The CosmicDistance Scale

A very important task in modern astronomy is the measurement of distances to things that are very far away. We have seen earlier some methods for measuring distances to relatively nearby objects.

### The Measurement of Distances: Standard Candles

At very large distances such as those to galaxies beyond the local group or the local supergroup, astronomers can no longer use the methods such as trigonometric parallax or Cepheid variables that we have discussed before because the parallax shift becomes too small, and because at sufficiently large distances we can no longer even see individual stars in galaxies.

At those distances, astronomers turn to a series of methods that use standard candles: objects whose absolute magnitude is thought to be very well known. Then, by comparing the relative intensity of light observed from the object with that expected based on its assumed absolute magnitude, the inverse square law for light intensity can be used to infer the distance.

### Example of a Standard Candle: Type Ia Supernovae

One example of a standard candle is a type Ia supernova. Astronomers have reason to believe that the peak light output from such a supernova is always approximately equivalent to an absolute blue sensitive magnitude of -19.6. Thus, if we observe a type Ia supernova in a distant galaxy and measure the peak light output, we can use the inverse square law to infer its distance and therefore the distance of its parent galaxy.

Because type Ia supernovae are so bright, it is possible to see them at very large distances. Cepheid variables, which are supergiant stars, can be seen at distances out to about 10-20 Mpc; supernovae are about 14 magnitudes brighter than Cepheid variables, which means that they can be seen about 500 times further away. Thus, type 1a supernovae can measure distances out to around 1000 Mpc, which is a significant fraction of the radius of the known Universe.

### A Comparison of Methods for the Virgo Cluster

The following table lists a variety of methods for determining large distances as applied to the same problem: determining the distance to the Virgo Cluster of galaxies.

Distance Methods Applied to the Virgo Cluster
Method Uncertainty (Mag) Distance (Mpc) Uncertainty (Mpc) Range (Mpc)
Cepheids 0.16 14.9 1.2 20
Novae 0.40 21.1 3.9 20
Plan. Nebulae 0.16 15.4 1.1 30
Glob. Clusters 0.40 18.8 3.8 50
S. Bright. Fluct. 0.16 15.9 0.9 50
Tulley-Fisher 0.28 15.8 1.5 >100
D-Sigma 0.50 16.8 2.4 >100
Supernova (1a) 0.53 19.4 5.0 >1000
Source: An Introduction to Modern Astrophysics, B. W. Carrol and D. A. Ostlie (Addison-Wesley, 1996)

We shall not discuss the details of how all these methods work, but we note that there is reasonably good agreement on the distance to the Virgo Cluster (the average among the different techniques is approximately 15 Mpc). This gives us some confidence that these methods can be used to measure large distances. The last column (Range) gives the largest distance at which these methods can be used. We see that distances in excess of 1000 Mpc may be measured.

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