Pgfplots fillbetween and Tikz \shade

Question

I am trying to replace the rainbow in this MWE

\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{pgfmath}
\usepackage{amsmath}
\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}


\usepackage[%
        %decimalsymbol=comma,
        locale=DE,
]{siunitx}

\usepgfplotslibrary{fillbetween}

\pgfplotsset{compat=1.16}

\begin{document}
    \begin{tikzpicture}[samples=200, scale=1.15,declare function={
        planck(\x,\T)=(374177152466412/\x^5)/(exp(14387.77/(\x*\T))-1);
    }]
    \begin{axis}[
    xmin=0,
    xmax=3,
    xlabel={$\omega$ [\si{\hertz}]},
    ymin=0,
    ylabel={$\rho (\omega; T)$ [\si{\joule\per\cubic\meter}]},
    ytick=\empty,
    no markers,
    grid=both,
    domain=0.1:3,
    ]
    \addplot+ [forget plot,name path=A] {planck(x,6000)};
    \addplot [forget plot,name path=B,samples=2] {0};
%-------------------------------
%   add shading code here...
%-------------------------------
    \addplot [forget plot,blue] fill between [of=A and B,soft clip={domain=.4:.47}];
    \addplot [forget plot,green] fill between [of=A and B,soft clip={domain=.47:.535}];
    \addplot [forget plot,yellow] fill between [of=A and B,soft clip={domain=.535:.6}];   
    \addplot [forget plot,orange] fill between [of=A and B,soft clip={domain=.6:.66}];             
    \addplot [forget plot,red] fill between [of=A and B,soft clip={domain=.66:.72}];

    \pgfplotsinvokeforeach{3000, 4000, 5000, 6000}
    {
        \addplot {planck(x,#1)};
        \addlegendentryexpanded{$T = #1\,\si{\kelvin}$}
    }
    \end{axis}
    \end{tikzpicture}
\end{document}

with the shaded rainbow from this answer

\documentclass{article}
\usepackage[named]{xcolor}
\usepackage{pgffor}
\usepackage{tikz}
\usetikzlibrary{shadings}

\pgfdeclareverticalshading{rainbow}{100bp}
{color(0bp)=(red); color(25bp)=(red); color(35bp)=(yellow);
color(45bp)=(green); color(55bp)=(cyan); color(65bp)=(blue);
color(75bp)=(violet); color(100bp)=(violet)}
\begin{document}
\begin{tikzpicture}
\shade[shading=rainbow,shading angle=270] (0,0) rectangle (5cm,\textheight);
\end{tikzpicture}
\end{document}

How is it possible to "mix" the tikz and pgfplots code?

Thank you very much!

Answer 1

shading can be used more or less instead of fill, so my answer to your previous question Planck's blackbody curve with "rainbow" in Tikz can be easily modified, you just need

\addplot [shading=rainbow, shading angle=90, forget plot, draw=none, domain=5:10] {planck(x,5000)} \closedcycle;

instead of what I used there. Modify the domain to whatever is correct.

(By the way, you seem to have made two accounts, I think you can have them merged: https://tex.stackexchange.com/help/merging-accounts)

\documentclass[border=3.14mm,tikz]{standalone}
\usepackage{siunitx}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}

\usetikzlibrary{shadings}

\pgfdeclareverticalshading{rainbow}{100bp}
{color(0bp)=(red); color(25bp)=(red); color(35bp)=(yellow);
color(45bp)=(green); color(55bp)=(cyan); color(65bp)=(blue);
color(75bp)=(violet); color(100bp)=(violet)}

\begin{document}
    \begin{tikzpicture}[
      samples=100,
      declare function={
        planck(\x,\T)=(\x^3)/((pi^2)*(exp(2000*\x/(\T))-1));
      }]
    \begin{axis}[
        xmin=0,
        xlabel={$\omega$ [\si{\hertz}]},
        ymin=0,
        ymax=pi,
        ylabel={$\rho (\omega; T)$ [\si{\joule\per\cubic\meter}]},
        ytick=\empty,
        no markers,
        grid=both,domain=0.1:40,
        style={ultra thick}]

      \addplot [shading=rainbow, shading angle=90, forget plot, draw=none, domain=5:10] {planck(x,5000)} \closedcycle;

    \pgfplotsinvokeforeach{3000, 4000, 5000}
    {
        \addplot {planck(x,#1)};
        \addlegendentryexpanded{$T = #1 [\si{\kelvin}]$}
    }

    \end{axis}
    \end{tikzpicture}
\end{document}

Answer 2

Like this?

    \documentclass{standalone}
    \usepackage{pgfplots}
    \usepackage{pgfmath}
    \usepackage{amsmath}
    \usepackage[ngerman]{babel}
    \usepackage[utf8]{inputenc}


    \usepackage[%
            %decimalsymbol=comma,
            locale=DE,
    ]{siunitx}

    \usepgfplotslibrary{fillbetween}
    \usetikzlibrary{shadings}
    \pgfplotsset{compat=1.16}

    \pgfdeclareverticalshading{rainbow}{100bp}
    {color(0bp)=(red); color(25bp)=(red); color(35bp)=(yellow);
    color(45bp)=(green); color(55bp)=(cyan); color(65bp)=(blue);
    color(75bp)=(violet); color(100bp)=(violet)}

    \begin{document}
        \begin{tikzpicture}[samples=200, scale=1.15,declare function={
            planck(\x,\T)=(374177152466412/\x^5)/(exp(14387.77/(\x*\T))-1);
        }]
        \begin{axis}[
        xmin=0,
        xmax=3,
        xlabel={$\omega$ [\si{\hertz}]},
        ymin=0,
        ylabel={$\rho (\omega; T)$ [\si{\joule\per\cubic\meter}]},
        ytick=\empty,
        no markers,
        grid=both,
        domain=0.1:3,
        ]
        \addplot+ [forget plot,name path=A] {planck(x,6000)};
        \addplot [forget plot,name path=B,samples=2] {0};
    %-------------------------------
    %   add shading code here...
    %-------------------------------
        \addplot [forget plot,shading=rainbow,shading angle=270] 
fill between [of=A and B,soft clip={domain=.4:.72}];
     %   \addplot [forget plot,green] fill between [of=A and B,soft clip={domain=.47:.535}];
    %    \addplot [forget plot,yellow] fill between [of=A and B,soft clip={domain=.535:.6}];   
    %    \addplot [forget plot,orange] fill between [of=A and B,soft clip={domain=.6:.66}];             
    %    \addplot [forget plot,red] fill between [of=A and B,soft clip={domain=.66:.72}];

        \pgfplotsinvokeforeach{3000, 4000, 5000, 6000}
        {
            \addplot {planck(x,#1)};
            \addlegendentryexpanded{$T = #1\,\si{\kelvin}$}
        }
        \end{axis}
        \end{tikzpicture}
    \end{document}