Alcock-Paczyński effect on void-finding Implications for void-galaxy cross-correlation modelling

Under the assumption of statistical isotropy, and in the absence of directional selection effects, a stack of voids is expected to be spherically symmetric, which makes it an excellent object to use for an Alcock-Paczy & nacute;ski (AP) test. This test is commonly carried out using the void-galaxy cross-correlation function (CCF), which has emerged as a competitive probe, especially in combination with the galaxy-galaxy auto-correlation function. Current studies of the AP effect around voids assume that void-centre positions are influenced by the choice of fiducial cosmology in the same way as galaxy positions. We show that this assumption, though prevalent in the literature, is complicated by the response of void-finding algorithms to shifts in tracer positions. Using stretched simulation boxes to emulate the AP effect, we investigate how the void-galaxy CCF changes due to its presence, revealing an additional effect imprinted in the CCF that must be accounted for. The effect originates from the response of void finders to the distorted tracer field - which leads to reduction of the amplitude of the AP signal in the CCF - and thus depends on the specific void-finding algorithm used. We present results for four different void-finding packages, namely REVOLVER, VIDE, voxel, and the spherical void finder in the Pylians3 library, demonstrating how incorrect treatment of the AP effect results in biases in the recovered parameters, regardless of the technique used. Finally, we propose a method to alleviate this issue without resorting to complex and finder-specific modelling of the void-finder response to AP.