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.
|
Technically Speaking: Tulley-Fisher Relation and Distances
An important method for determining the distance to spiral galaxies
is called the Tulley-Fisher Relation. This relation
notes that there is a very strong correlation between the luminosity
of a spiral galaxy and its rotation speed. It follows that by measuring the
rotation speed of a spiral galaxy the luminosity can be inferred and
thus the distance, when this is compared with the apparent brightness.
For nearby galaxies one can resolve opposite sides of the galaxy and
measure the Doppler shift separately to estimate the rotation speed.
As noted earlier in discussing the masses of galaxy clusters, for
more distant spirals the rotation speed can be related to broadening
of spectral lines. Thus, a careful study
of line broadening for distant spiral galaxies can lead to a rotational
speed and thus a distance.
|
|
Standard Candles
At very large distances such as those to galaxies further away than
nearby clusters, astronomers can no longer use the methods such as
trigonometric parallax or Cepheid variables that we have discussed before. The
parallax shift becomes too small and
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 often
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: Type Ia Supernovae
As we already saw in Chapter 21,
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
and visual magnitude
of -19.5. 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.
They can be used to
measure distances out to around 1000-2000 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
|
| Planetary Nebulae |
0.16 |
15.4 |
1.1 |
30
|
| Globular Clusters |
0.40 |
18.8 |
3.8 |
50
|
| Surface Brightness
Fluctuation |
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 (Ia) |
0.53 |
19.4 |
5.0 |
>1000
|
|
|
|
|
Source: An Introduction to Modern
Astrophysics, B. W. Carrol and D. A. Ostlie
|
We shall not discuss the details of how all these methods work, but we note that
there is reasonably good agreement among these methods 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.