The Microwave BackgroundThe Microwave Background - TBC Prof. Guido Chincarini This part of the...
Transcript of The Microwave BackgroundThe Microwave Background - TBC Prof. Guido Chincarini This part of the...
Cosmology 2004/2005 1
The Microwave Background - TBC
Prof. Guido ChincariniThis part of the lectures introduce the MWB and ends stating three
problems which could be developed in many details and of great interest:
1) The Relation between the motion of the solar system and the distribution of Matter in the Universe. See the Potent Method.
2) The study of the anisotropies and of the irregualrities on the Microwave maps and their relation to:
a) The foreground contaminationb) The finger prints of matter on radiation.
3) The epoch of the reionization and the comparison of the quasars observations with numerical simulations and the estimates of theWMAP mission.
Cosmology 2004/2005 2
Cosmology 2004/2005 3
Cosmology 2004/2005 4
The youngest bound objects
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Cosmology 2004/2005 6
The Ω census0.01 0.1 1.0
HDM Massive Neutrinos
0.30.001 0.003 0.03
BaryonsStars
CDM
MatterGas
Photons
Light Neutrinos
Total
ΛGravity Waves
Cosmology 2004/2005 7
Gamow et al. - Alpher & Herman• A great prevision and no reward ?:
– R.B. Partridge (1995):3K The Cosmic Microwave Background Radiation.– R.A. Alpher and R. Herman Physics Today August 1988.– Gamow,G. 1956 September Scientific American.– Gamow,G. 1952 The Creation of the Universe, Viking Press– Gamow, G., 1946, Phys. Rev., 70, 572 and Erratum Corrige in 71, 273.
• Alpher and Herman considered the possibility to carry out a radio search to detect the background but were informed by their colleagues observer that the technology at the time was no sensitive enough for that detection.
• Weinberg in Gravitation and Cosmology (1972 Page 510) misses the point when he states :
– “A somewhat more detailed analysis along these lines, carried out in 1950 by Alpher and Herman, gave T0 = 5 degrees. Unfortunately, Alpher and Herman went on to express doubts as to whether this radiation would have survived until the present.”
– When A&H mentioned those doubts, they were discussing cosmic rays and not the Thermal microwave cosmic radiation.
Cosmology 2004/2005 8
A very Brief Summary - MWB• 1915 General Relativity – The Λ problem.• 1925 The expanding Universe.• 1946 – 1950 Big Bang Nucleosynthesis – Gamow, Alpher & Herman –
Predictions.• 1961 Sandage – Two parameters and a Model. However the evolving
Universe –• 1965 Dicke & Co. – Penzias and Wilson• 1970 Dipole Peebles – Zeldovich• 1970 – 1980 Anisotropies – See the Creta meeting Editors Abell &
Chincarini.• 1990 COBE: FIRAS & COBRA• 1992 COBE DMR Anisotropies
– End of the upper limits era– Low resolution however. Excellent estimate of the Temperature.
• 2000 Boomerang MAXIMA etc Maps and Spherical Harmonics Peak estimate.
• 2002 WMAP High resoluion maps.• ……….. The story continues …
Cosmology 2004/2005 9
Gamow 1948• If we form the heavy elements from elementary particles, and more
precisely usingProtons and Neutrons
• Then one of the fundamental reaction is that to form Deuterium:n + p => d + γ
• And this reaction happens at a temperature of about:T ~ 109 degrees
• On a temperature somewhat larger that 109 degress the γ photons dissociate the Deuterium as soon as it forms.
• That is we must have a T § 109. Furthermore we must be able to accumulate Deuterium as a first step to build up heavier elements.
• The density is also critical. I must have a density high enough to allow a reasonable probability for the reaction.
• On the other hand the density must not be too high. I can not overproduce heavy elements since the amount of Hydrogen must remain the highest one as I observe.
• Then I have an interplay between the cosmological model which changes density and Temperature as a function of time and the nuclear reaction rates.
Cosmology 2004/2005 10
How fast ?
n(t) σNumber of encounters = n σ v tOr\1 enclounter every seconds
I assume 1 encounter=1 reactionv t
For the reaction to occur at the desired temperature it must be that theThe reaction rate is smaller than the expansion time of the Universe since
otherwise theTemperature decreases and the reaction has not time to occurr.
1/(n σ v ) < texp or (n σ v ) >1
We now look at the Cosmology – Note that we are considering theearly phases of the Universe. In this case Ω (t) is very close to 1. That
is I can consider a flat Universe with the term k = 0 :
Cosmology 2004/2005 11
When
( )
( ) ( ) ( )
( ) ( )
( ) ( )( )
2 22
2
2 4
Tot Rad 2
0r r ,0
2
r rr ,0 0 2
r ,0 0 r
a 8 G kcH 1 ~ 0 ; k and termscana 3 a 3
be disregarded in t he earlyUniverse
8 G ta T; t ta 3 c
By preserving Black Body as we shall show
aT t Ta t
T t T tT a
T a T t
π ρ ΛΩ Λ
π ρ σρ ρ
− = − = − −
= = =
=
( )
24r2
62 r
r 2
T8 G3 c
T8 GT t3 c
σπ
σπ
=
=
Cosmology 2004/2005 12
( )
24
r
4
r 2 2
2 2
4
The solution is
3c32 GT t
t3 T 3t
32 Gt c 32 G
3c 3ct32 G 32 G T
π σ
σρπ π ρ
π ρ π σ
=
= = ⇒ =
= =
Remember this is strictly valid only for the radiation dominated Universe. The extension is an approximation
7.56 10-15
For T=109 t = 230.5 sec and trasforming T=109 in velocity:n(t)= 1/(σ v t ) = 1018 nucleons cm-3
Cosmology 2004/2005 13
Look at this From Thermal History Slides
( )( )
( )( )
( ) ( )( )
( ) ( ) ( )( )
( )( )
ee e e
ee
e
Deuterium Deuterium
e
H km s Mpc
a t tRadiation ta t t H
ta t tDust ta t t H
a tt slide t
a t z
a t a t a tT t T
a t a t
0
12
1702
3
00 0 0
31.52
17 110
0
00
65 / /
12
4.75 10 ;2 13
110 4.75 10 8.98 101
230.5
=
= ⇒ = =
= ⇒ =
= = = = +
= =( )( )e Deuterium e
e
t ta t t t
Kelvin
1 22 3
0 0
2111 32
11 17230.5 8.98 10 2.58.98 10 4.75 10
= =
= =
Cosmology 2004/2005 14
And( ) ( ) ( )
( )
( )( )
( )( )
Deuterium e Deuterium e
e e
H
a tn t n
a t
a t a t t ta t a t t t
cm m
cm
3
00
31 232 3
18 18
0 0
32111 32
8 311 17
8 3
230.5
10 10
230.5 8.98 10 1.47 10 *8.98 10 4.75 10
1.47 10 1.67 10
− −
− −
= =
= = =
= = ⇔
( ) ( )( )B B B
B
g g cm BarionsNowadays
HhG
h g cmG
24 32 3
22 0
22 5231 3
8
2.4 10 /:
30.028
3 0.02 0.65 100 10 / 3.09 10^ 243 100 1.58 108 8 6.67 10
Ω ρ Ωπ
Ωπ π
− −
− −−
=
≈ = =
= = =
Cosmology 2004/2005 15
We also have:
( ) ( )
12 4
r ,00 r ,0 0 r ,0 02
r 4
12
1 170 0 0
0 0
T t 3ca t a T a T a tT t 32 G3c
32 G
a t 2; t H flat 2.86 10 sec H 72a t 3
π σπ σ
−
= = =
= = = ⇒ =
Cosmology 2004/2005 16
The Discovery + Confirmation
Roll & Wilkinson 1966
Cosmology 2004/2005 17
Some History
Cosmology 2004/2005 18
The CN Molecules lines had been observed by Adams (1941), McKellar(1941) and others in the spectra of several stars. McKellar estimated that an excitation Temperature of a few Kelvin wa needed for the excitation. Only after Penzias and Wilson discovery Field and Hitchcock (1966), Shklovskii (1966) and Thaddeus and Clauser (1966) made the connection with the Microwave Background.
Cosmology 2004/2005 19
Cosmology 2004/2005 20
Spectrum after WMAP ObservationsSee also: http://map.gsfc.nasa.gov/m_mm.html
Cosmology 2004/2005 21
The Dipole
Cosmology 2004/2005 22
What happens during the expansion• I have a black body radiation Bν per unit solid angle.• If I divide by hν I get the number of photons.• If I divide by c I get the density of radiation and T is the Temperature.• When the volume expand I assume I conserve the number of photons. • This is true and however we should look into the mechanisms capable of
creating and destroying the photons.• What are the mechanisms by which at z < 109 it is possible to create
photons or change their Energy?– Thermal Bremstrahlung.(free – free)
• This is a function of the density of baryons– Compton – Electrons scatter photons – Radiative Compton – A second photon is produced in the e+γ scatter.
• These are a function of the Energy and density. The reaction are important only at very high Temperatures and density. Can be disregarded at lower Temperatures.
• I could also use the invariant Iν/ν3. Or again by stating that I preserve the law of physics, the BB therefore, and the number of photons, I get again Iν/ν3 to be invariant (By Invariant we mean a Lorentz invariant)
Cosmology 2004/2005 23
( ) ( )
( ) ( ) ( )
( )( )
( )( ) ( ) ( )
( ) ( )
( ) ( )
( )( )
( )( ) ( )
( )( )
3 21 2 1 1
2
3
3
3
2 3
3
3
2 h cI B erg s cm ster Hz ; Photons are inVolumeV t
hexp 1kT
8 V tu d 4 dN t dhh c exp 1kT
a t a t a t; d d ; V t V t
a t a t a t
a t a t8 V t
a t a tdN t dN t
a th
a tc exp
kT
ν ν
ν
νν
π νν π ννν
ν ν ν ν
π ν
ν
−− − − −= =
−
= = −
′ ′ ′= = =′ ′ ′
′′ ′ ′ ′= =
′ ′
( )( )
( ) ( )
( )( )
2
3
a t 8 V td d
ha t c exp 1kT
1
a tdefining T T
a t
π νν ν
ν′ ′ ′
′ ′=′ − ′ −
′ =′
Cosmology 2004/2005 24
Problem• We observe an object which emits Black Body radiation and is at
temperature T in its reference frame. The object is at redshift z subtending a solid angle dΩ. What is the flux. What is the redshift assuming a Doppler motion rather than a cosmological?
• We will use of the fact that Iνν3 is an invariant.
( )
( ) ( )
obs emit 3obs 3 emit
observed obs obs obs emit43 3obs emit
emit 4emit4 4
I IFlux I d d d1 z
I d T1 z 1 z
ν νν
ν
νΩ ν Ω ν ν Ω νν ν
Ω Ων σ
= = = =
+
= =+ +
∫ ∫ ∫
∫
• I conserve the blackbody spectrum and all I measure is equivalent to a BlackBody spectrum at z=0 with a Temperature of T/(1+z).
• The invariance holds in general, that is it does not make any difference of how we interpret the redshift, we always have the same result.
Cosmology 2004/2005 25
Black Body - nγ/nB
( ) ( ) ( )
( )
( ) ( )
( )
44 15 13 3
34 3r 2
3 42 3
2 x0 0 0
46 4
2 3
photons 30
4u T B T d T 7.56 10 2.7 4.02 10 erg cmc
u T h4.5 10 g cm ; xc kT2h c 2h kT x dxB T d d
h c h e 1exp 1kT
2.77 10 T15
8 c 8 kN dh cexp 1kT
νπ ν σ
νρ
νν ν
ν
π
π ν πνν
− − −
− −
−∞ ∞ ∞
−
−∞
= = = =
= = =
= = = − −
=
= = −
∫
∫ ∫ ∫
∫2 2
x0
T kT x dx 398.1h h e 1
∞ = − ∫
Cosmology 2004/2005 26
0
2 29 229 2 240 0 0
0 ,c 0 H B( 0.02 ) 24
5 2 7 20 0 0 0
B
Matter and Radiation :3H 1.87 10 h1.87 10 h ; m 1.67 10 ; n8 G 1.67 10
n1.110 h ; 3.6 10 h
n
Ω
γ
Ωρπ
Ω Ω
−− −
= −
−
= = = = =
= =
Cosmology 2004/2005 27
More about Radiation – Specific Heat
• The energy of each molecule of a monoatomic gas is 3/2 k T.• We indicate with N the number density of molecules. See Landau
and Lifshitz for the definitions.
( )
3V ,m V ,r
V V
5 168V ,m
33 15V ,r
E 3 EC Nk and for a BB C TT 2 T
3 3kN 10 1.38 10C 2 2 1.4 10C T 7.56 10 2.7
σ
σ
− −
−
−
∂ ∂ = = ⇒ = = ∂ ∂
= = =
This is a result in the same direction of the number of photons versus the number of baryons. To change by 1 degree the Radiation temperature we need about 108 times the energy needed to change by 1 degree the matter.
Cosmology 2004/2005 28
Entropy
( )
( )
( )
4
3T T 3 3
0 0
3B
3
B3 2
3 33 x0
Density of Energy u Tdu 4 T dT 4Entropy S T a tT T 3
Density of particles n a tS 4Entropy per baryon T constn 3 n
8 kT x dx Sn T a t constc h e 1 nγ
γ
σ
σ σ
σ
π ∞
=
≡ = = = ∝
∝
≡ = =
= ∝ ∝ ⇒ = −
∫ ∫
∫
Cosmology 2004/2005 29
The MWB - Observations
Cosmology 2004/2005 30
The Dipole
• The small value of the anisotropy, β=v/c ~ 10-3, simplify the derivation since we can disregard relativistic effects.
• It is not, as often simplified, a simple Doppler effect.• The Doppler effect will increase the energy of the photon
in the direction of the motion of the factor ν/ν0 = (1+βcosθ). On the other hand the interval of frequencies dνalso increases of the same factor dν = dν0 (1+β cosθ).
• Since the Temperature is defined in terms of Energy per unit frequency, see for instance the Black Body, the net effect of Doppler is that the Temperature does not change. That is from above ν/dν = ν0 / dν0.
Cosmology 2004/2005 31
The moving observerSee Peebles Physica Review 23 October 1968 Vol 174, Page 2168
• The observer who moves in a certain direction will collect, in the direction θof the motion, more photons than the steady observer. The latter colectscdt * Area * density and the former (cdt + v*dt cosθ) *Area * density. That is a factor
• difference.• A second effect acts on the solid angle in the following way and accounting
for the effect of aberration, that is by moving the angular position of an object changes.1. I use the relativistic transformation of velocities.2. The observer is moving with a velocity v. The photons collected have energy E
in the range dE3. The solid angle dΩ can be written as dΩ = dφ sinθ dθ = dφ d(cosθ). 4. The two observers agree on the Number of photons they collected, that is
dN=dN’.5. The Numbe of photns per unit volume, solid angle and energy interval is n(E,θ).6. The observers also agree on the Area A0 of the detector.
( )c dt v dt Area CosCos
c dt Area1
θβ θ
+= +
Cosmology 2004/2005 32
Detailsyx
x yx x2 2
x y
x y
x
u /u vu ; u ; the photons come from and .u u1 v 1 vc c
u c Cos ; u c Sin
c Cos v c Sin /u ; u andCos Cos1 v 1 vc c
vCosu CoscCos Cosc 1 Cos1 vc
γθ θ
θ θ
θ θ γθ θ
θ θ βθ θ β θ
−′ ′ ′= =− −
= − = −
− − −′ ′= =+ +
+′ +′ = − = =++
θ θ′
v
Cosmology 2004/2005 33
Useful relations
( )
( ) ( ) ( )( ) ( )
( )
( )
2 2
2
2
2
2
2
Cos 11 cos ' 11 Cos 1 Cos 1 Cos
coscos ; cos cos 1 cos cos1 cos 1 cos
d cos 1d 2 d cos 2 d cos 2 d cosd cos 1 Cos
1d d1 Cos
θ β β γβ θ ββ θ β θ β θ
θ β γθ β θ θ β θ θβ θ β θ
θ βΩ π θ π θ π θθ β θ
βΩ Ωβ θ
−
−
+ −− = − = =
+ + +
′ − ′ ′= + = + =′ ′− −
−′ ′ ′= = =+
−′ =+
Cosmology 2004/2005 34
That isFor the Energy transformation see for instance French S.R. Page 210
( ) ( )
( ) [ ]
( ) ( ) ( )
2
2 22
xx
0 0
In a similar wayd cos 1d d cos d dd cos 1 cos 1 cosdt dt ; the photon comes toward me
p cosE E vp E 1 v E 1 v ; same forE c
dN n E , dE d dt A cos dN n E, dEd dtA v cos
n E ,
θ γΩ θ Ω Ωθ β θ γ β θ
γθγ γ γ ν
θ Ω θ θ Ω θ
−′′ ′= = =
′ ′ ′− −
′=
′ = + = + = +
′ ′ ′ ′ ′ ′ ′ ′= = = +
′ ′ ′( ) ( )( ) ( )
( )( )
( )
( )( )
( )
2
22
22
22
2
22
d 1n E, dt1 cos 1 cos1 cos
1 cosdn E, dt1 cos1 cos
1n E, n E,1 cos
Ω γθ θ γβ θ γ β θγ β θ
γ β θΩ γθ γβ θ γγ β θ
νθ θνγ β θ
−
−
′′= =
′− +′−
′−′′ =
′−′−
′ = = ′ −
Cosmology 2004/2005 35
Using Planck Equation
( ) ( ) ( )( )
( ) ( ) ( ) ( ) ( )
( ) ( )( )( ) ( ) ( )
2 3
22
2 32 22 2
22 233 322
8 c 1n E , n E,h 1 cos 'exp 1kT
8 cSlide 33 n E, 1 cos 1 cos
hexp 1kT
8 1 cos c8 c 8 c1 cos
h hh 1 cosexp 1 expexp 1kT kTkT
π νθ θ
ν γ β θ
π νθ γ β θ γ β θ
ν
π γν β θπ ν π νγ β θ
ν νγν β θ
−
−
−− −
′′ ′ ′ = = =
′ −− ′
=> = + = + −
+′= = +
′ + − − ′ ′ ( ) ( )
( ) ( ) ( )2
1
h 1 cos 1 cosh 1kT kT T T
1 1T T 1 cos T T1 cos 1 cos
γν β θ γ β θν
γ β θ γγ β θ γ β θ
−
+ += =
′ ′
′ = + = =′ ′− −
⇒
Cosmology 2004/2005 36
Approximating
( )
( )
( ) ( )( ) ( ) ( ) ( )
( )( ) ( ) ( )
( )
1 12 22 2
2
0 0
0
1T T for semplicity I use1 cos
seriesf 0 1
cos 1f 0 1 1 21 cos1 cos
f 0 cos
T T f 0 f 0 T 1 cos
T T T T T T cosT cosT
θ ϑγ β θ
β
ϑβ β β ββ θβ θ
β β β ϑ
β β β β ϑ
ϑ ∆ β ϑ∆ β ϑ
−
′ ′= ≡′−
= =
′ = = − + − −′−′−
′ = =
′ ′= ∗ = + = = + ′ − ≡ − = =
=
Cosmology 2004/2005 37
More for fun – A satellite
x vt y h emits signals with frequencyν= =
θ
x=0x1 x2
h
Ground
Obs
Cosmology 2004/2005 38
The satellite Frame• Two Pulses, from x1 and x2
separated by τ.• Time to reach the observer are
r1/c and r2/c .
The Observer• Pulse separated by γτ = γ/ν
since τ = 1/ν• The observer measures a time
separation τ′ = r2/c-r1/c+γτ• Due to the large distance of
the satellite and the small sepration between x2 and x1we can write:
r1-r2 ~(x2-x1) cosθ=vγτcosθ and
τ′ = r2/c-r1/c+γτ = -vγτcosθ/c + γτ= γτ (1-v cosθ/c) or
ν′ = ν / [γ (1-β cosθ)]
Cosmology 2004/2005 39
The observed motion – First Question
• After correction for the motion of the Eart, rotation and revolution about the Sun we obtain the heliocentric velocity which is:
370.6≤0.4 km/sL=264.31≤0.17B=48.5≤0.10
• After making correction for the rotation of our galaxy and for the motion of our galaxy respect the Local Group of galaxies (see later) we have:
VLG-MWB=627≤22km/sL=276≤3B=30≤3
Cosmology 2004/2005 40
Next Slides are the Introduction to the Large Scale Structure
Cosmology 2004/2005 41
Cosmology 2004/2005 42
K Band λ=13 mm, ν=22.8 Ghz
Cosmology 2004/2005 43
Ka Band λ=9.1 mm, ν=33 Ghz
Cosmology 2004/2005 44
Q Band λ=7.3 mm, ν=40.7 Ghz
Cosmology 2004/2005 45
V Band λ=4.9 mm, ν=60.8 Ghz
Cosmology 2004/2005 46
W Band λ=3.2 mm, ν=93.5 Ghz
Cosmology 2004/2005 47
The Cleaned anisotropy map
Cosmology 2004/2005 48
The anisotropy – II Question
The first detailed, all-sky picture of the infant universe. The WMAP image reveals 13 billion+ year old temperature fluctuations (shown as color differences) that correspond to the seeds that grew to become the galaxies. Encoded in the patterns are the answers to many age-old questions, such as the age and geometry of the Universe.
Cosmology 2004/2005 49
The second question
• The seeds of in_homogeneitiesexist in the Universe since the very beginning and during the period matter and radiation were coupled these in_homogeneities were present both in the radiation and in the matter.
• After decoupling matter perturbations grew or dissipated but the print of the Microwave had to be visible and correlate to the distribution of matter we see now.
• That is the anisotropies are of fundamental importance to the understanding of the Universe, its formation and evolution.
• It is also apparent that in order to see the foot print of galaxies or smaller objects we need a very good resolution.
Cosmology 2004/2005 50
The resolution of the MWB
• I show on the right Figure the comparison between the COBE satellite and the WMAP.
• COBE with a resolution of about 7 degrees could only show the correlation with the very large structures.
• The relation between angular and linear size is about:
θ(L)=34.4” (Ωh)(l0/1 Mpc)
Cosmology 2004/2005 51
The Finger prints – Courtesy of ?(Search again)
• We believe that large scale structure in the universe grew out of small perturbations in the early universe through gravitational instability. This implies that the photon-baryon fluid moves in a gravitational potential well before last scattering.
• This assumes a Newtonian representation of perturbations. The response of the fluid to the gravitational potential fluctuations allow us to measure the properties of the fluid in an expanding universe known to be filled with dark matter, which allows us to extract basic cosmological parameters, as well as those of the seed perturbations, which can be used to pin down the nature of large scale structure formation in the universe.
Cosmology 2004/2005 52
Accuracy of Parameters
Each point is the mean of various observations and it is clearly how small are the observational errors.
This Figure is shown simply to show that by analyzing the distribution of the irregularities, after subtraction of foreground disturbing, but extremely interesting objects, the Cosmological parameters can be derived very accurately.
Cosmology 2004/2005 53
Cosmology 2004/2005 54
How it works
• By going back in time, from left to the right, objects and structures become fuzzy and while showing structures they move toward recombination where the decoupling between matter and radiation occurred. Here we find the Microwave background radiation and the foot print left from matter to radiation via the strong coupling due to Thomson scattering.
Cosmology 2004/2005 55
Ω As a function of scale size
• The plot shows that the value of the density parameter Ω increases as a function of the scale length.
• This is equivalent to say that the Mass to Luminosity ratio increases with scale length.
• An analogous result had been derived long ago (early seventies) by H.J. Rood who showed that the Mass to Luminosity ratio of extragalactic system is a function of the Virial mass.
• The reader search in the literature for this resul and discusses it.
Cosmology 2004/2005 56
Cosmology 2004/2005 57
III Question
• And we conclude this part with the problem of re_ionization. According to the new observation of WMAP the epoch of reionization occurred at zr = 20-9
+10.• Recent observations of quasars at z > 6 showed that
re_ionization is very near z ~ 7 and this was in reasonable agreement with the observations.
• This need to be discussed and set in a common and reasonable framework.