arXiv subjects

Yoichi Takeda

Publications and source records attributed to Yoichi Takeda.

At least 55 records · Page 3Linked to original sources

arXiv2017

On the observational characteristics of lithium-enhanced giant stars in comparison with normal red giants

With an aim to shed light on the origin of Li anomaly observed in a small fraction of red giants, we carried out a spectroscopic study on the observational characteristics of selected 20 bright Li-rich giants, in comparison with a large number of normal late G-early K giants, where special attention was paid to clarifying any difference between two samples with respect to stellar parameters, rotation, activity, kinematic properties, and chemical abundances of Li, Be, C, O, Na, S, and Zn). Our targets are roughly divided into 'bump/clump group' and 'luminous group' according to the position on the HR diagram. Regarding the former group, Li-enriched giants and the corresponding normal giants appear practically similar except for Li, suggesting that surface Li enhancement in this group may be a transient episode which normal giants undergo at some certain evolutionary stage. Meanwhile, those Li-rich giants belonging to the latter group appear more anomalous in the sense that they tend to show larger rotational velocities, and that their elemental abundances (e.g., those of C and O derived from high-excitation lines) are apt to show apparent overabundances, though this might be due to some spurious effect reflecting the difficulty of abundance derivation in stars of higher rotation and activity. Our analysis confirmed considerable Be deficiency as well as absence of 6Li as the general characteristics of Li-rich giants under study, which implies that engulfment of planets is rather unlikely for the cause of Li-enrichment.

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arXiv2017

Does the radial-tangential macroturbulence model adequately describe the spectral line broadening of solar-type stars?

In incorporating the effect of atmospheric turbulence in the broadening of spectral lines, the so-called radial-tangential macroturbulence (RTM) model has been widely used in the field of solar-type stars, which was devised from an intuitive appearance of granular velocity field of the Sun. Since this model assumes that turbulent motions are restricted to only radial and tangential directions, it has a special broadening function with notably narrow width due to the projection effect, the validity of which has not yet been confirmed in practice. With an aim to check whether this RTM model adequately represents the actual solar photospheric velocity field, we carried out an extensive study on the non-thermal velocity dispersion along the line-of-sight (V_los) by analyzing spectral lines at various points of the solar disk based on locally-averaged as well as high spatial-resolution spectra, and found the following results. First, the center-to-limb run of V_los derived from ground-based low-resolution spectra is simply monotonic with a slightly increasing tendency, which contradicts the specific trend (an appreciable peak at theta~45 deg) predicted from RTM. Second, the V_los values derived from a large number of spectra based on high-resolution space observation revealed to follow a nearly normal distribution, without any sign of peculiar distribution expected for the RTM case. These two observational facts indicate that the actual solar velocity field is not such simply dichotomous as assumed in RTM, but directionally more chaotic. We thus conclude that RTM is not an adequate model at least for solar-type stars, which would significantly overestimate the turbulent velocity dispersion by a factor of ~2. The classical Gaussian macroturbulence model should be more reasonable in this respect.

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arXiv2017

The K2-ESPRINT Project VI: K2-105 b, a Hot-Neptune around a Metal-rich G-dwarf

We report on the confirmation that the candidate transits observed for the star EPIC 211525389 are due to a short-period Neptune-sized planet. The host star, located in K2 campaign field 5, is a metal-rich ([Fe/H] = 0.26$\pm$0.05) G-dwarf (T_eff = 5430$\pm$70 K and log g = 4.48$\pm$0.09), based on observations with the High Dispersion Spectrograph (HDS) on the Subaru 8.2m telescope. High-spatial resolution AO imaging with HiCIAO on the Subaru telescope excludes faint companions near the host star, and the false positive probability of this target is found to be <$10^{-6}$ using the open source vespa code. A joint analysis of transit light curves from K2 and additional ground-based multi-color transit photometry with MuSCAT on the Okayama 1.88m telescope gives the orbital period of P = 8.266902$\pm$0.000070 days and consistent transit depths of $R_p/R_\star \sim 0.035$ or $(R_p/R_\star)^2 \sim 0.0012$. The transit depth corresponds to a planetary radius of $R_p = 3.59_{-0.39}^{+0.44} R_{\oplus}$, indicating that EPIC 211525389 b is a short-period Neptune-sized planet. Radial velocities of the host star, obtained with the Subaru HDS, lead to a 3σ upper limit of 90 $M_{\oplus} (0.00027 M_{\odot})$ on the mass of EPIC 211525389 b, confirming its planetary nature. We expect this planet, newly named K2-105 b, to be the subject of future studies to characterize its mass, atmosphere, spin-orbit (mis)alignment, as well as investigate the possibility of additional planets in the system.

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arXiv2016

Photospheric carbon and oxygen abundances of F-G type stars in the Pleiades cluster

In order to investigate the carbon-to-oxygen ratio of the young open cluster M45 (Pleiades), the C and O abundances of selected 32 F-G type dwarfs (in the effective temperature range of Teff~5800-7600K and projected rotational velocity range of vesini~10-110km/s) belonging to this cluster were determined by applying the synthetic spectrum-fitting technique to C I 5380 and O I 6156-8 lines. The non-LTE corrections for these C I and O I lines were found to be practically negligible (less than a few hundredths dex). The resulting C and O abundances (along with the Fe abundance) turned out nearly uniform without any systematic dependence upon Teff or vesini. We found, however, in spite of almost solar Fe abundance ([Fe/H]~0), carbon turned out to be slightly subsolar ([C/H]~-0.1) while oxygen slightly supersolar ([O/H]~+0.1). This lead to a conclusion that [C/O] ratio was moderately subsolar (~-0.2) in the primordial gas from which these Pleiades stars were formed ~120--130 Myr ago. Interestingly, similarly young B-type stars are reported to show just the same result ([C/O]~-0.2), while rather aged (~1-10 Gyr) field F-G stars of near-solar metallicity yield almost the solar value ([C/O]~0) on the average. Such a difference in the C/O ratio between two star groups of distinctly different ages may be explained as a consequence of orbit migration mechanism which Galactic stars may undergo over a long time.

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arXiv2016

Sulfur and zinc abundances of red giant stars

Sulfur and zinc are chemically volatile elements, which play significant roles as depletion-free tracers in studying galactic chemical evolution. However, regarding red giants having evolved off the main sequence, reliable abundance determinations of S and Zn seem to be difficult despite that a few studies have been reported so far. Given this situation, we tried to establish the abundances of these elements for an extensive sample of 239 field GK giants (-0.8 < [Fe/H] < +0.2), by applying the spectrum-fitting technique to S I 8694-5, S I 6757, and Zn I 6362 lines and by taking into account the non-LTE effect. Besides, similar abundance analysis was done for 160 FGK dwarfs to be used for comparison. The non-LTE corrections for the S and Zn abundances derived from these lines turned out < 0.1(-0.2) dex for most cases and not very significant. It revealed that the S I 6757 feature is more reliable as an abundance indicator than S I 8694-5 for the case of red giants, because the latter suffers blending of unidentified lines. The finally resulting [S/Fe]-[Fe/H] and [Zn/Fe]-[Fe/H] relations for GK giants were confirmed to be in good agreement with those for FGK dwarfs, indicating that S and Zn abundances of red giants are reliably determinable from the S I 6757 and Zn I 6362 lines. Accordingly, not only main-sequence stars but also evolved red giant stars are usable for tracing the chemical evolution history of S and Zn in the regime of disk metallicity by using these lines.

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arXiv2016

The K2-ESPRINT Project V: a short-period giant planet orbiting a subgiant star

We report on the discovery and characterization of the transiting planet K2-39b (EPIC 206247743b). With an orbital period of 4.6 days, it is the shortest-period planet orbiting a subgiant star known to date. Such planets are rare, with only a handful of known cases. The reason for this is poorly understood, but may reflect differences in planet occurrence around the relatively high-mass stars that have been surveyed, or may be the result of tidal destruction of such planets. K2-39 is an evolved star with a spectroscopically derived stellar radius and mass of $3.88^{+0.48}_{-0.42}~\mathrm{R_\odot}$ and $1.53^{+0.13}_{-0.12}~\mathrm{M_\odot}$, respectively, and a very close-in transiting planet, with $a/R_\star = 3.4$. Radial velocity (RV) follow-up using the HARPS, FIES and PFS instruments leads to a planetary mass of $50.3^{+9.7}_{-9.4}~\mathrm{M_\oplus}$. In combination with a radius measurement of $8.3 \pm 1.1~\mathrm{R_\oplus}$, this results in a mean planetary density of $0.50^{+0.29}_{-0.17}$ g~cm$^{-3}$. We furthermore discover a long-term RV trend, which may be caused by a long-period planet or stellar companion. Because K2-39b has a short orbital period, its existence makes it seem unlikely that tidal destruction is wholly responsible for the differences in planet populations around subgiant and main-sequence stars. Future monitoring of the transits of this system may enable the detection of period decay and constrain the tidal dissipation rates of subgiant stars.

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arXiv2016

The K2-ESPRINT Project IV: A Hot Jupiter in a Prograde Orbit with a Possible Stellar Companion

We report on the detection and early characterization of a hot Jupiter in a 3-day orbit around K2-34 (EPIC~212110888), a metal-rich F-type star located in the K2 Cycle 5 field. Our follow-up campaign involves precise radial velocity (RV) measurements and high-contrast imaging using multiple facilities. The absence of a bright nearby source in our high-contrast data suggests that the transit-like signals are not due to light variations from such a companion star. Our intensive RV measurements show that K2-34b has a mass of $1.773\pm0.086M_J$, confirming its status as a planet. We also detect the Rossiter-McLaughlin effect for K2-34b and show that the system has a good spin-orbit alignment ($λ=-1_{-9}^{+10}$ degrees). High-contrast images obtained by the HiCIAO camera on the Subaru 8.2-m telescope reveal a faint companion candidate ($Δm_H=6.19\pm 0.11$ mag) at a separation of $0\farcs36$. Follow-up observations are needed to confirm that the companion candidate is physically associated with K2-34. K2-34b appears to be an example of a typical "hot Jupiter," albeit one which can be precisely characterized using a combination of K2 photometry and ground-based follow-up.

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arXiv2016

High-Contrast Imaging of Intermediate-Mass Giants with Long-Term Radial Velocity Trends

A radial velocity (RV) survey for intermediate-mass giants has been operated for over a decade at Okayama Astrophysical Observatory (OAO). The OAO survey has revealed that some giants show long-term linear RV accelerations (RV trends), indicating the presence of outer companions. Direct imaging observations can help clarify what objects generate these RV trends. We present the results of high-contrast imaging observations or six intermediate-mass giants with long-term RV trends using the Subaru Telescope and HiCIAO camera. We detected co-moving companions to $γ$ Hya B ($0.61^{+0.12}_{-0.14} M_\odot$), HD 5608 B ($0.10 \pm 0.01 M_\odot$), and HD 109272 B ($0.28 \pm 0.06 M_\odot$). For the remaining targets($ι$ Dra, 18 Del, and HD 14067) we exclude companions more massive than 30-60 $M_\mathrm{Jup}$ at projected separations of 1arcsec-7arcsec. We examine whether these directly imaged companions or unidentified long-period companions can account for the RV trends observed around the six giants. We find that the Kozai mechanism can explain the high eccentricity of the inner planets $ι$ Dra b, HD 5608 b, and HD 14067 b.

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arXiv2016

A non-LTE study of silicon abundances in giant stars from the Si I infrared lines in the zJ-band

We investigate the feasibility of the Si I infrared (IR) lines as Si abundance indicators for giant stars. We find that Si abundances obtained from the Si I IR lines based on the local thermodynamic equilibrium (LTE) analysis show large line-to-line scatter (mean value of 0.13dex), and are higher than those from the optical lines. However, when the non-LTE effects are taken into account, the line-to-line scatter reduces significantly (mean value of 0.06dex), and the Si abundances are consistent with those from the optical lines. The typical average non-LTE correction of [Si/Fe] for our sample stars is about $-$0.35dex. Our results demonstrate that the Si I IR lines could be reliable abundance indicators provided that the non-LTE effects are properly taken into account.

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arXiv2016

Oxygen abundance determination of B-type stars with the OI 7771-5A lines

Oxygen abundances of 34 B-type stars in the effective temperature range of Teff~10000-28000K with diversified rotational velocities (vesini~ 0-250km/s) were determined from the OI triplet lines at 7771-5A, with an aim to examine whether this OI feature can be a reliable abundance indicator for such high-temperature stars including rapid rotators. It revealed that the required non-LTE abundance correction is distinctly large (ranging from ~-0.6dex to ~-1.7dex) and its consideration is indispensable. On the condition that the non-LTE effect is taken into account, this triplet is a useful O abundance indicator (with a precision of <~0.2dex) up to Teff <~25000K, since its total equivalent width is sufficiently large (>~200mA). In contrast, it is not adequate for abundance derivation for stars at Teff >~25000K, where its strength rapidly drops down toward a hardly detectable level (except for sharp-lined stars) and its sensitivity to Teff or log g becomes considerably large. The resulting non-LTE oxygen abundances turned out to be almost normal (i.e., near-solar around ~8.7-8.8 within +/-~0.2dex) for most stars without any dependence upon projected rotational velocity as well as luminosity (or mass), which is consistent with the prediction of recent stellar evolution calculations.

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arXiv2016

A Pair of Giant Planets around the Evolved Intermediate-Mass Star HD 47366: Multiple Circular Orbits or a Mutually Retrograde Configuration

We report the detection of a double planetary system around the evolved intermediate-mass star HD 47366 from precise radial-velocity measurements at Okayama Astrophysical Observatory, Xinglong Station, and Australian Astronomical Observatory. The star is a K1 giant with a mass of 1.81+-0.13M_sun, a radius of 7.30+-0.33R_sun, and solar metallicity. The planetary system is composed of two giant planets with minimum mass of 1.75^{+0.20}_{-0.17}Mjup and 1.86^{+0.16}_{-0.15}Mjup, orbital period of 363.3^{+2.5}_{-2.4} d and 684.7^{+5.0}_{-4.9} d, and eccentricity of 0.089^{+0.079}_{-0.060} and 0.278^{+0.067}_{-0.094}, respectively, which are derived by a double Keplerian orbital fit to the radial-velocity data. The system adds to the population of multi-giant-planet systems with relatively small orbital separations, which are preferentially found around evolved intermediate-mass stars. Dynamical stability analysis for the system revealed, however, that the best-fit orbits are unstable in the case of a prograde configuration. The system could be stable if the planets were in 2:1 mean-motion resonance, but this is less likely considering the observed period ratio and eccentricity. A present possible scenario for the system is that both of the planets have nearly circular orbits, namely the eccentricity of the outer planet is less than ~0.15, which is just within 1.4sigma of the best-fit value, or the planets are in a mutually retrograde configuration with a mutual orbital inclination larger than 160 degree.

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arXiv2015

Characterization of the K2-19 Multiple-Transiting Planetary System via High-Dispersion Spectroscopy, AO Imaging, and Transit Timing Variations

K2-19 (EPIC201505350) is an interesting planetary system in which two transiting planets with radii ~ 7 $R_{Earth}$ (inner planet b) and ~ 4 $R_{Earth}$ (outer planet c) have orbits that are nearly in a 3:2 mean-motion resonance. Here, we present results of ground-based follow-up observations for the K2-19 planetary system. We have performed high-dispersion spectroscopy and high-contrast adaptive-optics imaging of the host star with the HDS and HiCIAO on the Subaru 8.2m telescope. We find that the host star is relatively old (>8 Gyr) late G-type star ($T_{eff}$ ~ 5350 K, $M_s$ ~ 0.9 $M_{Sun}$, and $R_{s}$ ~ 0.9 $R_{Sun}$). We do not find any contaminating faint objects near the host star which could be responsible for (or dilute) the transit signals. We have also conducted transit follow-up photometry for the inner planet with KeplerCam on the FLWO 1.2m telescope, TRAPPISTCAM on the TRAPPIST 0.6m telescope, and MuSCAT on the OAO 1.88m telescope. We confirm the presence of transit-timing variations, as previously reported by Armstrong and coworkers. We model the observed transit-timing variations of the inner planet using the synodic chopping formulae given by Deck & Agol (2015). We find two statistically indistinguishable solutions for which the period ratios ($P_{c}/P_{b}$) are located slightly above and below the exact 3:2 commensurability. Despite the degeneracy, we derive the orbital period of the inner planet $P_b$ ~ 7.921 days and the mass of the outer planet $M_c$ ~ 20 $M_{Earth}$. Additional transit photometry (especially for the outer planet) as well as precise radial-velocity measurements would be helpful to break the degeneracy and to determine the mass of the inner planet.

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arXiv2015

Physical Properties of Gliese 229B Based on Newly Determined Carbon and Oxygen Abundances of Gliese 229A

Recently Tsuji & Nakajima (2914) and Tsuji, Nakajima & Takeda (2015) have developed a method of molecular line spectroscopy of M dwarfs with which Carbon and oxygen abundances are derived respectively from CO and H2O lines in the K band. They applied this method to Gl229A, the primary star of the brown dwarf companion, Gl229B. The derived abundances of Gl229A are logAc=-3.27+/-0.07 and logAo=-3.10+/-0.02, which are close to the classical values of the solar abundances of carbon and oxygen. We generate model spectra of Gl229B for the metallicity of Gl229A as well as for the classical solar metallicity. We find that the differences of the resulting spectra are not so large for the differences of the metallicity of 0.1 dex or so, but we now discuss the spectrum of Gl229B on the basis of the reliable metallicity. From the literature, the lower limit to the age of Gl229A is found to be 0.3Gyr. From the kinematics of Gl229A, we evaluate the upper limit to the age of Gl229A to be 3.0Gyr. The observed and model spectra are compared and goodness of fit is obtained in the range of model parameters, 750<Teff<1000K, and 4.5<logg<5.5. Among the candidates that satisfy the age constraint, the best combinations of model parameters are (Teff,logg)=(800K,47.5) and (850K,5.0), while acceptable combinations are (750K,4.75),(850K,4.75) and (900K,5.0).

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arXiv2015

Spectroscopic study of red giants in the Kepler field with asteroseismologically established evolutionary status and stellar parameters

Thanks to the recent very high-precision photometry of red giants from satellites such as Kepler, precise mass and radius values as well as accurate information of evolutionary stages are already established by asteroseismic approach for a large number of G-K giants. Based on the high-dispersion spectra of selected such 55 red giants in the Kepler field with precisely known seismic parameters (among which parallaxes are available for 9 stars), we checked the accuracy of the determination method of stellar parameters previously applied to many red giants by Takeda et al. (2008, PASJ, 60, 781), since it may be possible to discriminate their complex evolutionary status by using the surface gravity vs. mass diagram. We confirmed that our spectroscopic gravity and the seismic gravity satisfactorily agree with each other (to within ~0.1 dex) without any systematic difference. However, the mass values of He-burning red clump giants derived from stellar evolutionary tracks (~2-3 Msun) were found to be markedly larger by ~50% compared to the seismic values (~1-2 Msun) though such discrepancy is not seen for normal giants in the H-burning phase, which reflects the difficulty of mass determination from intricately overlapping tracks on the luminosity vs. effective temperature diagram. This consequence implies that the mass results of many red giants in the clump region determined by Takeda et al. (2008) are likely to be significantly overestimated. We also compare our spectroscopically established parameters with recent literature values, and further discuss the prospect of distinguishing the evolutionary status of red giants based on the conventional (i.e., non-seismic) approach.

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arXiv2014

Near Infrared Spectroscopy of M Dwarfs. II. H2O Molecule as an Abundance Indicator of Oxygen

Based on the near infrared spectra (R~20000) of M dwarfs, oxygen abundances are determined from the ro-vibrational lines of H2O. Although H2O lines in M dwarfs are badly blended each other and the continuum levels are depressed appreciably by the collective effect of numerous H2O lines themselves, quantitative analysis of H2O lines has been carried out by referring to the pseudo-continua both on the observed and theoretical spectra. For this purpose, the pseudo-continuum on the theoretical spectrum has been evaluated by the use of the recent high-precision H2O line-list. Then, we propose a simple and flexible method of analyzing equivalent widths (EWs) of blended features by the use of a mini curve-of-growth (CG), which is a small portion of the usual CG around the observed EW. The mini CG is generated by using the theoretical EWs evaluated from the synthetic spectrum by exactly the same way as the EWs are measured from the observed spectrum. The observed EW is converted to the abundance by the use of the mini CG, and the process is repeated for all the observed EWs line-by-line or blend-by-blend. In cool M dwarfs, almost all the oxygen atoms left after CO formation are in stable H2O molecules, which suffer little change for the uncertainties due to imperfect modelling of the photospheres. Then the numerous H2O lines are excellent abundance indicators of oxygen. The oxygen abundances are determined to be logAo between -3.5 and -3.0 in 38 M dwarfs. The resulting O/C ratios plotted against logAc appear to be systematically smaller in the carbon-rich M dwarfs, showing the different formation histories of oxygen and carbon in the chemical evolution of the Galactic disk. Also, O/Fe ratios in most M dwarfs are closer to the solar O/Fe ratio based on the classical high oxygen abundance rather than on the recently downward revised low value.

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arXiv2014

On the oxygen abundances of M 67 stars from the turn-off point through the red-giant branch

With an aim to examine whether the surface oxygen composition suffers any appreciable change due to evolution-induced mixing of nuclear-processed material in the envelope of red giants, abundance determinations for O/Fe/Ni based on the synthetic spectrum-fitting method were performed by using the moderate-dispersion spectra in the 7770-7792A region (comprising O I 7771-5, Fe I 7780, and Ni I 7788 lines) for 16 stars of the old open cluster M 67 in various evolutionary stages from the turn-off point through the red giant branch. We could not find any meaningful difference in the oxygen abundances between the non-giant group (T_eff > 5000 K) and the red-giant group (T_eff < 5000 K), which are almost consistent with each other on the average (despite that both have rather large dispersions of a few tenths dex caused by insufficient data quality), though only one giant star (S 1054) appears to show an exceptionally low O abundance and thus needs a more detailed study. This result may suggest that oxygen content in the stellar envelope is hardly affected (or changes are insignificant) by the mixing of H-burning products in the red-giant phase, as far as M 67 stars of low mass (~1.3 M_sun) are concerned, which is consistent with the prediction from the conventional stellar evolution theory of first dredge-up.

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arXiv2014

Can surface oxygen abundances of red giants be explained by the canonical mixing theory?

Extensive oxygen abundance determinations were carried out for 239 late-G/early-K giant stars of 1.5-5 M_sun by applying the spectrum-fitting technique to O I 7771-5 and [O I] 6300/6363 lines based on the high-dispersion spectra in the red region newly obtained at Okayama Astrophysical Observatory. Our main purpose was to clarify whether any significantly large (<~0.4-0.5 dex) O-deficit really exists in these evolved stars, which was once suspected by Takeda et al. (2008, PASJ, 60, 781) from the analysis of the [O I] 5577 line, since it (if real) is inexlainable by the current theory and may require the necessity of special non-canonical deep mixing in the envelope. We found, however, that the previous [O/H]_5577 results (differential abundances relative to the sun) were systematically underestimated compared to the more reliable [O/H]_7773 (from O I 7771-5 triplet lines) or [O/H]_6300 (from [O I] 6300 line) obtained in this study. Comparing the updated [O/Fe] ratios with the theoretically predicted surface abundance changes caused by mixing of nuclear-processed products dredged-up from the interior, we concluded that the oxygen deficiency in these red giants is insignificantly marginal (only by <~0.1 dex), which does not contradict the expectation from the recent theoretical simulation. This consequence of reasonable consistency between theory and observation also applies to the extent of peculiarity in [C/Fe] and [Na/Fe], which were also examined by reanalyzing the previous equivalent-width data of C I 5052/5380 and Na I 6160 lines.

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arXiv2014

Global Analysis of KOI-977: Spectroscopy, Asteroseismology, and Phase-curve Analysis

We present a global analysis of KOI-977, one of the planet host candidates detected by {\it Kepler}. Kepler Input Catalog (KIC) reports that KOI-977 is a red giant, for which few close-in planets have been discovered. Our global analysis involves spectroscopic and asteroseismic determinations of stellar parameters (e.g., mass and radius) and radial velocity (RV) measurements. Our analyses reveal that KOI-977 is indeed a red giant in the red clump, but its estimated radius ($\gtrsim 20R_\odot=0.093$ AU) is much larger than KOI-977.01's orbital distance ($\sim 0.027$ AU) estimated from its period ($P_\mathrm{orb}\sim 1.35$ days) and host star's mass. RV measurements show a small variation, which also contradicts the amplitude of ellipsoidal variations seen in the light-curve folded with KOI-977.01's period. Therefore, we conclude that KOI-977.01 is a false positive, meaning that the red giant, for which we measured the radius and RVs, is different from the object that produces the transit-like signal (i.e., an eclipsing binary). On the basis of this assumption, we also perform a light-curve analysis including the modeling of transits/eclipses and phase-curve variations, adopting various values for the dilution factor $D$, which is defined as the flux ratio between the red giant and eclipsing binary. Fitting the whole folded light-curve as well as individual transits in the short cadence data simultaneously, we find that the estimated mass and radius ratios of the eclipsing binary are consistent with those of a solar-type star and a late-type star (e.g., an M dwarf) for $D\gtrsim 20$.

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