We present an analysis of the effect of feedback from O- and B-type stars with data from the integral field spectrograph MUSE mounted on the Very Large Telescope of pillar-like structures in the Carina Nebular Complex, one of the most massive star-forming regions in the Galaxy. For the observed pillars, we compute gas electron densities and temperatures maps, produce integrated line and velocity maps of the ionised gas, study the ionisation fronts at the pillar tips, analyse the properties of the single regions, and detect two ionised jets originating from two distinct pillar tips. For each pillar tip we determine the incident ionising photon flux $Q_mathrm{0,pil}$ originating from the nearby massive O- and B-type stars and compute the mass-loss rate $dot{M}$ of the pillar tips due to photo-evaporation caused by the incident ionising radiation. We combine the results of the Carina data set with archival MUSE data of a pillar in NGC 3603 and with previously published MUSE data of the Pillars of Creation in M16, and with a total of 10 analysed pillars, find tight correlations between the ionising photon flux and the electron density, the electron density and the distance from the ionising sources, and the ionising photon flux and the mass-loss rate. The combined MUSE data sets of pillars in regions with different physical conditions and stellar content therefore yield an empirical quantification of the feedback effects of ionising radiation. In agreement with models, we find that $dot{M}propto Q_mathrm{0,pil}^{1/2}$.
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