# Compute the total stellar mass of galaxy with major influence of Red Giants luminosity

Suppose that all stars in this galaxy were born in a single major-merger burst event about 10 Gyr ago

If the luminosity in the B band (absolute magnitude in B-band is equal to -21.22) is dominated by stars of in the RG branch, with masses $$m \sim 1\,\text{L}_{\odot}$$ (within $$\sim 10\%$$) and average luminosities $$\sim 1000\,\text{L}_{\odot}$$.

How can I estimate the total stellar mass of this galaxy using the Schechter relation ?

I think that I have to use the definition of Schechter law:

$$N(L)\ \mathrm {d} L=\phi^{*}\left({\frac{L}{L^{*}}}\right)^{\alpha}\mathrm {e}^{-L/L^{*}}{\frac{\mathrm {d} L}{L^{*}}}$$

or maybe Salpeter relation : $$\text{d}N=0.06\,\times\,M^{-2.35}\,\text{d}M$$

But how to introduce the parameters of Red-Giants of $$1\,\text{M}_{\odot}$$ with $$L=1000\,\text{L}_{\odot}$$.

Initially, I calculate the fraction of masse between $$m_{1}=0.9$$ and $$m_{2}=1.1\,\text{M}_{\odot}$$ :

$$\text{d}N(m_{1}

Anyone could see the trick to compute total stellar mass from these parameters with above laws ?

Regards

• No one has an idea about the trick to compute total mass stellar from the parameters that I have used in my little calculation ? – youpilat13 Dec 17 '18 at 14:03
• The Schechter function for galaxy luminosity is not relevant; it describes the relative numbers of different galaxies as a function of their luminosity, and has nothing to do with luminosities of individual stars within a single galaxy. – Peter Erwin Dec 17 '18 at 16:03
• -@Peter Erwin. ok, let's forget Schechter. Have you got an idea to compute the mass of this galaxy, from Salpeter IMF, the fact that we suppose a burst $10^9$ years ago and that the luminosity in B-band is dominated by red-giants ? – youpilat13 Dec 17 '18 at 20:28