19,982 research outputs found
A critique of scaling behaviour in non-linear structure formation scenarios
Moments of the BBGKY equations for spatial correlation functions of
cosmological density perturbations are used to obtain a differential equation
for the evolution of the dimensionless function, ,
where is the mean relative pair velocity. The BBGKY equations are closed
using a hierarchical scaling ansatz for the 3-point correlation function.
Scale-invariant solutions derived earlier by Davis and Peebles are then used in
the non-linear regime, along with the generalised stable clustering hypothesis
( const.), to obtain an expression for the asymptotic value of , in
terms of the power law index of clustering, ,and the tangential and
radial velocity dispersions. The Davis-Peebles solution is found to require
that tangential dispersions are larger than radial ones, in the non-linear
regime; this can be understood on physical grounds. Finally, stability analysis
of the solution demonstrates that the allowed asymptotic values of ,
consistent with the stable clustering hypothesis, lie in the range . Thus, if the Davis-Peebles scale-invariant solution (and the
hierarchical model for the 3-pt function) is correct, the standard stable
clustering picture ( as ) is not allowed in the
non-linear regime of structure formation.Comment: 14 pages, no figures. Scheduled to appear in ApJ, Mar 1 issue. Final
version, contains added discussion to match the accepted versio
Accurate determination of the Lagrangian bias for the dark matter halos
We use a new method, the cross power spectrum between the linear density
field and the halo number density field, to measure the Lagrangian bias for
dark matter halos. The method has several important advantages over the
conventional correlation function analysis. By applying this method to a set of
high-resolution simulations of 256^3 particles, we have accurately determined
the Lagrangian bias, over 4 magnitudes in halo mass, for four scale-free models
with the index n=-0.5, -1.0, -1.5 and -2.0 and three typical CDM models. Our
result for massive halos with ( is a characteristic non-linear
mass) is in very good agreement with the analytical formula of Mo & White for
the Lagrangian bias, but the analytical formula significantly underestimates
the Lagrangian clustering for the less massive halos $M < M_*. Our simulation
result however can be satisfactorily described, with an accuracy better than
15%, by the fitting formula of Jing for Eulerian bias under the assumption that
the Lagrangian clustering and the Eulerian clustering are related with a linear
mapping. It implies that it is the failure of the Press-Schechter theories for
describing the formation of small halos that leads to the inaccuracy of the Mo
& White formula for the Eulerian bias. The non-linear mapping between the
Lagrangian clustering and the Eulerian clustering, which was speculated as
another possible cause for the inaccuracy of the Mo & White formula, must at
most have a second-order effect. Our result indicates that the halo formation
model adopted by the Press-Schechter theories must be improved.Comment: Minor changes; accepted for publication in ApJ (Letters) ; 11 pages
with 2 figures include
On the Spatial Correlations of Lyman Break Galaxies
Motivated by the observed discrepancy between the strong spatial correlations
of Lyman break galaxies (LBGs) and their velocity dispersions, we consider a
theoretical model in which these starbursting galaxies are associated with dark
matter halos that experience appreciable infall of material. We show using
numerical simulation that selecting halos that substantially increase in mass
within a fixed time interval introduces a ``temporal bias'' which boosts their
clustering above that of the underlying population. If time intervals
consistent with the observed LBGs star formation rates of 50 solar masses per
year are chosen, then spatial correlations are enhanced by up to a factor of
two. These values roughly correspond to the geometrical bias of objects three
times as massive. Thus, it is clear that temporal biasing must be taken into
account when interpreting the properties of Lyman break galaxies.Comment: 5 Pages, 2 Figures, Accepted for Publication in ApJ Letter
Bias and Hierarchical Clustering
It is now well established that galaxies are biased tracers of the
distribution of matter, although it is still not known what form this bias
takes. In local bias models the propensity for a galaxy to form at a point
depends only on the overall density of matter at that point. Hierarchical
scaling arguments allow one to build a fully-specified model of the underlying
distribution of matter and to explore the effects of local bias in the regime
of strong clustering. Using a generating-function method developed by
Bernardeau & Schaeffer (1992), we show that hierarchical models lead one
directly to the conclusion that a local bias does not alter the shape of the
galaxy correlation function relative to the matter correlation function on
large scales. This provides an elegant extension of a result first obtained by
Coles (1993) for Gaussian underlying fields and confirms the conclusions of
Scherrer & Weinberg (1998) obtained using a different approach. We also argue
that particularly dense regions in a hierarchical density field display a form
of bias that is different from that obtained by selecting such peaks in
Gaussian fields: they are themselves hierarchically distributed with scaling
parameters . This kind of bias is also factorizable, thus in
principle furnishing a simple test of this class of models.Comment: Latex, accepted for publication in ApJL; moderate revision
Deriving the Nonlinear Cosmological Power Spectrum and Bispectrum from Analytic Dark Matter Halo Profiles and Mass Functions
We present an analytic model for the fully nonlinear power spectrum P and
bispectrum Q of the cosmological mass density field. The model is based on
physical properties of dark matter halos, with the three main model inputs
being analytic halo density profiles, halo mass functions, and halo-halo
spatial correlations, each of which has been well studied in the literature. We
demonstrate that this new model can reproduce the power spectrum and bispectrum
computed from cosmological simulations of both an n=-2 scale-free model and a
low-density cold dark matter model. To enhance the dynamic range of these large
simulations, we use the synthetic halo replacement technique of Ma & Fry
(2000a), where the original halos with numerically softened cores are replaced
by synthetic halos of realistic density profiles. At high wavenumbers, our
model predicts a slope for the nonlinear power spectrum different from the
often-used fitting formulas in the literature based on the stable clustering
assumption. Our model also predicts a three-point amplitude Q that is scale
dependent, in contrast to the popular hierarchical clustering assumption. This
model provides a rapid way to compute the mass power spectrum and bispectrum
over all length scales where the input halo properties are valid. It also
provides a physical interpretation of the clustering properties of matter in
the universe.Comment: Final version to appear in the Astrophysical Journal 544 (2000).
Minor revisions; 1 additional figure. 25 pages with 6 inserted figure
Angular separations of the lensed QSO images
We have analyzed the observed image separations of the gravitationally lensed
images of QSOs for a possible correlation with the source redshift. Contrary to
the previously noted anti-correlation based on a smaller data set, no
correlation is found for the currently available data. We have calculated the
average image separations of the lensed QSOs as a function of source redshifts,
for isothermal spheres with cores in a flat universe, taking into account the
amplification bias caused by lensing. The shape of the distribution of average
image separation as a function of redshift is very robust and is insensitive to
most model parameters. Observations are found to be roughly consistent with the
theoretical results for models which assume the lens distribution to be (i)
Schechter luminosity function which, however, can not produce images with large
separation and (ii) the mass condensations in a cold dark matter universe, as
given by the Press-Schechter theory if an upper limit of 1-7
M is assumed on the mass of the condensations.Comment: 20 pages, 7 postscript figures, accepted for publication in The
Astrophysical Journa
The Pairwise Peculiar Velocity Dispersion of Galaxies: Effects of the Infall
We study the reliability of the reconstruction method which uses a modelling
of the redshift distortions of the two-point correlation function to estimate
the pairwise peculiar velocity dispersion of galaxies. In particular, the
dependence of this quantity on different models for the infall velocity is
examined for the Las Campanas Redshift Survey. We make extensive use of
numerical simulations and of mock catalogs derived from them to discuss the
effect of a self-similar infall model, of zero infall, and of the real infall
taken from the simulation. The implications for two recent discrepant
determinations of the pairwise velocity dispersion for this survey are
discussed.Comment: minor changes in the discussion; accepted for publication in ApJ; 8
pages with 2 figures include
Confronting cold dark matter cosmologies with strong clustering of Lyman break galaxies at
We perform a detailed analysis of the statistical significance of a
concentration of Lyman break galaxies at recently discovered by
Steidel et al. (1997), using a series of N-body simulations with
particles in a (100\himpc)^3 comoving box. While the observed number density
of Lyman break galaxies at implies that they correspond to systems
with dark matter halos of \simlt 10^{12}M_\odot, the resulting clustering of
such objects on average is not strong enough to be reconciled with the
concentration if it is fairly common; we predict one similar concentration
approximately per () fields in three representative cold dark matter
models. Considering the current observational uncertainty of the frequency of
such clustering at , it would be premature to rule out the models, but
the future spectroscopic surveys in a dozen fields could definitely challenge
all the existing cosmological models a posteriori fitted to the universe.Comment: the final version which matchs that published in ApJ Letters (Feb
1998); compared with the previous versions, the predictions for the SCDM
model are slightly changed; Latex, 11 pages, including 3 ps figure
Calibrating the Galaxy Halo - Black Hole Relation Based on the Clustering of Quasars
The observed number counts of quasars may be explained either by long-lived
activity within rare massive hosts, or by short-lived activity within smaller,
more common hosts. It has been argued that quasar lifetimes may therefore be
inferred from their clustering length, which determines the typical mass of the
quasar host. Here we point out that the relationship between the mass of the
black-hole and the circular velocity of its host dark-matter halo is more
fundamental to the determination of the clustering length. In particular, the
clustering length observed in the 2dF quasar redshift survey is consistent with
the galactic halo - black-hole relation observed in local galaxies, provided
that quasars shine at ~10-100% of their Eddington luminosity. The slow
evolution of the clustering length with redshift inferred in the 2dF quasar
survey favors a black-hole mass whose redshift-independent scaling is with halo
circular velocity, rather than halo mass. These results are independent from
observations of the number counts of bright quasars which may be used to
determine the quasar lifetime and its dependence on redshift. We show that if
quasar activity results from galaxy mergers, then the number counts of quasars
imply an episodic quasar lifetime that is set by the dynamical time of the host
galaxy rather than by the Salpeter time. Our results imply that as the redshift
increases, the central black-holes comprise a larger fraction of their host
galaxy mass and the quasar lifetime gets shorter.Comment: 10 pages, 5 figures. Submitted to Ap
Constraints on z~10 Galaxies from the Deepest HST NICMOS Fields
We use all available fields with deep NICMOS imaging to search for J dropouts
(H<28) at z~10. Our primary data set for this search were the two J+H NICMOS
parallel fields taken with the ACS HUDF. The 5 sigma limiting mags were 28.6 in
J and 28.5 in H. Several shallower fields were also used: J+H NICMOS frames
available over the HDF North, the HDF South NICMOS parallel, and the ACS HUDF.
The primary selection criterion was (J-H)>1.8. 11 such sources were found in
all search fields using this criterion. 8 of these were clearly ruled out as
credible z~10 sources, either as a result of detections (>2 sigma) blueward of
J or their colors redward of the break (H-K~1.5). The nature of the 3 remaining
sources could not be determined from the data. The number appears consistent
with the expected contamination from low-z interlopers. Analysis of the stacked
images for the 3 candidates also suggests contamination. Regardless of their
true redshifts, the actual number of z~10 sources must be <=3. To assess the
significance of these results, two lower redshift samples (a z~3.8 B-dropout
and z~6 i-dropout sample) were projected to z~8-12 using a (1+z)^{-1} size
scaling. They were added to the image frames, and the selection repeated,
giving 15.6 and 4.8 J-dropouts, respectively. This suggests that to the limit
of this probe (0.3 L*) there has been evolution from z~3.8 and possibly from
z~6. This is consistent with the strong evolution already noted at z~6 and
z~7.5 relative to z~3-4. Even assuming that 3 sources from this probe are at
z~10, the rest-frame continuum UV (~1500 A) luminosity density at z~10
(integrated down to 0.3 L*) is just 0.19_{-0.09}^{+0.13}x that at z~3.8 (or
0.19_{-0.10}^{+0.15}x including cosmic variance). However, if none of our
sources is at z~10, this ratio has a 1 sigma upper limit of 0.07. (abridged)Comment: 13 pages, 3 figures, 2 tables, accepted for publication in the
Astrophysical Journal Letter
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