========================================================================== J/AJ/81/807 Deprojection of the r^1/4^ law tables (Young, 1976) The following files can be converted to FITS (extension .fit .fgz or .fiZ) table2.dat ========================================================================== Query from: http://vizier.u-strasbg.fr/cgi-bin/VizieR?-source=J/AJ/81/807 ==========================================================================
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Beginning of ReadMe : J/AJ/81/807 Deprojection of the r^1/4^ law tables (Young, 1976) ================================================================================ Tables of functions for a spherical galaxy obeying the r^1/4^ law in projection Young P.J. <Astron. J. 81, 807 (1976)> =1976AJ.....81..807Y ================================================================================ ADC_Keywords: Models ; Galaxies, photometry; Photometry, surface Abstract: A spherical galaxy with reduced surface brightness, J=B(alpha)/B_e_, obeying the r^1/4^ law, logJ=-3.3307 (alpha^1/4^-1), where alpha is the reduced radius, alpha=r/r_e_ (r_e_ is the effective radius), is deprojected to find the corresponding 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 10^-6^<=R/r_e_<=260. In addition the projected surface brightness B(alpha) and integrated luminosity within alpha are tabulated for the range 10^-6^<=alpha=r/r_e_<=260. Conversion factors to cgs units and to M_sun_, pc, km/s, L_sun_ units are given. Asymptotic expansions for the space density rho(s) in the ranges s=<10^-4^ and s>=10^-1^ are derived, and it is demonstrated that the projection of the expansion for s<=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 M_T_, the effective radius r_e_, the velocity dispersion sigma_v_, the central density rho_c_ and the mass M_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, sigma_v_.