The Carina High-Contrast Imaging Project for massive Stars (CHIPS) I. Methodology and proof of concept on QZ Car ($\equiv$ HD93206)

Massive stars like company. However, low-mass companions have remained extremely difficult to detect at angular separations ($\rho$) smaller than 1" (~1000-3000 au considering typical distance to nearby massive stars) given the large brightness contrast between the companion and the central star. Constraints on the low-mass end of the companions mass-function for massive stars are however needed, for example to help distinguishing between various scenarios for the formation of massive stars. To obtain statistically significant constraint on the presence of low-mass companions beyond the typical detection limit of current surveys ($\Delta \mathrm{mag} \lesssim 5$ at $\rho \lesssim 1$"), we initiated a survey of O and Wolf-Rayet stars in the Carina region using the SPHERE coronagraphic instrument on the VLT. In this first paper, we aim to introduce the survey, to present the methodology and to demonstrate the capability of SPHERE for massive stars using the multiple system QZ~Car. High-contrast imaging techniques, such as angular- and spectral-differential imaging techniques as well as PSF-fitting, were applied to detect and measure the relative flux of companions in each spectral channel of the instrument. We detected 19 sources around the QZ~Car system with detection limits of 9~mag at $\rho > 200$~mas for IFS and as faint as 13~mag at $\rho$ > 1".8 for IRDIS (corresponding to sub-solar masses for potential companions). All but two are reported here for the first time. Based on this proof of concept, we showed that VLT/SPHERE allows us to reach the sub-solar mass regime of the companion mass function. This paves the way for this type of observation with a large sample of massive stars to provide novel constraints on the multiplicity of massive stars in a region of the parameter space that has remained inaccessible so far.