and the resulting slow fall-off of the density perturbation in the condensate. This behavior is specific to neutral condensates; for charged condensates the super-current is screened exponentially on length scales of the order of the penetration depth $\lambda$. The solution of Eq. (\[eq:AS:curlv\]) for a charged condensate is $$\begin{aligned}
\label{eq:AS:vp}
{\bf v}_p = \frac{\hbar}{2m_p\lambda}
K_1\left(\frac{r}{\lambda}\right)\hat \theta ,\end{aligned}$$ where $K_1$ is the Bessel function of imaginary argument; as for $r\gg \lambda$, $K_1(r/\lambda) \simeq {\rm exp} (-r/\lambda)$, therefore the superfluid circulation decays exponentially; in the opposite limit $r\ll \lambda$, $K_1(r/\lambda) \simeq \lambda/r$ and Eq. (\[eq:AS:vp\]) assumes a form identical to Eq. (\[eq:AS:vn\]).

At the [*global hydrodynamic*]{} level the relevant scales are of the order of the size of the system, which in neutron stars is of the order of kilometers. On these scales the hydrodynamic and thermodynamic variables are course-grained quantities, i.e. they are averages over a large number of vortices. The solution (\[eq:AS:vn\]) does not minimize the energy $E-{\bf L\cdot \Omega}$ of a rotating superfluid, where $E$ and $\bf L$ represent the kinetic energy and the angular momentum respectively. The energy acquires its minimum for a superfluid flow which to a high precision mimics a rigid body rotation i.e., $v_n = 