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The Cosmic Web! What Does Our Universe Look Like on the Largest Scale?

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The Cosmic Web! What Does Our Universe Look Like on the Largest Scale? Lecture III The Cosmic Web! what does our Universe look like on the largest scale? aurorasimionescu.wordpress.com/teaching “Large-scale structure” refers to spatial scales larger than single galaxies: superclusters, clusters, groups, filaments, walls, voids What structure is our own Galaxy embedded in? The Local Group What structure is our own Galaxy embedded in? The Virgo Supercluster: a ~ 60 Mpc flattened structure, centered on the Virgo Cluster; the Local Group is at the outskirts. We are falling towards Virgo with ~ 300 km/s, and will get there in about 10 - 15 Gyr What structure is our own Galaxy embedded in? The Laniakea Supercluster find locations where peculiar velocity flows diverge, rather than defining structures based on galaxy number overdensity R. Brent Tully et al. Nature 513, 71 (2014) Redshift surveys To map and quantify the LSS (and compare with theoretical predictions), we need redshift surveys: mapping the 3-D distribution of galaxies in space (2D position on the sky plus redshift used as distance indicator) The 2dF (2 degree Field) redshift survey done with the 3.9-m Anglo-Australian telescope from 1997-2002 – Redshifts of ~ 250,000 galaxies with B < 19.5 mag, covering 5% of the sky reaching to z ~ 0.3 The Sloan Digital Sky Survey (SDSS) done with a dedicated 2.5-m telescope at Apache Point Observatory in New Mexico – Multicolor imaging to r ~ 23 mag, and spectra of galaxies down to r < 17.5 mag, reaching to z ~ 0.7; final data release covers 35% of sky and spectra from 3 million objects The 2dF Galaxy Redshift Survey How do we quantify Large-Scale Structure? If galaxies are clustered, they are “correlated”. This is usually quantified using the (c+v)T0 p1+β 2-pointλ0 =correlation function= λ, ξ0, defined as an “excess probability” of finding p1 v2/c2 p1 β another galaxy− at a distance− r from some galaxy, relative to a uniform random p1+β distributionλ0 =(1+.z)λ0 = p1 β λ0 − Letn ¯ be the average number density of galaxies. The probability of finding a galaxy in the volume element dV is: P1 =¯ndV The probability of finding a galaxy in the volume element dV at location x and another galaxy at location y is: 2 P2 =(¯ndV ) [1 + ⇠(x, y)] 2 If the galaxies are uncorrelated, P2 =(P1) and ⇠ = 0. For a statistically homogeneous and isotropic universe, ⇠ can only depend on r = x y . | − | 1 (c+v)T0 p1+β λ0 = = λ0 p1 v2/c2 p1 β − − p1+β λ0 =(1+z)λ0 = p1 β λ0 − Letn ¯ be the average number density of galaxies. The probability of finding a galaxy in the volume element dV is: P1 =¯ndV The probability of finding a galaxy in the volume element dV at location x and another galaxy at location y is: 2 P2 =(¯ndV ) [1 + ⇠(x, y)] 2 If the galaxiesCorrelation are function uncorrelated, measured by 2dFP2 =(P1) and ⇠ = 0. For a statistically homogeneousRoughly a power-law and isotropic universe, ⇠ can only depend on r = x y . γ | − | ⇠(r)= r − r0 For galaxies⇣ of⌘ average brightness, r0~5Mpc and γ~1.7 ! Βrighter galaxies are clustered more strongly than fainter ones; redder galaxies are clustered more strongly than bluer ones (this is related to galaxy evolution!) E. Hawkins et al. 2003, MNRAS 346,78 1 (c+v)T0 p1+β λ0 = = λ0 p1 v2/c2 p1 β − − p1+β λ0 =(1+z)λ0 = p1 β λ0 − Letn ¯ be the average number density of galaxies. The probability of finding a galaxy in the volume element dV is: P1 =¯ndV The probability of finding a galaxy in the volume element dV at location x and another galaxy at location y is: How do we quantify Large-Scale Structure? 2 An alternative description of the statistical properties of a randomP2 field=(¯ isndV the ) [1 + ⇠(x, y)] Fourier power spectrum, P(k). The larger P(k), the larger the amplitude of fluctuations on length scale L=2π/k. 2 ! If the galaxies are uncorrelated, P2 =(P1) and ⇠ = 0. For a statistically The density fluctuations homogeneousare decomposed into and a sum isotropic of plane waves universe, of the form⇠ can only depend on r = x y . δ(x)=⌃a cos(x k) | − | k · P(k) describes the mean of the squares |ak|2 of the amplitudes, averaged over all |k|=k. γ P(k) and the correlation function⇠(r are)= relatedr through− a Fourier transform. r0 ⇣ ⌘ 2dF measurement of P(k) W.J. Percival et al., MNRAS 337, 1068 (2002) Of course P(k) and ξ (r) depend on cosmic time! 1 Challenges in quantifying Large-Scale Structure via power spectra and correlation functions, I Very different images can have the same power spectrum! ! Knowing only the power spectrum is sufficient to fully describe a random field ONLY in the special case of a Gaussian random field ! (δ(x) is Gaussian) ! The phase space information (ensemble of peculiar velocities) is important, in addition to the spatial distribution. Challenges in quantifying Large-Scale Structure via power spectra and correlation functions, II • brighter galaxies are clustered more strongly than fainter ones; redder galaxies are clustered more strongly than bluer ones • density fluctuations in mass and in light are not necessarily the same! (so-called “galaxy biasing”) Smaller fluctuations ride atop of the larger density waves, which lift them up in bunches; thus the highest peaks (densest fluctuations) are clustered more strongly than the average ones. This bias gets stronger at higher redshifts! Le Fevre et al. Large-scale structure formation and evolution Structure Formation and Evolution! From this (Δρ/ρ ~ 10 -6)! to this ! (Δρ/ρ ~ 10 +2)! to this! (Δρ/ρ ~ 10 +6)! (c+v)T0 p1+β λ0 = = λ0 p1 v2/c2 p1 β − − p1+β λ0 =(1+z)λ0 = p1 β λ0 − Letn ¯ be the average number density of galaxies. The probability of finding a galaxy in the volume element dV is: P1 =¯ndV The probability of finding a galaxy in the volume element dV at location x and another galaxy at location y is: (c+v)T0 p1+β λ0 = = λ0 p1 v2/c2 p1 β − − 2 P2 p=(¯1+β ndV ) [1 + ⇠(x, y)] λ0 =(1+z)λ0 = p1 β λ0 − 2 If the galaxies are uncorrelated, P2 =(P1) and ⇠ = 0. For a statistically homogeneous and isotropicLetn ¯ be the universe, average number⇠ can density only of galaxies. depend The on probabilityr = x of findingy . a galaxy in the volume element dV is: | − | δ(x)=⌃akcos(x k) · P1 =¯ndV (c+v)T0 p1+β λ0 = = λ0 p1 v2/c2 p1 β − − p1+β The probability of finding a galaxy in the volume element dV at location x and λ0 =(1+z)λ0 = p1 β λ0 − another galaxy2 6 at location y is: ↵ 32⇡Z e neni 2⇡ h⌫/kB T ✏⌫ = 2 e− gff(T,⌫) Letn ¯ be the average number density3m of galaxies.c3 The probabilityP32 k=(¯ndVTm of finding) [1 + ⇠(x, y)] a galaxy in the volume element dV is: e r B e 2 If the galaxies are uncorrelated, P2 =(P1) and ⇠ = 0. For a statistically ↵ P1 =¯ndV ✏⌫ is flat for h⌫homogeneous<< kBT andand isotropic exponentially universe, ⇠ can only decreasing depend on r for= xh⌫y >k. BT . ∆TheTSZ probability of finding a galaxy in the volume element dV at location x and | − | = f(⌫)y δ(x)=⌃akcos(x k) TCMBanother galaxy at locationc y is: · γ 2 r − P2 =(¯ndV ) [1 + ⇠(x, y)] 2 6 ⇠(r)= 32⇡Z e neni 2⇡ r0 2↵ h⌫/kB T If the galaxies are uncorrelated, P2 =(P1✏)⌫ and= ⇠ = 0. For3 a statistically e− gff(T,⌫) homogeneous and isotropic universe, ⇠ can only depend3 onmerc= x y .3kBTme ⇣ ⌘ | −r| δ(x)=⌃akcos(x k) ↵ · ✏⌫ is flat for h⌫ << kBT and exponentially decreasing for h⌫ >kBT . ∆TSZ = f(⌫)y TCMB c 2 6 ↵ 32⇡Z e neni 2⇡ γ h⌫/k T @⇢ ✏ = r −e− B g (T,⌫) Equations⌫ of3 mmotionc⇠3(r)= of3 kuniformTm expandingff universe @t + (⇢v)=0 e r Br0 e r↵· @v ✏⌫ is flat for h⌫ << kBT andP exponentially⇣ ⌘ decreasing for h⌫ >kBT . +(v∆TSZ = )f(v⌫)y= r Φ @t TCMB toc account ⇢for expansion with time, it is useful to γ · r r − −transformr to comoving coordinates 2 ⇠(r)= @⇢ Φ =4⇡Gr0⇢ ⇤ +r=a(t)x;( ⇢v=vd)=0r/dt=(ȧ/a)r+u! ⇣ ⌘ @t r · r − Hubble’s@v +( law:v v=) vHr=, thus H=P ȧ/a andΦ ! u is the peculiar@t velocity expressed inr ⇢comoving coordinates 2 · r − r @⇢ a(t)Φ is=4 called⇡G the⇢ “scale⇤ factor" @t + (⇢v)=0 @v r · P r − +(v )v = r Φ 2 Now, @considert · rthe evolution− ⇢ r of a spherical volume of radius L(t)=Ld 0a(t)L (if we chooseGM small L 2Φ =4⇡G⇢ ⇤ thenr GR corrections− become small and we can use Newtonian dynamics).2 =d 2ExpansionL 2GM will slow down because of gravitational pull of matter insidedt sphere: L −2 = 2 d2L GM 3 dt − L = 3 2 2 L L u u dt − L V =4⇡ ⇢ = ⇢ + L3 V =4u⇡ ⇢ = ⇢m +m 2 V =4⇡ ⇢ = ⇢ + 3 2 c 3 m c2 3 c 4⇡G⇢m with respect to a pointa¨ =in time where3 a we know the density to be ρ0 4⇡G⇢m ⇢ (t−)=⇢ a3/a(t)3 a¨ = 3 a m 0 0 − so,3 in a matter3 dominated Universe, we obtain ⇢m(t)=⇢0a0/a(t) 4⇡G⇢ a3 (deceleration must be non-zero! 0 0 1 Here is where Einstein added his cosmological a¨ = 2 3 a constant term at first to force ä to be 0) − 3 3 2 4⇡G⇢0a0 2˙a 8⇡G⇢0a0 2˙aa¨ = d(˙a )/dt = 3 a2 = 3 d( 1/a)/dt 3 − − − 2 8⇡G⇢0a0 1 2 1 a˙ = 3 a kc − 1 1 (c+v)T0 p1+β λ0 = = λ0 p1 v2/c2 p1 β − − p1+β λ0 =(1+z)λ0 = p1 β λ0 − Letn ¯ be the average number density of galaxies.
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