For any given redshift (z), we have two values for the distance −

• Angular Diameter Distance (d_A)
• Luminosity Distance (d_L)

There is no unique definition of “cosmological” distance in the universe. The choice of the distance depends on the purpose and convenience of application.

To test the predicted trend of how angular size of an object varies with redshift, a standard size yardstick is needed in the sky. This should be an object which −

• is very luminous, so that it can be detected at z > 1.

• is very large, so that we can resolve its angular size.

• has not morphologically evolved over cosmologically significant time (z ∼ 1 corresponds to a look back time of about 7 Gyr).

Some objects (like cD galaxies) satisfy the first two criteria. But almost every object is found to morphologically evolve with time. In general, astrophysical objects (extended sources) tend to be intrinsically smaller in the past because they are still forming.

Luminosity Distance

Luminosity distance depends on cosmology. The dependence of luminosity distance on cosmology makes it a useful measure of the cosmological parameters.

The cosmological parameters can be estimated if we can find a standard candle that does not intrinsically evolve and exists from the local to the high redshift universe.

A standard candle is one which does not differ in its luminosity from source to source. The premise is that any difference in the estimated luminosity of standard candles has to be due to cosmology. One such candle is Type Ia Supernovae.

Type 1a Supernovae (SNe)

These are the result of explosion of a white dwarf after sufficient mass accretion from its companion, a red giant or similar main sequence star, in a binary system. After the red giant comes closer than the Roche lobe distance of the White dwarf, the mass transfer begins and eventually the white dwarf explodes giving out huge amount of energy, leaving no core behind. These are called Type 1a Supernovae. The typical rate of Type 1a Supernovae explosion in a galaxy is 1 per century.

The search for Type 1a SNe has been going on with different teams −

• High z Supernova Search Team (Brian Schmidt, Adam Reiss et al.)
• Supernova Cosmology Project (Saul Perlmutter et al.)

There has been another research team called Carnegie Supernovae Project who has given similar results.

The similarity of results from different teams show the cosmological nature of Type 1a SNe. Hence, they are efficient standard candles.

Points to Remember

• There is no unique definition of “cosmological” distance in the universe.

• Angular Diameter Distance and Luminosity Distance are the most used.

• A standard candle is the one which does not differ in its luminosity from source to source.

• Type 1a SNe satisfies the criteria of being a standard candle.