  A {\em vortex pair} solution of the incompressible $2d$ Euler equation in
vorticity form $$ \omega_t + \nabla^\perp \Psi\cdot \nabla \omega = 0 , \quad
\Psi = (-\Delta)^{-1} \omega, \quad \hbox{in } \mathbb{R}^2 \times (0,\infty)$$
is a travelling wave solution of the form $\omega(x,t) = W(x_1-ct,x_2 )$ where
$W(x)$ is compactly supported and odd in $x_2$. We revisit the problem of
constructing solutions which are highly $\varepsilon$-concentrated around
points $ (0, \pm q)$, more precisely with approximately radially symmetric,
compactly supported bumps with radius $\varepsilon$ and masses $\pm m$. Fine
asymptotic expressions are obtained, and the smooth dependence on the
parameters $q$ and $\varepsilon$ for the solution and its propagation speed $c$
are established. These results improve constructions through variational
methods in [14] and in [5] for the case of a bounded domain.
