The Dark Side of the Sun A Plea for a Next-Generation Opacity Calculation
aa r X i v : . [ a s t r o - ph . S R ] A p r The Dark Side of the Sun
A Plea for a Next-Generation Opacity Calculation
Regner Trampedach , , Space Science Institute, 4750 Walnut St., Boulder, CO 80301, USA; [email protected] Stellar Astrophysics Centre, Dept. of Physics and Astronomy, Ny Munkegade120, Aarhus University, DK–8000 Aarhus C, Denmark Laboratory for Atmospheric and Space Physics, University of ColoradoBoulder, 3665 Discovery Dr., Boulder, CO 80303, USA
Abstract.
Is the Sun likely to have a more opaque interior than previously thought?The solar oxygen (or abundance) problem can be solved with higher interior opacities,reconciling abundance analyses based on 3D convective atmospheres with the helio-seismic structure of the solar interior. This has been known for more than a decade, butlast year we learned that the absorption by just iron may contribute 7% more to the solaropacity at the bottom of the convection zone than predicted by any opacity calculationso far, and by OP05 in particular. I find that artificial changes to the absorption (cali-brated against the iron experiment) by other elements in a solar mixture give an opacityincrease of a shape and magnitude that can restore agreement between modern abun-dance analysis and helioseismology. This suggests that improved opacity calculationswill solve the solar oxygen problem.
1. Our Problem with the Sun and Attempts to Solve it
The solar abundance determinations by Asplund et al. (2005)—updated by Asplundet al. (AGSS09, 2009) and refined by Scott et al. (2015a,b) and Grevesse et al. (2015)—have disrupted the previous convergence of solar models towards observations (Bahcallet al. 2005; Delahaye & Pinsonneault 2006; Guzik & Mussack 2010). The main partof the previous convergence was between solar structure and evolution models andhelioseismology (e.g., Christensen-Dalsgaard et al. 1996; Schou et al. 1998; Brun et al.1999; Boothroyd & Sackmann 2003; Di Mauro 2003).Solar atmosphere modeling, on the other hand, has had persistent problems inthat same time period, mostly hampered by being one dimensional (1D). The solaratmosphere is convective, and convection is inherently a three dimensional (3D) phe-nomenon (Trampedach 2010) although classically treated in the mixing-length formu-lation (MLT) by Böhm-Vitense (1958). This formulation adds at least three free param-eters to the problem with the primary one, α , typically being adjusted to reproduce thewings of the Balmer lines (Fuhrmann et al. 1993). This gives values of α ≈ . α ∼ . i blendwith the forbidden [O i ] line at 630 nm (Allende Prieto et al. 2001). With the symmetriclines of 1D atmospheres, this blend was underappreciated as it could not be quantified.Agreement on the detailed line shapes also means that blends can be left out, and abun-dances can be determined from fits to the actual line profiles instead of the integratedquantity of equivalent widths that is blind to blends. Undetected blends, of course, re-sult in overestimated abundances. Grevesse et al. (2013) provide a scathing critique oftheir own classic solar abundances based on 1D atmosphere models.
2. An Opacity Solution?
Bahcall et al. (2004), Basu & Antia (2004), and Montalbán et al. (2004) showed thata ∼
20% Gaussian opacity increase in the solar interior, peaking at the bottom of theconvection zone, would restore the previous helioseismic agreement based on clas-sic abundances. Christensen-Dalsgaard & Houdek (2010) found the actual opacity-increase profile needed to restore helioseismic agreement with a AGSS09-mix solarmodel. Whether such opacity increases were at all realistic was not known at the time.Measurements of the iron opacity under conditions similar to those at the bottomof the solar convection zone (Bailey et al. 2007; Bailey et al. 2015) gave values signif-icantly higher than predicted by any theoretical calculation to date. By including theirmeasured Fe absorption in a Rosseland average for a solar mixture with opacities byBadnell et al. (OP05, 2005), a 7% increase over the theoretical tables is obtained.
3. What if Other Elements Are also More Opaque?
We carried out an enhancement experiment on the absorption coe ffi cients of the OP05opacities: it was calibrated by broadening the OP05 absorption to qualitatively matchthe Fe absorption measured by Bailey et al. (2015) and by multiplying the cross-sectionsby a constant factor to give the reported 7% increase of the Rosseland mean. The cru-cial step is the extrapolation to the other elements and ions. Using the number of boundelectrons in the radiating ion as a measure of our ignorance of atomic physics, the en-hancement factor is made proportional to it (but excluding changes to the well-knownheDarkSide ofthe Sun 3 Figure 1. Opacity increase required to restore agreement with helioseismology(dashed and dot-dashed curves) along the stratification of a solar model. Blue dottedcurve shows the opacity enhancement when only the absorption by iron is broadenedto match the experiment (Bailey et al. 2015). Solid blue curve when iron absorptionis also increased by 15% calibrated to match the experiment, indicated with the ver-tical dashed line. The magenta curves show the same but extended to all elementswith the increase being proportional to the number of closed subshells. hydrogen- and helium-like ions). For a solar stratification the thusly enhanced Rosse-land mean is larger than the normal OP05 opacity by about 12%, peaking just below theconvection zone as shown in Fig. 1. Both shape and amplitude are very similar to thoseneeded to reconcile models with helioseismology (Christensen-Dalsgaard & Houdek2010, dot-dashed line in Fig. 1). This result is not sensitive to how the bound electronsare counted, whether individually or in closed shells or subshells (as shown in Fig. 1),and simply reflects the abundance of bound electrons in a solar model. That the opacityincrease required to solve the solar problem has this shape strengthens our suspicionthat the opacity is indeed the culprit. If the required opacity change peaked instead inthe core, it would be more natural to suspect problems with the nuclear reaction rates,their screening, or extra mixing processes.Interestingly, the single dominant contributor to the opacity enhancement outlinedabove is iron, followed by nine other elements each peaking with about 1% additionalopacity spread across the solar radiative zone. This means the result is not contingenton every element behaving according to the assumptions of this numerical experiment.The underlying assumption of this numerical experiment is obviously the veracity ofthe Bailey et al. (2015) experiment. We are eagerly awaiting confirmation from otherexperiments (e.g., at NIF, Heeter et al. 2017) and for other elements while appreciatingthe daunting tasks such experiments represent.New calculations of Rosseland mean opacities have been published by the OPASteam (Le Pennec et al. 2015) and the next-generation Los Alamos opacity team (Colganet al. 2016) resulting in better agreement with solar sound-speed profiles, but only by13–25% of that needed to reconcile models with seismology. Trampedach
Acknowledgments.
RT acknowledges funding from NASA grant NNX15AB24G.Funding for the Stellar Astrophysics Centre is provided by The Danish National Re-search Foundation (Grant DNRF106).
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