<p>The relation between <a href="http://en.wikipedia.org/wiki/Absolute_magnitude" rel="nofollow">absolute magnitude</a> $M$ 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.</p>

<p><a href="http://www.ucolick.org/~cnaw/sun.html" rel="nofollow">Taking the absolute magnitude 4.08 of the sun on the I-band</a> 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.</p>

<p>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.</p>

<p>A similiar approach has been used in <a href="http://www.ifa.hawaii.edu/reu/2007research/whiting.pdf" rel="nofollow">this paper</a>.</p>

CC BY-SA 3.0
2014-04-18T02:57:22.650Z
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
CC BY-SA 3.0
2014-04-18T03:07:03.920Z
I guess you could just integrate over a reasonable range, better if tuned for your given galaxy.
Py-ser
CC BY-SA 3.0
2014-04-18T10:44:47.277Z
@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
CC BY-SA 3.0
2014-04-18T14:34:14.583Z
@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
CC BY-SA 3.0
2014-04-18T14:46:32.233Z
@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
CC BY-SA 3.0
2014-04-19T02:54:01.310Z
@Gerald Thank you so much. That makes total sense now. I understand M/L is only really for main sequence stars, but I have other corrections I can apply along the way to get a better estimate. Thank you!
AfroBoy
CC BY-SA 3.0
2014-04-20T21:25:30.793Z
@AfroBoy Welcome! Glad to have been able to help you, at the end.
Gerald
CC BY-SA 3.0
2014-04-17T15:05:35.707Z
2014-04-18T19:28:06.380Z
2014-04-18T19:28:06.380Z
Gerald
<p>To estimate galaxy stellar mass with broadband photometry, you want to compare your observations to the <a href="http://ned.ipac.caltech.edu/level5/March10/Walcher/Walcher6.html" rel="nofollow noreferrer">spectral energy distribution</a> (SED) of the galaxy. There are synthetic SED libraries which will generate SEDs for different types of galaxies with different masses. </p>

<p><img src="https://i.sstatic.net/9rnNT.png" alt="An example galaxy SED"></p>

<p>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 <a href="http://irsa.ipac.caltech.edu/applications/2MASS/PubGalPS/" rel="nofollow noreferrer">2MASS</a> observations.</p>

CC BY-SA 3.0
2014-07-22T19:30:18.993Z
2014-07-22T19:30:18.993Z
Aaron
<p>Given the magnitudes (in the i-band) of certain galaxies, I would like to calculate their <strong>stellar mass (in terms of solar masses)</strong>. So far, I have calculated their absolute magnitudes and gotten to working out the mass-light ratio $M/L$ for each galaxy.</p>

<p>e.g. $M/L=0.563$</p>

<p>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 ($18.44Mpc$).</p>

<p>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. </p>

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

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

CC BY-SA 3.0
2014-04-17T05:40:38.277Z
Have you already seen http://ned.ipac.caltech.edu/level5/March05/Read/Read_contents.html ?
Alexander Janssen
CC BY-SA 3.0
2014-04-17T07:25:45.367Z
@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
<mass><luminosity>
Stellar mass of galaxies
AfroBoy
# Stellar mass of galaxies

(Asked by: username_0 on 2014-04-17)

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?

**Tags:** mass, luminosity
> **Comments:**
> **username_1**: Have you already seen http://ned.ipac.caltech.edu/level5/March05/Read/Read_contents.html ?  
> **username_0**: @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.  

---

## 2 answers

### Answer by username_2 on 2014-04-17. Score: 1 | Accepted answer

The relation between [absolute magnitude](http://en.wikipedia.org/wiki/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](http://www.ucolick.org/~cnaw/sun.html) 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](http://www.ifa.hawaii.edu/reu/2007research/whiting.pdf).

> **Comments:**
> **username_0**: 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.  
> **username_3**: I guess you could just integrate over a reasonable range, better if tuned for your given galaxy.  
> **username_2**: @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?  
> **username_0**: @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.  
> **username_2**: @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.  
> **username_0**: @Gerald Thank you so much. That makes total sense now. I understand M/L is only really for main sequence stars, but I have other corrections I can apply along the way to get a better estimate. Thank you!  
> **username_2**: @AfroBoy Welcome! Glad to have been able to help you, at the end.  

---

### Answer by username_4 on 2014-07-22. Score: 0

To estimate galaxy stellar mass with broadband photometry, you want to compare your observations to the [spectral energy distribution](http://ned.ipac.caltech.edu/level5/March10/Walcher/Walcher6.html) (SED) of the galaxy. There are synthetic SED libraries which will generate SEDs for different types of galaxies with different masses.

![An example galaxy SED](https://i.sstatic.net/9rnNT.png)

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](http://irsa.ipac.caltech.edu/applications/2MASS/PubGalPS/) observations.


---

