References
Blaizot, J.P., et al., ‘Study of Potentially Dangerous Events During Heavy-Ion Collisions at the LHC: Report of the LHC Safety Study Group’, CERN, European Organization For Nuclear Research, Theoretical Physics Division, CERN 2003–001, 28 February 2003.
Dimopoulos, Savas, et al., ‘Black Holes at the Large Hadron Collider’, Physical Review Letters, 15 October 2001, Vol 87, Issue 16, pp 161602–1 to 161602–4.
‘Fight to save Earth from tiny Black Hole’, Sydney Morning Herald, 2 April 2008, p 9.
Jaffe, R.L., et al., ‘Review of speculative “disaster scenarios” at RHIC’, Reviews of Modern Physics, 1 October 2000, Vol 72, Issue 4, pp 1125–1140.
Kolbert, Elizabeth, ‘Crash Course: Can a seventeen-mile-long collider unlock the Universe?’, The New Yorker, 14 May 2007.
Leake, Jonathan, ‘Big Bang machine could destroy Earth’, The Sunday Times (London), 18 July 1999.
Matthews, Robert, ‘A Black Hole ate my planet’, New Scientist, 28 August 1999.
Muir, Hazel, ‘Dark destroyers’, New Scientist, Inside Science No 154, 19 October 2002, Insert pp 1–4.
Mukerjee, Madhusree, ‘A little Big Bang’, Scientific American, March 1999, pp 60–65.
Overbye, Dennis, ‘A giant takes on Physics’ biggest questions’, The New York Times, 15 May 2007.
Parikh, Maulik K., et al., ‘Hawking Radiation as tunneling’, Physical Review Letters, 11 December 2000, Vol 85, Issue 24, pp 5042–5045.
Walker, Gabrielle, ‘The biggest thing in Physics’, Discover Magazine, 13 August 2007, pp 45–49.
Black Holes Don’t Suck
‘Black Hole’! The name certainly conjures up the image of a sci-fimenace. Black Holes are truly strange ‘places’ where the Laws of Physics are turned completely inside out. And the expression ‘Black Hole’ has now eclipsed the ‘Bottomless Pit’ as something that takes, and takes, and takes—and never gives anything back.
Most of us wrongly believe that Black Holes are a kind of Cosmic Vacuum Cleaner, sucking everything around them into their voracious maw. The truth is that if the Sun were to be replaced by a Black Hole with the same mass as the Sun, the Earth would still maintain the same orbit—and would not get sucked in.
Black Holes come in a range of sizes, from possibly the size of an atom to about ten times bigger than our solar system. The largest one known is about 18 billion Solar Masses. (A ‘Solar Mass’ is an astronomical unit of mass equal to the mass of our Sun, i.e. 2 x 1030kg.)
The American Association of Astronomers states that practically every galaxy has a Black Hole at its centre. There’s a massive one of about 3.7 million Solar Masses located about 26,000 light years away at the centre of our galaxy, the Milky Way. But right next door to it (only a few light years away) is another Black Hole. It’s much smaller, only about 1,300 Solar Masses. And there are probably a few million smaller ones scattered throughout our galaxy.
The path to understanding Black Holes has been long and hard, earning scientists several Nobel Prizes.
A Few Numbers
Diameter of Sun = 1.4 million km
Mass of Sun = 2 x 1030 kg = 1 Solar Mass
Diameter of Earth = 12,750 km
Mass of Earth = 6 x 1024 kg
Mass of Moon = 7 x 1022 kg
Distance from Sun to Earth = 1 Astronomical Unit = 150 million km = 8.3 light minutes = 1AU
Distance from Sun to Pluto = 29–49 AU = 4.4–7.4 billion km. Average distance of 5.9 billion km = 5.5 light hours = 40 AU
Distance to Nearest Star, Proxima Centauri = 4.42 light years
Distance to centre of Milky Way = 26,000 light years
Diameter of Milky Way = 100,000 light years
Age of Universe = 13.7 billion years
Age of Sun = 4.6 billion years
Speed of Light = 300,000 km/sec
Nucleus of an atom = 2–12 x 10-15 m
Entire atoms = about 100,000 x 10-15 m
Black Holes
A Black Hole is a region of Space in which the gravitational field is so powerful that nothing, not even light, can escape its pull after having fallen past its event horizon.
The anatomy of a Black Hole
A static Black Hole
History of Black Hole Concept
In 1783, the British clergyman and amateur geologist/scientist, Reverend John Michell, started the Black Hole ball rolling. He wondered about a body in Space falling towards a truly huge star, say 500 times the size of the Sun (which is about 1.4 million km in diameter). In a letter to his friend Henry Cavendish (the English chemist and physicist who in 1798 made the first accurate measurement of the density of the Earth), which was published by The Royal Society, Michell stated that ‘a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently…all light emitted from such a body would be made to return towards it by its own proper gravity’.
Scientists already knew that objects had gravity, and that this gravity would attract other objects. But back then, nobody knew if gravity would affect something as wispy and ephemeral as light. John Michell must have been a deep thinker to ponder such a bizarre concept. He called this heavy star a ‘Dark Star’, because if all the light that it emitted were sucked back by its own gravity, it would be ‘dark’.
Soon after, in around 1795, the brilliant French astronomer and mathematician Pierre Simon, Marquis de Laplace, independently came up with the same concept of light interacting with enormously massive objects.
Gravity is Just Curved Space
At this time, scientists did not really believe that gravity would affect light. But in 1915, Albert Einstein published his ‘General Theory of Relativity’ in which ten equations known as Einstein’s Field Equations describe the fundamental force of gravitation as curved Space-Time and energy. Einstein said that the Fabric of Space-Time was made up of three space dimensions (left–right, backwards–forwards and up–down, or if you have studied highschool geometry, x, y and z) and one time dimension (that usually ticks away at one second per second). The special properties of Space-Time limits what you can do. For example, you always have to move forward in time, and you can’t shift matter or information faster than the speed of light.
Einstein said that a mass (such as a star) would warp or twist this Fabric of Space-Time. Think of the Fabric of Space-Time as being like a sheet of rubber. In empty Space with no objects to provide mass, the sheet is flat. But a star has mass, and this mass somehow curves the local Space-Time. A star makes a big dent in the rubber sheet, a planet makes a medium-sized dent and a small asteroid makes a tiny one. Light just follows the Fabric of Space-Time—running across the dents and bumps in the Fabric. This is how and why light is affected by gravity.
In 1916, the physicist and astronomer Karl Schwarzschild was the first to discover exact solutions to some of Einstein’s Field Equations. Black Holes were a part of his bizarre mathematical solutions—in fact, they are an essential part of the solutions of Einstein’s Field Equations. But even Einstein thought that this was just a mathematical accident, and in no way related to the real Universe, as he believed that stars could never shrink small enough to make a Black Hole.
The thinking all began to change in 1967 when the first Neutron Star was discovered by Jocelyn Bell and Antony Hewish. This proved that strange ultra-dense objects actually do exist in the Universe.
The structure of a Neutron Star is very strange. Its ‘atmosphere’ is made of ordinary atoms (such as those found on Earth) and electrons—but is only about one metre thick! It has a solid crust about 1.5 km thick, under which everything is ‘liquid’. But it’s a very strange ‘liquid’—mostly naked neutrons, and about a hundred million to a billion times denser than a White Dwarf (a small faint star of enormous density, which itself is a million times denser than water). This gives a Neutron Star an escape velocity of about half the speed of light, with a surface gravity about a million million times greater
than that experienced on Earth.
One way to understand these ultra-dense objects is to consider the workings of ‘escape velocity’.
Curved space bends light
‘Put your hand on a hot stove for a minute and it seems like an hour. Sit with a pretty girl for an hour and it seems like a minute. That’s relativity.’ Einstein
In this diagram the Space-Time fabric of our solar system is seen bent by the gravitational force of the Sun. In the absence of a gravitational field, light travels along a straight path (dotted line of Star A). A gravitational field produced by a massive object will bend the trajectory of the light ray (Star A) like a ball rolling along a warped table.
Escape Velocity
In 1783, John Michell was using the concept of ‘escape velocity’, i.e. the velocity needed to ‘escape’ from a gravity well.
Here’s how it works. If you throw a rock upwards, pretty soon it falls back down again. If you throw it upwards ten times faster, the rock takes longer to fall down—but it will still fall back to Earth. But if you propel the rock up with a speed of 11.2 km/sec, it will never fall back down to Earth. So the ‘escape velocity’ of planet Earth is 11.2 km/sec (or approximately 40,300 kph).
A Black Hole has such a massive density compared to its size, that its escape velocity is equal to the speed of light, or even greater. This means that light itself can never escape. In other words, we can never see it, hence the name ‘Black Hole’.
History of the Name ‘Black Hole’
In 1964, Ann Ewing wrote for the 18 January issue of Science News Letter about a meeting of the American Association for the Advancement of Science. Part of the meeting was about astrophysics. She wrote: ‘According to Einstein’s general theory of relativity, as mass is added to a degenerate star a sudden collapse will take place and the intense gravitational field of the star will close in on itself. Such a star then forms a “black hole” in the universe.’
And in 1967, according to the Scientific American, the famous physicist John Wheeler popularised the phrase in a public lecture called ‘Our Universe: The Known and Unknown’. ‘Wheeler recalls discussing such “completely collapsed gravitational objects” at a conference in 1967, when someone in the audience casually dropped the phrase “black hole”. Wheeler immediately adopted the phrase for its brevity and “advertising value”…’ Well, one thing is sure—‘Black Hole’ is certainly a lot easier to say than ‘completely collapsed gravitational object’.
Black Hole Formation
In many cases, a Black Hole evolved from a star. Stars are born in a ‘Stellar Nursery’ as protostars. A small protostar of less than 0.075 Solar Masses will turn into a Brown Dwarf. A heavier protostar (between 0.075 and 0.5 Solar Masses) will then get hot enough for nuclear burning to become a Red Dwarf. A protostar between 0.5 and 8 Solar Masses will eventually turn into a White Dwarf.
But a star’s final evolution is very different if it starts off quite massive, say, more than about 20–25 Solar Masses. After the protostar stage, it lives as a large star, about 5 million km in diameter. It will burn hydrogen for about ten million years, and then expand to about 50 million km in diameter. It will then burn helium in its core for about one million years, and expand enormously to about 700 million km in diameter. (Just for comparison, in our solar system, the Earth is about 150 million km from the Sun, while Mars is about 225 million km away from the Sun.) It will burn its way quickly up the Periodic Table, getting through carbon, neon, oxygen and silicon in just 1,000 years, until it gets to iron. Once it gets to iron, the nuclear furnace is extinguished, because getting to elements heavier than iron needs an input of energy. Now that the nuclear fires are out, there is no longer any outward rush of radiation. So the star collapses, releasing a huge amount of gravitational energy, and explodes.
Burning—Nuclear or Chemical
Chemical burning is something we see all the time—in a forest fire where the carbon in the trees combines with the oxygen in the atmosphere, or on a gas stove where the carbon in the methane gas combines with the surrounding oxygen in the atmosphere. In each case, carbon combines with oxygen to give carbon dioxide and energy (usually heat).
Nuclear burning is very different in two ways.
First, it doesn’t need any oxygen. Instead, two elements combine to give a third element (and sometimes a fourth). For example, two hydrogen atoms combine to make a helium atom. But the mass of the atom of helium produced is slightly less than the mass of the two hydrogen atoms. There is some mass missing. This mass is converted directly into energy. (You can work out how much by Einstein’s famous equation, E = mc2, where ‘E’ is the energy produced, ‘m’ is the mass that is turned into energy and ‘c’ is the speed of light.)
Second, nuclear burning delivers absolutely enormous amounts of energy, much much more than chemical burning.
After all the nuclear burning, we now have a collapsing star weighing more than approximately 2.5 Solar Masses. In this case, it will shrink so far that it will collapse into a point with infinite density and zero volume. Let me just emphasise that the density is not just colossally high, but infinite. And the volume is not just very small, but zero.
The technical name for this ‘thing’ with infinite density and zero volume is a ‘Singularity’—but the popular name is ‘Black Hole’. And this point in Space is hidden inside what is called the Event Horizon.
By the way, the term ‘Black Hole’ is a little ambiguous—it can refer just to the Singularity or, more usually, to the Event Horizon with the Singularity inside it.
A Star is Born
Stars are born in what astronomers call a ‘Stellar Nursery’. This is a much more romantic name than a Giant Molecular Cloud (GMC), but they are the same thing.
This is a simplified diagram of how stellar evolution begins. The first stage is the formation of a Protostar, which is a large vortex of dust and gas that accumulates matter. This large star will collapse into a variable star, which eventually settles down into a main sequence star and will continue to accrete matter as long as the supply lasts.
Event Horizon
Black Holes don’t actually have a physical surface, but instead they have the so-called Event Horizon—the point of no return—which has the shape of a sphere around its central Black Hole. At the Event Horizon, the escape velocity is equal to the speed of light.
Inside the Event Horizon, every ray of light, and every possible particle of matter, has to take a path towards the Singularity. The Space-Time Fabric inside an Event Horizon is curved in such a way that all roads lead to the Singularity. For that reason, once anything (light, any other energy, or matter) crosses the Event Horizon, it can never leave, and is doomed to end up at the central Singularity.
Suppose that our Sun was magically compressed so that its density got high enough to set off the gravitational collapse that would lead to infinite density and a Singularity or Black Hole. The Singularity would have zero volume. But the Event Horizon would be 3 km away. It is not a physical space or barrier—in fact, if you were falling into a supermassive Black Hole, you would hardly notice crossing the Event Horizon on the way into the Black Hole.
Sizes of Black Holes
It seems that Black Holes can cover a range of sizes, from the microscopic to the super supermassive.
But how do you measure the size of a Black Hole when it is just a point in Space with mass and zero volume? Well, you forget the Singularity, and just calculate the size of the Event Horizon. The exact formula for the Schwarzschild Radius of the Event Horizon of a non-rotating, non-charged Black Hole is given by:
rsh (km) = 2GM/c2
where ‘G’ is Newton’s Constant of Gravity, ‘M’ is the mass of the Black Hole and ‘c’ is the speed of light.
But a simple approximation for the radius is:
rsh (km) = 3 x mass of Black Hole/mass of Sun
So if you had a Black Hole with the mass of the Sun, the Event Horizon would have a radius of 3 km. But Black Holes seem
to come in all sizes. A Black Hole with the mass of the Earth would have an Event Horizon 18 mm in diameter.
Black Holes—Supermassive or Heart of Darkness
Black Holes come in all sizes, so let’s begin with the Big Mothers.
Most of these range from 100,000 to one billion Solar Masses, with sizes ranging from 600,000 km to 6 billion km in diameter.
The biggest known Black Hole so far clocks in at 18 billion Solar Masses and goes under the name of OJ 287. Part of a binary Black Hole system, its companion is about 200 times less massive, only (!) 90 million Solar Masses.
Sgr A* (see also p 245), the Black Hole at the middle of our galaxy, the Milky Way, is about 3.7 million Solar Masses (about 20 million km in diameter). Most Black Holes at the centre of galaxies have major bursts of activity (such as cataclysmic blasts of X-rays) every few days. But Sgr A* is very quiet at the moment, with hardly any activity—it’s almost on a starvation diet. However, about 350 years ago, it was gobbling stars and frantically gulping and slurping huge clouds of gas and other matter at the rate of a million million tonnes per second—and it did this for about ten years. It was also blasting out huge amounts of gamma radiation, which hit an enormous gas cloud, called Sig B2, about 350 light years from Sgr A*. After this gas cloud absorbed the gamma rays, it then began emitting vast quantities of X-rays which are only now hitting Earth.
Science is Golden Page 18