Introduction

Cosmology and distance measurements

How old is the Universe? How fast is it expanding? Will it one day start to contract? These are fundamental cosmological questions that have long awaited satisfactory answers. The fate of the Universe is closely linked with the future behaviour/evolution of its expansion rate. If the expansion slows down suffi ciently then the Universe may one day start to contract again. Observations currently suggest that it is more likely that the Universe will continue to expand forever.

Figure 2: The Fate of the Universe This graph relates the size of the Universe with time - in other words it shows how it expands and/or contracts with time. The different lines ‘in the future’ (to the right in the diagram) show different models for the fate of the Universe - an ever-expanding Universe or a contracting Universe.

Figure 3: Receding Galaxies This diagram illustrates how the galaxies recede from each other due to the expansion of the Universe.

Figure 4: Remote Galaxies with High Redshifts This image, taken by the Wide-Field and Planetary Camera (WFPC2) of the Hubble Space Telescope, shows many galaxies, billions of light years away. Most of the fuzzy patches are galaxies containing billions of stars. The galaxies in this image are receding from us at high velocities.

The expansion makes all galaxies recede from a given observer (e.g. on Earth) and the further away they are, the faster they recede. The expression known as Hubble’s law (formulated by Edwin Hubble in 1929) describes the relation between the distance of a given object and its recession velocity, v. Hubble’s law is:

v = H₀ * D

It states that the galaxies in our Universe are fl ying away from each other with a velocity, v, proportional to the distance, D, between them.

H₀ is a fundamental property of the Universe – the Hubble constant – important in many cosmological questions and is a measure of how fast the Universe is expanding today. The age of the Universe, t, can be approximated by the inverse (or reciprocal) of the Hubble constant H₀:

t = 1 / H₀

The value of H₀ has enormous signifi cance for estimates of the age of our Universe. But how do we measure it? To determine H0, we ‘simply’ need to measure both the recession velocity, v, and the distance, D, for an object, usually a ga laxy, or, even better, for many galaxies and fi nd the average measurement.

The recession velocity is relatively easy to determine: we can measure the so-called redshift of the light from the galaxy. Redshift is a direct consequence of an object’s motion away from us. It is a Doppler-shift of the light from the individual galaxies, resulting in a shift of the wavelength of the light from the galaxies towards the red end of the spectrum. As the wavelength of red light is longer than blue light, the wavelength of the light from the galaxies has increased during its journey to the Earth. The fractional change in wavelength due to the Doppler- shift is called the redshift and galaxies with a high redshift have high recession velocities.

Figure 5: Henrietta Leavitt The understanding of the relative brightness and variability of stars was revolutionised by the work of Henrietta Swan Leavitt (1868-1921). Working at Harvard College Observatory, Leavitt calibrated the photographic magnitudes of 47 stars precisely to act as standard references or ‘candles’ for the magnitudes of all other stars. Leavitt discovered and catalogued over 1500 variable stars in the nearby Magellanic Clouds. From this catalogue, she discovered that brighter Cepheid variable stars take longer to vary, a fact used today to calibrate the distance scale of our Universe (Courtesy of AAVSO).

Using Cepheids as distance estimators

Measuring the distance to an astronomical object is much more diffi cult and is one of the greatest challenges facing astronomers. Over the years a number of different distance estimators have been found. One of these is a class of stars known as Cepheid variables.

Cepheids are rare and very luminous stars that have a very regularly varying luminosity. They are named after the star ä-Cephei in the constellation of Cepheus, which was the fi rst known example of this particular type of variable star and is an easy naked eye object.

In 1912 the astronomer Henrietta Leavitt observed 20 Cepheid variable stars in the Small Magellanic Cloud (SMC). The small variations in distance to the individual Cepheid variable stars in the Cloud are negligible compared with the much larger distance to the SMC. The brighter stars in this group are indeed intrinsically brighter and not just apparently brighterbecause they are closer. Henrietta Leavitt uncovered a relation between the intrinsic brightness and the pulsation period of Cepheid variable stars and showed that intrinsically brighter Cepheids have longer periods. By observing the period of any Cepheid, one can deduce its intrinsic brightness and so, by observing its apparent brightness, calculate its distance. In this way Cepheid variable stars can be used as one of the ‘standard candles’ in the Universe that act either as distance indicators themselves or can be used to calibrate (or set the zero point for) other distance indicators. Cepheid variables can be distinguished from other variable stars by their characteristic light curves (see Fig. 6).

Figure 6: Typical Cepheid light curve The light curve for a Cepheid variable star has a characteristic shape, with the brightness rising sharply, and then falling off much more gently. The amplitude of the variations is typically 1-2 magnitudes.

The most accurate measurements of both velocity and distance are naturally obtained for objects that are relatively close to the Milky Way. Before the NASA/ESA Hubble Space Telescope was available, ground-based observatories had detected Cepheid variables in galaxies with distances up to 3.5 Megaparsecs (see the defi nition of Megaparsecs in the Mathematical Toolkit) from our own Sun. However, at this sort of distance, another velocity effect also comes into play. Galaxies attract each other gravitationally and this introduces a non-uniform component to the motion that affects our measurements of the uniform part of the velocity arising from the expansion of the Universe. This non-uniform part of the velocity is known as the peculiar velocity and its effect is comparable with the expansion velocity in our local part of the Universe. In order to study the overall expansion of the Universe, it is necessary to make reliable distance measurements of more distant galaxies where the expansion velocity is signifi cantly higher than the peculiar velocity. Hubble has measured Cepheid variables in galaxies with distances of up to ~20 Megaparsecs.

Before Hubble made these measurements astronomers argued whether the Universe was 10 or 20 billion years old. Now the agreement is generally much better – the age of the Universe is believed to be somewhere between 12 and 14 billion years.

One of the Hubble’s Key Projects had as a longterm goal a more accurate value for the Hubble constant and the age of the Universe. Eighteen galaxies located at different distances have been monitored to reveal any Cepheid variables. One of these galaxies is M100.

Figure 7: The Spiral Galaxy M100 If we could observe our galaxy, the Milky Way, face on from an extragalactic space vessel, its shape would be similar to the Spiral Galaxy M100. Spiral galaxies are rich in dust and gas. The dust shows up in this image as dark lanes running between the majestic spiral arms. M100 is a popular target for amateur astronomers and is located in the spring sky in the direction of the constellation of Coma Berenices. The image was taken with Hubble’s Wide Field and Planetary Camera 2. Blue colours correspond to regions with young hot stars.

M100 – a Grand Spiral

The galaxy M100 is a magnifi cent spiral galaxy in the large Virgo cluster of galaxies. The Virgo cluster contains 2,500 galaxies. M100 is a rotating system of gas, dust and stars similar to the Milky Way and is viewed face on. The name M100 stems from the fact that it is number 100 in the Messier catalogue of non-stellar objects.

M100 is one of the more distant galaxies where accurate measurements of Cepheid variables have been made. This exercise is based on Hubble’s images and data from this galaxy.

Figure 8: Hubble tracks down Cepheid variable stars in M100 Hubble’s high resolution camera detected and picked out one of the Cepheid variable stars used in this exercise. The star is located in a star-forming region in one of the galaxy’s spiral arms (the star is at the centre of the box).