Oscillating K giants with the WIRE satellite: determination of their asteroseismic masses
aa r X i v : . [ a s t r o - ph ] J a n Draft version December 12, 2018
Preprint typeset using L A TEX style emulateapj v. 2/19/04
OSCILLATING K GIANTS WITH THE
WIRE
SATELLITE:DETERMINATION OF THEIR ASTEROSEISMIC MASSES
D. Stello , H. Bruntt , H. Preston , and D. Buzasi (Received 2007 December 5) Draft version December 12, 2018
ABSTRACTMass estimates of K giants are generally very uncertain. Traditionally, stellar masses of single fieldstars are determined by comparing their location in the Hertzsprung-Russell diagram with stellarevolutionary models. Applying an additional method to determine the mass is therefore of significantinterest for understanding stellar evolution. We present the time series analysis of 11 K giants recentlyobserved with the
WIRE satellite. With this comprehensive sample, we report the first confirmationthat the characteristic acoustic frequency, ν max , can be predicted for K giants by scaling from thesolar acoustic cut-off frequency. We are further able to utilize our measurements of ν max to determinean asteroseismic mass for each star with a lower uncertainty compared to the traditional method, formost stars in our sample. This indicates good prospects for the application of our method on the vastamounts of data that will soon come from the COROT and Kepler space missions. Subject headings: stars: fundamental parameters — stars: oscillations — stars: interiors INTRODUCTION
According to theoretical calculations of stellar evolu-tion, stars of a large mass range, corresponding to main-sequence spectral classes from late B to K, all end upin roughly the same part of the Hertzsprung-Russell (H-R) diagram when they evolve to become red giants withspectral classes from late G to M. Here, the evolutiontracks are closely spaced, which makes it difficult to es-timate the mass, and hence to determine the progenitorof a red giant star from its position in the H-R diagram.The investigation of stellar oscillations (asteroseis-mology), in particular solar-like oscillations, provides aunique tool to probe the interior and hence also the massof stars. Much excitement therefore followed the firstclear evidence of solar-like oscillations in a red giant star(Frandsen et al. 2002). Subsequently, researchers haveseen evidence of oscillations in about a dozen K and lateG type giants, both in nearby field stars (De Ridder et al.2006; Barban et al. 2007; Tarrant et al. 2007) and mem-bers of the open cluster M67 (Stello et al. 2007).However, it remains uncertain if accurate mode fre-quencies are possible to obtain, since observational indi-cations are that mode lifetimes could be too short (Stelloet al. 2006), in disagreement with theory (Houdek &Gough 2002). Further, these stars might pulsate pre-dominantly in radial mode overtones as suggested byChristensen-Dalsgaard (2004) or indeed show additionalnon-radial pulsations as indicated by Hekker et al. (2006)and Kallinger et al. (2007). Without a full understand-ing of which modes we observe, we cannot exploit thefull potential of the asteroseismic analysis.In this paper we aim at utilizing the characteristicacoustic frequency, denoted ν max . This asteroseismicquantity is relatively insensitive to the mode lifetime andthe number of excited modes, but still enables us to ob-tain information about the stellar interiors. In particular, School of Physics, University of Sydney, NSW 2006, Australia;[email protected]. US Air Force Academy, Colorado Springs, CO 80840, USA. we will use ν max to estimate the masses of a sample ofK giants observed with the star tracker on the Wide-FieldInfrared Explorer ( WIRE ) satellite. OBSERVATIONS AND DATA REDUCTION
During its lifetime
WIRE observed more than 40evolved stars, of which we have selected a subset of 11K giants that all have long time series and good noisecharacteristics. The time series span from 15 to 61 days,and the observations were obtained from February 2004to May 2006. In Fig. 1 we show the location of the giantsin the H-R diagram, together with stars that have previ-ously been reported to show evidence of solar-like oscilla-tions. We extracted the complete set of evolution tracks( M = 0 . ⊙ ) from the BaSTI database (Pietrinferniet al. 2004), based on their alpha-enhanced standard so-lar models without overshooting (Z=0.0198, Y=0.273).We only plot a representative subset of tracks in Fig. 1.We obtain the raw light curves using the pipeline de-scribed by Bruntt et al. (2005). Data reduction proceedsin two stages. First, we remove obviously aberrant pointsfrom the time series. This is done by examination ofinstrumental magnitude, FWHM of the stellar profile,centroid position, and background level as a function oftime. Generally, the majority of data points examined inthis way fall into a well-defined group with a small per-centage of outliers, which are removed. We next removeeffects from high levels of scattered light at the beginningof each orbit by phasing each time series at the satelliteorbital period, and then subtract a smoothed version ofthe phased light curve. The resulting mean-subtractedtime series is used for the analysis described below.The WIRE star tracker obtained images of each starwith a cadence of 2 Hz, providing a few million observa-tions per star. However, with the expected long oscilla-tion period of the K giants (
P > ∼ µ Hz. STELLAR PARAMETERS
To facilitate our investigation we have derived the stel-lar parameters for each star. This enables us to predictthe characteristic acoustic frequency, ν max , pre , where wewould expect to see excess power in the Fourier spec-trum. The stellar parameters are listed in Table 1, andsorted according to ν max , obs , which is the frequency ofthe observed excess power (see Sect. 4).In the following we explain each column of Ta-ble 1. The V magnitude is obtained from the SIMBADdatabase, derived as the mean of the listed values fromup to six sources, and the standard deviation is adoptedas a conservative uncertainty. The infrared K band mag-nitude is taken from 2MASS (Cutri et al. 2003), the par-allax, π , is from the new Hipparcos release (van Leeuwen2007), and the effective temperature is derived using the T eff -( V − K ) relation by Alonso et al. (1999). The in-ternal error of the T eff -( V − K ) relation is only 25 K.However, we adopt σ T eff = 100 K as a realistic uncer-tainty, in agreement with Kuˇcinskas et al. (2005). Thecolor-temperature relation requires as input [Fe/H], butis insensitive to log g . For five stars in our sample, spec-troscopic information is available within a uniform col-lection (McWilliam 1990), and they all agree with hav-ing solar metallicity. Hence, we assume solar metallicityfor all our targets, which is reasonable for such nearbystars. The spectroscopically determined effective tem-peratures are in good agreement with those derived inTable 1. Three stars have interferometrically calibrated T eff (Blackwell & Lynas-Gray 1998; di Benedetto 1998),which also agree with our quoted values.We then derive the luminosity from log( L/ L ⊙ ) = − [ V + BC − /π ) + 5 − M bol , ⊙ ] / .
5, where BC isthe bolometric correction obtained from the BC -( V − K )relation by Alonso et al. (1999), and M bol , ⊙ = 4 .
75 isthe solar absolute bolometric magnitude (recommenda-tion of IAU 1999). Since these are all nearby stars weneglect interstellar absorption, A V , but we do include σ A V in the error budget. In general, the relative con-tributions to σ L from the individual uncertainties are σ BC > σ A V > σ π > σ V , with σ BC being dominated by σ T eff , while σ π and σ V are negligible for most stars.The quoted range in the photometric mass, M phot (seeTable 1), corresponds to the lowest and highest massesof all tracks that go through the 1 σ -error box in the H-Rdiagram, while taking mass loss into account in the stel-lar models (mass loss parameter η = 0 .
4; see Pietrinferniet al. (2004) and references herein). We note that thisapproach will always underestimate the true mass rangewithin the 1 σ -error box due to the non-zero mass step,∆ M , in our grid of tracks, which is ∆ M = 0 . ⊙ for0 . < M/ M ⊙ < .
0, ∆ M = 0 . ⊙ for 2 . < M/ M ⊙ < .
0, and ∆ M = 0 . ⊙ for 3 . < M/ M ⊙ < .
0. Hence,if a track is just outside the error box, our quoted massrange will be smaller by almost one mass step. Withinthe age of the universe, none of the tracks with progen-itor mass M . .
85 M ⊙ and solar metallicity have yetevolved to the red giant phase (see Fig. 1). Hence, we usethe 0 .
90 M ⊙ track to define the minimum masses . It is We note that for sub-solar metallicities we would expect to seered giants with masses below 0 .
85 M ⊙ . beyond the scope of this Letter to go into detail about ad-ditional systematic errors in these mass estimates, origi-nating from metallicity, overshooting, and differences inevolution codes.Finally, we calculate the frequency, ν max , pre (see Ta-ble 1), where the highest excess power from solar-likeoscillations is expected in the Fourier spectrum. This isobtained by scaling the acoustic cut-off frequency of theSun (Brown et al. 1991) ν max = M/ M ⊙ ( T eff / . L/ L ⊙ ν max , ⊙ , (1)where we use the solar value, ν max , ⊙ = 3021 ± µ Hz,found from 10 independent 30-day time series from theVIRGO instrument on board the SOHO spacecraft, us-ing the same approach as for the K giants (see Sect. 4).Equation 1 has been shown to give very good estimates ofthe frequency of maximum oscillation power based on ob-servations of mostly less evolved stars with relatively wellconstrained masses (Bedding & Kjeldsen 2003) comparedto our targets. As with M phot , we also quote a range for ν max , pre , which states the extreme values of ν max , pre thatare within the 1 σ -error box in the H-R diagram. To il-lustrate this we show an H-R diagram close-up of ourtarget stars in Fig. 2. The black dots correspond to thestellar parameters given in Table 1 (heading: “Derived”),and the 1 σ -error boxes and HD numbers are also shown.We plot L , T eff for selected values of ν max , pre along eachevolution track, which clearly shows the complexity ofestimating ν max from the stellar position in this part ofthe H-R diagram. Note that, similar to Fig. 1, only a se-lected sample of all evolution tracks are plotted. Alongeach evolutionary track, a given value of ν max , pre (shownas identical symbols) can occur up to three times, twiceon the red giant branch (ascending and descending), andonce while ascending the asymptotic giant branch. Inany region where the tracks cross, the mass, and hence ν max , is not uniquely determined by the location in theH-R diagram. The last two columns in Table 1 will beexplained in the following section. ASTEROSEISMIC ANALYSIS
To look for evidence of solar-like oscillations, we firstcalculate the Fourier spectrum of each star, which isshown in amplitude (= √ power) in Fig. 3. The mono-tonic green curve is a fit to the noise, described by σ ( ν ) = a/ν + σ in power. The parameters a and σ are determined following the approach by Stello et al.(2007). In addition, we smooth each spectrum (redcurve) to remove the detailed structure of the excesspower. Smoothing was done using a moving box av-erage twice with a width equal to twice the expectedfrequency separation of adjacent radial modes derivedas: ∆ ν = ( M/ M ⊙ ) . ( R/ R ⊙ ) − . . µ Hz (Kjeldsen& Bedding 1995). We note that the location of the ex-cess hump in the smoothed spectrum does not dependstrongly on the mass adopted in the calculation of ∆ ν .From Fig. 3 we see a clear trend of excess power shift-ing to higher frequency from top to bottom. A powerexcess at higher frequencies generally corresponds to lessluminous stars, but this trend is modulated by mass andtemperature, in agreement with Eq. 1. The gray shadedareas in each panel indicate the predicted region of theexcess power (Table 1, Col.8). We further note that thescillating K giants with the WIRE satellite 3amplitude seems to decrease as the width of the envelopeincreases. Similar trends can be seen in Kjeldsen et al.(2005) for less luminous stars.Despite the large uncertainty in the stellar masses, M phot , and hence in ν max , pre , our results in Fig. 3 con-firm that Eq. 1 is valid for K giants in a large luminosityrange. Now, if we turn the argument around, assumingthat Eq. 1 is exact, and hence interpret any observeddeviation from this relation to be largely due to an in-accurate “photometric” mass, we can use it to infer an“asteroseismic” mass. To obtain the asteroseismic masswe measure ν max by first subtracting the noise fit fromthe smoothed spectra, and then we locate the maximumof the residual (see Table 1, Col.9). By smoothing weobtain a more robust measure than trying to locate thestrongest oscillation mode. To estimate the uncertaintyof ν max , obs , we make 20 simulations of each time seriesfollowing the approach by Stello et al. (2004). The simu-lations show that ν max , obs has an uncertainty of roughly10%, but it varies somewhat from star to star, due to dif-ferences in pulsation characteristics, the duration of thetime series, and the noise level. We found that our resultsdo not depend strongly on the adopted mode lifetime, τ ,in the range 3 d < τ <
20 d, that we investigated. Wethen finally determine M seis using Eq. 1.Our results show that for stars located in the regionwhere evolution tracks cross, M seis has a lower 1 σ un-certainty than the M phot mass range (assuming Eq. 1 isexact). In regions without crossings the benefit from hav-ing measured ν max , obs is less obvious. For those stars, weneed longer time series to obtain a lower uncertainty in ν max , obs , which generally dominates the uncertainty onour mass estimate. For a few stars we are able to mea-sure the large frequency separation, ∆ ν , which poten-tially can give a more precise mass estimate than ν max .However, for our present data ν max provides the smallestmass uncertainties. CONCLUSIONS
We have analyzed photometric time series of 11 nearbyK giants obtained with the
WIRE satellite. The Fouriertransforms show clear evidence that oscillation powershifts to higher frequencies for less luminous stars, as an-ticipated from scaling the solar frequency of maximumpower, ν max , ⊙ . We were able to measure ν max and madesimulations of each star to obtain a realistic uncertaintyof the measurement. Using a simple scaling relation,which relates this frequency to the stellar parameters T eff , L/ L ⊙ , and M/ M ⊙ , we estimated an asteroseismicmass. For several stars this approach provides a signifi-cantly lower uncertainty of the mass relative to the clas-sical mass estimate based purely on comparing stellarevolution tracks with the location in the H-R diagram.These results show exciting prospects for the cur-rent COROT mission (Baglin & The COROT Team1998) and the upcoming Kepler satellite (Christensen-Dalsgaard et al. 2007), which will both provide muchmore extended times series than WIRE . With longer timeseries we can potentially acquire lower uncertainties inthe ν max measurements, and hence more precise mass es-timates. This will indeed be possible with Kepler, whichwill obtain parallaxes, and hence luminosities, of its tar-get stars. Our approach could be particularly valuablein cases where the oscillation power does not allow accu- rate detection of the large frequency separation, ∆ ν , dueto an insufficient number of modes with high signal-to-noise. This might, in fact, include most faint solar-likepulsators, as well as bright giant stars if indeed the modelifetime does not increase with increasing oscillation pe-riods (Stello et al. 2006).We acknowledge the financial from the ARC, DASC,and FNU. This research has made use of the SIMBADdatabase, operated at CDS, Strasbourg, France. Wethank Tim Bedding to comments on the manuscript. Stello et al. REFERENCESAlonso, A., Arribas, S., & Mart´ınez-Roger, C. 1999, A&AS, 140,261Baglin, A., & The COROT Team. 1998, in IAU Symp. 185: NewEyes to See Inside the Sun and Stars, Vol. 185, 301Barban, C., et al. 2007, A&A, 468, 1033Bedding, T. R., & Kjeldsen, H. 2003, PASA, 20, 203Blackwell, D. E., & Lynas-Gray, A. E. 1998, A&AS, 129, 505Brown, T. M., Gilliland, R. L., Noyes, R. W., & Ramsey, L. W.1991, ApJ, 368, 599Bruntt, H., Kjeldsen, H., Buzasi, D. L., & Bedding, T. R. 2005,ApJ, 633, 440Christensen-Dalsgaard, J. 2004, Sol. Phys., 220, 137Christensen-Dalsgaard, J., Arentoft, T., Brown, T. M., Gilliland,R. L., Kjeldsen, H., Borucki, W. J., & Koch, D. 2007, Comm. inAsteroseismology, 150, 350Cutri, R. M., et al. 2003, 2MASS All Sky Catalog of point sources(Pasadena: NASA/IPAC)De Ridder, J., Barban, C., Carrier, F., Mazumdar, A., Eggenberger,P., Aerts, C., Deruyter, S., & Vanautgaerden, J. 2006, A&A, 448,689di Benedetto, G. P. 1998, A&A, 339, 858Frandsen, S., et al. 2002, A&A, 394, L5Guenther, D. B., et al. 2007, Comm. in Asteroseismology, 151, 5 Hekker, S., Reffert, S., Quirrenbach, A., Mitchell, D. S., Fischer,D. A., Marcy, G. W., & Butler, R. P. 2006, A&A, 454, 943Houdek, G., & Gough, D. O. 2002, MNRAS, 336, L65Kallinger, T., et al. 2007, preprint (astro-ph/0711.0837)Kjeldsen, H., & Bedding, T. R. 1995, A&A, 293, 87Kjeldsen, H., et al. 2005, ApJ, 635, 1281Kuˇcinskas, A., Hauschildt, P. H., Ludwig, H.-G., Brott, I.,Vanseviˇcius, V., Lindegren, L., Tanab´e, T., & Allard, F. 2005,A&A, 442, 281McWilliam, A. 1990, ApJS, 74, 1075Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2004, ApJ,612, 168Stello, D., et al. 2007, MNRAS, 377, 584Stello, D., Kjeldsen, H., Bedding, T. R., & Buzasi, D. 2006, A&A,448, 709Stello, D., Kjeldsen, H., Bedding, T. R., De Ridder, J., Aerts, C.,Carrier, F., & Frandsen, S. 2004, Sol. Phys., 220, 207Tarrant, N. J., Chaplin, W. J., Elsworth, Y., Spreckley, S. A., &Stevens, I. R. 2007, MNRAS, 382, L48van Leeuwen, F. 2007, Hipparcos, the New Reduction of the RawData, Astroph. and Sp. Sc. Lib., Vol. 350 (Springer Dordrecht) scillating K giants with the
WIRE satellite 5
TABLE 1Stellar parameters of the
WIRE
K giants.
Literature Derived Evolution tracks AsteroseismologyHD
V V − K π T eff L/ L ⊙ M phot / M ⊙ ν max , pre ν max , obs M seis / M ⊙ (mag) (mag) (mas) (K) a ( µ Hz) ( µ Hz)41047 5.543(05) b a The adopted 1 σ uncertainty of T eff is 100 K. b Numbers in parentheses are uncertainties, e.g. for HD41047 the V magnitude and its uncertainty is 5 . ± .
005 mag.
Stello et al.
Fig. 1.—
H-R diagram with our 11 target stars including 1 σ -error boxes. Additional bright field stars (filled star symbols) and M67cluster members (empty star symbols) that show evidence of solar-like oscillations are marked. Dashed lines indicate the approximatelocation of the classical instability strip. Solid lines are evolution tracks. scillating K giants with the WIRE satellite 7
Fig. 2.—
H-R diagram of region around our target stars (solid dots inside 1 σ -error boxes). Gray lines are a representative sample ofevolution tracks. The additional symbols show points along the evolution tracks corresponding to a given value of ν max , pre (values areindicated for each symbol). Stello et al.
Fig. 3.—
Amplitude spectra of the 11 K giants (HD numbers are indicated). Note the increasing amplitude scale on the ordinate. Ineach panel the red solid line is a smoothed version of the spectrum and the green monotonically decreasing line is a fit to the noise. Grayshaded areas indicate the frequency interval of ν max , pre . The dotted line marks one third of the WIRE orbital frequency, and σ wn is thesquare root of the mean power in the range: 70–80 µµ