The expected isotropic distribution curves in galactic alignment

Galactic alignment may be a probe of galaxy formation. In such studies, comparisons between the observational distribution of the spin vectors of galaxies and the assumed isotropic distribution are usually performed to try to decide whether alignment exists or not. It has been pointed out that the isotropic distribution that is usually adopted suffers from severe selection effects for the location of cluster and inclination of galaxies. We repeated this simulation for the expected isotropic distribution, and these selection effects were confirmed. Moreover, our results show that the selection effect for the location of cluster can be sidestepped by using the appropriate reference frame, if there is no selection for inclination. This result is especially useful in studies of galactic alignment using samples measured by fitting a certain isophotal level