Spectroscopy of Faint Kepler Mission Exoplanet Candidate Host Stars
Stellar properties are measured for a large set of Kepler Mission exoplanet candidate host stars. Most of these stars are fainter than magnitude, in contrast to other spectroscopic follow-up studies. This sample includes many high-priority Earth-sized candidate planets. A set of model spectra are fitted to optical spectra of 268 stars to improve estimates of T, log(g), and [Fe/H] for the dwarfs in the range K. These stellar properties are used to find new stellar radii and, in turn, new radius estimates for the candidate planets. The result of improved stellar characteristics is a more accurate representation of this Kepler exoplanet sample and identification of promising candidates for more detailed study. This stellar sample, particularly among stars with T K, includes a greater number of relatively evolved stars with larger radii than assumed by the mission on the basis of multi-color broadband photometry. About 26% of the modelled stars require radii to be revised upwards by a factor of 1.35 or greater, and modelling of 87% of the stars suggest some increase in radius. The sample presented here also exhibits a change in the incidence of planets larger than as a function of metallicity. Once [Fe/H] increases to , large planets suddenly appear in the sample while smaller planets are found orbiting stars with a wider range of metallicity. The modelled stellar spectra, as well as an additional 84 stars of mostly lower effective temperatures, are made available to the community.
The NASA Kepler Mission employs a space-based 0.95 m aperture Schmidt telescope to observe a single 115 square degree field of view and obtain nearly continuous light curve coverage for over 156,000 stars. The satellite was launched in March 2009 and began science observations in May 2009 with a primary mission objective of detecting the transits of small planets orbiting near the habitable zone of Sun-like stars (Borucki et al., 2010).
Once detrended for instrumental signatures and long-term stellar variations, the Kepler light curves are searched for transit signals that are vetted to eliminate likely false positives (transit-like signals due to causes other than transiting planets; see Batalha et al., 2010). The periodicity and amplitude of the transits provide initial estimates for orbital periods and sizes of candidate planets. However, these planet size estimates are derived from modeling the light curves with a parameter reflecting the planet-to-star radius ratio and so depend on the uncertainty of the radius of the host star. Understanding the properties of the host stars, especially stellar radii, is therefore critical to meeting many of the mission objectives. In order to identify the most promising candidates, refine knowledge of the host star properties, and identify additional false positives, a follow-up observing program was undertaken to obtain optical spectra of candidate host stars. The resulting spectra are fitted with models to determine the three stellar properties T, log(g), and [Fe/H]. These parameters are then used to revise the stellar and candidate planet radii. This program is one of several providing ground-based follow-up reconnaissance spectroscopy of candidate exoplanet host stars as part of the Kepler Follow-up Program (Gautier et al., 2010).
The target sample is described in §2, the observational methods in §3, and the data reduction in §4. In §5 model fits are used to determine the stellar properties T, log(g), and [Fe/H] along with an analysis of their uncertainties. These stellar parameters are used in §6 to find fits for each star on sets of isochrones and derive revised stellar and planetary radii. The results are discussed in §7 and presented in a table listing the stellar properties for 220 candidate exoplanet host stars. The public availability of the data are discussed in §8 and the findings from these data are summarized in §9.
2 Target Sample
The target stars are selected from a list of candidate exoplanet host stars known as Kepler Objects of Interest (KOIs) identified by the mission following a battery of tests that is designed to identify false positives. These tests include a manual inspection of each light curve and analysis of any pixel-level flux and centroid variations during the candidate transits (Batalha et al., 2010). Having passed the initial false positive identification tests unscathed, KOIs can be considered reasonable targets for planet characterization and confirmation as bona-fide planets using ground-based follow-up observations. At this point, the KOI list contains some unidentified false positives with a rate that depends on the system’s properties. Theoretical calculations have been used to predict the rate of false positives due to eclipsing binaries, especially cases where flux of a third star is blended with the eclipsing binary. Morton & Johnson (2011) predicted an overall false positive rate of 5% based on galactic structure models, the expected binary star population and eclipse depths. Later, Morton (2012) pointed out that because the KOI list still contains some candidates with V-shaped light curves, a higher false positive rate might be expected. Fressin et al. (2013) carried out a recent analysis that included simulating eclipsing binaries as background sources or as members of heirarchical triple systems and systems where true planets had their light curves blended with the flux of other stars. Their analysis predicted a higher overall false positive rate of 9.4% with a dependence on the presumed planet radius and galactic latitude. The highest false positive rate of 17.7% was predicted for giant planet candidates. Recent observational studies have also pointed toward a significant false positive rate. Santerne et al. (2012) conducted a radial velocity survey and estimated a 35% false positive rate among short-period giant planet candidates. Colón et al. (2012) used multi-color light curves to find two out of a sample of four short-period small planet KOIs were actually eclipsing binary stars, necessitating a comparably high false positive rate. Stellar classification spectroscopy can identify false positives in cases where stellar properties are found to be incorrect, however other types of observations are typically better suited to identifying individual false positive candidates.
Our spectra were most often the first follow-up observations taken of the faint stars of interest. Up to this point, these stars have normally been characterized based only on modelling of the broadband photometry contained in the Kepler Input Catalog, a ground-based survey of the Kepler field (KIC; Brown et al., 2011). The stellar properties determined in the KIC were designed to select optimal target stars for the mission prior to launch. The ideal target stars were small (ie. dwarfs) for which transits by a given size planet produce relatively large signals. The KIC allowed Kepler to select mostly small stars, but within the sample, stars exhibit a range of properties that are not always accurately determined.
A list of current active KOIs is maintained by the Community Follow-up Program (CFOP555https://cfop.ipac.caltech.edu/) and is continuously updated as the Kepler satellite observations are reduced and vetted for new candidates, or as follow-up observations help to identify some KOIs as false positives. The properties of the KOIs in our sample have likewise changed over the course of the mission. The highest priority targets, and those selected to be included in the sample, generally fall into one or more of the following categories: (1) KOIs that are requested for observation as part of an intensive study of a single star or a small number of host stars, (2) KOI stars that are candidates to be hosts of small planets (), (3) KOIs in which the candidate planets orbit in a predicted habitable zone, and (4) KOI stars that harbor multiple candidate planets.
Because the KOIs are also being pursued by other spectroscopic follow-up programs and we wish to avoid unnecessary overlap, we have also selected targets on the basis of apparent brightness. The target stars span an apparent brightness range , where is the Kepler bandpass magnitude (Brown et al., 2011). Figure 1 shows the magnitude distribution of our target sample along with the current set of KOI stars. It also includes the magnitude distribution of those stars with new stellar radius estimates (see §6). At the bright end of the magnitude range, , the follow-up coverage by other groups is fairly extensive (the Kepler Follow-up Program reported approximately 90% of these stars as having had spectral follow-up through the 2012 observing season). To our knowledge, our spectroscopic sample is by far the largest for candidate host stars of (). Such faint stars may prove too difficult or time consuming for other follow-up methods (e.g., highly precise radial velocity measurements), however they are quite important to the overall mission goals due to their large numbers (ie. two thirds of currently-active KOI stars have and two thirds of planet candidates with radii less than occur around these fainter stars). A full understanding of Kepler exoplanet statistics requires large follow-up studies of the faint stars, or at least those of highest priority. Finally, note that a few otherwise high priority targets are excluded from the observations due to visible crowding by other stars since the modelling described here is not designed for composite spectra.
Figure 2 shows distributions of planet orbital periods and radii for the same data sets, namely our sample and that of all KOIs. The entire KOI sample is dominated by planets smaller than . As Kepler obtains increasingly long time coverage light curves, the relative fractions of small planets and those in long-period orbits grows and the lower right hand regions in the plots of Figure 2, where habitable terrestrial planets may be located, are becoming increasingly well populated. As shown in Figure 2, the observed sample has a similar distribution to the entire KOI sample, but contains relatively fewer stars harboring large planets and relatively more candidates with long-period orbits.
We observed KOIs in the Kepler field (115 square degrees centered at , ) on 48 nights during using the National Optical Astronomy Observatory (NOAO) Mayall 4m telescope on Kitt Peak and the facility RCSpec long-slit spectrograph with one of its pixel CCDs (either T2KA or T2KB). The spectrograph configuration was the same on each observing run. The slit was 1.0 wide by 49 long and oriented with a position angle of 90. The KPC-22b grating in second order was used to disperse the spectra with 0.72 Å pixel at a nominal resolution of Å. The spectra covered a wavelength range between 3640Å and 5120Å, but were out of focus at both ends where the fluxes could not be reliably calibrated. The effective wavelength range was therefore reduced to a Å region. The scale along the slit in each spectrum was 0.69.
The observing procedure was basically the same each night. The telescope autoguider was used during each observation and each pointing began with an exposure of the instrument’s comparison arc lamp spectrum (HeNeAr or FeAr) for wavelength calibrations. Following that, normally a single exposure was taken of each target star. The exposure times ranged between 5 and 20 minutes for most KOIs, although a few required longer integrations due to faintness or poor observing conditions. The faintest targets requiring an exposure time exceeding 20 minutes were observed in two exposures to reduce the density of cosmic ray hits per exposure and aid in their removal during reduction. The KOIs or other stars (e.g., for flux calibrations) were all observed at an airmass of less than . At the high end of this airmass range, the atmospheric dispersion for objects in the Kepler field remained sufficiently parallel to the slit at the latitude of Kitt Peak, and permitted efficient operations at a single instrument rotation. At least one spectrophotometric standard star selected from Massey et al. (1988) or Stone (1977) was observed each night. Calibration data consisting of bias frames, quartz lamp flat field exposures, and comparison lamp exposures were taken during the daytime.
4 Data Reduction
The data reduction is primarily based on various IRAF666IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. packages for performing image reduction and the onedspec package for extracting and calibrating the spectra. The first step is reducing the sets of bias and quartz flat lamp exposures. The overscan bias level is subtracted from each bias frame and it is trimmed to a useful data section. These bias frames are averaged to create a master. The overscan bias level is subtracted from each flat field frame followed by any (residual) bias pattern in the master bias. The flat frames are then averaged while rejecting cosmic ray hits. We normalize this master flat by fitting a smooth curve to its shape along the dispersion axis (rows) and normalizing each row of the flat by this curve. Object spectra frames are reduced by subtracting the overscan bias, trimming them, and subtracting any residual bias pattern. They are then divided by the normalized flat field.
The onedspec package task doslit is the basis of spectral extraction and calibration using the spectrophotometric standard stars. To reduce the systematic trends that may result from the variation in telescope focus with wavelength across the spectrum (a significant effect with this spectrograph configuration), a relatively wide aperture is defined to extract each spectrum. This is based on a cut through the CCD column at where the stellar profile along the slit is broad and representative of the wavelength region used for much of the spectral modelling. We measure sky flux in regions extracted from both sides of the stellar spectrum, and subtract it. The aperture defined by the stellar spectrum is used to extract a comparison lamp spectrum for each object. A sensitivity function is found for each night based on the ratio of the standard star to its standard curve in the IRAF database of KPNO IRS standards and used to correct the science targets and supply a relative flux level. The comparison lamp spectra are used to determine wavelength as a function of columns in order to resample the spectra to a linear wavelength scale set to closely match the sampling of the 2-D spectra.
5 Stellar Characterization
5.1 Overview of the Stellar Characterization Methodology
We developed specialized software and procedures for this program. These are first used to find the basic stellar properties T, log(g), and [Fe/H], by fitting the observed spectra to theoretical model spectra (§5). Following that, stellar and planetary radii are estimated based on the best fits of the basic stellar properties to Yale-Yonsei isochrones in (§6).
The model-fitting methods employed here rely on comparisons between observed spectra and existing synthetic spectra calculated from stellar atmosphere models and line modelling codes. Model spectra are available from the literature on a grid of discrete values for T, log(g), and [Fe/H]. The process followed here finds the best physical properties for each observed spectrum by evaluating the rms of the residuals between the observed spectrum and each model. Following that, an interpolated value is found for each stellar property by evaluating the goodness-of-fit over the grid of models. Ideally, a best-fitting model spectrum could be identified for each star and the physical properties associated with the model would then be assigned to the star. In practice, the spectral models fail to accurately predict all of the features in the observed spectra and fits often need to be restricted to specific wavelength intervals containing features that are both well represented by the models and sensitive to the parameters being sought (e.g., see Valenti & Fischer, 2005). Furthermore, systematic errors in determining stellar properties can be introduced by errors in the relative spectral flux calibration and the discrete values of the model atmosphere sets. Errors in the stellar parameters can be correlated as well, complicating the situation.
In order to test the methods employed here and refine them to work on KOI stars, we observed a large number of “test stars” that have published stellar properties. Experimentation has shown that the fits can reproduce the relative stellar properties for these stars, but with systematic offsets from their literature values. The final fitting methods adopted are ones that best reproduced the literature values, once corrections for these systematic offsets were made. In essence, we adopted the test stars and their published properties as a standard set and worked to find methods that maximized the fitting precision.
The model fits are confined to a relatively narrow wavelength region at the long wavelength end of the spectra (see § 5.4). This region contains the important H absorption line, which is strong in the hotter stars of our sample. Its strength and profile is dependent on effective temperature and surface gravity. Multiple atomic metal lines are also present, the strongest ones are due to low ionization states of Fe, Cr, Mn, Ni, Ti and Mg. For cooler stars, a prominent broad molecular feature appears from MgH (near 4780Å) and eventually from TiO (near 4760Å) at the lowest temperatures. These features, and the range of stellar atmosphere conditions over which they are useful diagnostics, limit the stars that we can model using these procedures. During the fitting, the strength of the metal lines drives our estimate of [Fe/H], while the strength and profile of H is largely responsible for driving the fits of T and log(g). The strength of MgH is not very well represented in the synthetic spectra (Weck et al., 2003) nor does this feature appear to be particularly helpful for fitting the cooler range of our spectra where it appears. The stars that could be fit most effectively and for which we had representative test stars were dwarfs within the effective temperature range (approximate spectral types K2V through F0V) as discussed in §5.5. For this reason, only stellar properties for KOIs within this temperature range are reported here.
5.2 Model Spectra
The fits are based on a set of synthetic model spectra made publicly available by Coelho et al. (2005). These model spectra are calculated using their extensive line calculation codes along with the model stellar atmospheres of Castelli & Kurucz (2003). They represent predictions for non-rotating stars with relative metal abundances set to the solar values of Grevesse & Sauval (1998). The model set includes spectra calculated for stars that lie at discrete points on a 3-D grid defined by the parameters T, log(g), and [Fe/H]. The model spectra are calculated at wavelength steps of 0.02Å and with a range and spacing between adjacent values of each parameter as follows: T between 3500 K and 7000 K in steps of 250 K, log(g) between 1.0 and 5.0 in steps of 0.5, and [Fe/H] between and in steps of 0.5 with an additional set of models at [Fe/H].
5.3 Test Stars
The methods used to fit model spectra to the observations are the result of experiments fitting models to a set of spectra obtained for 44 test stars while attempting to reproduce the physical parameters previously published for these stars. These stars were representative of the majority of the KOIs we planned to target. Physical data taken from the literature for these stars is given in Table 1 along with the model fitting results discussed later. The test stars include a set of 20 exoplanet host stars characterized by the HATnet project (Bakos et al., 2002). The HAT stars are dwarfs ranging in T between 4591 K and 6600 K, log(g) between 4.13 and 4.63, and metallicities between and . Typical uncertainties in their stellar properties are 80 K for T, 0.04 in log(g), and 0.08 for [Fe/H]. The atmospheric parameters of these stars have been estimated by combining spectroscopic fits with light curve modelling. The properties T and [Fe/H] were found using the model atmospheres and line synthesis code provided by the software Spectroscopy Made Easy (SME; Valenti & Piskunov, 1996) and log(g) was found by modelling the transit light curve parameterized by the ratio of the orbital semi-major axis to the stellar radius, , in the manner of Sozzetti et al. (2007). A second set of 6 dwarfs from the work of Valenti & Fischer (2005) was observed. These stars ranged in T between 4969 K and 5903 K, log(g) between 3.97 and 4.85, and [Fe/H] between and based on SME and Kurucz (1992) ATLAS9 atmosphere models. Another set of 4 dwarfs are KOIs that had also been observed by other Kepler follow-up programs using high-resolution spectroscopy (labelled with KOI or Kepler designations). These programs utilized SME along with other constraints. We also observed a number of evolved stars, including a set of 5 giants in the Kepler field for which properties have been derived from astroseismological analysis (Kallinger et al., 2010) with updated results as determined in Kallinger et al. (2012). These stars ranged in T between 4153 K and 4893 K, log(g) between 1.66 and 3.27, and [Fe/H] between and . A set of 8 bright giants from Luck & Heiter (2007) was included. The stellar properties adopted for this work were those Luck & Heiter (2007) derived spectroscopically using Fe i and Fe ii lines. Their spectral line fits were based on MARCS (Gustafsson et al., 2003) atmosphere models and a variant of the MOOG line synthesis code (Sneden, 1973). These stars had properties determined from high-resolution spectroscopy and spanned a T range from 4605 K to 7000 K, a log(g) range from 2.49 to 3.31, and a [Fe/H] range from to . In addition to the giants, a single dwarf from Luck & Heiter (2007) is included.
5.4 Model-Fitting Method
To determine stellar properties for both our test stars and KOI stars, we apply an iterative method of fitting model spectra to our observations, finding one stellar atmosphere parameter at a time, and in many cases holding other parameters at fixed values until the best-fitting set of stellar properties is identified. First we describe the basic procedures common to every fitting iteration, and then follow that with the details of each iteration.
To prepare the model spectra, the model data of Coelho et al. (2005) are re-binned at a wavelength sampling of 0.3Å for calculation speed. Then, for each observed spectrum, the models are resampled onto the wavelength scale of the observed spectra and smoothed using a Gaussian kernel with a FWHM of 1.5Å to match the observed resolution. Next, based on experiment, a specific wavelength interval is chosen for each fitting step. The first procedure during each iteration is to find the cross-correlation function between the observed and model spectra, where the mean fluxes of both spectra have been subtracted. We use the location of the cross-correlation function peak to shift the model spectra to match the observations (correcting for any wavelength calibration errors and, to first order, any Doppler shift). Next, with the mean flux (F) of our observed spectrum normalized (but with no normalization relative to a continuum flux done), we scale the flux of each model spectrum to minimize the rms residuals of the fit. This scaling is done with either one or two free parameters:
Here, represents the model flux, the parameter A represents a simple scaling factor, and B an additional term that corrects slope differences between the observations and model. During some iterations, B is fixed at zero. The parameter B proved to be useful in our tests and probably removes systematic errors that might otherwise adversely affect the fits.
We apply the aforementioned procedures in the following step-by-step process:
An initial value for [Fe/H] is found by fitting over Å for the full set of models while including B as a free parameter. The value of [Fe/H] for the model having the minimum rms of fitting residuals is taken as an initial estimate.
An initial value of T is found by restricting our fits to models with [Fe/H] equal to that found in step 1. Here, the fit is done over the wavelength interval Å and B is fixed at zero. The value of T for the model having the minimum rms of the fitting residuals is taken as an initial estimate.
The spectrum is refit to find [Fe/H] in the manner of step 1, but this time the model set is restricted to include only those models having T equal to that found in step 2. See Figure 3 (top panel) for an example fit to the spectrum of KOI 2931 where [Fe/H] is determined to be dex during an application of this step.
The spectrum is refit to find T in the manner of step 2, but this time the model set is restricted to include only those models having [Fe/H] equal to that found by step 3. See Figure 3 (middle panel) for an example fit to the spectrum of KOI 2931 where T is determined to be K during an application of this step.
The value of log(g) is determined while holding fixed the values of [Fe/H] and T at the values found in steps 3 and 4 respectively. This best-fitting model represents the best gridpoint fit to the observed spectrum. See Figure 3 (bottom panel) for an example fit to find for KOI 2931 during the application of this step.
Finally, an interpolated value for each parameter is found as described below and illustrated in Figure 4 for the case of KOI 2931. First, each parameter is fitted in turn, keeping the values for the two parameters not being fit fixed to match their values in the model found in step 5. The set of models fit is thus a function of a single parameter. The rms values of the fitting residuals for these models are considered as a function of the parameter value. To find a minimum over a continuous distribution of the parameter value, a cubic spline is fit through these data points to locate the minimum. Then a set of points is selected surrounding this minimum and a quadratic function is fit through them. The minimum of the quadratic function is taken to be the interpolated parameter value. In cases where the minimum lies at the edge of the grid of parameter values, no interpolation can be done. The spectra in such cases are noted and their fits are treated with extra caution.
5.5 Calibrations Using Test Star Fits
As mentioned previously, the stellar properties derived from model fits such as those performed here are subject to systematic errors that are difficult to resolve. Instead of finding a fitting method free of such errors (which might not be possible), we have chosen to calibrate these errors based on fits to a set of test star spectra with the previously-published spectral properties described in §5.3. Once the systematic errors are properly calibrated, a post-fitting correction is possible. At the same time, this approach permits an estimate of the uncertainties in the final stellar properties.
The results of the model fits to the 44 test star spectra are given in Table 1. For each star, the previously-published properties are listed with their uncertainties. Following those are the values from the fits to our spectra (not yet corrected for the systematic errors we are attempting to quantify here). The columns under the heading “difference in values” list the value for each parameter from this work minus the previously-published value. To make the comparison, we plot the difference between our measured parameter and those from the other literature as a function of our parameter values. The results are shown in Figures 5, 6, and 7 for [Fe/H], T, and log(g) respectively. In each figure, the error bars represent the uncertainties quoted for the previously-published values. Note that in these figures, only some of the test star data are shown, namely a subset of 24 spectral fits that satisfy one or both of the following restrictions expressed in terms of the interpolated parameter values obtained during step 6 of the model fitting procedure:
The values of the parameter limits in equations 2 and 3 are chosen specifically so that after applying the corrections for systematic errors the same limits are expressed using convenient parameter values as discussed below. The reason that 20 of the 44 test star spectra are excluded from the fits is that when all of the data are plotted it became clear that only the stars falling within the restricted ranges in equations 2 and 3 behaved in a manner that would make accurate calibration possible. Furthermore, Equations 2 and 3 are chosen to exclude ranges in stellar properties that some KOIs may have, but which are not represented among our test stars. The parameters measured for stars outside of this range were either less accurate or exhibited large systematic deviations from their literature values. In any case, it is still possible to distinguish how the stars outside of this range differed from those inside the range (e.g., that they were cooler or had lower log(g)values).
All three of Figures 57 show that there are systematic trends in the differences between the parameter values fit here and the previously-published values. Note that there are stars among this set measured using different methods, but all lie along the same linear trends. To quantify these trends, an unbiased linear least squares fit to all of the points is found and shown in the figures. These fits lead to corrective relationships that can be used to place the measured stellar properties on a scale defined by the test stars:
Here, the corrected value of the parameter is labelled parenthetically with “(corr.)” and is expressed as a function of the uncorrected parameter obtained during step 6 of the method described if §5.4. Using equations 46, the range over which the corrections are applicable (ie. the range over which the spectral fits can be calibrated) can now be expressed in terms of the corrected stellar properties:
The scatter of points around the linear fits in Figures 57 provides an estimate for the uncertainties in the corrected stellar parameters. The distribution of the points around the linear fits can be described in terms of standard deviations, where dex for [Fe/H], K for T, and for log(g). The scatter reflects a combination of the uncertainties from the previous measurements and those presented here. To determine the contribution to the total uncertainty from the latter, one could determine an error on each parameter that, when added in quadrature to the uncertainties in the parameters quoted in the literature, would result in the linear fit having . To do this, the 1-sigma errors on the new parameter values would need to be , , and . Evidently for [Fe/H] and T the uncertainties quoted for the literature values tend to dominate the total uncertainty so that this method could underestimate the uncertainty of the new parameter fits. This may be the result of at least some of the uncertainties quoted in the literature having been overestimated. In contrast, for log(g), the contribution of the new uncertainties to the total error is larger and this method is useful to estimate the uncertainty.
However, since there may be unknown effects that could influence the fits, we have chosen to adopt a more conservative uncertainty on each measurement. The standard deviations of data around the fitted lines probably represents an upper limit to uncertainties within this well-characterized range of stellar properties. With that in mind, we have adopted a uncertainty of 75 K for T, 0.10 dex for [Fe/H], and 0.15 for log(g). The stellar properties of our modelled stars are given in Table 2 and referenced by KOI number and KIC identification number.
6 Revised Stellar and Planetary Radii
In total, 368 good quality spectra were obtained of 352 stars. From this master sample, 226 spectra for 220 stars had high enough quality, were not now known to harbor false positive planets, and had appropriate stellar atmospheric parameters to allow a new estimate of stellar radius and hence new estimates of exoplanet candidate radii. A total of 368 exoplanet candidates orbit these 220 stars. The Kepler magnitude distribution of these 220 stars is shown in Figure 1.
To begin, the 226 stellar spectra were separated into three [Fe/H] ranges: (), (), and (). Within each [Fe/H] range, measured effective temperature and surface gravity were used to estimate stellar luminosity using the so-called Version 2 Yale-Yonsei (YY) isochrones (Demarque et al., 2004) with solar abundance ratios (i.e. ) and [Fe/H] , , and , respectively, as provided in the on-line version777http://www.astro.yale.edu/demarque/yyiso.html. Stellar luminosity in solar units was estimated for a given (T,log(g)) estimate by determining the median stellar luminosity in the ranges T K and log(g) . Given the magnitude of the (T,log(g)) uncertainties, it was deemed appropriate to search the on-line YY Version 2 isochrone grid without further interpolation. Stellar radius in solar units was then estimated using the standard relation
Stellar radii uncertainties can be estimated in two ways. First, within the search box defined by the (T,log(g)) uncertainties, the standard deviation of the mean luminosity can be computed. The radii uncertainty was estimated as follows:
Second, 6 stars were observed at least twice and sometimes four times on separate nights during different observing runs separated by months. Stellar radius uncertainty can be estimated from the dispersion in stellar radius estimates from these individual observations. From both methods in combination, a conservative uncertainty for of is adopted.
The new stellar radii estimates are provided in Table 2. Only a portion of this long table is presented here. The entire table is made available in the electronic version. For stars observed multiple times, individual radii estimates were averaged into a single value. How do these new estimates compare to the best previous available radii estimates from the Kepler Science Analysis System (KSAS)888The KSAS was a Kepler Mission database storing the best available estimates for stellar and candidate planet properties. Stellar radii were based on KIC photometry for most stars in the magnitude range of interest here.? As Figure 8 illustrates, there is a formal offset towards larger radii estimates. The radii of 87% of these stars are revised upwards (and 13% downwards), although some of these revised radii are insignificant given the uncertainties in the stellar radii. For about 26% (58) of the stars, the revised radii are skewed upwards with . As Figures 8 and 9 illustrate, these stars tend to to be more evolved than the sample as a whole and relative to their properties listed by KSAS. In other words, it appears that many KIC stars are larger than previously assumed. In turn, exoplanet candidates orbiting those stars must be larger by the same relative amount.
Revised exoplanet candidate radii estimates can be derived from the revised stellar radii measurements from the simple geometric approximation:
where initial stellar and exoplanet radii come from KSAS. Stellar radii use solar units () while exoplanet candidate radii use Earth radius units (). The on-line Table 3 provides the revised exoplanet candidate radii.
Figure 10 compares revised exoplanet candidate radii to the characteristics of their host stars. As previously shown by Buchhave et al. (2012) and discussed in §7, exoplanet candidates with are much more likely to be associated with higher metallicity stars, while smaller exoplanet candidates are found around stars spanning the entire metallicity range of our sample.
The new stellar characteristics derived from this spectroscopic study have refined the properties of a large sample of KOIs, revealing statistical trends and identifying a number of individual KOIs as excellent targets for more detailed follow-up and potential confirmation as systems harboring small habitable zone planets.
In §6 we found that 26% of the KOI stars had radii significantly larger than their values based on the initial photometric data available to the mission. This effect could be due to systematic errors in the photometrically-derived stellar properties like log(g), selection effects in the magnitude-limited KOI sample, transit detectability dependence on stellar radius, or a combination of factors. In the case of these data, almost all of the stars with radii revised upwards by a factor of 1.35 or greater have T5200 K, and their positions on the log(g)log(T) plot of Figure 8 show that many represent a population of relatively evolved stars compared to the other stars of comparable effective temperature.
The lower log(g) values measured here may be compared to those of Verner et al. (2011) who used asteroseismic methods on the Kepler light curve data to determine radii for 514 solar-type stars in the apparent magnitude range . For stars with log(g) dex and a wide range of effective temperature, the mean asteroseismic log(g) values were 0.23 dex lower than those reported in the KIC. The corresponding stellar radii were larger as well. Another sample of stars with asteroseismic log(g) values was compared to KIC log(g) by Bruntt et al. (2012). They found asteroseismic log(g) values were lower than those in the KIC by an average of 0.05 dex. They attributed the lower mean difference with respect to the KIC to the inclusion of stars with log(g) in the sample, for which asteroseismic log(g) values are in better agreement. Verner et al. (2011) noted that their asteroseismic sample could be skewed by a Malmquist bias, which would preferentially select more evolved and intrinsically brighter stars, as well as by the improved detectability of the higher amplitude oscillations associated with stars of lower log(g). In the case of the spectroscopically analyzed sample presented here, the Malmquist bias would be in effect along with the counteracting bias favoring detectability of transits across smaller stars. These two biases were examined by Gaidos & Mann (2013) who predicted that the Malmquist bias would have the dominant effect, and the transit sample should be relatively overabundant in large stars compared to stars at the same temperature and apparent brightness. In addition to biases in the KOI sample as a whole, this spectroscopic sample was constructed to include many of the (relatively rare) smallest planet candidates for follow-up, a choice that may also select KOI stars with anomalous radii. It is clear that a full understanding of these biases is necessary to get better estimates for planet occurrence rates and that large, spectroscopic samples like the one presented here will play an important role. A similar spectroscopic study of “control” stars, perhaps Kepler stars showing no transits, may be of merit as well.
The revised values for stellar and planet radii have some implications for the mission goal to determine the frequency of Earth-sized planets orbiting Sun-like stars in a habitable zone. The radii of some planets must be revised significantly upwards, perhaps pushing them outside the size range likely for rocky Earth-like bodies. An additional effect is that higher luminosities implied by an increase in stellar radius move the habitable zones for these stars outwards from the star. As a consequence, the orbital periods of habitable zone planets must be longer.
Despite the apparent decrease in the number of small planets, these spectra provide additional evidence to favor certain candidates as among the most interesting targets for the goals of the Kepler Mission. An example candidate host star is KOI2931, the star shown in Figures 3 and 4. KOI2931 hosts a single known planet candidate, KOI2931.01, with an orbital period of 99.248 days. With new stellar properties T K, log(g), [Fe/H] and , the planet radius of KOI2931.01 is estimated to be 2.1 . The isochrone fit for this star corresponds to a stellar mass of and a planet equilibrium temperature of 326 K is found assuming an albedo of 0.3 and a circular orbit. KOI2931.01 is one example of a good candidate for a super-Earth orbiting in the habitable zone.
A correlation between the incidence of relatively large planet candidates and relatively high host star metallicity (selecting large planets at ) was previously seen spectroscopically in a smaller sample of brighter KOI stars by Buchhave et al. (2012). The KOI stars in their sample were almost all brighter than , but our and their data sets overlap in apparent brightness.
There are various ways to examine the significance of the apparent deficit of large planet candidates around low metallicity host stars ([Fe/H]) in this sample. First, note that 5 planet candidates in this sample (225.01, 998.01, 1067.01, 1226.01 and 1483.01) are all too large () while the remainder are reasonable sizes for planets (). These 5 objects are considered likely false positives and excluded from further consideration. This results in 46 candidate planets orbiting host stars of [Fe/H] and 317 orbiting host stars of [Fe/H]. A K-S test comparing the planet size distributions of the these two samples reveals a difference with a confidence level of 98%. As a second test, random subsamples of 46 candidate planets are drawn from the sample of 317 candidates orbiting host stars with [Fe/H] and compared to the 46 candidate planets orbiting lower metallicity stars. A set of 1 million random subsamples reveals that the most probable number of large planet candidates () orbiting high metallicity host stars is 8 or 9, and that 2 or fewer large planet candidates occur just 0.4% of the time (2 is the number of large planet candidates orbiting the low metallicity host stars).
A fraction of the candidate planet sample may be false positives and this effect is considered next. Note that 38 known or likely false positives have already been removed from the sample of 352 stars as part of creating the candidate planet sample, but others likely remain. Also, 243 out of 363 planet candidates are members of multi-planet systems and these have a very high likelihood of being true planets rather than eclipsing binary stars (Lissauer et al., 2012). However, multi-planet systems may still be considered false positives in the sense that their planet radii can be underestimated due to host star blending (Fressin et al., 2013). A detailed treatment might be useful to simulate the effects of false positives in the sample, but a simpler approach is taken here. If a liberal reduction is made to the sample size in an effort to simulate the removal of false positives, it will weaken inferences drawn from these data. Fressin et al. (2013) predict false positive rates in five planet size ranges: 17.7% for , 15.9% for , 6.7% for , 8.8% for and 12.3% for . When individual planets are removed from our sample at these rates, the K-S test signficance of the differences in planet size distribution on host star metallicity drops to 96%. The test of selecting random samples of high metallicity stars to match the sample size of the low metallicity stars reveals that 2 or fewer large planet candidates occur around high metallicity stars 1.7% of the time.
The tests show a dependence between host star metallicity and the occurance rate of large transiting planets, much like for the sample of Buchhave et al. (2012). It is not surprising to see a similar pattern in these data, but the fainter stars analyzed here probe a significantly larger volume of space, showing that these effects persist across the different stellar populations. The apparent threshold value of metallicity is chosen at [Fe/H] to match the appearance of the lower left panel in Figure 10, but the discrete and relatively sparse set of model spectra used to determine [Fe/H] may slightly distort this plot. The lines drawn at were also chosen by eye, but could have as well been taken at a somewhat smaller radius (ie. at ). There are no obvious trends in the incidence of planet candidates with with respect to either log(g) or T. Similarly, no dependence was found between metallicity and the number of planets detected around the KOI stars. Given the lack of large planets detected (in short period orbits) around low metallicity host stars, the efficiency of planet migration may be dependent on metallicity, or perhaps large planets simply cannot form around such stars at any orbital distance.
8 Data Availability
The reduced spectra and products from our model fits are made available on the CFOP website. The CFOP website organizes data for each KOI and confirmed Kepler exoplanets, including the products of many follow-up observations. The data products contributed from this spectroscopy program include the reduced spectrum data files, stellar properties, plots of the spectra, fitted synthetic models plotted alongside the observed spectra (similar to Figure 3) and plots similar to Figure 4 showing the interpolation between gridpoint fit values. Additional follow-up spectra and their fits will be added in the future.
A spectroscopic analysis of a large sample of stars known as Kepler Objects of Interest (KOIs) is presented. In the case of most of these KOIs, the stellar characterization, and by extension candidate planet properties, had been based on broadband photometry available from the pre-launch Kepler Input Catalog survey. Spectral follow-up, like that presented here, proves important to improve the accuracy of the KOI stellar properties, identify interesting individual planet systems and perform accurate statistical studies of the KOI list as a whole. The results of model spectra fits (values for T, log(g), and [Fe/H]) are given for 268 stars. Isochrone fits are used to provide revised radii for 220 KOI stars and their 368 planets. The spectra and results from this survey are made available to the public through the online CFOP archive.
The spectral and isochrone fits reveal that many of the KOI stars have larger radii than previously assumed. About 26% of the stars for which new radii were determined require corrections to their assumed radii of a factor of 1.35 or greater, and the isochrone fits for 87% of the stars suggest some increase in radius. The stars requiring the largest upward adjustment in radius represent a relatively evolved subset of the sample. The increases in stellar radii also require a reevaluation of the radii derived for the planet candidates hosted by these stars. The planet radii need to be scaled upwards by approximately the same ratio as their host stars.
Despite the fact that the revised planet radii are overall larger than previously assumed, there are candidate planets in this sample that are now better vetted and continue to be likely small planets in the habitable zone of Sun-like stars. The example of KOI2931 is presented as a good candidate for a super-Earth planet orbiting in the habitable zone of a 4991 K dwarf.
The frequency of large KOI planets in the sample depends on host star metallicity in a manner similar to that found for a sample of brighter KOI stars by Buchhave et al. (2012). The fainter, larger sample of K dwarf KOIs analyzed in our program shows that these results extend through a larger volume of space and that the occurrence of large planets () depends on a threshold metallicity near [Fe/H]. The large planet candidates are found almost exclusively around stars with metallicity higher than this value. In contrast, small planet candidates are found around stars spanning the full metallicity range examined in this study.
- Bakos et al. (2002) Bakos, G. Á., Lázár, J., Papp, I., Sári, P. & Green, E. M. 2002, PASP, 114, 974
- Bakos et al. (2007) Bakos, G. Á. et al. 2007, ApJ, 670, 826B
- Bakos et al. (2009a) Bakos, G. Á. et al. 2009a, ApJ, 696, 1950B
- Bakos et al. (2009b) Bakos, G. Á. et al. 2009b, ApJ, 707, 446B
- Bakos et al. (2011) Bakos, G. Á. et al. 2011, ApJ, 742, 116B
- Barclay et al. (2012) Barclay, T. et al. 2012, in prep.
- Batalha et al. (2010) Batalha, N. M. et al. 2010, ApJ, 713L, 103B
- Béky et al. (2011) Béky, B. et al. 2011, ApJ, 734, 109B
- Borucki et al. (2010) Borucki, W. J. et al. 2010, Science, 327, 977
- Brown et al. (2011) Brown, T. M., Latham, D. W., Everett, M. E., & Esquerdo, G. A. 2011, AJ, 142, 112
- Bruntt et al. (2012) Bruntt, H. et al. 2012, MNRAS, 423, 122
- Buchhave et al. (2010) Buchhave, L. A. et al. 2010, ApJ, 720, 1118B
- Buchhave et al. (2011) Buchhave, L. A. et al. 2011, ApJ, 733, 116B
- Buchhave et al. (2012) Buchhave, L. A. et al. 2012, Nature, 486, 375B
- Castelli & Kurucz (2003) Castelli, F. & Kurucz, R. L. 2003, in Proc. of the 210th Symposium of the IAU at Uppsala University, Uppsala, Sweden, 17-21 June, 2002. ed. by N. Piskunov, W. W. Weiss, & D. F. Gray. Published on behalf of the IAU by the Astronomical Society of the Pacific, A20
- Coelho et al. (2005) Coelho, P., Barbuy, B., Meléndez, J., Schiavon, R. P., Castilho, B. V. 2005, A&A, 443, 735
- Colón et al. (2012) Colón, K. D., Ford, E. B. & Morehead, R. C. 2012, MNRAS, 426, 342
- Demarque et al. (2004) Demarque, P., Woo, J.-H., Kim, Y.-C., Yi, S. K., 2004, ApJS, 155, 667D
- Doyle et al. (2011) Doyle, L. R. 2011, Science, 333, 1602D
- Fischer & Valenti (2005) Fischer, D. A. & Valenti, J. 2005, ApJ, 622, 1102
- Fressin et al. (2013) Fressin, F. et al. 2013, ApJ, 766, 81
- Gaidos & Mann (2013) Gaidos, E. & Mann, A. W. 2013, ApJ, 762, 41G
- Gautier et al. (2010) Gautier, T. N. et al. 2010, arXiv 1001.0352
- Grevesse & Sauval (1998) Grevesse, N. & Sauval, A. J. 1998, Space Sci. Rev., 85, 161
- Gustafsson et al. (2003) Gustafsson, B., Edvardsson, B. Eriksson, K., Mizuno-Wiedner, M., Jørgensen, U. G. & Plez, B. 2003, in ASP Conf. Proceedings Vol. 288, Stellar Atmosphere Modeling, ed. I. Hubeny, D. Mihalas & K. Werner (San Francisco: ASP), 331
- Hartman et al. (2009) Hartman, J. D. et al. 2009, ApJ, 706, 785
- Hartman et al. (2011a) Hartman, J. D. et al. 2011a, ApJ, 726, 52H
- Hartman et al. (2011b) Hartman, J. D. et al. 2011b, ApJ, 728, 138H
- Holman et al. (2010) Holman, M. J. et al. 2010, Science, 330, 51H
- Howell et al. (2012) Howell, S. B. et al. 2012, ApJ, 746, 123H
- Kallinger et al. (2010) Kallinger, T. et al. 2010, A&A, 522, A1
- Kallinger et al. (2012) Kallinger, T. et al. 2012, A&A, 541, 51K
- Kovacs et al. (2007) Kovács, G. et al. 2007, ApJ, 670L, 41K
- Kurucz & Avrett (1981) Kurucz, R. L. & Avrett, E. H. 1981, SAOSR, 391
- Kurucz (1992) Kurucz, R. L. 1992, in Proceedings of the 149th Symposium of the International Astronomical Union, The Stellar Populations of Galaxies, ed. B. Barbuy & A. Renzini (Dordrecht: Kluwer), 225
- Latham et al. (2009) Latham, D. W. et al. 2009, ApJ, 704, 1107L
- Lissauer et al. (2012) Lissauer, J. L. et al. 2012, ApJ, 750, 112L
- Luck & Heiter (2007) Luck, R. E., & Heiter, U. 2007, AJ, 133, 2464
- Massey et al. (1988) Massey, P., Strobel, K., Barnes, J. V. & Anderson, E. 1988, ApJ, 328, 315
- Morton (2012) Morton, T. D. 2012, ApJ, 761, 6
- Morton & Johnson (2011) Morton, T. D. & Johnson, J. A. 2011, ApJ, 738, 170
- Noyes et al. (2008) Noyes, R. W. et al. 2008, ApJ, 673L, 79N
- Quinn et al. (2012) Quinn, S. N. et al. 2012, ApJ, 745, 80Q
- Santerne et al. (2012) Santerne, A. et al. 2012, A&A, 545, 76
- Sneden (1973) Sneden, C. A. 1973, PhD Thesis, Univ. of Texas, Austin
- Sozzetti et al. (2007) Sozzetti, A., Torres, G., Charbonneau, D., Latham, D. W., Holman, M. J., Winn, J. N., Laird, J. B., O’Donovan, F. T. 2007, ApJ, 664, 1190
- Stone (1977) Stone, R. P. S. 1977, ApJ, 218, 767
- Torres et al. (2007) Torres, G. et al. 2007, ApJ, 666, L121
- Torres et al. (2010) Torres, G. et al. 2010, ApJ, 715, 458T
- Valenti & Fischer (2005) Valenti, J. A. & Fischer, D. A. 2005, ApJS, 159, 141V
- Valenti & Piskunov (1996) Valenti, J. A. & Piskunov, N. 1996, A&AS, 118, 595
- Verner et al. (2011) Verner, G. A. et al. 2011, ApJ, 738, L28
- Weck et al. (2003) Weck, P. F., Schweitzer, A., Stancil, P. C., Hauschildt, P. H. & Kirby, K. 2003, ApJ, 582, 1059
|Stellar properties from the literature||Values from this work||Difference in values|
|BD+05 3640||5104||44||4.85||0.06||-1.14||0.03||5079||4.01||-1.34||-25||-0.842||-0.196||Valenti & Fischer (2005)|
|HAT-P-2aaStar is one of 24 used to calibrate the model fits (see §5.5)||6290||110||4.21||0.09||0.12||0.08||6274||3.77||0.04||-16||-0.440||-0.080||Bakos et al. (2007)|
|HAT-P-3aaStar is one of 24 used to calibrate the model fits (see §5.5)||5185||46||4.58||0.04||0.27||0.04||5072||3.95||0.49||-113||-0.630||0.220||Torres et al. (2007)|
|HAT-P-4aaStar is one of 24 used to calibrate the model fits (see §5.5)||5860||80||4.14||0.04||0.24||0.08||5787||3.42||0.25||-73||-0.720||0.010||Kovacs et al. (2007)|
|HAT-P-6aaStar is one of 24 used to calibrate the model fits (see §5.5)||6570||80||4.22||0.03||-0.13||0.08||6487||3.97||-0.30||-83||-0.250||-0.170||Noyes et al. (2008)|
|HAT-P-8aaStar is one of 24 used to calibrate the model fits (see §5.5)||6200||80||4.15||0.03||0.01||0.08||6073||3.25||-0.10||-127||-0.900||-0.110||Latham et al. (2009)|
|HAT-P-10aaStar is one of 24 used to calibrate the model fits (see §5.5)||4980||60||4.56||0.02||0.13||0.08||4954||4.58||0.17||-26||0.020||0.040||Bakos et al. (2009a)|
|HAT-P-12||4591||60||4.61||0.01||-0.36||0.04||4391||4.21||-0.36||-200||-0.400||0.000||Hartman et al. (2009)|
|HAT-P-13aaStar is one of 24 used to calibrate the model fits (see §5.5)||5653||90||4.13||0.04||0.41||0.08||5639||4.15||0.50||-14||0.020||0.090||Bakos et al. (2009b)|
|HAT-P-14aaStar is one of 24 used to calibrate the model fits (see §5.5)||6600||90||4.25||0.03||0.11||0.08||6432||4.51||-0.16||-168||0.260||-0.270||Torres et al. (2010)|
|HAT-P-16aaStar is one of 24 used to calibrate the model fits (see §5.5)||6158||80||4.34||0.03||0.17||0.08||6005||3.88||0.16||-153||-0.460||-0.010||Buchhave et al. (2010)|
|HAT-P-18aaStar is one of 24 used to calibrate the model fits (see §5.5)||4803||80||4.57||0.04||0.10||0.08||4857||4.72||-0.05||54||0.150||-0.150||Hartman et al. (2011a)|
|HAT-P-19aaStar is one of 24 used to calibrate the model fits (see §5.5)||4990||130||4.54||0.05||0.23||0.08||5010||4.47||0.40||20||-0.070||0.170||Hartman et al. (2011a)|
|HAT-P-20||4595||80||4.63||0.02||0.35||0.08||4315||3.71||-0.02||-280||-0.920||-0.370||Bakos et al. (2011)|
|HAT-P-21aaStar is one of 24 used to calibrate the model fits (see §5.5)||5588||80||4.33||0.06||0.01||0.08||5544||3.86||0.10||-44||-0.470||0.090||Bakos et al. (2011)|
|HAT-P-22aaStar is one of 24 used to calibrate the model fits (see §5.5)||5302||80||4.36||0.04||0.24||0.08||5284||3.96||0.45||-18||-0.400||0.210||Bakos et al. (2011)|
|HAT-P-25aaStar is one of 24 used to calibrate the model fits (see §5.5)||5500||80||4.48||0.04||0.31||0.08||5478||4.08||0.50||-22||-0.400||0.190||Quinn et al. (2012)|
|HAT-P-26aaStar is one of 24 used to calibrate the model fits (see §5.5)||5079||88||4.56||0.06||-0.04||0.08||5029||4.25||0.06||-50||-0.310||0.100||Hartman et al. (2011b)|
|HAT-P-27aaStar is one of 24 used to calibrate the model fits (see §5.5)||5300||90||4.51||0.04||0.29||0.10||5314||4.25||0.50||14||-0.260||0.210||Béky et al. (2011)|
|HAT-P-28aaStar is one of 24 used to calibrate the model fits (see §5.5)||5680||90||4.36||0.06||0.12||0.08||5586||3.83||0.25||-94||-0.530||0.130||Buchhave et al. (2011)|
|HAT-P-29aaStar is one of 24 used to calibrate the model fits (see §5.5)||6087||88||4.34||0.06||0.21||0.08||5943||4.09||0.31||-144||-0.250||0.100||Buchhave et al. (2011)|
|HD3411||4657||100||2.59||0.10||0.31||0.17||4867||2.33||0.22||210||-0.260||-0.090||Luck & Heiter (2007)|
|HD7578||4715||100||2.64||0.10||0.24||0.17||4914||3.14||0.50||199||0.500||0.260||Luck & Heiter (2007)|
|HD8599||4957||100||3.11||0.10||-0.18||0.17||5022||2.66||0.06||65||-0.450||0.240||Luck & Heiter (2007)|
|HD23596aaStar is one of 24 used to calibrate the model fits (see §5.5)||5903||44||3.97||0.06||0.22||0.03||5783||3.49||0.26||-120||-0.480||0.040||Valenti & Fischer (2005)|
|HD172310aaStar is one of 24 used to calibrate the model fits (see §5.5)||5414||44||4.60||0.06||-0.42||0.03||5417||4.72||-0.58||3||0.120||-0.160||Valenti & Fischer (2005)|
|HD199442||4605||100||2.49||0.10||0.19||0.17||4777||2.34||0.17||172||-0.150||-0.020||Luck & Heiter (2007)|
|HD201891||5688||44||4.39||0.06||-1.12||0.03||5760||3.08||-1.13||72||-1.310||-0.010||Valenti & Fischer (2005)|
|HD204642||4733||100||2.90||0.10||0.08||0.17||4966||3.31||0.30||233||0.410||0.220||Luck & Heiter (2007)|
|HD210752||5835||44||4.37||0.06||-0.64||0.03||5761||3.36||-0.68||-74||-1.010||-0.040||Valenti & Fischer (2005)|
|HD211607||4992||100||3.17||0.10||0.13||0.17||5039||3.14||0.19||47||-0.030||0.060||Luck & Heiter (2007)|
|HD213619aaStar is one of 24 used to calibrate the model fits (see §5.5)||7000||100||4.29||0.10||0.04||0.17||6750||4.10||-0.61||-250||-0.190||-0.650||Luck & Heiter (2007)|
|HD216259||4969||44||4.81||0.06||-0.63||0.03||4793||4.16||-0.93||-176||-0.650||-0.300||Valenti & Fischer (2005)|
|HD219615||5003||100||2.83||0.10||-0.52||0.17||4923||1.99||-0.58||-80||-0.840||-0.060||Luck & Heiter (2007)|
|HD223869||4957||100||3.31||0.10||-0.02||0.17||5005||3.25||0.16||48||-0.060||0.180||Luck & Heiter (2007)|
|Kepler-9aaStar is one of 24 used to calibrate the model fits (see §5.5)||5777||61||4.49||0.09||0.12||0.04||5763||4.00||-0.07||-14||-0.490||-0.190||Holman et al. (2010)|
|Kepler-16||4450||150||4.65||0.00||-0.30||0.20||4062||3.45||-0.55||-388||-1.200||-0.250||Doyle et al. (2011)|
|Kepler-21aaStar is one of 24 used to calibrate the model fits (see §5.5)||6131||44||4.00||0.10||-0.15||0.06||5928||3.25||-0.20||-203||-0.750||-0.050||Howell et al. (2012)|
|KOI245aaStar is one of 24 used to calibrate the model fits (see §5.5)||5369||44||4.57||0.01||-0.34||0.04||5241||4.33||-0.55||-128||-0.240||-0.210||Barclay et al. (2012)|
|KIC1432587||4165||65||1.66||0.01||-0.02||0.18||4709||2.32||-0.18||544||0.660||-0.160||Kallinger et al. (2012)|
|KIC10777816||4893||64||3.27||0.00||-0.22||0.18||5020||2.86||-0.10||127||-0.410||0.120||Kallinger et al. (2012)|
|KIC12306763||4153||71||1.83||0.01||-0.23||0.18||4729||2.32||0.22||576||0.490||0.450||Kallinger et al. (2012)|
|KIC12470054||4830||79||3.15||0.00||-0.29||0.18||4961||3.24||0.36||131||0.090||0.650||Kallinger et al. (2012)|
|KIC12506577||4418||74||2.20||0.01||0.18||0.18||4735||2.22||-0.48||317||0.020||-0.660||Kallinger et al. (2012)|
|KOI||Kepler ID||22Uncertainty in log(g) is||33Uncertainty in [Fe/H] is||R44Uncertainty in R is R||notes|
Note. – Values in the notes column flag the following conditions: (a) ; (b) ; (c) and ; (d) and ; (e) ; (f) model fit reached a parameters limit (g) Now known to be a false positive.
|Planet ID||Parent star||log()|