重子声学振荡In cosmology.docx

重子声学振荡In cosmology, baryon acoustic oscillations (BAO) refers to an overdensity or clustering of baryonic matter at certain length scales due to acoustic waves which propagated in the early universe.1 In the same way that supernova experiments provide a standard candle for astronomical observations,2 BAO matter clustering provides a standard ruler for length scale in cosmology.1 The length of this standard ruler (150 Mpc in todays universe3) can be measured by looking at the large scale structure of matter using astronomical surveys.3 BAO measurements help cosmologists understand more about the nature of dark energy (the acceleration of the universe) by constraining cosmological parameters.1 宇宙学中,重子声学振荡(BAO)是指由于声波在早期宇宙中传播而在一定尺度上形成的高密度区域或者重子物质的结团.超新星实验为天文学观测提供了一个”标准烛光”,与此相同,BAO造成的物质结团在宇宙学中为长度提供了一个”标准尺度”.这个标准尺度的的长度(在今天的宇宙中大概是1.5亿秒差距)可以通过天文巡天查看物质的大尺度结构来测量.BAO的测量通过限制宇宙学参数的方式来帮助宇宙学家了解更多的暗能量(即宇宙的加速膨胀)的本性.Contents1 The Early Universe2 Cosmic Sound3 Standard Ruler4 BAO Signal in the Sloan Digital Sky Survey5 BAO and Dark Energy Formalism 5.1 General Relativity and Dark Energy 5.2 Measured Observables of Dark Energy6References7 External links目录1 早期宇宙2 宇宙的声音3 标准尺度4 斯隆数字巡天(Sloan Digital Sky Survey)中的BAO信号5 BAO与暗能量的公式化形式 5.1广义相对论与暗能量 5.2 暗能量的可测量性6 参考文献7 外部链接The Early Universe早期宇宙The early universe consisted of a hot, dense plasma of electrons and baryons (protons and neutrons). Photons (light particles) traveling in this universe were essentially trapped, unable to travel for any considerable distance before interacting with the plasma via Thomson scattering.4 As the universe expanded, the plasma cooled to below 3000 Ka low enough energy such that the electrons and protons in the plasma could combine to form neutral hydrogen atoms. This recombination happened when the universe was around 400,000 years old, or at a redshift of z = 1100.4 Photons rarely interact with neutral matter, therefore at recombination the universe suddenly became transparent to photons, allowing them to decouple from the matter and free-stream through the universe.4 In other-words, the mean free path of the photons became on the order of the size of the universe. The cosmic microwave background (CMB) radiation is light emitted after recombination which is only now reaching our telescopes. Therefore when we look at Wilkinson Microwave Anisotropy Probe (WMAP) data, we are looking back in time to see an image of the universe when it was only 400,000 years old.4 早期宇宙由一种热的,致密的电子和重子(质子和中子)的等离子体构成.在这样的宇宙中,光子(轻的粒子)的传播基本上会被阻挡住,在通过汤姆逊散射跟等离子体相互作用之前根本无法传播.随着宇宙的膨胀,等离子体的温度降至3000开以下-该温度足够低以至等离子体中的电子跟质子可以结合成中性的氢原子.这个再复合的过程发生在宇宙的年龄约40万年的时候,也即红移1100的时候.光子几乎不跟中性物质发生相互作用,因此对光子来说,在再复合的时候宇宙骤然透明,从而使其从物质退耦并在宇宙中自由流动.换句话说,光子的平均自由程成为跟宇宙尺度一个数量级的.宇宙微波背景辐射(cosmic microwave background, CMB)是再复合之后发出的光线,并且刚刚到达我们的望远镜.因此当我们查看威尔金森微波各向异性探测器(Wilkinson Microwave Anisotropy Probe, WMAP)的数据的时候,我们是在沿着时间往回看一幅宇宙年龄只有40万年的时候的图像. Figure 1: Temperature anisotropies of the CMB based on the five year WMAP data.5图一: 基于WMAP五年数据的CMB温度各向异性图.WMAP indicates (Figure 1) of a smooth, homogeneous universe with density anisotropies of one part in 105.4 However, when we observe the universe today we find large amounts of structure and density fluctuations. Galaxies, for instance, are 106 times more dense than the universes mean density.6 The current belief is that the universe was built in a bottom-up fashion, meaning that the small anisotropies of the early universe acted as gravitational seeds for the structure we see today. Overdense regions attract more matter, while underdense regions attract less, and thus these small anisotropies we see in the CMB become the large scale structures we observe in the universe today. WMAP展示了(图一)一个平滑的,均匀的宇宙,带有十万分之一的密度各向异性.然而,当我们观测今天的宇宙的时候,我们发现有大量的结构和密度涨落.比如星系,其密度比宇宙的平均密度要大100万倍.现在人们认为,宇宙以自下而上的方式建成,就是说早期宇宙中那些小的密度的各向异性就起到了今天我们看到的结构的引力种子的作用.高密度的区域吸引更多的物质,而低密度的区域吸引的更少,因此这些我们在CMB上看到的小的各向异性变成了我们今天在宇宙中看到的大尺度结构.Cosmic Sound宇宙的声音Imagine an overdense region of the primordial plasma. While overdensity gravitationally attracts matter towards it, the heat of photon-matter interactions creates a large amount of outward pressure. These counteracting forces of gravity and pressure create oscillations, analogous to sound waves created in air by pressure differences.3 设想一个原初等离子体的高密度区域.尽管高密度区域通过引力将物质吸引向自己,光子和物质相互作用的加热产生了强大的向外的压强.这些方向相反的引力和压强产生了振荡,跟空气中的压强差产生声波一样.Consider a single wave originating from this overdense region in the center of the plasma. This region contains dark matter, baryons and photons. The pressure results in a spherical sound wave of both baryons and photons moving with a speed slightly over half the speed of light89 outwards from the overdensity (Figure 2, row 1). The dark matter only interacts gravitationally and so it stays at the center of the sound wave, the origin of the overdensity. Before decoupling, the photons and baryons move outwards together (Figure 2, rows 2-3). After decoupling (Figure 2, row 4) the photons are no longer interacting with the baryonic matter so they diffuse away (Figure 2, rows 5-6). This relieves the pressure on the system, leaving a shell of baryonic matter at a fixed radius. This radius is often referred to as the sound horizon.3 Without the photo-baryon pressure driving the system outwards, the only remaining force on the baryons is gravitational. Therefore, the baryons and dark matter (still at the center of the perturbation) form a configuration which includes overdensities of matter both at the original site of the anisotropy and in a shell at the sound horizon (Figure 2, row 7-8).3 考虑起源于等离子体中心的高密度区域的一个波.该区域包含暗物质,重子还有光子.压强生成了一个重子和光子的球面波,以约为光速一半的速度从高密度区域向外传播(图2第一行).暗物质仅通过引力进行相互作用,所以其呆在声波的中心,也即声波起源的高密度区域.退耦之前,重子跟光子一起向外运动(图二,第二到三行).退耦之后(图二,第四行)光子不再跟重子物质发生相互作用,所以它们弥散开来(图二,第五到六行).这个过程降低了作用在这个系统上的压强,在一定的半径处留下了一个重子物质的壳.这个半径即通常所指的声学视界.失去了光子-重子的压强向外驱动整个系统,唯一还留在重子上的力就是引力.因此,重子和暗物质(仍然呆在扰动的中心)形成了这样的一个轮廓,即包含有这个各向异性起源处的高密度物质和声学视界处的高密度的物质(图二,第七到八行).The ripples in the density of space (shown at the bottom of Figure 2) continue to attract matter and eventually galaxies formed in a similar pattern, therefore one would expect to see a greater number of galaxies separated by the sound horizon than by nearby length scales.3 This particular configuration of matter occurred at each anisotropy in the early universe, and therefore the universe is not composed of one sound ripple, but many overlapping ripples. As an analogy, imagine dropping many pebbles into a pond and watching the resulting wave patterns in the water.6 It is not possible to observe this preferred separation of galaxies on the sound horizon scale by eye, but one can measure this signal statistically by looking at the separations of large numbers of galaxies. 空间密度的涟漪持续吸引物质(如图二的底部所见),并且最终星系以相似的方式形成,因此人们期望看到大量的以声学视界而非近邻尺度为间距的星系.这种特殊的物质轮廓在早期宇宙中任意的各向异性尺度上都会产生,因此宇宙并非仅由一个声波的涟漪构成,而是由许多的涟漪叠加在一起.类似地可以这样想像,把许多的石子扔进一个池塘并观察水中最终的波纹的特征.这种以声学视界为长度的星系间距的首选尺度不可能直接被眼睛看到,但是人们可以通查看大量的星系之间的距离来以统计的方式来测量到这一信号. Figure 2: BAO soundwave propagating outward from a single overdensity over time. The baryon density is shown in the left-most column, the photon density is in the middle column, and a graph of the mass profiles are in the right-most column.7图二:BAO的声波随着时间从一个高密度处向外传播.最左边的一列展示了重子的密度,中间那列为光子的密度,最右边则为质量轮廓的图解.Standard Ruler标准尺度The physics of the propagation of the baryon waves in the early universe is fairly simple, so cosmologists can predict the size of the sound horizon at recombination. In addition the CMB provides a measurement of this scale to high accuracy.3 However in the time between present day and recombination the universe has been expanding. This expansion is well supported by observations and is one of the foundations of the Big Bang Model. In the late 90s, observations of supernova2 determined that not only is the universe expanding, it is expanding at an increasing rate. Better understanding the acceleration of the universe, or dark energy, has become one of the most important questions in cosmology today. In order to understand the nature of the dark energy, it is important to have a variety of ways of measuring this acceleration. BAO can add to the body of knowledge about this acceleration by comparing observations of the sound horizon today (using clustering of galaxies) to the sound horizon at the time of recombination (using the CMB).3 Thus BAO provides a measuring stick with which to better understand the nature of the acceleration, completely independent from the supernova technique. 早期宇宙中重子声波传播的物理过程相当简单,因此宇宙学家可以预言再复合时期的声学视界的尺度.此外,CMB提供了对这个尺度的高精度的测量.然而,在今天到再复合时期之间的时间内,宇宙一直在膨胀.宇宙的膨胀得到了观测的很好的支持,并且是大爆炸模型的基石之一.90年代后期,超新星的观测指出宇宙不仅在膨胀,而且在加速膨胀.加深对宇宙加速膨胀,或说暗能量的了解,已经成为现今宇宙学中最重要的问题之一.为了了解暗能量的本性,用多种方法测量这种加速就非常重要.通过把对现在的声学视界的观测(通过星系的成团性)跟再复合时期的声学视界的尺度(通过CMB)进行比对,BAO可以增加人们关于这种加速过程的知识.所以BAO提供的这种测量可以使人们更好地理解这种加速的本质,而且这是一种完全独立于超新星的方法.BAO Signal in the Sloan Digital Sky Survey斯隆数字巡天中的BAO信号The Sloan Digital Sky Survey (SDSS) is a 2.5-m wide-angle optical telescope at Apache Point Observatory in New Mexico. The goal of this five-year survey was to take images and spectra of millions of celestial objects. The result of compiling the Sloan data is a three-dimensional map of the objects in the nearby universe. The SDSS catalog provides a picture of the distribution of matter such that one can search for a BAO signal by seeing if there is a larger number of galaxies separated at the sound horizon. 斯隆数字巡天(SDSS)是一个2.5米的宽视场光学望远镜,位于新墨西哥州的Apache Point天文台.这项耗时五年的巡天项目的目的是拍摄上百万天体的图像和光谱.编纂斯隆数据的结果就是得到一个三维的近邻宇宙中天体的三维图.SDSS星表提供了一个物质分布的图像以使人们能够通过看是否存在大量的间距为声学视界的星系来搜寻BAO信号.The Sloan Team looked at a sample of 46,748 luminous red galaxies (LRGs), over 3816 square-degrees of sky (approximately five billion light years in diameter) and out to a redshift of z = 0.47.3 They analyzed the clustering of these galaxies by calculating a two-point correlation function on the data.10 The correlation function () is a function of comoving galaxy separation distance (s) and describes the probability that one galaxy will be found within a given distance bin of another (See SDSS Detection Figure).11 One would expect a high correlation of galaxies at small separation distances (due to the clumpy nature of galaxy formation) and a low correlation at large differences. The BAO signal would show up as a bump in the correlation function at a comoving separation equal to the sound horizon. This signal was detected by the SDSS team in 2005.3. SDSS confirmed the WMAP results that the sound horizon is 150 Mpc in todays universe.3 斯隆团队检视了一个包含46748个亮红星系(luminous red galaxies, LRG)的样本,这些样本分布于超过3816平方度的天区上(直径约50亿光年)并远至红移0.47.他们通过计算两点相关函数的方式分析了这些星系的成团性.相关函数 ()是星系的共动间距的函数并且描述了在距离一个星系一定的尺度内找到另一个星系的几率(参见斯隆探测的图).人们期望星系在小的间距上有强的相关性(由于星系形成的结团性质)而在大尺度的距离上相关性则比较低.BAO信号则表现为相关函数在等于声学视界的尺度处的一个突起.这一信号在2005年被斯隆团队探测到.SDSS证实了WMAP的关于在今天的宇宙中声学视界的尺度约为1.5亿秒差距的结果.BAO and Dark Energy FormalismBAO与暗能量的公式化形式General Relativity and Dark Energy广义相对论与暗能量In general relativity, the acceleration of the universe is parametrized by a scale factor a(t) which is related to redshift:4广义相对论中,宇宙的加速度通过尺度因子来参数化,尺度因子通过如下的公式跟红移联系起来: a(t)=(1+z(t)-1file:/Users/yuebin/Documents/Fanyi/Baryon_acoustic_oscillations_files/ff0508349e854deeda22d77f9c6206c0.png The Hubble parameter, H(z), in terms of the scale factor is:哈勃参数,H(z),以尺度因子来表示为: H(t)=fracdot a a file:/Users/yuebin/Documents/Fanyi/Baryon_acoustic_oscillations_files/4a6a63a6d28e80301879e8036d8c2a49.pngwhereis the time-derivative of the scale factor. The Friedmann equations express the expansion of the universe in terms of Newtons gravitational constant, GN, the mean pressure, P, the Universes density , the curvature, k, and the cosmological constant, :4其中 是尺度因子对时间的导数.弗里德曼方程用牛顿引力常数G_N,平均压强P,宇宙密度,曲率k和宇宙学常数的形式表示出了宇宙的膨胀:file:/Users/yuebin/Documents/Fanyi/Baryon_acoustic_oscillations_files/15f8400c33bd7efd9acaa8d3e6b4bfd6.pngfile:/Users/yuebin/Documents/Fanyi/Baryon_acoustic_oscillations_files/fa4eb64bebf93f540cd1d8b2f15d2577.pngH2=left(fracdot aaright)2=frac8pi G3rho-frackc2a2+fracLambda c23.dot H+H2=fracddot aa=-frac4pi G3left(rho+frac3pc2right)+fracLambda c23Observational evidence of the acceleration of the universe implies that (at present time) . Therefore the following are possible explanations:12宇宙加速膨胀的观测证据表明(今天的时间).因此以下为可能的解释:The universe is dominated by some field or particle that has negative pressure such that the equation of state:宇宙被某种具有负的压强的场或者粒子主宰,其状态方程为:file:/Users/yuebin/Documents/Fanyi/Baryon_acoustic_oscillations_files/151bd542b0dc745fb022e50f706fe622.pngw=fracPrho -1/3There is a non-zero cosmological constant, .宇宙学常数不为0.General relativity is incorrect and therefore the Friedmann equations are not applicable.广义相对论是错误的,因此弗里德曼方程不适用.In order to differentiate between these scenarios, precise measurements of the Hubble parameter as a function of redshift are needed.为了在这些观点之间做出区分,就需要精确测量哈勃常数作为红移的函数.Measured Observables of Dark Energy暗能量的可测量性The density parameter, , of various components, x, of the universe can be expressed as ratios of the density of x to the critical density, rho_c:12宇宙各种组分x的密度参数可以表示为x的密度跟临界密度rho_c之间的比率:file:/Users/yuebin/Documents/Fanyi/Baryon_acoustic_oscillations_files/dc3dda15b67217abf527c835b42a51cb.pngfile:/Users/yuebin/Documents/Fanyi/Baryon_acoustic_oscillations_files/42f19a811be890e47190ad9b30489927.pngrho_c=frac3H28pi GOmega_x=fracrho_xrho_c=frac8pi G rho_x3H2The Friedman equation can be rewritten terms of the density parameter. For the current prevailing model of the universe, CDM, this equation is as follows:12弗里德曼方程可以表示为密度参数的形式.就目前流行的宇宙模型,来说,此方程如下:file:/Users/yuebin/Documents/Fanyi/Baryon_acoustic_oscillations_files/b6d51483c6be4cd5f279c46a7854691f.pngH2(a)=left(fracdot aqright)=H_02leftOmega_m a-3+Omgea_r a-4+Omega_k a-2+Omega_Lambda a-3(1+w)rightwhere m is matter, r is radiation, k is curvature, is dark energy, and w i