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The ionizing radiation of massive stars sculpts the surrounding neutral gasinto pillar-like structures. Direct signatures of star formation throughoutflows and jets are observed in these structures, typically at their tips.Recent numerical simulations have suggested that this star formation couldpotentially be triggered by photoionising radiation, driving compressive modesof turbulence in the pillars. In this study we use recent high-resolution ALMAobservations of $^{12}\mathrm{CO}$, $^{13}\mathrm{CO}$, and $\mathrm{C}^{18}\mathrm{O}, \; J = 2-1$ emission to test this hypothesis for pillars in theCarina Nebula. We analyse column density and intensity-weighted velocity maps,and subtract any large-scale bulk motions in the plane of the sky to isolatethe turbulent motions. We then reconstruct the dominant turbulence driving modein the pillars, by computing the turbulence driving parameter $b$,characterised by the relation $\sigma_{\rho/\rho_0} = b \mathcal{M}$ betweenthe standard deviation of the density contrast $\sigma_{\rho/\rho_0}$ (with gasdensity $\rho$ and its average $\rho_0$) and the turbulent Mach number$\mathcal{M}$. We find values of \mbox{$b\sim0.7$--$1.0$} for most of thepillars, suggesting that predominantly compressive modes of turbulence aredriven in the pillars by the ionising radiation from nearby massive stars. Wefind that this range of $b$ values can produce star formation rates in thepillars that are a factor $\sim 3$ greater than with $b \sim 0.5$, a typicalaverage value of $b$ for spiral-arm molecular clouds. Our results providefurther evidence for the potential triggering of star formation in pillarsthrough compressive turbulent motions.

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