Three Lectures on Astrophysics and Cosmology

Three Lectures on Astrophysics and Cosmology • A Brief History of Cosmology • The Most Luminous Radio Galaxies • Galaxy Formation and Fluctuations in the Cosmic Microwave Background Radiation – What You Really Need to Know 1 A Brief History of Cosmology • Observational Cosmology to 1926 • Theoretical Cosmology to 1939 • Post-War Observational and Theoretical Cosmology to the 1990s • Where we are now 2 The Books of the Lecture Chapter 19 includes many To appear in March 2006. useful derivations and results 3 1. Observational Cosmology to 1926 4 Early Speculations The earliest cosmologies were speculative cosmologies. Rene´ Descartes The Thomas Wright An Thomas Wright An World (1636) Original Theory of the Original Theory of the Universe (1750) Universe (1750) 5 Early Speculations The hierarchical (fractal) Universe of Kant (1755) and Lambert (1761) Immanuel Kant had speculated that the flattening of celestial objects was due to their rotation. The early cosmologies were speculative ideas without quantitative support of observation. The first quantitative estimates of the scale and structure of the Universe were made by William Herschel. 6 William Herschel Herschel’s star counts provided the first quantitative evidence for the island Universe picture of Wright, Kant, Swedenborg, and Laplace. 7 Herschel’s 40-foot Telescope at Slough This photograph was taken by John Herschel within months of the announcement of the discovery of the photographic process by Daguerre and Fox-Talbot in 1839. 8 Herschel’s Model of the Galaxy Herschel assumed that all stars have the same absolute luminosities. The importance of interstellar extinction had yet to be appreciated. 9 John Michell and William Herschel • In 1767, Michell had already shown that Herschel’s assumption of the constancy of the absolute luminosities of stars was incorrect from observations of bright star clusters. This was the introduction of statistical concepts into stellar statistics. He pointed this out before Herschel created his map of the Galaxy. Herschel ignored the problem • 1802: Herschel measured the magnitudes of visual binary stars - he then agreed with Michell. • The 40-foot telescope showed that the stellar system was unbounded. • Herschel lost faith in his model of the Galaxy. 10 William Parsons 3rd Earl of Rosse Lord Rosse’s restored 72-inch telescope at Sketch of M51 by Lord Rosse from Birr Castle, Ireland observations with the 72-inch Telescope at Birr. 11 James Keeler and the Crossley Reflector at the Lick Observatory Keeler’s image of M51 of 1900. While commissioning the Crossley reflector, The Crossley reflector at the Lick Keeler obtained spectacular images of Observatory on Mount Hamilton. faint spiral galaxies. 12 The 100-inch Hooker Telescope at Mount Wilson The Telescope weighed 100 tonnes and was completed in 1918. This instrument dominated observational cosmology until the commissioning of the Palomar 200-inch telescope in 1948. 13 The “Great Debate” What is commonly referred to as “The Great Debate” revolved around two issues: (1) What is the size of our Galaxy? (2) Are the spiral nebulae Galactic or extragalactic objects? The structure of the Galaxy from Star Counts by Johannes Kapteyn (1921). Distribution of Globular Clusters in the Galaxy due to Shapley (1918). 14 Aspects of the “Great Debate” • J. Scheiner (1899) obtained a spectrogram of M31 and stated that the spectrum suggested a cluster of Sun-like stars. • The central role of van Maanen’s measurements of the proper motions of spiral arms from 1916 onwards. If the spiral nebulae were extragalactic, the motions of the arms would approach or exceed the speed of light. The observations were only definitively refuted by Edwin Hubble in 1933. • Variable stars in spiral nebulae were discovered by Duncan in 1922. This led to a flurry of activity. • Henrietta Leavitt had used observations with the 24-inch Bruce telescope at Arequita to discover the period luminosity relation for Cepheids in the Magellanic Clouds. 15 The Characteristic Light Curve of a Cepheid Variable The Cepheid variable stars are characterised by a rapid rise in brightness followed by a slower decline. 16 Henrietta Leavitt and the Cepheid Variable Stars in the Magellanic Clouds (1912) Henrietta Leavitt, like Annie Cannon, was profoundly deaf. Her major contribution was the determination of the magnitude scale of stars in the North Polar Sequence from m = 2to21. Henrietta Leavitt’s period-luminosity relation for Cepheid variables in the Magellanic Henrietta Leavitt Clouds. 17 The Extragalactic Nature of the Spiral Nebulae In 1925, Hubble used Cepheid variables to show that M31 is outside our own Galaxy. In 1926, he presented a complete description of galaxies as extragalactic systems. Edwin Hubble 18 Hubble (1926) This paper was the pioneering description of galaxies as extragalactic systems. • Morphological classification of galaxies. • Numbers of different types. • Estimates of mass-to-luminosity ratios • Mean mass density of the Universe and comparison with Einstein’s static model. He noted that the 100-inch telescope could observe typical galaxies to about 1/600 of the radius of the Einstein Universe and that “. with reasonable increases in the speed of plates and sizes of telescopes it may become possible to observe an appreciable fraction of the Einstein Universe.” In 1928 George Ellery Hale began his campaign to raise funds for construction of the Palomar 200-inch telescope. He obtained a grant of $6,000,000 from the Rockefeller Foundation for the telescope before the year was out. 19 2. Theoretical Cosmology to 1939 20 Nikolai Lobachevsky and Janos Bolyai Working independently in Kazan in Russia and Transylvania in the period 1825–1830, Lobachevsky and Bolyai solved the problem of the existence of geometries which violated Euclid’s fifth axiom. These were the first self-consistent hyperbolic (non-Euclidean) geometries and led to Riemann’s introduction of quadratic differential forms and his discovery of spaces of positive (spherical) curvature. In his great text On the Principles of Geometry, Lobachevsky worked out the minimum parallax of any star in hyperbolic geometry θ =arctan(a/R) where a is the radius of the Earths orbit and R the radius of curvature of the geometry. In his textbook, he found a minimum value of R ≥ 1.66 × 105 AU. This was 8 years before Bessel’s announcement of the first successful parallax measurement of 61-Cygni. In his papers of 1829–30, Lobachevsky remarked, ‘There is no means other than astronomical observations for judging the exactness which attaches to the calculations of ordinary geometry.’ 21 The Route to General Relativity Unlike Einstein’s other great discoveries, the route to General Relativity was to prove to be long and tortuous. Four ideas were important in the development of the theory: • The influence of gravity on light. • The principle of equivalence. • Riemannian space-time. • The principle of covariance. The key technical developments were the mathematics of quadratic differential forms and the absolute differential calculus. 22 Einstein and Grossmann Towards the end of 1912, he realised that what was needed was non-Euclidean geometry. Einstein consulted his old school friend, Marcel Grossmann, about the most general forms of transformation between frames of reference for metrics of the form 2 µ ν ds = gµν dx dx . He came back with the answer that the most general transformation formulae were the Riemannian geometries, but that they had the ‘bad feature’ that they are non-linear. Einstein recognised that, on the contrary, this was a great advantage since any satisfactory theory of relativisitic gravity must be non-linear. 23 Einstein’s Universe Once General Relativity was formulated, Einstein realised in 1917 that he had the tools with which to derive the first fully self-consistent model of the whole Universe. At that time, the expansion of the Universe had not been discovered. To create a static Universe, he had to introduce the cosmological constant Λ. When the cosmological constant is introduced, the equation which describes the variation of the scale factor R with cosmic epoch becomes 2 d R 4πGρ0 1 = − + ΛR. dt2 3R2 3 The first term on the right-hand side describes the deceleration due to gravity. The second term describes what Zeldovich called ‘the repulsive effect of the vacuum’. The significance of the Λ-term was unknown at the time. 24 Einstein on the Introduction of the Cosmological Constant Einstein believed that he had incorporated Mach’s Principle into General Relativity. In his words, “The inertial structure of space-time was to be exhaustively conditioned and determined by the distribution of material throughout the Universe.” The extension of the field equations was “not justified by our actual knowledge of gravitation”, but was “logically consistent”. (1917) The cosmological term was “necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocities of stars”. (1934) 25 The de Sitter Solution Almost immediately, a major spanner was thrown in the works by Willem de Sitter, who showed that there existed solutions of Einstein’s cosmological field equations, even if there were no matter present in the Universe. 2 2 2 2 r 2 2 2 2 r 2 2 ds =dr − R sin (dφ +cos φ dθ )+cos c dt . R R The interpretation of the result was the subject of controversy, but it did show a redshift effect with distance which became known as the de Sitter effect. In 1919, Einstein showed that the cosmological constant appears naturally as a constant of integration in the development of General Relativity and is set to zero in the standard development. Many cosmologists argued that rather it should be determined observationally whether or not it is zero. 26 Lanczos (1922) In 1922, Cornelius Lanczos showed that, by a simple change of coordinates, the de Sitter solution could be interpreted as an expansion of the system of coordinates in hyperbolic space.

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