Galaxies and Cosmology

Galaxies

An individual galaxy may contain from only a few thousand to thousands of billions of stars bound together by the force of their own gravity. There may be as many as a hundred billion galaxies in the Universe and, because light travels at a finite speed, if we look at the most distant galaxies we are looking far back into time, approaching the beginning of the Universe itself.

Our galaxy - the Milky Way

 
Milky_Way
A simple diagram of the Milky Way
 

The figure shows a schematic picture of our galaxy. The most obvious feature of our galaxy is that the stars are generally distributed in a disk and that we observe this disk from within, about two-thirds of the way out to the edge. This means that when you look up at the sky on a clear, dark night you can see a bright band marking this disk - we call this the Milky Way. This disk is about one thousand light years (or 300 parsecs) thick and about 30 kpc across. It contains large quantities of gas and dust.

Within the disk the stars are not evenly distributed. Hot, blue-white, bright stars are formed from clouds lying along spiral arms. These stars then disperse around the disk according to their individual speeds and eventually die, spewing out material back into the gaseous disk. The stars rotate around the centre, the Sun takes about 220 million years to complete one orbit.

The main concentration of stars in our galaxy is in a central bulge a few thousand light years across. The bulge is slightly flattened and gradually fades out into the disk and halo of the galaxy. The very centre of the galaxy is in the constellation of Sagittarius (visible from the Southern hemisphere). It is hidden from our direct optical view by dust clouds along the line of sight but we can use radio and infrared telescopes to probe this region.

Milky_Way_Maps
Two all sky maps showing the Milky way in optical (top) and infrared (bottom).
Note the ability of IR to penetrate the dust clouds and so show the "true" distribution of stars.
 

Surrounding the whole of the galaxy is an enormous spherical halo, more than 30 kiloparsecs across. This was the shape of the galaxy before it collapsed to form the rotating disk. The oldest stars in the galaxy are found in the halo , especially in the spherical concentrations of Population II stars (globular clusters).

LMC_and_SMC
The Milky Way, SMC and LMC behind the Cerro Tololo Inter-American Observatory
Image courtesy of NOAO/AURA/NSF.
 

Very close to our galaxy (about 55 kpc away) are two small companion galaxies called the Large and Small Magellanic Clouds. The picture above shows the LMC (lower left), SMC (above) and the Milky Way as seen from the Cerro Tololo Inter-American Observatory in the Chilean Andes.

Types of galaxy - the Hubble sequence

Not all galaxies are spirals like our own, some galaxies are elliptical in shape, others spiral with a bar across the centre, still others are irregular. In 1925, Edwin Hubble classified galaxies according to their shape in a diagram called the Hubble Sequence or sometimes 'The Tuning Fork Diagram' (see figures below). The sequence contains elliptical, spiral, barred-spiral and irregular galaxies. Most galaxies are in fact elliptical, including both the largest and smallest known. The Milky Way is a spiral galaxy. About a quarter are irregular. Note that this diagram is not meant to indicate an evolutionary sequence. The formation and evolution of galaxies is still not fully understood.

Hubble_Tuning_Fork
A Schematic Diagram of the Hubble Tuning Fork
 


Hubble_Tuning_Fork
 

There is no trace of structure in elliptical galaxies (see figure below). They appear to contain very little dust or gas so new stars are no longer forming and therefore their stars are very old, including many red giants. Their apparent shape depends on their inclination to the line of sight - an E0 galaxy may in fact be elongated but appear circular because we view it from the end.

The central bulge of a spiral galaxy contains old stars like an elliptical galaxy but the spiral arms contain most of the gas and dust and it is here that new stars are continuously being formed. Glowing clouds of ionised hydrogen (HII regions) and hot young stars make the spiral arms look pink and blue in photographs.

Barred-spirals are ones in which the central bulge is stretched out into a bar

Three_Galaxies
 

Clusters of galaxies

  Example_Cluster
CL0024+1654 - A Galaxy Cluster
 

We have seen that stars group together to form galaxies. In fact, galaxies are also mutually attracted towards one another by their own gravity and form groups known as clusters. A single cluster may contain thousands of galaxies. Furthermore, clusters of galaxies themselves group together to form, wait for it, superclusters!

Our Galaxy belongs to a small cluster called the Local Group. Three spirals (The Milky Way, Andromeda - M31, and M33) are the largest, the remaining 18 are dwarf elliptical and irregular galaxies. The whole group is about a megaparsec across. Probably the most famous cluster of galaxies is the nearby Virgo cluster (see below). It is about 20 megaparsecs away and has several thousand members. All types of galaxy are found in this cluster and there is no strong concentration towards the centre. Many clusters contain a central large elliptical galaxy (a cD galaxy) [Recall the use of Brightest Cluster Galaxies as distance estimators].

Virgo_Cluster
The Virgo Cluster of Galaxies
 


Hubble's Law

The modern science of observational cosmology began with the discovery of the expansion of the universe in the 1920's.
 
Galaxy_Spectrum
An Example Galaxy Spectrum
 

The integrated spectrum of an entire (normal) galaxy is just the light of thousands of millions of faint stars. In general, they are composed of continua with superposed absorption (and some emission) lines. The absorption lines are broader than from a single star because each star is moving at a different speed relative to us and hence the line is doppler-shifted. In spirals the width measures the rotation of the galaxy, in ellipticals the random motion of the stars. However, if the galaxy as a whole is moving toward or away from us then the centre of the line will be shifted to the blue or the red, respectively.


Hubbles_Diagrams
Hubble's original galaxy recession vs. distance results (left) and some modern data (right). Note the different quantities on the axes!
 

The figure on the left above illustrates the original form of the Hubble diagram. Note that the distances were greatly underestimated at this time. Next to it is the modern equivalent where apparent magnitudes of standard candles are plotted against redshift.

Redshifted_Spectra
Redshifted Galaxy Spectra
Note that spectra have been moved up and down the graph for clarity and the colours are for illustration only!
 

Redshift z is given by

Redshift
 

where Δλ = λ1 - λo is the difference between the wavelength at which a line is observed λ1 and the rest wavelength at which it is emitted λ0. For small redshifts,

Redshift2
 

where v is the recession velocity of the galaxy and c is the speed of light.

Note for large redshifts (e.g. the most distant normal galaxy has a redshift of between 3 and 4, radio galaxies of 4 and quasars of 5) this formula is more complex.

The linear relationship Hubble discovered is then

Hubble_Law
 

where H0 is referred to as Hubble's constant and d is the distance of the galaxy. This relationship is interpreted as expansion of the whole universe since it seems to be universal at large distances. It breaks down at small distances because random, so-called peculiar, motions of galaxies dominate.

  2df_cones
2DF survey "slice-diagrams"
 

Because of the simple linear relationship between redshift and distance, Hubble's law can used as a distance indicator for galaxies at greater than about 20 Mpc. In fact, it is basically the only way of getting distances beyond about a few 100 Mpc. The 2 degree field (2DF) project using the wide-field optical fibre-based spectrometer on the Anglo-Australian Telescope aims to obtain redshifts for a quarter of a million galaxies using an optical fibre-based spectrometer (they have recently gone past 100,000 galaxies). The figure to the right shows a pair of "slice-diagrams" - plots of velocity of recession (or distance or redshift) versus angular position on the sky - for the 2DF survey.

The exact value of Hubble's constant is still a matter of great debate with numbers in the range 50-100 km/s/Mpc leading to uncertainties of a factor of two in the absolute distance scale. (If the current (2003) results from the WMAP satellite are confirmed, then H0 = 71 km/s/Mpc to within about 5%). As we shall see below its value relates directly to the age of the universe.

Cosmological parameters and the Big Bang

Cosmological parameters

The simplest models for the expansion of the universe smooth out all structure such as stars and galaxies and assume that we are not in a special position from which to observe the universe - they assume the universe is homogeneous and isotropic.

In such a universe, we can represent all distances by a dimensionless number multiplied by a universal time-dependent scale factor R(t). As the universe expands, the relative distances between points does not change but the scale factor increases. If we write the distance between two points as s then s = x R(t) where x is the dimensionless distance (a constant for that pair of points) and R(t) is the scale factor which changes with time but is the same everywhere in the universe. Then the velocity with which one point recedes from the other is given by

Expansion_Scale
 

where

dRdt
 

This shows that at a particular time the speed of recession of one point from another is just proportional to their separation s at that time. This is Hubble's law and the Hubble constant H0 is just the ratio R°/R at the present time indicated by the subscript 0. Note that in practise the value of the Hubble 'constant' will change with time.

If the universe had been expanding at a constant rate since it began, then the age would just be given by 1/H0, simply by considering a straight-line graph of R(t). For values of H0 = 50-100 km/s/Mpc we obtain ages (10-20) x 109 yrs.

  Expansion_vs_Omega
The evolution of the Universe for different values of Ω0
 

However, if we include for the gravitational effect of the matter in the universe which would act to slow down the expansion we can see that 1/H0 is only an upper limit on the age of the universe (see figure).

In fact there are two possible regimes, one in which the mass in the universe is not sufficient to halt the expansion and so this continues forever and another in which the universe eventually begins to collapse back in on itself due to its own gravity. The parameter which describes this behaviour is called the density parameter Ω0 and its value now is given by

Omega
 

where ρ0 is the mean density of the universe now and ρc is the critical density required to cause the universe to gradually slow down and coast out to a point at which

Rdot_tend_zero_as_t_tend_inf
 

So, for Ω0 = 0 we have an empty universe which always expands at the same rate, for Ω0 = 1, we have a universe which stops expanding after infinite time and for Ω0 > 1 we have a universe which stops expanding after a finite time and recollapses.

A universe with Ω0 < 1 is often called an open universe, one with Ω0 = 1 a flat universe, and one with Ω0 > 1 a closed universe. This terminology arises from Einstein's theory of general relativity which interprets cosmological models in terms of the geometry of space-time. A flat universe is one in which normal Euclidean geometry applies and there is zero curvature, in a closed universe there is positive curvature (e.g. a sphere) and in an open universe negative curvature (e.g hyperboloid with a saddle point).

In the Ω0 = 1 model the age of the universe is less than 1/H0, in fact it equals 2/3 of this.

Dark Matter

Adding up the mass of all the visible matter in galaxies gives Ω0 ~ 0.003.

If this were all the matter there were, then the universe would be open and expand forever. However, we know from rotation curves of galaxies and motions of galaxies within clusters that there are significant amounts of 'dark matter'.

The most reliable way to find the mass of a spiral galaxy is to measure the speed at which it rotates as a function of the distance from the centre. This is best done using the 21 cm emission line from clouds of neutral hydrogen orbiting the visible galaxy made up of stars (radio emission is not obscured by dust in the disc).

If we equate the gravitational force on a body of mass M rotating in a circle of radius R at speed V around an object whose mass is M, with the force resulting from circular motion, then we obtain

Rotation_Curve_Equation
 

  Rotation_Curve
A diagram of a galaxy rotation curve.
 

An example rotation curve of a galaxy is given here. You can show that the bulge (where V proportional to R) must have approximately uniform density whereas far out (V is constant, the flat part of the rotation curve) then the mass within radius R is proportional to R. As the rotation curve appears flat for as far as we can measure it this means the mass keeps on increasing well out beyond the visible light from the stars. This is the best evidence for the existence of 'dark matter'.

The nature of the dark matter this is unknown. It could be dead stars (old white dwarfs, neutron stars, black holes), very faint low-mass stars (brown dwarfs) or some exotic form of matter. It is estimated that as much as 90% of the mass of a spiral galaxy may be outside the visible disc. Similar dark matter exists on the scales of clusters of galaxies.

Including the effects of this dark matter it seems that the value of Ω0 must be more like 0.1-1. In other words, the present-day universe is quite close to being 'flat'. In fact, the theory of inflation, in which the universe went through a phase of extremely rapid expansion very early in its evolution, predicts that the value of Ω0 should be exactly 1.

Remember a flat universe has density equal to the critical density and its age is given by (2/3)(1/H0). Taking into account the uncertainty in the value of H0, the range of ages is about (7-13) x 109 yr. The current best estimate of the ages of the oldest stars in globular clusters is about (12-16) x 109 yr. Things are a bit tight!

The currently fashionable way out of this problem is to introduce an additional constant into the solution for R(t). This constant, the cosmological constant Λ , was first introduced by Einstein to stop his model universe expanding - this was before observations had shown that the real universe was expanding! In fact, a positive value for Λ has the effect of introducing a repulsive force which opposes gravity and is directly proportional to distance. We don't see such an effect on small scales so its value must be very small. However, its introduction would allow a universe with an age longer than the standard Hubble time 1/H0 and therefore not in conflict with the age of globular clusters.

The recent results from the WMAP experiment indicate that Ω0 = 1 with contributions of about 4% normal matter, 23% dark matter and 73% from Λ.

The standard model of the Hot Big Bang

Obviously if the universe is expanding, rewinding it in time will lead to a point at which the universe is infinitely dense (a singularity) and from which it began to expand - this is the so-called 'big bang'.

The Big Bang model assumes:

The Big Bang is regarded as a successful model because it explains three observational facts:

We have already dealt with the observational evidence for an expanding universe.

Primordial nucleosynthesis

For the first 10 or 15 minutes of the Universe the temperature is sufficiently high (a few times 109 K) that nuclear fusion reactions can produce light elements such as deuterium (21H), helium-3 (32He), helium-4 (42He) and lithium-7 (73Li). This process ends once the universe has expanded to the point where the temperature and density are too low for the reactions to continue. Although, later, these elements tend to be used up to form heavier elements in stars, they appear to have universal abundances e.g. by observing metal-poor galaxies one can get reasonable estimates of the primordial abundances which applied before stellar fusion reactions modified things.

Part of the Big Bang theory are models that predict the relative fractions of the primordial elements. The predictions of these models almost exactly match the measurements of the primordial abundances.

The microwave background

The universe remained in a state of equilibrium between matter and radiation for a long time. The material was fully ionized and photons scattered off electrons whilst electrons collided with ions ensuring a constant redistribution of energy.

However, once the universe cooled to about 3,000 K, collisions between particles lacked the strength to dissociate any neutral hydrogen atoms that may have formed (by a proton capturing an electron). At this time, some half a million years after the big bang, the matter was no longer fully ionized, the photons found themselves free to travel large distances as the number of free electrons to scatter off was drastically reduced. This is the era of 'decoupling' when the matter and radiation effectively go their separate ways and cool independently.

At the time of decoupling the Big Bang model predicts the radiation would have had a blackbody spectrum characterised by a temperature T ~ 3000 K. As the universe expanded this effectively cooled such that T proportional to 1/R. Since decoupling, the universe has expanded in size by a factor 1000, hence we would predict that a general background of radiation with a blackbody spectrum of temperature ~ 3 K ought to permeate the universe.

A 3 K blackbody spectrum peaks at around 1 mm which is difficult to observe because detectors are hard to build and it is near the cutoff for atmospheric absorption. The radiation (the so-called microwave background) was discovered accidentally by Penzias and Wilson in 1965. In the late 1980s, the COBE satellite (COsmic Background Explorer) was launched and the spectrum was determined to be a very good match to a blackbody. After COBE we can now say two important things about the microwave background:
  CoBE_Spectrum
Fit to the CoBE blackbody data
Note that the error bars are 400 times larger than normal!
 

  1. Its spectrum is extremely close to that of a blackbody with T=2.726 +/- 0.010 K;
  2. After correction for the dipole anisotropy resulting from the motion of the Earth, Sun and Galaxy with respect to the overall expansion of the universe, and removing a contribution from stars in the Milky Way, the intensity is highly isotropic (the same in all directions), to about one part in one hundred thousand - see the figure below. This measurement has been improved upon by the WMAP satellite this year (2003)


CoBE_Maps
All-sky maps from CoBE
The top map is the "raw" data and is dominated by dopper shifts due to the motion of the Earth and Sun relative to the background.
The middle map has this dipole removed.
Finally, the bottom map also has contributions form stars in the Milky Way removed to just leave the background. Blue areas are is slightly hotter than red areas, but the contrast is tiny.
 

The first property is strong support for the hot big bang. The second property implies that the assumption of isotropy in most cosmological models is an accurate one - the universe does indeed look much the same in all directions. However the tiny fluctuations that are present (the famous 'ripples' or the 'face of God') are believed to represent the seeds from which structure like clusters of galaxies eventually formed. This process is not fully understood but probably also requires the presence of large amounts of dark, non-baryonic, matter.

Before decoupling the universe was opaque to radiation because the photons were all scattered by the free electrons. The microwave background represents the limit to which we can see using photons - we will not be able to see further back in time unless we rely on something like neutrinos which, because they interact much less strongly with matter meant they decoupled at an earlier stage; unfortunately this also means they're very hard to detect! The microwave background is therefore a realistic horizon beyond which we are going to find it very hard to see. The PLANCK space mission due to fly in 2007 will investigate the microwave background at much higher angular resolution and sensitivity than COBE or WMAP and will help to solve some of the problems that still confront cosmology.