本帖最后由 gohomeman1 于 2010-8-1 23:56 编辑
英文原文是<Nature>上的一篇文章.跟这篇文章相关的还有一个英文的新闻,<绿堤望远镜使用"强度映射技术"来揭示神秘的暗能量>
http://www.nsf.gov/news/news_summ.jsp?cntn_id=117366"
Hydrogen 21-cm Intensity Mapping at redshift 0.8
红移0.8处的中性氢21厘米辐射强度映射
Tzu-Ching Chang(1,2), Ue-Li Pen(2), Kevin Bandura(3), & Jeffrey B. Peterson(3)
张慈锦(1,2),彭威礼(2),Kevin Bandura(3), Jeffrey B. Peterson(3)
1 IAA, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan
2 CITA, University of Toronto, 60 St.George St., Toronto, ON, M5S 3H8, Canada
3 Department of Physics, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213,USA
1 中央研究院天文与天体物理研究所,台湾,台北市10617邮政23-141号信箱
2 多伦多大学加拿大理论天体物理研究所, 加拿大安大略省多伦多市圣乔治街60号,邮编M5S 3H8
3 卡耐基梅隆大学物理系,美国宾夕法尼亚州匹兹堡市福布斯大街5000,邮编15213
Observations of 21-cm radio emission by neutral hydrogen at redshifts z∼0.5 to∼2.5 are expected to provide a sensitive probe of cosmic dark energy(1,2). This is particularly true around the onset of acceleration at z∼1, where traditional optical cosmology becomes very difficult because of the infrared opacity of the atmosphere. Hitherto, 21-cm emission has been detected only to z=0.24(3). More distant galaxies generally are too faint for individual detections but it is possible to measure the aggregate emission from many unresolved galaxies in the ’cosmic web’. Here we report a three dimensional 21-cm intensity field at z=0.53 to 1.12. We then co-add HI emission from the volumes surrounding about ten thousand galaxies (from the DEEP2 optical galaxy redshift survey(4)). We detect the aggregate 21-cm glow at a significance of∼4 sigma.
通过对红移约0.5到2.5之间的中性氢的21厘米辐射进行观测,人们有望对宇宙中的暗能量进行一次灵敏的探测(参考文献1,2). 在红移约为1,也就是宇宙膨胀刚开始加速时这种方法特别有效,因为在这种情况下,传统的光学宇宙学由于地球大气的红外不透明度的影响而变得非常困难.迄今为止,人们对21厘米辐射的探测最远只到红移0.24处(参考文献3).更远的星系由于太暗弱而很难被单个地探测到,不过人们可以测量”宇宙网络 (cosmic web)”中许多不可分辨的星系的聚集辐射.我们在这里发布一个红移在0.53到1.12之间的3维的21厘米辐射场,然后一并在里面加上包含上万星系的体积内的中性氢辐射(来自DEEP2光学星系红移巡天(参考文献4)).我们认为我们在4个标准差的程度上探测到了星系的21厘米聚集光辉.
The DEEP2 optical redshift survey(4) provides a rich sample for study of the Universe at redshifts near one. The team recorded optical spectra for 50,000 faint galaxies out to redshift z = 1.4, utilizing the DEIMOS spectrograph on the Keck II telescope. The DEEP2 sample consists of four survey fields, each∼120’x30’ in size. Roughly 10,000 of the DEEP2 galaxies fall in the redshift range which overlaps the range of the radio data described below.
DEEP2 光学红移巡天(文献4)为研究红移1附近的宇宙提供了丰富的样本.利用凯克II望远镜上的DEIMOS摄谱仪,DEEP2的团队记录下了5万个暗弱星系的光谱,红移达到了1.4. DEEP2的样本由4个巡天区域组成,每个的角尺度约120’x30’.其中大约有1万个星系落在了跟下文将要描述到的射电观测数据重合的红移范围之内.
Using the Green Bank Telescope (GBT), we recorded radio spectra across two of the DEEP2 fields. We are searching for redshifted HI 21-cm emission, and for such emission the radio spectra span the redshift range 0.53 < z < 1.12. This corresponds to a comoving distance 1400 to 2600/h Mpc assuming a CDM cosmology(5). The full-width-half-maximum GBT beam is about 15’, which corresponds to 9 h−1 comoving Mpc at z = 0.8 so the angular resolution falls far short of that needed to separate one galaxy from the next. In the redshift dimension the spatial resolution is much higher than the transverse resolution. To keep the data set manageable we average in frequency to a resolution 430kHz, or 2/h comoving Mpc. Unlike the optical survey we make no attempt to detect individual galaxies with the radio data. More observational details can be found in the Supplementary Information Section 1.
我们使用绿堤射电望远镜(Green Bank Telescope, GBT)记录到了2倍DEEP2范围内的射电谱.我们在其中寻找红移之后的21厘米辐射,其发射时的红移在0.53到1.12之间.在冷暗物质(CDM) 宇宙模型下,其对应的共动距离在1400/h到2600/h兆秒差距之间(文献5). GBT波束的半高全宽(full-width-half-maximum)约15’, 在红移0.8时对应着9/h兆秒差距的共动尺度, 所以其分辨率远不足以把一个星系跟另一个星系分辨出来. 在红移的维度上其空间分辨率要远高于横向的分辨率.为了使这些数据易于处理,我们把频率的分辨率平均到了430kHz,或说2/h共动兆秒差距.不同于光学巡天,我们根本就没打算用射电的数据来探测单个的星系.更多观测细节可以在补充材料的第一部分中找到.
We have two goals for the radio observations. First, we examine whether it is possible to map the cosmic web in three dimensions, without detecting individual galaxies, a technique called ‘intensity mapping’. Second, we measure the 21 cm brightness and neutral gas density at high redshift. To accomplish the first goal we study the 21 cm data by itself. For the second goal we draw on the DEEP2 galaxy positions as guides, using them to locate likely bright spots of the 21 cm glow. If sufficient gas is present, and if the intensity mapping technique is viable, it will be possible to use this technique to economically map over 50 times the volume that has so far been surveyed.
我们的射电观测有两个目的.首先,我们要实验是否可以使用一种叫做”强度映射”的技术在不探测单个星系的情况下来绘出宇宙网络的三维图.其次,我们要测量高红移的21厘米辐射的亮度和中性气体的密度.为了实现第一个目标,我们只需要研究21厘米数据本身.而为了实现第二个目标,我们要画出DEEP2的星系位置作为向导,使用它们来定位可能的21厘米光辉的亮点.如果存在足够多的气体并且强度映射的技术是可行的话,人们就有可能使用这种技术绘出50倍当前巡天所能达到的体积的图.
To get to the 21 cm signal we must remove two much brighter sources of flux from the data, Radio Frequency Interference (RFI) from terrestrial transmitters and broadband (continuum) emission by astronomical sources within and outside of the Milky Way.
为了得到21厘米信号,我们必须把两个亮得多的源从数据里面移出去,也就是来自人造的发射装置的射频干扰和来自银河系内外的天文源的宽波段(或者连续谱)发射线.
We use polarization to identify and excise unwanted signals. Television, mobile telephone transmitters, and other terrestrial sources produce strongly polarized flux which remains polarized even after scattering. The GBT has two linearly polarized feed antennas at the focus of the parabolic reflector. RFI entering the feed antenna sidelobes produces signals in the data stream that correlate between the two polarization channels. 21-cm emission is not polarized, so we calculate the cross-correlation coefficient between the two polarizations and cut any flux with coefficient greater than 2%. This removes ∼5% of the data. The radio data, after this cut, is shown in the top panel of Figure 1. At this stage of the analysis astronomical continuum sources present a fluctuation of brightness temperature across the sky of rms amplitude∼125 mK, which is about a thousand times larger than the HI signal.
我们使用偏振来识别及去除不想要的信号.电视,移动电话发射塔,以及其它的人造的源会产生强偏振的辐射,即使在散射之后这些辐射依然是偏振的.GBT在抛物线反射面的焦点处有两个线偏振馈电天线.进入馈电天线旁瓣的射频干扰在数据流中产生的信号在两个偏振通道里互相关联.21厘米辐射是非偏振的,所以我们计算两个偏振的交叉相关系数,并去掉任何相关性大于2%的信号.这个过程删掉了约5%的数据.经过这个去除过程之后的信号,由图1中最上面一幅图展示出来.此时,天体的连续谱源表现为一个横跨天空的,均方差约为125毫开的亮温度扰动,比中性氢的信号大了约一千倍.
We remove astronomical continuum flux using a new matrix-based method(6). After a calibration procedure described in the Supplementary Information we arrange the data into a matrix in which the row index represents celestial coordinates, and the column index represents the observation frequency (redshift). All three panels in Figure 1 show such matrices. Continuum sources, including bright radio sources, blends of weak extragalactic sources, and Galactic synchrotron sources, extend across all columns of the matrix. They show up as horizontal stripes in the top panel of Figure 1. In contrast, 21-cm sources are tightly localized to a few columns. Within this matrix, a continuum source can be factored into a product of a function of position (for an isolated point source this is the beam pattern of GBT), and a low order function of frequency (the smooth spectrum),T(x,ν)=f(x)g(ν),The functions f(x) and g(ν) are singular eigenmodes of the matrix, so we perform a singular-value decomposition (SVD) to detect continuum flux, which we subtract. We are then left with the brightness temperature field Tb, shown in the middle panel of Figure 1. The SVD technique is non-parametric. No particular mathematical form for the spectra of the continuum sources is assumed.
我们使用一个新的基于矩阵的方法来移除天体的连续辐射(文献 6).在经过一个如补充材料中所描述的定标过程之后,我们用一个矩阵来存储这些数据,矩阵的行序表示天球坐标,而列序则代表观测到的频率(红移).图一中的三幅图都是这样的矩阵.连续辐射源,包括亮的射电源,混在一起的弱的河外源,以及银河系内的同步辐射源,会横跨矩阵所有的列,也就是图一最上面的那幅图中的水平横条.与此相对,21厘米源只是紧紧地局限于很少的几列之内.在这个矩阵之内,连续辐射源可以被因式分解为一个位置函数(对于孤立的点源来说这就是GBT的波束方向图)跟一个低阶的频率函数(平谱)的乘积,T(x,ν)=f(x)g(ν),函数f(x)和g(ν)是这个矩阵的奇异本征模,所以我们通过奇异值分解(singular-value decomposition, SVD)来探测连续辐射并将其扣除.然后我们就有了亮温度 Tb场,如图一的中间那幅图所示.SVD方法是不依赖于参数的.我们不需要为连续辐射源的谱假设某种特殊的形式.
We next examine the radio data without referring to the optical survey. After foreground subtraction, keeping only the component that is consistent over several days, we find the intensity field has a temperature fluctuation 464±277 μK
,on pixel scales of (2/h)^3 comoving Mpc^3, Note that our resolution element, (9/h)^3 comoving Mpc^3, is larger than the pixel. The noise in this measurement exceeds that expected from the antenna temperature and is likely due to residuals of emission by terrestrial transmitters and errors in the astronomical continuum removal process. Because of the weak statistical significance, this fluctuation amplitude should be treated an upper limit to the 21-cm brightness auto-correlation, rather than a detection of cosmic structure.
接下来我们在不参照光学巡天的情况下来检查射电的数据.在扣除掉前景并只保留数天内一致的成分之后,我们发现在每个像素对应着(2/h)^3共动立方兆秒差距的程度上,辐射强度场的温度涨落为464±277 μK, 请注意我们的分辨率是(9/h)^3共动立方兆秒差距,比这个像素要大.这个测量的噪音比期望中的来自天线温度的噪音要大,可能是人造发射器的残余辐射, 也可能是在移除天体连续辐射过程中的误差. 由于其统计显著性较弱,这个涨落应当被视为21厘米亮度自相关的上限,而不能说已经探测到了宇宙结构.
To further reduce uncertainty we proceed with the cross-correlation (stacking) technique. Cross-correlation reduces the error because terrestrial RFI and residuals of the continuum sources are randomly located compared to the locations of optically bright galaxies. To carry out the cross correlation we arrange the DEEP2 data in the same matrix as the radio data, as shown in Figure 1 . We calculate the weighted cross correlation between the data in the bottom two panels of the figure, producing the correlation function in Figure 2. We detect significant cross-correlation power out to lag 10/hcomoving Mpc.
为了进一步减小不确定性,我们接下来要使用交叉相关的技术.交叉相关之所以可以减小误差是因为人为的射频干扰以及连续辐射源的位置跟光学上亮的星系相比是随机的.为了做交叉相关,我们把DEEP2的数据也放在同样的矩阵里面,如图一所示.我们计算该图中下两幅图的加权交叉相关,其相关函数如图2所示.一直偏移到10/h共动兆秒差距,我们都探测到了相当可观的交叉相关.
To check this cross-correlation result we carry out a statistical null test. We randomize the optical redshifts many times, each time repeating the correlation calculation. We find no significant correlation in the randomized sets and we use the bootstrap variance to estimate the uncertainties in our measurements. The null test confirms that the residual RFI and astronomical continuum sources are unlikely to cause false detection of 21-cm emission.
为了检验这个交叉相关的结果,我们进行了一个零统计测试.我们多次随机分配光学红移,每次都重新计算相关性.在随机化后的数据中我们没有发现显著的相关性, 我们使用拔靴残差(bootstrap variance)来估计我们的测量的不确定性.零统计测试证实了残留的射频干扰跟天体的连续辐射不可能让我们探测到虚假的21厘米辐射.
The measured cross correlation can be compared to a model prediction. Locations of optically cataloged galaxies are known to be correlated amongst themselves, and 21-cm emission is also thought to originate in galaxies. We therefore model the cross-correlation by adopting the DEEP2 optical galaxy auto-correlation power law(7) ,ξ(R)=(R/R₀)^(-1.66),where R0 = 3.53/h Mpc at z=0.8, which we convolve with the telescope primary beam in the transverse direction. In the radial direction we must account for peculiar velocities. The pairwise velocity distribution is modeled as a Gaussian with standard deviation σ₁₂=395 km/sec,using the relationσ₁₂∼H(z)R₀.The expected correlation, calculated using this model, is plotted in Figure 2 using the best fit value of the correlation amplitude.
我们测量到的交叉相关可以跟一个模型的预言做比较.人们认为光学星表中的星系互相之间是相关联的,而21厘米辐射又是起源于星系的.我们假设DEEP2光学星系的自相关是一个幂律形式(文献7),ξ(R)=(R/R₀)^(-1.66),其中在红移0.8处R0=3.53/h 兆秒差距,在切向我们把这个相关函数跟望远镜的初始波束做卷积.而在径向,我们就必须考虑本动速度。相对速度分布(pairwise velocity distribution)满足高斯分布,由关系σ₁₂∼H(z)R₀,(文献7,8)得出其标准偏差是σ₁₂=395 km/sec.图二给出了使用这个模型计算出的最佳拟合的交叉相关值.
We use the correlation amplitude to constrain the neutral hydrogen density at redshift 0.8. The cross-correlation \xi between the optical galaxy density field and the neutral hydrogen temperature field is related to the density structure by (e.g.,1)
where \Delta T_b is the neutral hydrogen 21-cm brightness temperature fluctuations, Tb = 284 μK is the 21-cm mean sky brightness temperature at z = 0.8,ΩHI=ρHI/ρc,0 is the HI density over the present-day critical density,\Omega_m the matter density, and h is the current expansion rate in units of 100 km/s Mpc−1. \delta_{opt} is the optical density field, which is related to the neutral hydrogen density field,δHI=brδ_opt,where b=<δ²HII>½/<δ²opt>½ is the bias factor, and r=<δHIδopt>/(<δ²HI><δ²opt>)^½ is the stochasticity. Note that |r|<=1,and our data show r to be positive. The effective \delta^2_{opt} values for DEEP2 Field-3 and Field-4 calculated with simulations described in Supplementary Information are 2.3 and 3.3, respectively. A cosmic hydrogen fraction ρHI/ρ_b=0.75 is assumed.
我们使用相关程度来限制红移0.8处的中性氢密度.光学星系密度场跟中性氢温度场之间的交叉相关跟密度结构的关系为(来自文献1)
其中ΔΤb 是中性氢21厘米亮温度涨落,Tb = 284微开是红移0.8处天空的21厘米平均亮温度. ΩHI=ρHI/ρc,0 为中性氢的密度除以今天的临界密度,\Omega_m 是物质密度,h是现在宇宙的膨胀速率,以100千米每秒每兆秒差距为单位.\delta_{opt}是光学密度场,跟中性氢密度场的关系为 δHI=brδ_opt ,其中 是偏袒系数,而 是随机性。请注意|r|<=1,而且我们的数据表明r为正值.用补充材料中的数值模拟计算的DEEP2 的场-3和场-4的等效的(δopt)^2 分别为2.3和3.3.在这里我们假设宇宙中氢的比例是ρHI/ρ_b=0.75.
The correlation function at zero lag has a 21-cm brightness temperature 157±42 μK ,at a mean effective redshift of z = 0.8, from which we infer a value of ΩHI=(5.5±1.5)×10^-4×(1/rb) .Combining all data in Figure 2, the statistical significance of the detection is at the four sigma level.
在平均的等效红移0.8处,零偏移处的相关函数对应的21厘米亮温度是157±42 μK ,我们据此得出 ΩHI=(5.5±1.5)×10^-4×(1/rb).把图二中所有的数据合在一起的话,我们的统计显著性在四个标准差的水平.
The cross correlation technique measures only the 21-cm component that clusters near optically bright galaxies. There may be additional neutral gas at high redshift that is more broadly distributed, or the gas may be clumped, but at locations not near the DEEP2 galaxies. If so, our fitting of the optical galaxy correlation function to the data underweights this component. Our detection should therefore be treated as a lower bound to the total neutral gas density.
交叉相关技术只是测量了光学上亮的星系附近聚集的21厘米成份.在高红移处,可能还有分布更为广泛,或者成团块但是不靠近DEEP2中星系的中性气体.如果这样的话,那我们拟合的光学星系的相关函数就可能低估了这种成分.所以我们的探测应该被视为总的中性氢密度的一个下限.
We estimate the contribution of the DEEP2 galaxies to the total zero-lag 21-cm flux variance is~20% of the total. The radio data has many galaxies in each independent resolution element so we can not separate flux in the zero-lag bin due to the 21-cm emission of the DEEP2 galaxies themselves from that due to aggregate emission of other galaxies concentrated nearby. The effective resolution element in this survey is (9/h Mpc)^3,determined by the telescope angular resolution and pairwise velocity dispersion. On average there are five DEEP2 galaxies in each resolution element. We assume these have 21 cm luminosities similar to low redshift galaxies in estimating their contribution.
我们估计DEEP2星系对整个零偏移的21厘米流量的贡献在20%的程度.在每个独立的分辨单元内,射电的数据包含有很多的星系,所以我们不可能在零偏移的数据段内把来自DEEP2星系本身的辐射和来自聚集于其附近的星系的辐射区分开来.我们的巡天的分辨单元是 (9/h Mpc)^3.由天线的角分辨率和相对速度弥散决定.平均来说,一个分辨单元内有5个DEEP2星系.在估算这个星系的贡献的时候,我们假设它们的21厘米光度跟低红移的星系是一样的.
At z~1, the neutral gas density \Omega_{HI} is particularly difficult to measure. At low redshifts (using HST), \Omega_{HI} has been measured via the Lyman-alpha-line absorption of ultraviolet light from distant quasars. Extrapolating to redshift 1.2, ΩHI=(7.2±2.2)×10^-4
is found9. Similar observations can also be made with ground based telescopes at redshifts above two, since these wavelengths penetrate the atmosphere. However at redshift z = 2.2, a substantially lower neutral hydrogen content ΩHI=(3.9±0.7)×10^-4 is found(10).Despite the high redshift, the ground based measurement is consistent with the measured present day value 11. This implies little evolution of the average gas density, at conflict with the clear evolution of star formation rate. Our data constrain the combination \Omega_{HI}rb, but there is so far no observational constraint on the 21-cm stochasticity r or the bias b. Theoretical estimates of rb lie in the range 0.5 to 2, a range too wide for the 21 cm data to weigh in. With further 21 cm observations r can be measured by detecting both the auto and cross correlations, and b can be determined by measuring velocity space distortions12. This in turn would allow measurement of the neutral gas density at z~1 via 21 cm intensity mapping.
在红移~1的时候,中性气体的密度\Omega_{HI}特别难以测量.在低红移的时候,(使用哈勃空间望远镜,HST)人们已经通过赖曼阿尔法谱线对遥远类星体的紫外吸收光的吸收测到了\Omega_{HI}.将其外插到红移1.2, 人们得到ΩHI=(7.2±2.2)×10^-4 (文献9).在红移高于2的时候,类似的观测也可以使用地基的望远镜做到,因为这个波段的光可以穿过大气.然而,在红移2.2时候,人们测到的中性氢非常少, ΩHI=(3.9±0.7)×10^-4 (文献10).如果忽略掉这是高红移时候的话,这个地基望远镜测到的值跟今天的值是一致的(文献11).这表明气体的平均密度没怎么演化,而恒星形成率是有很清楚的演化效应的,二者之间存在矛盾.我们的数据限制了\Omega_{HI}rb但是到目前为止没有观测可以限制21厘米辐射的随机性r和偏袒b.理论估计rb在0.5到2之间,这个范围太宽了以致21厘米的数据难以发挥作用.对于更进一步的21厘米观测来说,r可以通过探测自相关和交叉相关来得到,而 b则可以通过测量速度空间弥散得到(文献12).这将使得通过21厘米强度映射测量中性气体的密度成为可能.
参考文献(略)
Acknowledgements We are grateful to the GBT support staff, in particular Toney Minter and Paul Ruffle, for their generous help with the observation. We thank Kevin Blagrave, Olivier Dor´e, Patrick McDonald, Sievers, Kris Sigurdson, Renbin Yen for many useful discussions. We acknowledge financial support by NSERC, NSF, and NRAO. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
致谢: 我们对于GBT的技术支持人员感激不尽,特别是 Toney Minter 和Paul Ruffle, 感谢他们为观测提供慷慨的帮助. 我们感谢Kevin Blagrave, Olivier Dor’e, Patrick McDonald, Sievers, Kris Sigurdson以及严人斌,我们跟他们进行了许多有用的讨论.我们得到了NSERC,NSF以及NRAO的资助.美国国家射电天文台是美国国家自然科学基金会的一个设备,依据大学联合体的合作协议运行(operated under cooperative agreement by Associated Universities, Inc).
Author Contribution T.-C.C. and U.-L.P. analyzed and interpreted the data. K.B. conducted the remote observations. J.B.P. was in charge of the paper writing. All authors were present at the telescope for the on-site observations and contributed to the writing of the manuscript and Supplementary Information.
作者贡献: 张紫锦以及彭威礼分析并对数据进行阐释. K.B实施了远程观测. J.B.P负责撰写文章.所有的人都到望远镜锁所在的站点进行了观测并对撰写本文的草稿和补充材料做出了贡献.
Competing Interests The authors declare that they have no competing financial interests.
利益竞争: 作者声明其资助没有利益方面的竞争.
Correspondence Correspondence and requests for materials should be addressed to T.-C. Chang. (email: XXXX).
通信:通信及索取材料应当与张紫锦联系(邮件:XXXX)
Figure 1 Spectra of DEEP2 Field-4. The top two panels show radio flux arranged with redshift horizontal and right ascension vertical. Each panel contains data collected in two declination bins, separated by 15’, roughly one GBT beam width. The higher declination strip occupies the top half of each panel. The pixels are 2 h−1 comoving Mpc in size in each dimension. The top panel shows measured flux after the polarization cut has removed the brightest terrestrial emission. The rms fluctuation of the map is 128mK. Vertical structures in the top panel are due to residual RFI: the wide stripes are digital television signals and narrow vertical features are analog television carriers. Redshift windows free of RFI are rare on the right side of the plot, which corresponds to greater redshift and lower frequency. The horizontal bright stripes are due to continuum emissions
by astronomical sources( NVSS J022806+003117 and NVSS J022938+002513), and the width of these stripes shows the GBT beam width. The middle panel shows the inverse-variance-weighted radio brightness temperature, after subtraction of continuum sources.The weighted rms fluctuation is 3.8mK. Even though the standard deviation of the flux values in this images has been reduced by more than a factor of 30 compared to the top panel, residual RFI and continuum emission dominates the overall variance. The bottom panel shows the optical galaxy density in the DEEP2 catalog, smoothed to match the resolution of the radio data. The rms fluctuation of the map is 1.8. The cross correlation
function in Figure 2 is calculated by multiplying the middle and bottom panels with a relative displacement (lag) in redshift, then calculating the variance of the product map.
图一, DEEP2场-4的谱. 最上面两幅图展示了射电流量,横坐标是红移,纵坐标是赤经.每幅图的数据都是来自于两个相距15角秒的赤纬段,大概也就是GBT的波束宽度.每幅图的上半部分是高赤纬的部分.每个像素对应的尺度为2/h共动兆秒差距.最上面的图表示的是已经通过偏振方法移除掉最亮的天体源后的流量,其扰动的均方差是128 毫开.该图中的纵向结构是残余的射频干扰,宽的竖条是数字电视的信号,窄的则是模拟电视的.图的右边对应着更高的红移和更低的频率,此处没有射频干扰的红移窗口很少.亮的横条是天体的连续辐射(NVSSJ022806+003117 和 NVSS J022938+002513),横条的宽度即为GBT的波束的宽度.中间的图展示的是反方差权重的射电亮温度,连续辐射源已经被扣除掉了.加权后的均方差是3.8毫开.跟上面的图相比,尽管该图中标准差已经被减小了30倍,其主要的方差仍然是来自于残余的射频干扰和连续辐射.最下面的图展示了DEEP2 的光学星系密度,该密度已经被平滑过以跟射电数据的分辨率相匹配.该图的均方差扰动为1.8.在计算图二的交叉相关时,是把最下面的图在红移上做一个相对平移再跟中间的图相乘,并计算相乘后的方差.
Figure 2 The cross correlation between the DEEP2 density field and GBT HI brightness temperature. The crosses are the measured cross-correlation temperature, while error bars are the 1\sigma bootstrap errors generated using randomized optical data, and the diamonds are the mean null-test values over 1,000 randomizations as described in SI; the same bootstrap procedure performed on randomized radio data returns very similar nulltest values and error bars. The solid line is a DEEP2 galaxy correlation model which assumes a power law correlation and includes the GBT telescope beam pattern as well as velocity distortions, and uses the best-fit value of the cross-correlation amplitude.
图二 DEEP2密度与GBT的中性氢亮温度之间的交叉相关. 叉号是测量到的温度的交叉相关,而误差则是用随机化后的光学数据得到的一个标准差程度的拔靴法误差,菱形则是1000个随机的零偏移测试的平均值,如补充材料中所述;把同样的拔靴法用在随机化后的射电数据上得到的零偏移测试的值和误差棒跟前面非常相似.实线是一个DEEP2星系的相关模型,假设为幂律的形式并且计入GBT望远镜的波束特征和速度畸变,并使用交叉相关的最佳拟合值.
补充材料(略)
英文的原文出自:
http://arxiv.org/abs/1007.3709 |
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