A black hole is a massive object with such powerful gravity that not even light may escape from it. Black holes only have three unique properties which are mass, charge, and spin. At one time black holes were a speculative phenomena, but astronomers now understand that black holes are a relatively common and important occurrence in our Universe, unfortunately the public and science fiction still seems to be in dark. There are a lot of misconceptions about black holes:
- If the Sun was replaced by an equal mass black hole then the Earth would fall into it. In reality we would continue to orbit about the center of mass of the new black hole object and about eight minutes later after the Sun was removed it would be dark on Earth (that is how long it takes light from the sun to get to us).
- Supermassive black holes distort the space time around them in a very extreme way. Actually, the larger the black hole the smaller the distortion and tidal forces around it such that a very massive black hole hardly distorts the space time outside its event horizon, of course, every black holes does very strange things with space time inside the event horizon.
- Tiny black holes created by particle accelerators like the LHC may destroy Earth. The truth is that these tiny black holes would evaporate extremely rapidly via Hawking Radiation and they have such a small gravitational interaction they would not pull in any other matter.
- Black holes lead to extra dimensions. Why don't you jump into one and tell astrophysicists what you find?
Black holes are strange objects. Massive black holes shape the evolution of galaxies, charged black holes are thought not to exist, and spinning black holes pull space itself around at close to the speed of light. According to Einstein mass tells space time how to curve and space time tells mass how to curve. So all mass distorts space in a small manner, but black holes create what are known as singularities where the mathematics which describes the curvature of space time breaks down.
You can solve the equations of general relativity and see how black holes arise, but they also arise in the context of standard Newtonian physics. Consider a rocket launching from earth into space. In order for the rocket to free itself from the gravitational pull of Earth it must be moving at the
escape velocity (the actual situation is much more complicated than this, but suffice to say
it's... complicated). We can find the escape velocity for any object of mass, m, away from a more massive object of mass M by setting the object's kinetic energy, 1/2 m v
2, equal to the potential energy of the object in the massive object's gravitational field, GMm/r, where G is Newton's gravitational constant. A terrible thing happens when you consider what happens if the object had a velocity equivalent to the speed of light, c. Suddenly you find there in a mass and radius combination which creates and object so dense from which not even light can escape. The radius to which an object must be compressed to form a black hole is known as the Shwarzchild radius or the event horizon.
Karl Schwarzchild was a German mathematician who was working as an artillery lieutenant during World War I when he was the first person to solve the Einstein field equations. He found a solution corresponding to a physical object with strange properties: apparently matter and energy could enter, but not exit ( again it is actually more complicated as Hawking has taught us, but I digress ). His solution known as the Schwarzschild metric is a rather succinct description of the spacetime around a non-spinning black hole:
The details of this equation aren't important here. I have shown it for two reasons. First, it really is a thing of beauty that some of you will hopefully appreciate. Second, is the realization that as the radius of the object r approaches the Schwarzchild radius r
s the denominator becomes zero and dividing by zero is next to impossible. This is the
singularity. The singularity is unavoidable as no mathematical trick or coordinate transformation can rid the Schwarzchild metric of all singularities.
The astronomy of supermassive black holes
Observations of other galaxies, particularly nearby galaxies, reveal compelling evidence that nearly all galaxies have a super massive black hole at their center. The Milky Way has a supermassive black hole at its center known as Sgr A*. How these black holes form is not well understood, but it must have been long ago when the universe was very young such that the black holes had time to grow. They may form from the collapse of some of the first stars created in the Universe known as Pop III stars or they may form from the monolithic collapse of a cold could of gas in the early Universe. Many galaxies emit very high energy radiation from their centers (ultraviolet, X-ray or gamma ray) that is easily explained by a super massive black hole at their center. These galaxies are said to have Active Galactic Nuclei (AGN), but our Milky Way does not emit such high energy radiation. This an interesting and lucky fact that astronomers have explained by noting that if gas is actively falling onto a black hole it forms and accretion disk which heats up to very high temperatures. Thus matter falling into a black hole emits massive amounts of powerful radiation just
before it falls into the black hole. Active galactic nuclei are especially correlated with galaxies which have just undergone mergers with other galaxies which are gas rich; the theory, which is backed up by simulations and observations, says that when gas rich galaxies merge gas funnels into the central super massive black holes and induces a period of high luminosity. The black hole at the center of our Milky Way also undergoes periods of gas accretion or luminosity spikes in the X-ray to radio bands. One such event in May of 2003 was a powerful flare seen located just a few milli-arcseconds from the position of Sgr A* which corresponds to less than ten Schwarzschild radii from the black hole position.
Observing supermassive black holes
How do we know that we have really observed black holes not something else? This is a hard question and astronomers may often talk about compact massive objects instead of black holes if they are not certain about a particular object in the sky. In the case of the supermassive black hole at the center or our Milky Way more direct observations are possible. Astronomers have been watching Sgr A* for decades, but only with modern instruments has powerful evidence come to light. Observations of flare events close to the Schwarzschild radius of a suspected black hole like the event described above are one way. Also watching the gravitational influence of the dark object is another:
The movie above was made with high resolution near-infrared observations over many years (in the bottom left corner is the year of the observations) on the 10 meter Keck telescope in Mauna Kea by a group at UCLA led by Andrea Gehez. These stars are right at the center of the Milky Way in the immediate vicinity of Sgr A* and they are moving in a Keplerian orbit around a central mass which is unseen in optical light. The stars are moving at speeds up to 1400 km/s (or 3 million mph) and so using Kepler's laws of motion the central object is estimated to be four million solar masses. The object is also very minute. Given this great mass and small size astrophysicists only have one explanation for the object. In the near future radio astronomers plan to use interferometry to directly image the event horizon of Sgr A*.
An unexpected relationship between black holes and galaxies
We have good reason to believe that nearly all galaxies contain a central supermassive black hole. Furthermore, the mass of the central black hole strongly correlates with the mass, velocity dispersion, and momentum parameter of the corresponding host galaxy. The most interesting relation is that of the central black hole mass with the velocity dispersion of stars in the host galaxy bulge. This is known as the m-σ relation which has a very simple basic scaling:
Thus the mass of the central black hole and the velocity of nearby stars is highly correlated. This is an empirical relation and so the value of 5 here is approximate (for example in the plot below the value is 5.8 and in some previous work was as low as 4). This relation was discovered and reported in the literature in 2000 by two independent groups (Gebhardt et al. and Ferrarese et al.), but astronomers are still seeking a theoretical model able to elucidate the origin for the correlation.
What is so amazing is how strong the correlation is over a range of galaxy and black hole sizes as seen in the log-log plot above from a very recent paper on the archive by
Feoli and Mancini which complied data from Hu 2009. Even a hundred million solar mass black hole will not have a significant gravitational effect on the stars in the bulge of a galaxy (the black hole is big, but there are billions of stars and they are far away from the black hole's gravitational force which of course drops as distance
-2) so the m-σ relation is somewhat of a mystery. Likely the current relation is dependent upon the galaxy and black hole co-evolution (as evidenced by the fact that the empirical scaling is only measured for cosmologically very close galaxies). Theorists and
rock bands continue to search for a coherent explanation.
Look up and find your local black hole
Lets try and bring black holes back down to Earth by stargazing. The nearest (super massive) black hole is at the center of our Milky Way Galaxy in the constellation Sagittarius. Sagittarius according to Greek mythology is a
centaur archer who was shot with a poisoned arrow and in honor he was given a place in the sky in the constellation Sagittarius. The arrow of Sagittarius points towards the bright star Antares in Scorpius, but it also points to the galactic center and the super massive black hole that lies there. A modern interpretation of the constellation is as a teapot which is as I have outlined it
here, but I think the image of a centaur shooting an arrow in the heart of our galaxy is much more dramatic.
Sagittarius is best viewed during summer nights (this paragraph has been kind of western history and northern hemisphere centric, sorry) and can be found between the constellations Ophiuchus and Capricornus near the galactic plane. The actual object that is identified as the super massive black hole at the center of our galaxy is the luminous compact radio object Sagittarius A* (or Sgr A*) which is not visible in the optical spectrum. Another way to identify Sgr A* is that Scorpius almost wraps his tail around it. Look for Saggitarius's arrow and Scorpius's tail and you will have found a super massive black hole; happy sky hunting.
Gebhardt, K., Bender, R., Bower, G., Dressler, A., Faber, S., Filippenko, A., Green, R., Grillmair, C., Ho, L., Kormendy, J., Lauer, T., Magorrian, J., Pinkney, J., Richstone, D., & Tremaine, S. (2000). A Relationship between Nuclear Black Hole Mass and Galaxy Velocity Dispersion The Astrophysical Journal, 539 (1) DOI: 10.1086/312840
Genzel, R., Schödel, R., Ott, T., Eckart, A., Alexander, T., Lacombe, F., Rouan, D., & Aschenbach, B. (2003). Near-infrared flares from accreting gas around the supermassive black hole at the Galactic Centre Nature, 425 (6961), 934-937 DOI: 10.1038/nature02065
Ghez, A., Salim, S., Weinberg, N., Lu, J., Do, T., Dunn, J., Matthews, K., Morris, M., Yelda, S., Becklin, E., Kremenek, T., Milosavljevic, M., & Naiman, J. (2008). Measuring Distance and Properties of the Milky Way’s Central Supermassive Black Hole with Stellar Orbits The Astrophysical Journal, 689 (2), 1044-1062 DOI: 10.1086/592738_(cropped).jpg)
