Edwin Hubble and The Expanding Universe
	Edwin Powell Hubble (1889 - 1953) is renowned for determining that there are other galaxies in the Universe beyond the Milky Way, and for observing that the universe is expanding at a constant rate. Hubble was a tall, elegant, athletic, man who at age 30 had an undergraduate degree in astronomy and mathematics, a legal degree as a Rhodes scholar, followed by a PhD in astronomy. He was an attorney in Kentucky (joined its bar in 1913), and had served in WWI, rising to the rank of major. He was bored with law and decided to go back to his studies in astronomy.
[Hubble identifies a new galaxy - 1924] In 1919 he began to work at Mt. Wilson Observatory in California, where he would work for the rest of his life. He was researching nebulae, fuzzy patches of light in the sky. In 1924, he announced the discovery of a Cepheid, or variable star, in the Andromeda Nebulae. Since the work of Henrietta Leavitt had made it possible to calculate the distance to Cepheids, he calculated that this Cepheid was much further away than anyone had thought and that therefore the nebulae was not a gaseous cloud inside our galaxy, like so many nebulae, but in fact, a galaxy of stars just like the Milky Way. Only much further away. Until now, people believed that the only thing existing ouside the Milky Way were the Magellanic Clouds. The Universe was much bigger than had been previously presumed. [Hubble finds proof that the universe is expanding - 1929] Before Hubble's Andromeda discovery, Vesto Slipher had investigated the spiral nebulae. Analyzing the light from the nebulae, Slipher found that nearly all of them appeared to be moving away from Earth. Slipher knew that a shift toward red suggested the body was moving rapidly away from the observer. But he had no way to measure the distances to these reddish bodies. However, using the period-luminosity scale discovered by Henrietta Leavitt, Hubble had found and measured 23 other galaxies out to a distance of about 20 million light years. Hubble's brilliant observation was that the red shift of galaxies was directly proportional to the distance of the galaxy from earth. That meant that things farther away from Earth were moving away faster. In other words, the universe must be expanding. He announced his finding in 1929. The ratio of distance to redshift was 170 kilometers/second per light year of distance, now called Hubble's constant. The numbers were not exactly right, and refinements in measuring techniques and technology have changed all of Hubble's early figures.
[Hubble's Law] Hubble compared the distances he measured for galaxies with their Doppler shift of spectral lines. He discovered that the universe is expanding! Galaxies show redshifted spectral lines. The greater the distance, the higher the recession velocity.
Using Hubble's law, the distance to a galaxy can be determined by its redshift, z. At low velocities, z ~ vr/c. Redshift resulting from the Hubble flow is often called the cosmological redshift.
Hubble's law is very special. If we are galaxy A, the velocities are: What do people on galaxy B see? The same expanding universe! There is no center to the universe. We learned that Hubble's law tells us, for galaxies: v = H0×d. Since the universe is expanding, galaxies were closer together in the past. Extrapolating backwards, all the galaxies were on top of one another! When was this? If the universe has been expanding uniformly, the time for this is: t=d/v. Also, v = H0×d by Hubble's law. Thus, t=1/H0. Suppose H0 = 75 km/sec/Mpc which is the most popularly accepted value these days, an estimate of the age of the universe is about 1.3×1010 years (13 billion years). One of the fundamental quests in astronomy today is the determination of the distance scale in the universe. When you look at the sky at night, how can you translate what you see into a three-dimensional picture? Are brighter objects brighter because they are closer, or because they are intrinsically brighter? Are bigger objects bigger because they are closer, or because they are intrinsically bigger? These and other questions have been pushed to the forefront of astronomy as ever improving technology enables us to see objects billions of light years away. How big is the universe? How old is it? How is matter distributed within it? Why is the universe the way it is? How did it come to be that way?

The Cosmological Distance Ladder

The basic philosophy of the distance scale ladder is to use one distance measuring technique to calibrate another that can be used to larger distances.

1. Primary distance indicators As mentioned the primary indicators are the most reliable. Here we will just mention the most reliable methods of the many ingenious ones invented.

1.1 Parallax The first rung on the cosmological distance ladder is the parallax method and also the most certain. By using the elliptic orbit of the Earth around the Sun as a baseline, small annual rocking motions of the nearest stars can be detected. Distances to the stars within approximately 40 pc, can be derived from relatively simple geometric considerations. With the new incredible observations made by the Hipparcos satellite it is expected to increase the range of this method to at least 100 pc! 1.2 Proper motions of clusters The next step out is taken with the converging-point method, which uses the proper motion of open clusters. Since the mean velocity of a cluster with respect to the Sun is large compared to the proper motions of the stars individually, stars in an open cluster can as a good approximation be said to move towards the same point in the Universe. The canonical application for this method is measuring the distance to the Hyades. where d is the distance to the cluster in pc, vris the radial velocity in units of km/s, μ, the tangential proper motion in units of arcseconds per year and θ, is the angle between vr and v - the total velocity. The sizes of the stars correspond to their apparent magnitude. The length of the vectors correspond to values of the proper motions of the stars. With this method the distance to the Hyades has been determined to 45.7+/-0.8 pc. A rather precise determination, but still with a significant error. 1.3 Main-sequence fitting Once the distance to the Hyades is determined, distances to other open clusters may be determined by assuming that the main sequence of clusters have the same position in a colour-magnitude diagram. This method is known as main-sequence fitting and has been applied out to distances of approximately 10 kpc. By shifting the main-sequences up and down the distance modulus of a cluster and thereby its distance can be deduced. If we superpose the plot of colours and absolute magnitudes, M, of the Hyades stars on a plot of the colours and apparent magnitudes, m, of the cluster under investigation, we can shift the main-sequences vertically up and down. By assuming that the two main sequences have the same physical properties, we can get the differences between the apparent and absolute magnitudes of the investigated cluster directly, i.e. the distance modulus (recall, m - M = 5log10d - 5, where d is the distance in pc). 1.4 Miscellaneous stellar techniques A range of other stellar methods exist: Statistical parallaxes - By measuring proper motions and radial velocities of groups of stars, it is possible statistically to derive distance out to approximately 500 pc. Luminosity classes of stars - The luminosity of a star, and thus its distance through its apparent magnitude, can be determined by different spectroscopic and photometric methods. W Virginis stars - A variable type with a period-luminosity relation with a good deal of scatter. Mira variables - Also variable stars with another period-luminosity relation. Brightest red giants in globular clusters - Has the advantage that the stars are bright, but does for various reasons have a high level of scatter. Eclipsing binaries - Through spectroscopy and photometry, colours are deduced, and the mass-luminosity relation together with Keplers law does the rest. 1.5 RR-Lyrae stars and Cepheids The pulsating variables, RR Lyrae stars, are old population II stars and are common in globular clusters. The observations find a relation between their absolute magnitude and metallicity. This makes RR Lyrae stars an important step in the distance ladder. But since they have rather low luminosities, this step does not take us much further than M31. The distances to Cepheids are more well-determined through the period-luminosity (-Colour) relation: The relatively tight period-luminosity relation allows us to probe relatively large distances. Currently an HST Key Project probes Cepheids in several galaxies out to distances of ~ 15 Mpc.

2. Secondary distance indicators We need secondary estimators to take the next steps out. The most important of these will be mentioned briefly in the following.

2.1 Tully-Fisher relation The Tully-Fisher relation is one of the most used secondary distance indicators for spiral galaxies because of the relatively cheap way this leads to distances. The relation connects the width of the 21cm HI line with the absolute magnitude of the galaxy. 2.2 Dn - σ method Dressler et al. found a narrow relation between Dn, the diameter of a circular diaphragm within which the integrated surface brightness has a level of μ, and, σ, the velocity dispersion (Dn ∝ σ4/3). The dispersion of the relation is between 15% and 20 %. 2.3 Fundamental Plane Djorgovski and Davis and Faber et al. found relations for elliptical galaxies between three observables, which can be expressed by log re = A log σ - B <μ>e + C, where re is the effective radius, σ is the central velocity dispersion and <μ>e the mean surface brightness enclosed within re. The relation has become known under the name Fundamental Plane (FP), since the equation forms a two-dimensional hyperplane in the space spanned by these three observables. The FP method has a very low scatter in the measured distances within separate clusters - 11%, but the method has a much larger scatter from cluster to cluster. This makes the total scatter amount to nearly 20%. 2.4 Supernovae Supernovae of especially type Ia are much used and very promising standard candles. Since supernovae are some of the brightest objects in the Universe they are visible to high redshifts. The current record is held by a supernova at a redshift z=0.458! The distances can be estimated because supernovae of type Ia seem to have remarkable homogeneous light and colour variations with time. Especially the distribution of absolute magnitudes at maximum light seems to be very narrow, σM ~ 0.2. Some cases, where the supernova has been unusually red or spectroscopically peculiar, have been found not to follow this relation. 2.5 Sunyaev-Zel'dovic effect When the Cosmic Microwave Background Radiation (CMBR) passes through a cluster of galaxies containing hot (~108 K) intracluster gas, a dimunition of the CMBR can be measured due to scattering of the CMBR photons in the gas. Combining the gas mass derived from the temperature, and an assumption of hydrostatic equilibrium, with the microwave distortion can give a measure of the physical depth of the cluster. This, combined with the angular extension of the cluster, can give us its distance. This method reaches very far out into the Universe, and may in the following years, with the much awaited improvement in microwave observations, prove to be an exceptionally interesting technique for measuring really cosmological parameters. 2.6 Gravitationally lensed QSOs The time delay between fluctuations in the multiple images of distant gravitational lensed QSOs is also a very interesting technique. It has been applied with success to the double QSO system QSO 0957+561, and an upper limit of H0 = 70 km/s/Mpc has been measured. These observations also probe very far and might one day prove to be really useful. The problem with this method is, that it is very dependent on the modeling of the lensing mass in front of the QSO, which gives rise to relatively large uncertainties. 2.7 Other estimators A large number of other secondary estimators have been used: Brightest stars in galaxies HII region sizes Luminosity distribution of globular clusters Luminosity classes of spirals Galaxy sizes Brightest cluster galaxies The size of planetary nebulae Surface brightness fluctuations Each of these methods has larger scatter in its relation than the methods mentioned above, but many interesting results have nevertheless been obtained with them.

Large Scale Structure
Fornax is a small cluster of spiral and elliptical galaxies near our Local group.	The central region of the Coma cluster populated with large elliptical galaxies. This is one of the densest known regions on this scale in the universe.	Virgo, an irregular cluster, is the nearest large cluster of galaxies.
[Groups and clusters of galaxies] Galaxies are preferentially found in groups or larger agglomerations called clusters. The Local Group consists of our own galaxy, the larger spiral galaxy Andromeda (M31) and several smaller satellites, including the Large and Small Magellenic Clouds. Regular clusters have a concentrated central core and a well-defined spherical structure. These are subdivided according to their richness, that is, the number of galaxies within 1.5 Mpc of the centre (known as the Abell radius). Typically, they have a size in the range 1-10 Mpc and a mass M ~ 1015 solar masses (one followed by 15 zeros, that is, a million billion suns). The Coma cluster shown here is a very rich cluster with thousands of ellipticals inside the Abell radius. Irregular clusters have no well-defined centre, a similar range of sizes, but they are generally poorer with a mass 1012 - 1014 solar masses (i.e. a thousand to a hundred thousand million suns). An example is the nearby Virgo cluster.
[Large-scale structures] Superclusters: These usually consist of chains of about a dozen clusters which have a mass of about 1016 solar masses (ten million billion suns). Our own Local Supercluster is centred on Virgo and is relatively poor having a size of 15Mpc. The largest superclusters, like that associated with Coma, are up to 100Mpc in extent. The system of superclusters forms a network permeating throughout space, on which about 90% of galaxies are located. The Great Attractor: Measurements of peculiar velocities---deviations away from the Hubble flow - are achieved by comparing redshifts and galactic distance indicators. These have revealed enormous coherent motions on scales in excess of 60Mpc. Consistent with these flows, our own galaxy is moving at about 600km/s towards a distant object dubbed the 'Great Attractor'. This lies at a distance of 45Mpc and has a mass approaching 5×1016 solar masses.	The CfA survey showing large scale structures out to a distance of 150 Mpc, that is, about 2% of the distance to the edge of the observed universe. Galaxy positions are plotted as white points and large filamentary and sheet-like structures are evident, as well as bubble-like voids (CfA).
Voids, sheets & filaments: Deep redshift surveys reveal a very bubbly structure to the universe with galaxies primarily confined to sheets and filaments. Voids are the dominant feature and have a typical diameter of about 25Mpc. They fill about 90% of space and the largest observed, Bootes void, has a diameter of about 124Mpc. Other features that have been observed are the 'Great Wall', an apparent sheet of galaxies 100Mpc long at a distance of about 100Mpc.