Cosmic voids are underdense regions within the large-scale structure of the Universe, spanning a wide range of physical scales -- from a few megaparsecs to the largest observable structures. Their distinctive properties make them valuable cosmological probes and unique laboratories for galaxy formation studies. A key aspect to investigate in this context is the galaxy bias, b, within voids -- that is, how galaxies in these underdense regions trace the underlying dark-matter density field. We aim to measure the dependence of the large-scale galaxy bias on the distance to the void center and to evaluate whether this bias profile varies with the void properties and identification procedure. We applied a void identification scheme based on spherical overdensities to galaxy data from the IllustrisTNG magnetohydrodynamical simulation. For the clustering measurement, we used an object-by-object estimate of large-scale galaxy bias, which offers significant advantages over the standard method based on ratios of correlation functions or power spectra. We find that the average large-scale bias of galaxies inside voids tends to increase with void-centric distance when normalized by the void radius. For the entire galaxy population within voids, the average bias rises with the density of the surrounding environment and, consequently, decreases with increasing void size. Due to this environmental dependence, the average galaxy bias inside S-type voids -- embedded in large-scale overdense regions -- is significantly higher (łangle b〉_ ̊m in > 0) at all distances compared to R-type voids, which are surrounded by underdense regions (łangle b〉_ ̊m in < 0). The bias profile for S-type voids is also slightly steeper. Since the two types of voids host halo populations of similar mass, the measured difference in bias can be interpreted as a secondary bias effect.
Montero-Dorta et al. (Tue,) studied this question.