33: Lecture Special Astronomical Objects
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The Planck Scale
The Planck mass Astrophysicists and cosmologists like to work in a convenient (to them at least) set of units known as the Planck Scale. This set of units use both relativity and quantum equations such as E = mc2 , = h/p, C = h/mc, and E = hf . As a first example, we can define the Planck mass mP as hc = 5.46 10-8 kg G The above is the definition given in the textbook, and in the Wolfram Mathematica reference. However, other sources use h instead of h for which mP hc = 2.18 10-8 kg G The Planck mass was introduced by Max Planck himself. It is obviously a macroscopic unit, many orders of magnitude greater than the proton mass for example. The physical significance of the Planck mass is that it is the smallest mass possible in general relativity for a black hole. The Planck mass has a Schwarzchild radius equal to the Compton wavelength divided by . The Planck mass is also the mass of the Planck particle, a hypothetical minuscule black hole whose Schwarzchild radius equals the Planck length, which is defined next. mP The Planck length The Planck length P is defined in the textbook as Gh G h = 4.05 10-35 m or P = 1.62 10-35 m 3 3 c c The Planck length may play a role in quantum gravity theories as possibly the smallest possible length at which gravity effects quantum predictions. In turn the Planck length may cure general relativity of the black hole singularity problem. P The Planck time The Planck time tP is the time it takes light to move one Planck length distance: P Gh P G h = = 1.35 10-43 s or tP = = 5.39 10-44 s 5 5 c c c c As mentioned previously, physics theories break down at times before the Planck time. So the Planck time is taken as the first moment of the Big Bang. tP
Lecture 33: Special Astronomical Objects
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Stellar Evolution
The Ultimate Fate of Stars When stars have burned through all of their nuclear fusion fuel, there are three ultimate outcomes according to the star's mass M with respect to the Sun's mass MS . Both general relativity and quantum mechanics play important roles, even though the two theories do not reconcile: 1) White Dwarf for M < 1.4MS . The 1.4MS is called the Chandrasekhar limit which allows the free electrons in the star to exert enough pressure to prevent further collapse. A white dwarf might have a final radius of 1% of the Sun's radius. 2) Neutron Star for 1.4MS < M < 3MS . For this range of masses, the pressure against further collapse is generated by neutrons instead of electrons. The neutrons are created by reverse beta decay when the density of electrons and protons in the star becomes large enough. We have seen that the volume of a neutron star is given by 1 V = N 6.5 2 h m3 G n
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where N is the number of neutrons in the star N = M/mn . Somewhat paradoxically at first, the volume of a neutron star decreases as the number of neutrons N increases. The optional problem 16.12 explores this apparent contradiction. 3) Black Hole M > 3MS . Chandrasekhar originally thought that stars with a mass greater than 1.4MS would collapse into black holes, but the theoretical discovery of the neutron star idea in the 1930s pushed the black hole limit to 3MS . Neutron stars were discovered in 1967 in the form of a pulsar, the equivalent of a lighthouse beam rapidly sweeping around the sky.
Lecture 33: Special Astronomical Objects
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Astronomical Objects
Galaxies Galaxies are immense collections of individual stars, some of which like our Sun do have their own planetary systems. The mutual gravitational attraction of the stars keeps a galaxy together.
Milky Way Galaxy
200-400 billion stars, Spiral Arms galaxy Formed 13.6 billion years ago Sun about 26,000 light-years from the center All stars rotate about the center of the galaxy The Sun takes 250 million years to complete its "orbit" Andromeda galaxy is the largest "nearby", 106 light-years
Figure 1: Description of the Milky Way Galaxy
By studying the rotational speeds of stars about the center of the Milky Way galaxy as a function of their distance from the center of the galaxy, we can learn about the possibility of a super-massive black hole at the center of the galaxy, and the appearance of dark matter throughout the galaxy. Galaxies are typically receding from us, a feature of the Big Bang. The galaxies furthest away are receding the fastest, in line with Hubble's Law. The furthest galaxy discovered to far appears to have a redshift of 10 units, meaning that it was formed only 460 million years after the Big Bang, and the light has taken more than 13 billion years to reach the Earth.
Lecture 33: Special Astronomical Objects
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Active Galactic Nuclei
Quasars In the 1960s, as telescopes became more powerful, astronomers began discovering thousands of galactic objects which were emitting immensely powerful quantities of electromagnetic radiation. The first of these was discovered to be 3 billion light years away from the Earth. Their radiation outputs were larger than normal galaxies with hundreds of billions of stars. These strong radiation sources were named quasars, meaning quasi-stars, or more commonly quasi-stellar objects.
Z > 5 Quasar in red circle HST Picture of a Gravitationally-Lensed Quasar
What's happening near the centre of this cluster of galaxies? At first glance it appears that several strangely elongated galaxies and fully five bright quasars exist there. In reality, an entire cluster of galaxies is acting as a gigantic gravitational lens that distorts and multiply-images bright objects that occur far in the distance. The five bright white points near the cluster centre are actually images of a single distant quasar. Hubble This Space Telescope image is so detailed that even the host galaxy surrounding the quasar is visible. Close inspection of the above image will reveal that the arced galaxies at 2 and 4 o'clock are actually gravitationally lensed images of the same galaxy. A third image of that galaxy can be found at about 10 o'clock from the cluster centre.
Figure 2: Images of quasars
The ultimate origin of the radiation output must be a super-massive black hole at the center of the quasar which is devouring nearby mass. Quasars are generally thought to date from soon after the beginnings of the universe, 12 billion years ago, when the universe was much smaller in extent. By examining the brightness variation of a quasar over a short period of time, astronomers have concluded that quasars are relatively small objects, just a few light-hours or light-days in extent, meaning not much larger than our own solar system. In other words, quasars are not galaxies themselves which are hundreds of thousands of light years in extent, but quasars produce more output energy than an entire galaxy.
Lecture 33: Special Astronomical Objects
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Active Galactic Nuclei
Blazar Blazars are very compact and highly variable energy sources, assumed to be powered by a super-massive black hole at the center of a host galaxy. Blazars produce a collimated relativistic jet energy, and by chance some of these blazars have their energy jets pointed in the direction of the Earth. Dust, gas, and perhaps even whole stars are gobbled up into the black hole. As this ionized matter spirals into the black hole, before the event horizon, prodigious amounts of electromagnetic radiation are produced. Several hundred of these objects are known as of 2003.
Blazars: A subset of quasar objects
Figure 3: Schematic pictures of blazars
Blazars were discovered in 1991 using a satellite observatory called the Compton Gamma Ray Observatory. Just as with the Hubble Space Telescope (HST), the CGRO needed to be put in orbit above the Earth's atmosphere which absorbs the characteristic high energy, gamma ray radiation, just the way the ozone layer absorbs harmful ultraviolet radiation from the Sun. The general term for these objects (quasars, blazars, gamma ray bursters) is Active Galactic Nuclei. The term doesn't refer directly to the nucleus of any atom, but rather thinks of these objects as being at the center of galaxies, and deriving their energies from gravitational potential changes.
Lecture 33: Special Astronomical Objects
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Active Galactic Nuclei
Gamma Ray Bursters Another class of objects producing copious amounts of energy are the Gamma Ray Bursters (GRB). These were discovered by accident during the Cold War in the 1960s. Military satellites designed to detect gamma ray radiation coming from the Earth's surface instead saw bursts of gamma radiation coming towards the Earth from unknown sources in the sky. The bursts lasted only a short time and seemed to occur randomly. The origin of the GRBs remained a mystery until after 1996. A new ItalianDutch satellite was launched which able to detected a broader band of radiation from the GRB which lasted a longer time. This enabled operators of the HST and ground based telescopes to point their instruments in the direction of the sky seen by the satellite. Eventually astronomers were able to prove that the longer-lived GRBs were enormous extra-galactic (outside the Milky Way) s...