Cosmology - Redshift and Radiation ASTR 2120 Sarazin

Transcription

1 Cosmology - Redshift and Radiation ASTR 2120 Sarazin

2 Test #1 Monday, February 26, 11-11:50 am ASTR 265 (classroom) Bring pencils, paper, calculator You may not consult the text, your notes, or any other materials or any person You may bring a 3x5 card with equations ~2/3 Quantitative Problems (like homework problems) ~1/3 Qualitative Questions Multiple Choice, Short Answer, Fill In the Blank questions No essay questions

3 Test #1 (Cont.) Material: Chapters 20, 21, 22, 23 Normal Galaxies, Galaxy Formation, Spiral Arms, Extragalactic Distance Scale, Clustering and Clusters of Galaxies, Dark Matter, AGNs, Theory of AGNs, Cosmology (Basics Facts, Models w/o Dark Energy, Models with Dark Energy, Alternative Models, Tests, Concordance Cosmology Homeworks 1-4 Know pc, AU, M solar, L solar, R solar, H 0, T CMB No problem set week of Feb to allow study for test

4 Test #1 (Cont.) Review Session: Discussion session Friday, February 23, 3-4 pm ** Note back to original time for this week only **

5 Cosmology - Redshift and Radiation ASTR 2120 Sarazin

6 Redshift in Cosmology λ obs λ em = r obs r em z = λ obs λ em λ em = λ obs λ em 1 1+ z = r obs r em Big Bang : r em 0 z Wavelengths just expand with Universe!! Really, it could not have turned out to be simpler or nicer!

7 Redshift in Cosmology

8 Redshift in Cosmology Example: The Hubble Ultra Deep Field contains a galaxy with a redshift of z = 10 When this galaxy emitted the light we now see, the Universe was (1+z) = 11 times smaller than it is today!!

9 Cosmic Microwave Background (CMB) T = K Awfully cold - who cares? a) Most of known heat and free energy in Universe b) Most of photons in Universe N(photons)/N(protons) ~ 10 9 (Homework problem) Where did this big number come from? Why isn t it bigger? If matter and antimatter were symmetric p + p 2γ N(photons)/N(protons) Bright and shiny (but empty) Universe!!

10 Cosmic Microwave Background VERY hot in the past: (CMB) Theorem: Redshifted and expanded blackbody = blackbody at redshifted temperature λ T γ = constant (T γ CMB temperature) T γ ( z) = ( 1+ z)t γo

11 Cosmic Microwave Background Example: (CMB) The Hubble Ultra Deep Field contains a galaxy with a redshift of z = 10 When this galaxy emitted the light we now see, the CMB temperature was (1+z) = 11 times larger than it is today = 30 K

12 CMB at z=10 Galaxy Belliac Labs 30 K Pensiac Wilsoniac

13 Cosmic Microwave Background (CMB) λ T γ = constant (T γ CMB temperature) T γ ( z) = ( 1+ z)t γo (1 + z) = r o / r e as Big Bang is approached, so T at Big Bang

14 Hot Big Bang

15 Radiation-Dominated Era In early Universe, CMB dominates dynamics and gravity Compare to matter ρ m r 3 = constant (mass conservation) ρ m (z) = ρ 0 (r o /r) 3 = ρ 0 (1+ z) 3 n γ r 3 = constant n γ = n γo (r o /r) 3 = n γo (1+ z) 3 hν ~ kt (r o /r) = (1+ z) ρ γ = u γ /c 2 ~ n hν γ (1+ z) 4 T 4

16 Radiation-Dominated Era ρ γ (z) = ρ γo (r o /r) 4 = ρ γo (1+ z) 4 ρ γ (z)/ρ m (z) = (ρ /ρ γo mo )(1+ z) as Big Bang is approached ρ mo = ρ o = Ω ρ M crit (1/ 3) gm/cm 3 ρ γo = gm/cm 3 (homework) (ρ /ρ γo mo ) 10 4 ρ γ > ρ m for z >10 4

17 Radiation-Dominated Dynamics Solve Cosmic Expansion Equation for ρ = ρ γ (r o /r) 4 not (r o /r) v2 = GM 1 r 2 Kro2 c 2 Cons. of Energy As r 0, 1 st term on r.h.s. dominates as M and (1/r) ( v 2 = dr + * - ) dt, 2 = 2GM r = 2G(4π / 3)ρ γ r 3 r 2

18 Radiation-Dominated Dynamics " $ # dr dt % ' & 2 = 8πGρ γ r2 3 +, - d(r /r o ) dt. / 0 2 = 8πG 3 ρ " r γ $ # r o % ' & 2 ρ γ = ρ γo (r /r o ) 4 +, - d(r /r o ) dt. / 0 2 = 8πG 3 ρ " γo(r /r o ) 4 r $ # r o % ' & 2 = 8πG 3 ρ " r γo$ # r o % ' & 2 d(r /r o ) dt = 8πG 3 ρ γo " $ # r r o % ' & 1

19 " $ # " $ # " $ # Radiation-Dominated Dynamics r r o r r o r r o % ' d(r /r ) o = 1 & dt 2 % ' & 2 T γ T γo = = 2 8πG 3 ρ γo % " ' = $ 32πG & # 3 " $ # r r o % ' & 1 ρ γo d(r /r o ) 2 % ' & 1/4 dt " = $ 32πG # 3 = 8πG 3 ρ γo t + const. (= 0) t 1/2 ρ γo % ' & 1/4 t 1/2

20 Radiation-Dominated Dynamics Correct for neutrinos T γ K t 1/2 (t in sec) for T γ > 30,000 K Very Hot!

21 Hot Big Bang

22 Thermal History of Universe ASTR 2120 Sarazin Alpher, Gamow (floating in Ylem), & Hermann

23 Thermal History of Universe Do in two passes: t > 10-6 seconds, physics pretty well understood Very early history, more speculative and more exotic physics. Tie in to frontiers of physics

24 Thermal History of Universe George Gamow

25 Thermal History of Universe T γ K t 1/2 (t in sec) for T γ > 30,000 K t 10-6 sec, T K kt m p c 2 ~ m particle c 2 for most particles particle + antiparticle 2γ Example : p + p 2γ N particles N antiparticles N γ Bubbling sea of particles and antiparticles p, p,n,n,e,e +,γ,ν,ν,π,ω,... etc.

26 Thermal History of Universe 10-5 sec t 1 sec, K < T K kt < m particle c 2 for most particles Most particles (except e s, ν s) can be destroyed but not made particle + antiparticle 2γ 2γ particle + antiparticle a) Unstable particles decay t 1/2 ~ to sec << t Exception: neutron, t 1/2 = 11 minutes p, p,n,n,e,e +,γ,ν e,ν e,ν µ,ν µ,ν τ,ν τ,(dark matter particles)

27 Thermal History of Universe 10-5 sec t 1 sec, K < T K b) Antimatter annihilates p + p 2γ (no reverse) n + n 2γ If matter/antimatter symmetric, this is very efficient N p /N γ 10-18, not 10-9 as observed (homework) If pure matter, N p ~ N γ initially, would still be true Need small, but non-zero asymmetry N p N p N p ~ 10 9

28 Thermal History of Universe 10-5 sec t 1 sec, K < T K N p N p N p ~ 10 9 Existence of matter today requires Universe had a small matter/antimatter asymmetry by 1 sec

29 Thermal History of Universe 10-5 sec t 1 sec, K < T K c) Electrons and neutrinos still produced kt >> m e c 2 e,e +,ν e,ν e d) Protons and neutrons in equilibrium p + + e n +ν e p + +ν e n + e +, etc. View p + & n as different states (isotopic spin) of same particle

30 Thermal History of Universe 10-5 sec t 1 sec, K < T K View p + & n as different states (isotopic spin) of same particle N n = e ΔE /kt = e Δmc 2 /kt = e (m n m p )c 2 /kt N p n p ΔE=(m n -m p )c 2

31 Thermal History of Universe N n = e ΔE /kt = e Δmc 2 /kt = e (m n m p )c 2 /kt N p 1 sec t 10 3 sec, K < T 3 x 10 8 K (m n -m p )c 2 /k ~ K N n /N p decreases After a few seconds, T < m e c 2 /k ~ 6 x 10 9 K, can t make electrons anymore e + + e 2γ (no reverse) Reactions between n, p stop n + e + p + +ν e, etc. stop

32 Thermal History of Universe N n = e ΔE /kt = e Δmc 2 /kt = e (m n m p )c 2 /kt N p 1 sec t 10 3 sec, K < T 3 x 10 8 K Neutron to proton ratio freezes out at N n N p /8 What happens to neutrons? n p + + e +ν e, beta decay, t 1/2 =11 minutes If nothing else happened, neutrons would decay away

33 Fusion During Big Bang 1 sec t 10 3 sec, K < T 3 x 10 8 K ρ baryons 10-2 gm/cm 3 Hotter, lower density than center of star, but not completely dissimilar Differences from star: a) Very little time (minutes) No weak reactions No pp reaction (10 10 years in Sun) b) Free neutrons Never true in stars except SN, only last 11 minutes

34 Fusion During Big Bang p + n 2 H +γ 2 H + p 3 He +γ 3 He + n 4 He +γ and similar

35 Fusion During Big Bang

36 Fusion During Big Bang p + n 2 H +γ 2 H + p 3 He +γ 3 He + n 4 He +γ and similar No significant reactions beyond 4 He In stars, requires Triple-Alpha reaction, very slow, not enough time in Big Bang Lose energy between 4 He and 12 C, only reaction is 3 4 He 12 C

37 Fusion During Big Bang 3α reaction

38 Fusion During Big Bang p + n 2 H +γ 2 H + p 3 He +γ 3 He + n 4 He +γ and similar No significant reactions beyond 4 He In stars, requires Triple-Alpha reaction, very slow, not enough time in Big Bang Lose energy between 4 He and 12 C, only reaction is 3 4 He 12 C

39 Fusion During Big Bang

40 Fusion During Big Bang Fusion in Big Bang makes H & 4 He Traces of 2 H & 3 He Tiny bits of 6 Li, 7 Li, 7 Be

41 Fusion During Big Bang How much helium? Fusion reactions up to helium very efficient All neutrons helium Initially, N n ~ N p / 8 Do arithmetic (homework problem), find Y = 0.22 (mass fraction of helium) X = 0.78 (mass fraction of hydrogen) Agree with values in oldest stars

42 Fusion During Big Bang How much 2 H (deuterium), 3 He (helium-3), Li? p + n 2 H +γ 2 H + p 3 He +γ 3 He + n 4 He +γ Fusion reaction rate depends on density of baryons ρ baryons High density = less 2 H, 3 He, more Li Low density = more 2 H, 3 He, less Li

43 Fusion During Big Bang

44 Fusion During Big Bang Gives ρ baryons at t = 1 sec, T = K ρ baryons (today) = ρ baryons (1 sec) x (r / r o ) 3 = ρ baryons (1 sec) x (1 + z) -3 T (1 sec) = T (today) x (1 + z) (1 + z ) = K / K ρ baryons (1 sec) gives ρ baryons (today)!!

45 Fusion During Big Bang

46 Fusion During Big Bang Gives ρ baryons at t = 1 sec, T = K ρ baryons (today) = ρ baryons (1 sec) x (r / r o ) 3 = ρ baryons (1 sec) x (1 + z) -3 T (1 sec) = T (today) x (1 + z) (1 + z ) = K / K ρ baryons (1 sec) gives ρ baryons (today)!! ρ baryons (today) = 3.5 x gm/cm 3 Ω (baryons) = ρ baryons / ρ crit = Ω b = 0.044

47 Fusion During Big Bang Ω b = << Ω M Dark matter not anything which was ordinary matter at t = 1 second Not planets, brown dwarfs (MACHOs) Not black holes from stars or collapse of matter Dark Matter = weakly interacting particles made in Big Bang!