三点相关函数研究进展

三点相关函数或傅里叶空间的重谱(bispectrum)是研究由引力不稳定性演化产生的大尺度结构非高斯性质的最低阶统计量。介绍了相关函数的基本理论知识;结合观测和数值模拟的测量结果,以及暗晕模型预言的三点相关函数,阐述了三点相关函数及其傅里叶变换的重谱的研究进展。     

强IRAS远红外源的CO谱线观测

用紫金山天文台青海站的１３７ｍ射电望远镜对２７个强ＩＲＡＳ远红外源（流量Ｆ１００μｍ５００Ｊｙ）进行了ＣＯ（１－０）的谱线观测．观测表明,２７个强ＩＲＡＳ源全部与分子云成协,并与大质量星的形成或早期演化有关．其中１３个源是第一次给出ＣＯ（１－０）的谱线测量结果．本文对这一类源ＣＯ发射的性质进行了简单的讨论．     

LAMOST二维光纤光谱抽谱方法的研究

对LAMOST二维光纤光谱数据处理系统中的抽谱方法进行了阐述,分析了抽谱中关键参数采样点选取对结果的影响,并根据高斯分布函数的特性以及实验情况确定了采样点的选取范围,解决了抽谱结果出现负值的问题.进一步针对大噪声背景下抽谱存在误差较大的问题,提出了基于频域滤波思想的改进抽谱方法.首先利用快速傅立叶变换和低通滤波器将影响光纤实际轮廓的尖锐噪声滤除,然后再进行正常的抽谱.利用LAMOST二维光纤光谱数据处理系统提供的模拟数据进行了实验测试,结果表明改进抽谱方法的可行性与有效性.     

AO0235＋164射电波段宽带谱指数周期性变化的研究

收集了AO0235＋164天体射电4．8GHz和14．5GHz波段的光变测量数据,并获得了长期的光变曲线,从光变曲线可以看出其活动是非常剧烈的。利用Jurkevieh方法和自相关函数方法分别对AO0235＋164射电波段宽带谱指数进行周期性分析,并对流量和谱指数进行相关性分析,研究结果表明：（1）AO0235＋164天体射电波段4．8GHz-14．5GHz对应的宽带谱指数,可能存在5．30年的光变周期,与Liu等人用功率谱法在射电波段发现其流量密度可能存在5．59±0．47年的光变周期基本吻合;（2）宽带谱指数与流量密度之间存在相关性。     

强IRAS远红外源的CO谱线预测

用紫金山天台青海站的１３．７ｍ射电望远镜以２７个强ＩＲＡＳ远红外源（流量Ｆ１００μｍ≤５００Ｊｙ）进行了ＣＯ（１－０）的谱线预测。观测表明,２７个强ＩＩＲＡＳ源全部与分子云成协,产与大质量星的形成或早期演化有关。其中１３个源是第一次给出ＣＯ（１－０）的谱线测量结果,本对这一类源ＣＯ发射的性质进行了简单的讨论。     

恒星自转的引力昏暗效应对谱线的影响

对于快速自转的恒星,谱线的等值宽度（ＥＷ）受引力昏暗效应的影响,即使自转速度达到临界也是很小的;而谱线半宽（ＦＷＨＭ）受引力昏暗效应影响相对较大,在（ω≈０．９９）时,相对变化达到８％．对于光谱型在Ｂ０～Ｂ９范围内的主序星,谱线半宽的相对变化在自转速度较小时（ω＜０．８）与光谱型无关;在自转速度较大时（ω≈０．９９）,谱线半宽的相对变化随光谱次型的增加而下降．     

修改引力宇宙学下的大尺度结构非线性演化

主要研究了修改引力论在非线性尺度上的表现。现在已经存在很多修改引力论的模型,如f（R）,DGP,Mond等,但是在工作中并没有使用别人已经提出的修改引力论方法,因为首先不可能去对所有的修改引力论模型都进行研究;其次重点研究的是修改引力对于宇宙中的物质分布在非线性尺度上的影响,而各种修改引力论对于物质聚集的影响是相似的,都可以通过一个参数表达出来。因此笔者提出一种修改引力论的方法,引进了一个简单参数ζ。这个参数ζ定义为G_eff/G/-φ/Ψ,这里G_eff是有效牛顿常数,G是牛顿常数,φ和Ψ则是时空度规的标量扰动方程中的两个势。这个ζ参数在广义相对论的基础上修改了物质粒子受到的加速度,加大或者减小这个参数会相应地改变物质粒子的加速度,进而会加快或者减慢大尺度结构的形成。这种对大尺度结构在线性尺度上的影响可以通过理论计算得到,但是大尺度结构的非线性增长无法通过理论计算得出,现在只有借助已经发展得比较成熟的数值模拟方法来研究这个问题。该文修改了现在已经比较成熟的数值模拟程序GADGET-2,加入了ζ参数。在进行数值模拟之前,首先检验了数值模拟的质量分辨率、模拟尺度,以及初始红移对最终物质功率谱的影响,并且证实修改后的GADGET-2程序是正确的。设定不同ζ参数的值,ζ=0.8,0.9,1.0,1.1,1.2,1.5,这里ζ=1.0对应标准宇宙学,然后对每个ζ值运行了一组数值模拟。为了减少数值效应对最终结果的影响,并且突出显示修改引力论在非线性尺度上的表现,没有简单直接地使用不同ζ值物质功率谱来做比较,而是精巧地设置不同ζ值的输出红移,使不同ζ值在其对应的输出红移处有相同的线性功率谱,并且最终使用了ξ=ζ≠1.0/ζ=1.0这个比值参数来研究修改引力论在非线性尺度上的表现。通过宇宙学尺度上的数值模拟和高精度的小波物质功率谱方法,我们研究了ζ参数对物质在非线性尺度上增长的影响。通过ξ这个参数,在线性功率谱相同的时候,比较了不同ζ参数的功率谱在非线性尺度上相对于标准宇宙学模型的偏离。得到重大的发现:大尺度结构在非线性上的增长并不是想象的那样,较大的ζ参数加大了物质粒子的加速度,进而在线性和非线性尺度上都加快了结构形成,反而是在线性功率谱相同的时候,较大值的ζ给出了较小的非线性功率谱。这个发现也证明HKLM假定的不正确,从而证明基于这个假定的功率谱拟合公式（PD96,Smith2003）不适用于修改引力论,直接将这些功率谱拟合公式推广到修改引力论是不正确的。基于这个ζ参数的修改引力论模型,利用一系列的数值模拟的结果,为修改引力论提出了一个新的拟合公式。这个新的拟合公式不是对现有的这些拟合公式做推广,而是借助于标准宇宙学下的非线性功率谱,通过几个简单的参数就可以得到对应不同ζ值的非线性功率谱,而且其精度保证在5%以内。利用这套数值模拟的结果,我们进而研究ζ修改引力论下的本动速度场的功率谱、暗晕的质量方程,以及暗晕的性质。这些工作为我们从观测上区分修改引力论和广义相对论提供了理论指导。     

恒星自转的引力昏暗效应对谱线的影响

对于快速自转的恒星,谱线的等值宽度（ＥＷ）受引力昏暗效应的影响,即使自转速度达到临界也是很小的,而谱线半宽（ＦＷＨＭ）受引力昏暗效应影响相对较大,在（ｗ＝０．９９）时,相对变化达到８％。对于光谱型在Ｂ０￣Ｂ９范围内的主序星,谱线半宽的相对变化在自转速度较小时（ｗ〈０．８）与光谱型无关,在自转速度较大时（ｗ＝０．９９）,谱线半宽的相对变化随光谱次型的增加而下降。     

球状星团系统的比频、金属度和质量谱

评述了球状星团系统研究中的比频、金属度和质量谱三大问题，就目前的认识和存在的问题进行了讨论。指出不同星系球状星团比频之间的差别表明了需要有各种不同的球状星团形成模型；球状星团金属度的分布表明球状星团可能有三个形成时期，分别与三类形成模型效应；尽管对数正态初始质量的数值模拟初步结果与观测结果符合得更好，然而幂函数的初始质量谱在物理上能很好地与球状星团形成联系起来。     

BL Lac天体的谱性质

研究了等离子体反应堆模型,统一解释活动星系核的辐射性质,特别是ＢＬＬａｃ天体的谱性质．具体的物理过程是:大量相对论电子从中心天体注入周围的等离子体反应堆中,通过同步辐射快速损失能量,同时这些电子同步吸收反应堆中不透明的光子,产生一个稳定、各向同性的幂律分布,其谱指数为γ＝３;然后,这些相对论电子通过等离子体反应堆的爆发或其表面扩散过程逃逸出来,产生低频的同步辐射;来自等离子体反应堆的高频辐射表现出快速的谱变化,即流量减小时谱变陡．另外,还详细分析了具有辐射损失和相对论电子注入的同步辐射源的性质．     

The non-linear bispectrum with initial spectral index −1

Bispectrum, or three-point correlation function in Fourier space, is the lowest order non-Gaussian statistic to study the large-scale structure produced by gravitational instability. In Fourier space, the 2-dimensional density field has the same statistical properties as the 3-dimensional field, and compared with the 3-dimensional fast Fourier transform (FFT), the 2-dimensional FFT can save a lot of computer resources. In a combination of 2- and 3-dimensional FFTs and using a high-resolution N-body numerical simulation with the initial spectral index -1, we have measured the bispectrum from the weakly linear regime to the strongly nonlinear regime. All possible effects of numerical artefacts on the power spectrum and bispectrum, such as particle discreteness, force softening, finite box size and alias effect, are considered and strictly corrected. In contrast with what previous researchers assumed, it is revealed that the reduced bispectrum depends on the triangle shape and scale even in the strongly nonlinear regime, and increases with the wave number. And based on the measured results, a new fitting formula for the bispectum suitable for cosmological models with an initial spectral index −1 is obtained.     

FAst STatistics for weak Lensing (FASTLens): fast method for weak lensing statistics and map making

With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever-greater precision. However, this increased accuracy also places greater demands on the statistical tools used to extract the available information. To date, the majority of lensing analyses use the two-point statistics of the cosmic shear field. These can be either studied directly using the two-point correlation function or in Fourier space, using the power spectrum. But analysing weak lensing data inevitably involves the masking out of regions, for example to remove bright stars from the field. Masking out the stars is common practice but the gaps in the data need proper handling. In this paper, we show how an inpainting technique allows us to properly fill in these gaps with only   N log  N   operations, leading to a new image from which we can compute straightforwardly and with a very good accuracy both the power spectrum and the bispectrum. We then propose a new method to compute the bispectrum with a polar fft algorithm, which has the main advantage of avoiding any interpolation in the Fourier domain. Finally, we propose a new method for dark matter mass map reconstruction from shear observations, which integrates this new inpainting concept. A range of examples based on 3D N -body simulations illustrates the results.     

A fitting formula for the non-linear evolution of the bispectrum

We present a fitting formula for the non-linear evolution of the bispectrum in cold dark matter (CDM) models, obtained from measurements in high-resolution numerical simulations. The formula interpolates between the perturbative and highly non-linear regimes, and generalizes previous results obtained for scale-free initial conditions.     

Large-scale structure, the cosmic microwave background and primordial non-Gaussianity

Cosmic microwave background and large-scale structure data will shortly improve dramatically with the Microwave Anisotropy Probe and Planck Surveyor , and the Anglo-Australian 2-Degree Field and Sloan Digital Sky Survey. It is therefore timely to ask which of the microwave background and large-scale structure will provide a better probe of primordial non-Gaussianity. In this paper we consider this question, using the bispectrum as a discriminating statistic. We consider several non-Gaussian models and find that in each case the microwave background will provide a better probe of primordial non-Gaussianity. Our results suggest that if microwave background maps appear Gaussian, then apparent deviations from Gaussian initial conditions in galaxy surveys can be attributed with confidence to the effects of biasing. We demonstrate this precisely for the spatial bispectrum induced by local non-linear biasing.     

The three-point function in large-scale structure – I. The weakly non-linear regime in N-body simulations

This paper presents a comparison of the predictions for the two- and three-point correlation functions of density fluctuations, ξ and ζ , in gravitational perturbation theory (PT) against large cold dark matter (CDM) simulations. This comparison is made possible for the first time on large weakly non-linear scales (>10  h ⁻¹ Mpc) thanks to the development of a new algorithm for estimating correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the three-point statistics with simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as those presented here, were limited to small scales where leading-order PT gives a poor approximation. Here we also propose and apply a method for separating the first-order and subsequent contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime where simulations do reproduce the leading-order (tree-level) predictions of PT for the reduced three-point function   Q ₃∼ ζ / ξ ²  . For steeply decreasing correlations (such as the standard CDM model) deviations from the tree-level results are important even at relatively large scales, ≃20 Mpc  h ⁻¹. On larger scales ξ goes to zero and the results are dominated by sampling errors. In more realistic models (such as the ΛCDM cosmology) deviations from the leading-order PT become important at smaller scales   r ≃10 Mpc  h ^-1  , although this depends on the particular three-point configuration. We characterize the range of validity of this agreement and show the behaviour of the next-order (one-loop) corrections.     

Exact shearing box solutions of magnetohydrodynamic flows with resistivity, viscosity and cooling

Axisymmetric incompressible modes of the magnetorotational instability (MRI) with a vertical wavenumber are exact solutions of the non-linear local equations of motion for a disc (shearing box). They are referred to as 'channel solutions'. Here, we generalize a class of these solutions to include energy losses, viscous, and resistive effects. In the limit of zero shear, we recover the result that torsional Alfvén waves are exact solutions of the non-linear equations. Our method allows the extension of these solutions into the dissipative regime.
These new solutions serve as benchmarks for simulations including dissipation and energy loss, and to calibrate numerical viscosity and resistivity in the zeus3d code. We quantify the anisotropy of numerical dissipation and compute its scaling with time and space resolution. We find a strong dependence of the dissipation on the mean magnetic field that may affect the saturation state of the MRI as computed with zeus3d . It is also shown that elongated grid cells generally preclude isotropic dissipation and that a Courant time-step smaller than that which is commonly used should be taken to avoid spurious anti-diffusion of magnetic field.     

Gaussianity of the cosmic microwave background: smooth goodness-of-fit tests applied to interferometric data

We adapt the smooth tests of goodness-of-fit developed by Rayner and Best to the study of the non-Gaussianity of interferometric observations of the cosmic microwave background (CMB). The interferometric measurements (visibilities) are transformed into signal-to-noise ratio eigenmodes, and then the method is applied directly in Fourier space. This transformation allows us to perform the analysis in different subsets of eigenmodes according to their signal-to-noise ratio level. The method can also deal with non-uniform or incomplete coverage of the UV plane. We explore here two possibilities: we analyse either the real and imaginary parts of the complex visibilities (Gaussianly distributed under the Gaussianity hypothesis) or their phases (uniformly distributed under the Gaussianity hypothesis). The power of the method in discriminating between Gaussian and non-Gaussian distributions is studied by using several kinds of non-Gaussian simulations. On the one hand, we introduce a certain degree of non-Gaussianity directly into the Fourier space using the Edgeworth expansion, and afterwards the desired correlation is introduced. On the other hand, we consider interferometric observations of a map with topological defects (cosmic strings). To these previous non-Gaussian simulations we add different noise levels and quantify the required signal-to-noise ratio necessary to achieve a detection of these non-Gaussian features. Finally, we have also studied the ability of the method to constrain the so-called non-linear coupling constant f _NL using χ² simulations. The whole method is illustrated here by application to simulated data from the Very Small Array interferometer.     

Cosmological Perturbation Theory and the Spherical Collapse model — I. Gaussian initial conditions

We present a simple and intuitive approximation for solving the perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for tree-graphs (i.e. at leading order). We find that the non-linear evolution in Lagrangian space is then given by a simple local transformation over the initial conditions, although it is not local in Euler space. This transformation is found to be described by the spherical collapse (SC) dynamics, as it is the exact solution in the shearless (and therefore local) approximation in Lagrangian space. Taking advantage of this property, it is straightforward to derive the one-point cumulants, ξ_J, for both the unsmoothed and smoothed density fields to arbitrary order in the perturbative regime. To leading-order this reproduces, and provides us with a simple explanation for, the exact results obtained by Bernardeau. We then show that the SC model leads to accurate estimates for the next corrective terms when compared with the results derived in the exact perturbation theory making use of the loop calculations. The agreement is within a few per cent for the hierarchical ratios S _J  = ξ _J /ξ ^{J −1}₂. We compare our analytic results with N -body simulations, which turn out to be in very good agreement up to scales where σ ≈ 1. A similar treatment is presented to estimate higher order corrections in the Zel'dovich approximation. These results represent a powerful and readily usable tool to produce analytical predictions that describe the gravitational clustering of large-scale structure in the weakly non-linear regime.     

Accurate estimators of power spectra in N-body simulations

A method to rapidly estimate the Fourier power spectrum of a point distribution is presented. This method relies on a Taylor expansion of the trigonometric functions. It yields the Fourier modes from a number of fast Fourier transforms (FFTs), which is controlled by the order N of the expansion and by the dimension D of the system. In three dimensions, for the practical value   N = 3  , the number of FFTs required is 20.
We apply the method to the measurement of the power spectrum of a periodic point distribution that is a local Poisson realization of an underlying stationary field. We derive an explicit analytic expression for the spectrum, which allows us to quantify – and correct for – the biases induced by discreteness and by the truncation of the Taylor expansion, and to bound the unknown effects of aliasing of the power spectrum. We show that these aliasing effects decrease rapidly with the order N . For   N = 3  , they are expected to be, respectively, smaller than  ∼10⁻⁴  and 0.02 at half the Nyquist frequency and at the Nyquist frequency of the grid used to perform the FFTs. The only remaining significant source of errors is reduced to the unavoidable cosmic/sample variance due to the finite size of the sample.
The analytical calculations are successfully checked against a cosmological N -body experiment. We also consider the initial conditions of this simulation, which correspond to a perturbed grid. This allows us to test a case where the local Poisson assumption is incorrect. Even in that extreme situation, the third-order Fourier–Taylor estimator behaves well, with aliasing effects restrained to at most the per cent level at half the Nyquist frequency.
We also show how to reach arbitrarily large dynamic range in Fourier space (i.e. high wavenumber), while keeping statistical errors in control, by appropriately 'folding' the particle distribution.