Spherical bias in the 3D reconstruction of the ICM density profile in galaxy clusters

X-ray observations of galaxy clusters are routinely used to derive radial distributions of intracluster medium (ICM) thermodynamical properties, such as density and temperature. However, observations only allow access to quantities projected on the celestial sphere, so an assumption on the three-dimensional distribution of the ICM is necessary. Usually, spherical geometry is assumed. The aim of this paper is to determine the bias due to this approximation on the reconstruction of the ICM density radial profile of a cluster sample and on the intrinsic scatter of the density profiles' distribution particularly when the substructures of clusters are not masked We used simulated clusters for which we can access the three-dimensional ICM distribution. In particular, we considered a sample of 98 simulated clusters drawn from project. For each cluster, we simulated 40 different observations by projecting the cluster along 40 different lines of sight. We extracted the ICM density profile from each observation, assuming the ICM to be spherically distributed. For each line of sight, we then considered the mean density profile over the sample and compared it with the three-dimensional density profile given by the simulations. We thus derived the spherical bias in the density profile by considering the ratio between the observed and the input quantities. We also studied the bias in the intrinsic scatter of the density profile distribution by performing the same procedure. We find a bias in the density profile, b_n, smaller than $10%$ for R and it increases up to ≈ 50% for larger radii. The bias in the intrinsic scatter profile, b_s, is higher, reaching a value of ≈ 100% for R≈ R_ . We find that the bias for both of the analyzed quantities strongly depends on the morphology composition of the objects in the sample. For clusters that do not show large-scale substructures, both b_n and b_s are reduced by a factor of two. Conversely, for systems that do show large-scale substructures, both b_n and b_s increase significantly.