2010 年十年领悟 [ 见解 ] 和十大突破 http://www.sciencemag.org/site/special/insights2010/ http://www.sciencemag.org/content/330/6011.tochttp://www.sciencemag.org/content/330/6011.toc

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《科学》

精确宇宙学

世纪之交 -----3 朵乌云： 3D 宇宙 [eprint arXiv:1010.1307]

3D 3D UniverseUniverse

宇宙学家在做什么？3 件事！ 1 为什么！ 2 是什么！ 3 应该是什么！

我们的宇宙我们的宇宙

Hubble 参量观测数据与宇宙学模型限制

H(z) the observational Hubble parameter data (OHD)

张同杰 马骢 [2010 级硕士 ] 北京师范大学天文系

Hubble Parameter Cosmology Hubble Parameter Cosmology or H(z) or H(z) CosmologyCosmology

Lensing cosmologyLensing cosmology

Lee Jounghun, Pen,Ue-Li. ApJ, 686: L1–L4, 2008

SN cosmology; GRB cosmologySN cosmology; GRB cosmology

Simulation, Weak lensing,Simulation, Weak lensing,WaveletWavelet

Zhang, Tong-Jie; Yu, Hao-Ran; et al, ApJ, 728, 35

Yu, Hao-Ran; Zhang, Tong-Jie et al arXiv:1012.0444

Hubble parameter H(z)Hubble parameter H(z)

Cosmological application: Cosmological application: Joan Simon, Licia Verde, and Raul Jimenez. PRD Joan Simon, Licia Verde, and Raul Jimenez. PRD 71, 71, 123001 (2005)123001 (2005)

Luminosity distance VS Hubble parameter Hubble parameter

1. The integral smears out information about E o S 2. The integral make the luminosity distance have only a weak discriminating power with respect to different possible histories of E

o S

Limitations using luminosity distance2001 PRL 86

今天今天 OutlineOutline

一一 . Observational methods for H(z). Observational methods for H(z) 二 . Power of Observational Hubble

parameter data[OHDOHD] -- H(z) 三、 Future of OHD

一一 . . Observational methods for Observational methods for H(z)H(z)

1. the differential age method: different 1. the differential age method: different age of the oldest galaxies in each redshift age of the oldest galaxies in each redshift bin;bin;

2. the radial BAO size method: the baryon 2. the radial BAO size method: the baryon acoustic oscillation (BAO) along theacoustic oscillation (BAO) along the

line-of-sight direction from the line-of-sight direction from the spectroscopic galaxy samples;spectroscopic galaxy samples;

3. the GW method: compact-binary object- 3. the GW method: compact-binary object- observation.observation.

1. the differential age method

1. Measure the age difference, Dt, between two passively evolving galaxies that formed at the same time but are separated by a small redshift interval Dz;

2. Infer the derivative dz/dt from the ratio Dz/Dt. At high redshifts, z=1–2, H(z) would constrain the EoS of

DE, while at low redshifts, z<0.2, it would determine the Hubble constant, H_0.

Galaxies samples:The fair samples of passively evolving galaxies

1.Similar metallicities Similar metallicities 2. Low star formation rates (i.e., a red 2. Low star formation rates (i.e., a red

color)color)

So, the average age of their stars would far So, the average age of their stars would far exceed the age difference between the exceed the age difference between the two galaxy samples.two galaxy samples.

Age-redshift relation of the galaxiesAge-redshift relation of the galaxies

----Edge or Envelope----Edge or Envelope

Joan Simon, Licia Verde, and Raul Jimenez [upenn]. PRD 71, 123001 (2005)

9 data point = 8+1 1 data---Sloan Digital Sky Survey(SDSS)[R. Jimenez et al, ApJ.593, 622

(2003)] 8 data----GeminiDeep Survey (GDDS) survey [R. G. Abraham et al.,

Astron. J. 127, 2455(2004)] and archival data [T. Treuet al, MNRAS. 308, 1037 (1999)]

Key advantageKey advantage

Differential ages are less sensitive to Differential ages are less sensitive to systematics errors systematics errors than absolute than absolute ages.ages.

Two new H(z) data sets Stern, D., Jimenez, R.et al. 2010, JCAP 02(2010)008

[astro-ph/0907.3149] Two samples: 1. the SPICES sample. Most of the spectra were

taken at the Keck telescope; 2. The VVDS [49] is the VIMOS-VLT survey carried out by the VLT/ESO telescope

1+8+2=11

2. the radial BAO size method2. the radial BAO size method

the baryon acoustic oscillation (BAO) the baryon acoustic oscillation (BAO) along the line-of-sight direction from along the line-of-sight direction from the spectroscopic galaxy samplesthe spectroscopic galaxy samples

CREDIT: WMAP & SDSS websites

CM

B

Looking back in time; angles imply distance

GA

LAX

IES

D. J. Eisenstein et al., Astrophys. J. 633, 560 (2005)

standard ruler

Detection of BAO

BAO methodBAO method The comoving sizes of cosmological object The comoving sizes of cosmological object

[standard ruler] of feature at redshift z [standard ruler] of feature at redshift z in line-of-sight and transver directionsin line-of-sight and transver directions observed sizesobserved sizes

Two-point correlation functionTwo-point correlation function

Updated data sets: Updated data sets: 13=[1+8+2] 11 [OHD] + 2 [BAO]13=[1+8+2] 11 [OHD] + 2 [BAO]

1. Ma Cong, Zhang Tong-Jie [arXiv:1007.3787] ApJ, 730:74 (8pp), 2011 2. Zhang, Tong-Jie; Ma, Cong; Lan, Tian

Hindawi Publishing Corp. Hindawi Publishing CorporationAdvances in Astronomy Volume 2010, Article ID 184284, 14 pages [eprint arXiv:1010.1307]

Ze-Long,yi, Tong-Jie Zhang, Modern Physics letters A, 22,41-53(2007)

(arXiv:astro-ph/0607301)

( arXiv:astro-ph/0605596)

3. GW method-Standard siren3. GW method-Standard siren[[ 汽笛汽笛 ]]

SN or Gamma ray burst [GRB]—electromagnetic SN or Gamma ray burst [GRB]—electromagnetic wave--standard candle [gamma-ray bursts] wave--standard candle [gamma-ray bursts]

Compact-binary object-- continuous GW— Compact-binary object-- continuous GW— determine luminosity distance to the binaries determine luminosity distance to the binaries with a high precision with a high precision

standard sirenstandard siren

Future space-based gravitational wave Future space-based gravitational wave detectorsdetectors

Such as DECI-hertz Interferometer Gravitational-wave Such as DECI-hertz Interferometer Gravitational-wave

Observatory (Observatory (DECIGODECIGO) and Big-Bang Observer ) and Big-Bang Observer

((BBOBBO)) 1. sensitive to GW in 0.1-1Hz band1. sensitive to GW in 0.1-1Hz band 2. detect GW sources2. detect GW sources

[1]. Cosmological GW background during Inflation[1]. Cosmological GW background during Inflation

[2]. Mergers of an intermediate-mass black hole[2]. Mergers of an intermediate-mass black hole

[3]. A large number of(10^6) neutron star (NS) binaries: [3]. A large number of(10^6) neutron star (NS) binaries: cosmological parameters can be accurately measured by cosmological parameters can be accurately measured by DECIGO and BBO with a precision of 1%. DECIGO and BBO with a precision of 1%.

The advantage of the standard sirensThe advantage of the standard sirens

1. the expected 1. the expected numbernumber of sources (NS of sources (NS binaries) is much larger than that of the type Ia binaries) is much larger than that of the type Ia supernovae;supernovae;

2. the sources are distributed deeply enough at 2. the sources are distributed deeply enough at

higher redshiftshigher redshifts..

Atsushi et al arXiv:1011.5000 OHD from GWOHD from GW

二 . Power of Observational Hubble paramer data H(z)

[eprint arXiv:1007.3787]

Two QuestionsTwo Questions 1. Can future observational determinations of the 1. Can future observational determinations of the

HubbleHubble

parameter be used as a viable alternative to current SN Ia parameter be used as a viable alternative to current SN Ia data?data?

2. If so, how many more data points need?2. If so, how many more data points need?

Answer via an exploratory, statistical approach Answer via an exploratory, statistical approach with simulated datawith simulated data

(1) simulated (1) simulated HH((zz) data sets;) data sets; (2) an “evaluation” model;(2) an “evaluation” model; (3) a well-defined “figure of merit” (FoM).(3) a well-defined “figure of merit” (FoM).

Data set simulationData set simulationError simulation Upper line:σ+ = 16.87 z + 10.48, Lower line:σ− = 4.41 z + 7.25 Midline:σ0 = 10.64 z + 8.86 Error: σ (z)-Gaussian N(σ0(z), ε(z)) where ε(z) = (σ+−σ−)/4.

Deviation simulation Hsim(z) = Hfid(z) + ΔH with σ(z)ΔH =Hsim(z)−Hfid(z)-Gaussian N(0,σ (z))

500 realizationEach-128 data points

Figure of Merit[FoM]Figure of Merit[FoM] and and The degeneracy of confidence The degeneracy of confidence regionsregions

FoM-the area enclosed by the contour of P(Ωm,ΩΛ| {Hi}) = exp(−Δχ2/2)Pmax, Δχ2 =6.17

ConclusionsConclusions 1. more than 60 future measurements of 1. more than 60 future measurements of HH((zz)[z-0-)[z-0-

2]comparable with those obtained: SN Ia ConstitutionT; 2]comparable with those obtained: SN Ia ConstitutionT; 2. lower the error of future 2. lower the error of future HH((zz) measurements to 3% , ∼60 ) measurements to 3% , ∼60

measurements [z=0measurements [z=0..11, , 11..0] achieve the same result;0] achieve the same result; 3. Our result furthers a conclusion of Lin et al. (2009) and 3. Our result furthers a conclusion of Lin et al. (2009) and

Carvalho et al. (2008), that OHD plays almost the same role as Carvalho et al. (2008), that OHD plays almost the same role as that of SNIa for the joint constraints on theΛCDMmodel.that of SNIa for the joint constraints on theΛCDMmodel.

三、三、 Future of Future of OHDOHD1. Observational cost1. Observational cost ： ConstitutionT data[Wei Hao] ：： a subset of the a subset of the

Constitution compilation, a combination of the ground-Constitution compilation, a combination of the ground-based CfA3 SN observations (Hicken et al. 2009b) and based CfA3 SN observations (Hicken et al. 2009b) and Union, a larger compilation of legacy SNe and space-Union, a larger compilation of legacy SNe and space-based observations (Kowalski et al. 2008). The CfA3 based observations (Kowalski et al. 2008). The CfA3 sample alone requires sample alone requires 10 nights 10 nights for each of the for each of the 185 SNe observed.185 SNe observed.

OHDOHD: The current OHD from age-dating does not require space-based observations. Stern et al. (2010): 24 galaxy cluster containing target chronometer galaxies were obtained in only two nights using the Keck I telescope. Crawford et al. (2010): the South African Large Telescope is capable of measuring H(z) to 3% at an individual redshift in ∼180 hr.

2. Increase of quality and 2. Increase of quality and numbernumber

Crawford et al. (2010) analyzed the observational requirement of measuring H(z) to 3% at intermediate redshifts with age-dating.

The Baryon Oscillation Spectroscopic Survey (BOSS): constrainH(z) with 2% precision at z ≈ 0.3,0.6 by measuring BAO imprints in the galaxy field, and at z ≈ 2.5 using the Lyα absorption spectra of quasars. And it also could extend H(z) measurement into deeper redshift.

Future CMB observation programs, such as the Atacama Cosmology Telescope[ACT], may be able to identify more than 2000 passively evolving galaxies up to z ≈ 1.5 via SZ effect, and their spectra can be analyzed to yield age measurements that will yield approximately 1000 H(z) determinations with 15% error (Simon et al. 2005).

总的结论 the OHD set alone is potentially the OHD set alone is potentially

capable of being used in place of capable of being used in place of current SNIa data sets if it is large current SNIa data sets if it is large enough.enough.

Ma, Cong; Zhang, Tong-Jie, ApJ,730,74 (2011). [eprint arXiv:1007.3787]

Open questions 1. 利用差分年龄观测，是否一定要用高分辨率光谱？是否可以

改变数据处理方式，通过类似于 LAMOST 的低分辨率光谱完成？

2. 星族形成、演化的模型对差分年龄有直接影响。 3. 利用差分年龄定 H(z), 目前没有很系统的观测

specification ，更没有专门化的观测计划。因此 Fisher matrix 的输入值还有一些不确定性。

4. 21cm 线，尚无高红移的直接观测。从现在到测出 21cm背景的 BAO 、乃至测出 H(z), 还有多少路要走？

5. BAO 用于宇宙学模型限制，特别是从 BAO 得到的 H(z) ，并没有完全消除对“ fiducial model” 的依赖性。这一点能否更好地解决？

我们的关于 H(z) 的工作 [10] (1). Ma, Cong; Zhang, Tong-Jie, ApJ,730,74 (2011). [eprint arXiv:1007.3787]

(2). Zhang, Tong-Jie; Ma, Cong; Lan, Tian, Invited paper: Advances in Astronomy, 184284(2010)[eprint arXiv:1010.1307] (3). Zhai, Zhong-Xu; Wan, Hao-Yi; Zhang, Tong-JiePhysics Letters B, Volume 689, Issue 1, p. 8-13(2010) (eprint arXiv:1004.2599) (4). Wan, Hao-Yi; Yi, Ze-Long; Zhang, Tong-Jie; Zhou, Jie Physics Letters B, Volume 651, Issue 5-6, p. 352-356 (08/2007) (arXiv:0706.2737) (5). Yi, Ze-Long; Zhang, Tong-Jie, Modern Physics Letters A, Vol. 22, No. 1 (01/2007) 41-53 (arXiv:astro-

ph/0605596)

谢谢！