“Dark Stars”
In the late 1700s geologist John Mitchell and mathematician Pierre-Simon Laplace postulated the existence of objects referred to as “dark stars.” These were hypothetical objects whose mass would stipulate a surface escape velocity that would exceed the velocity of light.It wasn't until nearly 120 years later that the concept of a black hole began to gain some real mathematical and scientific support from the seminal work of Einstein's theory of General Relativity and Karl Schwarzschild’s solutions to Einstein's field equations. Even so, Einstein viewed black holes as being more of an interesting theoretical exercise than a realistically possible natural phenomenon. Still, the notion continued to gain traction as theoreticians further defined and refined the properties and structure of these still-theoretical entities.
It wasn't until 1971 that black holes began to gain observational support with the discovery of Cygnus X-1.
An Invisible Companion: First Evidence
In the constellation Cygnus, astronomers noticed an x-ray source that was quite different from other previously observed x-ray sources in that it would “flicker” as opposed to producing the more rhythmic repeating signal of pulsars. Dubbed Cygnus X-1, this x-ray source had a signature that looked more like a candle trying to stay lit in a breeze. The flickering was so fast that it could not be an object occulting the x-ray source since it would require that object to be moving across the line of sight at faster than light speeds. On top of that, there were occasional bursts of radio emissions emanating from the same point in the sky. That point was later identified to be a star designated HDE 226868, a blue supergiant, spectral class B0, with an estimated surface temperature of 31,000 K. This star was not likely the source of the x-ray emissions since B class stars do not have enough surface temperature to emit significantly in the x-ray bands.Subsequent spectrographic analysis of HDE 226868 showed Doppler wobbling with a shift characteristic of a spectroscopic binary. The period was measured to be 5.6 days but only one star was visible. HDE 226868, based on its spectral classification, is estimated to have a mass of 30 Mʘ, while its unseen partner is estimated to have a mass of 7 Mʘ. That is considerably above the threshold for neutron star. The only compact object that fits the bill for HDE 226868’s missing companion is a black hole.
Astronomers are confident that this was the first observational evidence of the stellar mass black hole that fully corroborates theory. It is far from unequivocal proof, however. It is referred to as a black hole candidate. [Lewin 06]
A Simple Portrait of Darkness
Black holes are interesting in that they are the most extreme objects in the universe and yet they are extremely simple to describe having only three basic characteristics. They can be described by mass, by charge and by spin and that's it!Nonrotating black holes, the simplest of all, also called Schwarzschild black holes, are described only by their mass. If an intrepid astronaut were to encounter a 10 Mʘ Schwarzschild black hole in the course of his travels he would see a perfectly dark region… no color, no texture, nothing. But, he would detect the curvature of spacetime and the increasing "gravitational
Figure 1 Nonrotating black hole (artist impression)
pull" as he moved closer to the dark region. He may likely see the background stars lensed around the black hole’s boundary so it in d appear that this dark region was surrounded by a shimmering ring of light. [Fig. 1]
It is only the black hole’s mass that describes its very simple structure. It can be defined as an object with enough mass to raise its surface escape velocity to be equal to, or exceed, the speed of light. As shown by…
where
So let's get back to our astronaut’s black hole. He steers his ship into a safe, but close, orbit around the black hole. Using Kepler’s 3rd Law he is able to accurately measure the object’s mass of precisely 10 Mʘ.
Next he wants to know how close a “safe” orbit is. For that he needs to know the radius of the point-of-no-return… the black hole’s event horizon. Using the equation derived by Schwarzschild…
he plugs in the 10 Mʘ value for M (or about 1.99 X 1031 kg) that works out to a Schwarzschild radius of only about 29.5 km. Compare that to our 1 Mʘ Sun’s radius of 695,500 km!
Since our astronaut is on a mission of scientific exploration he decides to send a probe to the black hole’s horizon to gather data. To make it easy to identify against the background of stars the probe is flashing a brilliant white light, once every second. He launches the probe directly toward the center of the region of darkness tracking it by its flashing white light and also by the telemetry that the probe is sending back to the ship. So far, other than the probe’s rapid acceleration towards its destination nothing unusual is happening.
As our probe gets closer to the black hole's event horizon the astronaut begins to notice something unusual. The white light that has been flashing consistently once per second seems to be slowing down a bit. It couldn't be that the batteries are draining because the probe had a full charge. Something else… the white light doesn't seem to be quite as white as it was before. It is starting to show a redder tint. What the astronaut is seeing are relativistic effects experienced by the probe as it accelerates toward the strong gravitational field. The closer that the probe gets to the event horizon time slows down as viewed by the astronaut and his frame of reference. Flashes of light are not only longer but the intervals of darkness between flashes are lengthening as well. But if our probe could tell us what was happening from its perspective everything would appear to be normal the beacon would be flashing at 1 flash per second.
The strong gravitational field also causes a gravitational red shift. It's as if the wavelength of light is being stretched as it tries to escape the powerful gravity and its distortion if spacetime.
So as our astronaut continues to observe the probe's descent into darkness the probe continues to flash redder until the beacon can only be seen in the infrared. Its time is slowing to the point that the intervals between each flash are growing to be multiples, then exponents of each other. The last view our astronaut has of the probe it appears to be motionless in the deep infrared. It never actually appears to cross the event horizon.
What the probe is experiencing however is quite different. Even though the astronaut has a bizarre view of its journey everything appears to be quite normal on the probe even as it crosses the event horizon. Its strain-gauge sensors do detect an uneven gravitational pull since the nose of the craft is closer to the black hole’s center of mass then the after portion. It is being tidally stretched. The force differential continues to increase until the probe is ripped apart, eventually into thin streams of particles accelerating toward the center known as the singularity. Then, even the particles are shredded.
Unfortunately, no telemetry reaches the astronaut's ship after it crosses the event horizon. It’s signal is lost along with the image of the flashing light appear to be frozen in time at the ‘surface.”
It’s All Relative
Clearly no definition of black holes is adequate if we do not take relativity into account. Einstein's General Theory of Relativity describes how matter shapes space-time and then how matter moves through it. As I mentioned before, one of the consequences of General Relativity was the prediction that a large mass compressed into a small volume could distort space-time to the extent that the slope of the gravitational well could become, undefined. [Fig. 2]
Figure 2 Rubber sheet analogy
That would be problematic for anything or anyone who crossed that horizon since all possible futures point only toward the center of mass, the singularity.
Mass, Charge and Spin
As we will see when we examine how black holes form there needs to be enough mass compressed into a small enough volume for the gravitational force to overwhelm the electromagnetic and nuclear forces that resist further compression. When that limit is reached the force of gravity becomes irresistible and matter collapses into a theoretical point of infinite density known as the singularity. However, most astrophysicists believe that quantum effects will govern the maximum possible compression and zero volume is not possible.The second property the black hole can exhibit is electrostatic charge. Charged black holes are thought to be rare however, since the electromagnetic force is so much more powerful than the gravitational force a black hole with charge would effectively “reach out” and be quickly neutralized by opposite charges attracted from the interstellar medium.
When we add the third property of spin that's when things get really interesting and really weird.
If you were to take a child's toy top and spin it so that it was happily balancing on its point it would have the identical properties as it would have if it was resting on a tabletop except for its angular momentum. This is not the case with black holes. They are relativistic objects. A rotating black hole can actually drag space-time around with it. The property is known as frame-dragging. To visualize it imagine space-time being a rotating fluid that is spiraling and accelerating down a bathtub drain.
The complex mathematics of a rotating black hole was best described by University of Texas astrophysicist Roy Kerr. Rotating black holes are likely to be common and some can have extreme rates of rotation. The black hole candidate GRS 1915+105 was discovered in 1992. It is an x-ray source and a spectroscopic binary a distance of 11 kpc. Studies have indicated that it is a heavy stellar black hole at 10 to 18 Mʘ spinning at an astonishingly high 69,000 rpm (1,150 rps). [Castro 1996] This is near the theoretical limit.
Black Holes in Cross-Section
Let's take a closer look at the structure of a Kerr black hole [Fig. 3]. Since the rotation of the black hole twists space-time along due to frame dragging the structure is a bit more complex than a nonrotating Schwarzschild black hole. There is more to the Kerr black hole than the singularity at the center of mass and an event horizon. In fact, even the singularity is different in that it is not defined as the point but rather because of the sweep of space-time it assumes a ring-like configuration. This is still the region were space-time curvature becomes infinite but because of frame dragging it’s smeared out, coplanar to the plane of rotation. Moving away from the singularity we encounter the event horizon which has a roughly spherical shape. As in a nonrotating black hole is the point of no return but there is an interesting twist.
Figure 3 A rotating black hole
In a Reissner-Nordstrøm black hole there are two event horizons where time and space flip. Roger Penrose described that region as something freakishly bizarre since that's where all the matter and energy falling into a black hole piles up. In their 1989 paper Canadian physicists Eric Poisson and Werner described that region as a violent zone of "inflationary instability.” It's where everything… mass, energy, pressure, everything… keeps growing exponentially! And yet, all futures are still directed downward toward the singularity. It's a frightening concept, the mathematics even more so. [Poisson 1989]
Surrounding the event horizons is an interesting region that has the shape of an oblate spheroid called the ergosphere. This is a region where you paradoxically have to expend energy to remain still. Frame dragging is sweeping space-time around the rotating black hole. This is analogous to trying to swim against the current of a powerful river. You either swim like crazy against the flow or you are carried downstream at relativistic velocities. In fact, you would need to be swimming faster than the speed of light in order to be still and this is impossible. Interestingly, an object is not doomed to oblivion in the ergosphere (assuming it could withstand the fragmentation, radiation and temperatures). Penrose theorized that rotational energy can actually be extracted from a rotating black hole so that an object falling into the ergosphere could be split with one part spiraling inward to the event horizon and the other part ejected outward like a slingshot carrying with it some of the angular momentum of the rotating black hole and now having a greater mass-energy than it had when it went in. The mass-energy of the divided portion that fell in became negative and the positive mass-energy was transferred to the ejected object along with extra angular momentum.
Just beyond the ergosphere and the static limit of a black hole is the photon sphere. Imagine a beam of light, say the image of a distant star, grazes a black hole. Photons of light traveling at particular angles can actually become trapped in an orbit around the black hole circling it until perturbed. But these orbits are inherently unstable so they would be most likely to occur in nonrotating black holes. The radius of the photon sphere in a Schwarzschild black hole is 1.5 times the Schwarzschild radius.
Maelstrom
If a black hole was to exist in isolation, ignoring the contortions of space-time, it might be viewed as a tranquil place… dark, distorted, weird but uninteresting. But if a stellar mass black hole exists as part of a binary pair then the stage could be set for a spectacular maelstrom.The x-ray flickering that we observed coming from black hole candidate Cygnus X-1 [Fig. 4] is likely the signature of a black hole feeding off its larger companion. Material from the larger star is filling its Roche lobe and extending beyond it, crossing the Lagrangian point and cascading toward the black hole. As it spirals inward it forms an accretion disk. As the material’s velocity increases it is subject to high frictional (thermal) heating and also to plasma current heating. The matter that came from the companion star now begins to glow in the x-ray bands at a Tmax of millions Kelvin. [Poutanen 2007]
Not all the energy from accretion is radiated outward. Some of it crosses the event horizon and falls inward and is lost. Some is launched away. All that rapidly spiraling and charged material has a property of being able to set up powerful magnetic field lines. A black hole that is accreting matter can become a dipole.
Figure 4 Cygnus X-1 in X-rays from ESA / INTEGRAL
While some of the accreting material will spiral into the event horizon some of the superheated plasma gets caught up and ejected by the magnetic flux in twin relativistic jets perpendicular to the axis of rotation. [Fig. 5] This phenomenon occurs at the stellar mass level as well as at the supermassive black hole level in the hearts of most galaxies.
Figure 5 Twin jets of subatomic particles ejected by magnetic flux perpendicular to the axis of rotation.
Small, Medium and Supersized, BH Formation
We have very strong evidence for the existence of two classes of black holes. The first being the stellar mass black hole and the second being supermassive black holes that can have masses in the billions of solar masses. Two other types of black holes have been hypothesized and they include microscopic black holes that may have formed during the Big Bang and also intermediate mass black holes that may exist in the hearts of globular clusters or some dwarf galaxies. First let's consider the stellar mass black hole.Stellar Mass Black Holes
When a massive star nears the end of its life it continues to fuse heavier elements from lighter ones all the while maintaining its hydrostatic equilibrium. For most of its brief 10 million year main sequence lifetime the star burned hydrogen into helium. But with about one million years to go the hydrogen supply in the core begins to exhaust resulting in an inward crush due to gravity and soaring temperatures. When the core temperatures rise past 170 million Kelvin helium begins to fuse into carbon and oxygen.With just one thousand years to go new cycles of fuel exhaustion followed by rounds of fusion convert the carbon and oxygen into neon and magnesium, then into oxygen and magnesium, followed by silicon and sulfur. A cutaway of the star would look like a hot thermonuclear onion. The silicon and sulfur core has a temperature approaching 2 billion K and just days to live. The pressure of collapse drives the core temperature beyond 3 billion K and then silicon and sulfur core begins to fuse iron but because iron fusion takes in more energy than it produces hydrostatic equilibrium is destabilized. When the sphere of iron rises to a mass of 1.44 Mʘ , the Chandrasekhar limit, it collapses in less than a fraction of a second. The core collapses at velocities reaching nearly 1/4 the speed of light and showering the universe with neutrinos. The rebounding shockwave produces a Type II supernova, one of the most powerful explosions in nature that obliterates the progenitor star. Depending upon the core mass of the progenitor a Type II supernova can leave behind one of two types of relics.
On the lean side of a ≈ 3-4 Mʘ threshold (the Tolman-Oppenheimer-Volkoff limit) the resulting relic is a neutron star, a peculiar object that is essentially a dense aggregation of tightly packed neutrons. The second and even more extreme type of relic is the black hole. It results when the progenitor star’s core has a mass in excess of the ≈ 3-4 Mʘ limit. At those masses, even neutron degeneracy pressure (resulting from the Pauli Exclusion Principle) cannot resist the inward crush of gravity. Hydrostatic equilibrium collapses, the dead star’s mass reaches near infinite density, space-time curvature approaches infinity and the new black hole is born. (There is some uncertainty here however. Beyond the Tolman-Oppenheimer-Volkoff limit of ≈ 3-4 Mʘ Quark degeneracy pressure may resist further collapse although this is an area of ongoing research.) [O’Connor 2001]
There are other ways for stellar mass black holes to form other than core-collapse supernovae. Black holes can also form the merger of compact objects such as two neutron stars or neutron stars and white dwarfs.
As these compact objects tightly orbit each other they are engaged in a fatal dance. Gravitational interaction produces gravity waves that radiate away the angular momentum (orbital energy) of the two stars. This makes it inevitable that the two compact objects will at some point merge. When they do their combined mass easily exceeds the TOV limit and a new black hole is born in a brief, but powerful shower of gamma rays that heralds its arrival. This is one hypothesized explanation for the observation of short duration gamma ray bursts.
Supermassive Black Holes
At the other end of the size spectrum are the true giants. These are the black holes that reside in the hearts of most galaxies.Since the invention of the optical telescope the center of the galaxy has been off limits to observation due to intervening gas and dust. Only with the advent of infrared and radio astronomy have we been able to explore what is going on at the heart of the Milky Way. The view has been fascinating!
Several teams have been exploring the curious orbital dynamics of stars surrounding a radio source known as Sagittarius A*, Sgr A* for short, at the galactic center. It was discovered in 1974 by astronomers Bruce Bailick and Robert Brown using radio interferometry techniques. Just about 28 years later a team led by Rainer Schodel of the Max Planck Institute for Extraterrestrial Physics reported tracking a star designated S2 that appeared to be ignored it around an unseen object. Recently, another team led by UCLA’s Dr. Andrea Ghez has been using the advanced adaptive optics of the Keck telescope in Hawaii to study the Sgr A* region and S2 (along with other stars) with unprecedented resolution. Over the past 16 years astronomers have been tracking the positions of these stars and plotting their orbits. It becomes readily apparent is that they are orbiting something truly gargantuan. S2 has nearly completed one observed revolution around the massive unseen object and has a period of 15.56 years.
Figure 6 Orbital dynamics of stars surrounding Sgr A*
Analysis of S2’s Keplerian orbit [Fig. 6] shows that it is orbiting an object with a mass of about 4 million Mʘ. The object has a radius no larger than 45 AU. On closest approach to Sgr A*, S2 is whipping around with a ballistic velocity of nearly 2% of the speed of light! Speeds in excess of 5,000 km/s! Only one known object with such low luminosity could have a mass of 4 million Mʘ occupying a volume with a radius of 45 AU… that is a supermassive black hole. This is pretty solid empirical evidence for the SMBH.
Further research has indicated however, that Sgr A*, the radio emissions source, may not correspond exactly to the black hole's center of mass. The radio emissions seem to be arising from a bright spot near the hole’s event horizon in the accretion disk or in a relativistic jet. This is another area of ongoing investigation.
There doesn't seem to be an upper limit in terms of the size of the supermassive black hole but it is proportional to its host galaxy. The largest SMBH we have identified resides in the giant elliptical galaxy M87. It has a mass estimated to be a staggering 6.4 billion Mʘ! M87 is also unusual in that it has a prominent relativistic jet shooting out from its nucleus almost certainly powered by the black hole at its heart. [Fig. 7] This jet is estimated to be 5,000 ly long and is tightly collimated but the Chandra observatory has detected lobes of matter extending nearly a quarter million light years away from the jet in both directions.
Figure 7 M87's relativistic jet
SMBH Formation
How supermassive black holes form is not entirely clear. We do know however is that they appear to be at the centers of most galaxies and the mass of the supermassive black hole seems to be proportional to the mass of the galactic bulge. This relationship correlates across many galaxies not just the Milky Way. This is known as the M-sigma relation and implies a co-evolution of the galaxy with its supermassive black hole. Further, there is a relation between galaxy’s bulge and the dark matter halo that surrounds most if not all galaxies. There appears to be a clear and inextricable connection between the dark matter halo, the galactic bulge and the supermassive black hole. [Umeda 2009]In fact, this is an interaction that needs to be considered, and is often overlooked. For example, when modeling a galaxy’s SMBH. Gebhardt & Thomas in 2009 showed that just accounting for a dark matter halo increased the black hole’s mass of the giant elliptical galaxy M87 by a factor of two [Schulze 2011]
However, what would that interaction look like? If the black hole was rotating, would there be a dark matter accretion disk (maybe superposed on any baryonic matter accretion disk) due to relativistic frame dragging? The dark matter accretion disk would be "cold" since there is no friction or blackbody radiation in the absence of electromagnetic interaction. File this under speculation.
Some theories propose that sometime between 300,000 and 1 million years after the Big Bang over-densities of matter (within dark matter halos) collapsed to form supermassive black holes as active galactic nuclei concurrently with the galaxies themselves. The big question is what happened in between? What is the connection between the collapsing gas cloud and the supermassive black hole? Astronomers are unsure if the intermediate step was from the aggregation of stellar mass black holes, or the collapse of highly speculative supermassive "relativistic stars," or did the proto-galaxy collapse directly into a supermassive black hole at the very start?
Again, this is an area of ongoing investigation.
Intermediate Mass Black Holes
We have seen powerful and convincing evidence for the existence of stellar-mass black holes and the supermassive black holes that reside in the hearts of most galaxies but where are the intermediate mass black holes? There is a mass distribution gap. Is there some principle that says that a black hole can grow to only 40 or 50 Mʘ? Is there a mechanism that prevents the aggregation of matter in the hearts of galaxies in amounts less than the supermassive variety, a choke point?At a conference at UC Berkeley last March I asked UCLA professor Andrea Ghez what her thoughts were about the evidence pointing to the existence of intermediate mass black holes and she responded that they are “still a matter of some controversy.” Frankly, this surprised me since it seems counterintuitive. Why couldn't there be intermediate mass black holes forming in the hearts of globular clusters? Some have speculated that ultra-luminous x-ray sources (ULX’s) could be the direct result of intermediate mass black holes (or IMBH’s) swallowing matter. And the M-sigma relation predicts the existence of IMBH’s in lower luminosity or dwarf galaxies with masses ranging from 104 to 106 Mʘ. The biggest problem doesn't seem to be a lack of direct observational evidence for their existence but rather a lack of a formation mechanism that's airtight.
Primordial Black Holes
In 1971, Stephen Hawking laid some seminal groundwork in theoretical astrophysics when he proposed the notion of primordial black holes. These black holes, in the billions, may have formed in the enormous mass-energy densities that existed in the fraction of a second after the Big Bang. These primordial black holes would've occupied a volume equal to that of subatomic particle but contained a mass equal to that of the mountain.Hawking further went on to show that primordial black holes would have a limited lifetime (t) especially given their small mass, a lifetime of roughly 10 billion years. Lifetime???
Are Black Holes Forever?
In short, no. In quantum mechanics the uncertainty principle allows for (actually it requires) the creation of virtual particles out of nothing. These particles exist for the briefest of moments before annihilating each other. The creation of these particle-antiparticle pairs violates conservation of mass-energy laws for an instant, but since the pairs immediately annihilate themselves the sum of the pairs is zero and all is well. Strange as it sounds these virtual particles do exist. They have been experimentally verified and exert a measurable pressure.But at the extreme edge of a black hole's event horizon something really weird happens. When two virtual particles are created one dashes across the event horizon and is lost into the black hole. The other survives and escapes into surrounding space and importantly, it reduces the black holes mass by a tiny amount. Over time the mass lost is cumulative.
From the point of view of an observer outside the black hole it would appear that the black hole created and emitted a particle. In fact, it would appear that the black hole would be emitting a measurable flux of particles that would cause it to "glow." It's not a paradox because the particle creation and emission is taking place on our side of the event horizon so that the black hole is, indeed, black. Interestingly, the energy for the glow is coming at the expense of the mass lost in the hole. So over time the black hole shrinks, and the more it shrinks the faster it will radiate (the greater the flux) until it explodes into a flash of radiation.
Hawking can claim credit for the theoretical discovery of black hole evaporation. The particles radiating away from an evaporating black hole are referred to as Hawking radiation. Curiously, this gives black holes temperature. And the evaporation rate (and temperature) of a black hole is inversely proportional to its mass. The smaller the black hole higher the evaporation rate and the higher the temperature as in…
Even so, black hole evaporation can be ponderously slow. You can estimate a 1 Mʘ black hole to take over 1067 years to evaporate as expressed by…
In other words, we’re in for a considerable wait. It is possible however that we may see the lingering gamma ray flashes associated with the evaporation of the primordial black holes that may have been formed during the Big Bang. They are predicted to have a unique gamma ray signature and so far none have been detected.
Unanswered Questions Remain
There are still mysteries however… where are all the stellar mass black holes? Theoretically, there should be vast numbers of black holes. [Ozell 2010] In the 13.7 billion year history of the universe there must have been unaccountable billions of stars massive enough to form Type II supernovae that have collapsed into black holes. Where are they? Sure, they can be difficult to detect given their dark nature but to date the count of verifiable stellar mass black hole candidates numbers just in the dozens.For example, there was the demise of supernova SN 1987a, the most studied supernova in history. The progenitor star was an unusual class B3 blue supergiant with a mass of about 20 Mʘ in the Large Magellanic Cloud at an estimated distance of 51.4 kpc. [Gilmozzi 1987] Twenty-four years later despite intense observational study the remnant is still missing.
Figure 8 SN 1987a
Our studies have taken us to the theoretical boundaries of these most extreme of objects either by indirect observation through powerful telescopes or through supercomputer modeling. Even though we may never directly observe a black hole in situ we can say with confidence that they are real and they are extraordinary!
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