Calculating Absolute Magnitude

Going back to some "Freshman Astronomy" as Martin White said in the meeting today. The absolute magnitude i-band (M) and apparent i-band magnitude (m) are related by the following equation:

m = M + DM + K (Eqn. 1)

Where DM is the distance modulus and K is the K-correction.

The distance modulus is defined as follows:

DM = 5 log₁₀ ( D_L / 10pc ) (Eqn. 2)

where D_L is the luminosity distance, defined as follows:

D_L = (1+z)*D_M (Eqn. 3)

where D_M is the comoving distance and z is the redshift.

The K-correction is calculated the following way:

K = -2.5 (1+α_ν)log₁₀ (1+z) (Eqn. 4)

α_ν= -0.5 according to Richards et. al 2006

So.... putting that all together:

M = m -DM - K

M = m - 5 log₁₀ ( (1+z)*D_M / 10pc ) + 2.5 (0.5)log₁₀ (1+z)

I've decided to use this table from Richards et.al. 2006 to do the k-corrections, because it corrects for both the emission line and continuum components, where as the equation above just corrects for the continuum.

References:
http://www.mporzio.astro.it/~fiore/agn/richards_2006.pdf
http://arxiv.org/pdf/astro-ph/9905116