Variation of fundamental constants

Stellar evolution constraints on new physics: Jordi’s contributions

Constrains from Pop. III stars

Constrains from BBN

Conclusion

Stellar evolution constraint on new physics

Alain Coc (Centre de Spectrométrie Nucléaire et de Spectrométrie de Masse, Orsay)

Variation of the fundamental constants

1937 : Dirac develops his Large Number hypothesis.

Assumes that the gravitational constant was varying as the inverse of the age of the universe.

Physical theories involve constants

These parameters cannot be determined by the theory that introduces them; we can only measure them.

These arbitrary parameters have to be assumed constant:- experimental validation- no evolution equation

Variation of the fundamental constants

Theoretical motivations from string theories, extra dimensions,..

In string theory, the value of any constant depends on the geometry and volume of the extra-dimensions

• Opens a window the extra-dimensions • Why do the constants vary so little ?• Why have the constants the value they have ?• Related to the equivalence principle and allow tests of GR on astrophysical scales [dark matter/dark energy vs modified gravity debate]

By testing their constancy, we thus test the laws of physics in which they appear.

See reviews : J.-P. Uzan in Rev. Mod Phys. 2003, Living Rev. Relativity 2011; E. García-Berro, J. Isern & Y.A. Kubishin in Astron. Astrophys. Rev. 2007

Claim of an observed variation of the fine structure constant [Webb et al. 1999]

Equivalence principle and constants (© J.-Ph. Uzan)

In general relativity, any test particle follow a geodesic, whichdoes not depend on the mass or on the chemical composition

2- Universality of free fall has also to be violated

1- Local position invariance is violated.

In Newtonian terms, a free motion implies

Imagine some constants are space-time dependent

Mass of test body = mass of its constituants + binding energy

But, now

Possible variation of fine structure constant

/ = (-0.57 ± 0.10) × 10-5 [Webb et al. (1999), Murphy et al. (2003),….]

/ = (-0.06 ± 0.06) × 10-5 [Chand et al. (2004)]

Observations of atomic lines in cosmological clouds

Constraints at earlier times / higher red shift :

BBN (z ~ 108) CMB (z ~ 1000)Pop III stars (z ~ 10 – 15 )

Atomic clocks

Oklo phenomenon

Meteorite datingQuasar absorptionspectra

CMB

BBN

Physical systems

Local obs

QSO obs

CMB obs

Pop III stars

Uzan, Liv. Rev. Relat., arXiv:1009.5514

z = 0

z ~ 0.2

z ~ 4

z ~ 10-15

z ~ 103

z ~ 108

[Coc, Nunes, Olive, Uzan, Vangioni]

[Ekström, Coc, Descouvemont, Meynet, Olive, Uzan, Vangioni]

Variations of gravitational constant G

in SNIa [Gaztañaga, García-Berro, Isern, Bravo & Domínguez 2001]

in White Dwarfs [Althaus, Córsico, Torres, Lorén-Aguilar, Isern & García-Berro 2011]

Extra cooling of WD by axion emission

Stellar evolution constraints on new physics: Jordi’s contributions

SNIa: wery bright standard candles can be observed at redshift up to z 1

WD: faint but long-lived (~1/H0), numerous, compact with evolution (cooling) relatively well undestood

Axions in particle physics and astrophysics

Axion : scalar particle introduced to solve the strong CP problem

Weak coupling with matter (mean free path ~1023 cm in solar conditions amd ma = 1 eV)

Different models

• “KVSZ” axions coupled to hadrons and photons

• “DFSZ” axions also coupled with electrons

ga

gaee

Electric/magnetic field

Axions in particle physics and astrophysics

Axions from astrophysical sources

• Increased energy loss induced by virtual photons from Coulomb field (e.g. in the sun) or electrons (White Dwarfs)

• Photon-axion oscillation on long distance within a magnetic field

Axions detection

• From astrophysical sources (CAST)

• Photon regeneration within a magnetic field (OSQAR)

Wall

Evolution of White Dwarfs

• Evolution time scale ~ Hubble time

• No more nuclear energy source

• Early neutrino energy loss

• Cooling of degenerate core through opaque envelope

• Late release of latent heat from crystallization and gravitational setting

Finite age of the galactic disk

Brightest wing of WD luminosity function little sensitive to

• age of Galaxy (10-13 Gy)

• star formation rate

[Isern, García-Berro, Torres & Catalán 2008]

Axion WD cooling studies: Luminosity function

Isothermal degenerate

core

Non-degenerate enverope

Axion WD cooling studies: Luminosity function

LphotonsLaxions

Lneutrinos

Energy loss from axion emission in WD: Laxions gaee

2 Tcore4 [Nakagawa et al. 1988]

and gaee ma cos2 (cos2~1)

Axion luminosity as a function of ma cos2

10 (ma cos2 =) 5

1

0.1

0.01

Affects brightest wing of WD luminosity function

and favour ma cos2 5 meV in agreement with WD drift in pulsation period (coming next) [Isern, García-Berro, Torres & Catalán 2008]

ma cos2 = 0, 5, 10

10

0

Low luminosity wing sensitive to variations of gravitational constant G [García-Berro, Hernanz, Isern, & Mochkovitch 1995]

WD cooling studies: Pulsating WD

“G117-B15A” a pulsating WD with a period of 215 s observed for > 30 y

€

1

Π

dΠ

d t∝

1

T

dT

d t+L (WD models)

Additional cooling from axion emission increase pulsation period [Isern et al. 1992]

Observations [Kepler et al. 1991; 2000; 2005; 2009] versus models [Córsico et al. 2001; Bischoff-Kim et al. 2008]

Most recent observations [Kepler et al. 2009] ma cos2 < 11 meV [Isern et al. 2010]

Astrophysical context : Massive Pop. III stars

Astrophysical context

Born within a few 108 years, typical redshift z ~ 10 – 15

First stars were probably very massive : 30 M < M < 300 M

(but theoretically uncertain)

Zero metallicity (BBN abundances) Very peculiar stellar evolution

Observations of metal-poor stars (Pop. II) allow us to investigate the first objects (Pop. III) formed after the Big Bang

Constraint from C and O observations in Pop. II

Learn about the formation of the elements and nucleosynthesis processes, and how the Universe became enriched with heavy elements

The triple alpha reaction, stellar evolution and variation of fundamental constants

12C production and variation of the strong interaction [Rozental 1988]

C/O in Red Giant stars [Oberhummer et al. 2000; 2001]

1.3, 5 and 20 M stars, Z=Z up to TP-AGB

Limits on effective N-N interaction ( NN < 5 10-3 and /< 4 10-2)

C/O in low, intermediate and high mass stars [Schlattl et al. 2004]

1.3, 5, 15 and 25 M stars, Z=Z up to TP-AGB / SN

Limits on resonance energy shift (-5 < ER < +50 keV)

C/O (solar) 0.4

This study : stellar evolution of massive Pop. III stars

We choose typical masses of 15 and 60 M stars

Triple alpha influence in both He and H burning

Limits on effective N-N interaction and on fundamental couplings

Coupled variations of fundamental couplings:

To / variations correspond variations in the Higgs field v.e.v., the Yukawa couplings, QCD, quark masses,….

resulting in changes in the Nucleon-Nucleon interaction, directly related to the binding energy (BD) of the deuteron,

affecting the 8Be ground state energy and the ““Hoyle state”” energy in 12C,

and modifying the 312C triple alpha reaction rate.

The triple alpha reaction, stellar evolution and variation of fundamental constants

Importance of the triple-alpha reaction

Helium burning (T = 0.2-0.3 GK)

Triple alpha reaction 312C

Competing with 12C(,)16O

Hydrogen burning (T 0.1 GK)

Slow pp chain (at Z = 0)

CNO with C from 312C

Three steps :

8Be (lifetime ~ 10-16 s) leads to an equilibrium

8Be+12C* (288 keV, l=0 resonance, the “Hoyle state”)

12C*12C + 2

Resonant reaction unlike e.g. 12C(,)16O

Sensitive to the position of the “Hoyle state”

Sensitive to the variation of “constants”

The “Hoyle state”

Observation of the level at predicted energy [Dunbar, Pixley, Wenzel & Whaling, PR 92 (1953) 649] from 14N(d,)12C*

Observation of its decay by 12B(-)12C* +8Be and confirmation of J=0+ [Cook, Fowler, Lauritsen & Lauritsen PR 107 (1957) 508]

Phys. Rev. 92 (1953) 1095

Ajzenberg & Lauritsen (1952)

The triple-alpha reaction

1. Equilibrium between 4He and the short lived (~10-16 s) 8Be : 8Be

2. Resonant capture to the (l=0, Jπ=0+) Hoyle state: 8Be+12C*(12C+)

Simple formula used in previous studies

1. Saha equation (thermal equilibrium)

2. Sharp resonance analytic expression:

€

NA2 ⟨σv⟩ααα = 33 / 26NA

2 2π

Mα kBT

⎛

⎝ ⎜

⎞

⎠ ⎟

3

h5γ exp−Qααα

kBT

⎛

⎝ ⎜

⎞

⎠ ⎟

Approximations

1. Thermal equilibrium

2. Sharp resonance

3. 8Be decay faster than capture

with Q= ER(8Be) + ER(12C) and

Nucleus 8Be 12C

ER (keV) 91.840.04

287.60.2

(eV) 5.570.25 8.31.0

(meV) - 3.70.5

ER = resonance energy of 8Be g.s. or 12C Hoyle level (w.r.t. 2 or 8Be+)

Hoyle state

Minnesota N-N force [Thompson et al. 1977] optimized to reproduce low energy N-N scattering data and BD (deuterium binding energy)

-cluster approximation for 8Beg.s. (2) and the Hoyle state (3) [Kamimura 1981]

Scaling of the N-N interaction

VNucl.(rij) (1+NN) VNucl.(rij)

to obtain BD, ER(8Be), ER(12C) as a function of NN :

Hamiltonian:

Nuclear microscopic calculations

€

H = T ri( )i=1

A

∑ + VCoul. rij( ) + VNucl . rij( )( )i< j=1

A

∑

Where VNucl.(rij) is an effective Nucleon-Nucleon interaction

Link to fundamental couplings

through BD or NN

Numerical rate calculation

At “low temperatures”, capture via resonance tails [Nomoto et al. 1985] requires numerical integration

Even more important when resonances are shifted upwards with larger widths

• Charged particle widths :

(E) = (ER) PL(E,RC) / PL(ER,RC) with

PL(E,RC) = (FL2(,kRC)+GL

2(, kRC))-1

the penetrability

• Radiative widths : (E) E2L+1 (with L=2 here)

(E) (E) / ((E) + (E)) (E) if (E) (E) in analytic expression

Numerical Analytic

Calculated rates compared to NACRE

NACRE = “A compilation of charged-particle induced thermonuclear reaction rate”,

Angulo et al. 1999

Effect from

resonances tails

Rates Rates / NACRE

HHe

burning

Negligible effect expected

The 12C(,)16O reaction

In competition with 312C during He burning

Tails of broad resonancesTypical 12C(,)16O S-factor extrapolation at low energy [F. Hammache, priv. comm.]

Geneva code but no rotation [Hirschi et al. 2004] adapted to Pop III [Ekström et al. 2008]

15 and 60 M models

X = 0.75325, Y = 0.24675 and Z = 0.

No mass loss

NACRE rates except for 12C(,)16O [Kunz et al. 2002]

Computations stopped at the end of core He-burning

Astrophysical / Physical ingredients

Influence on HR diagram (15 M )

15 M

CHeB

Contraction + pp

CNO

CN

O

CN

O

Composition at the end of core He burning

The standard region: Both 12C and 16O are produced.

The 16O region: The 3 is slower than 12C(,)16O resulting in a higher TC and a conversion of most 12C into 16O

The 24Mg region: With an even weaker 3, a higher TC is achieved and 12C(,)16O(,)20Ne(,)24Mg transforms 12C into 24Mg

The 12C region: The 3 is faster than 12C(,)16O and 12C is not transformed into 16O

Faster 3

Lower TC

Final stage : core of 3.55-3.84 M composed of 24Mg, 16O or 12C according to NN or BD

15 M Z = 0

Composition at the end of core He burning

The standard region: Both 12C and 16O are produced.

The 16O region: The 3 is slower than 12C(,)16O resulting in a higher TC and a conversion of most 12C into 16O

The 24Mg region: With an even weaker 3, a higher TC is achieved and 12C(,)16O(,)20Ne(,)24Mg transforms 12C into 24Mg

The 12C region: The 3 is faster than 12C(,)16O and 12C is not transformed into 16O

Faster 3

Lower TC

Final stage : core of 3.55-3.84 M composed of 24Mg, 16O or 12C according to NN or BD

60 M Z = 0

Links between the N-N interaction and em

1. Effective (Minnesota) N-N interaction: BD/BD 5.77 NN

2. and meson exchange potential model BD [Flambaum &

Shuryak 2003]

3. and meson properties QCD and (u, d,) s quark masses

4. From em(MGUT) ~ S(MGUT): QCD em and c, b, t quark masses

5. With mq=hv relations between h (Yukawa coupling), v (Higgs vev) and em [Campbell & Olive (1995); Ellis et al. 2002]

€

BD

BD

= − 6.5 1+ S( ) −18R[ ]Δα em

α em

~ −1000Δα em

α em

Assuming R ~ 30 and S ~ 200, typical but model dependent values

[Coc et al. 2007]

BD/BD -(0.1 to 1000) /

Constrains on the variations of the fundamental constants

From stellar evolution of zero metallicity 15 and 60 M at redshift z = 10 - 15

• Excluding a core dominated by 24Mg NN > -0.005 or BD/BD > -0.029

• Excluding a core dominated by 12C NN < 0.003 or BD/BD < 0.017

• Requiring 12C/16O close to unity -0.0005 < NN < 0.0015 or

-0.003 < BD/BD < 0.009

BBN (z~108) : -3.2 10-5 < / < 4.2 10-5 [Coc et al. 2007]

Pop. III (z = 10 -15) : -3 10-6 < / < 10-5 [Ekström et al. 2010]

Quasars (0.5 < z < 3) : / < 10-5 [Chand et al. (2004)]

Pop. I (z0) NN < 5 10-3 and / < 4 10-2 [Oberhummer et al. 2000]

same conditions

Variation of fundamental couplings in BBN

We limit ourselves to the effect on np and n(p,)D cross sections as

the 4He abundance is essentially determined by the np weak rates,

n(p,)D is the starting point of BB nucleosynthesis and

difficult to determine the effects on other reactions

Important quantities: deuterium binding energy (BD), neutron lifetime (n), neutron-proton mass difference (Qnp) and electron mass (me).

€

np →dγ → Γnp →dγ 1+5

2+

BD

0.07

⎛

⎝ ⎜

⎞

⎠ ⎟ΔBD

BD

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

Variation of fundamental couplings in BBN

• R and hence H (slightly) depend on me (e+e- annihilation)

me = hev (v Higgs field v.e.v.; h Yukawa couplings)

• weak rates depend on GF, Qnp and me GF=1/2v2

Qnp=Cste emQCD+(hd-hu)v [Gasser & Leutwyler, 1982]

• n(p,)D cross section depend mostly on BD

[Dmitriev, Flambaum & Webb, 2004]

Variation of fundamental couplings and BBN

Individual variationsCoupled variations

• Set limits on variations of fundamental couplings

• ( solution compatible with 4He, 3He, D and 7Li)

Coc, Nunes, Olive, Uzan, Vangioni, 2007

The 12 reactions of standard BBN

Influence of 1H(n,)D reaction rate

n(p,)d 0.7

(at WMAP/CDM baryonic density)

Conclusions

Stellar evolution of massive pop III stars w.r.t. the 3 alpha reaction

15 and 60 M stars, Z=0 Very specific stellar evolution

Triple alpha influence in both He and H burning

Core of 3.55-3.84 M composed of 24Mg, 16O or 12C according to NN or BD

Conservative constraint on Nucleosynthesis: if 12C/16O ~1

-0.0005 < NN < 0.0015 or -0.003 < BD/BD < 0.009

Limits on fundamental couplings (model dependent)

-3 10-6 < / < 10-5

Future : Direct observations of Supernovae at z ~ 10

JWST (6 m, ~2014) and

ELT (40 m, 2016-2018)

Main collaborators

Elisabeth Vangioni, Jean-Philippe Uzan

(Institut d’Astrophysique de Paris)

Sylvia Ekström, Georges Meynet

(Observatoire de Genève)

Pierre Descouvemont

(Université Libre de Bruxelles)

Keith Olive (U. of Minnesota)