Photometric distance D_L relates the observed radiation flux F to the true luminosity L via the formula F = L / (4π D_L²). It includes a correction for the expansion of the universe: photons lose energy due to redshift (wavelength increases), and the time between the arrival of successive photons also stretches. As a result, D_L = (1+z) D_M, where z is the redshift, and D_M is the comoving transverse distance. For nearby objects, D_L ≈ D_M, but for distant galaxies (z ~ 1 and higher) the difference becomes significant. D_L is precisely what is measured using standard candles—objects of known luminosity, like Type Ia supernovae.
History
The concept originates from the work of Edwin Hubble, who in 1929 established the proportionality of redshift to distance. The formula for photometric distance in relativistic cosmology was derived within the framework of the Friedmann–Lemaître–Robertson–Walker metric. The Supernova Cosmology Project (Saul Perlmutter) and the High-Z Supernova Search Team (Brian Schmidt, Adam Riess) in 1998 used Type Ia supernovae as standard candles and discovered a deviation of D_L from the linear law, which indicated accelerated expansion. This became direct observational evidence for the existence of dark energy. Adam Riess and Saul Perlmutter are present in the list of scientists.
How it works
The relationship between apparent magnitude m and absolute magnitude M is given by the distance modulus: m − M = 5 log₁₀(D_L / 10 pc). For an object with known absolute luminosity (standard candle), measuring the peak apparent magnitude yields D_L. Within general relativity, D_L is expressed through solutions to the Friedmann equations, which follow from Einstein's equations for a homogeneous isotropic universe. The value of D_L depends on the densities of matter Ω_m, dark energy Ω_Λ, curvature Ω_k, and the Hubble constant H₀. Therefore, measuring D_L for a set of objects at different z allows placing constraints on cosmological parameters, in particular on the equation of state of dark energy w.
In practice
The method is used to measure distances to Type Ia supernovae, which led to the discovery of the accelerating expansion of the universe. Without it, modern cosmology would lose its ruler.
Fun fact
Looking at a galaxy with redshift z=1, we receive light dimmed by a factor of four just due to the expansion of space—the photometric distance turns out to be twice the comoving distance.
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