Luminosity distance DL is defined in terms of the relationship between the absolute magnitude M and apparent magnitude m of an astronomical object.
which gives:
where DL is measured in parsecs. For nearby objects (say, in the Milky Way) the luminosity distance gives a good approximation to the natural notion of distance in Euclidean space.
The relation is less clear for distant objects like quasars far beyond the Milky Way since the apparent magnitude is affected by spacetime curvature, redshift, and time dilation. Calculating the relation between the apparent and actual luminosity of an object requires taking all of these factors into account. The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance.
Another way to express the luminosity distance is through the flux-luminosity relationship. Since,
where F is flux (W·cm−2), and L is luminosity (W), or where F is flux (erg·s−1·cm−2), and L is luminosity (erg·s−1). From this the luminosity distance can be expressed as:
The luminosity distance is related to the "comoving transverse distance" by the equation:
where z is the redshift. is a factor that allows you to calculate the comoving distance between two objects with the same redshift but at different positions of the sky; if the two objects are separated by an angle, the comoving distance between them would be . In a spatially flat universe, the comoving transverse distance is exactly equal to the radial comoving distance, i.e. the comoving distance from ourselves to the object.
Famous quotes containing the word distance:
“Though there were numerous vessels at this great distance in the horizon on every side, yet the vast spaces between them, like the spaces between the stars,—far as they were distant from us, so were they from one another,—nay, some were twice as far from each other as from us,—impressed us with a sense of the immensity of the ocean, the “unfruitful ocean,” as it has been called, and we could see what proportion man and his works bear to the globe.”
—Henry David Thoreau (1817–1862)