Thursday, June 9, 2011

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 ( DL / 10pc ) (Eqn. 2)

where DL is the luminosity distance, defined as follows:

DL = (1+z)*DM (Eqn. 3)

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

The K-correction is calculated the following way:

K = -2.5 (1+αν)log10 (1+z) (Eqn. 4)

αν= -0.5 according to Richards et. al 2006

So.... putting that all together:

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

I've decided to use this table from Richards 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.


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