exist and still be stable, it will blowup sooner or later. Why should a BH singularity if it exists be stable and then regard the BB singularity was not stable? Well that is a double standard for singularities. Any way I have concluded that the force of gravity can be extremely strong but is limited, I call it the G force boundary, which will safely eliminate the possibility of the existence of singularities of any kind.
    Black holes should outshine any star, but we don’t see such objects, because they don’t exist!
    A simple test to detect black holes( if they exist) is to base it on the good old concept of the bending of star light around a massive body. And in this case if that massive body is a BH we should see a halo of back ground stars projected all around the alleged BH position because of the extreme light bending close to the event horizon. Every star on one side of the BH should produce an image on the other side of the BH. Some of the star light approaching directly the BH will be absorbed and some of the star light skimming tangentially near to the event horizon will be severely deflected many degrees, even 360 degrees or even orbit multiple times before heading out.
    This means a BH will swing round the light from every star in the foreground or background of the sky to be seen from any direction that we observe. Therefore, if they exist, BHs must out shine any other bright star in the sky. Specially, the SMBH that is alleged to exist at the center of many galaxies is surrounded by all the stars of the galaxy and therefore if they exist shoud shine brightly. If the BH is far away it should at least shine like a bright star, if it is close by to discern a small angular disc then we should see a black spot in the middle of the apparent bright object. Black holes are not dark after all. It is just that we have so far not observed such bright objects in the sky.
    Tissa Perera

    Link to this
  8. 8. matthewfrancis 1:58 pm 09/13/2011

    My apologies for not checking in on comments recently.

    johnthetraveler: gravity waves entering the event horizon will not leave again, so they obey the same rules as light and matter when reaching a black hole. Two black holes orbiting each other can produce gravity waves, but these are traveling outward away from the event horizons, rather than being trapped.

    christina anne knight: it is true that general relativity is a classical theory, but it’s well-tested in a wide variety of contexts. The singularity may or may not exist (and certainly any valid quantum theory of gravity will have something to say about it), but it’s tucked away inside the event horizon, inaccessible to experiment, so I deliberately avoided talking too much about it.

    For the purposes of astrophysics and astronomy, the black hole is the event horizon, the ergosphere, and other “external” features.

    Link to this
  9. 9. christinaak 3:12 pm 09/13/2011

    thanks for responding matthew francis. i concede that general relativity has been validated within as you say “…a wide variety of contexts.” however, the space-time structure within black holes is altogether different from that found anywhere else. infinities in general normally indicate that there is a problem that needs addressing in a theory. the implied existence of singularities by general relativity indicates that there is a problem with the theory when applied to black holes. it is hoped that a quantum theory will address and eliminate this problem by placing a limit on space-time curvature. it is also reasonable to conclude that there may me be a limit on the amount of information that can be contained within a discrete unit of space. hence my suggestion that the volume within a black hole is composed of an incredible amount of smallest discrete units of space-time which remain in what i would call a state of ‘gravistatic eqilibrium’. in addition, because i think an evolutionary cyclic model best explains the the socalled fine-tuning of the cosmic parameters in our present universe, i also suggest that the info preserved in a state of ‘gravistatic equilibrium’ within black holes provides the ‘cosmogenetic space-time connection’ between cosmic cycles. another point i want to make is that we do not presently know the role of dark matter and dark energy (if there is any) in black hole formation. my own hypothesis is that if dark energy and dark matter exist then they are homologous (do borrow terminology from biology) structures along with the third type of matter which is ‘normal’ or baryonic matter. if these other types of matter exist it is likely that different fundamental forces are involved than the electromagnetic, weak and strong forces. also there is no reason to assume that these extra-normal types of matter operate within the confines of the same dimensional structure as that of baryonic matter which also may explain the difficulty in detecting them (although all three types of matter are probably interacting gravitationally). i go into more detail about these and other ideas in my book which has been ignored (but because i understand the history of science i am not surprised) thus far. anyway thanks for the opportunity to respond. now that it appears that the higgs boson probably does not exist maybe other ideas will be considered.

    Link to this
  10. 10. johnthetraveller 12:51 pm 09/15/2011

    Thanks for replying Matthew. I hadn’t expected you to, but very welcome. I’m aware that I might be displaying my ignorance, but:

    When I talked of gravity escaping the event horizon, I had been referring to the fact that the black hole mass inside the horizon is exerting gravitational attraction on objects outside the event horizon. Doesn’t that mean that waves or particles are crossing the horizon?

    If the gravitational attraction is instead caused by curvature of space that is outside the event horizon, doesn’t that mean that gravity is not associated with a wave or particle?

    Link to this
  11. 11. mdillingham 5:04 pm 09/21/2011

    Assuming that they could meet, what would happen if a black hole generated by the collapse of regular matter collided with a black hole generated by the collapse of antimatter?

    Are the properties that cause the two types of matter to annihilate on contact lost when the density goes to infinity?

    Link to this

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