Holes within galaxies: The egg or the hen?

Unsustained matter distributions unescapely collapse unless fragmentation and centrifugal or pressure support take place. Starting from the above evidence, supermassive compact objects at the centre of large-mass galaxies (defined as “holes”) are conceived as the end-product of the gravitational collapse of local density maxima (defined as “central collapse”) around which positive density perturbations (overdensities) are located. At the beginning of evolution, assumed to occur at recombination epoch, local density maxima are idealized as homogeneous peaks, while the surrounding envelopes are described by a power-law density profile, ρ(r) ∝ rb-3, 0 ⩽ b ⩽ 3, where b = 0 represents a massless atmosphere and b = 3 a homogeneous layer. The dependence of the density profile on a second parameter, chosen to be the ratio between peak and total (truncated) mass, κ = Mpk/Mtr, is analysed. Overdensity evolution is discussed in the context of quintessence cosmological models, which should be useful in dealing with the virialized phase. Aiming to describe the central collapse, further investigation is devoted to a special case where the quintessence effect is equivalent to additional curvature (w = -1/3), and overdensities exhibit the selected density profile at recombination epoch. A redshift-dependent, power-law relation between hole and (nonbaryonic) dark halo mass is used to express the dependence of the fractional mass, κ, on the overdensity mass, M = Mtr, where the homogeneous peak and overdensity mass are related to the hole and dark halo mass, respectively. Computations are performed for a wide range of masses, -1 ⩽ log(M/M10) ⩽ 6, and mean overdensity heights, 1⩽ν⩽4, up to the end of central collapse, and density profiles of related configurations are determined together with additional parameters. The central collapse is completed in early times, no longer than a few hundredths of Gyr, which implies hole formation when proto-haloes, proto-bulges, and proto-disks are still relaxing. No appreciable change in evolution (up to the end of central collapse) is found with regard to different mean overdensity heights related to equal masses. On the other hand, it is recognized that homogeneous peaks collapse (in dimensionless coordinates) “faster” with respect to surroundings envelopes, in low-mass overdensities than in large-mass overdensities. In conclusion, it is inferred that gravitational collapse of homogeneous peaks within overdensities may be a viable mechanism for hole generation.