Absolute stellar parameters of KIC 09246715 – a double-giant eclipsing system with a solar-like oscillator
We present our results of a combined analysis of radial velocity and light curves of a double-lined spectroscopic and eclipsing binary KIC 09246715, observed photometrically by the Kepler satellite, and spectroscopically with the OAO-1.88m telescope with the HIgh-Dispertion Echelle Spectrograph (HIDES). The target was claimed to be composed of two red giants, one of which is showing solar-like oscillations. We have found that the mass and radius of the primary are M and R, and of the secondary: M and R, which confirms the double-giant status. Our secondary is the star to which the oscillations were attributed. Results of its previous asteroseismic analysis are in agreement with ours, only significantly less precise, but the subsequent light-curve-based study failed to derive correct mass and radius of our primary. KIC 09246715 is one of the rare cases where asteroseismic parameters of a solar-like oscillator were confirmed by an independent method, and only the third example of a Galactic double-giant eclipsing binary with masses and radii measured with precision below 2%.
The unprecedented photometric precision of the Kepler mission (Borucki et al., 2010) has opened new possibilities in various fields of astronomy, including studies of eclipsing binaries and asteroseismology. The former has been known for many decades to provide accurate and precise stellar parameters, sometimes not possible to derive with other methods (e.g. absolute radii). Since the discovery of pulsating sdB stars (Kilkenny et al., 1994) and solar-like oscillations in stars other than the Sun (Brown & Gilliland, 1994; Kjeldsen & Bebbing, 1995), asteroseismology became another technique capable of providing such results. Until the launch of CoRoT and Kepler satellites the number of other stars showing the solar-like oscillations was very low, but now it is counted in thousands, and contains main sequence, as well as giant stars.
Absolute values of fundamental stellar parameters have multiple applications in modern astronomy, but they need to be known with precision of at least 2–3% (Lastennet & Valls-Gabaud, 2002). The best possible characterisation comes from double-lined spectroscopic and eclipsing binaries, that also show pulsations. Such systems are extremely useful for testing stellar evolution models, as the masses and radii can be, in principle, measured with two independent techniques. Around 50 eclipsing systems containing oscillating giants have been reported by Gaulme et al. (2013, hereafter: G13), but without spectroscopic follow up. Only (catalog KIC~08410637), composed of an oscillating giant and a main-sequence star, has been studied in more detail (Frandsen et al., 2013), and a very good precision in absolute parameters has been achieved. Despite being very useful in general, currently the asteroseismic measurements usually do not give results of sufficient precision. Nevertheless, the large number of known oscillating stars undoubtedly shows the importance of this technique. Discovery and characterisation of the “keystone” double-lined spectroscopic, eclipsing and oscillating systems will help to test and enhance the capabilities of asteroseismology directly. In this work we present such an example.
2 The target
The system (catalog KIC~09246715) (HD 190585, , hereafter: K0924) was identified as an eclipsing binary by the Kepler mission, and was listed in the Kepler Eclipsing Binaries Catalog (KEBC; Prša et al., 2011; Slawson et al., 2011). It was not reported as a double-lined spectroscopic binary till now. According to G13 and Gaulme et al. (2014, hereafter: G14), it is composed of two red giants, one of which is showing solar-like oscillations with peak frequency and separation of Hz, Hz (G13), or Hz, Hz (G14). Activity is also reported, in a form of periodic ( d) brightness modulations coming from spots.
Using asteroseismology G13 and G14 first derived mass and radius of the oscillating star. Then they combined it with results of light curve modelling (i.e. ) and Kepler’s 3rd law, inferring the properties of the other component: 2.06(13) M, 8.10(18) R for the oscillating component (their primary), and 1.1(3) M, 6.8(1) R or 3.3(5) M, 9.7(2) R for the other, but described the latter solution as less probable. With our spectroscopy, we are able to directly revise their results, confronting the asteroseismology with direct modelling of the light and radial velocity (RV) curves of this system.
Eclipsing binaries composed of two red giants, like K0924, are relatively rare, and not many such systems have their components parameters measured with high precision. The on-line DEBCat catalog (Southworth, 2015), which lists detached eclipsing binaries with masses and radii measured down to 2-3%, contains only two such Galactic systems – HD 187669 (Hełminiak et al., 2015) and ASAS J180052-2333.8 (Suchomska et al., 2015) – and a handful of others found in LMC and SMC (e.g. Pietrzyński et al., 2013; Graczyk et al., 2014). Therefore K0924 is also important for studying the late stages of stellar life and testing the models of evolution and structure.
3 Data and methodology
The system K0924 is one of the targets we have observed as a part of a larger spectroscopic project, aimed for characterisation of northern detached eclipsing binaries, including objects selected from the Kepler field. All of them have been observed and analysed in a similar way, and the detailed description of the observing procedure, data reduction, stability tests, orbit and light curve fitting, etc. will be explained in a forthcoming paper (Hełminiak et al., in prep.). However, we shortly present them below.
We follow the convention that the primary component is the one being eclipsed during the deeper minimum (the primary eclipse). In our case, the primary is the slightly more massive and larger star.
3.1 Observational data
In this study we make use of the publicly available Kepler mission photometry. We used the de-trended relative flux measurements , that were later transformed into magnitude difference , and finally the KEBC value of was added. The de-trended data were downloaded directly from KEBC, where currently only the long-cadence measurements for this star are available.
A total of 8 spectra were taken during several runs between July 2014 and late April 2015, at the 1.88-m telescope of the Okayama Astrophysical Observatory with the HIgh-Dispersion Echelle Spectrograph (HIDES; Izumiura, 1999). The instrument was fed through a circular fiber, for which the light is collected via a circular aperture of projected on-sky diameter of 2.7 arcsec, drilled in a flat mirror that is used for guiding (Kambe et al., 2013). An image slicer is used in order to reach both high resolution () and good efficiency of the system. Wavelength calibration was based on ThAr lamp exposures taken every 1-2 hours, which gave the stability of the instrument at the level of 40-50 m s, as measured from multiple observations of four RV standards. Each science exposure was 1500 seconds long, but due to unstable atmospheric conditions, the resulting signal-to-noise ratio () usually varied between 75 and 105 (63 at one time). Spectra were reduced with dedicated IRAF-based scripts, that cope with the mosaic character of the HIDES detector. Reduction included correction for overscan, bias, flat field, cosmic rays and bad pixels, as well as extraction and wavelength calibration of 53 orders (4360–7535 Å).
3.2 Light curve analysis
For the light curve (LC) fit we used version 28 (v28)
of the code JKTEBOP (Southworth et al., 2004a, b), which is based on the
EBOP program (Popper & Etzel, 1981). The complete long-cadence Q0-Q17 curve was
first used to find the best-fitting parameters, including period ,
primary (deeper) eclipse mid-time , eccentricity , periastron longitude
, inclination , ratio of fluxes , ratio of central surface
brightnesses , sum of the fractional radii (in units of
major semi-axis ), and their ratio . A small but clear increase in brightness was
noticed around both eclipses, so we also fitted
reflection coefficients, and got and .
Logarithmic limb darkening (LD) law (Klinglesmith & Sobieski, 1970) was assumed, with coefficients
(fixed in the fit) interpolated from the the tables published on the PHOEBE
The JKTEBOP does not fit for spots or oscillations, however, it offers a number of algorithms to properly include systematics in the error budget. We assumed that after years of nearly continuous observations they are averaged out over the orbital period, and decided to treat them as a correlated noise and run the residual-shifts (RS) procedure to calculate reliable uncertainties (Southworth et al., 2011). To run RS on the whole Q0-Q17 curve would take almost two weeks on the computer we used, so for the errors estimation we decided to split the data and analyse each chunk separately, and then calculate weighted averages of the resulting parameters. Due to its long period, reaching almost the time span of two quarters of Kepler data, both eclipses were not always visible during the same quarter. Adjacent quarters with only primary and only secondary minimum were merged together into one set and cropped, so the resulting light curve time span was around 90 days and covered both minima. This was done for Q6+Q7, Q8+Q9, Q10+Q11, and Q12+Q13. Both eclipses were observed in Q3, Q5 and Q14. No eclipses were seen in Q0, Q1, Q2, Q4, Q15, Q16 and Q17, which were rejected from the RS stage. Because of the long period, and reflection coefficients, as well as the LD coefficients, were first held fixed, only perturbed later during the proper RS stage. The final parameter errors were obtained by adding in quadrature the formal error of the weighted average and the rms of the results for each quarter.
3.3 Radial velocities and orbital fit
RVs were measured with our own implementation of the two-spectra cross-correlation function technique TODCOR (Zucker & Mazeh, 1994) with synthetic spectra computed with ATLAS9 and ATLAS12 codes (Kurucz, 1992) as templates. Single measurement errors were calculated with a bootstrap approach (Hełminiak et al., 2012). Flux ratios ( in Zucker & Mazeh, 1994) were also calculated, and used as input for JKTEBOP. For this, only orders from the Kepler bandpass were used, with weights corresponding to the total response factor at a wavelength equal the center of a given spectral order. The RVs obtained from our HIDES spectra, together with their errors and of the spectra, are listed in Table 1.
The RV measurements were analysed with the code V2FIT, which fits a double-Keplerian orbit by using the Levenberg-Marquartd algorithm. As free parameters, we set the time of periastron passage , the velocity semi-amplitudes , the primary’s systemic velocity , and the difference in components systemic velocities . Period , eccentricity and periastron longitude were kept fixed on values found in JKTEBOP. In order to find reliable uncertainties, that include the influence of systematics coming possibly from the pulsations and low number of spectra, we run 10000 bootstrap iterations. As expected, we found the systematics to be the dominant source of parameter errors.
3.4 Absolute values of parameters
The absolute values of parameters and their uncertainties were calculated with the JKTABSDIM code, available together with JKTEBOP. This simple code combines the spectroscopic and light curve solutions to derive a set of stellar absolute dimensions (), and related quantities (). If desired, it also calculates distance, but requires multi-color photometry, , and both effective temperatures as input. Due to lack of such data, we did not attempt to estimate the distance.
The light and RV curves are presented in Figures 1 and 2, respectively. Values of stellar parameters can be found in Table 2. We have found that the mass and radius of the primary are M and R, and of the secondary: M and R. K0924 is composed of two very similar stars that evolved significantly from the main sequence. We reached a good precision of 1.1% in masses and 1.1–1.5% in radii, which makes our results valuable for further comparison with models of stellar structure and evolution, and places K0924 in a very small group of double-giant systems with precisely measured masses and radii. Precision in masses is mainly hampered by the low number of spectra, and likely by the influence of spots, oscillations, and instrument distortions on the RV measurements, which may explain the apparently non-random residuals. Precision in radii is lowered by the oscillations, which we did not model and reduce, but treated as a red noise in the light curve, and included in the error budget.
These results are different from G13, who give 1.7(3) M and 7.7(4) R for the oscillating component, and 0.8(7) M and 5.9(3) R for the other, as well as from G14, who give, analogously, 2.06(13) M R, and 1.1(3) M R. Note that both previous studies adopt the opposite definition of primary/secondary, and solar-like oscillations are found on the star that we define as the secondary, i.e. slightly less massive according to our orbital solution. First, both stars have almost equal masses and radii, while the solution of G14 gives and . Our mass ratio close to 1 comes directly from the spectroscopy (Fig. 2), and its value is very robust. The ratio of radii was constrained using the spectroscopic flux ratios from TODCOR, which we also find reliable – a quick inspection of any of the spectra reveals that the lines of both components are of similar depths, meaning similar effective temperatures and levels of continuum, and the peaks of cross-correlation function were of basically the same height. Finally, a quick comparison with evolutionary models (see next Section) shows that there is no isochrone that reproduces the results of previous studies. This means that the asteroseismology provides correct, yet less precise, stellar parameters, but light curve solutions should be supported by spectroscopic values of mass and flux ratios. It has also been found in the case of KIC 08410637 by Frandsen et al. (2013). Moreover, some conclusions presented in G14 should now be treated with caution.
It is worth to note that despite very large separation, the system might have reached or is close to a form of a tidal equilibrium. If the reported period d is related to the rotation, it would coincide with the value of d, which is the value of rotation expected for the given orbital period and eccentricity in the state of pseudo-synchronisation (Hut, 1981; Mazeh, 2008).
In Figure 3 we compare our results, i.e. masses and radii, with the theoretical PARSEC isochrones (Bressan et al., 2012), that include calculation of absolute magnitudes in the Kepler photometric band. In this set of models the solar metallicity is reached for =0.0152.
From Figure 3 one can deduce that the system may be 950 Myr old, if solar metallicity is assumed. At this stage, however, the age and are strongly degenerated on the mass-radius plane (Hełminiak et al., 2015). Both components are probably on the red giant branch, before the red clump stage. It would be possible to reproduce both the observed radii on the red clump, by assuming a lower metallicity (), but then the system would be even younger (600–700 Myr) and of much earlier spectral type than suggested by the KEBC effective temperature of 4699 K. Both components likely have nearly equal ’s, and the spectra show many features, so we find the 4700 K, 950 Myr and solar metallicity solution more probable, however with some caution about the temperature itself (see further text).
We also checked the value of metallicity of dex, given in the Mikulski
Archive for Space Telescopes (MAST)
Due to rapid changes in the stellar structure during the red giant phase (compared to the main sequence), the isochrones predict a variety of possible temperatures within the range of masses we found for K0924. However, the evolution in is related to the growth of the star, so we can use the radii estimates to predict temperatures of both components. However, due to lack of any estimate that we find reliable, we can not pick any certain scenario. On the 950 Myr, solar-metallicity isochrone, we find K, and K. On the 780 Myr, dex isochrone we get K, and K. Finally, the 1.04 Gyr, 0.20 dex gives K, and K. To obtain temperatures around 4700 K, one would have to use an isochrone for even higher metallicity. The difference in predicted temperatures is large enough for the modern spectral analysis methods to distinguish between solar and sub-solar cases. Note also that the ratio of predicted values of temperatures is much closer to 1 than 1.04, which was found by (Gaulme et al., 2014) in the light-curve fit, and that in their solution the oscillator (our secondary) is cooler. The K0924 system would benefit from further spectroscopy (to disentangle the component spectra) and multi-band photometry, that altogether would allow for precise temperature and metallicity determination. It would also improve the age estimation, and precision in masses and radii even more.
Finally, taking into account the similarities of the two components, we suspect that both stars may show similar oscillations that blend in the light curve, and may have confused G14, although the mass and radius of their pulsating component, and the 2014 values of and are in agreement (within errors) with our solution. We used our results to reproduce the expected peak frequency and frequency splitting , using the formulae of Kjeldsen & Bebbing (1995):
with the reference values from Mosser et al. (2013), also used in G13. Our results predict and 8.69(15) Hz for the primary and secondary (oscillator in G13 and G14), respectively. The peak frequency is however dependent on the temperature, and for the discussed range of 4700–5300 K we get 104–98 Hz for the primary, and 110–104 Hz for the secondary. In particular, the peak frequencies differ by less than the separation and perhaps two modulations have been mixed in the analysis of G13 and G14.
We have obtained precise mass and radius measurements of two giant components of a detached eclipsing binary KIC 09246715. The secondary component was previously reported to show solar-like oscillations, and our results confirm mass and radius derived from asteroseismology. We have, however, found that the other star – our primary – has very similar properties, thus we suspect that both components may in fact show very similar oscillations. We may conclude that the asteroseismology is a promising method of measuring stellar masses and radii, and that the correct estimation of these parameters for both components of a binary can not be done from light curves only, but still requires spectroscopic information.
- affiliation: Subaru Research Fellow
- affiliation: Graduate University for Advanced Studies, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
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