# Black Holes - No need to be afraid!

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Black Holes seem to have a bad press that is largely undeserved.  The lecture will explain what Black Holes are, how we can discover them even through they cannot be seen and how Stephen Hawking has shown that they are not totally black!

Gresham Lecture, Wednesday 27 October 2010

Black Holes – No need to be afraid!

Professor Ian Morison

Black Holes – do not deserve their bad press!

Black holes seem to have a reputation for travelling through the galaxy “hovering up” stars and planets that stray into their path.  It’s not like that.  If our Sun were a black hole, we would continue to orbit just as we do now – we just would not have any heat or light.  Even if a star were moving towards a massive black hole, it is far more likely to swing past – just like the fact very few comets hit the Sun but fly past to return again.  So, if you are reassured, then perhaps we can consider….

What is a black Hole?

If one projected a ball vertically from the equator of the Earth with increasing speed, there comes a point, when the speed reaches 11.2 km/sec, when the ball would not fall back to Earth but escape the Earth's gravitational pull.  This is the Earth's escape velocity.  If either the density of the Earth was greater (so its mass increases) or its radius smaller (or both) then the escape velocity would increase as Newton's formula for escape velocity shows:

(0 is the escape velocity, M the mass of the object, r0 its radius and G the universal constant of gravitation.)

If one naively used this formula into realms where relativistic formula would be needed, one could predict the mass and/or size of an object where the escape velocity would exceed the speed of light and thus nothing, not even light, could escape.  The object would then be what is termed a black hole.

Suppose that the density of the Earth was vastly increased but it was able to retain its present size so the escape velocity just reached the speed of light at the surface and so became a black hole.  The surface of the Earth would then become what is termed the event horizon of the black hole.  If the mass remained constant but the diameter of the Earth then reduced under the effects of the immense gravity, the region, whose diameter was the original diameter of the Earth and from which nothing could escape, would remain exactly the same size.  The fundamental point is that the diameter of the event horizon bears no relationship to the size of the matter forming the black hole, only its mass.  As we shall see, we believe that virtually all (if not all) of the interior of a black hole is empty space.

Black holes have no specifically defined size or mass; until recently we had only found evidence for black holes in two circumstances.  The first, with masses of many millions of solar masses, are found the heart of galaxies and are called super-massive black holes whilst the second are believed to result from the collapse of a giant star of perhaps 20 solar masses whose stellar core has a mass exceeding ~ 3 solar masses. This is the point at which we believe that neutron degeneracy pressure (which allows stellar cores in the range 1.4 to 3 solar masses to form neutron stars) can no longer prevent gravitational collapse.  More recently evidence has been building for what are called intermediate mass black holes having a mass of perhaps 40,000 solar masses which have been found at the centre of what have in the past been classified as globular clusters.  Omega Centauri is one such cluster, but the evidence of a black hole coupled with the fact that it contains many more young stars than globular clusters implies that, instead, it might be the remnant core of a dwarf galaxy whose outer stars have been stripped off by the gravitational effects of our own galaxy.

The idea of a black hole can also be thought of in terms of Einstein’s General Theory of Relativity.  This states that a massive body distorts the space around it making it curved so that light, for example, no longer travels in straight lines but curves round the location of the mass.  A black hole is simply when the mass is so great that the curvature of space traps the light which can no longer escape.

A Schwarzschild Black Hole

In the simplest case in which the stellar remnant is not rotating, the spherical surface surrounding the remnant within which nothing can escape is called the event horizon which has a radius, called the Schwarzschild radius, given by

RS = 2 GM/c2

The interior of an event horizon is forever hidden from us, but Einstein's theories predict that at the centre of a non-rotating black hole is a singularity, a point of zero volume and infinite density where all of the black hole’s mass is located and where space-time is infinitely curved.  This author does not like singularities; in his view they are where the laws of physics are inadequate to describe what is actually the case.  We know that somehow, Einstein's classical theories of gravity must be combined with quantum theory and so relativity can almost certainly not predict what happens at the heart a black hole.

Particle physics tells us that nucleons are thought to be composed of up quarks and down quarks.  It is possible that at densities greater than those that can be supported by neutron degeneracy pressure, quark matter could occur - a degenerate gas of quarks.  Quark-degenerate matter may occur in the cores of neutron stars and may also occur in hypothetical quark stars.  Whether quark-degenerate matter can exist in these situations depends on the, poorly known, equations of state of both neutron-degenerate matter and quark-degenerate matter.  Some theoreticians even believe that quarks might themselves be composed of more fundamental particles called preons and if so, preon-degenerate matter might occur at densities greater than that which can be supported by quark-degenerate matter.  Could it be that the matter at the heart of a black hole is of one of these forms?

Let’s just suppose that the matter at the heart of a 10 solar mass black hole was in the form of quark degenerate matter.  How big might it be?   The diameter of a 1.4 solar mass neutron star is ~20 km. Neutrons have a diameter of ~10-15 m and it is suspected that quarks have a diameter of ~10-18 m.  As the volume goes as the cube of the diameter, the volume of a quark mass of 1.4 solar masses would be (103)3 smaller, that is 109 times smaller or 20,000 / 1,000,000,000 m in diameter = 0.0002 m =  0.02 mm!  As the black hole would be ~7 times more massive, the quark mass would be ~ about 2 times larger or 0.04 mm.  That is pretty small!  [Note: I have never seen this calculation done, nor can I find any such thing on the web – so be warned it may be totally erroneous!]

The more massive a black hole, the greater the size of the Schwarzschild radius: if one a black hole with a mass 10 times greater than another will have a radius ten times as large. A black hole of one solar mass would have a Schwarzschild radius of 3 kilometres, so a typical 10-solar-mass stellar black hole would have an event horizon whose radius was 30 kilometres.

Kerr Black Holes

There is a theorem, called the “no-hair” theorem that postulates that all black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism are completely characterized by only three observable properties; their mass, electric charge, and angular momentum.   Once matter has fallen into the event horizon all other information (the word "hair" is a metaphor for this) about the matter "disappears" and is permanently lost to external observers.  [This is somewhat contentious, as the theorem violates the principle that if complete information about a physical system is known at one point in time then it should be possible to determine its state at any other time.]

On the large scale matter is neutral, so it is not though that black holes would carry an electromagnetic charge but, on the other hand, the stars, dust and gas that might go to form a black hole have angular momentum – rotational energy - such as has a spinning star.  Thus, in general black holes are though to be spinning.  This makes them both much more interesting, but at the same time far more complex!  The solutions for a rotating black hole were first solved by Roy Kerr in 1963 and are thus called Kerr Black Holes.  The vast majority of black holes in the universe are initially though to be of this type, but there is a mechanism named after Roger Penrose that theoretically allows spinning black holes to lose angular momentum and so they might eventually turn into Schwarzschild Black Holes.

Like a Schwarzschild black hole there is a singularity at its heart of a Kerr Black Hole surrounded by an event horizon, but beyond this is an egg shaped region of distorted space called the ergosphere caused by the spinning of the black hole, which "drags" the space around it.  [This is called frame dragging and gives a way of observing that a black hole is rotating.]  The boundary of the ergosphere and the normal space beyond is called the static limit.  An object within the ergosphere can gain energy from the hole’s rotation and be ejected so removing angular momentum from the black hole in what is called the Penrose process.  But, of course, if an object crosses the event horizon it can never escape.  [However there is a caveat to this described at the end of the transcript.]

A Kerr Black Hole

Measuring the Spin

In 2006 using the NASA's Rossi X-ray space telescope, a measurement was made of the spin rate of a stellar mass black hole called GRS 1915+105 in the constellation Aquilla. GRS 1915+105 is a binary-star system. Gas from a "normal" companion star is attracted by the black hole’s gravity and spills towards it.  The gas spirals into the black hole rather like water swirling down a drain and forms what is called an accretion disk.  As the gas gets closer, it speeds up to conserve angular momentum.  Friction makes the gas in the accretion disk heat up it emits visible and ultra violet light and, in the inner part of the accretion disk closest to the black hole where the temperatures of the gas can exceed 1 million degrees, X-rays.  It turns out that there is an innermost stable orbit around the black hole and the faster the black hole is spinning the closer this is to the outer edge of the ergosphere.  It was found that this orbit had a diameter of ~30km.

Using ground based observations, the mass of the black hole has been estimated at 14 solar masses.  If it had no spin, this would imply an event horizon radius of 42 km. If it were spinning such that the edge of the ergosphere was moving at the speed of light its radius would be 21 km.  [This would give an absolute spin rate of 1,150 revolutions per second.]

Their result implies that the event horizon has a radius of 25km and a spin rate of  950 rotations per second – this being the  is the rate at which spacetime is spinning, or is being dragged round,  right at the black hole event horizon.

How can we discover them?

Could we see them?

Though no one has ever seen a Black Hole directly, it is, at least in principle, possible to “see” one if one could get near enough.  This is due to the fact that its mass distorts the space-time around it forming a gravitational lens which distorts what we see beyond it.  The “lens” acts rather like the base of a wine glass or the “bubble” glass in the window of an old cottage and tends to convert point sources into arcs or even circles which are called Einstein rings.  The two images below indicate what one might observe  if one was near enough to a Black Hole lying between us and the Milky Way.  As the distorted image of the Milky Way surrounds a totally black circle, it could be said that we are “seeing it” though of course we only see its silhouette.

A near-by Black Hole between us and the Milky Way

By Gravitational Micro Lensing

The gravitational lensing effect (see diagram below) of a large mass gives us a second way in which they could be detected.  As it acts rather like a convex lens or magnifying glass it would brighten the image of a star that lay behind it.  This has been observed thousands of times when a nearby star passes in front of a distant one.  In what is called a gravitational microlensing event, the brightness of the lensed star can increase by many times.  [Should the foreground star have a planet in orbit around it that also passes in front of the distant star this can also cause it to brighten, so providing a method of detecting extra solar planets.]  If, as might be expected, there were black hole stellar remnants orbiting within the galaxy then these would also give rise to lensing events so enabling their presence to be detected.

On the left hand side of the image below are two images of a starfield observed with a ground-based telescope which shows the brightening of a star due to a gravitational microlensing event.   On the right is a Hubble Space Telescope image of the same field which clearly resolves the lensed star and so determines its true brightness.   From the increase in brightness it is possible to calculate that the mass of the foreground object must be at least 6 solar masses.  If it were a star, it would be visible and outshine the background star.  As no foreground star is seen, one deduces that the lensing mass must be a Black Hole.

By determining the mass of an unseen stellar companion

If a stellar mass black hole, formed when a massive star ends its life in a supernova explosion, existed in isolation, it would be very difficult to detect except by gravitational micro-lensing as described above.  However, many stars exist in binary systems.  In a binary system in which one of the components is a black hole, its gravity can pull matter off the companion star forming an accretion disk of gas swirling into the black hole.  As the gas spins up as it nears the black hole due to conservation of angular momentum, the differential rotation speeds give rise to friction and the matter in the accretion disk reaches temperatures of more that 1 million K.  It thus emits radiation, mostly in the X-ray part of the spectrum.  X-Ray telescopes have now detected many such X-ray binary systems, some of which are believed to contain a black hole.

If the unseen companion object exceeds a calculated mass of ~ 3 solar masses, then it is likely to be a black hole.  An excellent candidate in our own galaxy is Cygnus X-1 - so called because it was the first X-ray source to be discovered in the constellation Cygnus and is the brightest persistent source of high energy X-rays in the sky.  Usually called Cyg X-1, it is a binary star system that contains a super-giant star with a surface temperature of 31,000 K (with its spectral type lying on the O and B boundary) together with a compact object.  The mass of the super-giant is between 20 to 40 solar masses and observations of its orbital parameters imply a companion of 8.7 solar masses.  This is well above the three solar mass limit of a neutron star, so it is thought to be a black hole.

There follows a case study of the discovery of one of the best Black Hole candidates in our galaxy and in which the author had a small role.

In the summer of 1975, an X-Ray satellite called Ariel IV, built and operated by Leicester University, detected one of the strongest sources of X-rays that had ever been observed.  It lay in the constellation Monoceros, over to the left of Orion.  Unfortunately, in those days, X-ray satellites were not able to give accurate positions so enabling the star system which gave rise to the flare to be determined and thus enable follow up observations at other wavelengths.

The author was contacted by Professor Ken Pounds who asked if the Jodrell Bank Telescopes could be used in an attempt to locate the source of the X-ray flare as it was likely that it would be producing significant radio emission as well.  He immediately used the Mk II telescope to observe the region of sky indicated by the Ariel IV observations, but no bright radio source was observed.  It appears that no other optical or radio telescopes were able to detect the source of the X-ray emission at this time either.

Unfortunately, a second telescope that could be combined with the Mk II to make a superb survey instrument was in use by some guest observers, but a week or so later we regained its use and were able to make a sensitive sky survey centred on the nominal position.  In those days paper charts were used and the sky map produced stretched some 20 ft across.  By great luck, we had surveyed just sufficient sky to find the radio waves being emitted by the flaring object:  it was within 4 inches of the edge of our chart - far from the nominal position. This was an exciting day for the author!  Its precise position and our follow up radio observations were published in the journal “Nature” adjacent to the original X-ray results.  It has two names Monoceros X1 and A0620-00, this latter name being a shortened version of our position: Right Ascension of 06 hours, 22 minutes, 44.5 seconds and Declination of -00 degrees, 20 arc minutes and 45 arc seconds.

Extensive observations during the 1980’s established that this was arguably the best stellar mass Black Hole candidate yet discovered.  The X-ray flare having been caused by matter infalling from a companion star into an accretion disk surrounding the black hole.  A0620-00 had previously flared in 1917, since when the density had slowly built up until it became unstable and exploded releasing a massive burst of X-rays.  The flare observed in 1975 is the most intense ever observed.  So why do we believe that a Black Hole was the cause of these X-ray outbursts?   At the position we derived is seen a K type star.  These have typical masses of 0.5 to 0.8 Msun.  From Doppler measurements of its spectrum it is possible to deduce that it is orbiting an unseen object with a period of 0.32 days with a maximum radial velocity of 460 km/s.  A pair of such measurements may be familiar to you as it is the way a planet can be inferred to be orbiting a star and which then allow one to calculate its distance from the star and its minimum mass.  In this case, when there are two massive co-orbiting objects, the observed motion only allows us to calculate their combined mass which is ~10.5 solar masses. So taking a mass of 0.8 Msun for the K type star, this implies that the mass of the unseen companion must be ~9.7 Msun.  This is well above the minimum mass of a stellar derived black hole.  Lying at a distance of 3,500 light years it is thought to be the nearest black hole to our solar system.

Supermassive Black Holes

We now believe that at the centre of all large elliptical and spiral galaxies there exists black holes of vastly greater mass than those resulting from the evolution of individual stars - with the most massive thought to contain several billion solar masses!  Initially, the evidence for them was indirect as they were believed to provide the energy to power what are called active galaxies.  These are galaxies where some processes going on within them make them stand out from the normal run of galaxies particularly in the amount of radio emission that they produce.  At the heart of our galaxy, lies a radio source called Sgr A*, one of the strongest radio sources in our galaxy.  However this would be too weak to be seen at if our Milky Way galaxy was at a great distance and our galaxy would therefore be termed a "normal" galaxy.  However there are some galaxies that emit vastly more radio emission and shine like beacons across the universe.  Because most of the excess emission lies in the radio part of the spectrum, these are called radio galaxies.  Other galaxies produce an excess of X-ray emission and, collectively, all are called active galaxies.  Though relatively rare, there are obviously energetic processes going on within them that make them interesting objects for astronomers to study.

We believe that the cause of their bright emissions lies right at their heart in what is called an active galactic nucleus - or AGN where matter is currently falling into the black hole fuelling the processes that give rise to the X-ray and radio emission.

These highly luminous objects were first discovered by radio astronomers in a in a series of experiments to measure the angular sizes of radio sources.  In the early 1960's, the signals received with the 75-m Mark I radio telescope at Jodrell Bank were combined with those from smaller telescopes located at increasingly greater distances across the north of England.  It was discovered that a number of the most powerful radio sources had angular sizes of less than one arc second.  So small, in fact, that they would appear as "stars" on a photographic plate. They were thus given the name "Quasi-Stellar-Object" (looking like a star) or "Quasar" for short.  This meant that they were very hard to identify until their precise positions were known. The first quasar to be identified was the 273rd object in the third Cambridge catalogue of radio sources so it had the name 3C273.

Though its image, taken by the 5-m Hale telescope, looked very like a star, a jet was seen extending ~ 6 arc seconds to one side.  It was discovered that its distance was about 2,500 million light years - then the most distant object known on the Universe.  But 3C273 is one of the closer quasars to us and the most distant currently known lies at a distance of ~13 billion light years!    So quasars are some of the most distant and most luminous objects that can be observed in the Universe.

One of the most powerful active galaxies in our neighbourhood of the visible universe is the giant elliptical galaxy, M87, which lies at the heart of the Virgo Cluster.  It is thought that a 3 billion solar mass lies at its centre which is accelerating particles (mostly electrons) close to the speed of light along its rotation axis forming a jet 6,500 light years long.

The jet within the galaxy M87

Let's consider what happens as a star begins to fall in towards the black hole.  As one side will be closer to the black hole than the other, the gravitational pull on that side will be greater than on the further side.  This exerts a force, called a tidal force, which increases as the star gets closer to the black hole.  The final effect of this tidal force will be to break the star up into its constituent gas and dust.  A second thing also happens as the material falls in.  It is unlikely that a star would be falling in directly towards the black hole and would thus have some rotational motion - that is, it would be circling around the black hole as well as gradually falling in towards it.  As the material gets closer it has to conserve angular momentum and so speeds up - just like an ice skater bringing her arms in toward herself.  The result of the material rotating round in close proximity at differing speeds is to produce friction so generating heat that causes the material to reach temperatures of more than a million degrees.  Such material gives off copious amounts of X-ray radiation which we can observe, but only if we can see in towards the black hole region.  This is surrounded by a torus (or doughnut) of material called the accretion disc that contains so much dust that it is opaque.  But if, by chance, this torus lies roughly at right angles to our line of sight then we can see in towards the black hole region and will observe the X-ray emission.

This is the case in the active galaxy NGC 4261.  The Hubble Space telescope image on the right shows a giant disk of cold gas and dust, about 300 light years across, that fuels a possible black hole at the core of the galaxy.  This disk feeds matter into the black hole, where gravity compresses and heats the material as described above.  Particles accelerated from the vicinity of the black hole produce two opposed jets of particles which, as they are decelerated, give off radio emission to form the two radio “lobes” that we observe.  The jets are aligned perpendicular to the disk, like an axle through a wheel – exactly as we would expect if a rotating black hole forms the "central engine" in NGC 4261.

Nuclear fusion of hydrogen can convert just under 1% of its rest mass into energy.  What is less obvious is that the act of falling into a gravitational potential well can also convert mass into energy.  In the case of a super massive black hole energy equivalent to at least 10% of the mass can be released before it falls within the event horizon giving the most efficient source of energy that we know of!  This energy release often results in the formation of two opposing jets of particles moving away from the black hole along its rotation axis.  Moving at speeds close to that of light, these "bore" a hole through the gas surrounding the galaxy and in doing so the particles will be slowed down - or decelerated.   They then produce radiation across the whole electromagnetic spectrum that allows us to observe the jets.  If one of the jets happen to be pointing towards us, the observed emission can be very great and so these objects can be seen right across the universe.

An interesting exercise is to calculate how much mass a quasar must "consume" in order to give their observed brightness.  If we assume that 10% of the mass is converted into energy, then E = 1/10 mc2, giving m = 10 E/ c2.  The brightest quasars have luminosities of order 1041 watts. (That is, 1041 joules/sec, so that we must use 3 x 108 m/sec for our value of c.) This equation will then give the mass required per second.

msec       =   10 x 1041 / (3 x 108)2   kg

=   1.1 x 1025 kg

So the mass per year                myear               =    86400 x 365 x 1.1 x 1025 kg

=    3.5 x 1032 kg/year

As usual, this can be converted into solar masses:

Msun/year         =    3.5 x 1032 / 2 x 1030

=   ~175 solar masses

The size of the Active Galactic Nucleus

There is a simple observation of Quasars that can give us an indication of the size of the emitting region around the black hole.  It has been observed that the light and radio output of a quasar can change significantly over periods of just a few hours.  Perhaps surprisingly, this can provide a reasonable estimate of its size as the following "thought experiment" will show.

Suppose the Sun surface instantly became dark.  We would see no change for 8.32 minutes due to the light travel time from the Sun to the Earth.  Then we would first see the central region of the disc go dark as this is nearest to us and the light travel time from it is least.  This dark region would then be seen to expand to cover the whole of the Sun's visible surface.  This is because the light from regions of the Sun further from us would still be arriving after the light from the central region was extinguished.  The time for the change to occur would be given by:  t = rsun /c.

The radius of the Sun is 695,000 km so the time for whole of the Sun to darken would be given by:

695000 / 3 x 105 seconds    =  2.31 seconds.

It is thus apparent that a body cannot appear to instantaneously change its brightness and can only do so on time scales of order of the light travel time across the radiating body.

Suppose that an AGN is observed to significantly change its brightness over a period of 12 hours.

12 hrs is 12 x 60 minutes =  720 minutes.

As light can travel 1 AU in 8.32 minutes the scale size of the object must be of order

720 / 8.32  AU  =   ~ 86 AU.

Calculating the Mass of Super-massive Black Holes

In recent years astronomers have gained more direct evidence of the presence of super-massive black holes by measuring the speed at which stars or dust are rotating around the centre of the galaxy in which it resides.   Two examples follow, firstly for the galaxy M84 that lies in the Virgo Cluster some 50 million light years distant and, secondly, for our own Milky Way Galaxy.

M84

At the right of the following figure is an observation taken with the Hubble Space Telescope Imaging Spectrograph of a strip across the centre of the galaxy M84 as shown in the image on the left.

The right hand plot shows the Doppler shift in the spectra of the material rotating around the galactic centre.  Moving downwards toward the centre, there is a sudden blue shift, indicating rapid motion of the gas towards us.  The Doppler shift indicates that the velocity toward us reaches a speed of about 400 km/s at a distance only 26 light years from the centre.  Crossing the centre, the sign of the radial velocity rapidly reverses to give a redshift indicating a similar speed away from us.

The most obvious interpretation of these data is that there is a large rotating disk around the nucleus of M84 that is seen in cross section - an interpretation strengthened by the fact that its nucleus is very active and emits jets of particles that give rise to strong radio emission.

The observations allow us to compute the mass of the central region in exactly the same way that we can calculate the mass of the Sun knowing how fast we are rotating around it and its distance along with experimentally derived value of the Universal Constant of Gravitation, G.

M = r v2/G

(M = mass of central region of the Galaxy.  m = mass of a small volume of the observed gas.  r = distance of the gas from centre of the galaxy.  v = velocity of the gas around the centre)

26 Ly = 26 x 9.46 x 1015 m   =   2.4 x 1017 m, v = 4.0 x 105 m/sec

This gives:  M = 2.4 x 1017 x (4 x 105)2/ 6.67 x 10–11 kg

= 5.9 x 1038 kg

= 5.9 x 1038 / 2 x 1030   Msun

= 2.93 x 108 Msun

= ~ 300 million Msun

It is expected that most of this mass will be in a black hole near the centre of the galaxy.  The same calculation as was used to find the Schwarzchild radius for a stellar mass black hole can be used to find the approximate size of this super-massive black hole:

Schwarzchild radius       =  RS  = 3.0 x M/MSUN  km

=  3.0 x  5.9 x 1038 /  2 x 1030 km

=  8.8 x 108 km

This is somewhat less than the size of the orbit of the planet Venus.

The Milky Way Galaxy

At the centre of our Galaxy is a strong radio source called Sagittarius A*.  As we know that that the regions surrounding super-massive black holes tend to emit strongly in the radio part of the spectrum, it has long been thought that one lay at its heart.  In the infra-red it is possible to eliminate the effects of the Earth’s atmosphere and produce images that are limited only by the diameter of the telescope.  In the case of the 10m Keck Telescopes on Mauna Kia this ~1/25th of an arc second, roughly equivalent to that of the Hubble Space Telescope in the visible part of the spectrum.  This resolution has enabled individual stars near the centre of the galaxy to be imaged and, with observations taken over a period of 15 years, has enabled the orbits of a number of stars to be determined.  As we have seen above, a knowledge of the periods and major axes of their orbits enable the mass of the body that they are orbiting to be found and this is exactly what the team from UCLA (University of California, Los Angeles) have achieved.

The image shows the central, 1 arc second by 1 arcs second region of our galaxy as observed in the infra-red by the Keck Telescope in 2010.  Plotted on top of the image are the 15 year tracks of 7 stars which are orbiting the galactic centre.  Of particular note are the stars S0-2, which orbits with a period of just 15.78 years, and S0-16 which came to within 45 AU of the galactic centre at which time it was moving at 12,000 km/second!  The best fit to the data gives a mass for the central body of 4.1 million solar masses and is the best evidence yet for the presence of a super-massive black hole at the centre of our own galaxy.

Black Holes and Galaxy Formation

There has long been an astronomical chicken-and-egg problem: which comes first - galaxies or black holes?  That is, do black holes play a role in the formation of galaxies and hence come first, or do they form later in the life of a galaxy as material at their heart collapse down under gravity to form the black hole.

As we have seen, astronomers have been able to weigh both galaxies and the black holes found within them.  It seems that, in general, there is a direct relationship between the mass of a black hole and the mass of the central bulge of stars and gas in the galaxy around it.  The black holes usually weigh about one one-thousandth of the mass of the galactic bulge implying that there must be some symbiotic link between them.

It was once thought that super-massive black holes were the endpoints of galaxy evolution but observations in recent years have lead many astronomers to come to the conclusion that black holes and galaxies co-evolve and it now widely thought that black holes play an important part in their formation and evolution. As the sensitivity of our telescopes has improved, researchers have been able to look at more distant (and hence older) galaxies. Here the linear relationship seems to fail with the black holes being more massive than expected.  This would imply that the black holes come first and somehow build up the galaxy around them with some theorizing that the strong winds and jets surrounding black holes could help feed star formation and so induce galaxies to grow.

Support for this hypothesis has come from observations of the quasar HE0450-2958.  This is called the "naked quasar" as it is the only quasar for which a host galaxy has not yet been detected.  It does however have a galaxy nearby which is extremely rich in bright and very young stars and which is forming stars at a rate equivalent to about 350 Suns per year, one hundred times more than rates for typical galaxies in the local Universe.  It is believed that this is because the quasar is spewing a jet of highly energetic particles towards its companion, accompanied by a stream of fast-moving gas, an injection of matter and energy that, it is though, is inducing the formation of stars.  Thus the black hole is “creating” a host galaxy with which, given its relative speed and velocity, it will merge in the future.  So the “naked quasar” will then finally reside inside a host galaxy like all other quasars."

Computer simulations in recent years have helped us to understand why the mass of a galaxy is proportional to the mass of the black hole within.  It was likely that the small irregular galaxies formed in the early universe contained small black holes at their centres and they grow as gravity pulls them together.  In the process, the black holes at their centre also merge together and so grow to reach their observed masses of perhaps a billion solar masses. Due to the turbulence of the gas during such a merger, many stars form but this is a self limiting process.  Matter falling into the black hole produces massive outflows of energy  (it becomes a quasar) which energises the surrounding gas so that it is blown away from the vicinity of the black hole - which then becomes dormant along with a cessation of star formation.  So with each galaxy merger, the black holes will coalesce and, in doing so, cause a burst of star formation.  The number if new stars then formed is related to the mass of the combined black holes so giving rise to the observed correlation between their mass and the mass of the central bulge of stars within the galaxy.

Computer simulation of the merger of two galaxies

Black holes are not entirely black

In the 1970's, Stephen Hawking showed that due to quantum-mechanical effects, black holes do actually emit radiation - they are not entirely black!  The energy that produces the radiation in the way described below comes from the mass of the black hole.  Consequently, the black hole gradually looses mass and, perhaps surprisingly, the rate of radiation increases as the mass decreases, so the black hole continues to radiate with increasing intensity, loosing mass as it does so until it finally evaporates.

The theory describing why this happens is highly complex and results from the quantum mechanical concept of virtual particles - mass and energy can arise spontaneously provided its disappears again very quickly and so does not violate the Heisenberg Uncertainty Principle.  In what are called vacuum fluctuations, a particle and an antiparticle can appear out of nowhere, exist for a very short time, and then annihilate each other.  These could for example be two photons of opposite spin.  Should this happen very close to the event of a black hole, it is possible for one particle fall across the horizon into the black hole while the other escapes.  In order to preserve total energy, the particle that fell into the black hole must have had a negative energy - equivalent to negative mass - which thus reduces the mass of the black hole. The particle that escapes carries energy away from the black hole and can, in principle, be detected so that it appears as if the black hole was emitting radiation.  This radiation is called Hawking Radiation.

Black holes can be said to have an effective temperature, called the Hawking temperature, which is proportional to the surface gravity of the black hole.  It turns out that the more massive the back hole, and hence the size of the Schwarzschild radius, the lower the surface gravity and the lower the effective temperature.  Even for stellar mass black hole this is exceedingly small, the order of 100 nanokelvin (10-7 degrees K) and, as the effective temperature is inversely proportional to mass, vastly less for super-massive black holes.

Consider an object placed in a bath of radiation at a certain temperature – say in a room at 20C, 293K.  Only if the object is hotter than this can it loose heat by radiation, if cooler it will absorb radiation and warm up.  Black holes exist in a universe whose space is now at an effective temperature of ~2.7 K due to the Cosmic Microwave Background (CMB) - the afterglow of creation left by the annihilation of antimatter and antimatter particles at the time of the Big Bang.  Unless a black hole has an effective temperature greater than this it cannot evaporate and will, in fact, gain energy and hence mass from the CMB photons that fall into it.  It will thus grow with time rather than shrink.  2.7K is vastly higher than the effective temperatures of even solar mass black holes so at this time in the universe none of the black holes that we know of can be evaporating.  To have a Hawking temperature larger than 2.7 K and so be able to evaporate, a black hole needs to be lighter than the Moon and would be an object with a diameter of less than a tenth of a millimetre.

Once a black hole begins to evaporate it loses mass and hence size.  Its Hawking temperature increases so it begins to radiate more strongly and so lose mass more quickly.  This is a runaway process so a black hole will finally disappear in a blinding flash of radiation.

On the other hand small black holes, should they exist, would evaporate in an instant.  If there have ever been (perhaps at the time of the big bang) black holes whose mass was comparable to that  of a car (which would have a diameter of ~10−24 m)  they would evaporate in the order of a nanosecond during which time it would outshine more than 200 of our Suns!

As described above, it is just possible that tiny black holes might be created in the collisions of particles in the Large Hadron Collider at CERN.  Some have worried that these might grow and consume the world!   But we believe that these would evaporate essentially as soon as they were created – on a time scale of 10−88 seconds!   It is thought that very high energy gamma rays will have created vast numbers of such micro black holes during the Earth’s history but, encouragingly, we are still here.

Simulated “black hole formation and decay event in the CERN ATLAS detector

We now believe that the Universe is expanding at an ever increasing rate due to the pressure derived from the “Dark Energy” that appears to make up 73% of the mass/energy of the Universe.  As the temperature of the CMB scales inversely with size, it is fall at an increasing rate too.   Eventually, in aeons, when the temperature of this relict radiation had fallen sufficiently and assuming Hawkin's theory is correct, stellar mass black holes will finally begin to evaporate - on a time scales of 10100 years!

Might Black Holes be evaporating now?

Let us suppose that, at the time of the big bang, black holes in a range of masses (and so effective temperatures) were created.  As the Universe cooled, the lighter ones could begin to evaporate followed by heavier ones until now, as mentioned above, those whose mass is comparable to that of the Moon.  The final moments of such an evaporation would give rise to massive bursts of gamma rays which our satellites could detect.  In fact we do observe what are termed gamma ray bursts, but it is thought (as will be described in a later lecture) that these are caused by the coalescing of two stellar remnants to form a black hole.  The fact that we cannot show that they are caused by the evaporation of a black hole is regarded as a pity by Stephen Hawking for, if they were, he would almost certainly win the Nobel Prize!

©Professor Ian Morison, Gresham College 2010

## Professor Ian Morison

### Professor of Astronomy

Ian Morison began his love of astronomy when, at the age of 12, he made a telescope out of lenses given to him by his...

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