Cosmic Distance Ladder
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.