Chapter three Sun’s model Major contributions in building the Sun’s model have been made by Eddington (1930’s), Hoyle (1950’s),Bahcall, Clayton (1980’s) and others. 1. Rate of energy generation W kg -1 (3.1)where X is hydrogen mass factor W kg -1 (3.2)where Z N is nitrogen mass factor These predict very rapid temperature dependence for power output, E  T n TnE ( W kg-1) PP5 x x x x x CNO5 x x x x x x *CNO rapidly overtakes PP, rates equal at 1.7 x 10 7 K Sun’s central temperature is believed to be 1.56 x 10 7 K, hence importance of neutrino experiments is to try to find which fusion reactions occur.

2. Mystery of the missing solar neutrinos 2.1 The flux of neutrinos predicted --But few of the details are open to observation because the whole process is obscured by million of kilometres of stellar matter --But the cover-up is not complete -- Neutrinos can escape almost without interaction from the heart of a star. --The neutrino flux from the Sun  a direct window to the interior and its nuclear reactions. Estimate the flux of neutrinos: In the hydrogen burning process, Then neutrinos must be released at a rate of To escape from the Sun, each neutrino must travel a distance ~ The probability of interaction during this escape is is the average interaction cross-section with an electron or a nucleus the average density of electrons and nuclei in the sun is, so we have P~ Thus neutrinos do indeed escape almost unhindered from the sun and arrive some eight minutes later at the earth.

The neutrino flux at earth is : In Summary, the following fusion reactions give neutrinos Process F v (10 14 m -2 s -1 ) Emax(MeV) PPI : p + p  H e PP II: 7 Be + e-  7 Li PP III 8 B  8 Be + e * CNO cycle: 13 N  13 C + e CNO cycle: 15 O  15 N + e

2.2 Properties of neutrinos a) Massless (or nearly so?) but they have energy/ momentum b) Speed of light (or very close) c) Very weak interaction with matter, essentially all leave the Sun. If we can detect on Earth, we can measure reaction rates of various stages of H  He fusion and hence temperature of fusion reaction. No other technique could provide such a direct probe of conditions in the Sun’s core. 2.3 Detecting neutrinos a) First experiment Site: 1 mile down the abandoned Homestake gold mine in South Dakota, USA, to minimise cosmic rays:

The number of Argon 37 atoms detected gives the number of neutrino interactions in the chlorine vat  the solar neutrino flux. Detect principle: 37 Cl +  37 Ar + e+ The chief drawback of this reaction is that only neutrinos with E v > 0.81 MeV can be detected. From the table in the previous slide, this high threshold energy implies that neutrinos from the primary P-P fusion reaction cannot be detected. The neutrino from electron capture on 7 Be only just exceed the threshed and the probability of capture in 37 Cl is exceedingly low Most of neutrinos from 8 B decay have an energy well above the threshold for detection. Even though these neutrinos contribute a minor component of the neutrino flux from the sun, they are expected to dominate the capture rate in 37 Cl.

The actual capture rates depend on incident neutrino flux, the number of target 37 Cl nuclei and the energy-averaged neutrino capture cross-section. For the neutrinos from 8 B decay, the average capture cross-section 37 Cl is and a target containing N( 37 Cl) nuclei should give a capture rate of Because of the low probability of neutrino capture, a special unit called the solar neutrino unit (SNU) is used in neutrino astrophysics This is the capture rate per second per target nuclei Therefore the capture rate of neutrinos from 8 B decay in the SUN should be 6.1 SNU the capture rate of neutrinos from 7 Be : 1.1 SNU From N 13 : 0.1SNU and from O SNU. In total : (7.9  2.6) SNU Predicted capture rate of neutrinos

Data taken from 1969 until 1993 (24 years!!) gives observed rate = 2.55  0.2 SNU Result: The discrepancy (a deficit 69%) between the observed capture rate and the predicted capture rate of solar neutrinos in 37 Cl has and continues to be a subject of debate in astrophysics. b) SAGE and GALLEX collaborations began taking data in late A container with 12.2 tons of watered Gallium 71: which, after an interaction with a solar neutrino, becomes Germanium Ga +  71 Ge + e- a radioactive isotope with a half-life of days. From May 1991 to September 1993 observation gave a mean of SNU while theory predicts 132 SNU. This is a neutrino deficit of 40%. Why?

2.4 Reason for the discrepancy ? Possibilities: 1). Temperature of centre of Sun is lower than thought (15.2, not 15.6 x 10 6 K) Astrophysicists claim standard model better than 3% accurate. 2). Nuclear reaction rates incorrect If more of CNO, less of PP, we would see fewer neutrinos Nuclear physicists do not believe rates are wrong, but CNO is VERY temperature sensitive 3). Neutrino’s rest mass is not zero, so energy carried off is different An appealing possibility since it leads to much more research and speculation! 4). Neutrino changes on the journey to Earth: 3 types: electron, muon, tau neutrinos There is recent evidence for this. 5). Some other unsuspected problem with detectors

2.5 Solutions In 1998, a Kamiokande experiment on cosmic ray: --provided evidence that muon neutrinos can transform to tau neutrinos as they travel through the earth If electron neutrinos behave similarly, one could account for the low detection rate of solar neutrinos on earth -- because none of the solar neutrino experiments would detect an electron neutrino emitted during hydrogen burning if it changes to a muon or tau neutrino as it propagates through the sun or the earth The detection of muon or tau neutrinos from the sun would provide evidence for the transformation of electron neutrinos to muon or tau neutrinos

Recent experiment: Two kilometers down in the Sudbury Neutrino Observatory, sensors on the interior of these studded panels detect dim flashes when neutrinos interact with heavy water inside this ball The new data indicate that electron neutrinos oscillate with other flavors as they make their way to Earth. Because detectors have been less sensitive to muon and tau than to electron neutrinos, the result was a systematic undercounting of solar neutrinos Science News, Vol. 159, No. 25, June 23, 2001, p. 388