# Relationship betwen stellar mass loss and mass of stars

I am following the semi-empirical relationship of mass loss rate of a star with mass M, radius R and luminosity L.

$log(\dot{M}v_{inf}R^{1/2})=−1.37+2.07log(L/10^{6})$

where $v_{inf}=\frac{\sqrt{(2GM/R)}}{2.6}$

M, R and L are in solar unit.

I simplified the relationship for plotting purpose:

$log(\dot{M})=−1.37+2.07log(L)−2.07log(10^{6})−\frac{1}{2}log(2*G*M)+log(2.6)$

I hope my simplification is correct. If not, please direct me to the right path.

I need to plot a $log(\dot{M})−M$ relationship for mass range $20−100M_{\odot}$ for few different luminosities and compare it with the main sequence $log(\dot{M})−M$ relationship.

My first confusion came with the value of G. Since everything is in solar unit, I thought I need to set everything with respect to solar unit.

So I took $G=4 \pi^{2} M_{\odot}^{-1} Au^{3} yr^{-2}$

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I am not quite sure if this is the correct way to set G and L, so I plotted the data, and it looks like following:

But I was expecting higher mass loss for more massive stars. Please help me understand what am I doing wrong here.