arXiv subjects

Jun Pan

Publications and source records attributed to Jun Pan.

51 records · Page 3Linked to original sources

arXiv2006

Note on Redshift Distortion in Fourier Space

We explore features of redshift distortion in Fourier analysis of N-body simulations. The phases of the Fourier modes of the dark matter density fluctuation are generally shifted by the peculiar motion along the line of sight, the induced phase shift is stochastic and has probability distribution function (PDF) symmetric to the peak at zero shift while the exact shape depends on the wave vector, except on very large scales where phases are invariant by linear perturbation theory. Analysis of the phase shifts motivates our phenomenological models for the bispectrum in redshift space. Comparison with simulations shows that our toy models are very successful in modeling bispectrum of equilateral and isosceles triangles at large scales. In the second part we compare the monopole of the power spectrum and bispectrum in the radial and plane-parallel distortion to test the plane-parallel approximation. We confirm the results of Scoccimarro (2000) that difference of power spectrum is at the level of 10%, in the reduced bispectrum such difference is as small as a few percents. However, on the plane perpendicular to the line of sight of k_z=0, the difference in power spectrum between the radial and plane-parallel approximation can be more than 10%, and even worse on very small scales. Such difference is prominent for bispectrum, especially for those configurations of tilted triangles. The non-Gaussian signals under radial distortion on small scales are systematically biased downside than that in plane-parallel approximation, while amplitudes of differences depend on the opening angle of the sample to the observer. The observation gives warning to the practice of using the power spectrum and bispectrum measured on the k_z=0 plane as estimation of the real space statistics.

astro-ph↗

arXiv2005

Cosmological Three-Point Function: Testing The Halo Model Against Simulations

We perform detailed comparison of the semi-analytic halo model predictions with measurements in numerical simulations of the two and three point correlation functions (3PCF), as well as power spectrum and bispectrum. We discuss the accuracy and self-consistency of the halo model description of gravitational clustering in the non-linear regime and constrain halo model parameters. We exploit the recently proposed multipole expansion of three point statistics that expresses rotation invariance in the most natural way. This not only offers technical advantages by reducing the integrals required for the halo model predictions, but amounts to a convenient way of compressing the information contained in the 3PCF. We find that, with an appropriate choice of the halo boundary and mass function cut-off, halo model predictions are in good agreement with the bispectrum measured in numerical simulations. However, the halo model predicts less than the observed configuration dependence of the 3PCF on ~ Mpc scales. This effect is mainly due to quadrupole moment deficit, possibly related to the assumption of spherical halo geometry. Our analysis shows that using its harmonic decomposition, the full configuration dependence of the 3PCF in the non-linear regime can be compressed into just a few numbers, the lowest multipoles. Moreover, these multipoles are closely related to the highest signal to noise eigenmodes of the 3PCF. Therefore this estimator may simplify future analyses aimed at constraining cosmological and halo model parameters from observational data.

astro-ph↗

arXiv2005

The Monopole Moment of the Three-Point Correlation Function of the 2-degree Field Galaxy Redshift Survey

We measure the monopole moment of the three-point correlation function on scales $1\mpc-70\mpc$ in the Two degree Field Galaxy Redshift Survey (2dFGRS). Volume limited samples are constructed using a series of integral magnitudes bins between $M = -18 ... -22$. Our measurements with a novel edge-corrected estimator represent most, if not all, three-point level monopole or angular averaged information in the catalogue. We fit a perturbative non-linear bias model to a joint data vector formed from the estimated two- and three-point correlation functions. Two different models are used: an analytic model based on Eulerian perturbation theory including bias and redshift distortions, and a phenomenological bias model based on the direct redshift space measurements in the large Virgo simulations. To interpret the clustering results, we perform a three parameter Gaussian maximum likelihood analysis. In the canonical $-21 \sim -20$ volume limited sample we find $σ_8 = 0.93^{+0.06}_{-0.2}$, $b = 1.04^{+0.23}_{-0.09}$, and $b_2 = -0.06^{+0.003}_{-0.001}$. Our estimate of $σ_8$, is robust across the different volume limited samples constructed. These results, based solely on the large scale clustering of galaxies, are in excellent agreement with previous analyses using the Wilkinson Anisotropy Probe: this is a spectacular success of the concordance model. We also present two-parameter fits for the bias parameters, which are in excellent agreement with previous findings of the bias evolution in the 2dFGRS.

astro-ph↗

arXiv2005

Fast Edge Corrected Measurement of the Two-Point Correlation Function and the Power Spectrum

We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point function with an heuristically weighted edge corrected estimator. Once the correlation function is measured, we estimate the power spectrum via numerical integration of the Hankel transform connecting the two. We introduce an efficient numerical technique based on Gauss-Bessel-quadrature and double exponential transformation. This, combined with our, or any similar, two-point function estimator leads to a novel edge corrected estimator for power spectra. The pair of techniques presented are the Euclidean analogs of those developed and widely used in cosmic microwave background research for spherical maps.

astro-ph↗

arXiv2004

Three-point Correlation Functions of SDSS Galaxies in Redshift Space: Morphology, Color, and Luminosity Dependence

We present measurements of the redshift--space three-point correlation function of galaxies in the Sloan Digital Sky Survey (SDSS). For the first time, we analyze the dependence of this statistic on galaxy morphology, color and luminosity. In order to control systematics due to selection effects, we used $r$--band, volume-limited samples of galaxies, constructed from the magnitude-limited SDSS data ($14.5<r<17.5$), and further divided the samples into two morphological types (early and late) or two color populations (red and blue). The three-point correlation function of SDSS galaxies follow the hierarchical relation well and the reduced three-point amplitudes in redshift--space are almost scale-independent ($Q_z=0.5\sim1.0$). In addition, their dependence on the morphology, color and luminosity is not statistically significant. Given the robust morphological, color and luminosity dependences of the two-point correlation function, this implies that galaxy biasing is complex on weakly non-linear to non-linear scales. We show that simple deterministic linear relation with the underlying mass could not explain our measurements on these scales.

astro-ph↗

arXiv2004

Conditional Cumulants in Weakly Non-linear Regime

Conditional cumulants form a set of unique statistics which represent a sensible compromise between N-point correlation functions and cumulants measured from moments of counts in cells. They share accurate edge corrected estimators with $N$-point correlation functions, yet, they are as straightforward to measure and interpret as counts in cells. The conditional cumulants have three equivalent views as i) degenerate N-point correlation functions ii) or integrated monopole moments of the bispectrum iii) they are closely related to neighbour counts. We compute the predictions of weakly non-linear perturbation theory for conditional cumulants and compare them with measurements in simulations, both in real and redshift space. We find excellent agreement between theory and simulations, especially on scales >~20Mpc. Due to their advantageous statistical properties and well understood dynamics, we propose conditional cumulants as tools for high precision cosmology. Potential applications include constraining bias and redshift distortions from galaxy redshift surveys

astro-ph↗

arXiv2003

On Recovering the Nonlinear Bias Function from Counts in Cells Measurements

We present a simple and accurate method to constrain galaxy bias based on the distribution of counts in cells. The most unique feature of our technique is that it is applicable to non-linear scales, where both dark matter statistics and the nature of galaxy bias are fairly complex. First, we estimate the underlying continuous distribution function from precise counts-in-cells measurements assuming local Poisson sampling. Then a robust, non-parametric inversion of the bias function is recovered from the comparison of the cumulative distributions in simulated dark matter and galaxy catalogs. Obtaining continuous statistics from the discrete counts is the most delicate novel part of our recipe. It corresponds to a deconvolution of a (Poisson) kernel. For this we present two alternatives: a model independent algorithm based on Richardson-Lucy iteration, and a solution using a parametric skewed lognormal model. We find that the latter is an excellent approximation for the dark matter distribution, but the model independent iterative procedure is more suitable for galaxies. Tests based on high resolution dark matter simulations and corresponding mock galaxy catalogs show that we can reconstruct the non-linear bias function down to highly non-linear scales with high precision in the range of $-1 \le δ\le 5$. As far as the stochasticity of the bias, we have found a remarkably simple and accurate formula based on Poisson noise, which provides an excellent approximation for the scatter around the mean non-linear bias function. In addition we have found that redshift distortions have a negligible effect on our bias reconstruction, therefore our recipe can be safely applied to redshift surveys.

astro-ph↗

arXiv2001

Boundary Corrections in Fractal Analysis of Galaxy Surveys

The analysis of redshift surveys with fractal tools requires one to apply some form of statistical correction for galaxies lying near the geometric boundary of the sample. In this paper we compare three different methods of performing such a correction upon estimates of the correlation integral in order to assess the extent to which estimates may be biased by boundary terms. We apply the corrections illustrative examples, including a simple fractal set (Lévy flight), a random $β$-model, and a subset of the CfA2 Southern Cap survey. This study shows that the new ``angular'' correction method we present is more generally applicable than the other methods used to date: the conventional ``capacity'' correction imposes a bias towards homogeneity, and the ``deflation'' method discards large-scale information, and consequently reduces the statistical usefulness of data sets. The ``angular'' correction method is effective at recovering true fractal dimensions, although the extent to which boundary corrections are important depends on the form of fractal distribution assumed as well as the details of the survey geometry. We also show that the CfA2 Southern sample does not show any real evidence of a transition to homogeneity. We then revisit the IRAS PSCz survey and ``mock'' PSCz catalogues made using N-body simulations of two different cosmologies. The results we obtain from the PSCz survey are not significantly affected by the form of boundary correction used, confirming that the transition from fractal to homogeneous behaviour reported by Pan & Coles (2000) is real.

astro-ph↗

arXiv2000

Large-scale Cosmic Homogeneity from a Multifractal Analysis of the PSCz Catalogue

We investigate the behaviour of galaxy clustering on large scales using the PSCz catalogue. In particular, we ask whether there is any evidence of large-scale fractal behaviour in this catalogue. We find the correlation dimension in this survey varies with scale, consistent with other analyses. For example, our results on small and intermediate scales are consistent those obtained from the QDOT sample, but the larger PSCz sample allows us to extend the analysis out to much larger scales. We find firm evidence that the sample becomes homogeneous at large scales; the correlation dimension of the sample is D_2=2.992(3) for r>30 h^{-1} Mpc. This provides strong evidence in favour of a Universe which obeys the Cosmological Principle.

astro-ph↗

arXiv1995

Chemistry of Nanoscale Semiconductor Clusters

The ground state structures of small silicon clusters are determined through exhaustive tight-binding molecular dynamics simulation studies. These simulations revealed that \Si{11} is an icosahedron with one missing cap, \Si{12} is a complete icosahedron, \Si{13} is a surface capped icosahedron, \Si{14} is a 4-4-4 layer structure with two caps, \Si{15} is a 1-5-3-5-1 layer structure, and \Si{16} is a partially closed cage consisting of five-membered rings. The characteristic feature of these clusters is that they are all surface. Smalley and co-workers discovered that chemisorption reactivities of silicon clusters vary over three orders of magnitude as a function of cluster size. In particular, they found that \Si{33}, \Si{39}, and \Si{45} clusters are least reactive towards various reagents compared to their immediate neighbors in size. We provide insights into this observed reactivity pattern through our stuffed fullerene model. This structural model consists of bulk-like core of five atoms surrounded by fullerene-like surface. Reconstruction of the ideal fullerene geometry gives rise to four-fold coordinated crown atoms and $π$-bonded dimer pairs. This model yields unique structures for \Si{33}, \Si{39}, and \Si{45} clusters without any dangling bonds and thus explains their lowest reactivity towards chemisorption of closed shell reagents. We also explain why a) these clusters are substantially unreactive compared to bulk surfaces and b) dissociative chemisorption occurs on bulk surfaces while molecular chemisorption occurs on cluster surfaces. Finally, experiments on Si$_x$X$_y$ (X = B, Al, Ga, P, As, AlP, GaAs) are suggested as a means of verifying the proposed model.

chem-ph↗

arXiv1995

Growth Pattern of Silicon Clusters

Tight-binding molecular dynamics simulated annealing technique is employed to search for the ground state geometries of silicon clusters containing 11-17 atoms. These studies revealed that layer formation is the dominant growth pattern in all these clusters. Fullerene-like precursor structures consisting of fused pentagon rings are also observed. The atoms in all these clusters exhibit pronounced preference for residing on the surface.

chem-ph↗

arXiv1995

Structure of Silicon Clusters

We determined the structures of silicon clusters in the 11-14 atom size range using the tight-binding molecular dynamics method. These calculations reveal that \Si{11} is an icosahedron with one missing cap, \Si{12} is a complete icosahedron, \Si{13} is a surface capped icosahedron, and \Si{14} is a 4-4-4 layer structure with two caps. The characteristic feature of these clusters is that they are all surface.

chem-ph↗

arXiv1994

Chemical Reactions of Silicon Clusters

Smalley and co-workers discovered that chemisorption reactivities of silicon clusters vary over three orders of magnitude as a function of cluster size. In particular, they found that \Si{33}, \Si{39}, and \Si{45} clusters are least reactive towards various reagents compared to their immediate neighbors in size. We explain these observations based on our stuffed fullerene model. This structural model consists of bulk-like core of five atoms surrounded by fullerene-like surface. Reconstruction of the ideal fullerene geometry gives rise to four-fold coordinated crown atoms and $π$-bonded dimer pairs. This model yields unique structures for \Si{33}, \Si{39}, and \Si{45} clusters without any dangling bonds and thus explains their lowest reactivity towards chemisorption of closed shell reagents. This model is also consistent with the experimental finding of Jarrold and Constant that silicon clusters undergo a transition from prolate to spherical shapes at \Si{27}. We justify our model based on an in depth analysis of the differences between carbon and silicon chemistry and bonding characteristics. Using our model, we further explain why dissociative chemisorption occurs on bulk surfaces while molecular chemisorption occurs on cluster surfaces. We also explain reagent specific chemisorption reactivities observed experimentally based on the electronic structures of the reagents. Finally, experiments on \Si{x}X$_y$ (X = B, Al, Ga, P, As, AlP, GaAs) are suggested as a means of verifying the proposed model. We predict that \Si{x}(AlP)$_y$ and \Si{x}(GaAs)$_y$ $(x = 25, 31, 37; y = 4)$ clusters will be highly inert and it may be possible to prepare macroscopic samples of these alloy clusters through high temperature reactions.

chem-ph↗

arXiv1994

Magic Numbers of Silicon Clusters

A structural model for intermediate sized silicon clusters is proposed that is able to generate unique structures without any dangling bonds. This structural model consists of bulk-like core of five atoms surrounded by fullerene-like surface. Reconstruction of the ideal fullerene geometry results in the formation of crown atoms surrounded by $π$-bonded dimer pairs. This model yields unique structures for \Si{33}, \Si{39}, and \Si{45} clusters without any dangling bonds and hence explains why these clusters are least reactive towards chemisorption of ammonia, methanol, ethylene, and water. This model is also consistent with the experimental finding that silicon clusters undergo a transition from prolate to spherical shapes at \Si{27}. Finally, reagent specific chemisorption reactivities observed experimentally is explained based on the electronic structures of the reagents.

cond-mat↗

arXiv1994

Magic Numbers of Silicon Clusters

chem-ph↗