Scaling Relations of Clusters and Groups and Their Evolution

X-ray observations of the hot intra-cluster medium (ICM) in galaxy groups and clusters provide quantities such as their gas mass, X-ray luminosity, and temperature. The analysis of the scaling relations between these observable properties gives considerable insight into the physical processes taking place in the ICM. Furthermore, an understanding of the scaling relations between ICM properties and the total cluster mass is essential for cosmological studies with clusters. For these reasons, the X-ray scaling relations of groups and clusters have been a major focus of research over the past several decades. In this Chapter, after presenting the expectations from the self-similar model, based on the assumption that only gravity drives the evolution of the ICM, we discuss how the processes of gas cooling and non-gravitational heating are believed to be responsible for the observed deviations from the self-similar scenario. We also describe important complications that must be considered when measuring and interpreting the scaling relations.