Astronomy 218 Observational Cosmology Cosmological Principle The central tenet of cosmology is the cosmological principle, Viewed on a sufficiently large scale, the properties of the Universe are the same for all observers. Cosmology is generally not concerned with the study of the myriad of astronomical objects that make up the Universe, except to the extent that they tell us about the behavior of the Universe as a whole. The cosmological principle is the ultimate flowering of the revolution started by Copernicus, we do not occupy a special place in the Universe. Pencil-Beam Surveys In the 1980s, Kirshner, Oemler, Schechter & Schechtman took a complementary approach to the CfA redshift survey of Gellar & Huchra, the pencil-beam survey. This provided a measure of large-scale structure that was narrow but deep. It revealed the first void (the void in Boötes) but no structure larger than 200–300 Mpc in their survey which reached >2 Gpc. Largest Scales Obviously, the cosmological principle fails at small scales. Even at the scale of 50 Mpc, the perspective of an observer in the center of a supercluster differs markedly from that of an observer in a void. The largest structure known in the Universe, the Sloan Great Wall (~300 Mpc) tells us that the cosmological principle only applies on scales of Gpc. Scales below ~1 Gpc are the realm of astronomy. Isotropy & Homogeneity The statement that the Universe appears the “same to all observers” is catchy, but not quantifiable. A more precise statement is that universe is homogeneous — the same at every location — and isotropic — the same in every direction. Redshift and pencil surveys support the description of the Universe as homogenous (every Gpc-cube block appears much like the local Gpc-cube block) and isotropic (the Gpc- cube block to our left appears much like the Gpc-cube block to our right). The notion of the Universe that developed after the Copernican revolution was of a homogenous and isotropic Universe, infinite in space and static in time. Olbers’ Paradox The first observation that leads to modern cosmology is Olbers’ Paradox. As pointed out by numerous astronomers over time (Thomas Digges in 1576, Johannes Kepler in 1610, Edmund Halley in 1721, …) observations contradict this infinite model of the Universe because the night sky is mostly dark. As Heinrich Olbers elucidated most clearly in 1826, if the universe is homogeneous, isotropic, infinite, and unchanging, the entire sky would be as bright as the surface of the Sun. Surface Brightness How does an infinite, unchanging homogeneous and isotropic universe prevent a dark sky at night? For a single star of luminosity L at a distance r, its flux is the result of the inverse square law for geometric dilution. If the star has a radius, R✭, it will subtend a solid angle in steradians of the fraction of a sphere of radius r covered by a circle of radius R✭. The surface brightness of the star is independent of r. Bright Sky If the surface brightness Σ✭ is independent of distance, than distant stars contribute as much as nearby stars. If we assume a uniform density of stars in the Universe, n✭, then at a radius r, a thin shell of thickness dr contains 2 dN✭ = n✭ 4π r dr stars. The fraction of the shell’s area covered by stars is Summing over all shells with radius less than r tells the fraction of the sky covered by stars to this radius, 2 f → 1, making the night sky bright, as r → rOlb ≈ 1/n✭ π R ✭ Finite Universe Since the sky is largely dark at night, one of the assumed characteristics of the Universe must be wrong. It was possible that the errant assumption was homogeneity. In Olbers’ day, distances to stars were unknown (Bessel first measured parallax in 1838), so n✭ and/or R✭ could grow much smaller with distance. Infinite size could also be the errant assumption. If the radius of the Universe (or at least the distribution of stars), r0, is 2 smaller than rOlb, then f ≈ n✭ π R ✭ r0 < 1. The average surface brightness is Σ✭ f ≈ n✭ L r0 / 4π. Lord Kelvin in 1901 removed the assumption of infinite age. Since the speed of light had been measured as early as 1677 (by Römer in 1676), stars of age t0 or in a Universe of age t0 can only be seen to a distance r0 = ct0. The Age of the Universe
Kelvin’s assertion was ultimately proven by Hubble’s 1929 observation of Universal Recession. From Hubble’s law, ʋ = H0 d, we can estimate the age of the Universe as the time at which all galaxies are at zero distance, t0 = d/ʋ = d / (H0d) = 1/H0 −1 −1 For H0 = 70 km s Mpc , t0 = 14.0 Gyr. Conveniently, the age of the Universe is older than the oldest star.
The light from a star further than the horizon distance, r0 = c/H0 ~ 4300 Mpc, is unable to reach us. The Dark Sky By integrating the observed luminosity function for galaxies, we determined the total luminosity density. 8 −3 −3 ≈ 2 × 10 L☉ Mpc ≈ 10 W AU Since the light of most galaxies comes from stars, this luminosity density is a sum over all stars,