Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.
Concept
Press–Schechter formalism
Summary
The Press–Schechter formalism is a mathematical model for predicting the number of objects (such as galaxies, galaxy clusters or dark matter halos) of a certain mass within a given volume of the Universe. It was described in an academic paper by William H. Press and Paul Schechter in 1974.
In the context of cold dark matter cosmological models, perturbations on all scales are imprinted on the universe at very early times, for example by quantum fluctuations during an inflationary era. Later, as radiation redshifts away, these become mass perturbations, and they start to grow linearly. Only long after that, starting with small mass scales and advancing over time to larger mass scales, do the perturbations actually collapse to form (for example) galaxies or clusters of galaxies, in so-called hierarchical structure formation (see Physical cosmology).
Press and Schechter observed that the fraction of mass in collapsed objects more massive than some mass M is related to the fraction of volume samples in which the smoothed initial density fluctuations are above some density threshold. This yields a formula for the mass function (distribution of masses) of objects at any given time.
The Press–Schechter formalism predicts that the number of objects with mass between and is:
where is the index of the power spectrum of the fluctuations in the early universe , is the mean (baryonic and dark) matter density of the universe at the time the fluctuation from which the object was formed had gravitationally collapsed, and is a cut-off mass below which structures will form. Its value is:
is the standard deviation per unit volume of the fluctuation from which the object was formed had gravitationally collapsed, at the time of the gravitational collapse, and R is the scale of the universe at that time. Parameters with subscript 0 are at the time of the initial creation of the fluctuations (or any later time before the gravitational collapse).
Qualitatively, the prediction is that the mass distribution is a power law for
small masses, with an exponential cutoff above some characteristic mass that
increases with time.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.