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Problems for the Standard Solar Model Arising from the New Solar Mixture

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Problems for the Standard Solar Model Arising from the New Solar Mixture Mem. S.A.It. Vol. 79, 481 c SAIt 2008 Memorie della Problems for the standard solar model arising from the new solar mixture J.A. Guzik Thermonuclear Applications Group, X-2, MS T-085, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, e-mail: [email protected] Abstract. The solar photospheric abundances have been revised downward after re- analysis of the solar spectrum using improved atomic physics and three-dimensional dy- namical model atmospheres (Asplund et al. 2005). The revised photospheric Z/X is now 0.0165±0.0017 (Z ∼ 0.0122), lower than the previous determination of Grevesse & Sauval (1998) of 0.0230±0.0023 (Z ∼ 0.0171). Adopting these new abundances results in solar models that have sound speed discrepancies of about 1.4% below the convection zone base, as well as a too-shallow convection zone, and too-low convection zone helium abun- dance compared to those inferred from helioseismic data. Here we review attempts to re- store agreement, e.g., enhanced diffusive settling, increased opacities below the convection zone, increased neon abundance, and accretion of lower-Z material early in the sun’s main- sequence lifetime. While these proposed solutions mitigate the effects of the new abun- dances, no single change that restores agreement is physically justified, and a solution invoking combinations of changes seems contrived. The questions remain of whether we should adopt these new abundances, and, if they are confirmed, what are the implications for solar model physics and consequences for modeling the interiors of other stars. Key words. Sun: abundances – Sun: oscillations – Sun: evolution 1. Introduction Compared to the older Grevesse & Savual (1998; GS98) abundances, the AGS05 abun- Until 2004, we thought we knew very well the dance of C is lower by 35%, N by 27.5%, O by interior structure of the sun and how it reached 48%, and Ne by 74%. The abundances of ele- its present state. Evolved solar models with ments from Na to Ca are lower by 12 to 25%, the latest input physics (including diffusive set- and Fe is decreased by 12%. For the GS98 tling) reproduced the sound speed profile deter- abundances, the ratio of the element to hydro- mined from seismic inversions to within 0.4%, gen mass fraction Z/X = 0.023, and Z ∼ 0.018, as well as the seismically-inferred convection while, for the new abundances, Z/X = 0.0165, zone (CZ) depth and CZ helium abundance. and Z∼0.0122. However, new analyses of the sun’s spec- tral lines revise downward the abundances of Models evolved with the new abundance elements heavier than H and He, particularly mixture give worse agreement with helioseis- the abundances of carbon, nitrogen, and oxy- mic constraints; the sound-speed discrepancy gen that are contributing to the opacity just is 1.4% below the CZ base, and the CZ depth below the CZ (Asplund et al. 2005; AGS05). is shallow and CZ helium abundance low com- 482 Guzik: Problems for the standard solar model pared to those derived from seismic inversions. (Dappen¨ et al. 1988), or CEFF (Christensen- We are reluctant to dismiss these new abun- Dalsgaard & Dappen¨ 1992)), nuclear reaction dances because of the many improvements in rates (e.g., Angulo et al. 1999), and diffu- physics and models included, namely 3D dy- sive element settling (e.g., Burgers 1969; Cox, namical atmosphere models, non-local thermo- Guzik, & Kidman 1989; Thoul, Bahcall, & dynamic equilibrium corrections for important Loeb 1994). The solar models produced by the elements, and updated atomic and molecular Los Alamos group shown here use the OPAL data. Line profile shapes now agree nearly per- opacities, Ferguson et al. (2005) or Alexander fectly with observations. Also, it is impressive & Ferguson (private communication, 1995) that abundances derived from several different low-temperature opacities, SIREFF EOS (see atomic and molecular lines for the same ele- Guzik & Swenson 1997), and Burgers’ diffu- ment now are consistent. sion treatment as implemented by Cox, Guzik, Here we review the input and assump- & Kidman (1989; CGK89). tions for standard one-dimensional evolved so- The models are calibrated to the present so- lar models, results of helioseismic tests using lar radius 6.9599×1010 cm (Allen 1973), lumi- the old and new abundances, and ongoing at- nosity 3.846×1033 erg/g (Willson et al. 1986), tempts to resolve these discrepancies. This is mass 1.989×1033 g (Cohen & Taylor 1986), an update to an earlier review by Guzik (2006). age 4.54±0.04 Gyr (Guenther et al. 1992), and adopted photospheric Z/X ratio. For evolution models, the initial helium abundance Y, initial 2. Solar evolution modeling element mass fraction Z, and mixing length to Until recently, solar interior modelers have pressure scale height ratio α are adjusted so had little impetus to progress beyond one- that the final luminosity, radius, and surface dimensional spherical models of the sun, with Z/X match the observational constraints. perhaps the exception of introducing some ad- Helio- and asteroseismology has turned out ditional mixing below the CZ to deplete sur- to be an excellent way to test the physics of face lithium and reduce the small remaining stellar models. See the paper by Christensen- sound-speed discrepancy at the CZ base. For Dalsgaard for an introduction to stellar seis- the Grevesse & Noels (1993; GN93) or GS98 mology. Basu & Antia (2004a), Bahcall & abundances, the simplest ‘spherical sun’ as- Pinsonneault (2004), and Turck-Chieze` et al. sumptions appeared nearly adequate for solar (2004) authored some of the first papers to ex- modeling. These include one-dimensional zon- amine the effects of the new abundances on ing (concentric shells in hydrostatic equilib- solar models. Table 1 compares the calibrated rium), initial homogeneous composition, neg- evolution models of Guzik, Watson, & Cox ligible mass loss or accretion, neglecting rota- (2004, 2005; GWC04 and GWC05) using the tion and magnetic fields, simple surface bound- GN93 and AGS05 mixtures. For the AGSO5 ary conditions, mixing-length theory of con- model, the CZ Y abundance is low (0.2273) vection (e.g., Bohm-Vitense 1958), and no ad- and the CZ base radius 0.7306 R is shal- ditional mixing or structural changes from con- low compared to the seismically inferred CZ vective overshoot, shear from differential rota- Y abundance of 0.248±0.003 and CZ base ra- tion, meridional circulation, waves, or oscilla- dius of 0.713±0.001 R from Basu & Antia tions. (2004a). In addition, the latest physical data applied Figure 1 shows the differences between without modification produced good agree- inferred and calculated sound speed for cali- ment with helioseismology. Examples of these brated evolved models using the old and new data include opacities (e.g., OPAL (Iglesias & abundances, and Fig. 2 shows the observed mi- Rogers 1996) or OP (Seaton & Badnell 2004)) nus calculated frequency differences. The in- supplemented by low-temperature opacities ferred sound speed is from Basu et al. (2000). (e.g., Ferguson et al. 2005); equation of state The discrepancy with the new abundances is (e.g., OPAL (Rogers et al. 1996), MHD much larger than with the old abundances. Guzik: Problems for the standard solar model 483 GN93 Mixture Table 1. Calibrated model properties for GN93 10 GN93Mix and AGS05 mixtures Ferguson low-T Opac Asp05 Mixture 8 Model GN93 AGS05 6 Yo 0:2703 0:2570 Zo 0:0197 0:0135 α 1:770 1:995 4 ZCZ 0:0181 0:0124 YCZ 0:2418 0:2273 2 RCZB (R ) 0:7133 0:7306 0 GN93 Mixture -2 Asp05 Mixture Conv. Zone Base 500 1000 1500 2000 2500 3000 3500 4000 0.01 Calculated Frequency (µHz) Fig. 2. Observed minus calculated versus calcu- lated `=0, 2, 10, & 20 frequencies for models with 0.005 GN93 (triangles, pluses) and AGS05 (open circles) abundances. The triangle-labeled model uses the Ferguson et al. (2005) low-temperature opacities for 0 the GN93 mixture, whereas the model labeled with pluses uses 1995 Alexander & Ferguson opacities. -0.005 0 0.2 0.4 0.6 0.8 1 due to radiative damping of gravity waves; R (R ) tachocline mixing (also used with old abun- sun dances); convective overshoot; combinations Fig. 1. Difference between inferred and calculated of the above. The conclusion has been that it sound speeds for models with the GN93 and AGS05 is difficult to match simultaneously the new abundances. Z/X and helioseismic constraints for CZ depth, sound speed and density profiles, and CZ he- The uncertainties in sound speed inversions lium abundance by applying these changes. are much smaller than the differences between these curves, at most a few widths of the plot- ting line. The observational uncertainties for 4. Opacity increases the modes of Fig. 2 are less than 0.1 µHz Serenelli et al. (2005), Basu & Antia (2004b), Montalban et al. (2004), Bahcall, Serenelli, & 3. Attempts to restore agreement Pinsonneault (2004), Bahcall et al. (2005), and We are aware of the following changes applied Bahcall, Serenelli, & Basu (2005) investigated to solar models to attempt to mitigate the dis- the effects of increasing the opacities below crepancy with seismic constraints for the new the CZ. They find that opacity increases of up abundances: Increased opacities below the CZ to 21% from the OPAL values in a localized (11-21%); neon abundance increase (×∼4); in- region below the CZ reduce the sound-speed creased abundances (within uncertainty limits, discrepancy and improve the CZ depth. The or using alternative determinations); enhanced sound-speed discrepancies are a little smaller diffusive settling rates (×1.5 or more); accre- with a broader constant opacity increase of tion of lower-Z material early in the sun’s life- 11% applied over the 2 to 5 million K region time; structure modification below the CZ base below the CZ.
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