Our Sun. IV. The Standard Model and Helioseismology: Consequences of Uncertainties in Input Physics and in Observed Solar Parameters

Arnold I. Boothroyd (CITA), and I.-Juliana Sackmann (Caltech)

Astrophysical Journal, 583, 1004-1023   (2003)

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Abstract: Helioseismology provides a powerful tool to explore the deep interior of the Sun: for example, the adiabatic sound speed can be inferred with an accuracy of a few parts in 10,000. This has become a serious challenge to theoretical models of the Sun. Therefore, we have undertaken a self-consistent, systematic study of sources of uncertainties in the standard solar model, which must be understood before the helioseismic observations can be used as constraints on theory. We find that the largest uncertainty in the sound speed in the solar interior, namely, 3 parts in 1000, arises from uncertainties in the observed photospheric abundances of the elements; uncertainties of 1 part in 1000 arise from (1) the 4% uncertainty in the OPAL opacities, (2) the 5% uncertainty in the basic pp nuclear reaction rate, (3) the 15% uncertainty in the diffusion constants for the gravitational settling of helium, and (4) the 50% uncertainties in diffusion constants for the heavier elements. (Other investigators have shown that similar uncertainties arise from uncertainties in the interior equation of state and in rotation-induced turbulent mixing.) The predicted pre-main-sequence solar lithium depletion is a factor of order 20 (an order of magnitude larger than that predicted by earlier models that neglected gravitational settling and used older opacities), and is uncertain by a factor of 2. The predicted neutrino capture rate is uncertain by 30% for the Cl-37 experiment and by 3% for the Ga-71 experiments (not including uncertainties in the capture cross sections), while the B-8 neutrino flux is uncertain by 30%.

Download paper:

• Our Sun IV paper sun4preprint.ps.gz (gzip-compressed PostScript file: 176 kb, expands to 581 kb) -- 38 pages, including figures
• Our Sun IV paper sun4preprint.pdf (PDF file: 415 kb) -- 38 pages, including figures
• Also available at LANL preprint archive: astro-ph/0210128 (preprint CITA-2002-35)
• Color versions of the figures from the paper sun4color.tar.gz (gzip-compressed tar archive: 25 kb, expands to 240 kb) -- 8 color Postscript figures
• Density comparision figures (not included in paper) sun4rho.tar.gz (gzip-compressed tar archive: 22 kb, expands to 210 kb) -- 7 Postscript figures
• Color versions of these density comparison figures sun4rhocolor.tar.gz (gzip-compressed tar archive: 22 kb, expands to 210 kb) -- 7 color Postscript figures

Download data:

• The output describing a typical standard solar model (plain text file: 0.5 Mb) [note that several tables of output are contained in this file, plus some description of the solar model].
• A comparison of this model (plain text file: 11 kb) relative to the helioseismic reference profiles of Basu et al. (2000), ApJ, 529, 1084 [a summary of solar neutrino predictions is also given at the beginning of this file (ignoring neutrino oscillation effects)].
• A time-series of Solar parameters (plain text file: 47 kb) from the pre-main-sequence starting point to the present solar age. [Note that the actual t=0 starting point and earliest evolution down the Hayashi track are not necessarily physical, until the program has converged to a reasonable contracting model on the Hayashi track.]

In the notation of the above Sun IV paper, this solar model is "OPALeos-midT, Lsun=L_best", i.e., the OPAL equation of state was used at logT > 4.0 and, at lower T, a modified MHD equation of state (with added effects of molecules that include CNO as well as H); also, the present solar luminosity was taken to be the best value of Lsun_best = 3.842 * 10^33 erg/sec estimated (with an uncertainty of 0.4%) by Bahcall et al. (2001) ApJ, 555, 990 [rather than the older value of Lsun = 3.854 * 10^33 erg/sec, to which all luinosities in the tables are referenced: add delta logL = 0.0013543 to the logL values in the above files to get values of log(L/Lsun_best)].

NOTE that the above is intended as a fairly accurate standard solar model, but is not completely up to date; the older OPAL equation of state was used, not the more recent 2001 version, and the treatment of diffusion considers only hydrogen, helium, and "heavies" (i.e., all metals are assumed to diffuse similarly to iron). Also, an earlier (relatively large) estimated value of the present solar Z/X = 0.02448 from solar composition observations was used [note that this gives much better agreement with helioseismic measurements than more recent (smaller) estimates of the solar Z/X]. NO rotation effects were considered (therefore the present surface Li7 abundance from the model is much larger than the observed Solar value).