Amplitudes of solar-like oscillations: constraints from red giants in open clusters observed by Kepler
D. Stello, D. Huber, T. Kallinger, S. Basu, B. Mosser, S. Hekker, S. Mathur, R. A. Garcia, T. R. Bedding, H. Kjeldsen, R. L. Gilliland, G. A. Verner, W. J. Chaplin, O. Benomar, S. Meibom, F. Grundahl, Y. P. Elsworth, J. Molenda-Zakowicz, R. Szabó, J. Christensen-Dalsgaard, P. Tenenbaum, J. D. Twicken, K. Uddin
aa r X i v : . [ a s t r o - ph . S R ] J u l D RAFT VERSION J ULY
14, 2018
Preprint typeset using L A TEX style emulateapj v. 2/19/04
AMPLITUDES OF SOLAR-LIKE OSCILLATIONS: CONSTRAINTS FROM RED GIANTS IN OPEN CLUSTERSOBSERVED BY
KEPLER D ENNIS S TELLO , D ANIEL H UBER , T HOMAS K ALLINGER , S ARBANI B ASU , B ENO ˆ IT M OSSER , S ASKIA H EKKER , S AVITA M ATHUR , R AFAEL
A. G
ARC ´ IA , T IMOTHY
R. B
EDDING , H ANS K JELDSEN , R ONALD
L. G
ILLILAND , G RAHAM
A. V
ERNER , W ILLIAM
J. C
HAPLIN , O THMAN B ENOMAR , S ØREN M EIBOM , F RANK G RUNDAHL , Y VONNE
P. E
LSWORTH , J OANNA M OLENDA - ˙Z
AKOWICZ , R OBERT S ZAB ´ O , J ØRGEN C HRISTENSEN -D ALSGAARD , P ETER T ENENBAUM , J OSEPH
D. T
WICKEN , K AMAL U DDIN Draft version July 14, 2018
ABSTRACTScaling relations that link asteroseismic quantities to global stellar properties are important for gaining un-derstanding of the intricate physics that underpins stellar pulsation. The common notion that all stars in anopen cluster have essentially the same distance, age, and initial composition, implies that the stellar parameterscan be measured to much higher precision than what is usually achievable for single stars. This makes clus-ters ideal for exploring the relation between the mode amplitude of solar-like oscillations and the global stellarproperties. We have analyzed data obtained with NASA’s
Kepler space telescope to study solar-like oscillationsin 100 red giant stars located in either of the three open clusters, NGC 6791, NGC 6819, and NGC 6811. Byfitting the measured amplitudes to predictions from simple scaling relations that depend on luminosity, mass,and effective temperature, we find that the data cannot be described by any power of the luminosity-to-massratio as previously assumed. As a result we provide a new improved empirical relation which treats luminosityand mass separately. This relation turns out to also work remarkably well for main-sequence and subgiantstars. In addition, the measured amplitudes reveal the potential presence of a number of previously unknownunresolved binaries in the red clump in NGC 6791 and NGC 6819, pointing to an interesting new applicationfor asteroseismology as a probe into the formation history of open clusters.
Subject headings: binaries: general — open clusters and associations: individual (NGC 6791, NGC 6819,NGC 6811) — stars: fundamental parameters — stars: interiors — stars: oscillations —techniques: photometric INTRODUCTION
The highly complex processes involved in the excitationand damping of stochastically excited (solar-like) oscillations Sydney Institute for Astronomy (SIfA), School of Physics, University ofSydney, NSW 2006, Australia Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada Institute for Astronomy, University of Vienna, T¨urkenschanzstrasse 17,1180 Vienna, Austria Department of Astronomy, Yale University, P.O. Box 208101, NewHaven, CT 06520-8101 LESIA, CNRS, Universit´e Pierre et Marie Curie, Universit´e DenisDiderot, Observatoire de Paris, 92195 Meudon, France Astronomical Institute “Anton Pannekoek”, University of Amsterdam,PO Box 94249, 1090 GE Amsterdam, The Netherlands High Altitude Observatory, NCAR, P.O. Box 3000, Boulder, CO 80307,USA Laboratoire AIM, CEA/DSM-CNRS, Universit´e Paris 7 Diderot,IRFU/SAp, Centre de Saclay, 91191, Gif-sur-Yvette, France Department of Physics and Astronomy, Aarhus University, NyMunkegade 120, 8000 Aarhus C, Denmark Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,Maryland 21218, USA School of Physics and Astronomy, University of Birmingham, Edgbas-ton, Birmingham B15 2TT, UK Astronomy Unit, Queen Mary University of London, UK Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cam-bridge, MA, 02138, USA Instytut Astronomiczny Uniwersytetu Wrocławskiego, ul. Kopernika11,51-622 Wrocław, Poland Konkoly Observatory of the Hungarian Academy of Sciences, KonkolyThege Mikl´os ´ut 15-17, H-1121 Budapest, Hungary SETI Institute/NASA Ames Research Center, MS 244-30, Moffat Field,CA 94035, USA Orbital Sciences Corporation/NASA Ames Research Center, MS 244-30, Moffat Field, CA 94035, USA make estimation of their amplitudes from pulsation modellingparticularly challenging (e.g. Houdek 2006; Samadi et al.2007). A scaling relation for the amplitude has thereforebeen of significant interest since it was first introduced byKjeldsen & Bedding (1995). Their ‘
L/M relation’, basedon theoretical work by Christensen-Dalsgaard & Frandsen(1983) of near main-sequence stellar models, suggested thatthe amplitude in radial velocity would simply scale as theluminosity-to-mass ratio. Using observations of stars made inboth radial velocity and intensity Kjeldsen & Bedding (1995)also suggested that the amplitude in intensity, A λ , would scaleas A λ = (( L/L ⊙ ) / ( M/M ⊙ )) s λ/ T eff / r A , ⊙ , (1)where s = 1 , λ is the central wavelength of the photometricbandpass, and A , ⊙ the observed solar value at 500nm.They found empirically r = 2 . , which was a slight modi-fication to r = 1 . derived if they assumed the stellar oscil-lations to be purely adiabatic. Subsequent modelling by e.g.Houdek et al. (1999); Samadi et al. (2007) has lead to varia-tions of the L/M relation where, in essence, different powersof the
L/M ratio have been derived ( s = 0 . – . ). Recently,Verner et al. (2011) found s = 0 . –1.0 depending on T eff ofa large sample (642) of main-sequence and subgiant stars ob-served by Kepler (Koch et al. 2010).The existence of solar-like oscillations in red giantstars is now well established observationally, most re-cently from CoRoT (e.g. de Ridder et al. 2009) and
Ke-pler (e.g. Gilliland et al. 2010; Bedding et al. 2010b), as wellas theoretically (Dupret et al. 2009; Montalb´an et al. 2010;Di Mauro et al. 2011). Despite the significantly different Stello et al.structures of red giants compared to the stars and modelson which the
L/M relation has been founded, the absenceof an alternative has also seen this relation widely used forred giants, including several attempts to determine the bestmatching exponent, s (Stello et al. 2007; Mosser et al. 2010;Baudin et al. 2011). While the majority of results on red gi-ants are on field stars, the recent clear detections in open clus-ter red giants emerging from Kepler (Stello et al. 2010,PaperI) has opened up the seismic exploration of clusters and theadvances that clusters bring to the interpretation of asteroseis-mic data (Basu et al. 2011; Hekker et al. 2011; Miglio et al. inprep.; Stello et al. submitted). In particular, stars in an opencluster are thought to share a common distance and initialchemical composition, which allows one to derive the stellarluminosity to much higher precision than for most field stars.In addition, the common age of red giant stars within eachcluster implies that they have practically the same mass, re-sulting in a relatively low uncertainty on their measured meanmass assuming there is no significant mass loss (Miglio et al.in prep.). Combined with high quality standard photometrywe can therefore obtain more robust predictions of the am-plitudes from scaling relations and hence investigate these inways not possible for the field stars observed by the currentspace mission CoRoT and
Kepler .Based on only one month of
Kepler data of a single cluster,in Paper I we already demonstrated the potential for inves-tigating the
L/M relation by taking advantage of the com-mon cluster properties of the stellar sample. We now have
Kepler time-series photometry that span 10 times longer forstars in three open clusters (NGC 6791, NGC 6819, andNGC 6811), which exhibit distinctly different stellar masses.In this paper we are therefore extending considerably the anal-ysis of the amplitude scaling relation for solar-like oscilla-tions. OBSERVATIONS, TARGET SELECTION & CLUSTERPARAMETERS
The photometric time-series data were obtained between2009 May 12 and 2010 March 20 (observing quarters 1–4),providing approximately 14,000 data points per star obtainedin the spacecraft’s long-cadence mode ( ∆ t = 29 . min). Adetailed description of the data reduction from raw images tofinal light curves is given in Jenkins et al. (2010); Garcia et al.(2011) and Stello et al. (submitted).Our initial star sample was the one selected by Stello etal. (submitted), who used seismic and conventional mea-surements to identify cluster membership and blending ofeach star. We excluded the seismic non-members and furthertrimmed the sample by removing the brightest (largest) andfaintest stars, for which the measurement of the mode ampli-tude would not be reliable due to: (1) difficulty in determin-ing the noise level at low frequency in the power spectrum ofthe largest stars (oscillating at very low frequencies) and (2)low signal-to-noise and potential blending of the faintest stars.The increased flux in the photometric aperture from a blend-ing star, such as an unresolved binary companion, will tendto reduce the relative flux variation that we measure as theoscillation amplitude. To minimize this bias further, we ex-cluded a total of 23 spectroscopic binaries (Hole et al. 2009)and stars that we expected to be binaries based on their lo-cation in the color-magnitude diagram. This still left a largesample of 100 stars for further analysis. We finally investi-gated effects of blending of single stars based on the resultsby Stello et al.. Few of the blended stars indicated by Stello et F IG . 1.— H-R diagram of the selected cluster stars. Small gray sym-bols mark the known and potential binaries. Representative isochrones fromMarigo et al. (2008) (NGC 6791: 5.6 Gyr, Z = 0 . and NGC 6819:2.4 Gyr, Z = 0 . ) and Pietrinferni et al. (2004) (NGC 6811: 500 Myr, Z = 0 . ) are shown to guide the eye. al. showed lower than expected amplitudes, but no rigorouscriterion for when blending had a significant impact on theamplitude could be obtained from those results. We thereforedid not exclude any of our remaining stars that were listed asblends.We adopted the luminosities, masses and effective temper-atures from Stello et al. (submitted). We refer to Basu et al.(2011) and Hekker et al. (2011) for further details on thederivation on the mass and effective temperature, respectively.In summary, the average mass (here adopted for each star) is . ± . M ⊙ (NGC 6791), . ± . M ⊙ (NGC 6819),and . ± . M ⊙ (NGC 6811), while the luminosities andtemperatures of our final sample are shown in Figure 1 andhave typical uncertainties of ∼ and ∼ , respectively. MEASUREMENT OF OSCILLATION AMPLITUDES AND ν max Oscillation amplitudes were extracted by five differentteams using pipelines described in Hekker et al. (2010);Huber et al. (2009); Kallinger et al. (2010); Mathur et al.(2010); Mosser & Appourchaux (2009). These methods areall based on the measurement of the integrated oscillationpower, which we converted to an amplitude per radial mode.The integrated power was found either by smoothing thepower spectrum as described by Kjeldsen et al. (2008) or byfitting a Gaussian function to the oscillation power envelope.Figure 2 shows the former. To obtain the amplitude per radialmode the oscillation power ( P obs , Figure 2) is multiplied by ∆ ν to obtain the power per radial order, where ∆ ν is the fre-quency separation between consecutive radial orders. Finallywe divided by the factor, c , which is the effective number ofmodes per ∆ ν (Kjeldsen et al. 2008). We adopted the so-lar value c = 3 . from Bedding et al. (2010a), which agreeswell with the measured mean value for red giants (Mosser etal. submitted). We note that our final results (Sect. 4.3) weremplitudes of solar-like oscillations 3 F IG . 2.— Power spectrum of a typical star. The smoothed spectrum (solidwhite line) and fit to the stellar granulation background (dashed line) areshown. The oscillation power, P obs , is evaluated at the frequency of max-imum power, ν max . not affected significantly if we adopted the recent factor byBallot et al. (2011). Hence, the observed amplitude per radialmode, A obs ( l = 0) was derived as: A obs ( l = 0) = ( P obs ∆ ν/ . / . (2)For this we normalized the power spectra accordingto the amplitude-scaled version of Parseval’s theorem(Kjeldsen & Frandsen 1992), in which a sine wave of ampli-tude, A , provides a peak in the power spectrum of A . Thetypical uncertainty in the measured amplitude is ∼ .To explore whether the applied solar conversion factor, c ,provided reasonable amplitudes for red giants, we ran sim-ulations that as input took pulsation frequencies derived us-ing the ADIPLS code (Christensen-Dalsgaard 2008a) for arepresentative set of ASTEC models (Christensen-Dalsgaard2008b). Details of the simulator can be found in Chaplin et al.(2008). Following Christensen-Dalsgaard (2004), the inputmode amplitudes were scaled relative to the radial modes us-ing the mode inertia, I , as A ∝ I − . Despite significantdifferences in the frequency spectra of red giants comparedto the Sun, in particular the presence of many mixed modes(Dupret et al. 2009; Beck et al. 2011; Bedding et al. 2011),the pipelines returned amplitudes within 10% of the input val-ues. We regard this as acceptable given the uncertainty fromintrinsic scatter of the oscillations and the slightly differentapproaches for extracting the amplitudes in each pipeline, inparticular the fitting and subtraction of the stellar granulationbackground (Mathur et al. submitted). Based on a representa-tive set of stars, we found good agreement between the differ-ent pipelines. In this paper we show the results from the SYDpipeline (Huber et al. 2009), which provided amplitudes forthe widest range of stars, and we compare our final result withthe CAN pipeline (Kallinger et al. 2010), which exhibited thelargest overlap in stellar sample with the SYD pipeline. Bothpipelines show robust performances in their estimation of thestellar granulation background (Mathur et al. submitted). Werefer to Verner et al. (2011) and Mosser et al. (submitted) fordetailed amplitude comparisons.In addition to amplitude, the pipelines also measured thefrequency of maximum power, ν max (Figure 2). The uncer-tainties in ν max are typically 1–2%. RESULTS F IG . 3.— Observed amplitude versus ν max for stars in NGC 6791(red diamonds), NGC 6819 (purple triangles), and NGC 6811 (bluesquares). The binary stars are shown with small gray symbols. Theclump stars are marked. The dashed line shows a power law with slope − . . Colored lines are the cluster isochrones (Figure 1) where ampli-tude and ν max have been derived using Equation 1 with s = 0 . and ν max = ( M/M ⊙ ) / ( L/L ⊙ )( T eff / . µ Hz. The black crossat (10,100) indicates a typical 1- σ error bar. A obs versus ν max As noted by Stello et al. (2007); Mosser et al. (2010);Huber et al. (2010), it can be convenient to plot the measuredamplitude as a function of ν max , since the currently adoptedscaling relations predict a simple relation between the two. Inparticular, by dividing A λ ∝ ( L/M ) s T − r eff (Equation 1) by( ν max ) s ∝ ( M/L ) s T . s eff (Brown et al. 1991) and rearrang-ing, we obtain A λ ∝ ν − s max T . s − r eff . Hence, such a purely em-pirical plot allows one to make some inference on how the am-plitude depends on the stellar parameters L , M , and T eff evenwhen those are not very well known (e.g. Mosser et al. 2010;Huber et al. 2010; Huber et al. submitted; Mosser et al. sub-mitted).In Figure 3 we show the measured amplitude as a func-tion of ν max , where each set of symbols present results of onecluster. We also mark the location of the clump of helium-core burning stars for each cluster, which illustrates the largerange in ν max arising mainly from the difference in the stellarmass between the clusters.Guided by the fiducial dashed line, we see that stars withineach cluster roughly follow a power law with exponent − . ,but with a clear offset from one cluster to another by up to ∼ %. The more massive the stars, the lower the oscilla-tion amplitudes at a given ν max . This offset is not expectedfrom the scaling relations for A λ and ν max , as illustrated bythe isochrones in Figure 3. Since the scaling relation for ν max is probably good to within a few percent (Stello et al.2009; Belkacem et al. 2011), the observed offsets stronglysuggest that ( L/M ) s T − r eff does not adequately predict the am-plitude for these stars. From a large sample of field red giantsHuber et al. (2010) noted that the scatter in the amplitude ata given ν max was larger than expected from the uncertain-ties and that this indicated a spread in mass in their sample.However, a qualitative analysis was not attempted due to therelatively large uncertainties in the fundamental stellar param-eters. Fortunately, with our cluster sample we can directlyfit the measured amplitudes to their predictions derived fromwell-constrained stellar parameters. Stello et al. Fitting the
L/M relation
First, we fitted the observed amplitudes to the predictedamplitudes for NGC 6819. For this purpose we derived thepredicted amplitude using the
L/M relation (Equation 1)and adopting λ = 650 nm as the central wavelength ofthe Kepler bandpass, hence A obs , ⊙ = 3 . (peak scaled)(Michel et al. 2009). The least-squares fit resulted in s =0 . ± . when adopting the empirical value of r = 2 , whichis the value of r we will adopt in the following. Using r = 1 . only has the effect of increasing s by about 0.03. This resultis compatible with Paper I, which qualitatively found the bestmatch for s to be slightly higher than 0.7. When repeated forNGC 6791, we found s = 0 . ± . . The small number ofstars in NGC 6811 did not merit a fit on its own, but the twoother clusters already indicate inconsistent results.Hence, we tried next fitting all three clusters simultane-ously. Due to the correlation between M and T eff (the hotterand younger clusters have more massive stars; Figure 1), westill kept r fixed. Figure 4(a) shows the result. The best fitresulted in s = 0 . ± . . It is apparent that the clustersare offset from one another, as expected from Figure 3, butwe also see that the fit systematically underestimates the am-plitude for the most luminous stars. If r was treated as a freeparameter we did obtain a better fit overall, but it still un-derestimated the amplitudes of the stars in NGC 6791, andin particular the most luminous stars in the sample, by 20–30%. In summary, while the ( L/M ) s scaling provided ac-ceptable results when fitted to one cluster at a time (althoughgiving different results for s ), our analysis has demonstratedthat ( L/M ) s cannot explain the observations in all clusterssimultaneously. A new scaling relation for amplitudes
In the following, we therefore fitted the exponents on L and M independently, hence A λ ∝ L s M − t T − . The re-sult, shown in Figure 4(b), is a much improved fit where allthree clusters fall on top of each other and follow the one-to-one relation. The best fitting parameters are s = 0 . ± . and t = 1 . ± . – the same as we obtained from first con-verting A obs to a bolometric amplitude (Ballot et al., submit-ted) and then fitting to A bol ∝ L s M − t T − . For the starswith A obs & ppm the scatter of A obs / ( L . M − . T − ) is 14%, in perfect agreement with the quoted uncertainties on A obs , L , M , and T eff . The increased scatter (22%) towardslower luminosity stars is potentially due to remaining issuesof blending in the sample and/or an increase in the uncertain-ties of the measured amplitudes for the faintest stars. Thelatter was, however, not reflected in the estimated uncertain-ties reported by the pipelines showing only slightly increaseduncertainties at most. Again, under the adiabatic assumption( r = 1 . ) s would slightly increase (to 0.95) as would t (to1.8).To investigate the robustness of our fit we did the following.If we ignored the NGC 6811 stars in the fitting, the result andhence the excellent alignment of all three clusters was verysimilar ( s and t within σ ). This is perhaps not surprisinggiven the few stars in our NGC 6811 sample. Nevertheless,this result is reassuring since the amplitudes of NGC 6811 arethen correctly predicted from a fit based only on NGC 6791and NGC 6819. We further investigated the effect on the fitif we ignored all clump stars to obtain an even more homo-geneous sample, which showed practically no change to thebest fitting parameters. This indicates that any possible mass F IG . 4.— (a) Observed versus predicted amplitude for the best fitting rela-tion of the form A λ ∝ ( L/M ) s T − . Symbols are the same as in Figure 3.Binaries, which are shown with small gray symbols, were not included in thefit. (b) As panel (a) but fitting to A λ ∝ L s M − t T − . The inset shows the χ near its minimum. (c) Illustration of how well the fit in panel (b) predictsamplitudes for other main-sequence, subgiant, and red giant stars (see text). mplitudes of solar-like oscillations 5loss, which is expected to occur predominantly near the tipof the red giant branch, has no effect on our result. A smallsystematic change of a few percent on s and t was, however,observed by removing some of the most deviant stars at lowamplitudes. Finally, we repeated the fit on the sample of starsthat were in common between the SYD and CAN pipelines.The differences in s and t based on these different pipelineswere 2% and 15% in s and t , respectively, the latter only justwithin σ of the formal uncertainty.We finally tested the new scaling relation suggested byKjeldsen & Bedding (2011), but found it to overestimate theamplitude for the cluster stars similar to the result found byHuber et al. (submitted) and Mosser et al. (submitted). Main-sequence and subgiant stars
Now, with an improved scaling relation for red giant stars, itis interesting to see how well it applies to main-sequence andsubgiant stars. To investigate this we took amplitude measure-ments of the
Kepler field stars presented by Huber et al. (sub-mitted), the CoRoT F-type stars HD49933 and HD181420from Michel et al. (2008) (converted to A obs ( l =0 ) ), and Pro-cyon from Arentoft et al. (2008) and Huber et al. (2011). Theamplitude measurement in velocity of Procyon was convertedto intensity using models by Houdek (2010). We used our newscaling relation to predict the amplitudes based on L , M , and T eff from Huber et al. (submitted) ( Kepler sample), Bruntt(2009) (HD49933/181420), and Bonanno et al. (2007) (Pro-cyon). Given that the new relation is only based on the clusterred giants, it is remarkable how well it agrees for this broadrange of stars (Figure 4c). We note that the uncertainty in themass of the
Kepler ( ∼ –20%) and CoRoT ( ∼ –10%) fieldstars is significantly larger than for Procyon ( ∼ %) and thecluster stars ( ∼ –2%). While the values of s and t found inthis Letter are slightly different from, although still in agree-ment within the uncertainties, those found by Huber et al.(submitted) for the Kepler field stars, the qualitative agree-ment across all stars is quite similar to that found by Huber etal. (their Fig. 5).
Unresolved binaries
It is evident, particularly from Figure 4(b), that many of theknown and potential binaries (small gray diamonds and trian-gles) show relatively low amplitudes. For NGC 6791 we hadno spectroscopic determination of binaries, but a significantfraction of its red clump stars show lower than expected am-plitudes and hence strong evidence for ’diluted’ light curvesdue to the presence of unresolved binary companions. Thisshows a new exciting way of applying asteroseismology to identify binary stars and hence to probe the formation of thesestars in clusters, which will be investigated in detail in a forth-coming paper. CONCLUSIONS
Our analysis of solar-like oscillations in 100 red giant starsin three open clusters revealed that previously adopted scalingrelations based on the luminosity-to-mass ratio for predictingamplitudes are not adequate for red giants. We found an em-pirical scaling relation by fitting the observed amplitudes toa more general form than the previous
L/M relation. Theresult, A λ ∝ L . / ( M . T ) (3)and A bol ∝ L . / ( M . T eff ) , (4)which showed considerable improvement for red giants,turned out to also work remarkably well for main-sequenceand subgiant stars.Interestingly, the lower than expected amplitudes of somered clump stars in NGC 6791 and NGC 6819 revealed thatthey were likely unresolved binaries, many of which were notknown previously. This method for identifying binaries couldadd interesting new insight to the formation history of theseclusters.In this investigation we ignored any possible effect on am-plitude from metallicity differences (Samadi et al. 2007) ofthe three clusters, which have values of [Fe/H] NGC6791 ≃ . and [Fe/H] NGC6819 ≃ . (see Basu et al. 2011,and refer-ence therein), while it is unknown for NGC 6811. To improveon that will require better determination of the cluster metal-licities. In addition, we would need more clusters (with sig-nificantly different stellar parameters) to allow the fitting of arigorous empirical relation including one more free parametersuch as metallicity.With more Kepler data in the future, we expect to have clus-ter stars covering a large range of T eff , which will includeturn-off stars at the end of the main sequence, allowing us toalso fit the exponent, r , of the T eff dependence in the ampli-tude scaling relation.Funding for this Discovery mission is provided by NASA’sScience Mission Directorate. We thank the entire Kepler teamwithout whom this investigation would not have been possi-ble. We acknowledge support from the: ARC, NWO, NSF,Polish Ministry and Lend¨ulet program OTKA grants N-N203-405139, K83790, MB08C-81013.
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