# Stellar mass of galaxies

Given the magnitudes (in the i-band) of certain galaxies, I would like to calculate their stellar mass (in terms of solar masses). So far, I have calculated their absolute magnitudes and gotten to working out the mass-light ratio $M/L$ for each galaxy.

e.g. $M/L=0.563$

Values I have are the calculated $M/L$ for each galaxy, and the $i$-band apparent ($13.25$) and absolute ($-18.06$) magnitudes for the galaxy, as well as the distance ($18.44Mpc$).

From this I need to get the mass of the galaxy $M$ in terms of solar masses. Therefore I assume I first need to calculate the i-band luminosity for the galaxy in solar masses $L_i$. This is where I am stuck.

However, once I have $L_i$ next step would be ... $$M_g = 0.563 * L_i$$

Ultimately, given these values, how would I go about estimating the stellar mass of a galaxy in terms of solar masses?

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@AlexanderJanssen, thanks for that. Unfortunately it doesn't help me too much as that's applied to specific galaxy types, whereas I need it more generically. – AfroBoy Apr 17 '14 at 7:25

The relation between absolute magnitude $M$ and luminosity $L$ for stars $$\frac{L_{Star}}{L_{Sun}}=10^{(M_{Sun}-M_{Star})/2.5}$$ should also be appliable to i-band luminosities of galaxies.

Taking the absolute magnitude 4.08 of the sun on the I-band the luminosity of a galaxy with absolute magnitude −18.06 would be $$\frac{L_{Galaxy}}{L_{Sun}}=10^{(4.08−(-18.06))/2.5}=0.7178\cdot 10^9.$$ An order of magnitude estimate for the mass of the galaxy would be $0.563\cdot 0.7178\cdot 10^9=0.404\cdot 10^9$ solar masses.

But $M/L$ isn't necessarily biased the same way for the sun to $M_i/L_i$ as for the galaxy. Therefore you'll probably need to compare the spectrum of the sun with the spectrum of the galaxy to find out the ratios of the i-band fraction of the total emission. Absorption and extinction at different wavelength may be different, therefore determining kind of mean temperature of stars in the galaxy could help finding a more realistic estimate for the stellar mass.

A similiar approach has been used in this paper.

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thanks for that. That equation makes sense however $M_i$ is an unknown that I need to solve for, ye it's in both sides of the equation. – AfroBoy Apr 18 '14 at 2:57
I guess you could just integrate over a reasonable range, better if tuned for your given galaxy. – Py-ser Apr 18 '14 at 3:07
@AfroBoy On the right side of the equation you have the (probably known) $M_i/L_i$ mass-luminosity ratios. Might it be you confused $M_i$ with $M_*$ in this case? – Gerald Apr 18 '14 at 10:44
@Gerald Thanks again for your help. I think I'm getting confused in abstracts, so I've reworded the question with some more concrete details. – AfroBoy Apr 18 '14 at 14:34
@AfroBoy Thanks for the details! I'll try to solve it. The formula first given is applicable to main sequence stars, not necessarily to galaxies. – Gerald Apr 18 '14 at 14:46

To estimate galaxy stellar mass with broadband photometry, you want to compare your observations to the spectral energy distribution (SED) of the galaxy. There are synthetic SED libraries which will generate SEDs for different types of galaxies with different masses.

For each template you can figure out the expected luminosity in the I-band and find the best match. For this method, it's really best to have more than one point for comparison. Since the near IR will likely be a blackbody from your evolved stellar population, you might want to see if you can supplement your I-band data with 2MASS observations.

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