On the formation of elliptical galaxies

Abstract

It is suggested that elliptical galaxies are formed in an expansion from a steady-state situation in which the mean density is of order 10⁻⁸ g/cm³. Such an expansion is possible because the inhomogeneous steady-state theory has an instability in which the creation process is essentially cut-off, and in which expansion proceeds according to the Einstein-de Sitter law. The characteristic mass of the 'observable universe' at the onset of such an instability is ca. 10¹³M_⊙, and this is taken to set the upper limit to the masses of galaxies. We suggest that the condensation of elliptical galaxies depends on the presence of inhomogeneities, in particular that a galaxy is formed around a central mass concentration. Because the Einstein-de Sitter expansion law is the limiting case between expansion to infinity at finite velocity and a full-back situation, in which expansion stops at some minimum but finite density, a central condensation with mass appreciably less than that of the associated galaxies suffices to prevent continuing expansion. A mass of 10⁹M_⊙, for example, will restrain a total mass of ca. 10¹²M_⊙ from expanding beyond normal galactic dimensions. The emissivity, assumed to follow the mass distribution, can readily be calculated and is found to follow an r^−8/3 law, which results in a dependence on r^−5/3 when projection against the sky is considered. This law applies outside a central region with radius of order 30 parsecs. It is close to Hubble's law (1+r/a)⁻², with a an adjustable parameter, but actually seems to fit the observed I(r) curves better than Hubble's law. These considerations apply to a spherically symmetric case. Slight deviations from a spherically symmetric expansion with respect to the central object can be discussed by introducing a local rate of strain tensor, ε_ij. The resulting galaxy then has the shape of an ellipsoid with principal axes in the directions of the principal axes of ε_ij. In the special case where two axes are equal, the spheroid can be either prolate or oblate. Unless rotation is set up by a subsequent accretion of gas, the elliptical galaxies are not rotating. The ellipticities of the isophotal contours of the projected image should be closely constant, with a very slight increase outwards. It is shown that cases of high ellipticity must be comparatively rare. The origin of spiral galaxies, and the possibility of there being mixed spiral and elliptical forms, is briefly discussed.