# starting from SSP spectra to evaluate galaxy spectrum and observed mag

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, 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, 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?

• 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?) Aug 4, 2021 at 16:49
• 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... Aug 4, 2021 at 21:13