Scaling problem with plot and legend

Question

First of all look at these code-

f[r_] := 1 - (2*M)/r + Q^2/r^2 + (8/3)*Pi*P*r^2
mass = (3*Q^2 + 3*r^2 + 8*P*Pi*r^4)/(6*r) /. r -> rh; 
T[r_] := (-Q^2 + r^2 + 8*P*Pi*r^4)/(4*Pi*r^3)
veff[r_] := f[r]/r^2
rp = r /. Last[NSolve[D[veff[r], r] == 0, r, Reals]] /. M -> mass

rs = rp/Sqrt[f[rp]] /. M -> 0.9; 
Q = 0.1; 
P = 0.3315; 

plot = ParametricPlot[{rs*Cos[\[Theta]], rs*Sin[\[Theta]]}, {rh, 0.37, 0.6}, {\[Theta], 
0, 2*Pi}, Axes -> False, ColorFunctionScaling -> False, 
ColorFunction -> Function[{x, y, rh}, ColorData["SunsetColors"][Rescale[T[rh], 
{T[0.37],T[0.6]}]]], 
PlotLegends -> BarLegend[{"SunsetColors", {T[0.37], T[0.6]}}, LegendLabel -> 
Style[HoldForm[T], 14]]]

Now the plot gives the following figure-

The results are okay but clearly the plot colors does not match with the color bar. for example the color bar is showing only single color. the value 0.4 in color bar corresponds to the radius 0.8 which is different color in the plot.

Another issue is that I don't know why that blue horizontal line is there at one side of the center. That should not be there.

Can anyone help me? Thanks in advance.

Answer 1

$Version

(* "14.0.0 for Mac OS X ARM (64-bit) (December 13, 2023)" *)

Clear["Global`*"]

f[r_] := 1 - (2*M)/r + Q^2/r^2 + (8/3)*Pi*P*r^2
mass = (3*Q^2 + 3*r^2 + 8*P*Pi*r^4)/(6*r) /. r -> rh;
T[r_] := (-Q^2 + r^2 + 8*P*Pi*r^4)/(4*Pi*r^3)
veff[r_] := f[r]/r^2

rp = Assuming[{Q > 0, rh > 0, P > 0},
   r /. Last[Solve[D[veff[r], r] == 0, r, Reals]] /. M -> mass // 
    FullSimplify];

rs = rp/Sqrt[f[rp]] /. M -> 9/10;
Q = 1/10;
P = 3315/10000;

Use Legended and the option BoundaryStyle -> None

plot = Legended[
  ParametricPlot[{rs*Cos[θ], rs*Sin[θ]},
   {rh, 37/100, 3/5}, {θ, 0, 2*Pi},
   Axes -> False,
   ColorFunctionScaling -> False,
   ColorFunction -> Function[{x, y, rh},
     ColorData["SunsetColors"][
      Rescale[T[rh], {T[0.37], T[0.6]}]]],
   BoundaryStyle -> None],
  BarLegend[{"SunsetColors",
    {T[0.37], T[0.6]}},
   LegendLabel -> Style[HoldForm[T], 14],
   LegendMarkerSize -> 320]]