Tables of functions for a spherical galaxy obeying the 7-1/1 law in projection

A spherical galaxy with reduced surface brightness, J =B (a)IB , obeying the r 1/4 faw, log J = - 3.3307 (a114- 1), where a is the reduced radius, a = r I r (r is the effective radius), is deprojected to find the corre- sponding space density, mass, mean density, force, potential, escape velocity, and potential energy at each point in the galaxy. Numerical tabulations to five significant figures are given for 124 points in the range <5 = R Ir <260. In addition the projected surface brightness B (a) and integrated luminosity within a are tabulated for the range < a = r I r <260. Conversion factors to cgs units and to A; pc, km sec - 1, units are given. Asymptotic expansions for the space density p(s) in the ranges 5< 10 nd 5> are derived, and it is demonstrated that the projection of the expansion for 5 < 10-1 is almost indistinguishable from the r 1/4 law itself, apart from a small excess of luminosity in the central regions. Formulae and numerical tables of the luminosity distribution are given for use in galaxy photometry. Relations between the total galactic mass T the effective radius r , the velocity dispersion cr,, the central density p , and the mass A N and radius R N of the nucleus are derived. Here the "nucleus" is defined as the region within which stars having a velocity equal to the mean velocity dispersion in space, cr,, will be constrained to remain. Four numerical examples are given to illustrate the orders of magnitude of the above quantities for typical elliptical galaxies from supergiant E(e.g.,M87) to compact dwarf (e.g.,M32).