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Tracing the Initial Conditions and the Global Parameters through the Growth of Fluctuations. 1) Recapitulation of fluctuation growth 2) Observations of Mass Fluctuations 3) Implications for the global model. Fluctuation growth in the simplest case:. d is the fractional density contrast.
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Tracing the Initial Conditions and the Global Parameters through the Growth of Fluctuations 1) Recapitulation of fluctuation growth 2) Observations of Mass Fluctuations 3) Implications for the global model Obs.Big-Bang 03/04 HWR
Fluctuation growth in the simplest case: d is the fractional density contrast • equation of motion for a mini FRW Universe! • can be solved parametrically in the same way as we solved the Friedmann eqn. Obs.Big-Bang 03/04 HWR
Linear Growth Function D1(t) relates d at one epoch to another Einstein- de Sitter Obs.Big-Bang 03/04 HWR
Role of Pressure and Photons in Perturbation Growth • So far, we analyzed pressureless „cosmic dust“ • If a finite pressure (or velocity dispersion) is present, we need to include a term in the equation of motion • We need to specify an equation of state, e.g. • Now the spatial structure of the perturba-tion matters, so we take where is the comoving wavenumber. Then Obs.Big-Bang 03/04 HWR
only perturbations longer than the Jeans length grow • We know that at early epochs the radiation dominated the mass/energy density • One can still proceed with a Newtonian analysis , e.g. • If radiation dominates completely, then and the perturbation equation becomes Note that here (not a-3) Obs.Big-Bang 03/04 HWR
Consequences: (1) During the radiation dominated era (z 30,000) all matter is gravitationally coupled to the radiation • photons (relativistic gas) have a „sound speed“ of which results in a Jeans mass MJ of with and Note:total ~ (1 + z)4 if radiation dominates Obs.Big-Bang 03/04 HWR
no mass distortion 1017 Msun can grow before z ~ 10,000 (2) Until combination (z ~ 1000) ordinary (baryonic) matter is coupled to the ra- diation through Thompson scattering (3) After radiation-matter equality (z ~ 10,000) fluctuations in the non- baryonic dark matter can grow ~ a(t) Note: after recombination the radiation and matter stop interacting Jeans mass drops by 1010 Obs.Big-Bang 03/04 HWR
Schematic Evolution of the Jeans Mass Fig. 3 Jeans mass Obs.Big-Bang 03/04 HWR
Growth suppression after entering horizon Schematic Transfer Function [ =D1(t) ] Obs.Big-Bang 03/04 HWR
Lick Galaxy Map CfA Slice with Great Wall Observing the Clustering of Matter and Galaxies History: 1920- : galaxies in and around the local group are not distributed randomly 1950-1970: Shane and Wirtanen • made maps of the (projected) galaxy distribution • Non-random distribution on small to large scales 1980-1990: Geller, Huchra and many others • made maps of the 3D galaxy distribution • Depth variable redshift (not quite distance) 2000+: 2DF Redshift Survey / SDSS • 100,000 galaxies with spectra (Literature: e.g. Peacock: Cosmological Physics, p500-509) Obs.Big-Bang 03/04 HWR
Star-Forming Galaxies Red Galaxies State-of-the-Art Example: 2DFRS(from Peacock et al 2002) Obs.Big-Bang 03/04 HWR
Describing the Statistics of Clustering • There is no unique way to describe clustering! • Need to describe the degree of clustering not the particular configuration. • Isotropy: clustering = f(x,y,z) f(r) • Often-used measures are: • Angular or real-space correlation function • Genus curve • Smooth galaxies on different scales • Which fraction of the volume is filled by curves of a given over-/under-density • Counts-in cells • Main practical problems/issues: • Complicated search volumes • Finite number of tracers • Redshift space distortion Obs.Big-Bang 03/04 HWR
Correlation Functions • Excess probability of finding one galaxy (mass element) “near” another galaxy: - for a random (uniform) distribution: dP = n dV n: mean number density - a clustered distribution can be (incompletely) described by: dP(r) = n [1 + (r)] dV, where dP is the probability of finding a second object near an object at r = 0 (r): two-point (or, auto-) correlation function Note: (r) = < (x) (x+r) >, where (x) is the fractional over/under-density - to account for translation and rotation invariance (cosmological principle) often the Fourier transform is used P(k) | k|2 = (r) eikr d3r P(k): power spectrum - practical estimation: Obs.Big-Bang 03/04 HWR
If no redshifts (distances) are available, one can define the angular correlation function dP () = n (1 + w() ) d • Note: • understanding the sampling window function of a survey is crucial • usually one is measuring the correlation of tracers Obs.Big-Bang 03/04 HWR
Red galaxies Blue galaxies „Redshift“ Distance Angle on the sky The Clustering of Galaxies in the Present Day Universe (from the 2DFRS) • Redshift-space correlation Obs.Big-Bang 03/04 HWR
Axis ratio of the correlation in the space-velocity plane as a function of scale Infall Finger-of-God Finger-of-God and Inflow Signature • pairwise velocity dispersion from “finger-of-god”: 400km/s • Cosmic density estimate from inflow: b = W0.6/b = 0.43 0.07 Obs.Big-Bang 03/04 HWR
From Peacock et al 2002 More luminous/massive galaxies are more strongly clustered Galaxy Clustering vs. Galaxy Properties • Galaxies with little star-formation (~ “early types”) are much more strongly clustered on small scales • A.k.a. morphology-density relation • Presumably:dense environments lead to rapid/early completion of the main star-formation Obs.Big-Bang 03/04 HWR
Baryon wiggles? Cosmological Parameters from the Clustering of (Nearby) Galaxies Galaxy correlation now reflects: • initial fluctuations • growth rate (enter W and L) • transfer-function • Galaxy bias Comparison most straightforward in the linear regime >5-10 Mpc Obs.Big-Bang 03/04 HWR
Mass/Galaxy Clustering at high Redshift • Can one observe the growth of mass fluctuation and galaxy clustering directly? • Put a “point” between the CMB and the present epoch. • Two possible probes at z~3: • Galaxies (Ly-break galaxies) • The fluctuation inter-galactic medium (IGM): Ly-alpha forest • Galaxies:from Adelberger, Steidel and collaborators: • Ly-break galaxies at z~3 are nearly as clustered as L* galaxies now • (massive) galaxies were more biased tracers of the mass fluctuations than they are now. Obs.Big-Bang 03/04 HWR
The Ly-alpha Forest and Mass Fluctuations • What causes the fluctuation Ly-alpha absorption? • Collapsed objects (mini halos) • General density (+velocity) fluctuations Obs.Big-Bang 03/04 HWR
Simulating the Ly-alpha forest(Cen, Ostriker, Miralda 1994-; Croft, Katz, Weinberg, Hernquist 1996-) • Much of the Ly-alpha forest arises from modest density fluctuations and convergent velocity flows!! Obs.Big-Bang 03/04 HWR
From Croft et al 1998 Comparing Data and Simulations Obs.Big-Bang 03/04 HWR
The Correlation of IGM Absorptionat different redshifts • This probes the mass between galaxies • One can follow the evolution of structure with redshift Obs.Big-Bang 03/04 HWR
z=1100 z=0-3 Verde 2003 Combining the CMB with the low-z Universe • Until the last few years (BOOMERANG, MAXIMA, WMAP), the CMB fluctuations were measured on larger (co-moving) scales than the fluctuations measured in the low-z universe • Only joint extrapolation in redshift and scale possible! With new generation of z<5 LSS measurements and CMB experiments, a much more direct comparison is possible. Impressive confirmation of structure growth prediction!! Obs.Big-Bang 03/04 HWR
Combining the CMB with the late Universe • Until the last few years (BOOMERANG, MAXIMA, WMAP), the CMB fluctuations were measured on larger (co-moving) scales than the fluctuations measured in the low-z universe • Only joint extrapolation in redshift and scale possible! Note:the plot shows that there exists a “cosmological model” for which all fluctuations measurements agree Well, which model works? Obs.Big-Bang 03/04 HWR
Combining early and late I:Adding the “local distance scale” to the CMB From Spergel et al 2003 Obs.Big-Bang 03/04 HWR
Combining Early and LateConstraints • Note: • this is pre-WMAP, I.e. data from COBE + ground-based and baloon experiments! (from Peacock et al 2003) • h H0=100 Obs.Big-Bang 03/04 HWR
Theory Big Bang Inflation FRW/cosmological parameters WM=0.27,L=0.7,H0=70 (Non-baryonic) dark matter dominates (small) initial fluctuations Growth of density fluctuations Linear Observations Expansion,CMB,BBN Space is flat, CMB is uniform, fluctuations are scale free SN Ia, Galaxy Clustering, CMB Dynamics,lensing,BBN,CMB CMB CMB vs large-scale structure IGM fluctuations Galaxy large scale struture Let’s Recapitulate Obs.Big-Bang 03/04 HWR