Structure Formation and Evolution"

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1 Structure Formation and Evolution" From this (Δρ/ρ ~ 10-6 )! to this! (Δρ/ρ ~ )! to this! (Δρ/ρ ~ )!

4 How Long Does It Take?" The (dissipationless) gravitational collapse timescale is on the order of the free-fall time, t ff :! R! The outermost shell has acceleration g = GM/R 2! It falls to the center in:! t ff = (2R/g) 1/2 = (2R 3 /GM) 1/2 (2/Gρ) 1/2! Thus, low density lumps collapse more slowly than high density ones. More massive structures are generally less dense, take longer to collapse. For example:! For a galaxy: t ff ~ 600 Myr (R/50kpc) 3/2 (M/10 12 M ) -1/2! For a cluster: t ff ~ 9 Gyr (R/3Mpc) 3/2 (M/10 15 M ) -1/2! So, we expect that galaxies collapsed early (at high redshifts), and that clusters are still forming now. This is as observed!!

5 The Local Group"

6 The Local Supercluster"

7 The Nearby Superclusters"

$then the distribution can be described as a fractal with correlation dimension D 2 = const. If D 2 = 3, then the distribution is consistent with being simple, homogenous in 3-D.$

8 So, is the Universe Fractal?" For each galaxy, count the number of galaxies within distance R from it, N(<R). If! then the distribution can be described as a fractal with correlation dimension D 2 = const. If D 2 = 3, then the distribution is consistent with being simple, homogenous in 3-D.! But in the real universe D 2 const., since ξ (r) is not a pure power-law. Thus, the universe is not a fractal! (although it is pretty close)!

The Local Supercluster" Hinted at by H. Shapley (and even earlier), but really promoted by G. de Vaucouleurs! Became obvious with the first modern redshift surveys in the 1980 s!

9 The Local Supercluster" Hinted at by H. Shapley (and even earlier), but really promoted by G. de Vaucouleurs! Became obvious with the first modern redshift surveys in the 1980 s! A ~ 60 Mpc structure, flattened, with the Virgo cluster at the center; the Local Group is at the outskirts! Its principal axes define the supergalactic coordinate system (XYZ)! Many other superclusters known; and these are the largest (~ 100 Mpc) structures known to exist!

10 6000 Brightest Galaxies on the Sky" How would the picture of the 6000 brightest stars on the sky look?!

11 Stepping Out in Redshift Slices" Virgo / LSC! Fornax! (from Giovanelli & Haynes)!

12 Stepping Out in Redshift Slices" Perseus-Pisces! Hydra-Centaurus! (from Giovanelli & Haynes)!

13 Coma - A1367! Stepping Out in Redshift Slices" (from Giovanelli & Haynes)!

14 CfA2 Survey:" The Infamous" Stickman" Diagram " The 2nd generation redshift surveys were often done in slices which were thin in Dec and long in RA, thus sampling a large dynamical range of scales. This also helped reveal the large-scale topology (voids, walls, filaments).! Coma cluster:! Note the finger of God effect, due to the velocity disp. in the cluster!

15 Redshift Space vs. Real Space" Real space distribution! Fingers of God!!!!! The effect of cluster velocity dispersion! Thin filaments!!!!! The effect of infall! Redshift space apparent distrib.!

16 The Great Wall " a ~ 100 Mpc structure revealed in the CfA2 redshift survey! Up until then, redshift surveys revealed structures as large as can be fitted within the survey boundaries - but 100 Mpc turned out to be about as large as they come.! The next generation of surveys sampled 3-D volumes (rather than thin slices), sometimes with a sparse sampling (measure redshift of every n-th galaxy), and often used multi-object spectrographs.!

18 Las Campanas Redshift Survey" The first survey! to reach! the quasi-homogeneous regime!

19 SDSS Sky Coverage"

20 SDSS! Redshift! Survey"

21 Galaxy Distribution and Correlations" If galaxies are clustered, they are correlated! This is usually quantified using the 2-point correlation function, ξ (r), defined as an excess probability of finding another galaxy at a distance r from some galaxy, relative to a uniform random distribution; averaged over the entire set:! Usually represented as a power-law:! For galaxies, typical correlation or clustering length is r 0 ~ 5 h -1 Mpc, and typical slope is γ 1.8, but these are functions of various galaxy properties; clustering of clusters is stronger!

22 Galaxy Correlation Function" As measured by the 2dF redshift survey! Deviations from the power law:!

23 Galaxy Correlation Function" At sufficiently large scales, e.g., voids, ξ (r) must turn negative! If only 2-D positions on the sky are known, then use angular separation θ instead of distance r:! w(θ) = (θ/θ 0 ) -β, β = γ - 1!

24 Galaxy Biasing Suppose that the density fluctuations in mass and in light are not the same, but Or: (Δρ/ρ) light = b (Δρ/ρ) mass ξ(r) light = b 2 ξ(r) mass Here b is the bias factor. If b = 1, light traces mass exactly (this is indeed the case at z ~ 0, at scales larger than the individual galaxy halos). If b > 1, light is a biased tracer of mass. One possible mechanism for this is if the galaxies form at the densest spots, i.e., the highest peaks of the density field. Then, density fluctuations containing galaxies would not be typical, but rather a biased representation of the underlying mass density field; if 1-σ fluctuations are typical, 5-σ ones certainly are not.

25 High Density Peaks as Biased Tracers Take a cut through a density field. Smaller fluctuations ride atop of the larger density waves, which lift them up in bunches; thus the highest peaks (densest fluctuations) are a priori clustered more strongly than the average ones: Protocluster Protovoid Thus, if the first galaxies form in the densest spots, they will be strongly clustered, but these will be very special regions.

26 An Example From a Numerical Simulation All particles 1-σ peaks 2-σ peaks 3-σ peaks Gas/Stars (From an N-body simulation by R. Carlberg) Dark Matter

27 Galaxy Biasing at Low Redshifts While on average galaxies at z ~ 0 are not biased tracers, there is a dependence on luminosity: the more luminous ones are clustered more strongly, corresponding to higher peaks of the density field. This effect is stronger at higher redshifts. Biasing in the SDSS, Tegmark et al (2004)

28 ξ(r)! Brighter galaxies are clustered more strongly than fainter ones! Bright! This is telling us something about galaxy formation! Faint!

29 ξ(r)! Redder galaxies (or early-type, ellipticals) are clustered more strongly than bluer ones (or late-type, spirals)! That, too, says something about galaxy formation!

30 Evolution of Clustering But at higher redshifts (and fainter/deeper galaxy samples), the trend reverses: stronger clustering at higher redshifts = earlier times! (Hubble Deep Field data)

31 Clustering of Quasars is Also Stronger at Higher Redshifts How is this possible? Clustering is supposed to be weaker at higher z s as the structure grows in time. Evolution of bias provides the answer

32 Biasing and Clustering Evolution Strength of clustering 1-σ flucs. 3-σ flucs. 5-σ flucs. Higher density (= higher-σ) fluctuations evolve faster redshift At progressively higher redshifts, we see higher density fluctuations, which are intrinsically clustered more strongly Thus the net strength of clustering seems to increase at higher z s

33 Correlation Function and Power Spectrum" Given the overdensity field! Its Fourier transform is! Its inverse transform is! where is the wave number! The power spectrum is! Then! Correlation function and power spectrum are a Fourier pair!

34 An Example from Las Campanas Redshift Survey" Correlation function is easier to evaluate, but power spectra is what we need to compare with the theory!

35 The Observed Power Spectrum" (Tegmark et al.)!

36 Baryonic oscillations seen in the CMBR are detected in the LSS at lower redshifts" Thus, we can use the first peak as a stardard ruler at more than one redshift! 2dF (Percival et al.)! SDSS (Eisenstein et al.)!

37 Is the Power Spectrum Enough?" These two images have identical power spectra! (by construction)! The power spectrum alone does not capture the phase information: the coherence of cosmic structures (voids, walls, filaments )!

38 Clusters of Galaxies: Clusters are perhaps the most striking elements of the LSS Typically a few Mpc across, contain ~ luminous galaxies and many more dwarfs, masses ~ M Gravitationally bound, but may not be fully virialized Filled with hot X-ray gas, mass of the gas may exceed the mass of stars in cluster galaxies Dark matter is the dominant mass component (~ 80-85%) Only ~ 10-20% of galaxies live in clusters, but it is hard to draw the line between groups and clusters, and at least ~50% of all galaxies are in clusters or groups Clusters have higher densities than groups, contain a majority of E s and S0 s while groups are dominated by spirals Interesting galaxy evolution processes happen in clusters

39 The Virgo Cluster: Irregular, relatively poor cluster Distance ~ 16 Mpc, closest to us Diameter ~ 10 on the sky, 3 Mpc ~ 2000 galaxies, mostly dwarfs Galaxy& Map&

40 The Coma Cluster Visible&light& Nearest rich cluster, with >10,000 galaxies Distance ~ 90 Mpc Diameter ~ 4-5 on the sky, 6-8 Mpc X2Ray& X2ray&/&visible&overlay&

41 The Perseus Cluster

42 Virial Masses of Clusters: Virial Theorem for a test particle (a galaxy, or a proton), moving in a cluster potential well: E k = E p / 2 m g σ 2 / 2 = G m g M cl / (2 R cl ) where σ is the velocity dispersion Thus the cluster mass is: M cl = σ 2 R cl / G Typical values for clusters: σ ~ km/s R cl ~ 3-5 Mpc Thus, typical cluster masses are M cl ~ M The typical cluster luminosities (~ galaxies) are L cl ~ L, and thus (M/L) ~ in solar units Lots of dark matter!

Masses of Clusters From X-ray Gas Note that for a proton moving in the cluster potential well with a σ ~ 10 3 km/s, E k = m p σ 2 / 2 = 5 k T / 2 ~ few kev, and T ~ few 10 7 K X-ray gas Hydrostatic

43 Masses of Clusters From X-ray Gas Note that for a proton moving in the cluster potential well with a σ ~ 10 3 km/s, E k = m p σ 2 / 2 = 5 k T / 2 ~ few kev, and T ~ few 10 7 K X-ray gas Hydrostatic equilibrium requires: M(r) = - kt/µm H G (d ln ρ /d ln r) r If the cluster is ~ spherically symmetric this can be derived from X-ray intensity and spectral observations Typical cluster mass components from X-rays: Total mass: to M Luminous mass: ~5% Gaseous mass: ~ 10% Dark matter: ~85% Coma%cluster% Hydra%cluster%

44 Integrated Mass Profiles

Dark Matter and X-Ray Gas in Cluster Mergers: The Bullet Cluster (1E 0657-56) The dark matter clouds largely pass through each other,

45 Dark Matter and X-Ray Gas in Cluster Mergers: The Bullet Cluster (1E ) The dark matter clouds largely pass through each other, whereas the gas clouds collide and get shocked, and lag behind Blue: dark matter, as inferred from weak gravitational lensing (Bradac et al.)

46 A 520

Synyaev-Zeldovich Effect Clusters of galaxies are filled with hot X-ray gas The electrons in the intracluster gas will scatter the background photons from the CMBR to higher energies and distort the

47 Synyaev-Zeldovich Effect Clusters of galaxies are filled with hot X-ray gas The electrons in the intracluster gas will scatter the background photons from the CMBR to higher energies and distort the blackbody spectrum This is detectable as a slight temperature dip or bump in the radio map of the cluster, against the uniform CMBR background Spectrum% distor3on% Radio%map% Outgoing CMB photon Incoming CMB photon Galaxy Cluster with hot gas

48 SZ Clusters from Planck Keep an eye on the South Pole Telescope (SPT) as well

49 Clusters as Cosmological Probes From the evolution of cluster abundance, expressed through their mass function:

50 Clusters as Cosmological Probes

51 Central Dominant (cd) Galaxies in Clusters Many clusters have a single, dominant central galaxy. These are always giant ellipticals (ge), but some have extra-large, diffuse envelopes - these are called cd galaxies stellar halo These envelopes are probably just star piles, a remainder of many tidal interactions of cluster galaxies, sharing the bottom of the potential well with the ge galaxy

52 Diffuse Intracluster Light in Coma Cluster Gregg & West 1998

9.1 Large Scale Structure: Basic Observations and Redshift Surveys

9.1 Large Scale Structure: Basic Observations and Redshift Surveys Large-Scale Structure Density fluctuations evolve into structures we observe: galaxies, clusters, etc. On scales > galaxies, we talk about