ASTM041 Relativistic Astrophysics Notes 1 of 6 (QMUL)

AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 1. Objects studied in Relativistic Astrophysics

Lecture 1. Introduction 1. Objects studied in Relativistic Astrophysics This is one of them: Giant Disk of Cold Gas and Dust Fuels Possible Black Hole at the Core of NGC 4261

You probably can see here a black hole which “eats’’ gas and dust around it.

This is only one example. In this lecture we will see many other images.

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 1. Objects studied in Relativistic Astrophysics

First, we should understand why different astronomical objects and phenomena are selected to some sort of “family’’ unified under “family name’’ relativistic objects.

All astrophysical objects of mass M and radius R can be characterized by two dimensionless parameters:

which is some typical for the object velocity, say escape velocity or orbital velocity of some test particle moving around the object, divided by the speed of light, and

which is Newtonian gravitational potential, say on the surface of the object, divided by the speed of light squared.

These parameters show how strong gravitational fields are:

(For example)

Newtonian gravity

<<0.001

<<0.000001

Special relativity

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0

Post-Newtonian effects in Solar System White Dwarfs

0.005

0.000001

0.05

0.001

Neutron Stars

0.5

0.1

Gravitational waves Black Holes + Universe as a whole

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Not relevant

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 1. Objects studied in Relativistic Astrophysics

Every effect in laboratory, including the Solar System, corresponds to some stronger version in Relativistic Objects: (For example)

Weak gravitational fields in experiments and observations

Strong Gravitational fields in Relativistic objects

Static gravitational fields

Classical tests of General relativity in solar System and in Binary pulsars

Black holes without rotation

Stationary gravimagnetic fields

Current Experiment Gravitational probe B on the orbit around the Earth

Rotating black holes

Dynamical non-wave gravitational fields

CMB observations from Space and from South Pole

Hawking black hole evaporation of primordial Black holes

Gravitational waves

Detection of Gravitational waves by LIGO and in future by LISA

Sources of gravitational radiation like colliding Black holes

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 1. Objects studied in Relativistic Astrophysics

If at least one of the two parameters mentioned above is considerably different from zero, one should take into account that the space and time are not independent any more but they are related, they are “relatives”. This explains the titles of the two great Einstein’s theories: Special relativity is the theory about relation between space and time, the unity called space-time, in very special case when gravity is absent and the space-time is flat (not curved).

General relativity is the theory about relation between space and time, the unity called space-time, deals with more general case when gravity is nothing but manifestation of the fact that the space-time is curved (wrinkled).

All objects studied in relativistic astrophysics are SPACETIME WRINKLES!!!

Examples:

i. White dwarfs An object in which gravity is balanced by the pressure exerted by densely packed electrons. The object is about the size of the Earth and about as massive as the Sun. It is produced when a low-mass star dies after it runs out of nuclear fuel.

AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 1. Objects studied in Relativistic Astrophysics

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ii. Neutron stars and pulsars An object composed entirely of neutrons (neutral elementary particles). The object is little more than 10 miles across but has a mass somewhat larger than the Sun. It is produced when an intermediatemass star dies in a supernova explosion.

Hot gas (blue) was blown out by a stellar explosion almost 1000 years ago. A web of cooler gas (red) is also visible.

In the year 1054, ancient astronomers noted the appearance of a bright new star in the constellation Taurus (Bull). It was visible in broad daylight for more than a month before fading from view. This supernova (nova means new) was the explosion that marked the death of a massive star. What we observe in its place today is a supernova remnant, the glowing gaseous remains expelled into space by the exploding star.

The leftover energy from the explosion makes the remnant very bright at all wavelengths. The visible light and radio images are vaguely reminiscent of a Crab and highlight the turbulent filamentary structure of gas. The X-ray image shows a zoom by a factor four of the very central region.

All stars with a birth mass more than eight times that of the Sun die in a spectacular supernova. But if the star wasn't too much heavier than that, the stellar core survives the supernova as a neutron star (it is not massive enough to become a black hole). This is a dense ball of neutral elementary particles. It is somewhat more massive than the Sun, but is squeezed into a space little more than 10 miles across. The Crab supernova produced a neutron star, seen as the dot in the center of the X-ray image. The neutron star spins rapidly and emits a bright beam of radiation from its magnetic poles.

Like a cosmic lighthouse, this beams sweeps past the Earth 30 times per second.

We observe this as regular pulses and call such a neutron star a pulsar (short for pulsating star).

The exploding star has left a pulsar (central dot). Jets of X-ray emitting matter are expelled in opposite directions.

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 1. Objects studied in Relativistic Astrophysics

iii. Gravitational waves Small periodic variations in the gravitational force that propagate as ripples through the fourdimensional space-time of the Universe.

Two colliding black holes send ripples through the space-time fabric of the Universe that are called gravitational waves.

One of the two LIGO gravitational wave observatories (Hanford, WA, USA). In two 2.5 mile long pipes laser beams are used to search for gravitational waves.

The LISA observatory will consist of three satellites in orbit around the Sun. Laser beams between the satellites may detect gravitational waves.

AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 1. Objects studied in Relativistic Astrophysics

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iy. Black holes A black hole is an object that is so compact (in other words, has enough mass in a small enough volume) that its gravitational force is strong enough to prevent light or anything else from escaping.

The existence of black holes was first proposed in the 18th century, based on the known laws of gravity. The more massive an object, or the smaller its size, the larger the gravitational force felt on its surface. John Michell and Pierre-Simon Laplace both independently argued that if an object were either extremely massive or extremely small, it might not be possible at all to escape its gravity. Even light could be forever captured.

French scientist Pierre-Simon Laplace (1749-1827) was one of the first to discuss the possible existence of black holes.

The name "black hole" was introduced by John Archibald Wheeler in 1967. It stuck, and has even become a common term for any type of mysterious bottomless pit. Physicists and mathematicians have found that space and time near black holes have many unusual properties. Because of this, black holes have become a favorite topic for science fiction writers. However, black holes are not fiction. They form whenever massive but otherwise normal stars die. We cannot see black holes, but we can detect material falling into black holes and being attracted by black holes. In this way, astronomers have identified and measured the mass of many black holes in the Universe through careful observations of the sky. We now know that our Universe is quite literally filled with billions of black holes.

American physicist John Archibald Wheeler (1911- ) first introduced the term black hole and led many important studies into their properties.

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 2. Black Holes in Newtonian theory

2. Black Holes in Newtonian theory The most prominent objects studied by Relativistic Astrophysics are Black holes, mentioned before. Black holes are a consequence of general relativity, created by Einstein in 1916, 11 years after the special theory of relativity (1905). However, speculations on black holes predate even the special theory of relativity by over a century.

As we already know, in the late 1700’s John Mitchell in England and Jean Simon Laplace in France independently realized that celestial bodies that are both small and massive may become invisible. The basis for this speculation is the observation that the escape speed

where M and R are the stellar mass and radius, is independent of the mass of the test particle. Within Newton’s particle theory of light it seems quite reasonable that this should also apply to light, in which case light can no longer escape the star if the escape speed exceeds the speed of light

This happens when

this means that

In order words stars with a large enough mass and a small enough radius become “dark”. Laplace went on to speculate that such objects may not only exist, but even in as great a number as the visible stars. With the demise of the particle theory of light, however, these speculations also lost popularity, and dark stars remained obscure until well after the development of general relativity. It is very interesting that Rg appeared in pure non relativistic considerations is exactly equal to so called Schwarzschild radius which will appear in the theory of Black Holes within General relativity.

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 2. Black Holes in Newtonian theory

Examples: I. Gravitational redshift From well known formula of Special relativity we can calculate effective gravitational mass of a photon if the frequency of the photon is given:

From conservation of energy, neglecting transverse Doppler-

effect, we have In above formula “ob’’ corresponds to the point of observation and “em’’ corresponds to the point of emission of the photon. Thus

For black holes this should be large! Taking into account that in Newtonian limit We have

If

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 2. Black Holes in Newtonian theory

ii. Formation of black holes How to estimate its density at the moment of formation ?

To an order of magnitude

Extra exercise: For what value of mass this density is equal to the density of water (gold, air, atomic nucleus)?

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 2. Black Holes in Newtonian theory

iii. Tidal disruption How, using simple Newtonian estimates, evaluate the radius of tidal disruption for a star of mass m and radius r in the gravitational field of the black hole of mass M? Self-gravity force:

The tidal force:

The tidal radius is determined by

Thus

Finally, the radius of tidal disruption is

Interesting question : Is it possible for that radius to be smaller than gravitational radius?

What could happen with a star, say of solar mass, in this case?

Hint: Try this

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 3. Images of black hole candidates

3. Images of black hole candidates

The nucleus is probably the home of a black hole with a mass 10 million times that of our Sun.

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 3. Images of black hole candidates

When black holes collideâ&#x20AC;Ś

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 3. Images of black hole candidates

Black Hole-Powered Jet of Electrons and Sub-Atomic Particles Streams from the Center of Galaxy M87

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 3. Images of black hole candidates

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 3. Images of black hole candidates

The three galaxies above are believed to contain central, supermassive black holes.

The galaxy NGC 4486B (lower-left) shows a double nucleus (lower-right). The images of NGC 3377 and NGC 4486B are 2.7 arcseconds on a side, and for NGC 3379 the size is 5.4 arcseconds; the lower-right is a blow-up of the central 0.5 arcseconds of NGC 4486B.

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 4. Images of gravitational lenses

4. Images of gravitational lenses

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 4. Images of gravitational lenses

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AG Polnarev, Relativistic Astrophysics, 2007. Lecture 1, 4. Images of gravitational lenses

Galaxies Magnified by Galaxy Cluster Abell 1689's Graviational Lens

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