3.3 Extending the distance scale
Having reviewed some of the properties of galaxies, we are now in a position to return to the question of how we are to develop further our methods of measuring distance.
The various steps taken in determining larger distances from known smaller ones are often called ‘rungs in the distance ladder’. The process of constructing a rung has been:
Find a measurable quantity associated with a class of objects.
Observe how the measurable quantity depends on distance for objects close enough to have had their distances measured by the method of a previous rung.
Assume the same relationship holds for more distant objects of the same class, and hence calculate their distances.
Return to step 1, with a new measurable quantity.
The classes of objects (and distance indicators) for the first four rungs of the distance ladder were:
|Sun||(by radar ranging)|
|Nearby stars in our Galaxy||(by triangulation)|
|Our Galaxy and nearby galaxies||(using Cepheid variables)|
|Nearby and somewhat further off galaxies||(using Type Ia supernovae)|
These distance indicators all depended on recognising a particular type of star. But, as was mentioned in Section 3.1, individual stars can be resolved only in galaxies that are not too distant. For most galaxies, a method is needed which depends on recognising, or deducing, the luminosity of the galaxy as a whole. Although, as already noted, individual galaxies vary considerably in their luminosity, they occur in clusters. A simple rule which seems to work in practice is to assume that the third-brightest galaxy in all clusters has the same luminosity (a standard 1037 W lamp).
An alternative method is to separate galaxies into different types, with the assumption, or at least the hope, that the types have characteristic luminosities. There are certainly generic differences between spiral galaxies (Figure 11) and elliptical galaxies (Figure 12). But it is also well established that there is a useful correlation between the luminosities of spiral galaxies and their rotation speeds, which can be determined from (radio) observations of Doppler broadening.
Another method exploits the fact that some types of radio galaxy (so-called because they are strong emitters at radio frequencies) are fairly uniform in size, and radio interferometers can resolve very small angular separations – a thousand times smaller than those resolved by optical telescopes. The apparent size leads to an estimate of the distance of the galaxy. Because some radio galaxies are also visible at optical wavelengths, the optical and radio distance scales can be intercalibrated.
Yet another method should also be mentioned. It involves the behaviour of a single star in a galaxy, though one too distant to be resolved. We have already mentioned Type Ia supernovae. These are events that occur when a white dwarf (which itself originally resulted from the last stages in the active life of a medium-sized star) captures material from a companion star, and undergoes collapse to a neutron star. If instead of a medium-sized star one begins with a very massive star, then at the end of its active life it catastrophically collapses directly to a neutron star or black hole. This leads to a gigantic explosion even more energetic than a Type Ia supernova; it is called a Type II supernova. These explosions are bright enough to be visible at large distances – in some cases briefly shining more brightly than all the other stars of the galaxy put together. Unfortunately they are rather rare, occurring only once every hundred years or so in a typical galaxy. A Type II supernova explosion causes a spherical shell of hot gas to expand out of the star at high speed – thousands of kilometres per second. The spectral lines in the observed light from this shell (mostly from hydrogen and therefore easily identified) are blueshifted by its velocity towards us. Knowing this velocity from the amount of blueshift, the increase in size of the shell, month by month, can be calculated. Thus the shell is a source of known size, even though this cannot be resolved from an observed angular width. The temperature can be found from the overall shape of the continuous spectrum between the spectral lines. Knowing both the size and temperature of the shell, its total light output (that is, its luminosity) can be found. From this and the observed flux this and the observed flux density, the distance can be calculated using the inverse square law.
Remember, luminosity = 4r2 × flux density, where r is the distance.
Comment on the truth or otherwise of the following statements:
(i) Averaging statistically over the luminosities of its constituent galaxies, each cluster of galaxies can be assumed to have the same overall luminosity.
(ii) The distance-measuring method involving Type II supernovae relies on the fact that the shell of material thrown out by the explosion greatly exceeds the parent star in size, to the extent that it can be optically resolved.
Both statements are incorrect.
(i) The overall luminosity of a cluster cannot be used as a standard lamp because, as stated in Section 3.2, clusters can vary enormously in size from thousands of galaxies to a single galaxy. All one can say is that the luminosity of a typical galaxy in that cluster (averaged over a number of the galaxies it contains) is the same for each cluster.
(ii) The shell thrown out from the supernova cannot be resolved optically. Instead, the radius of the fireball at a given moment is calculated from the estimated speed of the ejected material and the time that has elapsed since the explosion. The colour (temperature) determines the light output per unit area. Hence, knowing the surface area from the radius, one arrives at an estimate of the luminosity of the supernova at the given time after the explosion. This luminosity is then compared to the measured flux density to obtain the distance to the star.