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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 $m_{2}=1.1\,\text{M}_{\odot}$ :

$$\text{d}N(m_{1}<m<m_{2})=\int_{m_{1}}^{m_{2}}\,\Phi(m)\,\text{d}m=0.06\,\dfrac{(0.9^{-1.35}-1.1^{-1.35})}{1.35} = 1.22 \%$$

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

Regards

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  • $\begingroup$ No one has an idea about the trick to compute total mass stellar from the parameters that I have used in my little calculation ? $\endgroup$ – youpilat13 Dec 17 '18 at 14:03
  • $\begingroup$ 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. $\endgroup$ – Peter Erwin Dec 17 '18 at 16:03
  • $\begingroup$ -@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 ? $\endgroup$ – youpilat13 Dec 17 '18 at 20:28

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