On the compressive nature of turbulence driven by ionising feedback in the pillars of the Carina Nebula

The ionizing radiation of massive stars sculpts the surrounding neutral gas into pillar-like structures. Direct signatures of star formation through outflows and jets are observed in these structures, typically at their tips. Recent numerical simulations have suggested that this star formation could potentially be triggered by photoionising radiation, driving compressive modes of turbulence in the pillars. In this study we use recent high-resolution ALMA observations of $^{12}\mathrm{CO}$, $^{13}\mathrm{CO}$, and $\mathrm{C}^{18} \mathrm{O}, \; J = 2-1$ emission to test this hypothesis for pillars in the Carina Nebula. We analyse column density and intensity-weighted velocity maps, and subtract any large-scale bulk motions in the plane of the sky to isolate the turbulent motions. We then reconstruct the dominant turbulence driving mode in the pillars, by computing the turbulence driving parameter $b$, characterised by the relation $σ_{ρ/ρ_0} = b \mathcal{M}$ between the standard deviation of the density contrast $σ_{ρ/ρ_0}$ (with gas density $ρ$ and its average $ρ_0$) and the turbulent Mach number $\mathcal{M}$. We find values of \mbox{$b\sim0.7$--$1.0$} for most of the pillars, suggesting that predominantly compressive modes of turbulence are driven in the pillars by the ionising radiation from nearby massive stars. We find that this range of $b$ values can produce star formation rates in the pillars that are a factor $\sim 3$ greater than with $b \sim 0.5$, a typical average value of $b$ for spiral-arm molecular clouds. Our results provide further evidence for the potential triggering of star formation in pillars through compressive turbulent motions.