Why can't Mathematica parallelize this?

Question

The following code makes mathematica print "ParallelTable::nopar1: [...] cannot be parallelized; proceeding with sequential evaluation."

(*Exit[]*)
Subscript[r, 1] = Abs[x + y I];
Subscript[r, 2] = Abs[x + y I - a];
plots = ParallelTable[
   ContourPlot[{Abs[Subscript[r, 1]]/Abs[Subscript[r, 2]] == 
        Subscript[c, 1], 
       Subscript[c, 2] == 
        Abs[Subscript[r, 2]] - Abs[Subscript[r, 1]]} /. a -> 5 // 
     Evaluate, {x, -6, 6}, {y, -6, 6}, 
    FrameTicks -> {Range[-6, 6, 1], Range[-6, 6, 1], None, 
      None}], {Subscript[c, 1], 0, 2, 0.1}, {Subscript[c, 2], -2, 2, 
    0.2}];
Animate[plots[[i]][[j]], {i, 1, Length[plots], 1}, {j, 1, 
  Length[plots[[1]]], 1}]

Why does this happen even when the expression in ParallelTable can be easily evaluated for any values of $c_1$ and $c_2$ ?

Note: "Right Click> convert to StandardForm" will make the subscripts readable.

Answer 1

It seems Mathematica does not like subscript variables for ParallelTable So if you define

r1 = Abs[x + y I];
r2 = Abs[x + y I - a];

then

plots = ParallelTable[
   ContourPlot[{Abs[r1]/Abs[r2] == c1, c2 == Abs[r2] - Abs[r1]} /. 
      a -> 5 // Evaluate, {x, -6, 6}, {y, -6, 6}, 
    FrameTicks -> {Range[-6, 6, 1], Range[-6, 6, 1], None, None}, 
    ContourStyle ->{{ColorData[10][c1*5]}, 
    Directive[Dashed, ColorData[10][(c2 + 2)*2.5]]}], {c1, 0, 2, 0.1}, {c2, -2, 2,
     0.2}];

produces

plots // Flatten // Show