aa r X i v : . [ a s t r o - ph . S R ] S e p SOLAR NEUTRINOS AND THE SUN
ALDO M. SERENELLI
Instituto de Ciencias del Espacio (CSIC-IEEC),Facultad de Ciencias, Campus UAB, Bellaterra, 08193, Spain
E-mail: [email protected] present updated standard solar models (SSMs) that incorporate the latestresults for nuclear fusion rates, recently published. We show helioseismic resultsfor high and low metallicity compositions and also for an alternative set of solarabundance, derived from 3D model atmospheres, which give intermediate results.For the high and low metallicity models, we show that current solar neutrino datacan not differentiate between models and that a measurement of the CNO fluxesis necessary to achieve that goal. A few additional implications of a hypotheticalmeasurement of CNO neutrinos, both in terms of solar and stellar physics, arediscussed.
1. Introduction
We present and discuss the results of our most up-to-date solar models. Part of thiswork is devoted to the solar abundance problem, that is, the mismatch between resultsof solar models and helioseismic inferences on solar structure when most the recentand sophisticated (using a 3D solar model atmosphere) determination of the solarcomposition is used. Results for neutrino fluxes are also presented. Together with anew analysis of solar neutrino data that incorporates latest results by the Borexinoexperiment, these results show that solar neutrino data can be equally well reproducedby solar models with both the high and low metallicity compositions. Currently,solar neutrinos can not yield information towards the solution of the solar abundanceproblem. However, this situation could be modified if a direct determination of CNOneutrinos is achieved. If such a measurement were done today, it would lead to a directmeasurement of the central C+N content of the Sun where uncertainties from solarmodels and neutrino properties represent only 10%. Possible implications of such ameasurement are discussed both in terms of solar and stellar physics. Finally, wespeculate with the possibility that the early evolution of the Sun and the interactionwith its protoplanetary disk can be constrained by determining the central content ofC+N. This might be of relevance in studies of the evolution of protoplanetary disksand planet formation theories.
2. Solar Models decade after the critical evaluation of the pp chain and CN cycle rates publishedin the Solar Fusion I paper1 ) a new revision, Solar Fusion II2 ) , has established a newset of recommended values and uncertainties for the pp-chains and CNO-bicycle crosssections. Results in Solar Fusion II account for the large effort of the nuclear physicscommunity, both experimental and theoretical, during the last 10 years. Astrophysicalfactors have been regularly updated in SSM3 , ) during this period. We now adopt asour standard the recommended values in Solar Fusion II; the most relevant changeswith respect to the previous values used in SSM calculations4 ) are given in Table 1.Changes in the central values of key reactions are modest: +2% for S , -2% forS , -5% for S , +6% for S , . The uncertainties are larger, in some cases by upto a factor of 2, than previous values. This has implications for the theoreticaluncertainties in the neutrino fluxes, although uncertainties in the solar compositioncontinue to dominate in most cases. Table 1: New (SFII) and previous values of relevant astrophysical factors.Reaction SFII Previous(keV-b) (keV-b)S . × − (1 ± . . × − (1 ± . . × (1 ± . . × (1 ± . . ± . . ± . . × − (1 ± . . × − (1 ± . , . ± . . ± . ↑ Most of the results presented here are based on two different sets of solar abun-dances. One is that of Grevesse & Sauval (1998), hereafter GS985 ) ; the other, thatfrom Asplund et al. (2009), hereafter AGSS096 ) . For both sets we adopt the mete-oritic scale for all refractory elements; silicon is the anchor point between the pho-tospheric and meteoric scales. The adopted solar abundances are of fundamentalimportance because the surface metal-to-hydrogen abundances ratio is a constraintsolar models have to fulfill. Many properties of the resulting model depend on theadopted solar metallicity, or composition. In particular, the metal-to-hydrogen massfractions ratio in the solar surface is ( Z/X ) ⊙ = 0 . § ) but the dominating effects are: use of a 3D-hydrodynamics model atmosphere, better selection of spectral lines (identificationof blends), detailed treatment of radiative transport in the line-formation modelingincluding non-local thermodynamic equilibrium for some elements.Caffau and collaborators (hereafter CO BOLD7 ) ) have also embarked in a similartask, the determination of solar abundances using 3D state-of- the-art model atmo-spheres. Interestingly, although the underlying structure of the model atmospheresby both Asplund’s and the CO BOLD groups are very similar, derived abundancesfor the CNO elements are not; results are summarized in Table 2 (error bars areincluded for CNO elements). Whereas differences arise from a number reasons, theselection of spectral lines used by each group for the abundance determinations seemsto be the dominant one. The treatment of blends and line broadening, for example,introduces non-negligible differences between the results of different groups.We note the CO BOLD results lay between the GS98 and AGSS09 values, infact, they are consistent within errors with both of them. Unfortunately, CO BOLDabundances have not been obtained at the moment for all elements and have tobe complemented with other sources8 ) ; abundances for these elements are given inparenthesis.It is not among the goals of the present work to make a critical analysis of thegoodness of the different solar abundance determinations present in the literature,neither to discuss the detailed results of solar models for each set of abundances. Wecontent ourselves by adopting GS98 and AGSS09 as two different standards whichprobably represent two extreme cases and on which to base our discussion. In ad-dition, we briefly present helioseismic results for a solar model using the CO BOLDabundances.
Table 2: Solar compositions used in this workElement GS98 AGSS09 CO BOLDC 8 . ± .
06 8.43 ± ± . ± .
06 7.83 ± ± . ± .
06 8.69 ± ± . Results Figure 1: Relative sound speed difference for SSMs with GS98 and AGSS09 compositions. Solidlines: new models incorporating SFII nuclear rates; dashed lines: previous generation of models.See text for more details.
The impact of solar abundances in the helioseismic properties of solar models hasbeen widely discussed in the literature.9 , , , , ) Solar models that use the AGSS09composition are not in agreement with helioseismic inferences of the solar interiorstructure. Discrepancies manifest themselves in a variety of ways: mismatch in thedetermination of the depth of the convective envelope, low solar surface abundance ofhelium, differences in the sound and density profiles, too low mean molecular weightin the solar core. We suggest the interested reader to refer to the vast literature on thesubject, a flavor of which is given in the references above, for details. Problems arepresent for standard solar models; they are even more acute for non-standard modelsthat attempt to include poorly understood dynamic effects13 ) . Most updated resultsfor SSMs using our two reference compositions, GS98 and AGSS09, have been recentlypresented14 ) and show small changes with respect to previous models. In Fig. 1 weshow the relative sound speed difference for SSMs with GS98 and AGSS09. For eachcomposition, the dashed line shows results for previous models, i.e. models using theset of astrophysical factors given in the third column of Table 1, whereas the solidline corresponds to models computed using the Solar Fusion II recommended values.Changes are small but noticeable, particularly towards the center ( R < . ⊙ ), andwithin the range of sensitivity of current helioseismic data15 ) . The responsible for thechanges is the slight increase in S because it produces a decrease in the temperaturef the central regions of the Sun. Since for an ideal gas c ∝ T /µ (here c is the soundspeed, T the temperature, and µ the mean molecular weight), and changes in µ arenegligible, then the model sound speed is reduced accordingly.As can be expected from the abundances listed in Table 2, when the CO BOLDvalues are used, the resulting solar structure lays somewhere in between SSMs that useeither GS98 or AGSS09. To illustrate this, the sound speed profile is given in Fig. 2.The improvement in the sound speed profile model with CO BOLD abundances withrespect to the model with AGSS09 comes about because the location of the base of theconvective envelope in the former is in better agreement with helioseismology. Otherhelioseismic constraints, e.g. surface helium abundance, show a similar behavior, withCO BOLD abundances giving results almost equally distant from GS98 and AGSS09.Values for these quantities are included in Fig. 2.
Figure 2: Relative sound speed difference for SSMs using the different solar abundances listed inTable 2. Values for the depth of the convective envelope in units of the solar radius and the massfraction of the surface helium abundance are also shown. For reference, the helioseismic values are R CZ / R ⊙ = 0 . ± .
001 and Y S = 0 . ± . The new SFII nuclear reaction rates do alter the predicted solar neutrino fluxes,particularly the fluxes associated with the ppIII chain and CN-cycle, mechanismsfor solar hydrogen burning that are relatively unimportant energetically. Changes inthe nuclear rates in SFII with respect to our previous set of preferred values havebeen described in § ) . The most significant changes area 5% decrease in the predicted B flux primarily because of the increase in S andthe increase in the N flux due to the larger S , and central abundance of C. Thencrease in C is a consequence of the lower SFII value for N(p, γ ) O, a reaction thatcompetes with the CN I cycle reaction N(p, α ) C and allows mass to flow out ofthe CN I cycle into CN II.Table 3 also includes the updated solar neutrino fluxes inferred from all availableneutrino data14 ) . The analysis includes the recent more precise Be measurement16 ) ,which is the main change with respect to previous analysis 17 , , ) . In Figure 3 weshow for the relevant neutrino fluxes a comparison between the two SSMs and solarfluxes, normalized to the GS98 SSM values. For the N and O fluxes only upperlimits can be established with current solar neutrino data. Except for the pp flux,experimental values lay in between SSM predictions for the two reference solar compo-sitions. For comparison of the SSM predictions with the fluxes inferred from neutrinodata, we use the χ function defined in 19 ) , with updated errors and correlations. Wefind χ = 3 . χ = 3 .
4, leading in both cases to P agrGS98 , AGSS09 = 90%. Thenew fusion cross sections from SFII and the new Borexino results lead to both modelspredicting solar neutrino fluxes in excellent agreement with inferred ones. From thisanalysis, we conclude that, currently, solar neutrinos can not differentiate betweensolar compositions. In both cases, excellent agreement with data is achieved.
Table 3: Neutrino fluxesFlux SFII-GS98 SFII-AGSS09 ∆ Solarpp 5 . ± . . ± . . +0 . − . )pep 1 . ± . . ± . . +0 . − . )hep 8 . ± .
30) 8 . ± .
30) +1.6% 18(1 +0 . − . ) Be 5 . ± .
07) 4 . ± .
07) -1.7% 4 . +0 . − . ) B 5 . ± .
14) 4 . ± .
14) -5% 5 . ± . N 2 . ± .
14) 2 . ± .
14) +5% ≤ . O 2 . ± .
15) 1 . ± .
15) +5-6% ≤ . F 5 . ± .
17) 3 . ± .
16) +2% ≤ χ /P agr
4. CNO neutrinos: what can be learned?
The Sun is almost entirely powered by proton-proton captures. However, nuclearenergy generated by the CNO bi-cycle dominates for more massive (1 . ⊙ ) or moreevolved stars. Detection of solar CNO neutrinos is the only direct observational proofof CNO as a source of nuclear energy in stars. Current SSMs predict that the CNObi-cycle contribute less than 1% to the solar luminosity; CNO solar neutrinos can testthis result.If, on the other hand, we assume nuclear processes in stars are well understood,a measurement of CNO solar neutrinos can be used to reveal properties of the solarinterior. In particular, N and O neutrinos have energies and fluxes which shouldbe within the capabilities of current and forthcoming liquid scintillator detectors like igure 3: Neutrino fluxes: comparison between experimental results and SSMs. Vertical lines denote1 σ model uncertainties. Solar values are represented by solid horizontal lines; dotted lines are 1 σ uncertainties. All fluxes normalized to GS98 SSM values. Borexino, KamLAND, and SNO+. Recently, a new analysis technique for subtractingthe
Bi background from the Borexino signal has been presented20 ) that could allowdetection of N and O neutrinos in a Borexino-like detector with 1 yr of data. Theprospects for precise measurements of CNO neutrinos are further improved with largerdetectors like SNO+.A direct goal of measuring CNO neutrinos is that they can be used to determineabundance of carbon plus nitrogen in the solar core. As discussed above, current solarneutrino data not only does not discriminate between high and low-metallicity solarcompositions but can not even favor one of them. Let us assume an optimistic scenarioin which both the Φ( N) and Φ( O) fluxes are measured to 10% precision. Moreover,let the central values perfectly align with results from one of the SSMs discussed above.If the GS98 SSMs values are used, i.e. Φ exp ( N) = 2 . × cm − s − and Φ exp ( O) =2 . × cm − s − , then we would get χ = 3 . χ = 13 . N) and Φ( O) at this level of precision would clearly favor solar modelswith a particular C+N content over the other. Clearly, these assumptions make upfor a very favorable case, but give a flavor of what can potentially be achieved.A more targeted approach can be used to determine the C+N abundance in thesolar core directly. One possible way has been laid out where the B solar neutrino fluxis used as a thermometer of the solar core21 ) . Because the temperature dependenceof the nuclear reactions that produce CNO and B neutrinos is very similar, manysources of uncertainty in the solar models affect them in the same way and can belmost completely cancelled out; these are the environmental factors . Using power-law expansions of solar neutrino fluxes22 ) , Φ( N+ O) can be expressed as a functionof Φ( B) as21 ) :Φ( N + O)Φ
SSM ( N + O) = X ( C + N ) X SSM ( C + N ) " Φ( B)Φ
SSM ( B) . × (1)[1 ± . ± . ± . ± . . Uncertainties in this equation are: 3% from the experimental B measurements, 2.6%from remainder of environmental uncertainties, 3.5% from neutrino parameters, and10% from nuclear cross sections. These uncertainty sources are experimental and un-der control, and can be eventually improved (except for the negligible environmentalcomponent). The SSM only acts as a scaling factor (and determining the precisevalue of the power-law exponent, but this changes little for different solar models). Ahypothetical measurement of Φ( N + O) can directly yield a determination of thecentral C+N abundance. The uncertainty from all other sources besides the hypo-thetical measurement amounts, today, to ∼
10% and are dominated by the nuclearphysics part. For reference, the difference in the C+N abundance brought about bythe change from the GS98 to the AGSS09 solar abundances is of the order 35%.There is not direct information about the composition of the solar (or any otherstar) core. Helioseismic information about the solar core is mostly sensitive to themean molecular weight and temperature; information about metallicity is of indirectnature, and usually degenerate with other quantities, such as the radiative opacityof stellar matter. CNO neutrinos would give direct information on the abundance ofmetals, in particular C+N, in the solar central regions. This would be in itself anoutstanding achievement. Together with other constraints on the solar composition,this could potentially be used to constrain, among other processes, the efficiency ofsettling of heavy elements in the Sun.Recently, it has been suggested that there are systematic differences between thesolar surface abundances and those of other stars, otherwise very similar to the Sun,depending on the presence and characteristics of the planetary system in each star23 ) .Tentatively, the cause for these differences has been ascribed to an interplay betweenrefractory elements been preferentially locked in planetesimals and protoplanetarydisk material been accreted to the Sun. If true, this idea would suggest the surfacecomposition of the Sun does not reflect the original composition of the protosolarnebula but rather it is the outcome of a mixture between composition of the primordialnebula and of chemically processed material from the protoplanetary disk. The solarcore, however, keeps memory of the primordial composition.Because CNO neutrinos offer a unique way of determining solar core metal content(at least of C and N), the interesting possibility arises they can be used to constraintthe evolution and interaction between the early Sun and its protoplanetary disk. Afirst step towards assessing the possibility the Sun has suffered such an accretion phaseas been recently discussed14 ) . In that work different accretion histories (varyingaccreted masses and compositions) have been considered and the resulting structureof solar models, both in helioseismic and solar neutrino aspects, analyzed. For reasonsof space, we can not summarize those results here. However, in terms of our presentdiscussion, possibly the most interesting result is that applying Eq. 1 (developed forSSMs) to the non-SSMs that include accretion, the central C+N abundance of themodels can be recovered with very good precision. Using the B, N, and O fluxesfor each of the models with accretion, we can use Eq. 1 to estimate the central contentof C+N in the model, X ν (CN). The relative difference between this estimation andthe actual C+N central abundance of the model, X mod (CN), is shown as a functionof X mod (CN) in Fig. 4. For illustration, results for the GS98 and AGSS09 SSMs areshown with black vertical lines. Neutrino fluxes alone allow the determination of thecentral C+N abundance with 6% accuracy for all models considered which, as can beseen, have quite large variations in the metallicity. This is better than the currentintrinsic uncertainty in the relation, 10%, dominated by uncertainties in astrophysicalfactors ( S , and S ). Results, therefore, are encouraging: scaling relations betweenneutrino fluxes and solar composition derived from SSMs seem to be applicable inquite general cases, even for cases where the central metallicity changes by more thana factor of 2, above of what can be reasonably expected given helioseismic and currentsolar neutrino constraints14 ) . Figure 4: Neutrino fluxes: comparison between experimental results and SSMs. Vertical lines denote1 σ model uncertainties. Solar values are represented by solid horizontal lines; dotted lines are 1 σ uncertainties. All fluxes normalized to GS98 SSM values.
5. Final remarks
Latest changes in the input physics of SSMs have a small effect on helioseismicquantities and do not have an impact on the solar abundance problem. A comparisonof the new analysis of solar neutrino data, including the latest results by Borexino,gainst model predictions show that current neutrino data can be equally describedby SSMs with high and low metallicity compositions. Both experimental B and Be fluxes lay right in between both model predictions for both GS98 and AGSS09compositions. On the other hand, a precise measurement of the N and O fluxesallows to extract the central C+N abundance with a model uncertainty of about10%. To the extent we have been able to test this result, it seems valid regardlessof SSMs being an accurate representation of the solar structure. A measurementof the CNO fluxes, and as a corollary of the central C+N abundance, has a widerange of implications not only for solar but also for stellar physics; here we havebriefly discussed a few of them: direct experimental determination of CNO-cycles assource of nuclear energy in stars, solar abundance problem, mixing processes in theSun and, more tentatively, early phases of solar evolution and interaction with theprotoplanetary disk.
6. Acknowledgements
I am grateful to the organizers of NEUTEL 11 for the invitation to participatein such a stimulating workshop. This work is partially supported by the EuropeanUnion International Reintegration Grant PIRG-GA-2009-247732, the MICINN grantAYA08-1839/ESP, by the ESF EUROCORES Program EuroGENESIS (MICINNgrant EUI2009-04170), by SGR grants of the Generalitat de Catalunya and by theEU-FEDER funds.
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