The velocity dispersion in the X-ray scaling laws

We used a sample of 20 poor groups of galaxies to study the low mass tail of the relationships among the X-ray temperature T, the X-ray luminosity L _x and the optical velocity dispersion σ. We obtained redshifts for the fainter members of these groups. We find that X-ray bright groups have more members and higher velocity dispersions on average. Using the fainter group members and Monte Carlo tests, we define the number of group members required to calculate a robust velocity dispersion. There is a tendency to underestimate the group velocity dispersion for samples of fewer than ∼ 10 members that introduces systematic errors in the slope of the relationships among L_x, T, and σ. A comparison with the data of Ponman and Mahdavi shows that our improved velocity dispersions provide better constraints on the relationship between the kinematics of the hot gas and galaxies in these common environments.