CMB acoustic peaks

1
CMB acoustic peaks
2
Potential fluctuations broken up by mode
hill
well
r, or time
3
Potential fluctuations broken up by mode
hill
well
dT/T
r, or time
baryon-photon fluid propagated this far since Big
Bang
4
Potential fluctuations broken up by mode
3rd acoustic peak fluid compression in potential
wells
hill
well
dT/T
time
2nd acoustic peak fluid compression in potential
hills
1st acoustic peak fluid compression in potential
wells
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Fluid oscillations in a potential well
Maximum fluid rarification
Maximum velocity maximum contribution to the
Doppler term
Maximum fluid compression
Graphic Wayne Hu
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Quantitative treatment of oscillations
In general there are three contributions to the
observed temperature
denser fluid is hotter
gravitational redshifting
90 deg out of of phase with the other two
Note for the Sachs-Wolfe plateau, the Doppler
term is insignificant
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Quantitative treatment of oscillations
Jeans analysis of small perturbations (linear
regime)
after applying assumptions
general solution
get B by using soln in the oscillator eqn
Constant A and the absence of the sin() term in
the solutions come from applying the boundary
conditions of the Sachs-Wolfe effect
?
velocity negligible at very early times and
large k (SW effect)
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Quantitative treatment of oscillations
Putting in values for A and B
The two contributions to temperature (i.e.
exlcuding the Doppler term)
The velocity Doppler contribution to temperature
(multiplied by i, 90deg out of phase)
line of sight velocity is a third of full v2
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Quantitative treatment of oscillations
First, third, etc (odd) acoustic
peaks Second, fourth, etc. (even) acoustic
peaks
enhanced by (16R) because fluid with baryons
compresses well!
fluid rarifaction in potential wells (smaller
amplitude than compression)
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Potential and Doppler terms no baryons
Potential hill
compressions hot spots
rarifactions cold spots
potential doppler
Potential well
Sachs-Wolfe effect (small k, large scales)
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Add baryons
Baryon drag decreases the height of
even-numbered peaks (2nd, 4th, etc.) compared to
the odd numbered peaks (1st, 3rd, etc.)
Potential well
3rd acoustic peak
1st acoustic peak
doppler term is also enhanced, but not as
much, because fluid with baryons is heavier,
moves slower
k (fixed t)
p 2p
3p 4p
2nd peak
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WMAP 3 year data
3D -gt 2D projection effects and smearing of
fluctuations on small scales due to
photon diffusion out of structures
convert positive and negative temperature
fluctuations to rms fluctuations (take squares
all positive)
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Growth of small density perturbationsSub-horizon
, Matter dominated
Jeans linear perturbation analysis applies
(proper)
Two linearly indep. solutions growing mode
always comes to dominate ignore decaying mode
soln.
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Why we need dark matter - I
Fractional temperature fluctuations in the CMB
are 1/105 The growth rate of density
perturbations in a non-relativistic component
is at most as fast as
a1/(1z) Recombination took place at
z1000 Then predict that today amplitude of
typical fractional overdensities should be 0.01

But,
in galaxies and clusters
observed
fractional overdensities 100
?
fluctuations that we see in the CMB

are not enough to give us structure today


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Why we need dark matter - II
Evolution of amplitude of a single k-mode
Because dark matter is not coupled to photons and
baryons its fluctuations can grow independently.
Baryon-photon fluid oscillates in the potential
wells of DM, but fluctuation amplitude is small
this is what we see as dT/T 1 part in 105. DM
fractional overdensities are larger at
recombination (but we do not see them
directly) After recombination baryons are let go
from photons, and fall into the potential wells
of DM.
log (fractional overdensity)
log (scale factor)
super-horizon sub-horizon all
grow at causal microphysics
same rate is now important