Improving the accuracy of observable distributions for galaxies classified in the projected phase space diagram

Context. Studies of galaxy populations classified according to their kinematic behaviours and dynamical state using the projected phase space diagram (PPSD) are affected by misclassification and contamination, leading to systematic errors in determining the characteristics of the different galaxy classes. Aims. We propose a method for statistically correcting the determination of galaxy properties’ distributions that accounts for the contamination caused by misclassified galaxies from other classes. Methods. Using a sample of massive clusters and the galaxies in their surroundings taken from the M<ns0:sc>ULTI</ns0:sc>D<ns0:sc>ARK</ns0:sc> P<ns0:sc>LANCK</ns0:sc> 2 simulation combined with the semi-analytic model of galaxy formation <ns0:sc>SAG</ns0:sc>, we computed the confusion matrix associated with a classification scheme in the PPSD. Based on positions in the PPSD, galaxies are classified as cluster members, backsplash galaxies, recent infallers, infalling galaxies, or interlopers. This classification is determined using probabilities calculated by the code <ns0:sc>ROGER</ns0:sc> along with a threshold criterion. By inverting the confusion matrix, we are able to get better determinations of distributions of galaxy properties, such as colour. Results. Compared to a direct estimation based solely on the predicted galaxy classes, our method provides better estimates of the mass-dependent colour distribution for the galaxy classes most affected by misclassification: cluster members, backsplash galaxies, and recent infallers. We applied the method to a sample of observed X-ray clusters and galaxies. Conclusions. Our method can be applied to any classification of galaxies in the PPSD, and to any other galaxy property besides colour, provided an estimation of the confusion matrix is available. Blue, low-mass galaxies in clusters are almost exclusively recent infaller galaxies that have not yet been quenched by the environmental action of the cluster. Backsplash galaxies are on average redder than expected.