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Formation of Galaxies and Clusters of Galaxies by Self-Similar Gravitational Condensation
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The study examines an expanding Friedmann cosmology with a gas of self‑gravitating masses as a framework for galaxy and cluster formation. The authors aim to show that successive gravitational condensation yields a self‑similar mass spectrum independent of the initial perturbation spectrum. They model condensation by treating bound aggregates as single massive particles, deriving a self‑similar distribution via linear perturbation theory while allowing nonlinear N‑body interactions to randomize positions and set the spectrum without ad hoc assumptions. Numerical experiments with 1000 bodies reveal that condensations can bootstrap to larger sizes faster than linear theory predicts, and the self‑similar model yields mass–radius relations that agree strikingly with observed galaxies and clusters, implying isothermal seed masses of 3×10¹⁰ M⊙ at recombination for galaxies and that clusters need only galaxy seeds. Published in The Astrophysical Journal (Feb 1974, DOI 10.1086/152650), the paper notes that cluster size could in principle constrain the deceleration parameter q₀, though current data provide only broad limits.
view Abstract Citations (4399) References (31) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Formation of Galaxies and Clusters of Galaxies by Self-Similar Gravitational Condensation Press, William H. ; Schechter, Paul Abstract We consider an expanding Friedmann cosmology containing a "gas" of self-gravitating masses. The masses condense into aggregates which (when sufficiently bound) we identify as single particles of a larger mass. We propose that after this process has proceeded through several scales, the mass spectrum of condensations becomes "self-similar" and independent of the spectrum initially assumed. Some details of the self-similar distribution, and its evolution in time, can be calculated with the linear perturbation theory. Unlike other authors, we make no ad hoc assumptions about the spectrum of long-wavelength initial perturbatidns: the nonlinear N-body interactions of the mass points randomize their positions and generate a perturbation to all larger scales; this should fix the self-similar distribution almost uniquely. The results of numerical experiments on 1000 bodies are presented; these appear to show new nonlinear effects: condensations can "bootstrap" their way up in size faster than the linear theory predicts. Our self-similar model predicts relations between the masses and radii of galaxies and clusters of galaxies, as well as their mass spectra. We compare the predictions with available data, and find some rather striking agreements. If the model is to explain galaxies, then isothermal "seed" masses of 3 x 1 0 M0 must have existed at recombination. To explain clusters of galaxies, the only necessary seeds are the galaxies themselves. The size of clusters determines, in principle, the deceleration parameter q0 presently available data give only very broad limits, unfortunately. Subject headings: cosmology - galaxies - galaxies, clusters of Publication: The Astrophysical Journal Pub Date: February 1974 DOI: 10.1086/152650 Bibcode: 1974ApJ...187..425P full text sources ADS | data products SIMBAD (6)