WMAP satellite. 16 Feb Feb Feb 2012

Transcription

1 16 Feb Feb Feb 2012 è Announcements è Problem 5 (Hrtle 18.3). Assume V * is nonreltivistic. The reltivistic cse requires more complicted functions. è Outline è WMAP stellite è Dipole nisotropy è Smll-scle nisotropy è Rough clcultion of the ngulr scle è Precise clcultion of the ngulr scle è Sound wves WMAP stellite

2 2 cosmology.nb Dve's notebook, (Greg Tucker )

3 cosmology.nb 3

4 4 cosmology.nb Five wvelength bnds. Ech ssembly compres two regions of the sky seprted by 140. Q: Why does ech ssembly compre two regions of the sky? One ssembly opertes t 22 GHz, one t 30 GHz, two t 40 GHz, two t 60 GHz, nd four t 90 GHz. Q: Why is there only one ssembly t 22GHz yet there re four t 90GHz? Dipole nisotropy Temperture of the entire sky. Hottest spot is 3mK hotter thn the verge. Pink is rdition of the Milky Wy Glxy, which hs different spectrum. There is specil frme in which the universe is t rest. We re moving with respect to this frme. On 21 June, we re moving towrd Pisces t 30 km s = Q: On 21 June, wht is the Doppler shift of the 2.7-K photons looking towrd Pisces? 90 from Pisces? 180 from Pisces? Q: On 21 June, wht is the temperture shift of the CBR towrd Pisces? 90 from Pisces? 180 from Pisces? The peculir velocities of glxies re bout 300 km s = A not unresonble vlue of the dipole nisotropy is 2.7 mk. The dipole nisotropy is mk towrd l, b = , (Bennett et l., 2003, ApJS, 148, 1). Motion of the sun in the Milky Wy is 215 km s. Milky Wy moves t 200 km s towrds Andromed. Net velocity of the locl group of glxies is km s towrd (l, b) = (276 ± 3, 30 ± 3 ) (Smoot et l, 1991, ApJ 371, L1,Kogut et l, 1993, ApJ 419, 1) WMAP ngulr size of fluctutions

5 cosmology.nb 5

6 6 cosmology.nb WMAP: Rough clcultion of the physicl size of the fluctutions Pln: Why is the lrgest nisotropy t n ngulr scle of 1? Fluctutions cn grow for the ge of the universe. The size is bout ct. We will clculte the ge of the universe (for given W 0 r ). Then clculte the size L precisely. We lredy know tht the ngle subtended by ruler t expnsion premeter nd comoving distnce r is q=l r. ü Age of the universe ü Using middle-school physics A cr is moving t 50mph. It is 100mi from us. How long hs the cr been trveling since it left? A glxy is moving from us t speed v. Its distnce is v = DH 0. Assume it hs lwys moved t this speed. Wht is the time since the Big Bng? t = D v = D DH 0 = H 0-1 Neglected effect: the glxy cn be slowing down or speeding up. ü Proper clcultion of expnsion vs time Friedmn's eqution reltes the expnsion prmeter t, mtter density r t, nd the rdius of curvture r 0. We wnt to integrte Friedmn's eqution to find t.

7 cosmology.nb 7 d H 0 dt 2 = W k0 +W m0-1 +W r0-2 +W v0 2 H 0 dt= W k0 +W m0-1 +W r0-2 +W v d H 0 t = 0 Wk0 +W m0 x -1 +W r0 x -2 +W v0 x dx Importnt & instructive cses: Mtter: H 0 t = 1 -Wm0 +W m0 x dx 0 Integrte 1 Sqrt 1 o ox 1, x, 0,, Assumptions 1 o 0, 1 0 o o o o o 1 o ArcSinh 1 1 o 1 o o The ge of the universe t expnsion prmeter t = H W m0 +W m0 - W m W 3 2 m0 1 -W m0 1 2 rcsinh 1-W -1 m W m0 W 1 2 m0 More specificlly, for W m0 = 0, H 0 t = For W m0 = 1, H 0 t = For W m0 = 2, H 0 t = x dx x = dx= 0 2 x-x Or. 1-1-x dx 1-1-x = rccos 1 - x x = 1 - cos h t = H 0-1 h-sin h Wht is the mximum vlue for the expnsion prmeter? At the present ( = 1), the ge of the universe is H 0-1 p Now H 0 t Rdition with W r0 = 1:

8 8 cosmology.nb H 0 t = 0 x dx= 0 xdx H 0 t = Integrte x Sqrt x 2 1 o o, x, 0,, Assumptions o 1, 1 0 o 2 1 o o 1 o H 0 t = W r - W 0 r - 2 W 0 r W 0 r - 1 For W 0 = 1, H 0 t = W 0 r = H 0 t Cption: time vs expnsion prmeter for universe with rdition only. Q: All of the models hve the sme slope t the present time. Why? Q: Why does it tke less time for the universe to expnd with lrger density of rdition? ü Plots ü Estimte of the ngulr size of the fluctutions for W mtter 0 = 1. q=l r Assume the universe is mtter dominted. r is expnsion prmeter t recombintion. Assume W 0 = 1. L = ge of universe -1 = H r 3 2 r = 2 H q= 1 3 r r 1 2

9 cosmology.nb 9 In[646]:= " " Out[646]= Now we need to do better job. 1. Rdition domintes in the erly universe. 2. How fst do sound wves go? 3. Prt of the speed of sound is ersed by the expnsion of the universe. (Hrtle 18.3). Sound wves before recombintion ü Physicl conditions t recombintion ü At recombintion, which hs the greter mss density, pressureless mtter or rdition? W m0 = 0.26 pressureless mtter, mostly drk mtter, mtter tht does not interct with light W b0 = bryons, ordinry mtter W r0 = 1.2μ10-5 rdition r b = r b0-3 r r =r r0-4 r m r r =r m0 r r0 At eq = (z = 3600), the mss-energy density of bryonic mtter nd rdition re equl. Q: At recombintion (=0.0009), which hs greter mss density, pressureless mtter or rdition? We will discuss sound wves, which hs to do with rdition nd mtter. Q: Does drk mtter prticipte in the sound wves? Q: At recombintion, re electrons pressureless? The energy of CBR photon is 2.3μ10-4 ev. ü At recombintion, which hs greter number density, bryonic mtter or rdition? At the present time, the mss of bryonic mtter is 938MeV. The mss of photon is 2.73 K K ev = 2.3μ10-4 ev. The number density n r n b = μ938 MeV 2.3μ10-4 ev = 1.1μ10 9. More precisely, becuse photons hve different energies, I need to integrte the Plnck number spectrum. n r = 0.41μ10 9 photon m -3 T K 3 n b = 0.25 nucleon m -3 W b0.043 H 0 72 km s Mpc 2 n r n b = 1.64μ10 9. The number of photons nd bryons do not chnge. As the universe expnds, the number of bryons in coexpnding box does not chnge. The number of bryons entering must equl the number exiting, becuse of homogeneity. Sme rgument is true for photons.