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%)