Question

Explain the concepts of “luminosity distance” and “proper distance”, and how they are different. How does the observed bolometric flux, f, from a distant source with luminosity, L, depend on redshift, z? What factor(s) cause(s) this redshift dependence? Describe the properties of a universe where the luminosity distance would be identical to the proper distance.

Answer 1

The proper distance corresponds to distance where a distant object would be at a specific moment of cosmological time, which can change over time due to the expansion of the universe.

If Intrinsic luminosity L of a distant object is known, we can calculate its luminosity distance by measuring the flux S and determine , which turns out to be equivalent to the expression above for . This quantity is important for measurements of standard candles like type Ia supernovae.

flux and luminosity and reshift are related as where L is the luminosity a0 is the scale factor r1 is the comoving distance z is the redshift.

flux depends upon redshift because of change in distance with redshift due to the expansion of the universe.

x is the proper distance and a is the scale factor,

Luminosity distance will be equal to the proper distance when z=0 and a=1, which corresponds to the present universe.

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