# Heatmap resolution issues

I am trying to plot a heatmap from the following code. I have a problem where the colour seems to stop before reaching the corners. Please can someone help me to make the colour run all the way to the edge? Also, am I doing something wrong with the axis labels? Why do they not appear as "x" and "y"? Thanks!

n = 100;
a = 1.05;
γ[a_, x_] := Gamma[a] - Gamma[a, x]
ρc[x_, y_, n_] :=
Sqrt[2/π]*Gamma[n - 1, x^2 + y^2]/Gamma[n - 1]*Abs[y]*Exp[2*y^2]*
Erfc[Sqrt[2]*Abs[y]]

Show[
DensityPlot[
ρc[x, y, n],
{x, -a*Sqrt[n], a*Sqrt[n]}, {y, -a*Sqrt[n], a*Sqrt[n]},
ScalingFunctions -> "Log",
ColorFunction -> "Rainbow", PlotLegends -> Automatic,
AxesLabel -> {x, y}
],
Graphics[
{Black, Thick, Circle[{0, 0}, Sqrt[n]]},
{Red, Thick, Line[{-Sqrt[n], 0}, {Sqrt[n], 0}]}
]
]


Increase PlotPoints

FrameLabel instead of Axeslabel

Some bracketing mistakes inside Graphics

I had to omit ScalingFunctions -> "Log" to get a result which is in accordance with Graphics

pl =
DensityPlot[\[Rho]c[x, y, n], {x, -a*Sqrt[n],
a*Sqrt[n]}, {y, -a*Sqrt[n], a*Sqrt[n]},
ColorFunction -> "Rainbow",
PlotLegends -> Automatic,
PlotPoints -> 60,
FrameLabel -> {x, y}];

gr =
Graphics[{{Black, Thick, Circle[{0, 0}, Sqrt[n]]}, {Red, Thick,
Line[{{-Sqrt[n], 0}, {Sqrt[n], 0}}]}}];

Show[pl, gr]


• See current update
– eldo
Commented Sep 18, 2023 at 15:15
• Thank you! (+1) Commented Sep 18, 2023 at 15:17
• You're most welcome
– eldo
Commented Sep 18, 2023 at 15:18
• Thank you very much! Is there any way I can make the axis label and numbers larger? Commented Sep 18, 2023 at 15:25
• Add the option LabelStyle -> 12
– eldo
Commented Sep 18, 2023 at 15:29