Sensitivity of low degree oscillations to the change in solar abundances
aa r X i v : . [ a s t r o - ph ] A p r Astronomy&Astrophysicsmanuscript no. article.zaatri07 c (cid:13)
ESO 2018October 28, 2018
Sensitivity of low degree oscillations to the change in solarabundances
A. Zaatri , , J. Provost , G. Berthomieu , P. Morel , and T. Corbard D´epartement Cassiop´ee, UMR CNRS 6202, Observatoire de la Cˆote d’Azur, BP 4229, 06304 Nice CEDEX 4, France Centre de Recherche en Astronomie, Astrophysique et G´eophysique, BP 63, Route de l’Observatoire, Bouzar´eah, 16340, Alger,Alg´erieReceived date / Accepted date
ABSTRACT
Context.
The most recent determination of the solar chemical composition, using a time-dependent, 3D hydrodynamical model of thesolar atmosphere, exhibits a significant decrease of C, N, O abundances compared to their previous values. Solar models that use thesenew abundances are not consistent with helioseismological determinations of the sound speed profile, the surface helium abundanceand the convection zone depth.
Aims.
We investigate the e ff ect of changes of solar abundances on low degree p-mode and g-mode characteristics which are strongconstraints of the solar core. We consider particularly the increase of neon abundance in the new solar mixture in order to reduce thediscrepancy between models using new abundances and helioseismology. Methods.
The observational determinations of solar frequencies from the GOLF instrument are used to test solar models computedwith di ff erent chemical compositions. We consider in particular the normalized small frequency spacings in the low degree p-modefrequency range. Results.
Low-degree small frequency spacings are very sensitive to changes in the heavy-element abundances, notably neon. Weshow that by considering all the seismic constraints, including the small frequency spacings, a rather large increase of neon abun-dance by about (0 . ± . ff ects g-mode frequencies, with relative frequency di ff erences between the old and the newmodels higher than 1.5%. Key words. sun:helioseismology, sun:abundances, sun:interior
1. Introduction
The precise measure of characteristics of the observed p-modeshas been used to probe most of the layers inside the sun. Forexample, seismic sound speed and density determinations canbe used to constrain the interior of the sun anywhere except atthe surface and in the core. Helioseismology also constrains tothe surface helium abundance and the depth of the convectionzone. However, the small number of p-modes (only low degreep-modes) able to reach the solar core is not su ffi cient to probethis region using inversion techniques. The solar core is crossedby thousands of g-modes, able to bring much information fromthis region. The g-modes have not yet been unambiguously iden-tified because of their evanescent nature through the convectionzone and low amplitude at the surface but ongoing work is de-voted to try to extract them for the existing long time series ofSOHO data and to propose new observational and strategies todetect them.New determinations of solar heavy element abundances us-ing a 3D, NLTE analysis of the solar spectrum has been pro-vided by Asplund et al. (2005; AGS). Previous 1D, LTE determi-nations are available (Grevesse and Noels 1993- GN; Grevesseand Sauval 1998 - GS). Relative to GN abundances, the newAGS abundances are, among others, lower in C , N , O , Ne ele-ments by respectively 0 .
16 dex, 0 .
19 dex, 0 .
21 dex and 0 .
24 dex.Consequently, the new chemical determination gives a smallermetallicity ZX compared to the older ones. The new determi- nation of solar elements is more accurate than the older one(Grevesse et al. 2005), but it has been shown that it leads to solarmodels that disagree with the helioseismological determinationsof solar internal structure parameters (e.g. Turck-Chi`eze et al.2004; Bahcall et al. 2005; Guzik et al. 2005).In this paper we study the sensitivity of the solar core proper-ties, through low degree p-modes and g-modes, to the change ofsolar mixture. The chemical solar abundances that we used arethose of Grevesse & Noels (1993), Grevesse & Sauval (1998)and Asplund et al. (2005). The other mixtures that we chose in-clude the solar abundances of Asplund et al (2005) changingmainly the neon abundance. This set of solar mixtures allowsus to study the influence of the neon abundance on small fre-quency separations and to test the possibility of improving theaccordance between models that use new abundances and helio-seismic observations (Antia et Basu 2005; Bahcall et al. 2005).This is indeed possible because neon photospheric abundancecannot be determined directly due to the lack of suitable absorp-tion lines in the solar spectrum induced by the noble gas natureof neon. The estimations of the solar Ne abundance are still con-troversial (Drake & Tesla 2005, Young 2005, Schmelz 2005).Here we analyze how the models fit both the global constraints(seismic sound speed, surface helium abundance and convectionzone depth) and the small frequency separations in the low de-gree p-mode frequency range. We use the determination of thesemode frequencies obtained from the GOLF experiment by Gellyet al. (2002) and more recently by Lazrek et al. (2007) who have Zaatri et al.: Sensitivity of low degree oscillations A ( Ne ) ( Z / X ) S Y S r ZC T c P M-GN
M-GS
M-GS ∗ M-AGS M3 M4 M5 M6 M7 M8 Table 1.
Global characteristics of the computed solar models. A ( Ne ) is the neon abundance in dex, ( Z / X ) S is the surface metal-licity, T c = T c ∗ − , T c the central temperature in Kelvin. P is the characteristic period (in minutes) of low degree gravitymodes. The di ff erent models are computed with the followingsolar abundances: M-GN: GN; M-GS: GS; M-GS ∗ : GS with sul-fur abundance of GN; M-AGS: AGS; M3, M4, M5, M6, M7:AGS with the indicated change of the neon abundance; M8: inaddition to the change of neon in AGS, C, N, O, Mg and Sihave been increased until the maximum of their error bars (seeAsplund et al. 2005) and Ar by 0.40 dex.corrected these frequencies for the solar cycle e ff ect. The sen-sitivity of gravity modes to the new abundances have also beenestimated. Preliminary results of this work have been presentedby Zaatri et al. (2006).
2. Solar models with new abundances
We have computed solar models with di ff erent sets of heavy el-ement abundances by using the stellar evolution code CESAM(Morel 1997). We use OPAL opacity tables , calculated for eachmixture, and Alexander and Ferguson opacity tables at low tem-peratures ( T < K ). Nuclear reaction rates are from NACREcompilation ( Angulo et al. 1999) and equation of state tablesare those of OPAL (Iglesias & Rogers 1991). We assume theconvection treatment given by Canuto and Mazitelli (1991). Allthe models include the microscopic di ff usion of the chemicalelements according to the Michaud & Pro ffi tt (1991) descrip-tion. Models are calibrated for a solar age t = R ⊙ = . × cm, L ⊙ = . × erg / s, Christensen-Dalsgaard et al. (1996)) and the solar surface metallicity Z / X of the various mixtures.Table 1 summarizes the characteristics of the solar modelsat both the surface and the core and their chemical compositionis given. The surface helium abundance and the location ofthe base of the convection zone Y s and r ZC are to be com-pared to their seismic determinations Y s = . ± . r ZC = (0 . ± . R ⊙ by Basu & Antia (2004). Theseauthors have demonstrated that these seismic determinations arenot sensitive to the change in solar abundances.Figure 1 shows relative di ff erences between seismic soundspeed and the one determined from our di ff erent solar models.Figure 2 shows a comparison between Y s and r ZC values of thecomputed models and their seismic determinations. The worseconcordance between the model using Asplund et al. abundancesand the seismic model is shown by a relative di ff erence in sound http: // / Research / OPAL / Fig. 1.
Relative sound speed di ff erences between the Sunand the models: M-GN (heavy full), M-GS (full), M-AGS(heavy dashed), M3 (dotted), M4 (short-dashed), M5 (dashed-dotted),M6 (long-dashed),M7 (dashed-3*dotted), M8 (heavydashed-dotted). Fig. 2.
Characteristics of the solar envelope, surface heliumabundance ( Y S ) and the location of the base of the convectionzone ( r ZC ), for the models: M-GN (filled circle), M-GS (filledtriangle), M-GS ∗ (open triangle), M-AGS (open star), M3 to M7which is a set of models that use AGS mixture by varying itsneon abundance (open star) and M8 (filled star). The box repre-sents the seismic values with their errors (Basu and Antia 2004).speed that peaks at 1.5% just below the convection zone. Thesurface helium abundance and the location of the base of theconvection zone are also very far from their seismic values.Models M3, M4, M5, M6 and M7 give an idea of how largethe neon abundance increase has to be in order to reduce thisdiscrepancy. In all these models the neon has been pushed out ofits error bar ( ± . Y s and r ZC far from their seismic box, even if theybecome better than the M-AGS ones. A slightly higher increaseof neon (e.g. M7) improves the surface envelope characteristics( Y s , r ZC ) but makes the sound speed much higher than the seis-mic one. Therefore, a compromise has to be found for the neonabundance value to satisfy Y s , r ZC and sound speed constraints. aatri et al.: Sensitivity of low degree oscillations 3 Fig. 3.
Upper panel left: Renormalized mean frequency small spacing δν as a function of the renormalized mean frequency smallspacing δν for the di ff erent models compared to GOLF observations (full box Gelly et al. 2002, dashed box Lazrek et al. 2007).Upper panel right : same for renormalized mean frequency small spacing δν as a function of the renormalized mean frequencysmall spacing δν . Lower panel: for comparison the same quantities are given before renormalization (in µ Hz), namely < δν > and < δν > as a function of < δν > . The small circle corresponds to a M-GN model calibrated at 4.65Gyr, the open trianglescorrespond to M-GS ∗ model.We estimate the neon abundance to be 8 . ± . ff erences between the models and the obser-vation. First, the lowest values of this range lead to models thathave Y S and r ZC values about 2 σ far from their seismic values.Second, its highest values infer models with relative di ff erencesbetween their sound speed profile and the seismic one that arejust three times lower than the relative di ff erence between M-AGS and seismic sound speed profiles at their peaks.In order to see the influence of the other heavy elementsabundances on the change of the considered model character-istics ( Y S , r ZC and sound speed) we constructed the M8 model.This model has a neon abundance that is situated at the bottomof our given neon increase interval (8.35dex) and has C, N, O,Si and Mg abundances that are increased until the maximum oftheir error bars (see Asplund et al. 2005). The abundance of ar-gon has also been increased by 0.4dex, as this element is anothernoble gas of the solar mixture. We deduce that the sound speedof the M8 model does not change much compared to the modelthat has the same increase of neon (M5), except at the deeper lay-ers of the sun. However, the values of Y S and r ZC become closerto their seismic values compared to those of the M5 model. Thismeans that the increase of other heavy element abundances in-side their error bars simultaneously improves the agreement be-tween the three considered seismic determinations and those ofthe models. This can lead to a reduction of the supposed val-ues of neon as they give good agreement in sound speeds to(8 . ± . ff erences betweenseismic and theoretical Y S and r ZC still have a maximum of 2 σ .For comparison we have considered the models M-GN andM-GS with the previous mixtures GN and GS. The model M- GN has a convective zone depth close to the seismic one buta too small surface helium abundance. On the contrary, modelM-GS has a good surface helium content but a thinner convec-tive zone. Since in Figure 2, the position of the M-GS modeldoes not follow the general trend of the other models, we havelooked in more detail at the di ff erences between the two mix-tures. We noted that the sulfur abundance of GS mixture (7.33dex) is larger than the GN value (7.21 dex), due to improved os-cillator strengths (Biemont et al. 1993), and than the AGS value(7.14 dex). We computed a model M-GS ∗ with the GS mixturebut with GN sulfur abundance. It appears that such a variationof sulfur notably lowers the surface helium abundance of themodel.
3. Fit to the low-degree small frequency spacingconstraints
Small low degree frequency spacings are a well known diagnos-tic of the solar core. In order to compare our theoretical resultsto the observational ones, we use the latest results of Lazrek etal. (2007) and those of Gelly et al. (2002) in the measurementof low degree solar frequencies from the GOLF experiment. Weexamine the small frequency spacings δν , δν and δν whichare combinations of acoustic modes penetrating di ff erently to-wards the center and that are thus very sensitive to this region. δν ( n ) = ν n ,ℓ = − ν n − ,ℓ = ,δν ( n ) = ν n ,ℓ = − ν n − ,ℓ = ,δν ( n ) = ν n ,ℓ = − ( ν n ,ℓ = + ν n − ,ℓ = ) . Zaatri et al.: Sensitivity of low degree oscillations
Fig. 4.
Relative frequency di ff erences between the gravity modes and the first low frequency p-modes of M-GN and M-AGS ( ⋄ ),M3 ( △ ), M4( ∗ ) , M5 ( (cid:3) ), M7( × ), M8( • ).However, the small spacings are slightly dependent on thesolar atmosphere which is highly simplified in the solar mod-els. Roxburgh & Vorontsov (2003) have demonstrated that theratio of the small to large separations of acoustic oscillationsis essentially independent of the structure of the outer lay-ers. We thus renormalize the small spacings by consideringthe ratios δν ( n ) / ∆ ν ( n , ℓ = δν ( n ) / ∆ ν ( n + , ℓ =
0) and δν ( n ) / ∆ ν ( n , ℓ =
1) where the large separation is given by: ∆ ν ( n , ℓ ) = ν n ,ℓ − ν n − ,ℓ We then compute both for our models and for the observa-tions the mean of these renormalized small frequency spacings δν , δν and δν for radial orders from 16 to 24. This corre-sponds to a frequency range about 2500 – 3600 µ Hz. The lowlimit of this range ensures that the behavior of the frequency isalmost asymptotic and the high limit corresponds to observedmodes with very high accuracy. For higher frequencies, the ac-curacy decreases rapidly. Figure 3 gives both renormalized andnon renormalized mean small spacings for the models of Table1 and for the observations. The dimensions of the symbols inthe upper panel of Figure 3 reflect the uncertainty on the plottedquantities corresponding to an uncertainty of 0 . µ Hz for thenumerical frequencies. It shows that the renormalization givesresults closer to the observations because it eliminates the di ff er-ences between surface properties of the models and the sun. Theremaining discrepancies are due to di ff erences in the structure ofthe deep solar interior.As expected, Figure 3 shows that the small frequency spacingsof the M-AGS model are far from the observations, contraryto those of the M-GN and M-GS models. We note that the M-GS model is closer to the observations than the M-GN model,contrary to the M-GS ∗ model. The small frequency spacings ofthe models that use an AGS mixture with di ff erent values of theneon abundance decrease as the neon increases in almost a reg-ular way. The model M7, which uses the highest value of neonabundance in our considered set of models, is shown to havethe best agreement between its small spacings and the observa-tions. However, this model has a much higher sound speed thanthe seismic one (see Figure1), which makes it a less acceptable model. We also show that a slight increase of some other heavyelements has an e ff ect on the change of small frequency spac-ings as well. We find that for the model M8 the three consideredrenormalized small spacings are closer to their observational de-terminations than those of the model M5.However the small spacings are also sensitive to the solarage, due to the change in time of the mean molecular weight inthe nuclear core.For example, Morel et al. (1997) showed that an increase inage of 100 Myr gives a decrease of 0 . µ Hz of both δν and δν ,with a small relative increase of sound speed of around 10 − and a slight increase of the thickness of the convection zone of0.002 R ⊙ and no noticeable change of the surface helium abun-dance.We added, in Figure 3 a GN model which is calibrated at4.65 Gyr to see the influence of the solar age on small frequencyspacings.After showing the influence of solar abundances on low degreesmall frequency spacings, we still believe that in order to resolvethe new abundances, a compromise between the neon abun-dance, the small frequency spacings and the constraints of thepreceding paragraph can be reached by slightly adjusting someheavy elements inside their error bars and the age of the sun. Oursuggested value of neon (8 . ± .
05) is confirmed by consider-ing the low degree small frequency spacing constraint.
4. Gravity modes
Adiabatic frequencies of the models have also been computedfor the range from 100 to 800 µ Hz and for low degrees(0 < ℓ <
6) including both g-modes and mixed modes. Theperiods of low frequency gravity modes are proportionalto the characteristic period P which is given in Table 1( P = π / R r ZC ( N / r ) dr , where N is the Brunt-V¨aiss¨al¨a fre-quency). The lowest P di ff erence between M-GN and theother models is obtained for M8, leading to the closest g-modefrequencies. The frequency di ff erences between the M-GNand the other models are given in Figure 4. We note that theg-modes are more influenced by the change of abundances than aatri et al.: Sensitivity of low degree oscillations 5 the low frequency p-modes. As expected the value of δν/ν atvery low frequency is close to its asymptotic value δ P / P . Thebiggest frequency di ff erence is obtained for M-AGS for whichlow g-mode frequencies are 1.5% lower. This di ff erence has aminimum for all the models around 250 µ Hz. It has been shownthat the g-modes around this frequency have a mixed character(Provost et al. 2000) and are sensitive to both the sound speedand the Brunt-V¨aiss¨al¨a frequency variations. Their frequenciesdo not depend much on any change in the models. The lowestdi ff erence in the frequencies compared to M-GN is obtainedfor M8 which is expected since they have very similar structureparameters.
5. Discussion and conclusion
We study the sensitivity of low degree frequency spacings to thechange on solar heavy element abundances. We constructed sev-eral solar models with di ff erent solar mixtures. The spacings areconsidered as helioseismic constraints of the solar core as theyare very sensitive to this deep region. Therefore, they are usedto test the reliability of the solar models in addition to the en-velope constraints (convection zone depth and helium surfaceabundance) and the sound speed profile. Surface e ff ects havebeen removed from these spacings by using a renormalizationprescribed by Roxburgh and Vorontsov (2003). Their observa-tional values have been taken from the recent GOLF measure-ments (Lazrek et al. 2007; Gelly et al. 2002).We found that low degree small frequency spacings are very sen-sitive to the metallicity of the models. The mean spacings of amodel using Asplund et al.(2005) abundances are much higherthan the ones of a model using Grevesse and Noels (1993) val-ues and are incompatible with those determined from the GOLFobservations. Similar results were found by Basu et al. (2007)by comparing BISON observations of low degree solar oscil-lations with models using di ff erent abundances and numericalcodes. They conclude that low surface metallicity models can beruled out. These two studies strengthen the fact that new solarabundances lead to solar models which disagree with helioseis-mology measurement in the core as well as in the other regionsof the solar interior.We confirm, as was also mentioned by several authors, thatthe sound speed profile, convection zone depth and heliumsurface abundance of a model using the revised abundances arealso far from their helioseismic determinations, unlike the onesof a model using the old abundances.In addition to these two main models we constructed five othermodels that use new solar abundances with a significant changeof the neon abundance. This has been done following the Antia& Basu (2005) suggestion to resolve the new abundances. Wefound that the small spacings are very sensitive to the neonabundance value and decrease almost regularly when the neonincreases. The discrepancy between models and observations isreduced simultaneously for the small frequency spacings andthe other constraints when the neon abundance is considerablyincreased. However, the neon abundance that gives the bestagreement between the models and the helioseismic determi-nations is hard to reach as it is a compromise solution betweenall these quantities. For instance, a model using a neon valueincreased by 0.45dex (M4) makes its sound speed very close tothe seismic sound speed but keeps its envelope characteristics(convection zone depth and helium surface abundance) far fromtheir observational values. A model using a neon abundance increased by 0.63dex (M7) has the opposite e ff ect.As expected, the search for the neon abundance value thatgives a good agreement between models using new abundancesand the seismic constraints including the small frequency spac-ings becomes easier if C, N, O, Si, Mg and Ar abundances arealso slightly increased. Other elements may also play a signifi-cant role. We show for example that an increase of sulfur abun-dance, as is the case for the GS mixture, noticeably increases thesurface helium abundance and lowers the small frequency spac-ings.Also, the solar age is a crucial feature in the determinationof low-degree frequencies. Indeed, we tested a model using oldabundances with an age 50 Myr older than the age we have usedto compute all the models (4.6Gyr) and found that this changebrings the spacings closer to the observations.In conclusion, we show that,if the new solar mixture ofAsplund et al. (2005) is confirmed, an increase of the neon abun-dance by (0 . ± . . ± . Z smaller than the value determined by Antiaand Basu (2006) from higher degree modes using the dimension-less sound speed derivative in the solar convection zone.Our last investigation in this work has been the calculationof g-mode frequencies since the detection of g-modes is oneof the current challenges of solar observers. As expected, thesolar model using new abundances has the highest frequencydi ff erences to the model using old abundances, which go up to 4 µ Hz. We show that modes with frequencies around 250 µ Hz anddegrees larger than 2 are less sensitive modes to the change inthe abundances, with di ff erences less than 2 µ Hz.
Acknowledgments : We thank B. Pichon for his technicalhelp, D.R. Alexander for giving us low temperature opacity ta-bles for the revised mixture and the OPAL group for their onlineopacity tables code. We are grateful to G. Grec and M. Lazrekfor communicating their results in advance of publication andto H.M. Antia for his constructive remarks. We also thank the“Programme Pluri-Formations Ast´erosismologie” from OCA forthe financial support.
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