# Birmingham July 2012

Saturday July 7th

The last lecture of the day was The Black Hole Hunter’s essential toolkit given by Dr Somak Raychaudhury

Black holes are believed to be a key ingredient of how galaxies have evolved which compensates a little for their bad press.

The escape velocity is the speed needed to “break free” from a gravitational field. The formula is shown below.

G is the universal gravitational constant; M is the mass of the planet etc. that the object is trying to escape from and r is the distance from the centre of gravity of that mass. The escape velocity from the Earth is 11.2 km/s, from the Sun it is 617.5km/s and from a black hole it is greater than the speed of light.

How can the escape velocity from a black hole be greater than the speed of light? The answer is that there is enough mass packed into it to make it dense enough. Increasing the mass and/or decreasing the radius means that anybody could turn into a black hole if they were small enough.

The idea of a body so massive that even light could not escape was first put forward by geologist Rev. John Michell in a letter written to Henry Cavendish in 1783. In 1796, mathematician Pierre-Simon Laplace promoted the idea. More work had to wait until 1915 when Albert Einstein worked out his theories of gravity and light. In 1916 Karl Schwarzschild worked out the maths describing the geometry of space and time. The Schwarzschild radius is the distance from the centre of an object, like a black hole, such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light. In 1931, Subrahmanyan Chandrasekhar showed how stars can collapse after their death to form black holes. Quantum mechanics has to be applied for black holes to be considered the natural end for massive stars.

This is the formula for the Schwarzschild radius and determines the size of the black hole. For an Earth mass it would be 2cm and for a solar mass it would be 4km.

A black hole is not a cosmic vacuum cleaner. It is only inside the event horizon that matter is pulled inexorably inwards. Far away from a black hole gravity is no different than for any other object with the same mass. If it were to replace the Sun the orbits in the Solar System would remain unchanged (though the Earth would get terrible cold).

If a star has a mass less than 1.4 times our Sun’s mass at its death it will form a white dwarf. There is a large mass loss at the end of its life.

If a star has between 1.4 to 4 times our Sun’s mass it will form a neutron star at its death.

If a star is much greater than 3 times our Sun’s mass it will form a black hole at its death.

White dwarfs are Earth sized and Neutron stars are about city size. The density of a neutron star is about 3xE17 kg/m^3. This is the equivalent to squeezing all the humans into a cube of size 1.5cm. The gravity on a neutron star is 2xE12N/kg with an escape velocity of 2xE6m/s. A black hole would have greater values than this.

There are about three types of black holes. Stellar mass black hole is about 3-100 times the mass of our Sun. Mid-size black hole is about 1000-100000 times the mass of our Sun. Super massive black hole is about million to billion times the mass of our Sun, Super massive black holes are found at the centre of galaxies and we don’t yet know how they form.

One approach for finding a black hole is to look for very fast moving stars at the centre of the galaxy using the 8m optical telescope (VLT).

Our galaxy, the Milky Way, is believed to have a black hole at its centre.

An image of the Milky Way’s galactic centre in the night sky above the Paranal Observatory in Chilie.

The large Magellanic cloud galaxy is a companion to our Milky Way. Photograph taken at ESO’s La Silla observatory in Chilie.

Infrared picture of the large Magellanic cloud which shows up stuff hidden by dust.

The Milky Way central black hole is about 4 million times the mass of our Sun. There is also believed thousands of 4-10 solar mass black holes.

Picture taken by the Hubble space telescope of the matter (stars) swirling around a smaller black hole (only 500 million suns) in a distant galaxy.

Reinhard Genzel and his team at the Max-Planck institute were the first to track the motions of stars at the centre of the Milky Way and showed that they were orbiting a very massive object, probably a black hole.

Andrea Ghez and her colleagues at UCLA have used the high resolution of the Keck telescope in infrared to peer into the centre of our galaxy. They have discovered many stars in highly elliptical orbits around the huge black hole there (Kepler’s laws apply to stars as well as planets).

Galactic Centre, W.M. Keck Observatory/UCLA. Narrow-field image of the Galactic Centre. The arrow marks the location of radio source Sge A*, a super massive black hole at the centre of our galaxy.

One of the stars in our galaxy, observed by Keck, has an orbital period of 15.2 years and this leads to a calculated value of the Schwarzschild radius equal to 2.2xE-7 PC, 0.08AU or 15 Solar radii. This in turn leads to a mass of 2.5xE6 of the mass of our Sun.

A second approach in looking for black holes is to look for ripples in space time from merging black holes. For this you need a gravitational wave telescope, which unfortunately hasn’t been invented yet. LIGO is a start. When two super massive black holes merge they will spiral towards each other first. This movement would be detected with the gravitational wave telescope but at the moment we have to rely on electromagnetic wave detection.

NGC 6240 is a well-studied nearby ultraluminous infrared galaxy. The galaxy is the remnant of a merger between two smaller galaxies. Astronomers have speculated that active galactic nuclei containing supermassive black holes may be responsible for the intense dust heating that produces the emission.

X ray image of NGC 6240 taken with the Chandra X ray Observatory superimposed on an optical image of the galaxy. The X ray emission from the two active galactic nuclei can be seen as bright blue sources.

A third approach is to use X ray telescopes to look for million degrees Celsius hot gas falling into a black hole. High temperatures result in the X rays being produced. And this makes black holes “visible”.

The best transmission through the atmosphere involves visible and radio waves. The atmosphere is transparent to them. In space you can use the entire electromagnetic spectrum.

It is difficult to form X-ray images as they are difficult to focus. Mirrors are used but X-rays impinging at normal incidence (that is, perpendicular) on any material are largely absorbed rather than reflected. Normal incidence mirrors, like those used for optical telescopes, are thus ruled out. For an X-ray telescope, you must select a material which reflects the X-ray photon (so that the X-rays are not absorbed) and design your telescope so that the X-ray photons hit the mirror at small, "grazing", incidence (so that they will be reflected). The most commonly used reflecting materials for X-ray mirrors are gold (used in the Suzaku, XMM, and Swift satellites) and iridium (used by the Chandra X-ray Observatory). For gold, the critical reflection angle at 1 keV is 3.72 degrees.

It was shown mathematically that a reflection off a parabolic mirror followed by a reflection off a hyperbolic mirror could lead to the focusing of X-rays. Several designs have been used in X-ray telescopes based on this principle: the Kirkpatrick-Baez design and a couple of designs by Wolter. So why focus X-rays at all? Focusing helps create a clearer and sharper image of the X-ray source. It also allows scientists to get a better measure of faint X-ray sources which they could not otherwise detect. Sharp images help scientists to understand the distribution of hot gas between galaxies, the physics of supernova remnant expansion, and many other important issues. The ability to make an X-ray telescope moved astronomy forward in a big leap; the creation of X-ray telescopes with better spatial resolution and larger effective collection areas will continue to reveal exciting new information about the workings of our Universe.

The Chandra X-ray Observatory is as good as Hubble.

If two stars orbit close enough to each other mass gets pulled from one and falls (accretes) into the other. The smaller mass star loses matter to the larger. X-ray binaries are a class of binary stars that are luminous in X-rays. The X-rays are produced by matter falling from one component, called the donor (usually a relatively normal star) to the other component, called the accretor, which is compact: a white dwarf, neutron star, or black hole. The infalling matter releases gravitational potential energy, up to several tenths of its rest mass, as X-rays. (Hydrogen fusion releases only about 0.7 percent of rest mass.) An estimated 1041 positrons escape per second from a typical hard low-mass X-ray binary.

An artist’s impression of an X-ray binary Lots of little neutron stars and black holes can be found in binary systems.

Chandra X-ray view of Centaurus A showing one relativistic jet from the central black hole. There are other kinds of black hole in this galaxy. The jets can’t be swallowed.

Black holes can “vomit” and hot things are ejected from the surface.

A microquasar is a smaller cousin of a quasar and it has common characteristics with it; strong and variable radio emission, and an accretion disc surrounding a compact object such as a black hole.

Artist’s impression of the microquasar.

V4641 Sagittarii (V4641 Sgr) is a variable X-ray binary star system in the constellation Sagittarius. It is the source of one of the fastest superluminal jets in our galaxy. In 1999 a violent outburst at V4641 Sgr revealed it to be the closest known black hole to Earth. Originally thought to be positioned approximately 1,600 light-years (100,000,000 AU) from Earth, later observations showed it to be at least 15 times farther away.