Distance modulus

The redshift distance modulus modz, in mag, is derived from the Virgo infall vvir, it can be used to determine the absolute magnitude knowing the apparent one.

It is defined as

modz = 5 log(D_L) + 25

where D_L is the luminosity-distance in Mpc, defined by the law of dimming of the observed flux: F ∝ L / D_L². (Because of the relativity and cosmological models, there is not a single definition of the distance. We may also define the proper distance D = cz/H₀, the angular-diameter distance D_A = D_L/(1+z)² and the comoving distance D_M = D_L/(1+z)).

D_L is derived from the cosmological redshift, assuming the following values for the Hubble constant and other cosmological parameters:

H₀ = 70 km/s/Mpc

Ω_M = 0.27

Ω_Λ = 0.73

The choice of vvir to estimate the cosmological redshift is a compromise. For large distances, v3k should be more appropriate. But the galaxies of the Local Universe share a similar bulk motion as the Galaxy, and correcting only the motion of the Galaxy would bias their distance determination. An improvement would be to use a model for the bulk motions in the Local Universe.

The parameter mod0 (redshift-independent modulus) is an estimate of the luminosity-distance independently of the redshift, and both parameters are combined into modbest, to provide the best distance estimate at any redshift.

HyperLeda

Questions: leda@univ-lyon1.fr