Graph Plotting Problem in Mathematica

[Stella.Physics]

Hello to all. I've been trying to plot some graphs on Mathematica but I have faced some troubles so far.

I am working on this paper by Lattimer on binary systems:

https://arxiv.org/abs/astro-ph/0002203

I am trying to reproduce Figure 11 but something seems to go wrong.

Here's what I have done so far:

we set $q=\frac{m_{ns}}{M_{bh}}$ the ratio of the neutron star mass and the black hole mass.

then we set the radius

$\frac{R_{l}}{a} = 0.46\bigg(\frac{q}{1+q}\bigg)^{1/3}$ with a being the semi major axis that follows
$a<2.8 \bigg[ \frac{m_{ns} m_{bh} (m_{ns}+m_{bh})}{〖M^3_ {\odot}〗} \bigg]^{\frac{1}{4}} R_{\odot}$

The first thing to plot is the neutron star radius versus the neutron star mass.

Then we must plot $\frac{d \ln{R}}{d \ln{m_{ns}}}$ versus $m_{ns}$ which derivative simply leads to $\frac{m_{ns}}{R} \frac{dR}{dm_{ns}}$

I've been trying to plot these functions for days but what I get is far from the desired results...

Any help would be very appreciated :)

 

[aheight]

It's a good idea to simplify a complicated problem, reducing it to it's basic concept and just get the basics working then add on step by step, pieces that would make the basic look more and more like the problem you're trying to solve. So just a quick overview of what you're trying to do looks like plotting a derivative. So if this was mine, I would first get working, plotting the derivative of a simple function like:

myf[x_] := x^2 + 3 x + 4;
myd[x_] = D[myf[x], x]
Plot[myd[x], {x, 0, 5}]

Now, I might add a more complicated function like myf[x_]:=Sin[x]+Log[x] and get that working and so on until I guide my code towards the problem I really want to solve so that if I just increment it a little bit by bit and something goes wrong I can go back a step and undo the last change I made then analyze why the newest changed caused my code to fail.

 

[Stella.Physics]

Thank you for your reply, aheight! Although I have tried this method, I will give it another shot... Thanks again :)