Hot Gold: Life at a Trillion Degrees

Paul StankusOak Ridge Nat’l Lab

Vanderbilt REU, July ‘07

Our approach: Applied Laziness

Solid, liquid, vapor; old stuff….

1337 oK

3129 oK(Somewhat higher at constant volume)

(Electron-Ion) Plasma

Ludwig Boltzmann Austrian

Distributions in classical statistical mechanics (1877)

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dP

dE(E;T)∝

dNStates

dEe−E / kT

E

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E ~ kT k (11,600 oK) 1eV

103 oK~ 0.1 eVOutermost electrons partially ionized

107 oK~ 1000 eV Nearly all electrons fully ionized

Nuclei change and come apart

1011 oK~ 8 MeV

Kepler’s Supernova (SN 1604) remnant

Disassemble nuclei completely

1010 oK~ 1 MeV

Colliding nuclei change identities

Photon gases

109 oK~ 0.1 MeVRadiation-Matter equivalence in Gold

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λ =v

f~

c

E /h~

hc

kT

E

V≡ ε ~

kT

λ3~

kT

hc kT( )3 =

k 4

hc( )3 T 4

Thermal wavelength

One photon per wavelength3

Photons T4

log(kT)

log()

Nuclei

Electrons/ positrons

log(kT)

1 Billion oK 1 Trillion oK

Start with light particles, no strong nuclear force

me m

1012 oK /T4

1 Billion oK 1 Trillion oK

Previous Plot

Now add hadrons = feel strong nuclear force

1012 oK /T4

1 Billion oK 1 Trillion oK

Previous Plots

Keep adding more hadrons….

1012 oK /T4

How many hadrons?

Density of particle mass states dNPart/dM increases exponentially with mass.

Prior to the 1970’s this was explained in several ways theoretically

Statistical Bootstrap Hadrons made of hadrons made of hadrons…

Regge Trajectories Stretchy rotators, first string theory

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dNParticles

dM~ exp M

TH

⎛ ⎝ ⎜ ⎞

⎠ ⎟

Broniowski, et.al. 2004TH ~ 21012 oK

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E ~ EdP

dE(E;T) dE

0

∞

∫ ~ EdNStates

dEexp −E /T( ) dE

0

∞

∫

Ordinary statistical mechanics:

Rolf Hagedorn GermanHadron bootstrap model and limiting temperature (1965)

Energy diverges as T --> TH

Maximum achievable temperature?

“…a veil, obscuring our view of the very beginning.” Steven Weinberg, The First Three Minutes (1977)

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E ~ MdNParticles

dMexp −M /T( ) dM

0

∞

∫ = M exp +M /TH( ) exp −M /T( ) dM0

∞

∫

~ Mexp −M1

T−

1

TH

⎡

⎣ ⎢

⎤

⎦ ⎥

⎛

⎝ ⎜

⎞

⎠ ⎟ dM

0

∞

∫

For thermal hadron gas (lazily set E=M):

/T4

D. GrossH.D. PolitzerF. Wilczek

American

QCD Asymptotic Freedom (1973)

“In 1972 the early universe seemed hopelessly opaque…conditions of ultrahigh temperatures…produce a theoretically intractable mess. But asymptotic freedom renders ultrahigh temperatures friendly…” Frank Wilczek, Nobel Lecture (RMP 05)

QCD to the rescue!Replace Hadrons

(messy and numerous)

by Quarks and Gluons (simple

and few)

Ha

dro

n g

as

Thermal QCD ”QGP” (Lattice)

21012 oK170 MeV

Non-ideal gases

Thermal QCD ”QGP” (Lattice)

Strong self-interactions

/T4Ideal Quark-Gluon Gas

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Atom

Hadrons

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Quark-Gluon

Plasma

EM Plasma

National Research Council Report (2003)

Eleven Science Questions for the New

Century

Question 8 is:

Also: BNL-AGS, CERN-SPS, CERN-LHC

BNL-RHIC Facility

Side-to-beam view

Along-the-beam view

Hot Zone

Au+Au at √sNN = 200 GeV

STAR Experiment at RHIC

Dense Medium Absorption

PHENIX PRL88 (2002) 022301

Jet-Medium Interaction?

Side-to-beam

Along-the-beam

PartonParton

Jet

Jet

Jet

Jet80% Depletion!

Away-side Disappearance

Pedestal&flow subtracted

STAR PRL 91, 072304 (2003)

Along-the-beam view

Proton-Proton Collision Nucleus-Nucleus Collision

Jet Jet Jet

Trigger particle

Pair opening angle

Suggestive of…Cherenkov cones? Mach cones?

Low High

Low High

Density, PressurePressure Gradient

Initial (10-24 sec) Thermalized Medium Early

Later

Fast

Slow

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v2 =px

2 − py2

px2 + py

2

Elliptic momentum anisotropy

PHENIX Data

Fluid dynamics predicts momentum anisotropy correctly for 99% of particles

produced in Au+Au

• Strong self-re-interaction

• Early thermalization (10-24 sec)

• Low dissipation (viscosity)

• Equation of state P/ similar to relativistic gas

What does it mean?

λMean Free Path ~ λde Broglie

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η Shear viscosity

s Entropy density< ~ 0.1

Quantum Limit! “Perfect Fluid!”

Ideal gas Ideal fluidLong mfp Short mfp

High dissipation Low dissipation

Data imply (D. Teaney):

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Beam energy

• High acceleration requires high P/ pressure/energy density. Hagedorn picture would be softer since massive hadrons are non-relativistic.

• Increase/saturate with higher energy densities. In Hagedorn picture pressure decreases with density.

Anisotropy increases with increasing beam energy & energy density

What does it mean?

Thermal photon radiation from

quarks and gluons?

Ti> 500 MeV

Direct photons from nuclear collisions suggest initial temperatures > TH

51012 oK

Summary: The States of Gold

1012 oK109 oK106 oK103 oK

Solid L Vapor EM Plasma gas

e+e- gas QGP

We think we’ve created T>1012 oK matter in the lab

It’s apparently very dense (opaque to high-E partons)

It apparently thermalizes very quickly (self-interaction)

It apparently behaves as a nearly-perfect fluid (very low viscosity, near quantum lower limit)

Conclusions

•Describing high-temperature matter is straightforward, if you’re lazy enough.

•Strong interaction/hadron physics made it hard to understand T > 100 MeV ~ 1012 K; QCD theory rescues high temperatures.

•We are only now delivering on a 30-year-old promise to test it experimentally. Matter with T > ~ 1012 K has been created in the lab and displays many surprising properties.

Backup material

Kolb & Turner, “The Early Universe”

QC

D T

rans

ition

e+e- A

nnih

ilatio

n

Nuc

leos

ynth

esis

D

ecou

plin

g

Mes

ons

free

ze o

ut

Hea

vy q

uark

s an

d bo

sons

free

ze o

ut

“Before [QCD] we could not go back further than 200,000 years after the Big Bang. Today…since QCD simplifies at high energy, we can extrapolate to very early times when nucleons melted…to form a quark-gluon plasma.” David Gross, Nobel Lecture (RMP 05)

Thermal QCD -- i.e. quarks and

gluons -- makes the very early universe tractable; but where is the experimental

proof?

g*S

The QCD quark-hadron transition is typically ignored by cosmologists as uninteresting

Weinberg (1972): Considers Hagedorn-style limiting-temperature model, leads to a(t) t2/3|lnt|1/2; but concludes “…the present contents…depends only on the entropy per baryon…. In order to learn something about the behavior of the universe before the temperature dropped below 1012oK we need to look for fossils [relics]….”

Kolb & Turner (1990): “While we will not discuss the quark/hadron transition, the details and the nature (1st order, 2nd order, etc.) of this transition are of some cosmological interest, as local inhomogeneities in the baryon number density could possible affect…primordial nucleosythesis…”

T(t)

a(t)(t)

t

How do we relate T to a,? i.e. thermodynamics

a(t) a Friedmann-Robertson-Walker (FRW) cosmology

Three basic solutions for a(t):

1. Relativistic gas, “radiation dominated”

P/ = 1/3 a-4 a(t) t1/2

2. Non-relativistic gas, “matter dominated”

P/ = 0 a-3 a(t) t2/3

3. “Cosmological-constant-dominated” or “vacuum-energy-dominated”

P/ = -1 constant a(t) eHt “de Sitter space”

The New Standard Cosmology in Four Easy Steps

Inflation, dominated by “inflaton field” vacuum energy

Radiation-dominated thermal equilibrium

Matter-dominated, non-uniformities grow (structure)

Start of acceleration in a(t), return to domination by cosmological constant and/or vacuum energy.

w=P/

-1/3

+1/3

-1

a eHt a t1/2 a t2/3

t

now

acc

dec

€

dE = TdS − PdVBasic

Thermodynamics

Sudden expansion, fluid fills empty space without loss of energy.

dE = 0 PdV > 0 therefore dS > 0

Gradual expansion (equilibrium maintained), fluid loses energy through PdV work.

dE = -PdV therefore dS = 0Isentropic Adiabatic

Hot

Hot

Hot

Hot

Cool

Golden Rule 1: Entropy per co-moving volume is conserved

Golden Rule 3: All chemical potentials are negligible

Golden Rule 2: All entropy is in relativistic species

Expansion covers many decades in T, so typically either T>>m (relativistic) or T<<m (frozen out)

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Entropy S in co - moving volume Δχ( )3preserved

Relativistic gas S

V≡ s = sParticle Type

Particle Type

∑ =2π 2

45

⎛

⎝ ⎜

⎞

⎠ ⎟T 3

Particle Type

∑ =2π 2

45

⎛

⎝ ⎜

⎞

⎠ ⎟g∗S T 3

g∗S ≡ effective number of relativistic species

Entropy density S

V=

S

Δχ( )3

1

a3=

2π 2

45g∗S T 3

€

T ∝ g∗S( )− 1

31

aGolden Rule 4:

Electron-Positron pairs appear

1010 oK

2me

~ 1 MeV Mass of e+ e- pair

1. B violation2. C,CP violation

3. Out of equilibrium

Sakharov criteria for baryogenesis

Most of the early universe is QCD!

Dissipation could be relevant here:

λMean Free Path ~ λde Broglie

€

η Shear viscosity

s Entropy density< ~ 0.1

Quantum Limit! “Perfect Fluid!”

Ideal gas Ideal fluidLong mfp Short mfp

High dissipation Low dissipation

Data imply (D. Teaney):