Quantifying the Redshift Space Distortion of the Bispectrum II: Induced
  Non-Gaussianity at Second Order Perturbation
  The anisotrpy of the redshift space bispectrum
$B^s(\mathbf{k_1},\mathbf{k_2},\mathbf{k_3})$, which contains a wealth of
cosmological information, is completely quantified using multipole moments
$\bar{B}^m_{\ell}(k_1,\mu,t)$ where $k_1$, the length of the largest side, and
$(\mu,t)$ respectively quantify the size and shape of the triangle
$(\mathbf{k_1},\mathbf{k_2},\mathbf{k_3})$. We present analytical expressions
for all the multipoles which are predicted to be non-zero ($\ell \le 8, m \le
6$ ) at second order perturbation theory. The multipoles also depend on
$\beta_1,b_1$ and $\gamma_2$, which quantify the linear redshift distortion
parameter, linear bias and quadratic bias respectively. Considering triangles
of all possible shapes, we analyse the shape dependence of all of the
multipoles holding $k_1=0.2 \, {\rm Mpc}^{-1}, \beta_1=1, b_1=1$ and
$\gamma_2=0$ fixed. The monopole $\bar{B}^0_0$, which is positive everywhere,
is minimum for equilateral triangles. $\bar{B}_0^0$ increases towards linear
triangles, and is maximum for linear triangles close to the squeezed limit.
Both $\bar{B}^0_{2}$ and $\bar{B}^0_4$ are similar to $\bar{B}^0_0$, however
the quadrupole $\bar{B}^0_2$ exceeds $\bar{B}^0_0$ over a significant range of
shapes. The other multipoles, many of which become negative, have magnitudes
smaller than $\bar{B}^0_0$. In most cases the maxima or minima, or both, occur
very close to the squeezed limit. $\mid \bar{B}^m_{\ell} \mid $ is found to
decrease rapidly if $\ell$ or $m$ are increased. The shape dependence shown
here is characteristic of non-linear gravitational clustering. Non-linear bias,
if present, will lead to a different shape dependence.
