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Scientific paper
Mar 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phdt........30g&link_type=abstract
Thesis (PH.D.)--CORNELL UNIVERSITY, 1982.Source: Dissertation Abstracts International, Volume: 42-12, Section: B, page: 4830.
Other
2
Scientific paper
A kinetic theory is developed that describes galaxy clustering in terms of correlation functions. The theory is based on the BBGKY equations, which are derived from a Lagrangian in co-moving coordinates. It is found that the Lagrangian may be expressed in three dynamically distinct limiting regimes, defined in terms of the relative dominance of the expansion velocity, v(,H)(' )(TBOND)(' )ax, and three-dimensional RMS relative peculiar velocity, C(' )(TBOND)(' )<(ax)('2)>(' 1/2). This observation further leads to the concept of a "thermal hubble sphere" (THS), whose radius, R(,H) (TBOND) C/H(,0), provides the analysis with a scale length. Being that observations to date of the two-point correlation function (xi)(r) largely coincide with Regime I (r << R(,H), C >> v(,H)), this analysis is carried out in that domain. The resulting equations are consistent in the appropriate limit with those found previously by Fall and Saslaw and Davis and Peebles. Nondimensionalization and (epsilon)-expansion schemes applied to the BBGKY hierarchy lead to a classification of model universes in terms of the density parameter (OMEGA) and N(,H) (TBOND) nV(,THS), where n is the mean proper number density of galaxies and V(,THS) (TBOND) 4/3(pi)R(,H)('3). The (epsilon) scheme incorporates the strong-coupling condition observed by Peebles and colleagues: (xi)(,12) << (xi)(,123) << (xi)(,1234) . . . and it differentiates among 25 separate models over the full ranges of (OMEGA) and N(,H). Six of these --three of which represent open universes and three, closed --are evaluated for a steady-state solution of (xi)(r). The results are a wide variety of analytic solutions, including exponentials, spherical Bessel functions and power laws. Their corresponding angular covariance functions, w((theta)), are calculated using Limber's equation and then compared with the data. It is found that there is a match only with an open universe having (xi)(r) (TURN) a(,0)r('-2) + a(,1)r('-1) - a(,2)r. A fit to the data yields the results 0.08(, )<(, )(OMEGA)(, )<(, )0.4 and 0.1(, )<(, )N(,H(, ))<(, )1, consistent with other independent observations. It is noted, furthermore, that likely values of R(,H) are compatible with the scale length attributed to the apparent bend in (xi)(r) (r(,0) (TURN) 9h('-1)Mpc) and which Fall argues is necessary for avoiding a divergence of the correlation energy per galaxy. Future calculations will exploit the theory's generality by eventually evaluating all correlation functions of interest in each of the three regimes.
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