the physics of baryons - cosmo-ufes
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The Physics of Baryons
J. A. de Freitas Pacheco
Laboratoire Lagrange - CNRS
Outline of the talk
• Appearance of the baryons in the Universe – the
quark-hadron phase transition
• Primordial nucleosynthesis
• Decoupling from radiation
• Recombination
• Distribution of baryons in the Universe
The appearance of baryons in the Universe – the quark-hadron phase transition
The transition occurs when the chemical potential of both phases are equal: q(P) = h(P)
The pressure of quark+ gluons
with geff = 47.5, B = 58 MeVfm-3 and A = 3.53 fm-3 (Brown et al. 1988 ; Bacileri et al. 1988)
The pressure of pions with g = 3
and y = m c2/kT The mass of all pions was taken to be equal to 140 MeV/c2
Solution of Pq-g = P y = 0.77048 T = 182 MeV tqh = 61.2 s
Variation of the total energy with
Total pressure: Pq-g + P + Pl remains constant during the transition but the total energy
varies x = fraction of matter in the quark phase
4
2 3
( )( )
2 ( )
g kTP I y
c
2 2( ) lg(1 )x
y
I y x x y e dx
3 ( ) 0d
H Pdt
1 2(1 )x x
2
2
8
3
GH
c
2 4
3
( )
90 ( )q g eff
kTP g B AkT
c
3 3 3
1 22941 1075 262tMeVfm MeVfm P MeVfm
Energy variation:
Integration 0 x 1 (t 2 – t 1 ) = duration of the phase transition = 41.3 s
2 1 2 2 1 2
1 2
24( ) ( )
( )t
dx GP x x
dt c
1 22 1
2( )
24 t tt
ct t arctg arctg
P PGP
Entropy conservation:
Friedman expansion:
“Mini-inflation” – after the
phase transition the universe is
20% bigger – energy provided by
the latent heat of the transition
1/3
12
1/3
1 2
1.557t
t
Pa
a P
1/ 2
2
1/ 2
1
1.294i
i
t ta
a t
Deconfinement with heavy ions collisions
Deconfinement Temperature
150-180 MeV
Energy Density
1-2 GeV.fm -3
After the phase transition – the ratio between protons and neutrons is the equilibrium value
Thus, just after the transition n/p = 0.9933
Equilibrium is maintained by the reactions
Equilibrium is broken when
At decoupling n/p = 0.248
22exp 1.294
n mcwith mc MeV
p kT
e
e
e
n p e
e n p
n p e
0.93 2.34bn v H T MeV t s
After decoupling , neutrons decay and interact with protons to produce deuterium
In this period the density of neutrons vary as
or, in terms of the particle concentration
equations of evolution
If deuterium is produced in quasi-equilibrium
with B = 2.225 MeV and
2n p D
/ , / /n n b p p b D D bX n n X n n and X n n
n nn p b D nD
n
p nn p b D nD
n
dX XX X n X
dt
dX XX X n X
dt
3n nn n p n nD
n
dn nHn n n v n
dt
3/ 2 /
2
2
3 4
B kTn p n
D bD
X X mkT e
X v n
2 324 2 3 30
3
0 0
( )33.9 10
8 ( )
effbb b MeV
N eff
g TH Tn h T cm
G m g T T
When the deuterium concentration reaches a critical value
New reactions take place leading to He synthesis
From the precedent equations
For bh2 = 0.022 Tc = 0.0714 MeV , tc = 396.6 s
and the neutron fraction or Xn 0.127
The abundance of helium is approximately Y(He) 2 X n = 0.254
Nucleosynthesis of He4 , He3 , D2 , Li7 can be used to fix the baryon content in the universe
/ 1n p DX X X
2 2 3 3
3 2 4
D D He n H p
H D He n
23 2.225exp 23.387 lg lg 1
2
n p
MeV b
D MeV
X XT h
X T
0 0exp cn n
n
t tX X
Determination of the baryon fraction
Extragalactic HII Regions (Izotov & Thuan 2010):
Y(He) = 0.25650.0010 bh 2 = 0.02480.0020
Quasars (Pettini et al. 2008) : D/H = 2.8 x 10 –5
bh 2 = 0.02130.0010
Vacca et al. (2011) 0.019 < bh 2 < 0.021 (including 7Li)
Fit of the acoustic peaks
WMAP – 7 years (Larson et al. 2010)
bh2 = 0.02260.0057
Planck (2013)
bh2 = 0.022070.00033
After the nucleosynthesis era, the expansion of the universe is still radiation dominated
until the matter energy density becomes dominant –
Using m h2 =0.143 (Planck) or Teq = 9100 K
Photons & baryons are still coupled - since the photon mean free path is less than c/H
Decoupling condition
under ionization equilibrium with
and numerical solution
4 2 2230 4 0
3
3(1 ) 1
30 8
meff
kT H cg z z
Gc
1 3340eqz
1
e T
c
n H
2 ( )
1
H
H
X F T
X n
( )
peH
p H
nnX
n n n
3/ 2
/
2
6 2 3
( )2
8.502 10 (1 )
I kTe
b
m kTF T e
n h z
1 1057
2880
0.0092
dec
dec
z
T K
residual ionization
The thickness of last scattering surface
The Thomson optical depth :
The probability for a photon be “last” scattered in the interval z, z+dz is
Maximum escape probability at
1+z = 1192
thickness at half-maximum
z 118
2
0
30 0
3 (1 )( ) ( )
8 (1 )
z z
T bs T H H
V m
cHdt z dzz cnX dz X z
dz G z
( ) ( )( ) s z sd z
P z edz
1000 1100 1200 13001 z
0.002
0.004
0.006
P z
Since the ionization decreases until “freezing” occurs, i.e.,
Freezing occurs at (1+z) 497 when XH,res 0.00051
Residual electrons interact with CMB photons, suffering a drag that keeps the matter
temperature near the radiation temperature. Matter temperature varies as
Define the Compton cooling timescale by
Thermal coupling is maintained as long as tc < H -1 or
Thermal coupling ends at (1+z) 95 – after, adiabatic losses
11/ ( )rec et T n H
2
3
0
( ( )) ( )(1 ) (1 )
H HB
V m
dX XT z n z
dz H z z
48
3 (1 )
m T r r Hr m
e H
dT a T XT T
dt m c X
19
4
,
3.69 10
/ (1 )
m mc
m H res m r
T Tt
dT dt z X T T
5/2 5 2(1 ) 2.34 10 mz h
2(1 )
25095
m
zT K
The Gunn-Peterson trough
Radiation shortward Lyman- is
completely absorbed for QSOs with z > 6
The Universe is reionized at lower
redshift since the transmitted flux at
Lyman- is not zero.
The Lyman- forest
Formation of intergalactic HII regions around massive halos
Ionization balance
In terms of the comoving volume (V = a-3Vp ) and using the particle conservation
where
Maximum possible volume
with
2( )
( )ion p uv
B ion p
d n V dNT n V
dt dt
0
3
0
1( )uv
B
dN n VdVT C
dt n dt a
2230
0 02
3
8
ionbion
p ion
nHn C n a n
G m n
max *
0 0
uv uv besc
m
N QV M f f
n n
60
*6.62 10 / 0.3 0.22uv escQ ph M f f
1/3
8
max max1.42 10 660M
r kpc for M M r kpcM
Define the filling factor F = ionized fraction of the causal volume of the universe
Working the different terms
Evolution of the filling factor
0
3
0
1( )ion uv ion
B
ion ion ionc c c
V dN n VdT C
dt V n V dt a V
**
0 0 * 0
0 0
3 3
1 1 1
( ) ( )
ion
ion c
uv uv uvesc esc
ion ionc c
ionB B
ion c
Vd dF
dt V dt
dN Q Q RMf f
n V dt n V n
n V nT C T C F
a V a
20 *
0
(1 )( ) (1 ) ( )
B uv escCn Q R fdFz F
dz H z n z H z
Evolution of the ionization filling factor
Thomson optical depth
20
0
( ) ( ) 0.090 0.0925(1 ) ( )
s e T
dzn z cF z Planck
z H z
F = 1 at z = 10.8
C = 1 and fesc = 0.22
UDFy – 38135539
Ly- galaxy at z = 8.555
(Lehnert et al. 2010 – Nature)
The mean ionizing photon intensity & the Lyman- absorption
Ionization produced by young formed stars
Photon production rate – Salpeter weighted IMF
Cosmic Star Formation Rate
Solution of the transfer equation
Ionization rate
60 16.62 10uvQ ph M
*( )( ) ( )
4
uv esc LL
Q R z f hj z
3 1
* 2.8
(0.0103 0.12 )( )
1 ( / 4.0)
zR z M Mpc yr
z
max
3 *
4
( ) ( )( ) (1 )
(1 ) ( ) 4 ( )
z
uv escv
z
cj z Q hc f R zI z z dz
z H z H z
0 *
30
( )4
2 (1 )L
v uv esc
L V m
I Q c f R zd
h H z
Ionization rate from Ly- data
Ionization equilibrium is assumed
2
12 12
22 6
12
3
( )
( )
(1 )1.2 10
(1 )
HILy
e
HI B e p
b
Ly
V m
n zef
m c H z
n n n
h z
z
Model parameters
fesc = 0.22 = 1.0 (homogeneous)
Stars from young galaxies are able to
reionize the intergalactic medium
The Nice Code
GADGET-II
Springel 2005
Gravitation
(tree code)
Hydrodynamics (SPH)
DARK MATTER
GAS SMBH
Introduction of BH seeds at potential
minima (z=15)
BH Growth
(« disk » and
HLB mode)
AGN activity (feedback)
STARS
Star formation (conversion of gas
into stars)
Ionisation, heating and
radiative cooling
Supernovae
(type Ia and II)
Galactic winds
Metal enrichment
SMBH
coalescences
The Nice Code
• Return of mass to the ISM – stellar winds & envelope ejection (PNe, SNe)
• Turbulent diffusion process of metals for chemical enrichment
• Local ionization of the gas by young massive stars
• Atomic infrared lines (besides H2 ) – cooling of neutral gas
• Supernovae – mechanical energy injected in a cavity of radius R(t)=V(t-t0) – (V=3000 km/s) – weighted by wi ~ 1/ri
n
• Time delay due to the lifetime of stars is taken into account either for SNII and SNIa
• AGNs
22
2 2 2 28
4
0.1
4.0 10 /2 10
d
BH
H
A
dEL
dt
MdE c HS H cr erg s
dt V MG
Diffuse medium photoionized gas NLA - features
WHIM Filaments & ICM BLA + OVI features
Stars = galaxies dense cold gas DLA features
Distribution of baryons
Evolution of the gas in different phases
Evolution of the metal content in different phases
Metallicities – Cold gas vs DLA
Oxygen abundances – cold gas phase blue galaxies – local universe
Cold & Hot Gas in Red Galaxies
Baryon Budget
For comparison Rasera & Teyssier (2005): at z = 0 Stars = 12.0% cold gas = 1.2% WHIM = 29.0% diffuse = 57.8%
Fraction of metals
Summary • Baryons appear quite early, when the universe was about 61s old, as a
consequence of a first order phase transition. A “mini inflation” occurs, driven
by the latent heat of the transition and nearly equal number of neutrons and
protons are formed
• When neutrinos decouple ( T ~ 0.93 MeV) the neutron-to-proton ratio is 0.248
and then nuclear reaction produce 2H, 3He, 4He and small amounts of 7Li
• Decoupling from photons occurs at z~1100 (or at T~2900 K)
• Freezing of the ionization fraction at z~500 with XH ~ 5x10 -4 - thermal
coupling between baryons and photons ends at z~95
• Reionization around z~10-11 due to star forming galaxies
• Baryons today are distributed in different phases: stars (14%), cold &dense gas
(7%), WHIM (43%) and diffuse ionized medium (36%)
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