What is recorded here?
Press and Schechter develop a statistical model connecting small gravitating seeds to a growing condensation mass spectrum, with a Gaussian-tail construction, a surviving maximum-variance self-similar branch and limited N-body tests. Instead of assuming that all galaxies start as large, smooth disturbances, Press and Schechter ask whether smaller gravitating lumps can build larger structures. They estimate how fluctuations in a volume lead to bound condensations in an expanding universe and obtain a mass distribution with a power-law small-mass part and an exponential cutoff. For their randomly positioned, maximum-variance case, the characteristic condensed mass grows with the square of the expansion factor. The argument uses a spherical accretion estimate to account for initially underdense material and assumes that overlap errors are only of order unity. It is a useful statistical model, not an exact count of real galaxies. Two1000-particle experiments provide tentative numerical support and suggest nonlinear growth effects. A note added in proof accepts Peebles’s correction: the more ordered initial-distribution branch has an invalid energy argument and its stated scaling formulas must not be retained. Later excursion-set theory offers a distinct first-crossing justification under specified filters; that later work remains separately credited.
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Scientific scope
The mass-distribution model uses specified Gaussian initial fluctuations, collapse thresholds and approximations. Its counting/normalization and scale-to-mass mapping are model assumptions, not an exact physical collapse proof. Nonlinear dynamics, mergers and finite simulations need further evidence. The later excursion-set first-crossing derivation is separately credited.
Read the original work
- William H. Press/Paul Schechter1974original425-438includingnoteaddedproof
- Bond/Cole/Efstathiou/Kaiser1991: distinctexcursion-set first-crossing approach
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People and systems
William H. Press; Paul Schechter
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English catalogue narrative
Press and Schechter: estimate a hierarchy of gravitating condensations
Press and Schechter develop a statistical model connecting small gravitating seeds to a growing condensation mass spectrum, with a Gaussian-tail construction, a surviving maximum-variance self-similar branch and limited N-body tests.
Instead of assuming that all galaxies start as large, smooth disturbances, Press and Schechter ask whether smaller gravitating lumps can build larger structures. They estimate how fluctuations in a volume lead to bound condensations in an expanding universe and obtain a mass distribution with a power-law small-mass part and an exponential cutoff. For their randomly positioned, maximum-variance case, the characteristic condensed mass grows with the square of the expansion factor. The argument uses a spherical accretion estimate to account for initially underdense material and assumes that overlap errors are only of order unity. It is a useful statistical model, not an exact count of real galaxies. Two1000-particle experiments provide tentative numerical support and suggest nonlinear growth effects. A note added in proof accepts Peebles’s correction: the more ordered initial-distribution branch has an invalid energy argument and its stated scaling formulas must not be retained. Later excursion-set theory offers a distinct first-crossing justification under specified filters; that later work remains separately credited.
Scientific scope
The mass-distribution model uses specified Gaussian initial fluctuations, collapse thresholds and approximations. Its counting/normalization and scale-to-mass mapping are model assumptions, not an exact physical collapse proof. Nonlinear dynamics, mergers and finite simulations need further evidence. The later excursion-set first-crossing derivation is separately credited.
People and systems
William H. Press; Paul Schechter