Galaxy clusters, similarity parameters and ratios between measurable characteristics
A M Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017, Russian Federation
The study of galaxy clusters provides insights into the different stages of the evolution of the Universe. Cluster observations measure luminosity, size, temperature and mass. What binds a cluster into a single entity is gravity, its force being proportional to the gravitational constant G. Because all these five quantities are measured in units of mass, length, and time, two nondimensional parameters, commonly known as similarity parameters, can be argued to characterize the system. One of these is the well known virial ratio of kinetic to potential energies. The velocities of galaxy clusters are not measured, however. The luminosity L and the constant G can be combined to introduce the dynamic velocity scale Uα=(LG)1/5. The ratio of this scale to the particle thermal velocity gives the similarity parameter Π 1, which is constant to within about 10% for all 30 objects studied, allowing the virial similarity parameter Π 2 to be estimated for 31 object. For nearby objects with a red shift of z ≤ 0.2 the parameter Π 2 is of order 10 and decreases with increasing z, i.e. with decreasing age. To test the quality of the data the value of G was determined using other measured quantities and found to be equal to its true value to within ≤ 6% and 28% for the close and distant objects, respectively. A number of other ratios between measured quantities are proposed and checked, showing a scatter of 10—20% from linearity in the numerical coefficients involved. Older clusters are, on average, larger in mass and size, implying that smaller clusters can be absorbed by large ones. The results obtained can be valid for clusters with a temperature of T > 1 keV, i.e. in the X-ray range of the spectrum. It is shown that knowing the temperature and the received X-ray intensity, it is possible to estimate the distance to the cluster.