CN Neutrinos and the Sun s Primordial Core Metalicity

CN Neutrinos and the Sun s Primordial Core Metalicity motivations: new photospheric abundances, helioseismology discrepancies, SNO+, and LUNA solar neutrinos as a high-precision astrophysics tool: constraining the nuclear, solar environmental, and flavor uncertainties metal differentiation: planetary formation and the convective zone Carolina International Symposium on Neutrino Physics Wick Haxton, INT & Dept Physics, University of Washington May 15-17, 2008

The Standard Solar Model Origin of solar neutrino physics: desire to test a rather simple model of low-mass, main-sequence stellar evolution local hydrostatic equilibrium: gas pressure gradient counteracting gravitational force hydrogen burning, dominated by the pp chain energy transport by radiation (interior) and convection (envelope) boundary conditions: today s mass, radius, luminosity; initial assumptions about H:He:Z Encountered neutrino anomalies that have led to the discovery of physics beyond the minimal standard model: now entering a period of precise astrophysics and laboratory measurements Re-opens the possibility of combining s and various surface observations (photospheric abundances, helioseismology) to make high-precision tests of solar physics

Perhaps the least convincing of the SSM assumptions: a homogeneous ZAMS sun as the sun formed from collapse of the primordial gas cloud, thought to have gone through a fully convective Hayashi phase in the subsequent Henyey phase to the ZAMS, sun develops a growing radiative core: core and surface no longer mix ZAMS conventionally defined as the time when thermonuclear energy generation compensates emissions classical description at some variance with modern simulations of cloud collapse, where the convective envelope develops earlier, spans the outer third of the proto-sun by radius, and resembles that of the modern sun Wuchterl and Klessen 2001 If the Z of late-stage accreted gas differed from that of the primordial gas cloud, core and convective zone could be chemically different Low-Z core models an example -- motivated by puzzles

CN Solar Neutrinos Bethe: a sharply T-dependent process for H burning needed to sustain massive MS stars pp chain vs CN cycle: primary vs. secondary: catalysts for CN cycle are pre-existing metals

At low T, controlling reactions are 14 N(p, ) and 12 C(p, ) ZAMS core temperature T7 1.34, at which ( 12 C) 2 10 7 y initial out-of-equilibrium burning of C is rapid Energy release produces thermal gradients sufficient to make core convectively unstable for 10 8 year ( 12 C) 4.6 10 9 y at T7 1.0 or R 0.18 Rsolar: most of the core s primordial C has been burned to 14 N 14 N(p, ) determines CN cycle equilibrium: ( 14 N) 4.6 10 9 y at T7 1.33: only the central 7% of the sun s mass has reached equilibrium 14 N(p, ) thus us acts as a bottleneck in low-mass MS stars

BSP08(GS) SSM (Pena-Garay and Serenelli) predicts a modest CNcycle contribution to solar energy generation of 0.8% but in principle measurable neutrino fluxes 13 N(β + ) 13 C E ν < 1.199 MeV φ =(2.93 +0.91 0.82) 10 8 /cm 2 s 15 O(β + ) 15 N E ν < 1.732 MeV φ =(2.20 +0.73 0.63) 10 8 /cm 2 s. (note the contribution of primordial 12 C burning to 13 N flux)

Reasons one might want to measure the CN neutrinos To determine directly solar core metalicity... To test the SSM postulate of a homogeneous ZAMS sun -- a key assumption important to helioseismology, the 8 B flux, and other predictions that depend on core metalicity To probe directly the reactions that we believe sustain massive MS stars -- including the earliest metal-free massive stars To help resolve a discrepancy that has arisen from new photospheric abundances determinations To provide information on metal differentiation in the last stage of the pre-solar disk, a key epoch in solar-system formation

Photospheric Abundances SSM required input: an estimate of core metalicity at t=0 Taken from meteoritic abundances or from photospheric absorption lines: the latter are the only practical way to determine the abundances of volatile heavy elements, such as C, N, O, Ne, Ar -- SSM then assumes a homogeneous zero-age sun characterized by these abundances These metals influence solar dynamics: free-bound transitions important to opacity, influencing local sound speed -- the volatile elements are important to the temperature region just below the convective zone The once excellent agreement between SSM and helioseismology due in part to this input (Grevesse & Sauval 1998)

The classic analyses modeled the photosphere in 1D, despite stratification, velocities, inhomogenieties But new 3D, parameter-free methods have been introduced, significantly improving consistency of line analyses Dynamic and 3D due to convection Mats Carlsson (Oslo) 007 Sun

1D vs Sun Averaged line profiles (from Asplund 2007) 3D vs Sun Spread in abundances from different C, O lines sources reduced from ~ 40% to 10% But abundances significantly reduced Z: 0.0169 0.0122 Makes sun more consistent with similar stars in local neighborhood Lowers 8 B flux by 20%: 5.95 4.72 10 6 cm 2 s vs. 391-day SNO salt phase result of (4.94 ± 0.21(stat) ± 0.36 ) 10 6 cm 2 s

But the resulting helioseismology: new (AGS 2005) abundances convective zone old (GS 1998) abundances Bahcall, Basu, Pinsonneault, Serenelli 2004

Discrepancy largest for T 2-5 10 6 K: C, N, O, Ne, and Ar are partially ionized, with O and Ne particularly important to the opacity Troubling because the previous concordance between the SSM and helioseismology helped the credibility of the SSM -- now there exists a significant discrepancy

The Sun as a Calibrated Laboratory Will argue that it is possible in principle to measure the sun s core metallicity via CN neutrinos to an interesting precision This result depends on several new developments the accuracy with which Super-Kamiokande has effectively calibrated the core temperature: the CN and 8 B fluxes are both critically dependent on Tc the tight constraints SNO and KamLAND have placed on oscillation parameters much improved measurements of key nuclear cross sections, particularly 14 N(p, ) but also S34 ideas for high-counting-rate experiments sensitive to CN s

LUNA and TUNL measurements of 14 N(p, ) Formicola (LUNA) et al. (2004); Imbriani et al. (2005); Bemmerer et al (2006); Lemut et al. (2006); Trautvetter et al. (2008); Runkle (TUNL) et al. (2005) S-factor mapped down to 70 kev adopted Imbriani S(0) = 1.61 ± 0.08 kev b, pending JINA r-matrix re-analysis of full data set Lemut et al. (LUNA)

7 Be, pep and CNO Recoil Electron Spectrum events/kton/yr/bin 1000 800 600 (from Mark Chen) 400 200 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 T e [MeV] Sat Mar 19 18:33:32 18:34:40 18:35:52 2005 SNO+: 1 kt deep scintillator experiment that will make outstanding use of SNOLab s depth: factor-of-70 reduction in long-lived cosmogenic 11 C, to 0.1 c/d/100 tons 10% CNO flux measurement predicted, based on BS05(OP) fluxes

Analysis For 19 SSM parameters j with significant uncertainties, consider α(i, j) ln [φ i/φ i (0)] ln [β j /β j (0)] N φ i = φ i (0) j=1 [ βj β j (0) ] α(i,j) Divide this dependence into environmental, nuclear, CN terms φ i = φ SSM i j {Solar} [ ] α(i,j) βj [ ] α(i,j) βj [ ] α(i,j) βj [ ] α(i,j) βj β j (0) β j (0) β j (0) β j (0) j {Metals C,N} j {Nuclear} j {C,N} bracketed environmental uncertainties: luminosity, radiative opacity, solar age, He and metal diffusion, fractional abundances of O, Ne, Mg, Si, S, Ar, and Fe -- not controlled nuclear uncertainties and in-transit neutrino physics uncertainties are controllable: subject to laboratory constraints

Monte Carlo SSM studies of 8 B, 13 N, 15 O correlations

Environmental β j Nuclear β j Source L Opacity Age Diffusion S 11 S 33 S 34 S 17 S e7 S 114 φ( 8 B) 7.16 2.70 1.38 0.28-2.73-0.43 0.85 1.0-1.0-0.020 φ( 13 N) 4.40 1.43 0.86 0.34-2.09 0.025-0.053 0.0 0.0 0.71 φ( 13 N)/φ( 8 B) 0.599 0.11-0.19 0.03 0.17-0.45 0.28-0.56-0.60 0.60 0.72 φ( 15 O) 6.00 2.06 1.34 0.39-2.95 0.018-0.041 0.0 0.0 1.00 φ( 15 O)/φ( 8 B) 0.828 0.07-0.18 0.20 0.16-0.69 0.37-0.74-0.83 0.83 1.02 Resulting proportionality removes 90% of the environmental uncertainty Exception: diffusion -- in addition to Tc, affects contemporary CN abundance Many studies indicate these proportionalities will remain valid for parameter variations far outside the SSM uncertainties

C, N β j Environment Abundance β j Source C N O Ne Mg Si S Ar Fe φ( 8 B) 0.027 0.001 0.107 0.071 0.112 0.210 0.145 0.017 0.520 φ( 13 N) 0.874 0.142 0.044 0.030 0.054 0.110 0.080 0.010 0.268 φ( 13 N)/φ( 8 B) 0.599 0.858 0.141-0.020-0.013-0.013-0.016-0.007 0.000-0.043 φ( 15 O) 0.827 0.200 0.071 0.047 0.080 0.158 0.113 0.013 0.393 φ( 15 O)/φ( 8 B) 0.828 0.805 0.199-0.018-0.012-0.013-0.016-0.007-0.001-0.038 dependence on heavy metals influencing Tc greatly reduced Note that the residual dependence on primordial C, N abundances, under a uniform adjustment in metals X/XSSM 1 +, behaves as (1 + ) 0.999 or (1 + ) 1.004 1 + the expected residual linearity

Fold the residual variations with SSM errors to get the in situ flux relation φ( 15 O) φ SSM ( 15 O) = [ ] φ SNO φ( 8 B) ( 8 0.828 B) φ SSM ( 8 B) [1 ± 2.6%(resid. environ.) ± 7.1%(nuclear)] ( X( 12 C) ) 0.805 ( X( 14 N) X( 12 C) SSM X( 14 N) SSM ) 0.199 1.5% of this uncertainty is due to estimated diffusion errors, 1.1% to the remaining 10 solar environmental parameters the nuclear error includes propagated pp chain/cn cycle uncertainties, has dropped significantly due to recent S114 and S34 work, and remains dominated by the 5% error on S114 - a lab astro quantity quantities that can be determined experimentally from terrestrial measurements of fluxes and weak mixing parameters: (SK at 3%)

Helpful to build flux relationship using the rates for ES experiments SNO+/Borexino (anticipated) and SK (1496-day data set) 4.935 ± 0.05(stat) +0.17 0.16(sys) 10 38 electron 1 s 1 with, e.g., φ( 8 B) φ SSM ( 8 B) = φ( 8 B) σ SK ( 8 B,δm 2 12,θ 12 ) φ SSM ( 8 B) σ SK ( 8 B,δm 2 12,θ 12 ) Rexp( SK 8 B) Rcal SK(8 B,δm 2 12,θ 12 ) (this anticipates a future combined analysis in which many correlated systematic uncertainties spectral shape, ES cross section,... now included in SK errors could be treated in the flux ratio) σ SK ( 8 B,δm 2 12,θ 12 ) = + P νμ (E ν,δm 2 12, sin 2 2θ 12 ) de ν φ 8 B norm (E ν ) T max (E ν ) T =0 [ P νe (E ν,δm 2 12, sin 2 2θ 12 ) T max (E ν ) T =0 dt σ es ν e (T ) ] 20.0 MeV dt σν es μ (T ) dɛ a f trigger (ɛ a )ρ(ɛ a,ɛ t = T + m e ) 5.0 MeV SuperK s apparent-energy interval, resolution, and triggering

The low-e analysis similar: a window of 0.8-1.3 MeV, based on the 8% Borexino resolution at 1 MeV, an Emax of 0.67 MeV from the 7 Be line neutrinos, and measured backgrounds Consequently the in situ flux relation becomes an experimental one R B/S exp (CN) [ R SK exp( 8 B) ] 0.828 = (1.120 ± 0.003) R B/S cal ( 15 O,δm 2 12,θ 12 )) Rcal SK(8 B,δm 2 12,θ 12 ) ( ) X( 12 0.805 ( C) X( 14 N) [1 ± 2.6%(resid. envir.) ± 7.6%(nuclear)] X( 12 C) SSM X( 14 N) SSM correction for the lower-e 13 N contribution in observation window ) 0.199 The last remaining step is the treatment of the anticorrelated flavor physics, which is constrained by SNO and KamLAND - again basically a lab uncertainty that will diminish. Use KamLAND combined analysis

High-E 8 B s are in the adiabatic MSW region where limiting behavior P νe (E ν ) 1 2 (1 cos 2θ 12) P increases as 12 increases while CN neutrinos are in the near-vacuum region with limiting behavior P νe (E ν ) 1 1 2 sin 2θ 12 P decreases as 12 increases We fold true Ps with detector responses, ranging over the KamLAND combined analysis ellipse The bottom line is a primordial abundances future experiment relation: Rexp B/S (CN) R B/S cal ( 15 O,δm 2 12,θ 12 )) = ( X( 12 C) X( 12 C) SSM ) 0.805 ( X( 14 N) X( 14 N) SSM ) 0.199 (1.120 ± 0.003)[1 ± 3.0%(SK exp) ± 2.6%(resid. environ.) ± 7.1%(nuclear)]

The numbers work out nicely as these errors are uncorrelated, the overall uncertainty in this theoretical relation is 9.6% this is comparable to anticipated experimental uncertainties that might result from a deep, kiloton-scale CN effort like SNO+ the limiting error is currently S114, a lab quantity now under revision: one gains rapidly as the current 5% 3.5% the second most limiting error is also a laboratory one, uncertainties in 12: this will continue to improve residual environmental uncertainties are below the level of SK uncertainties - the quality of the relationship depends entirely on the use of existing flux measurements to limit relative variations in the 8 B and CN fluxes recent changes (which modelers have used as a measure of the uncertainty) in the abundances of C and N (GS vs. AGS) are 30% and 32%, respectively future experiments may say something very new about primordial C, N

Why This Might be Important: Solar System Metal Differentiation Suppose we take the photospheric and helioseismic results at face value: the convective zone has a lower metal content than the radiative zone, where 97% of the mass resides Galileo, Cassini, and subsequent planetary modeling show that significant metal differentiation occurred quite late in the formation of the solar system, associated with formation of the gaseous giants initial collapse of the primordial gas cloud to form the proto-sun development of the nebular disk metal-rich grains and ice collect at the disk midplane formation of the 10 M rock cores of the giant planet, which scour out this enriched material rapid (1-10 My) formation of the gaseous envelopes, after the bulk of the nebular gas has already dissipated (Bodenheimer and Lin 2002) timing: the sun already has developed its radiative core The observed atmospheric enrichments indicate a total metal excess of (40-90) M, depending on planetary modeling uncertainties (Guillot 2005)

The indicated metal deficit in the convective zone is 50 M The planetary metal differentiation requires processing of a minimum of 2500 M of primordial gas: this corresponds to 35% of the mass of the convective zone Consistent with planetary dynamics: based on planetesimal deposition rates and the tidal radius of a fully-formed Jupiter ( 0.36 AU), Jupiter would have perturbed the orbits of 2500 M of gas (Podolak et al. 1993) Numerical calculations show that time scale for the sun to accrete gas, perturbed by a Jupiter-mass body orbiting at 5 AU, is short, ~ 5 10 5 y (Strom et al. 1993) Seems a provocative possibility: a single mechanism perturbs and segregates the last few percent of nebular gas, enriching the planets but depleting the convective zone

This is an argument for the continued importance of solar s as a probe of stellar physics -- and for continued efforts in the lab to make that probe increasingly precise Was the ZAMS sun homogeneous? If not, could a metal-depleted convective zone be a consequence of the metal differentiation accompanying planetary formation? And what about helioseismology? This picture suggests a fingerprint of the dilution might be found in the upper radiative zone -- a transition region between GS and AGS abundances, precisely where volatile elements like O dominate the opacity

Acknowledgements Talk based on arxiv: 0805.2013 WH + Aldo Serenelli John Bahcall Fellow, IAS All of our careers based of the friendship and creative physics of neutrino colleagues, three of whom we celebrate here Ettore Peter Frank