How can I put a label on a grid line using Callout[]?

Question

I have a .dat file named W11. Then I plotted it in Mathematica

ListPlot[{W11}
 , ImageSize -> Scaled[0.5]
 , PlotLabel -> Style["\[Alpha] = 0.5", Bold, FontSize -> 15]
 , PlotStyle -> {{Blue}}
 , PlotRange -> Automatic
 , GridLines -> {{0.3268350735*Pi}, {0}}
 , GridLinesStyle -> Directive[Thick, Gray]
 , PlotLegends -> 
  SwatchLegend[{Blue, Orange, Green, Yellow, Purple, Brown, Cyan, Red,
     Magenta}
   , {"\!\(\*SubscriptBox[\(\[Theta]\), \(1\)]\) = 0.1\[Pi]"}
   , LegendFunction -> (Framed[#, RoundingRadius -> 4, 
       FrameStyle -> Black] &)]
 , Joined -> {False}
 , Frame -> True
 , FrameStyle -> Directive[Thick, Black, Bold, FontSize -> 15]
 , Axes -> False 
 , FrameLabel -> {"\!\(\*SubscriptBox[
StyleBox[\"\[Theta]\",\nFontSize->16], \(0\)]\)", "<W>"}
 , LabelStyle -> {Black, Bold, 15}
 , FrameTicks -> {{Automatic, 
    None}, {{0, {Pi/4, Pi "/4"}, {Pi/2, Pi "/2"}, {3*Pi/4, 3*Pi "/4"},
      Pi}, None}}]

The resulting plot is shown below

As you can see from the plot, the vertical grid line is located at $0.3268350735\pi$. I want to put a label on the grid line using Callout. I want to use the Appearance->"Balloon". Then, I want to put it at the uppermost part of the frame and at the right side of the grid line, with the arrow tip pointing, of course, to the grid line. The label inside the gridline is $\theta_{0} = 0.3268350735\pi$. I can't figure out how to implement this. I hope someone could help me with this. Thanks!

Answer 1

Define a second dataset with a single element with a Callout wrapper with desired options, and set its style to None in ListPlot:

callout = Callout[{0.3268350735*Pi, 1.7}, 
   HoldForm[Subscript[θ, 0] == 0.3268350735 π], 
   Appearance -> "Balloon", 
   LeaderSize -> {40, 45 Degree, 40}, 
   LabelStyle -> 16];
ListPlot[{W11, {callout}}, 
 PlotStyle -> {Automatic, None}, 
 GridLines -> {{0.3268350735*Pi}, {0}}, 
 GridLinesStyle -> Directive[Thick, Gray], 
 Frame -> True]

where I used W11 from @rhermans's answer.

To place the label outside the frame, you need to add additional options (PlotRangeClipping, PlotRange, ImagePadding):

callout = Callout[{0.3268350735*Pi, 2.1}, 
   HoldForm[Subscript[θ, 0] == 0.3268350735 π], 
   Appearance -> "Balloon", LeaderSize -> {20, 45 Degree, 20}, 
   LabelStyle -> 16];
ListPlot[{W11, {callout}}, 
 PlotStyle -> {Automatic, None}, 
 GridLines -> {{0.3268350735*Pi}, {0}}, 
 GridLinesStyle -> Directive[Thick, Gray],
 Frame -> True, 
 ImageSize -> 500,
 PlotRange -> {0, 2.1},  
 PlotRangeClipping -> False, 
 ImagePadding -> {{Automatic, Automatic}, {Automatic, Scaled[.075]}}]

Answer 2

W11 = N@{Table[x, {x, 0, π, π/100}], 
     Sort@RandomReal[2, {101}]}\[Transpose];

putcallout[trace_, value_, label_String, position_] := 
 MapAt[Callout[#, label, position] &, trace, 
  Position[trace, First@Nearest[trace[[All, 1]], value]][[1, 1]]]

putcallout[W11, 0.3268350735*Pi,
  "\!\(\*SubscriptBox[\(θ\), \(0\)]\)=0.3268350735π", {0.5 \
π, 1.7}]

ListPlot[
 putcallout[W11, 0.3268350735*Pi, 
  "\!\(\*SubscriptBox[\(θ\), \(0\)]\)=0.3268350735π", {0.5 \
π, 1.7}]
 , ImageSize -> Scaled[0.5]
 , PlotLabel -> Style["α = 0.5", Bold, FontSize -> 15]
 , PlotStyle -> {{Blue}}
 , PlotRange -> Automatic
 , GridLines -> {{0.3268350735*Pi}, {0}}
 , GridLinesStyle -> Directive[Thick, Gray]
 , PlotLegends -> SwatchLegend[
   {Blue, Orange, Green, Yellow, Purple, Brown, Cyan, Red, Magenta}
   , {"\!\(\*SubscriptBox[\(θ\), \(1\)]\) = 0.1π"}
   , LegendFunction -> (Framed[#, RoundingRadius -> 4, 
       FrameStyle -> Black] &)
   ]
 , Joined -> {False}
 , Frame -> True
 , FrameStyle -> Directive[Thick, Black, Bold, FontSize -> 15]
 , Axes -> False
 , FrameLabel -> {"\!\(\*SubscriptBox[StyleBox[\"θ\",\n\
FontSize->16], \(0\)]\)", "<W>"}
 , LabelStyle -> {Black, Bold, 15}
 , FrameTicks -> {{Automatic, 
    None}, {{0, {Pi/4, Pi "/4"}, {Pi/2, Pi "/2"}, {3*Pi/4, 3*Pi "/4"},
      Pi}, None}}
 (*,Epilog\[Rule]{Point[ Callout[{0.3268350735*Pi,0},"www"]]}*)
 ]