Before the 1920's, it was thought that galaxies were in fact objects within our own Galaxy, possibly regions forming individual stars. They were given the name ``nebula'', which we now use to denote regions of gas and dust within galaxies.

At the turn of the century, Cepheid variable stars, a special class of pulsating stars that exhibit a particular period-luminosity relation, were discovered. As seen previously in Chapter 14, it was found that their intrinsic brightness was proportional to their period of variation and, hence, could be used for measuring the distances to nearby galaxies.

In the late 1920's, Hubble discovered similar Cepheid stars in neighboring galaxies as was found in our own Galaxy. Since they followed the same period-luminosity relation, and they were very faint, then this implied that the neighboring galaxies were very far away. This proved that spiral `nebula' were, in fact, external to our own Galaxy and suddenly the Universe was vast in space and time.

Today we know that a galaxy is a collect of stars, gas and dust bound together by their common gravitational pull. Galaxies range from 10,000 to 200,000 light-years in size and between 10⁹ and 10¹⁴ solar luminosities in brightness.

Galaxies have certain features in common. Gravity holds the billions of stars together, and the densest region is in the center, called a core or bulge. Some galaxies have spiral or pinwheel arms. All galaxies have a faint outer region or envelope and a mysterious dark matter halo.

The contents of galaxies vary from galaxy type to galaxy type, and with time. Many galaxies are grouped in large associations held by their own gravity called galaxy clusters.

Hubble sequence :

Almost all current systems of galaxy classification are outgrowths of the initial scheme proposed by American astronomer Edwin Hubble in 1926. In Hubble's scheme, which is based on the optical appearance of galaxy images on photographic plates, galaxies are divided into three general classes: ellipticals, spirals, and irregulars.

Distance Scale:

The most important value for an astronomical object is its distance from the Earth.

The determination of the distance scale begins with the construction of ladder of primary, secondary and tertiary calibrators in the search for a standard candle.

Primary Calibrators:

The construction of the distance scale ladder is a process of building of a chain of objects with well determined distance. The bottom of this chain is the determination of the scale of objects in the Solar System. This is done through radar ranging, where a radio pulse is reflected off of the various planets in the Solar System.

The most important value from solar system radar ranging is the exact distance of the Earth from the Sun, determined by triangular measurement of the Earth and terrestrial worlds. This allows an accurate value for what is called the Astronomical Unit (A.U.), i.e. the mean Earth-Sun distance. The A.U. is the ``yardstick'' for measuring the distance to nearby stars by parallax.

The parallax system is only good for stars within 300 light-years of the Earth due to limitations of measuring small changes in stellar position. Fortunately, there are hundreds of stars within this volume of space, which become the calibrators for secondary distance indicators.

Secondary Calibrators:

Secondary calibrators of the distance scale depend on statistical measures of stellar properties, such as the mean brightness of a class of stars. It has been known since the 1800's that stars follow a particular color-luminosity relation known as the Hertzsprung-Russell Diagram (see Chapter 10).

The existence of the main sequence for stars, a relationship between luminosity and color due to the stable, hydrogen-burning part of a star's life, allows for the use of spectroscopic parallax. A stars temperature is determined by its spectrum (some elements become ions at certain temperatures). With a known temperature, then an absolute luminosity can be read off the HR diagram.

The distance to a star is simply the ratio of its apparent brightness and its true brightness (imagine car headlights at a distance). The method allows us to measure the distances to thousands of local stars and, in particular, to nearby star clusters which harbor variable stars.

A variable star is a star where the brightness of the star changes over time (usually a small amount). This is traced by a light curve, a plot of brightness and time.

Particular variable stars, such as Cepheids, have a period-luminosity relationship. Meaning that for a particular period of oscillation, they have a unique absolute brightness.

The result is that it is possible to measure the light curve of Cepheids far away from the Sun in the Milky Way, and even in other galaxies, and determine their distances.

Tertiary Calibrators:

The nearby region of the Universe, known as the Local Group and is located at the edge of what is known as the the Virgo supercluster of galaxies. The use of Cepheid variables is limited to within the volume of space outlined by the Virgo system. Beyond this volume, we need a new set of distance indicators such as the SN-Ia luminosity or the Tully-Fisher relation.

The Tully-Fisher allows to calculate distances to other galaxies as far away as 200 Mpc.

Hubble's law:

In the 1930's, Edwin Hubble discoveried that all galaxies have a positive redshift. In other words, all galaxies were receding from the Milky Way.

By the Copernican principle (we are not at a special place in the Universe), we deduce that all galaxies are receding from each other, or we live in a dynamic, expanding Universe.

The expansion of the Universe is described by a very simple equation called Hubble's law: the velocity of the recession of a galaxy is equal to a constant times its distance (v = Ho x d). The constant "Ho" is called Hubble's constant and relates distance to velocity in units of kilometers per second per Megaparsec.

The Hubble's law allows distances to be estimated all the way to the edge of the observable universe (i.e., to the beginning of the Universe as we shall see in the next Chapter).

Using the distance indicators we can map the position of galaxies in the Universe, revealing huge structures over large scales in the galaxy distribution. Galaxies in the Universe are not distributed evenly, i.e. like dots in a grid. Surveys of galaxy positions have shown that galaxies have large scale structure in terms of clusters, filaments and voids. The mapping of this large scale structure may reveal the secrets behind the fate of the Universe, as we shall see in the next Chapter.

Dark Matter:

Are we seeing all the the matter in the Universe?

Evidence that this is not so is provided by the motions of stars and galaxies.

Rotation Curve of Galaxy:

The first indications that there is a significant fraction of missing matter in the Universe was from studies of the rotation of our own Galaxy, the Milky Way. The orbital period of the Sun around the Galaxy gives us a mean mass for the amount of material inside the Sun's orbit. But, a detailed plot of the orbital speed of the Galaxy as a function of radius reveals the distribution of mass within the Galaxy.

The simplest type of rotation is wheel rotation shown below.

Rotation following Kepler's 3rd law is shown above as planet-like or differential rotation. Notice that the orbital speeds falls off as you go to greater radii within the Galaxy. This is called a Keplerian rotation curve.

To determine the rotation curve of the Galaxy, stars are not used due to interstellar extinction. Instead, 21-cm maps of neutral hydrogen are used. When this is done, one finds that the rotation curve of the Galaxy stays flat out to large distances, instead of falling off as in the figure above. This means that the mass of the Galaxy increases with increasing distance from the center.

The surprising thing is there is very little visible matter beyond the Sun's orbital distance from the center of the Galaxy. So, the rotation curve of the Galaxy indicates a great deal of mass, but there is no light out there. In other words, the halo of our Galaxy is filled with a mysterious dark matter of unknown composition and type.

Cluster Masses:

Most galaxies occupy groups or clusters with membership ranging from 10 to hundreds of galaxies. Each cluster is held together by the gravity from each galaxy. The more mass, the higher the velocities of the members, and this fact can be used to test for the presence of unseen matter.

When these measurements were performed, it was found that up to 95% of the mass in clusters is not seen, i.e. dark. Can this dark matter be seen at other wavelengths?

Since the physics of the motions of galaxies is so basic (pure Newtonian physics), there is no escaping the conclusion that a majority of the matter in the Universe has not been identified, and that the matter around us that we call `normal' is special. The question that remains is whether dark matter is baryonic (normal) or a new substance, non-baryonic.

Baryonic Dark Matter:

We know of the presence of dark matter from dynamical studies. But we also know from the abundance of light elements that there is also a problem in our understanding of the fraction of the mass of the Universe that is in normal matter or baryons. The fraction of light elements (hydrogen, helium, lithium, boron) indicates that the density of the Universe in baryons is only 2 to 4% what we measure as the observed density.

It is not too surprising to find that at least some of the matter in the Universe is dark since it requires energy to observe an object, and most of space is cold and low in energy. Can dark matter be some form of normal matter that is cold and does not radiate any energy? For example, dead stars?

Once a normal star has used up its hydrogen fuel, it usually ends its life as a white dwarf star, slowly cooling to become a black dwarf. However, the timescale to cool to a black dwarf is thousands of times longer than the age of the Universe. High mass stars will explode and their cores will form neutron stars or black holes. However, this is rare and we would need 90% of all stars to go supernova to explain all of the dark matter.

Another avenue of thought is to consider low mass objects. Stars that are very low in mass fail to produce their own light by thermonuclear fusion. Thus, many, many brown dwarf stars could make up the dark matter population. Or, even smaller, numerous Jupiter-sized planets, or even plain rocks, would be completely dark outside the illumination of a star. The problem here is that to make-up the mass of all the dark matter requires huge numbers of brown dwarfs, and even more Jupiter's or rocks. We do not find many of these objects nearby, so to presume they exist in the dark matter halos is unsupported.

Non-Baryonic Dark Matter:

An alternative idea is to consider forms of dark matter not composed of quarks or leptons, rather made from some exotic material. If the neutrino has mass, then it would make a good dark matter candidate since it interacts weakly with matter and, therefore, is very hard to detect. However, neutrinos formed in the early Universe would also have mass, and that mass would have a predictable effect on the cluster of galaxies, which is not seen.

Another suggestion is that some new particle exists similar to the neutrino, but more massive and, therefore, more rare. This Weakly Interacting Massive Particle (WIMP) would escape detection in our modern particle accelerators, but no other evidence of its existence has been found.

The more bizarre proposed solutions to the dark matter problem require the use of little understood relics or defects from the early Universe. One school of thought believes that topological defects may have appears during the phase transition at the end of the GUT era. These defects would have had a string-like form and, thus, are called cosmic strings. Cosmic strings would contain the trapped remnants of the earlier dense phase of the Universe. Being high density, they would also be high in mass but are only detectable by their gravitational radiation.

Lastly, the dark matter problem may be an illusion. Rather than missing matter, gravity may operate differently on scales the size of galaxies. This would cause us to overestimate the amount of mass, when it is the weaker gravity to blame. This is no evidence of modified gravity in our laboratory experiments to date.