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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)

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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

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

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Equivalence principle and constants (© J.-Ph. Uzan) In general relativity, any test particle follow a geodesic, which does 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

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Possible variation of fine structure constant / = (-0.57 ± 0.10) × [Webb et al. (1999), Murphy et al. (2003),….] / = (-0.06 ± 0.06) × [Chand et al. (2004)] Observations of atomic lines in cosmological clouds Constraints at earlier times / higher red shift : BBN (z ~ 10 8 ) CMB (z ~ 1000) Pop III stars (z ~ 10 – 15 )

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Atomic clocks Oklo phenomenon Meteorite dating Quasar absorption spectra CMB BBN Physical systems Local obs QSO obs CMB obs Pop III stars Uzan, Liv. Rev. Relat., arXiv: z = 0 z ~ 0.2 z ~ 4 z ~ z ~ 10 3 z ~ 10 8 [Coc, Nunes, Olive, Uzan, Vangioni] [Ekström, Coc, Descouvemont, Meynet, Olive, Uzan, Vangioni]

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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/H 0 ), numerous, compact with evolution (cooling) relatively well undestood

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Axions in particle physics and astrophysics Axion : scalar particle introduced to solve the strong CP problem Weak coupling with matter (mean free path ~10 23 cm in solar conditions amd m a = 1 eV) Different models “KVSZ” axions coupled to hadrons and photons “DFSZ” axions also coupled with electrons g a g aee Electric/magnetic field

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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

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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

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Axion WD cooling studies: Luminosity function L photons L axions L neutrinos Energy loss from axion emission in WD: L axions g aee 2 T core 4 [Nakagawa et al. 1988] and g aee m a cos 2 (cos 2 ~1) Axion luminosity as a function of m a cos 2 10 (m a cos 2 =) Affects brightest wing of WD luminosity function and favour m a cos 2 5 meV in agreement with WD drift in pulsation period (coming next) [Isern, García-Berro, Torres & Catalán 2008] m a cos 2 = 0, 5, Low luminosity wing sensitive to variations of gravitational constant G [García-Berro, Hernanz, Isern, & Mochkovitch 1995]

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WD cooling studies: Pulsating WD “G117-B15A” a pulsating WD with a period of 215 s observed for > 30 y (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] m a cos 2 < 11 meV [Isern et al. 2010]

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Astrophysical context : Massive Pop. III stars Astrophysical context Born within a few 10 8 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

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The triple alpha reaction, stellar evolution and variation of fundamental constants 12 C 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 < and / < ) 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 < E R < +50 keV) C/O (solar) 0.4

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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 (B D ) of the deuteron, affecting the 8 Be ground state energy and the ““Hoyle state”” energy in 12 C, and modifying the 3 12 C triple alpha reaction rate. The triple alpha reaction, stellar evolution and variation of fundamental constants

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Importance of the triple-alpha reaction Helium burning (T = GK) Triple alpha reaction 3 12 C Competing with 12 C( , ) 16 O Hydrogen burning (T 0.1 GK) Slow pp chain (at Z = 0) CNO with C from 3 12 C Three steps : 8 Be (lifetime ~ s) leads to an equilibrium 8 Be+ 12 C* (288 keV, l=0 resonance, the “Hoyle state”) 12 C* 12 C + 2 Resonant reaction unlike e.g. 12 C( , ) 16 O Sensitive to the position of the “Hoyle state” Sensitive to the variation of “constants”

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The “Hoyle state” Observation of the level at predicted energy [Dunbar, Pixley, Wenzel & Whaling, PR 92 (1953) 649] from 14 N(d, ) 12 C* Observation of its decay by 12 B( - ) 12 C* + 8 Be and confirmation of J =0 + [Cook, Fowler, Lauritsen & Lauritsen PR 107 (1957) 508] Phys. Rev. 92 (1953) 1095

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Ajzenberg & Lauritsen (1952)

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The triple-alpha reaction 1.Equilibrium between 4 He and the short lived (~ s) 8 Be : 8 Be 2. Resonant capture to the (l=0, J π =0 + ) Hoyle state: 8 Be+ 12 C*( 12 C+ ) Simple formula used in previous studies 1.Saha equation (thermal equilibrium) 2.Sharp resonance analytic expression: Approximations 1.Thermal equilibrium 2.Sharp resonance 3. 8 Be decay faster than capture with Q = E R ( 8 Be) + E R ( 12 C) and Nucleus 8 Be 12 C E R (keV) 0.2 (eV)5.57 1.0 (meV) 0.5 E R = resonance energy of 8 Be g.s. or 12 C Hoyle level (w.r.t. 2 or 8 Be+ ) Hoyle state

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Minnesota N-N force [Thompson et al. 1977] optimized to reproduce low energy N-N scattering data and B D (deuterium binding energy) -cluster approximation for 8 Be g.s. (2 ) and the Hoyle state (3 ) [Kamimura 1981] Scaling of the N-N interaction V Nucl. (r ij ) (1+ NN ) V Nucl. (r ij ) to obtain B D, E R ( 8 Be), E R ( 12 C) as a function of NN : Hamiltonian: Nuclear microscopic calculations Where V Nucl. (r ij ) is an effective Nucleon-Nucleon interaction Link to fundamental couplings through B D or NN

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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) = (E R ) P L (E,R C ) / P L (E R,R C ) with P L (E,R C ) = (F L 2 ( ,kR C )+G L 2 ( , kR C )) -1 the penetrability Radiative widths : (E) E 2L+1 (with L=2 here) (E) (E) / ( (E) + (E)) (E) if (E) (E) in analytic expression Numerical Analytic

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Calculated rates compared to NACRE NACRE = “A compilation of charged-particle induced thermonuclear reaction rate”, Angulo et al Effect from resonances tails Rates Rates / NACRE H He burning

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Negligible effect expected The 12 C( , ) 16 O reaction In competition with 3 12 C during He burning Tails of broad resonances Typical 12 C( , ) 16 O S-factor extrapolation at low energy [F. Hammache, priv. comm.]

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Geneva code but no rotation [Hirschi et al. 2004] adapted to Pop III [Ekström et al. 2008] 15 and 60 M models X = , Y = and Z = 0. No mass loss NACRE rates except for 12 C( , ) 16 O [Kunz et al. 2002] Computations stopped at the end of core He-burning Astrophysical / Physical ingredients

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Influence on HR diagram (15 M ) 15 M CHeB Contraction + pp CNO

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Composition at the end of core He burning The standard region: Both 12 C and 16 O are produced. The 16 O region: The 3 is slower than 12 C( , ) 16 O resulting in a higher T C and a conversion of most 12 C into 16 O The 24 Mg region: With an even weaker 3 , a higher T C is achieved and 12 C( , ) 16 O( , ) 20 Ne( , ) 24 Mg transforms 12 C into 24 Mg The 12 C region: The 3 is faster than 12 C( , ) 16 O and 12 C is not transformed into 16 O Faster 3 Lower T C Final stage : core of M composed of 24 Mg, 16 O or 12 C according to NN or B D 15 M Z = 0

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Composition at the end of core He burning The standard region: Both 12 C and 16 O are produced. The 16 O region: The 3 is slower than 12 C( , ) 16 O resulting in a higher T C and a conversion of most 12 C into 16 O The 24 Mg region: With an even weaker 3 , a higher T C is achieved and 12 C( , ) 16 O( , ) 20 Ne( , ) 24 Mg transforms 12 C into 24 Mg The 12 C region: The 3 is faster than 12 C( , ) 16 O and 12 C is not transformed into 16 O Faster 3 Lower T C Final stage : core of M composed of 24 Mg, 16 O or 12 C according to NN or B D 60 M Z = 0

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Links between the N-N interaction and em 1.Effective (Minnesota) N-N interaction: B D /B D 5.77 NN 2. and meson exchange potential model B D [Flambaum & Shuryak 2003] 3. and meson properties QCD and (u, d,) s quark masses 4.From em (M GUT ) ~ S (M GUT ): QCD em and c, b, t quark masses 5.With m q =hv relations between h (Yukawa coupling), v (Higgs vev) and em [Campbell & Olive (1995); Ellis et al. 2002] Assuming R ~ 30 and S ~ 200, typical but model dependent values [Coc et al. 2007] B D /B D -(0.1 to 1000) /

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Constrains on the variations of the fundamental constants From stellar evolution of zero metallicity 15 and 60 M at redshift z = Excluding a core dominated by 24 Mg NN > or B D /B D > Excluding a core dominated by 12 C NN < or B D /B D < Requiring 12 C/ 16 O close to unity < NN < or < B D /B D < BBN (z~10 8 ) : < / < [Coc et al. 2007] Pop. III (z = ) : < / < [Ekström et al. 2010] Quasars (0.5 < z < 3) : / < [Chand et al. (2004)] Pop. I (z 0) NN < and / < [Oberhummer et al. 2000] same conditions

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Variation of fundamental couplings in BBN We limit ourselves to the effect on n p and n(p, )D cross sections as the 4 He abundance is essentially determined by the n p 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 (B D ), neutron lifetime ( n ), neutron-proton mass difference (Q np ) and electron mass (m e ).

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Variation of fundamental couplings in BBN R and hence H (slightly) depend on m e (e+e- annihilation) m e = h e v (v Higgs field v.e.v.; h Yukawa couplings) weak rates depend on G F, Q np and m e G F =1/ 2v 2 Q np =Cste em QCD +(h d -h u )v [Gasser & Leutwyler, 1982] n(p, )D cross section depend mostly on B D [Dmitriev, Flambaum & Webb, 2004]

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Variation of fundamental couplings and BBN Individual variations Coupled variations Set limits on variations of fundamental couplings ( solution compatible with 4 He, 3 He, D and 7 Li) Coc, Nunes, Olive, Uzan, Vangioni, 2007

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The 12 reactions of standard BBN

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Influence of 1 H(n, )D reaction rate n(p, )d 0.7 (at WMAP/ CDM baryonic density)

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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 M composed of 24 Mg, 16 O or 12 C according to NN or B D Conservative constraint on Nucleosynthesis: if 12 C/ 16 O ~1 < NN < or < B D /B D < Limits on fundamental couplings (model dependent) < / < Future : Direct observations of Supernovae at z ~ 10 JWST (6 m, ~2014) and ELT (40 m, )

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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)

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