Dependence of X-Ray Luminosity on Temperature for Groups andClusters with the Moving Median Statistics

We re-analyse the relationship between the x-ray luminosity
(L_X) and the temperature (T) of groups and clusters of galaxies, based on the largest sample of 40 groups and 188 clusters. We employ the moving median statistics for the data set, along with the proper linear regression. Our newly established L_X-T relations for groups and clusters show no significant difference within statistical uncertainties,
yielding L_X ∝ T^2.79±0.01 (groups) and L_X ∝ T^2.54±0.004 (clusters). This also supports the hierarchical scenario of structure formation in which groups are simply the scale-down version of clusters. It is argued that the break in the L_X-T relation on group scales detected in previous studies may suffer from sparse data sample and poor statistical methods.