1 The standard solar model and solar neutrinos Episode I: Solar observables and typical scales Episode II: Standard and non-standard solar models Episode III: Nuclear reactions and solar neutrinos Trieste Sept. 2002

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3 Main solar observables and typical scales Observables: Mass, Luminosity, Radius, Age, Metal content of the photosphere The typical scales Helioseismic data Rotation Magnetic fields

4 Who measured the solar mass? Galileo Cavendish Einstein Smirnov

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

6 Solar Luminosity The solar constant K o : amount of energy, per unit time and unit area, from the Sun that reaches the Earth, measured  to the direction to the Sun, without atmosphere absorption. Is not a constant, but varies with time (0.1% in a solar cycle). The value averaged over 12 years of the solar irradiance (and over diffent satellite radiometers) gives the solar luminosity: L o =4  d 2 K o =3.844(1  0.4%) erg/s

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

8 Solar Age Method: radioactive dating of oldest objects in the solar system (chondrite meteorites) 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 to Zero Age Main Sequence point t=4.57(1  0.4%) Gyr

9 Solar Metal abundance Spectroscopic measurements of the solar photosphere yield the relative abundances (in mass) of “Metals“ to H (Z/X) photo =0.0245(1  6%) Most abundant: O, C, N, Fe Results are generally consitent with the meteoritic abundances A remarkable exception: the solar Li content is depleted by 100 with respect to meteorites Note: Hydrogen abundance X  0.75

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

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

12 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 fulfilment our dream of controlling this latent power for the well- being of the human race - or for its suicide” The birth of Nuclear Astrophysics  =L o t  M o c 2

13 Can nuclear reaction occur into the sun? The temperature scale We have found P and  scales Need equation of state for T. Take Perfect gas and assume it is all hydrogen (ionized): kT= P/(2n p )=P m p /(2   1 keV (T  K) Note: kT>> e 2 /r  e 2 n 1/3 perfect gas reasonable However: KT<< e 2 /r nuc  1MeV

14 Nuclear Astrophysics grows Rutherford: kT too small to overcome Coulomb repulsion at nuclear distance. Nuclear fusion in star cannot occur according to classical physics Gamow (1928): discovery of tunnel effect. => Nuclear reactions in star can occur below the Coulomb barrier (Atkinson, Houtermans, Teller) von Weizsäcker (1938) : discovered a nuclear cycle, (CNO) in which hydrogen nuclei could be burned using carbon as a catalyst. Bethe (1938): worked out the basic nuclear processes by which hydrogen is burned (fused) into helium in solar (and stellar) interiors (pp chain) used the Gamow factor to derive the rate at which nuclear reactions would proceed at the high temperatures believed to exist in the interiors of stars. However, von Weizsäcker did not investigate the rate at which energy would be produced in a star by the CNO cycle nor did he study the crucial dependence upon stellar temperature. KT<< e 2 /r nuc

15 The gross solar structure Hot nucleus R < 0.1 R o M  0.3 M o ( nuclear reaction) Radiative zone 0.1  0.7 R o M  2/3 M o Convection zone 0.7  1 R o M  1/60 M o As temperature drops, opacity increases and radiation is not efficient for energy transport Photosphere: deepest layer of the Sun that we can observe directly

16 Helioseismology Birth: in 1960 it turns out that the solar surface vibrates with a period T  5 min, and an “amplitude” of about 1Km/s Idea: reconstructing the properties of the solar interior by studying how the solar surface vibrates (like one studies the deep Earth ’s structure through the hearthquake or just like you can tell something about a material by listening to the sounds that it makes when something hits it)

17 Procedure (1) By using Doppler effect, one measures the oscillation frequencies with a very high accuracy (  /   ) Most recent measurements come from apparatus on satellite: Soho (SOlar and Heliospheric Observatory)

18 Procedure (2) The observed oscillations are decomposed into discrete modes (p-modes) At the moment 10 4 p-modes are available Only p-modes observed so far =>oscillation driven by pressure involve solar structure only down to 0.1R

19 Helioseismic inferences The transition from radiation to convection: R b =0.711 (1 ± 0.14%) R The present He abundance at solar surface: Y photo = (1± 1.4%) The sound speed profile (with accuracy of order 0.5%…see next lesson) By comparing the measured frequencies with the calculated ones (inversion method) one can determine:

20 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

21 Magnetic field From the observation of sunspots number a 11 year solar cycle has been determined (Sunspots= very intense magnetic lines of force (3KG) break through the Sun's surface) the different rotation between convection and radiative regions could generate a dynamo mechanism and B= G near the bottom of the convective zone. A primordial 10 6 G field trapped in the radiative zone is proposed by some authors Anyhow also a 10 6 G field give an energy contribution << KT

22 Summary Main Solar observables: M,R,age, L, (Z/X) photo We can derive the typical scale of several physical quantities (need EOS for T) Only nuclear energy can substain sun/stars =>Birth of nuclear Astrophysics New Solar observables: oscillation frequencies =>Birth of Helioseismology

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24 Inversion method Calculate frequencies  i as a function of u =>  i  i (u j ) j=radial coordinate Assume Standard Solar Model as linear deviation around the true sun:  i  i, sun + A ij (u j -u j,sun ) Minimize the difference between the measured  i and the calculated  i In this way determine  u j  =u j  -u j, sun