CCN Neutrinos and the Sun’s Primordial CoreMetalicity
Wick Haxton
Institute for Nuclear Theory and Department of PhysicsBox 351550, University of Washington, Seattle WA 98195E-mail: [email protected]
Abstract.
I discuss the use of neutrinos from the CN cycle and pp chain to constrain theprimordial solar core abundances of C and N at an interesting level of precision. A comparisonof the Sun’s deep interior and surface compositions would test a key assumption of the standardsolar model (SSM), a homogeneous zero-age Sun. It would also provide a cross-check onrecent photospheric abundance determinations that have altered the once excellent agreementbetween the SSM and helioseismology. Motivated by the discrepancy between convective-zoneabundances and helioseismology, I discuss the possibility that a two-zone Sun could emerge fromlate-stage metal differentiation in the solar nebula connected with formation of the gaseous giantplanets.
1. Introduction
One of the initial motivations for pursuing solar neutrino physics was to test our understandingof main-sequence stellar evolution and the Standard Solar Model (SSM). In the past two decadesthis goal was put aside, as difficulties in understanding the pattern of solar neutrino fluxes ledto the discovery of solar neutrino oscillations. But because of the precision with which therelevant flavor physics is now known – and because the solar neutrino problem also spurredprogress in the nuclear physics of the Sun and the development of high-statistics detectors suchas Super-Kamiokande (SK) and SNO – the use of neutrinos as quantitative solar probe is now apractical possibility. Specifically, this talk summarizes recent arguments by Aldo Serenelli andme [1] that a measurement of the CN neutrino flux could test a key assumption of the SSM, thehomogeneity of the zero-age main sequence Sun. This assumption, the basis for equating theSSM’s primordial core metal abundances to today’s surface metal abundances, may now be insome degree of conflict with observation: recent 3D modeling of photospheric absorption lineshas led to a downward revision in the metal content of the solar convective zone [2], alteringhelioseismology in the upper radiative zone, where the temperature ∼ × K [3, 4, 5, 6]. Inthis region C, N, O, Ne, and Ar are partially ionized and particularly O and Ne have a significantinfluence on the radiative opacity.A quantitative comparison between the Sun’s surface and core abundances could prove usefulin understanding the chemical evolution of other gaseous bodies in our solar system, whoseinteriors are not as readily probed. The Galileo and Cassini missions found significant metalenrichments in the H/He atmospheres of Jupiter and Saturn, e.g., abundances of C and N of ∼ four times solar for Jupiter and ∼ a r X i v : . [ a s t r o - ph ] S e p " + ,!* ’ -. /$/"*"$&(!* !* , . !" = !% > !& A ! > !% A !’ B ! = !$ > !’ A,8C .,8C . D ,8C . ,8C . D ,8C . ,8C . D ,8C .E EE ! " + ,!* ’ -. /$/"*"$&(!* !* , . !" = !% > !& A ! > !% A !’ B ! = !$ > !’ A,8C .,8C . D ,8C . ,8C . D ,8C . ,8C . D ,8C .E EE Figure 1.
The right panel shows the CNO bi-cycle for hydrogen burning. The left compares theenergy produced in the CN cycle with that produced in the pp-chain, as a function of temperatureT , measured in units of 10 K. The results are normalized to the pp-chain energy production atthe Sun’s center and to solar metalicity, assuming equilibrium burning. The sharper CN-cycledependence on temperature is apparent. If approximated as a power law T x , x ranges between ∼
19 and ∼
22 over the range of temperatures typical of the Sun’s hydrogen-burning core. Thedot marks the point corresponding to the Sun’s center, T ∼ ∼ − M ⊕ , is very similar to the depletion that wouldbe needed in the convection zone to bring the photospheric abundances and helioseismology intoagreement. Serenelli and I raised the possibility that a two-zone Sun resulted from a processin which the last ∼
1% of nebular gas was scoured of its metals by the process of planetaryformation, then deposited on the early Sun to dilute the convective zone.
2. The CNO Bi-Cycle and its Neutrinos
The need for two mechanisms to burn hydrogen was recognized in the pioneering work of Betheand collaborators. The first, the pp-chain, dominates energy production in our Sun and otherlow-mass main-sequence stars and can be considered a primary process in which the chain’s“catalysts,” deuterium, He, and Be/ Li (the elements participating in the steps leading to He), are synthesized as the chain burns to equilibrium.But the sharper temperature dependence of a second mechanism, the CNO bi-cycle, is neededto account for the structure of more massive main-sequence stars. Unlike the pp-chain, the CNObi-cycle (Fig. 1) is a secondary process: the catalysts for H burning are the pre-existing metals.Thus the CNO contribution to energy generation is proportional to stellar metalicity. The CN-cycle, denoted by I in Fig. 1, operates in the Sun. The cycle conserves the number abundance,but alters the distribution of metals as it burns into equilibrium, eventually achieving equilibriumabundances proportional to the inverses of the respective rates.While responsible for only ∼
1% of solar energy generation, the CN cycle produces measurableneutrino fluxes. The slowest, rate-controlling reactions in the CN cycle are N(p, γ ) and C(p, γ ). The latter has reached equilibrium over most of the solar core. In fact, the rapidburning of C, as the cycle seeks equilibrium at the start of the main sequence, likely drivesconvective mixing of the early solar core for ∼ y. In contrast, the N lifetime is shorterhan the age of the Sun only in regions where T ∼ > .
33, which corresponds to R ∼ < . R (cid:12) intoday’s Sun, or equivalently the central 7% of the Sun by mass. Consequently, over a significantportion of the outer core, C has been converted to N, but further reactions are inhibited bythe N(p, γ ) bottleneck.The BSP08(GS) SSM [8] – which employs recent updates of metal abundances and of the N(p, γ ) S-factor – finds a modest CN-cycle contribution to solar energy generation of 0.8% andcorresponding neutrino fluxes N( β + ) C E ν ∼ < .
199 MeV φ = (2 . +0 . − . ) × / cm s O( β + ) N E ν ∼ < .
732 MeV φ = (2 . +0 . − . ) × / cm s . The ranges reflect conservative abundance uncertainties as defined empirically in [9]. The firstreaction is part of the path from C to N, while the latter follows N(p, γ ). Thus neutrinosfrom O β decay are produced in the central core: 95% of the flux comes from the CN-equilibrium region, described above. About 30% of the N neutrinos come from outside thisregion, primarily because of the continued burning of primordial C: this accounts for thesomewhat higher flux of these neutrinos.The SSM makes several reasonable assumptions, including local hydrostatic equilibrium (thebalancing of the gravitational force against the gas pressure gradient), energy generation byproton burning, a homogeneous zero-age Sun, and boundary conditions imposed by the knownmass, radius, and luminosity of the present Sun. It assumes no significant mass loss or accretion.The homogeneity assumption allows the primordial core metalicity to be fixed to today’s surfaceabundances. Corrections for the effects of diffusion of He and the heavy elements over 4.57 b.y.of solar evolution are included, and generally been helpful in improving the agreement betweenSSM predictions and parameters probed in helioseismology.The SSM postulate of a homogeneous zero-age Sun is based on the assumptions 1) thatthe early pre-main-sequence Sun passed through a fully convective, highly luminous Hayashiphase, mixing the Sun; and 2) that no chemical differentiation in the gas accreted onto the Sunoccurred after this phase, when the Sun develops a radiative core distinct from the convectivesurface zone.Solar surface abundances are known, determined from analyses of photospheric atomic andmolecular spectral lines. Traditionally the associated atmospheric modeling has been done in onedimension, in a time-independent hydrostatic analysis that incorporates convection via mixing-length theory. But much improved 3D models of the solar atmosphere have been developedrecently to treat the radiation-hydrodynamics and time dependence of this problem. This 3Danalysis led to a revision in solar metalicity from the previous standard, Z=0.0169 [10], toZ=0.0122 [2], thus altering SSM predictions. Hereafter we denote these as the GS and and AGSabundances, respectively.The predictions of solar models that use the GS solar composition, the most up to dateof which is the BPS08(GS) [8] but including also the BP00 [11], BP04 [12] and BS05(OP) [4]models, are in excellent agreement with helioseismology. But those computed with the revisedabundances are in much poorer agreement, with discrepancies exceeding 1% in the region justbelow the convective zone (R ∼ . − . (cid:12) ). Associated properties of the SSM, such asthe depth of the convective zone and the surface He abundance, are also now in conflict withhelioseismology. As discussed in [13], the discrepancies are significantly above measurement andsolar model uncertainties.The reduced core opacity also lowers the SSM prediction of the temperature-dependent Bneutrino flux by about 20%: the predicted B flux using the GS abundances and Opacity Project[14] opacities (model BPS08(GS)) is 5.95 × /cm s, which drops to 4.72 × /cm s whenAGS abundances are used (model BPS08(AGS)). These results can be compared to the Beutrino flux deduced from the NCD-phase SNO data set of [5.54 +0 . − . (stat) +0 . − . (sys)] × /cm s [15].
3. The Sun as a Calibrated Laboratory
It has been recognized for many years that a measurement of the CN-cycle solar neutrino fluxwould, in principle, determine the metalicity of this core zone, allowing a comparison withabundance determined from the solar atmosphere. In the past several years new developmentshave occurred that may make such a measurement practical: • Accurate calibrations of the solar core temperature by SNO and SK; • Tight constraints on the oscillation parameters and matter effects that determine the flavorcontent of the CN and B neutrino fluxes; • Recent measurements of the controlling reaction of the CN cycle, N(p, γ ), that havesignificantly reduced the nuclear physics uncertainties affecting SSM predictions of CN-cycle fluxes; and • New ideas for high-counting rate experiments that would be sensitive to CN-cycle neutrinos,and from which reliable terrestrial fluxes could be extracted.The analysis of [1], which examined whether CN neutrino experiments could place a significantconstraint on the solar core’s primordial metalicity, used previous SSM work in which thelogarithmic partial derivatives α ( i, j ) for each neutrino flux φ i are evaluated for the SSM inputparameters β j , α ( i, j ) ≡ ∂ ln [ φ i /φ i (0)] ∂ ln [ β j /β j (0)] , (1)where φ i (0) and β j (0) denote the SSM best values. This information, in combination with theassigned uncertainties in the 19 β j of the SSM, then provides an estimate of the uncertainty inthe SSM prediction of φ i . In particular, crucial to the current analysis is the dependence [9] onthe mass fractions (measured relative to hydrogen) of different heavy elements, β j = mass fraction of element jmass fraction of hydrogen ≡ X j . (2)Having this information not as a function of the overall metalicity Z , but as a function ofthe individual abundances, allows one to separate the “environmental” effects of the metals inthe solar core from the special role of primordial C and N as catalysts for the CN cycle. Byenvironmental effects we mean the influence of the metals on the opacity and thus the ambientcore temperature, which controls the rates of neutrino-producing reactions of both the pp-chainand CN cycle. In [1] the temperature-dependent B neutrino flux was used to calibrate theenvironmental effects of the metals and of other SSM parameters, thus isolating the special CN-cycle dependence on primordial C+N. This primordial abundance can be expressed, with verylittle residual solar model uncertainty, in terms of the measured B neutrino flux and nuclearcross sections that have been determined in the laboratory.The partial derivatives allow one to define the power-law dependencies of neutrino fluxes,relative to the SSM best-value prediction φ i (0) φ i = φ i (0) N (cid:89) j =1 (cid:34) β j β j (0) (cid:35) α ( i,j ) (3)where the product extends over N = 19 SSM input parameters. This expression can be used toevaluate how SSM flux predictions will vary, relative to φ i (0), as the β j are varied. Alternatively,he process can be inverted: a flux measurement could in principle be used to constrain anuncertain input parameter.The baseline SSM calculation used in [1], BPS08(AGS) [8], employed the recently determinedAGS abundances for the volatile elements C, N, O, Ne, and Ar, rather than the previous GSstandard composition. It should be noted that AGS includes a downward revision by 0.05 dexof the Si photospheric abundance compared to GS and, accordingly, a similar reduction in themeteoritic abundances. The partial derivatives needed in the present calculation are summarizedin Tables 1 (solar model parameters and nuclear cross sections) and 2 (abundances).The SSM estimate of uncertainties in the various solar neutrino fluxes φ i can be obtained byfolding the partial derivatives with the uncertainties in the underlying β j . In particular, it isconvenient to decompose Eq. ( 3) into its dependence on solar parameters and non-CN metals,nuclear S-factors, and the primordial C and N abundances, φ i = φ SSMi (cid:89) j ∈{ Solar and Metals (cid:54) =C , N } (cid:34) β j β j (0) (cid:35) α ( i,j ) (cid:89) j ∈{ Nuclear } (cid:34) β j β j (0) (cid:35) α ( i,j ) (cid:89) j ∈{ C , N } (cid:34) β j β j (0) (cid:35) α ( i,j ) (4)where the first term will be designated the “environmental” uncertainty – SSM solar parametersand metal abundances that primarily influence neutrino flux predictions through changes theyinduce in the core temperature. These are, respectively, the uncertainties in the photonluminosity L (cid:12) , the mean radiative opacity, the solar age, and calculated He and metal duffusion;and the fractional abundances of O, Ne, Mg, Si, S, Ar, and Fe. The estimated 1 σ fractionaluncertainties for the these parameters are given in [1]. The abundances of Mg, Si, S, and Fe aremeteoritic, while those of the volatile elements C, N, O, Ne, and Ar are photospheric.The next term contains the effects of nuclear cross section uncertainties on flux predictions.The β j are the S-factors for p+p ( S ), He + He ( S ), He+ He ( S ), p + Be ( S ), e + Be ( S e ), and p + N ( S ). The estimated 1 σ fractional uncertainties are also given in [1].The last term is the contribution of the primordial C and N abundances. As Table 2 shows,pp-chain neutrino fluxes are relatively insensitive to variations in these abundances, as theheavier nuclei like Fe have a more important influence on the core opacity. But the expected,nearly linear response of the N and O neutrino fluxes to these abundances is apparent.These are the abundances we would like to constrain by a future measurement of the N and O solar neutrino fluxes. Such a measurement begins to be of interest if these abundances couldbe determined with an accuracy significantly better than 30%.Were one to vary the 11 SSM parameters designated as “environmental” according to theirassigned uncertainties (taking them to be uncorrelated), a 7.5% SSM net uncertainty in φ ( N)would be obtained. This uncertainty would be one of dominant ones in the analysis of presentinterest. But, as discussed in [1] in more detail, these environmental uncertainties influenceneutrino fluxes through their impact on the core temperature, regardless of the details ofwhich parameters are varied. Consequently, there are strong environmental correlations betweendifferent neutrino fluxes, allowing one to form ratios of fluxes that are much less sensitive toenvironmental effects. Furthermore these correlations remain valid for parameter variations faroutside accepted SSM uncertainties.This is illustrated in the SSM Monte Carlo tests represented in Fig. 3. One finds that a fluxratio such as φ ( O) φ ( B) K , (5)where the exponent K ∼ .
828 is taken from the fit shown in Fig. 3, is much less sensitiveto environmental uncertainties than either the numerator or denominator separately. Thisis apparent from the entries in Tables 1 and 2. As φ ( B) can be taken from SK and SNOmeasurements, most of the environmental uncertainty in predicting φ ( O) can be eliminated. igure 2.
Results from SSM Monte Carlo simulations in which the 11 environmental parameters(see text) have been varied. The two left panels show the correlations between the B flux andthe two CN-cycle neutrino fluxes N and O. The slopes of the correlations are given in theplots, together with the 68.3% confidence level contours. The panels on the right show theresiduals from the fits, 2.8% and 2.6% for the N and O fluxes respectively − the residualenvironmental uncertainty that remains after making use of the B flux constraint.Effectively, φ ( B) becomes a “thermometer” constraining core temperature changes induced byvarying the environmental β j . In this way one obtains a more precise relationship between theCN flux, a quantity that should be measured quite accurately in next-generation experimentslike SNO+, and the core abundances of C and N.
4. The Analysis for Elastic Scattering and Neutrino Oscillations
The analysis requires a number of steps that will be summarized here, as more detail can befound in Ref. [1]. The total B flux (the instantaneous solar flux), normalized to the SSM bestvalue, can be related to rates that would be measured in terrestrial detectors by φ ( B) φ SSM ( B) = φ ( B) (cid:104) σ SK ( B , δm , θ ) (cid:105) φ SSM ( B) (cid:104) σ SK ( B , δm , θ ) (cid:105) ≡ R SKexp ( B) R SKcal ( B , δm , θ ) (6) able 1. Partial derivatives α ( i, j ) of neutrino fluxes with respect to solar environmental andnuclear cross section parameters.Environmental β j Nuclear β j Source L (cid:12) Opacity Age Diff. S S S S S e S φ ( B) 7.16 2.70 1.38 0.28 -2.73 -0.43 0.85 1.0 -1.0 -0.020 φ ( N) 4.40 1.43 0.86 0.34 -2.09 0.025 -0.053 0.0 0.0 0.71 φ ( N)/ φ ( B) . φ ( O) 6.00 2.06 1.34 0.39 -2.95 0.018 -0.041 0.0 0.0 1.00 φ ( O)/ φ ( B) . Table 2.
Partial derivatives α ( i, j ) of neutrino fluxes with respect to fractional abundances ofthe primordial heavy elements.C, N β j Environment Abundance β j Source C N O Ne Mg Si S Ar Fe φ ( B) 0.027 0.001 0.107 0.071 0.112 0.210 0.145 0.017 0.520 φ ( N) 0.874 0.142 0.044 0.030 0.054 0.110 0.080 0.010 0.268 φ ( N)/ φ ( B) . φ ( O) 0.827 0.200 0.071 0.047 0.080 0.158 0.113 0.013 0.393 φ ( O)/ φ ( B) . (cid:104) σ SK (cid:105) is an effective cross section that takes into account all of the neutrino flavor anddetector response issues (trigger efficiencies, resolution, cross section uncertainties, oscillations,etc.) that determine the relationship between a measured detector rate and the instantaneoussolar flux. The numerator of the ratio on the right is a directly measured experimental quantity:the SK elastic scattering rate for producing recoil electrons with apparent energies between5.0 and 20 MeV, per target electron per second. The denominator is a theoretical quantity,computed by folding the SSM best-value B flux produced in the Sun with the cross sectionfor ( ν x , e ) elastic scattering, averaged over a normalized B spectrum, defined for the specificexperimental conditions of SK, and including the effects of flavor mixing that alter the fluxduring transit from the Sun to the detector. This cross section is calculated from laboratorymeasurements of detector properties, the β decay spectrum, the underlying neutrino-electroncross sections, and most critically, the parameters governing oscillations. We describe thesefactors below.The experimental rate comes from the 1496 days of measurements of SK I [16]. From the SKI rate/kiloton/year 520 . ± . +18 . − . (sys) kton − y − . (7)we find R SKexp ( B), 4 . ± . +0 . − . (sys) × − electron − s − (8)(or ∼ ∼ ± (cid:104) σ SK ( B , δm , θ ) (cid:105) = (cid:90) dE ν φ B norm ( E ν ) (cid:34) P ν e ( E ν , δm , sin θ ) (cid:90) T max ( E ν ) T =0 dT σ esν e ( T ) P ν µ ( E ν , δm , sin θ ) (cid:90) T max ( E ν ) T =0 dT σ esν µ ( T ) (cid:35) (cid:90)
20 MeV5 MeV d(cid:15) a f trig ( (cid:15) a ) ρ ( (cid:15) a , (cid:15) t = T + m e ) (9)where φ B norm ( E ν ) is the normalized B neutrino spectrum. Equation (9) involves an integral overthe product of this spectrum and the energy-dependent oscillation probabilities. ( P ν e + P ν µ =1,assuming oscillations into active flavors. P ν µ can be defined as the oscillation probability toheavy flavors, if the effects of three flavors are considered.) A given E ν fixes the range of kineticenergies T of the scattered electron, over which an integration is done; in the laboratory frame T max = 2 E ν / ( m e + 2 E ν ). The integrand includes the elastic scattering cross sections σ es ( T ) forelectron and heavy-flavor neutrinos and the SK resolution function ρ ( (cid:15) a , (cid:15) t ), where (cid:15) t = T + m e is the true total electron energy while (cid:15) a is apparent energy, as deduced from the number ofphototube hits in the detector. Finally, an integral must be done over the window used by theexperimentalists, apparent electron energies (cid:15) a between 5 and 20 MeV. The deduced countingrate includes the triggering probability that a event of apparent energy (cid:15) a will be recorded inthe detector. Resolution and triggering functions for SK are given in [1].Similarly, the CN-cycle neutrino response for a detector like SNO+ is φ ( O) φ SSM ( O) ≡ R B/Sexp ( O) R B/Scal ( O , δm , θ ) = R B/Sexp (CN) / (1 + α (0 . , . R B/Scal ( O , δm , θ )) (10)where the experimental rate for O neutrinos has been written in terms of the total CN-neutrinorate R B/Sexp (CN) by introducing a correction factor α ∼ .
12 that accounts for the N neutrinocontribution. As discussed in [1], α can be measured in principle, but can also be evaluated fromtheory, with negligible uncertainty. No measurement of R B/Sexp (CN) currently exists, of course.But such measurements could be made in Borexino or SNO+, existing or planned detectorsusing large volumes of organic scintillator and placed quite deep underground. A window forthe apparent kinetic energy T of the scattered electron of 0.8-1.3 MeV has been discussed bythe Borexino group. As the Be 0.866 MeV line corresponds to T max ∼ Be neutrino recoil electrons.As discussed in [1], one can use Eqs. (6) and (10) in expressions based on Eq. (4), then ondividing obtain R B/Sexp (CN) R B/Scal ( O , δm , θ )) = (1 . ± . (cid:34) R SKexp ( B) R SKcal ( B , δm , θ ) (cid:35) . × [1 ± . . envir . ) ± . (cid:32) X ( C) X ( C) SSM (cid:33) . (cid:32) X ( N) X ( N) SSM (cid:33) . . (11)Effectively the SK rate has been used to limit SSM “environmental” uncertainties, leaving anerror budget dominated by the nuclear physics. But this source of error is under laboratorycontrol and will be reduced as nuclear reaction measurements continue. The last two terms arethe primordial abundances one would like to constrain. The role of the SSM in this equation is todefine a set of parameters and thus a set of reference rates, about which we then explore possiblevariations. Those variations generate the environmental and nuclear uncertainties discussedabove.The R cal factors in Eq. (11) contain additional uncertainties discussed in [1], includingone important one, that associated with neutrino oscillations. Apart from the dependenceon the solar density profile, this should be considered a laboratory uncertainty, analogous tonuclear cross sections. Uncertainties in oscillation parameters will continue to be refined byastrophysical, accelerator and reactor measurements.he LMA parameter uncertainties in SK and Borexino/SNO+ are anti-correlated. Most ofthe low-energy N neutrinos do not experience a level crossing, residing instead in a portion ofthe MSW plane where the oscillations are close to the vacuum oscillation limit, P ν e ( E ν ) → −
12 sin 2 θ , (12)so that an increase in the vacuum mixing angle θ decreases the ν e survival probability. Thehigher energy B neutrinos are largely within the MSW triangle, described by an adiabatic levelcrossing. The limiting behavior for an adiabatic crossing is P ν e ( E ν ) →
12 (1 − cos 2 θ ) (13)so that an increase in θ increases the survival probability. This anti-correlation thus leads tolarger effects in the ratio.The impact of this uncertainty on Eq. (11) was analyzed in [1], using the allowed regions for θ and δm obtained in KamLAND’s combined analysis, yielding R B/Scal ( O , δm , θ )) R SKcal ( B , δm , θ ) . = (1 ± . (cid:34) R B/Scal ( O , δm , θ )) R SKcal ( B , δm , θ ) . (cid:35) BV (14)where BV denotes the SSM best-value ratio.Thus the overall uncertainty budget in Eq. (11) includes the experimental uncertainty of theSK “thermometer” of 3%, residual solar environmental uncertainties at 2.6%, LMA parameteruncertainties at 4.9%, and nuclear S-factor uncertainties of 7.6%. The overall uncertainty in the“theoretical” relationship between a future SNO+ or Borexino CN-neutrino flux and core C/Nmetals is thus about 9.6%. As the nuclear physics uncertainty dominates, one would expectthis relationship to become more precise when ongoing analyses of data obtained by the LUNAcollaboration and others for N(p, γ ) are completed. An appropriate goal would be 3.5% in thisS-factor, a 30% improvement. The uncertainty in N(p, γ ) would no longer dominate the nuclearphysics error budget, but instead would be comparable to the contributions from S and S .However, the current 9.6% uncertainty is not a bad starting point, as first-generation CN-cycleneutrino experiments are expected to measure this flux to an accuracy of about 10%. Thatis, the theoretical uncertainty will not dominate the experimental uncertainty, even withoutanticipated nuclear physics improvements.
5. Future Experiments and Summary
The work reported here was motivated in part by new detectors that might enable a high-statistics measurement of the CN-cycle neutrinos. Two possibilities are Borexino and SNO+,detectors based on ultra-clean organic scintillation liquids. Borexino, which operates within GranSasso, must deal with a serious background, cosmogenic C (a β + source). The collaborationhas discussed a possible triple-coincidence veto [17] to limit this background.Because of SNOLab’s 6.0 km.w.e. depth, C will be much less troublesome in SNO+, anexperiment that will use the SNO cavity and about three times more scintillator than Borexino.Figure 3 shows a simulation of the expected SNO+ response, performed by the experimenters(Chen, private communication). (Note that the simulation is based on the BS05(OP) SSM andthe best-fit LMA solution to the solar neutrino problem, rather than the updated BPS08(AGS)used in this paper.) The CN-neutrino event rate for an energy window above 0.8 MeV wasfound to be 2300 counts/year. The experimenters concluded that SNO+ could determine theCN-neutrino rate to an accuracy of approximately 10%, after three years of running [18]. This igure 3.
A simulation of the Be, pep, and CNO electron recoil spectrum expected in SNO+.This figure is due to M. C. Chen [18].is an appropriate goal for such a first-generation CN-cycle neutrino measurement, as it wouldapproach the accuracy with which that flux could be related theoretically to the Sun’s primordialcore C and N abundances, as argued in this paper.One main point of this talk is that if a 10% measurement can be made, an analysis couldbe done that limits theoretical uncertainties to below this level, provided one uses SK as athermometer to eliminate environmental uncertainties. Indeed, both of the limiting errors insuch an analysis can be addressed in future laboratory measurements, namely nuclear crosssections ( ∼ ∼ ∼ ⊕ . Thismass is similar to the deficit of metals in the convective zone, were one to interpret thehelioseismology/photospheric abundance discrepancy in the most naive way. The raises aprovocative question: is it possible that the process that concentrated metals in the gaseousgiants also produced a large volume of metal-depleted gas that subsequently was accreted ontothe Sun’s surface? If so, late-stage accretion of depleted gas onto the Sun would have not onlydiluted the convective zone, but generated a transition zone in the modern Sun’s upper radiativezone − one that might alter helioseismology in that region. One would also expect abundanceanticorrelations between the atmospheres of the Sun and gaseous giants. While the suggestion ofa common chemical mechanism linking the convection zone and the gaseous giants is speculative,t provides additional motivation for exploiting the CN neutrinos as a quantitative probe of solarcore metalicity.
6. Acknowledgments
This work was supported in part by the Office of Nuclear Physics, US Department of Energy,under grant DE-FG02-00ER-41132.
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