Elsevier

Physics Reports

Volume 457, Issues 5–6, March 2008, Pages 217-283
Physics Reports

Helioseismology and solar abundances

https://doi.org/10.1016/j.physrep.2007.12.002Get rights and content

Abstract

Helioseismology has allowed us to study the structure of the Sun in unprecedented detail. One of the triumphs of the theory of stellar evolution was that helioseismic studies had shown that the structure of solar models is very similar to that of the Sun. However, this agreement has been spoiled by recent revisions of the solar heavy-element abundances. Heavy-element abundances determine the opacity of the stellar material and hence, are an important input to stellar model calculations. The models with the new, low abundances do not satisfy helioseismic constraints. We review here how heavy-element abundances affect solar models, how these models are tested with helioseismology, and the impact of the new abundances on standard solar models. We also discuss the attempts made to improve the agreement of the low-abundance models with the Sun and discuss how helioseismology is being used to determine the solar heavy-element abundances. A review of current literature shows that attempts to improve agreement between solar models with low heavy-element abundances and seismic inference have been unsuccessful so far. The low-metallicity models that have the least disagreement with seismic data require changing all input physics to stellar models beyond their acceptable ranges. Seismic determinations of the solar heavy-element abundances yield results that are consistent with the older, higher values of the solar abundance, and hence, no major changes to the inputs to solar models are required to make higher-metallicity solar models consistent with the helioseismic data.

Introduction

Arthur Eddington began his book “The Internal Constitution of the Stars” saying that “At first sight it would seem that the deep interior of the sun and stars is less accessible to scientific investigation than any other region of the universe. Our telescopes may probe farther and farther into the depths of space; but how can we ever obtain certain knowledge of that which is hidden behind substantial barriers? What appliance can pierce through the outer layers of a star and test the conditions within?” (Eddington, 1926). Eddington went on to say that perhaps we should not aspire to directly “probe” the interiors of the Sun and stars, but instead use our knowledge of basic physics to determine what the structure of a star should be. This is still the predominant approach in studying stars today. However, we now also have the “appliance” that can pierce through the outer layers of the Sun and give us detailed knowledge of what the internal structure of the Sun is. This “appliance” is helioseismology, the study of the interior of the Sun using solar oscillations. While solar neutrinos can probe the solar core, helioseismology provides us a much more detailed and nuanced picture of the entire Sun.

The first definite observations of solar oscillations were made by Leighton et al. (1962), who detected roughly periodic oscillations in Doppler velocity with periods of about 5 min. Evans and Michard (1962) confirmed the initial observations. The early observations were of limited duration, and the oscillations were generally interpreted as phenomena in the solar atmosphere. Later observations that resulted in power spectra as a function of wave-number (e.g., Frazier (1968)) indicated that the oscillations may not be mere surface phenomena. The first major theoretical advance in the field came when Ulrich (1970) and Leibacher and Stein (1971) proposed that the oscillations were standing acoustic waves in the Sun, and predicted that power should be concentrated along ridges in a wave-number v/s frequency diagram. Wolff (1972) and Ando and Osaki (1975) strengthened the hypothesis of standing waves by showing that oscillations in the observed frequency and wave-number range may be linearly unstable and hence, can be excited. Acceptance of this interpretation of the observations as normal modes of solar oscillations was the result of the observations of Deubner (1975), which first showed ridges in the wave-number v/s frequency diagram. Rhodes et al. (1977) reported similar observations. These observations did not, however, resolve the individual modes of solar oscillations, despite that, these data were used to draw initial inferences about solar structure and dynamics. Claverie et al. (1979) using Doppler-velocity observations, integrated over the solar disk were able to resolve the individual modes of oscillations corresponding to the largest horizontal wavelength. They found a series of almost equidistant peaks in the power spectrum just as was expected from theoretical models. However, helioseismology as we know it today did not begin till Duvall and Harvey (1983) determined frequencies of a reasonably large number of solar oscillation modes covering a wide range of horizontal wavelengths. Since then many sets of solar-oscillation frequencies have been published. A lot of early helioseismic analysis was based on frequencies determined by Libbrecht et al. (1990) from observations made at the Big Bear Solar Observatory in the period 1986–1990. Accurate determination of solar oscillations frequencies requires long, uninterrupted observations of the Sun, that are possible only with a network of ground based instruments or from an instrument in space. The Birmingham Solar Oscillation Network (BiSON; Elsworth et al., 1991, Chaplin et al., 2007a) was one of the first such networks. BiSON, however, observes the Sun in integrated light and hence is capable of observing only very large horizontal-wavelength modes. The Global Oscillation Network Group (GONG), a ground based network of telescopes, and the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) have now collected data for more than a decade and have given us an unprecedented opportunity to determine the structure and dynamics of the Sun in great detail. Data from these instruments have also allowed us to probe whether or not the Sun changes on the time-scale of a solar activity cycle.

Helioseismology has proved to be an extremely important tool in studying the Sun. Thanks to helioseismology, we know the most important features of the structure of the Sun extremely well. We know what the sound-speed and density profiles are (see e.g., Christensen-Dalsgaard et al., 1985, Christensen-Dalsgaard et al., 1989, Dziembowski et al. (1990), Däppen et al. (1991), Antia and Basu (1994a), Gough et al. (1996), Kosovichev et al. (1997) and Basu et al., 1997, Basu et al., 2000 etc.), which in turn means that we can determine the radial distribution of pressure. We can also determine the profile of the adiabatic index (e.g., Antia and Basu (1994a), Elliott (1996) and Elliott and Kosovichev (1998)). Inversions of solar-oscillation frequencies have allowed us to determine a number of other fundamental facts about the Sun. We know, for instance, that the position of base of the solar convection zone can be determined precisely (Christensen-Dalsgaard et al., 1991, Basu and Antia, 1997, Basu, 1998). Similarly, we can determine the helium abundance in the solar convection zone (Däppen and Gough, 1986, Christensen-Dalsgaard and Pérez Hernández, 1991, Kosovichev et al., 1992, Antia and Basu, 1994b). In addition to these structural parameters, helioseismology has also revealed what the rotational profile of the Sun is like. It had been known for a long time that the rotation rate at the solar surface depends strongly on latitude, with rotation being fastest at the equator and slowest at the poles. Only with helioseismic data however, we have been able to probe the rotation of the Sun as a function of depth (Duvall et al., 1986, Thompson et al., 1996, Schou et al., 1998b etc.).

The ability of helioseismology to probe the solar interior in such detail has allowed us to use the Sun as a laboratory to test different inputs that are used to construct solar models. For instance, helioseismic inversions have allowed us to study the equation of state of stellar material (Lubow et al., 1980, Ulrich, 1982, Christensen-Dalsgaard and Däppen, 1992, Basu and Christensen-Dalsgaard, 1997, Elliott and Kosovichev, 1998, Basu et al., 1999) and to test opacity calculations (Korzennik and Ulrich, 1989, Basu and Antia, 1997, Tripathy and Christensen-Dalsgaard, 1998). Assuming that opacities, equation of state, and nuclear energy generation rates are known, one can also infer the temperature and hydrogen-abundance profiles of the Sun (Gough and Kosovichev (1988), Shibahashi (1993), Antia and Chitre, 1995, Antia and Chitre, 1998, Shibahashi and Takata (1996) and Kosovichev (1996) etc.). These studies also provide a test for nuclear reaction rates (e.g., Antia and Chitre (1998) and Brun et al. (2002)) and the heavy-element abundances in the convection zone (e.g., Basu and Antia (1997) and Basu (1998)) and the core (e.g., Antia and Chitre (2002)).

One of the major inputs into solar models is the abundance of heavy elements. The heavy-element abundance, Z, affects solar structure by affecting radiative opacities. The abundance of some specific elements, such as oxygen, carbon, and nitrogen can also affect the energy generation rates through the CNO cycle. The effect of Z on opacities changes the boundary between the radiative and convective zones, as well as the structure of radiative region; the effect of Z on energy generation rates can change the structure of the core. The heavy-element abundance of the Sun is believed to be known to a much better accuracy than that of other stars, however, there is still a lot of uncertainty and that results in uncertainties in solar models. It is not only the total Z that affects structure, the relative abundance of different elements has an effect as well. Elements that affect core opacity are, in the order of importance, iron, sulfur, silicon and oxygen. The elements that contribute to opacity in the region near the base of the convection zone and thereby affect the position of the base of the solar convection zone are, again in the order of importance, oxygen, iron and neon. Although, the main effect of heavy-element abundances is through opacity, these abundances also affect the equation of state. In particular, the adiabatic index Γ1 is affected in regions where these elements undergo ionization. This effect is generally small, but in the convection zone where the stratification is adiabatic and hence the structure is determined by equation of state rather than opacity, this effect can be significant.

The importance of the solar heavy-element abundance does not merely lie in being able to model the Sun correctly, it is often used as the standard against which heavy-element abundances of other stars are measured. Thus the predicted structure of those stars too become uncertain if the solar heavy-element abundance is uncertain. Given that for most stars other than the Sun, we usually only know the position on the HR diagram, an error in the solar abundance could lead to errors in the predicted mass and age of the stars. Stellar evolution calculations are used throughout astronomy to classify, date, and interpret the spectra of individual stars and of galaxies, and hence errors in metallicity affect age determinations, and other derived parameters of stars and star clusters. The exact value of the solar heavy-element abundance determines the amount of heavy elements that had been present in the solar neighborhood when the Sun was formed. This, therefore, determines the chemical evolution history of galaxies.

Solar models in the 1990’s were generally constructed with the solar heavy-element mixture of Grevesse and Noels (1993). The ratio of the mass fraction of heavy elements to hydrogen in the Sun was determined to be Z/X=0.0245. Grevesse and Sauval (1998, henceforth GS98) revised the abundances of oxygen, nitrogen, carbon and some other elements, and that resulted in Z/X=0.023. In a series of papers Allende Prieto et al., 2001, Allende Prieto et al., 2002 and Asplund et al., 2004, Asplund et al., 2005a have revised the spectroscopic determinations of the solar photospheric composition. In particular, their results indicate that carbon, nitrogen and oxygen abundances are lower by about 35%–45% than those listed by GS98. The revision of the oxygen abundance leads to a comparable change in the abundances of neon and argon since these abundances are generally measured through the abundances ratio for Ne/O and Ar/O. Additionally, Asplund (2000) also determined a somewhat lower value (by about 10%) for the photospheric abundance of silicon compared with the GS98 value. As a result, all the elements for which abundances are obtained from meteoritic measurements have seen their abundances reduced by a similar amount. These measurements have been summarized by Asplund et al. (2005b, henceforth AGS05). The net result of these changes is that Z/X for the Sun is reduced to 0.0165 (or Z=0.0122), about 28% lower than the previous value of GS98 and almost 40% lower than the old value of Anders and Grevesse (1989). The change in solar abundances implies large changes in solar structure as well as changes in quantities derived using solar and stellar models, and therefore, warrants a detailed discussion of the consequence of the changes, and how one can test the new abundances. In this paper we review the effects of solar abundances on solar models and how the models with lower abundances stand up against helioseismic tests.

The review is written in a pedagogical style with detailed explanations of how the analysis is done. However, the review is organized in such a manner that not all readers need to read all sections unless they want to. We start with a description of how solar models are constructed (Section 2), this section also describes the sources of uncertainties in solar models (Section 2.4). In Section 3 we describe how helioseismology is used to test solar models as well as how helioseismology can be used to determine solar parameters like the convection-zone helium abundance, the depth of the convection zone and how input physics, like the equation of state, can be tested. In Section 4 we describe what helioseismology has taught us about the Sun and inputs to solar model thus far. Thus readers who are more interested in helioseismic results rather than techniques can go directly to this section. In Section 5 we give a short review of how solar abundances are determined and the results obtained so far. The consequences of the new abundances are described in Section 6. This section also includes a brief summary of the changes in the solar neutrino outputs (Section 6.3) and some consequences of the new abundances on models of stars other than the Sun (Section 6.5), though the latter discussion is by no means complete and comprehensive. Readers who are only interested in how the lower solar abundances affect the models would perhaps wish to go straight to this section. The next section, Section 7, is devoted to reviewing the numerous attempts that have been made to reconcile the low-metallicity solar models with the Sun by changing different physical inputs. In Section 8 we describe attempts that have been made to determine solar metallicity using helioseismic techniques. In Section 9 we discuss some possible reasons for the discrepancy between helioseismically determined abundances and the new spectroscopic abundances and we present some final thoughts in Section 10.

Section snippets

Making solar models

The Sun is essentially similar to other stars. The internal structure of the Sun and other stars obey the same principles, and hence we use the theory of stellar structure and evolution to make models of the Sun. However, since we have more observational constraints on the Sun, these constraints have to be met before we can call a model a solar model. Otherwise, the result is simply a model of a star that has the same mass as the Sun. As in the case of other stars, we know the effective

Helioseismology

As mentioned in the previous section one can put constraints on the inputs that go into constructing the model by comparing the structure of standard solar models with that of the Sun. Helioseismology gives us the means to do such a detailed comparison. In order to do so, oscillation frequencies of solar models need to be calculated first. In this section, we describe the basic equations used to describe solar oscillations and indicate how frequencies of solar models can be calculated. We then

Helioseismic results

Early observations of high-degree modes had provided significant constraints on the solar interior, however, detailed results had to wait for the availability of reliable frequencies of low- and intermediate-degree modes, as well as development of inversion techniques. In this section we describe what we have learned about solar structure. We also discuss the results of some tests of different inputs to solar models. The discussion is mainly restricted to results that are relevant for this

Solar abundances

The Sun is unique among stars in that there are multiple ways to determine its heavy-element abundance. Spectroscopy allows us to determine the heavy-element abundance of the solar photosphere, chromosphere and corona, and sometimes in sunspots. Solar abundances can also be determined from solar winds (cf., Bochsler (2007a)) and solar energetic particles (cf., Stone (1989) and Reames, 1994, Reames, 1998). And another important source of solar abundance information are C1 chondrites —

Consequences of the new abundances

Chemical composition enters the equations of stellar structure through input physics like the opacity, equation of state and nuclear energy generation rate. In studies of stellar evolution, it has been found that stars that have lower heavy-element abundances are bluer (higher effective temperature) and more luminous than higher-metallicity stars of the same mass and helium abundance (see e.g., Salaris and Cassisi (2005)). The Sun, however, has a known effective temperature, luminosity and age,

Attempts to reconcile low-Z solar models with the Sun

The large discrepancies between models constructed with the AGS05 abundances and the Sun have resulted in numerous attempts to change the inputs to solar models in order to reconcile the models with the helioseismic data. The proposals generally fall into four categories or combinations thereof. These are: (1) increasing input opacities, (2) increasing the heavy-element abundance of the radiative interior through increased diffusion, or alternatively, decreasing the heavy-element abundance of

Seismic estimates of solar abundances

Even before the current controversy over solar abundances started, there had been attempts to infer the heavy-element abundance of the Sun using helioseismic data, as was done for determining the abundance of helium, as an independent test of solar abundances. The efforts gained urgency once it was clear that solar models with the AGS05 abundances did not match helioseismic constraints, and that none of the changes made to bring the models back in concordance with helioseismology worked.

Like

Possible causes for the mismatch between seismic and spectroscopic abundances

Since attempts to modify low-metallicity solar models to bring them in agreement with seismic inferences have failed, and furthermore since seismic determinations of heavy-element abundances consistently yield higher values in agreement with GS98, it is worthwhile to examine the spectroscopic determinations that lowered the solar abundances in some detail. The problems could lie with the solar-atmosphere model used by AGS05, or perhaps with the abundance of any one of the elements, or perhaps

Concluding thoughts

The discussions presented in the previous sections clearly indicate that there is a large discrepancy between the heavy-element abundances needed to make solar models consistent with helioseismic data and the lowered solar heavy-element abundances as compiled by AGS05. The disagreement between the models and the Sun, as determined from helioseismology, covers almost the whole of the solar interior. As discussed in Section 6, the most obvious discrepancies between these models and the Sun are

Acknowledgments

The authors thank the referee for the comments on the first version of this review. They would like to thank the OPAL project for making it possible to calculate the opacities for different relative abundances. The authors would also like to thank Profs. Pierre Demarque and Sabatino Sofia for their comments on this article. Most of the results quoted in this work and the figures shown were obtained using data from the GONG and MDI projects. MDI is an instrument on board the Solar and

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