Compute the total stellar mass from a galaxy with Red Giants

[fab13]

Hello,

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 law of Schechter :

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

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

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

 

[fab13]

Really no one can help me about the trick to compute total stellar mass from the parameters that I have used ?