:}{\bf Q}\bm\tau-\gamma_2\bm{\tau \cdot Q}
+\lambda_1 \bm{\tau }\cdot \nabla \bm{\tau } \mathbf{=}-v_{0}\bm\nabla
\cdot \mathbf{Q}-\frac{v_{0}}{2}\nabla \rho
+\lambda _{2}\bm{\tau }\nabla \cdot \bm{\tau }+\frac{\lambda _{3}}{2}\nabla
\tau ^{2}+D_{\tau}\nabla ^{2}\bm{\tau }
\label{3.2}\\
%
\partial _{t}Q_{ij}-D_r(\alpha-\beta {\bf Q}{\bf :}{\bf Q}) Q_{ij}+v_0F_{ij}+\lambda _{4}G_{ij} =
\mathcal{D}_\rho( \partial _{i}\partial _{j}-\frac{\delta _{ij}}{2}%
\nabla ^{2}) \rho
+D_{s}\partial _{k}\left( \partial _{i}Q_{kj}+\partial
_{j}Q_{ik}-\delta _{ij}\partial _{l}Q_{kl}\right)
+D_{b}\nabla ^{2}Q_{ij}
\label{3.3}\end{gathered}$$

\[3\]

where again we have implicitly neglected active corrections to $D$, $D_\tau$, $D_s$ and $D_b$ to highlight the new, purely active terms. Activity enters in Eqs.  through the convective terms proportional to $
v_{0}$, the new terms with coefficients $\gamma_i$ and to $\lambda_i $, which vanish in equilibrium, as well as the terms proportional to ${\cal D}_Q$ and ${\cal D}_\rho$ that arise here from active corrections to interactions. Finally, the parameters $\alpha$ and $\beta$ controlling the mean field isotropic-nematic transition are also renormalized by activity. The homogeneous nonlinearities proportional to $\gamma_i$ in the polarization equation encode the fact that nematic order induces polar order. The latter is, however, only local as the equations do not a admit a homogeneous solution with nonzero $\bm\tau$. Further, the active modification of the interactions, yield the convective nonlinearities $\sim{\cal O}(\bm{\tau }\nabla \bm{\tau })$ that play a central role in the 