1. 1 Nuclear reactions in the Sun A first look at the SunA first look at the Sun A deeper look: helioseismologyA deeper look: helioseismology Neutrino: the spy of the innermost sunNeutrino: the spy of the innermost sun Nuclear reactions in the Sun, after SNO and KamLANDNuclear reactions in the Sun, after SNO and KamLAND Gianni Fiorentini @Santa Tecla 2003

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3. 3 A first look at the Sun Observables:Observables: -Mass -Luminosity - Radius, - Radius, - Metal content of the photosphere - Metal content of the photosphere - Age - Age Inferences on the typical scales of the solar interior ( , P, T)Inferences on the typical scales of the solar interior ( , P, T) M= 2 10 30 Kg R=7 10 8 m N p =M/m p =10 57 L=4 10 26 W

4. 4 Who measured the solar mass? Galileo Cavendish Kelvin Rolfs

5. 5 Solar mass Astronomy only deals with theAstronomy only deals with the extremely well determined Gaussian constant: G N M o =(132 712 438  5) 10 12 m 3 /s 2 Astrophysics needs M o, since:Astrophysics needs M o, since: - opacity is determined by N e  N p  M o /m p  10 57 N e  N p  M o /m p  10 57 - energy content/production of the star depends on N p. Cavendish by determining G N provided a measurement of M oCavendish by determining G N provided a measurement of M o The (poor) accuracy on G N (0.15%)reflects on M oThe (poor) accuracy on G N (0.15%)reflects on M o M o = 1.989 (1  0.15%) 10 33 gr  10 57 m p 1  errors M= 2 10 30 Kg

6. 6 Solar Luminosity Derived from measurements of the solar constant K o : the amount of energy per unit time and unit area, impinging from the Sun onto Earth.Derived from measurements of the solar constant K o : the amount of energy per unit time and unit area, impinging from the Sun onto Earth. Not precisely a constant, it varies with time (0.1% in a solar cycle). The average over 12 years of solar irradiance (and over different satellite radiometers) multiplied by Sun Earth distance, gives the solar luminosity:Not precisely a constant, it varies with time (0.1% in a solar cycle). The average over 12 years of solar irradiance (and over different satellite radiometers) multiplied by Sun Earth distance, gives the solar luminosity: L o =4  d 2 K o =3.844(1  0.4%) 10 33 erg/s (L o = 10 17 nuclear power plants) L=4 10 26 W

7. 7 Solar Radius Solar Radius The distance from the center of the sun to its visible surface (the photosphere)The distance from the center of the sun to its visible surface (the photosphere) Difficult to define the edge of the sunDifficult to define the edge of the sun Different methods and different experiments:Different methods and different experiments: R o =6.9598(1  0.04%) 10 10 cm R=7 10 8 m

8. 8 Solar Age Method: radioactive dating of oldestMethod: radioactive dating of oldest objects in the solar system (chondritic meteorites) Problems:Problems: –relationship between the age of the meteorite and the age of the sun –what is the the zero time for the sun? The age of the sun referred toThe age of the sun referred to Zero Age Main Sequence Zero Age Main Sequence t=4.57(1  0.4%) Gyr t=4.57(1  0.4%) Gyr

9. 9 Solar Metal abundance Spectroscopic measurements of the solar photosphere yield the relative abundances (in mass) of “metals“ to H (Z/X) photo =0.0233(1  6%)Spectroscopic measurements of the solar photosphere yield the relative abundances (in mass) of “metals“ to H (Z/X) photo =0.0233(1  6%) Most abundant metals: O, C, N, FeMost abundant metals: O, C, N, Fe Results are generally consistent with the meteoritic abundancesResults are generally consistent with the meteoritic abundances A remarkable exception: the solar Li content is depleted by 100 with respect to meteoritesA remarkable exception: the solar Li content is depleted by 100 with respect to meteorites Note: Hydrogen abundance X  0.75

10. 10 A remark: Helium abundance Helium was discovered in the Sun (1895), but its abundance cannot be accurately measured thereHelium was discovered in the Sun (1895), but its abundance cannot be accurately measured there Until a few years ago, estimate of the photospheric He abundance was taken the result of solar modelsUntil a few years ago, estimate of the photospheric He abundance was taken the result of solar models Helioseismology provides now an indirect measurement…..Helioseismology provides now an indirect measurement…..

11. 11  =3M o /(4  R o 3 )  1.5 g/cm 3 density:  =3M o /(4  R o 3 )  1.5 g/cm 3 pressureP  GM o 2 /R o 4  10 16 dine/cm 2 pressureP  GM o 2 /R o 4  10 16 dine/cm 2 Sound speed v s  (P/  ) 1/2  800 Km/s Sound speed v s  (P/  ) 1/2  800 Km/s photon mean free path*: =1/(n e  Th )photon mean free path*: =1/(n e  Th )  1/(10 24 cm -3 10 -24 cm 2 )  1 cm  1/(10 24 cm -3 10 -24 cm 2 )  1 cm (photon escape time  2 10 4 yr) (photon escape time  2 10 4 yr) Cumulated energy productionCumulated energy production  =L o t  10 -4 M o c 2  =L o t  10 -4 M o c 2 typical nuclear energy scale Typical scales *astrophyscists use “opacity”   =1/(  )

12. 12 Sun energy inventory The present heat flow L can be sustained by an energy source U for an age t provided that U>Lt : [yr] a)chemistry: U  (1eV)N p -> t ch =2 10 4 b)gravitation U  GM 2 /R-> t gr =3 10 7 c)nuclear U  (1MeV)N p -> t nu =2 10 10 Only nuclear energy can sustain the Solar luminosity over the sun age, t=4.5 10 9 y Can we prove that actually the Sun shines due to nuclear energy?

13. 13 A digression: The Earth energy inventory It is not at all easy to understand the dominant contribution to the Earth energy production. The present heat flow H E =40 TW can be sustained by an energy source U for a time t=U/H E : a)”chemistry”*): U=(0.1 eV)N p =6 10 31 J->t ch =5 10 10 y b)gravitationU=GM 2 /R=4 10 32 J->t gr =3 10 11 y c)nuclear **)U=(1MeV)N p,rad =6 10 30 J-> t gr =5 10 9 y -> Thus all energy sources seem capable to sustain H E on geological times. *) actually it means the solidification (latent) heat **)the amount of radioactive material is taken as M rad  10 -8 M Earth M= 6 10 24 Kg R=6 10 6 m N p =M/m p =10 51 H E =4 10 13 W

14. 14 What is the source of terrestrial heat? J Verhoogen, in “Energetics of Earth” (1980) N.A.S.: radioactivity 60 per cent if not 100 “ What emerges from this morass of fragmentary and uncertain data is that radioactivity itself could possibly account for at least 60 per cent if not 100 per cent of the Earth’s heat output”. total supply embarassingly large “If one adds the greater rate of radiogenic heat production in the past, possible release of gravitational energy (original heat, separation of the core…) tidal friction … and possible meteoritic impact … the total supply of energy may seem embarassingly large…” Determination of the radiogenic component is thus important Determination of the radiogenic component is thus important.

15. 15 The birth of Nuclear Astrophysics Eddington: Nature (1920) “Certain physical investigations in the past year make it probable to my mind that some portion of sub-atomic energy is actually being set free in a star. … If five per cent of a star's mass consists initially of hydrogen atoms, which are gradually being combined to form more complex elements, the total heat liberated will more than suffice for our demands, and we need look no further for the source of a star's energy…” In the same paper: “If indeed the sub-atomic energy in the stars is being freely used to maintain their great furnaces, it seems to bring a little nearer to fulfillment our dream of controlling this latent power for the well-being of the human race - or for its suicide”  =L o t  10 -4 M o c 2

16. 16 Nuclear reactions in the sun? The temperature scale We have found scales for P and We have found scales for P and  Need equation of state for deriving T.Need equation of state for deriving T. Use perfect gas equation assuming the Sun consists of fully ionized hydrogenUse perfect gas equation assuming the Sun consists of fully ionized hydrogen kT= P/(2n p )=P m p /(2   1 keV (T  1.2 10 7 K) (T  1.2 10 7 K) [Remark: kT>> e 2 /r  e 2 n 1/3 implies perfect gas reasonable][Remark: kT>> e 2 /r  e 2 n 1/3 implies perfect gas reasonable] However: kT<< e 2 /r nuc  1MeVHowever: kT<< e 2 /r nuc  1MeV

17. 17 The gross solar structure CoreCore R < 0.1 R o M  1/3 M o (the site of nuclear reactions) (the site of nuclear reactions) Radiative zoneRadiative zone (0.1  0.7) R o M  2/3 M o Convective zoneConvective zone (0.7  1) R o M  2% M o ( As temperature drops, opacity increases and radiation is not efficient for energy transport) PhotospherePhotosphere the very tiny layer of the Sun that we can observe directly

18. 18 How can we look at the solar interior? “If there are more things in heaven and Earth than are dreamt of in our natural philosphy, it is partly because electromagnetic detection alone is inadequate” We have two probes: Sound waves and Neutrinos

19. 19Helioseismology Birth: in 1960 it was found that the solar surface vibrates with a period T  5 min, Plan: reconstruct the properties of the solar interior by studying how the solar surface vibrates (as one studies the deep Earth ’s structure through hearthquakes or just like you can tell something about a material by listening to the sounds that it makes when something hits it)

20. 20 Method By means of Doppler effect on the emitted radiation, one can measure oscillations of the solar surface with a very high accuracyBy means of Doppler effect on the emitted radiation, one can measure oscillations of the solar surface with a very high accuracy Most recent measurements performed with SOHO satellite (SOlar and Heliospheric Observatory)Most recent measurements performed with SOHO satellite (SOlar and Heliospheric Observatory) http://sohowww.nascom.nasa.gov/

21. 21 The modes The observed oscillations are decomposed into discrete modes.The observed oscillations are decomposed into discrete modes. Some 10 4 modes are availableSome 10 4 modes are available Their frequencies are accurately determinedTheir frequencies are accurately determined (  /   10 -3 - 10 -4 ) So far, only p-modes have been observed, i.e. pressure driven oscillations.So far, only p-modes have been observed, i.e. pressure driven oscillations.

22. 22 Helioseismic inferences The sound speed profile (with accuracy of order 0.5%…see later)The sound speed profile (with accuracy of order 0.5%…see later) Locate the transition between radiative transport and convection:Locate the transition between radiative transport and convection: R b =0.711 (1 ± 0.14%) R The photospheric He abundance: Y photo = 0.249 (1± 1.4%)The photospheric He abundance: Y photo = 0.249 (1± 1.4%) By comparing the measured frequencies with the calculated ones (inversion method) one can determine:

23. 23 Standard Solar Model (SSM) Bahcall (1995): “A SSM is one which reproduces, within uncertainties, the observed properties of the Sun, by adopting a set of physical and chemical inputs chosen within the range of their uncertainties”.Bahcall (1995): “A SSM is one which reproduces, within uncertainties, the observed properties of the Sun, by adopting a set of physical and chemical inputs chosen within the range of their uncertainties”.

24. 24 SSM before Helioseismology: 3 data and 3 parameters In order to produce a SSM one had to study the evolution of an initially homogeneous solar mass M o up to the sun age t so as to reproduce L o, R o and (Z/X) photoIn order to produce a SSM one had to study the evolution of an initially homogeneous solar mass M o up to the sun age t so as to reproduce L o, R o and (Z/X) photo One can tune 3 parameters:One can tune 3 parameters: -the initial Helium abundance Y in -the initial metal abundance(s) Z in -“the mixing length” parameter  -“the mixing length” parameter  Up to here, the SSM is not such a big success….Up to here, the SSM is not such a big success….

25. 25 The impact of helioseismology on SSM Agreement of SSM with helioseismic data within very tiny errors (for u as well as Y ph R b..) 33 11 * Dziembowki et al. Astrop. Phys. 7 (1997) 77  U/U= (SSM-sun )/SSM

26. 26 List of applications of helioseismology By means of helioseismology one can constrain: rotation in the solar interiorrotation in the solar interior p+p cross sectionp+p cross section screening effectscreening effect solar age [A&A 343 (1999) 990]solar age [A&A 343 (1999) 990] diffusion efficiency [A&A 342 (1999) 492]diffusion efficiency [A&A 342 (1999) 492] existence of a mixed core [Astr. Phys. 8(1998) 293]existence of a mixed core [Astr. Phys. 8(1998) 293] Axion production in the sunAxion production in the sun WIMPs-matter interaction [hep-ph/0206211]WIMPs-matter interaction [hep-ph/0206211] Existence of extra-dimensions [PLB 481(2000)291]Existence of extra-dimensions [PLB 481(2000)291] Possible deviations from standard Maxwell- Boltzmann distribution [PLB 441(1998)291]Possible deviations from standard Maxwell- Boltzmann distribution [PLB 441(1998)291] SUN EXOTIC

27. 27 Solar rotation Solar surface does not rotate uniformely: T=24 days (30 days) at equator (poles). And the solar interior? Helioseismology (after 6 years of data taking) shows that below the convective region the sun rotates in a uniform way Note: E rot =1/2 m  rot R 2  0.02 eV E rot << KT

28. 28 An example: the helioseismic determination of p+p cross section (S pp ) Remind: S pp is not measured.Remind: S pp is not measured. The value used in SSM S pp (SSM)=4(1 ± 2%)The value used in SSM S pp (SSM)=4(1 ± 2%) x 10 -22 KeVb is derived from theory. Build solar models with different S ppBuild solar models with different S pp Consistency withConsistency with helioseismology requires: S pp =S pp (SSM)(1 ± 2%) This accuracy is comparable to the theoretical uncertainty:This accuracy is comparable to the theoretical uncertainty:  U/U (mod-SSM)/SSM Degli Innocenti et al. PLB 416 (1998) 365

29. 29 Can helioseismogy probe the core of the Sun? Accuracy degrades from 0.1 % to 1% as moving towards the solar center.Accuracy degrades from 0.1 % to 1% as moving towards the solar center. This follows form the fact that p modes do not propagate in the innermost part of the SunThis follows form the fact that p modes do not propagate in the innermost part of the Sun  =m p /[2x+3/4 Y+1/2 Z] mean molecular weight corecore energy radiative convective gener. transport transport

30. 30 Can helioseismogy measure the solar temperature? NO : to go from sound speed to temperature one needs the chemical compositionNO : to go from sound speed to temperature one needs the chemical composition e.g, for a perfect gas:e.g, for a perfect gas: kT=P/n=(P/  )  The abundances of elements (and EOS) is needed for translating sound speed into temperature.The abundances of elements (and EOS) is needed for translating sound speed into temperature.  =m p /[2x+3/4 Y+1/2 Z] mean molecular weight

31. 31 Can helioseismogy prove that the Sun is shining by nuclear reactions? Just indirectly : Standard Solar Models, which assume that solar energy is generated by means of H-fusion into Helium are consistent with helioseismology.Just indirectly : Standard Solar Models, which assume that solar energy is generated by means of H-fusion into Helium are consistent with helioseismology.

32. 32 A first summary The knowledge of M, R, L and age immediately determine the physical scales (T, P,  ) of the solar interior and show that nuclear reactions are the only sufficient source of solar power. Helioseismology provides an accurate picture of the solar interior, in excellent agreement with SSM calculations The accuracy of helioseismology degrades in the solar core. Helioseismology does not measure the temperature profile. We need a proof that nuclear energy sustains the Sun

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