|
|
| Line 1: |
Line 1: |
| The '''Press–Schechter formalism''' is a [[mathematical model]] for predicting the number of objects (such as [[galaxies]] or [[galaxy clusters]]) of a certain mass within a given volume of the Universe. It was described in a famous [[Academic paper|paper]] by [[William H. Press]] and [[Paul L. Schechter|Paul Schechter]] in 1974.<ref>[http://adsabs.harvard.edu/abs/1974ApJ...187..425P Formation of Galaxies and Clusters of Galaxies by Self-Similar Gravitational Condensation], W.H. Press, P. Schechter, 1974</ref>
| | Hello! <br>I'm French male :D. <br>I really like Figure skating!<br><br>Stop by my web blog: [http://gnlhookup.com/activity/p/1564147/ Дополнительная информация] |
| | |
| ==Background==
| |
| In the context of [[Dark matter|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 cosmology|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.
| |
| | |
| ==Result==
| |
| | |
| The Press–Schechter formalism predicts that the number of objects with mass between <math>M</math> and <math>M+dM</math> is:
| |
| | |
| :<math>N(M)dM = \frac{1}{\sqrt{\pi}}\left(1+\frac{n}{3}\right)\frac{\bar{\rho}}{M^2}\left(\frac{M}{M^*}\right)^{\left(3+n\right)/6}\exp\left(-\left(\frac{M}{M^*}\right)^{\left(3+n\right)/3}\right)dM</math> | |
| | |
| where <math>\bar{\rho}</math> is the mean (baryonic and dark) matter density of the universe, <math>n</math> is the index of the power spectrum of the fluctuations in the early universe <math>P(k)\propto k^n</math>, and <math>M^*</math> is a critical mass above which structures will form.
| |
| | |
| 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. Such functions had previously been noted by Schechter
| |
| as observed [[Luminosity function (astronomy)|luminosity functions]],
| |
| and are now known as Schechter luminosity functions. The Press-Schechter
| |
| formalism provided the first quantitative model for how such functions might
| |
| arise.
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| {{DEFAULTSORT:Press-Schechter formalism}}
| |
| [[Category:Astrophysics]]
| |
| [[Category:Mathematical modeling]]
| |
| | |
| | |
| {{Physics-stub}}
| |
Hello!
I'm French male :D.
I really like Figure skating!
Stop by my web blog: Дополнительная информация