<p><br />
I know that the galaxy spectrum, namely the flux per unit wavelength versus the wavelength, is the sum of the Simple Stellar Population (SSP) spectra at a fixed redshift (e.g. similar to eq. 1 in <a href="https://academic.oup.com/mnras/article/344/4/1000/968846" rel="nofollow noreferrer">Bruzual&amp;Charlot 2003</a>, but at fixed time). Then, integrating the spectrum of the galaxy in a certain filter band, I obtain the (observed,with the k-correction) magnitude.</p>
<p>Now I am wondering if the following operations to evaluate the galaxy spectrum and then the observed galaxy magnitude are equivalent or not:</p>
<p>METHOD (1):<br />
I have N SSP forming my galaxy at fixed redshift. I perform the first and second operations N time, for each SSP:</p>
<ul>
<li>convolving the SSP spectrum with a chosen filter and integrating it in the filter wavelength band (following e.g. <a href="https://iopscience.iop.org/article/10.1086/342935/fulltext/" rel="nofollow noreferrer">Blanton+03</a>, but beware that my fluxes are k-corrected, or redshifted) and obtain the observed AB magnitude <code>mag_i</code></li>
<li>from the observed AB magnitude, I compute the integrated flux in microJansky: <code>flux(uJy)_i = pow(10,(29-(mag_i+48.6)/2.5)</code>.
<br />
Now I want the total integrated flux (integrated flux of the galaxy):</li>
<li>I sum up the fluxes computed in the previous passage (coming from the observed AB mag of each SSP) <code>flux_tot = sum(flux_i)</code></li>
<li>From the total flux, I re-compute the observed mag  <code>mag_tot=2.5*(29-np.log10(flux_tot))-48.6</code>.</li>
</ul>
<p>METHOD (2)\</p>
<ul>
<li>I firstly sum up the spectra of the SSP all together, obtaining the galaxy flux per unit wavelength versus the wavelength</li>
<li>I convolve it with the filter, I integrate it in the wavelength band and obtain the observed AB mag <code>mag_gal</code>.</li>
</ul>
<p>In principle, the <code>mag_tot</code> of the first method and the <code>mag_gal</code> of the second method should be the same, right?</p>

CC BY-SA 4.0
2021-08-04T16:49:12.620Z
Yes, and the second method is (obviously) much more computationally efficient. (I'll admit I don't really see why in Method 1 you keep converting mag_i to flux(uJy)_i -- you should be getting flux_i after the convolution; how else do you determine mag_i?)
Peter Erwin
CC BY-SA 4.0
2021-08-04T21:13:30.313Z
yes, you're right. It's because SSP spectrum is normalized to 1 Msun, so I need to rescale it by the mass of the SSP (omitted in flux_i computation I show; I know I can directly rescale it in the integration, but I need this passages for my purpose). Now I wonder why the second method doesn't give me the same result of the first...
fslack
<galaxy><spectra><magnitude><flux><stellar-population>
starting from SSP spectra to evaluate galaxy spectrum and observed mag
fslack
# starting from SSP spectra to evaluate galaxy spectrum and observed mag

(Asked by: username_0 on 2021-08-04)

I know that the galaxy spectrum, namely the flux per unit wavelength versus the wavelength, is the sum of the Simple Stellar Population (SSP) spectra at a fixed redshift (e.g. similar to eq. 1 in [Bruzual&Charlot 2003](https://academic.oup.com/mnras/article/344/4/1000/968846), but at fixed time). Then, integrating the spectrum of the galaxy in a certain filter band, I obtain the (observed,with the k-correction) magnitude.

Now I am wondering if the following operations to evaluate the galaxy spectrum and then the observed galaxy magnitude are equivalent or not:

METHOD (1):  
I have N SSP forming my galaxy at fixed redshift. I perform the first and second operations N time, for each SSP:

* convolving the SSP spectrum with a chosen filter and integrating it in the filter wavelength band (following e.g. [Blanton+03](https://iopscience.iop.org/article/10.1086/342935/fulltext/), but beware that my fluxes are k-corrected, or redshifted) and obtain the observed AB magnitude `mag_i`
* from the observed AB magnitude, I compute the integrated flux in microJansky: `flux(uJy)_i = pow(10,(29-(mag_i+48.6)/2.5)`.
    
  Now I want the total integrated flux (integrated flux of the galaxy):
* I sum up the fluxes computed in the previous passage (coming from the observed AB mag of each SSP) `flux_tot = sum(flux_i)`
* From the total flux, I re-compute the observed mag `mag_tot=2.5*(29-np.log10(flux_tot))-48.6`.

METHOD (2)\

* I firstly sum up the spectra of the SSP all together, obtaining the galaxy flux per unit wavelength versus the wavelength
* I convolve it with the filter, I integrate it in the wavelength band and obtain the observed AB mag `mag_gal`.

In principle, the `mag_tot` of the first method and the `mag_gal` of the second method should be the same, right?

**Tags:** galaxy, spectra, magnitude, flux, stellar-population

> **Comments:**
> **username_1**: Yes, and the second method is (obviously) much more computationally efficient. (I'll admit I don't really see why in Method 1 you keep converting mag_i to flux(uJy)_i -- you should be getting flux_i after the convolution; how else do you determine mag_i?)  
> **username_0**: yes, you're right. It's because SSP spectrum is normalized to 1 Msun, so I need to rescale it by the mass of the SSP (omitted in flux_i computation I show; I know I can directly rescale it in the integration, but I need this passages for my purpose). Now I wonder why the second method doesn't give me the same result of the first...  

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## 0 answers

