Coloring and legending issue

[djymndl07]

Look at the following Image.
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.

I am using the following 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]]]



Can anyone help me? Thanks in advance.

 

[DrClaude]

Your color scale is based on T, but what you are plotting is rs. For rh in the range of the parametric plot, the values of rs go beyond the corresponding range in T, for example at rh = 0.6, rs ≈ 0.6, while the color scale goes tp to T[0.6] ≈ 0.53.