The link between solenoidal turbulence and slow star formation in
  G0.253+0.016
  Star formation in the Galactic disc is primarily controlled by gravity,
turbulence, and magnetic fields. It is not clear that this also applies to star
formation near the Galactic Centre. Here we determine the turbulence and star
formation in the CMZ cloud G0.253+0.016. Using maps of 3mm dust emission and
HNCO intensity-weighted velocity obtained with ALMA, we measure the
volume-density variance $\sigma_{\rho/\rho_0} = 1.3 \pm 0.5$ and turbulent Mach
number $\mathcal{M} = 11 \pm 3$. Combining these with turbulence simulations to
constrain the plasma $\beta = 0.34 \pm 0.35$, we reconstruct the turbulence
driving parameter $b = 0.22 \pm 0.12$ in G0.253+0.016. This low value of $b$
indicates solenoidal (divergence-free) driving of the turbulence in
G0.253+0.016. By contrast, typical clouds in the Milky Way disc and spiral arms
have a significant compressive (curl-free) driving component ($b > 0.4$). We
speculate that shear causes the solenoidal driving in G0.253+0.016 and show
that this may reduce the star formation rate by a factor of 7 compared to
nearby clouds.
