Problema di disegno 3D con TikZ

grafico

`\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
width=14cm,
height=12cm,
axis lines=center,
xlabel={$\theta$ (radianti)},
ylabel={$t$},
zlabel={$\dot{\theta}$},
xmin=-6.5, xmax=6.5,
ymin=0, ymax=5,
zmin=-3, zmax=3,
xtick={-6.28, -4.71, -3.14, -1.57, 0, 1.57, 3.14, 4.71, 6.28},
xticklabels={$-2\pi$, $-\frac{3\pi}{2}$, $-\pi$, $-\frac{\pi}{2}$, $0$, $\frac{\pi}{2}$, $\pi$, $\frac{3\pi}{2}$, $2\pi$},
ytick={0,1,2,3,4,5},
ztick={-3,-2,-1,0,1,2,3},
title={Curve $\dot{\theta} = \pm\sqrt{2(1+\cos(\theta))}$ nello spazio 3D ($\theta \dot{\theta} t$) a t=0},
view={20}{45},
legend pos=north west,
legend style={at={(0.05,0.95)}},
y dir=reverse,
xlabel style={at={(axis cs:6.5,0,0)},anchor=north west},
ylabel style={at={(axis cs:0,5.2,0)},anchor=south east},
zlabel style={at={(axis cs:0,0,3.2)},anchor=south east},
]

% Curve positive
\addplot3[red, samples=200, domain=-6.28:6.28]
({x}, {0}, {sqrt(2*(1+cos(deg(x))))});

% Curve negative
\addplot3[red, samples=200, domain=-6.28:6.28]
({x}, {0}, {-sqrt(2*(1+cos(deg(x))))});

\legend{$\dot{\theta} = \sqrt{2(1+\cos(\theta))}$, $\dot{\theta} = -\sqrt{2(1+\cos(\theta))}$}

\end{axis}
\end{tikzpicture}

\end{document}`

Come potete vedere dal file .pdf ci sono due rette orizzontali che vorrei non eliminare, ma farle cambiare di colore e tratteggiate, come si può fare?