• cosmological parameters;
  • cosmology: observations;
  • dark matter;
  • X-rays: galaxies;
  • X-rays: galaxies: clusters


This is the second of two papers investigating the spherical averaging of ellipsoidal galaxy clusters in the context of X-ray and Sunyaev–Zel’dovich (SZ) observations. In the present study, we quantify the orientation-average bias and scatter in observables that result from spherically averaging clusters described by either ellipsoidal generalizations of the Navarro–Frenk–White (NFW) profile or a nearly scale-free logarithmic potential. Although the mean biases are small and mostly <1 per cent, the flattest cluster models generally have a significant mean bias; i.e. averaging over all orientations does not always eliminate projection biases. Substantial biases can result from different viewing orientations, where the integrated Compton-y parameter (YSZ) and the concentration have the largest scatter (as large as σ∼ 10 per cent for YSZ), and the emission-weighted temperature (TX) has the smallest (σ≲ 0.5 per cent). The very small scatter for TX leads to YX and Mgas having virtually the same orientation biases. Substantial scatter is expected for individual clusters (up to σ∼ 8 per cent) in the correlation between YSZ and YX in comparison to the small mean bias (σ≲ 1 per cent) applicable to a random sample of clusters of sufficient size. For ellipsoidal NFW models, we show that the orientation bias for the total cluster mass attains a minimum near the radius r2500 so that the spherically averaged mass computed at this radius is always within ≈0.5 per cent of the true value for any orientation. Finally, to facilitate the accounting for orientation bias in X-ray and SZ cluster studies, we provide cubic polynomial approximations to the mean orientation bias and 1σ scatter for each cluster observable as a function of axial ratio for the ellipsoidal NFW models.