arXiv:1110.4456v1 [astro-ph.SR] 20 Oct 2011
SUBMITTED TO APJS
Preprint typeset using LATEX style emulateapj v. 11/10/09
A REVISED EFFECTIVE TEMPERATURE SCALE FOR THE KEPLER INPUT CATALOG
MARC H. PINSONNEAULT1, DEOKKEUN AN2, JOANNA MOLENDA-˙ZAKOWICZ3, WILLIAM J. CHAPLIN4,
TRAVIS S. METCALFE5, HANS BRUNTT6
Submitted to ApJS
We present a catalog of revised effective temperatures for stars observed in long-cadencemode in the Kepler
Input Catalog (KIC). We use SDSS griz filters tied to the fundamental temperature scale. Polynomials for griz
color-temperature relations are presented, along with correction terms for surface gravity effects, metallicity,
and statistical corrections for binary companions or blending. We compare our temperature scale to the pub-
lished infrared flux method (IRFM) scale for VTJKsin both open clusters and the Kepler fields. We find good
agreement overall, with some deviations between (J − Ks)-based temperatures from the IRFM and both SDSS
filter and other diagnostic IRFM color-temperaturerelationships. For field dwarfs we find a mean shift towards
hotter temperatures relative to the KIC, of order 215 K, in the regime where the IRFM scale is well-defined
(4000 K to 6500 K). This change is of comparable magnitude in both color systems and in spectroscopy for
stars with Teffbelow 6000 K. Systematic differences between temperature estimators appear for hotter stars,
and we define corrections to put the SDSS temperatures on the IRFM scale for them. When the theoretical
dependenceon gravity is accounted for we find a similar temperature scale offset between the fundamentaland
KIC scales for giants. We demonstrate that statistical corrections to color-based temperatures from binaries are
significant. Typical errors, mostly from uncertainties in extinction, are of order 100 K. Implications for other
applications of the KIC are discussed.
Subject headings: stars: fundamental parameters
One of the most powerfulapplications of stellar multi-color
photometryis the abilityto preciselyinfercrucialglobalprop-
erties. Photometric techniques are especially efficient for
characterizing large samples and providing basic constraints
for more detailed spectroscopic studies. Modern surveys fre-
quently used filters designed for the Sloan Digital Sky Survey
(SDSS; Aihara et al. 2011), however, while traditional corre-
lations between color and effective temperature (Teff), metal-
licity ([Fe/H]), and surface gravity (logg) have employed
other filter sets, typically on the Johnson-Cousins system.
In An et al. (2009a, hereafter A09) we used SDSS photom-
etry of a solar-metallicity cluster M67 (An et al. 2008) to de-
fine a photometric ugriz–Teffrelation, and checked the metal-
licity scale using star clusters over a wide range of metal-
licity. This scale was applied to the Virgo overdensity in
the halo by An et al. (2009b). The approach used is sim-
ilar in spirit to earlier work in the Johnson-Cousins filter
system (Pinsonneault et al. 2003, 2004; An et al. 2007a,b);
the latter effort used the color-temperature relationships of
Lejeune et al. (1997, 1998) with empirical corrections based
on cluster studies.
1Department of Astronomy, the Ohio State University, Columbus, OH,
2Department of Science Education, Ewha Womans University, Seoul
120-750, Republic of Korea; firstname.lastname@example.org.
3Astronomical Institute, University of Wrocław, ul. Kopernika 11, 51-
622 Wrocław, Poland
4School of Physics and Astronomy, University of Birmingham, Edg-
baston, Birmingham, B15 2TT, UK
5High Altitude Observatory, National Center for Atmospheric Re-
search, Boulder, CO 80307, USA
6Department of Physics and Astronomy, Aarhus University, DK-8000
Aarhus C, Denmark
Casagrande et al. (2010, hereafter C10); it is based on
the infrared flux method (IRFM). There are a number of
advantages of this approach, as discussed in C10, but there
is a lack of native SDSS data in the stars used to define
the calibration itself.Fortunately, the color-temperature
relationships in C10 are defined for JHKscolors in the Two
Micron All Sky Survey (2MASS; Skrutskie et al. 2006), and
the Kepler mission provides a large body of high quality griz
photometry for stars in the 2MASS catalog (Brown et al.
In this paper we use griz data in the Kepler Input Cata-
log (KIC) in conjunction with 2MASS to compare the effec-
tive temperature scale for the griz colors to the IRFM scale.
For this initial paper we concentrate on the mean relation-
ships between the two systems for the average metallicity of
the field sample, taking advantage of the weak metallicity
dependence of the color-Teffrelationships that we have cho-
sen. In a follow-up paper we add information from spectro-
scopic metallicity and logg determinationsto compareempir-
theoretical relationshipsused in the current work. Unresolved
binaries and extinctionerrors can be severe problems for pho-
tometric temperature estimates, and another goal of this work
is to quantify their importance.
Another important matter, which we uncovered in the
course of our research, concerns systematic errors in the griz
photometryin the KIC. For large photometric data sets, it can
be difficult to assess such errors. Fortunately, we can also
compare photometry used in the KIC with photometry in the
same fields from the SDSS; the latter is important for numer-
ous applications of data derived from the Kepler mission. We
will demonstrate that there are significant systematic differ-
ences between the two, and derive corrections to minimize
We therefore begin with a discussion of our method in Sec-
2 Pinsonneault et al.
FIG. 1.— Long-cadence data from the KIC (top) and with our revised
SDSS-based effective temperature scale (bottom). Data are binned in 100 K
increment. Dwarfs with KIC logg > 3.5 (open histogram) are separated from
giants with lower logg (shaded histogram).
tion2. We comparethe SDSS andKIC photometryandderive
and SDSS/griz temperature scales are compared to the KIC
dwarf temperatures in Section 3, where we also discuss the
impact of unresolved binaries and uncertainties in the extinc-
tion estimates. Our revised catalog is presented in Section 4,
and we discuss the implications in Section 5.
Our basic data come from the long-cadence sample in the
KIC. From this we extracted a primary sample of dwarfs in
the temperature range where our calibrations are best con-
strained; our procedureis given in Section 2.1. We uncovered
some offsets between KIC and native SDSS photometry, and
describe correction terms in Section 2.2. Our methods for de-
riving color-temperature relationships in griz are described in
Sections 2.3 and 2.4.
We tookgriz photometryfromtheKIC (Brown et al.2011);
photometric uncertainties were taken as 0.01 mag in gri and
0.03 mag in z. Errors were taken from the quadrature sum of
uncertainties in the individual filters. JHKsphotometry was
taken from the All Sky Data Release of the 2MASS Point
Source Catalog (PSC; Skrutskie et al. 2006)7, and checked
against complementary information in the KIC itself.
For our sample we chose long-cadence targets in the KIC;
our initial source had 161,994 candidates. We selected stars
with griz photometry detected in all of the bandpasses. This
sample was nearly complete in the 2MASS catalog. We ex-
cluded a small number of sources with 2MASS photometry
quality flags not equal to AAA (N = 3,602) and stars with
colors outside the range of validity of either the IRFM or
SDSS scales (N = 11,830), leaving us with a main sample
of 146,562 stars. We then further restricted our sample by
excluding stars with logg estimates below 3.5 dex in the KIC
(N = 19,663) for a dwarf comparison sample of 126,899. We
illustrate the distribution of stars in the sample in 100 K bins
in Figure 1, both in the initial catalog (top panel) and the re-
vised one in this paper (bottom panel). We did not use the gi-
ants in our comparison of the dwarf-based temperature scale
(Section 3), but we do employ theoretical logg corrections
to the photometric temperatures for the purposes of the main
catalog (see Sections 3.2 and 4.2).
2.2. Recalibration of the KIC Photometry
We adopted three primary color indices (g − r, g − i, and
g−z)as ourtemperatureindicatorsfortheSDSS filtersystem.
A preliminary comparison of colors yielded surprising inter-
nal differences and trends as a function of mean Teffin the
relative temperatures inferred from these color indices (see
below). Because the A09 color-color trends were calibrated
using SDSS photometryof M67, this reflects a zero-pointdif-
ference between the KIC and SDSS photometry in the color-
color plane. It is not likely that this difference is caused by
extinction or stellar population differences because all three
colors have similar sensitivities to extinction and metallicity.
Initially, we suspected problems with the SDSS calibration
(see An et al. 2008, for a discussion of zero-point uncertain-
ties). However, the differences seen were outside of the error
bounds for the SDSS photometry. For a fraction of the tar-
gets (about2%) the temperaturesinferredfrom differentcolor
sources (SDSS versus IRFM from 2MASS colors) are also
discordant by more than three standard deviations, in some
cases by thousands of degrees in Teff. We examine both phe-
About10% of the stars in the Kepler field are coveredin the
most recent data release (DR8) of the SDSS imaging survey
(Aihara et al. 2011). There is an overlap in the two photomet-
ric sets at 14 ? r ? 18. We compare photometry for stars in
common in Figure 2. With a 1′′search radius, we found that
the median differences(in the sense of the SDSS minus KIC),
after rejecting stars with differences greater than 0.2 mag on
both sides, are ∆g = −0.040, ∆r = −0.028, ∆i = −0.045, and
∆z = −0.042.
Inspection of Figure 2 shows that these differences are also
functions of color. Solid lines are a linear fit to the data after
an iterative 3σ rejection. The linear transformation equations
are as follows:
gSDSS= gKIC+0.0921(g − r)KIC−0.0985,
rSDSS= rKIC+0.0548(r − i)KIC−0.0383,
iSDSS= iKIC+0.0696(r − i)KIC−0.0583,
zSDSS= zKIC+0.1587(i − z)KIC−0.0597,
wherethe subscriptsindicateeither SDSS orKIC photometry.
It is possible that the SDSS photometry in the Kepler field
has some zero-pointshifts with respect to the main SDSS sur-
vey database; the SDSS photometry pipeline can fail to work
properly if the source density is too high. To check this, we
comparedtheKIC andthe DAOPHOTcrowded-fieldphotom-
etry (An et al. 2008) in the NGC 6791 field. Although the
sample size is smaller, a comparison of DAOPHOT and KIC
photometry in the NGC 6791 field yields systematic offsets
in the same sense as the field mean in all band passes. Given
A Revised Effective Temperature Scale for the Kepler Input Catalog3
FIG. 2.— Photometry comparisons between SDSS (DR8) and the KIC in
the sense of the former minus the latter. Comparisons are shown in griz from
top to bottom panels. Solid lines are a linear fit to the residuals.
that the cluster fiducial sequence from DAOPHOT photome-
trymatches that froman independentstudy(Clem et al. 2008)
relatively well (An et al. 2008), it is unlikely that the offsets
seen in Figure 2 are due to zero-pointissues in the SDSS pho-
We also checked the standard star photometry in
Brown et al. (2011), which is originally from the SDSS DR1
photometryfor 284 stars outside of the Kepler field. We com-
pared with the SDSS DR8 photometry, but did not find the
aforementioned trends outside of those expected from ran-
dom photometric errors: the mean differences (SDSS minus
KIC values) were −0.009, −0.004, +0.004, and +0.012 mag
in griz, respectively, with an error in the mean of the order
of 0.001 mag. Therefore, revisions of the standard magni-
tude system (SDSS DR1 versus DR8) do not appear to be the
explanation either. We also investigated the possibility of a
zero-point difference between the faint and bright stars in the
KIC, which had different exposures. However, the internal
dispersion of the KIC temperature estimates is the same for
both samples. Regardless of the origin, the differences be-
tween the SDSS and KIC photometry are present in the over-
lap sample, and we therefore adjusted the mean photometry
to be on the most recent SDSS scale.
We do believe that unresolved background stars explains
the occasional cases where different colors predict very dif-
ferent temperatures. In Figure 2 there are many data points
that have KIC magnitudes brighter than the SDSS ones. We
attribute these stars to blended sources in the KIC. The mean
FWHM of SDSS images is 1.4′′, while that of KIC photome-
try is 2.4′′.
To check on this possibility, we cross-checked 13,284 stars
in common between DR8 of the SDSS and our KIC sample.
312 stars had a resolved SDSS source within 2.4′′, while 20
have 2 or more such blended sources. 2.5% of the stars would
therefore have resolved blends between the resolution of the
two surveys. If we assume that the space density of blends
is constant, we can use the density of blends to estimate the
fraction present even in the higher resolution SDSS sample.
When this effect is accounted for, we would expect 3.8% of
the KIC sources to have a blended star within the resolution
limit of the KIC. The average such star was 2.85 mag fainter
than the KIC target, sufficient to cause a significant anomaly
in the inferred color-temperaturerelationships. A comparable
fraction of the catalog is likely to have similar issues. A sig-
nificant contribution from background stars would in general
combine light from stars with different temperatures. As a
result, one would expect different color-temperature relations
to predict discordant values. We therefore assess the internal
consistency of the photometric temperatures as a quality con-
trol check in our revised catalog to identify possible blends
2.3. Base Model Isochrone
We adopted stellar isochrones in A09 for the estimation of
photometric temperatures. Interior models were computed
using YREC, and theoretical color-Teff relations were de-
rived from the MARCS stellar atmospheres model: see A09
and An et al. (2009b) for details. These model colors were
then calibrated using observed M67 sequences as in our ear-
lier work in the Johnson-Cousins system (Pinsonneault et al.
2003, 2004; An et al. 2007a,b). The empirical color correc-
tions in ugriz were defined using M67 at its solar metallicity,
and a linear ramp in [Fe/H] was adopted so that the color cor-
rections become zero at or below [Fe/H]< −0.8. Detailed test
on the empiricalcolor correctionswill be presentedelsewhere
(An et al. 2012, in preparation).
As a base case of this work, we adopted the mean metal-
licity recorded in the KIC of [Fe/H]= −0.2.
licity is comparable to, or slightly below, that in the so-
lar neighborhood.For example, the Geneva-Copenhagen
Survey (Nordstrom et al.2004) has a mean [Fe/H] of
−0.14 dex with a dispersion of 0.19 dex; a recent revision by
Casagrande et al. (2011) raises the mean [Fe/H] to −0.07 dex,
which is a fair reflection of the systematic uncertainties. The
bulk of the KIC dwarfs are about 100 pc above the galac-
tic plane, and thus would be expected to have somewhat
lower metallicity. In the following analysis, we assumed
[Fe/H]= −0.2 when using griz- or IRFM color-Teffrelation-
4Pinsonneault et al.
ships, unless otherwise stated.
Table 1 shows our base model isochrone at [Fe/H]= −0.2
and the age of 1 Gyr. All colors are color-calibrated as de-
scribed above. Note that the isochrone calibration is defined
for the main-sequence only; the relevant corrections for the
lower gravities of evolved stars are described separately in
Section 3.2. The SDSS photometry did not cover the main-
sequence turn-off region of M67 because of the brightness
limit in the SDSS imaging survey at r ∼ 14 mag. As a re-
sult, the M67-based griz color calibration is strictly valid at
4000≤ Teff≤ 6000 K (see Figure 17 in A09).
From Table 1 we derived polynomial color-Teff relations
of our base model for convenience of use. The following
relationship was used over the temperature range 4080 K
≤ Teff(YREC) < 7000 K:
where x represents g − r, g − i, or g − z, and a0–a5are coef-
ficients for each color index as listed in Table 2. Difference
in Teffinferred from these polynomial equations compared to
those found in Table 1 from interpolation in the full tables are
at or below the 6 K level.
In Table 3 we provide the metallicity sensitivity of the
color-Teffrelations in the model isochrones at several [Fe/H].
To generate this table, we compared 1 Gyr old isochrones
at individual [Fe/H] with our fiducial model (Table 1) at
[Fe/H]= −0.2 for each color index, and estimated the Teffdif-
ference at a given color (individual models minus the fiducial
isochrone). The Teffat a fixed color generally becomes cooler
at a lower [Fe/H]. We use the metallicity corrections in the
comparisons with spectroscopic Teffwhere we have reliable
[Fe/H] measurements (see Section 3.4), but do not apply cor-
rections to the KIC sample (see Sections 3.1 and 4.2).
2.4. Photometric TeffEstimation
The stellar parameters for the KIC were generated using a
Bayesian method (see Brown et al. 2011, for a discussion).
We adopt a less ambitious approach focused on KIC stars
identified as dwarfs. The three key assumptions in our work
are that we define Teffat a reference [Fe/H] and the model
logg (Table 1), and that we adopt the map-based E(B − V) in
the KIC as a prior. Within this framework we can then derive
independent temperature estimates from the griz photometry
and infer the random Tefferrors. Uncertainties in the extinc-
tion, the impact on the colors of unresolvedbinaries, and pop-
ulation (metallicity and logg) differences can then be treated
as error sources. In the latter case, we can compute correction
terms to be used if there is an independent method of mea-
surement. This approach is not the same as the one that we
have employed in earlier studies, so a brief justification is in
The traditional approach to photometric parameter estima-
tion is to take advantage of the fact that different filter combi-
nations respond to changes in metallicity and extinction. If
one has the proper template metallicity and extinction, for
example, the answers from the various colors will agree; if
not, the pattern of differences can be used to solve for them
(see An et al. 2007a,b). The particular problem for the KIC
is that the available filter combinations are insensitive to both
(seeAn et al. 2009b, fora discussionofgriz-basedestimates).
This is good from the point of view of temperature errors,
but unfortunate for those interested in photometric metallici-
ties. The temperature estimates in Lejeune et al. (1997, 1998)
FIG. 3.— Internal dispersion in Teffestimates (solid line) and differences
between the mean griz-based Teffand that inferred from g − r (long-dashed),
g − i (short-dashed), and g − z (dotted). Original KIC photometry is used in
the top panel, while corrected KIC photometry is used in the bottom panel.
are insensitive to logg near the main sequence, and the IRFM
scale in C10 does not include an explicit logg dependencefor
the temperatures. As a result, we believe that the most fruitful
approach is to define a benchmark temperature estimate. If
additional color information or spectroscopic [Fe/H] data be-
come available, the relevant corrections can be applied, and
we present methods below to do so (Section 3).
The KIC gravities for cool stars are precise enough to be
used as a basis for corrections to the temperatures, and we do
so in Sections 3.2 and 4.2. The KIC metallicities are more
problematic, and we do not use them for temperature correc-
tions. Insteadthe metallicity sensitivity is includedas an error
source in our effective temperature estimates.
We adopted the map-based KIC catalog extinction esti-
mates (AV) and the Cardelli et al. (1989) standard extinction
curves with AV= 3.1E(B − V). Extinction coefficients in griz
were derived in A09: Ag= 1.196AV , Ar= 0.874AV , Ai=
0.672AV, and Az= 0.488AV. We further took AJ= 0.282AV,
AH= 0.180AV, AKs= 0.117AV, and AVT= 1.050AV, where VT
represents the TychoV passband (An et al. 2007a).
For a given extinction-corrected set of griz magnitudes,
we searched the best-fitting stellar template in the model
isochrone for each star in the KIC. The mean Teff was ob-
tained by simultaneously fitting the models in griz, assuming
0.01 mag error in gri and 0.03 mag error in z. We also esti-
mated Tefffrom each of our fundamental color indices (g − r,
g − i, and g − z) to readily identify and quantify the internal
consistency of our temperature determination.
In Figure 3 we plot the internal dispersion and the mean
trendsofTefffroma givencolorindexwith respect to the aver-
age error-weightedtemperaturefrom griz for all of the dwarfs
in our sample. The top panel shows the case of the original
A Revised Effective Temperature Scale for the Kepler Input Catalog5
BASE ISOCHRONE AT [FE/H]=−0.2
g − rg − i
g − z
KIC data, and the bottom panel shows the one for the cor-
rected KIC photometry. The magnitude corrections described
in Section 2.2 were motivated by concordancebetween SDSS
and the KIC. Nevertheless, the results when using the recal-
ibrated KIC photometry as temperature indicators were ex-
Although the internal agreement is not complete, the re-
maining differences in the bottom panel of Figure 3 are com-
parable to the zero-point uncertainties discussed in An et al.
(2008). We view this as strong supporting evidence for the
physical reality of the magnitude corrections illustrated in
Figure 2. We therefore recommend that the zero-points of
the KIC photometry be modified according to equations 1–4.
In the remainder of the paper, we use magnitudes and colors
adjusted using these equations.
3. REVISED TEFFSCALE FOR THE KIC
We begin by evaluating the Teff inferred from the IRFM
and the SDSS systems for dwarfs. We then use open clusters
and comparisons with high-resolution spectroscopy to estab-
lish agreementbetween the two scales, indicatingthe need for
correction to the KIC effective temperatures. We then eval-
uate the impact of binaries, surface gravity, and metallicity
on the colors. We provide statistical corrections to the tem-
6 Pinsonneault et al.
COEFFICIENTS FOR POLYNOMIAL COLOR-TeffRELATIONS
g − rg − ig − z
NOTE. — Coefficients in equation 5. These cofficients are valid at 4080 ≤ Teff<
7000 K, or 0.13 < (g − r)0< 1.34, 0.13 < (g − i)0< 1.90, and 0.07 < (g − z)0< 2.21,
peratures caused by unresolved binary companions, as well
as corrections for logg and metallicity. We then perform a
global error analysis including extinction uncertainties and
the mild metallicity dependence of our color-temperature re-
lationships. The latter is treated as a temperature error source
because we evaluate all KIC stars at a mean reference metal-
licity ([Fe/H]= −0.2).
3.1. Temperature scale comparisons for dwarfs
We have three native temperature scales to compare: the
one in the KIC, our isochrone-based scale from griz (here-
after SDSS or griz-based scale unless otherwise stated), and
one from the (J − Ks)-based IRFM. Below we compare the
mean differences between them and compare the dispersions
to those expected from random error sources alone. We find
and SDSS scales are closer, but some systematic differences
between them are also identified. In this section, we examine
various effects that could be responsible for these differences,
and finish with an overall evaluation of the error budget.
We computed IRFM and SDSS Teff estimates assuming
[Fe/H]= −0.2. In terms of the temperature zero-point, adopt-
ing this metallicity led to small mean shifts (+20 K in J − Ks,
−40 K in the griz-based Teffestimate) relative to those which
would have been obtained with solar abundance. In the com-
parisons below we repeatedly clipped the samples, rejecting
stars with temperature estimates more than three standard de-
viations from the mean, until we achieved convergence. This
typically involved excluding about 1 % of the sample. Such
stars represent cases where the extinction corrections break
down or where the relative colors differdrastically from those
expected for single unblended stars.
Random errors were taken from the photometric errors
alone and yield a minimum error in temperature. For the
SDSS colors we also computed the internal dispersion in the
three temperature estimates from g − r, g − i, and g − z, and
used the larger of either this dispersion or the one induced
by photometric errors as a random uncertainty. Median ran-
dom errors for the SDSS and IRFM temperatures were 40 K
and 171 K, respectively. We then comparedstars at fixed KIC
those inferred from the IRFM, those inferred from griz, and
the scale in the KIC itself. For a limited subset of stars, we
also had Tycho photometry, and computed temperatures from
VT− Ks. This sample is small, so we used it as a secondary
In Figures 4–5 we illustrate the differences between KIC
and the IRFM and SDSS, respectively. For the IRFM scale in
Figure 4, we compare Tefffrom J − Ks. In Figure 5 we com-
pare the mean SDSS temperatures inferred from griz to that
FIG. 4.— Comparisons of the temperatures inferred from IRFM (J − Ks)
as a function of KIC Teff. The color coding indicates the logarithmic number
density of stars with a temperature and temperature difference at the indicated
point (see legend).
FIG. 5.— Same as in Figure 4, but from griz colors.
in the KIC. In both cases we see a significant zero-point shift,
indicating a discrepancy between the fundamental effective
temperature scale and that adopted by the KIC.
TheTefffromthe IRFM andthe SDSS fromindividualcolor
indices (g − r, g − i, and g − z) are compared in Figure 6. The
IRFM scale for the Tycho VT and 2MASS Ksis used in the
bottom right panel. The central result (that the KIC scale is
too cool) is robust, and can also be seen in comparisons with
high-resolutionspectroscopictemperatureestimates (see Sec-
tion3.4 below). InSection 4.2we providequantitativetabular
information on the statistical properties of the sample.
The two fundamental scales (IRFM and SDSS) are close,
but not identical, for cooler stars; they deviate from one an-
other and the KIC above 6000 K (on the SDSS scale). As dis-
cussedin Section3.6below,thetotal internaldispersioninthe
griz temperature estimates is also consistently larger for cool
stars than that expected from random photometric uncertain-
ties alone, and there are modest but real offsets between the
two fundamentalscales even forcool stars. We thereforeneed
A Revised Effective Temperature Scale for the Kepler Input Catalog7
TeffCORRECTIONS FOR DIFFERENT [FE/H]
g − r
g − i
g − z
NOTE. — The sense of the difference is the model Teffat a given [Fe/H] minus that of the fiducial metallicity, [Fe/H]= −0.2. The Teffat a fixed color generally becomes cooler at a
lower [Fe/H]. In other words, the above correction factor should be added to the SDSS Teff, if the metallicity effects should be taken into account.
to understand the origin of these differences and to quantify
the random and systematic uncertainties in our temperature
Open clusters provide a good controlled environment for
testing the concordance of the SDSS and IRFM scales. The
SDSS scale was developed to be consistent with Johnson-
Cousins-based temperature calibrations in open clusters, so
a comparison of the An et al. and IRFM Johnson-Cousins
systems in clusters will permit us to verify their underlying
agreement. As we show below, the two scales are close for
cool stars and exhibit modest but real systematics for the hot-
ter stars. For the reasons discussed in the following section,
we therefore adopt a correction to our SDSS temperatures for
hot stars, making the two photometricsystems consistent. We
can also check our methodology against spectroscopic tem-
perature estimates, and need to consider uncertainties from
extinction, binary companions, and metallicity. We therefore
begin by defining an extension of our method to giants, which
can be checked against spectroscopy. We then look at open
cluster tests, spectroscopic tests, binary effects, and the over-
all error budget.
3.2. Tests of the temperature scale for giants
OurYREC Teffestimates arebased oncalibratedisochrones
(Table 1), which do not include evolved stars. About 14% of
the KIC sample are giants and subgiants with logg ≤ 3.5 as
estimated in the KIC, so a reliable method for assigning ef-
fective temperatures to such stars is highly desirable. Fortu-
nately, this is feasible because the color-temperaturerelations
for the bulk of the long cadence targets are not strong func-
tions of surface gravity. For the purposes of the catalog we
therefore supplement the fundamental dwarf scale with theo-
retical corrections for the effect of surface gravity on the col-
Theoretical model atmospheres can be used to quantify the
logg dependence of the color-temperature relations by com-
paring the spectral energy distributions of dwarfs and giants.
Figure 7 shows color-temperature relations along a 1 Gyr so-
lar abundance isochrone for g − r, g − i, g − z, and J − Ks.
The model isochrone was taken from the web interface of the
Padova isochrone database (Girardi et al. 2002; Marigo et al.
2008)8. As seen in Figure 7 the model color-Teffrelations are
moderately dependent on logg, and illustrate that our photo-
metric Teffneeds to be adjusted for giants.
8Pinsonneault et al.
FIG. 6.— Differences in Teffbetween the IRFM and SDSS scales as a function of KIC Teff: Teff(g − r) vs. Teff(J − Ks) (upper left); Teff(g − i) vs. Teff(J − Ks)
(upper right); Teff(g − z) vs. Teff(J − Ks) (lower left); Teff(griz) vs. Teff(VT− Ks) (lower right). The color coding defines the logarithmic number density of points
with the indicated temperature and temperature difference (see legend for details).
logg sensitivities in griz colors from the ATLAS9 model at-
mosphere (Castelli & Kurucz 2004). We convolved synthetic
spectra with the SDSS ugriz filter response curves9, and inte-
gratedfluxwithweightsgivenbyphotoncounts(Girardi et al.
2002). Magnitudeswere then put ontothe AB magnitudesys-
tem using a flat 3631 Jy spectrum (Oke & Gunn 1983).
We created a table with synthetic colors from logg = 0.0
to 5.0 dex with a 0.5 dex increment, and from 4000 K to
6000 K with a 250 K increment at [M/H]=−1.0, −0.5, +0.0,
and +0.2. Because YREC Teffvalues were estimated at the
fiducial metallicity, [Fe/H]= −0.2, we interpolated the color
table to obtain synthetic colors at this metallicity.
that Castelli & Kurucz (2004) adopted the solar mixture of
Grevesse & Sauval (1998), as in our YREC isochrone mod-
els (A09), so we assumed [M/H] in Castelli & Kurucz (2004)
is the same as the [Fe/H] value.
Figure 8 shows the correction factors in Teffas computed
from synthetic colors as a function of colors in g − r, g − i,
and g − z. We used our base isochrone to compute ∆Teffat
∆logg = 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 dex, where ∆logg
represents the difference between YREC logg and the logg
in the KIC. The sense of ∆Teffis that giants with lower logg
than the base model generally tend to have lower Teff than
main-sequence dwarfs in the color range considered in this
(0.42 < g − r < 0.82), so that the theoretical ∆Teffbecomes
zero at Teff> 4800 K. Otherwise the amplitude of theoretical
Teffvariations on the blue side (g − r ? 0.6) would be similar
to that of the red colors. Althoughthis is not strictly true if the
∆logg is largeforblue stars, those stars are rare because stars
on the giant branch (with the largest ∆logg) have g − r ? 0.5
at near solar metallicity. The correction factors are tabulated
in Table 4.
The biggest ∆Teff in Figure 8 is ∼ 100 K. However, the
effects of the logg corrections are moderate in the KIC. If
we take the mean ∆Teffcorrection in g − r, g − i, and g − z,
the mean differencein Teffbetween KIC and YREC decreases
from 190 K to 166 K for stars with logg ≤ 3.5. The statisti-
cal properties of the SDSS giant temperatures are compared
with spectroscopic data in Section 3.4 and with the KIC in
3.3. Tests with Open Cluster Data
The IRFM technique provides global color-metallicity-Teff
correlationsusing field samples, while clusters give snapshots
at fixed composition, which define color-Tefftrends more pre-
cisely. Deviations from color to color yield the internal sys-
tematic within the system, as the color-temperature relation-
ships defined in An et al. (2007b) are empirical descriptions
ofactualclusterdata. TheA09SDSSsystem, byconstruction,
agrees with the An et al. (2007b) Johnson-Cousins system;
A Revised Effective Temperature Scale for the Kepler Input Catalog9
NOTE. — The sense of the difference is that a positive ∆Teffmeans a higher Teffat a lower logg.
aThe logg values in the YREC model.
but we can check the concordance between the two scales
within the open cluster system.
We have two basic results from this comparison. First,
J − Ksbased temperatures from the IRFM are different from
other IRFM thermometers. J − Ksis also the only IRFM di-
agnostic available for the bulk of the KIC sample. When we
account for this, the underlying IRFM system and the SDSS
system are in excellent agreement for stars below 6000 K.
Second, there is a systematic offset between the IRFM and
SDSS scales above 6000 K. We therefore correct the high end
temperature estimates for the SDSS to put them on the IRFM
scale, which yields an internally consistent set of photometric
Figures 9–11 show how the IRFM Teffdeterminations are
internally consistent in the Jounson-Cousins-2MASS system
in B − V, V − IC, V − Ks, and J − Ksusing stars in four well-
studied clusters: The Hyades (red circles in Figure 9), Prae-
sepe (blue triangles in Figure 9), the Pleiades (Figure 10),
and M67 (Figure 11). All of the stars shown in these fig-
ures are likely single-star members of each cluster after ex-
cluding known (unresolved) binaries. In Figure 11, we show
results based on the two independent sets of M67 photometry
from Montgomery et al. (1993, blue triangles) and Sandquist
(2004, red circles). The compilationand individualsources of
the cluster photometry can be found in An et al. (2007b).
To construct Figures 9–11 we corrected observed mag-
nitudes for extinction using E(V − IC)/E(B − V) = 1.26,
E(V − Ks)/E(B − V) = 2.82, and E(J − Ks)/E(B − V) =
0.53 (An et al. 2007a).Foreground reddening values of
E(B − V) = 0.000 ± 0.002, 0.006 ± 0.002, 0.032 ± 0.003,
10Pinsonneault et al.
FIG. 7.— Main-sequence (solid; logg > 3.5) and post-main-sequence
(dashed; logg ≤ 3.5) color-temperature relationships for models along a
1 Gyr isochrone with solar composition. Colors illustrated are g − z, g − i,
g − r, and J − Ks(from top to bottom).
and 0.041±0.004 mag were used for the Hyades, Praesepe,
the Pleiades, and M67 respectively (An et al. 2007b). The
IRFM Teffequations in C10 include metallicity terms, and we
adopted [Fe/H]= +0.13±0.01, +0.14±0.02, +0.04±0.02,
and +0.00±0.01 dex for the Hyades, Praesepe, the Pleiades,
and M67, respectively, based on high-resolution spectro-
scopic abundanceanalysis (see referencesin An et al. 2007b).
Only the (B − V)-based estimates are significantly impacted
by metallicity corrections, and the relative abundance differ-
ences in these well-studied open clusters are unlikely to be
substantial enough to affect our results.
The ±1σ error bars in Figures 9– 11 are those propagated
from the photometric errors only. Mean differences in the
IRFM Teff and the errors in the mean are provided in Ta-
ble 5. Global differences are shown for stars at 4000< Teff≤
7400 K, and those cooler and hotter than 6000 K are shown
in the table. The σsysrepresents a total systematic error in
this comparison from the reddening and metallicity errors
(summed in quadrature); however, systematic errors are less
important than random errors because of the precise E(B −V)
and [Fe/H] estimates of these well-studied clusters.
The low-mass stars in the Pleiades are known to have
anomalously blue colors related to stellar activity in these
heavily spotted, rapidly rotating, young stars (Stauffer et al.
2003). The temperatureanomalyfor B −V at Teff?5000K in
Figure 10, which is ∼200 K largerthan that for more massive
stars, reflects this known effect and therefore is not a proper
test of internal consistency in old field stars (such as those in
the KIC). The M67 data may also be inappropriatefor the test
of the IRFM internal consistency, but with a different reason.
Two independent photometry sets lead to a different conclu-
FIG. 8.— Theoretical Teffcorrections forvarious ∆loggvalues with respect
to the fiducial isochrones. Corrections from ∆logg = 0.5 to ∆logg = 3.0
with a 0.5 dex increment are shown. A linear ramp was used to define
smoothly varying ∆Teffover 4800 < Teff< 5800 K. The sense is that giants
with lower logg than the base isochrone tend to have lower Teff.
sion: Montgomery et al. (1993) photometry shows internally
less consistentIRFM TeffforM67stars thanSandquist(2004).
A similar argument was made in An et al. (2007b), based on
the differentialmetallicity sensitivities of stellar isochrones in
different color indices (see Figure 11 in the above paper).
Our cluster tests based on the Hyades and Praesepe demon-
stratethe internalconsistencyofthe C10color-Teffrelationsin
B −V,V − IC, andV − Ks. The meandifferencesin Teffamong
these color indices are typically few tens of degrees for both
hot and cool stars (Table 5). However, the (J − Ks)−Teffre-
lation tends to produce hotter Teffthan those from other color
indices for these cluster stars (see bottom panel in Figure 9).
The mean differencesbetween Teff(V − IC) and Teff(J − Ks) are
95 K and 44 K for the Hyades and Praesepe, respectively.
There is also a hint of the downturn in the comparison for the
hotstars in theseclusters, where(J −Ks)−Teffproducescooler
temperatures than (V − IC)−Teffrelation. The ∼ 100 K offset
between the hot and the cool stars roughly defines the size of
the systematic error in the IRFM technique of C10 in J − Ks.
The Pleiades stars show a weaker systematic Tefftrend for
the cool and the hot stars than the Hyades and Praesepe. In
spite of this good agreement, we caution that this could be a
lucky coincidence because the Pleiades low-mass stars prob-
ably have slight near-IR excesses in Ks(Stauffer et al. 2003).
The main-sequence turn-off of M67 is relatively cool, so the
difference is only suggestive.
The top panel in Figure 12 shows comparisons between
the IRFM and YREC Teff estimates. The former is based
A Revised Effective Temperature Scale for the Kepler Input Catalog11
STATISTICAL PROPERTIES OF CLUSTERS COMPARISONS
Cluster Data4000 < Teff≤ 74004000 < Teff≤ 6000 6000 < Teff≤ 7400
Teff(B − V,IRFM)− Teff(V − IC,IRFM)
Teff(V − Ks,IRFM)− Teff(V − IC,IRFM)
Teff(J − Ks,IRFM)− Teff(V − IC,IRFM)
Teff(V − IC,IRFM)− Teff(MV,YREC)
Teff(J − Ks,IRFM)− Teff(MV,YREC)
aSystematic errors from reddening and metallicity, summed in quadrature. In the comparisons between IRFM and YREC, we also include effects of the cluster age and distance
bMMJ=Montgomery et al. (1993); S04=Sandquist (2004).
on the (V − IC)−Teffrelation in C10, just as those used for a
principal Teffestimator in the above comparisons (Figures 9–
11). The YREC Teffwas estimated using An et al. (2007b)
isochrones, which have the same underlying set of interior
models as those used in the current analysis. The model
Teffwas computed at a constant MV of individual stars, as-
suming (m − M)0= 3.33± 0.01, 6.33 ± 0.04, 5.63± 0.02,
and 9.61±0.03 mag for the distance moduli of the Hyades
(550 Myr), Praesepe (550 Myr), the Pleiades (100 Myr),
and M67 (3.5 Gyr), respectively (see references in An et al.
Table 5 lists weighted mean differences between YREC
and IRFM Teff. The mean difference between the (V − IC)-
based IRFM and the luminosity-based YREC Teff for cool
stars (Teff< 6000 K) is less than 20 K, but the differences
rise above 6000 K to the 50 K level. The difference between
the (J − Ks)-based IRFM and MV-based YREC Teffshows dif-
ferent offsets for the cool and hot stars; this trend is consistent
with the abovecomparisonbetween (J − Ks)-based IRFM and
other IRFM determination.
The bottom panel in Figure 12 shows comparisonsbetween
the YREC Teffand the average IRFM Tefffrom B −V, V − IC,
and V − Ks. Our results using J − Ksas a thermometer are
consistent with our earlier finding in Section 3.1 that C10
(J − Ks)-based Teffvalues are systematically cooler than those
from the griz-based YREC models for hot stars (above about
6000 K). The (J − Ks)-based Teffdiffer both from other IRFM
diagnostics and the values inferred from SDSS colors for
cooler stars, while the mean values inferred from the IRFM
are close to SDSS for the cooler stars.
We therefore conclude that the cool star temperature scales
are consistent, while there is evidence for a systematic de-
parture at the hot end. A similar pattern emerges when we
compare with spectroscopy, as discussed in the next section.
Caution is therefore required in assigning errors for stars with
formal temperature estimates above 6000 K.
Systematic Teffdifferences are shown in Figure 13. The red
line represents the difference with the (J − Ks)-based IRFM
Tefffor the open cluster sample (Hyades and Praesepe), while
the orangeline shows that with respect to the mean IRFM val-
ues from B −V,V − IC,V − Ks. Error bars indicate ±1σ error
in the mean difference. The difference between the average
IRFM scale and the SDSS scale in the clusters is less than
25 K on average from 4000–6000K, which we take as a con-
servative systematic temperature uncertainty in that domain.
The differences are moderately larger for the IRFM J − Ks
temperature alone, but that diagnostic is also different from
other IRFM thermometers for cool stars.
The differences in the hot cluster stars reflect actual differ-
ences in the calibrations, not issues peculiar to the photome-
try, extinction, or blending. We therefore attribute the compa-
rable differences seen in the KIC stars (gray band) as caused
by calibration issues in J − Ksrather than as a reflection of
systematics between the IRFM and SDSS systems. Further-
more, the SDSS calibration was based on M67 data, where
the hotter turnoff stars (Teff> 6000 K) were saturated. As a
12 Pinsonneault et al.
FIG. 9.— Internal consistency of the IRFM Teffestimates for the Hyades
(red circles) and Praesepe stars (blue triangles). Comparisons are shown for
each color index with respect to the Teffvalues determined from V − ICat
[Fe/H]= 0.13 for the Hyades and [Fe/H]= 0.14 for Praesepe. Error bars rep-
resent ±1σ uncertainty propagated from photometric errors.
result, we believe that an adjustment closer to the IRFM scale
is better justified.
A simple correction term, of the form below
Teff,SDSS< 6000 K : Teff,corr= Teff(SDSS),
6000 K ≤ Teff,SDSS< 7000 K :
Teff,corr= 0.8 (Teff(SDSS)−6000 K)+6000 K,
Teff,SDSS≤ 7000 K : Teff,corr= Teff(SDSS)−200 K
brings the two scales into close agreement across their mu-
tual range of validity. This empirical correction is indicated
by the black dashed line in Figure 13. Below we find offsets
similar in magnitude and opposite in sign between the IRFM
and spectroscopictemperatures for hotter stars. Althoughthis
does not necessarily indicate problems with the fundamental
scales, it does imply that systematic temperature scale differ-
ences are important for these stars.
3.4. Comparison with Spectroscopy
Spectroscopy provides a powerful external check on the
precision of photometric temperature estimates.
scopic temperatures are independent of extinction, and can
be less sensitive to unresolvedbinary companionsand crowd-
ing. In this section we therefore compare the photometric
and spectroscopic temperature estimates for two well-studied
samples in the Kepler fields. Bruntt et al. (2011, hereafter
B11) reported results for 93 stars with asteroseismic data,
including 83 stars in our sample. Molenda-˙Zakowicz et al.
(2011, hereafter MZ11) reported results for 78 stars, includ-
ing 45 targets in common with our sample. The MZ11 data
FIG. 10.— Same as in Figure 9, but for the Pleiades at [Fe/H]= 0.04. Note
that low-mass Pleiades stars (Teff? 5000 K) are known to have anomalously
blue colors in B − V. These stars could also have slight near-IR excesses,
which may have affected Teffvalues from J − Ks.
FIG. 11.— Same as in Figure 9, but for M67 at [Fe/H]= 0.0. Red circles
and blue triangles represent comparisons based on the S04 and MMJ93 pho-
A Revised Effective Temperature Scale for the Kepler Input Catalog 13
FIG. 12.— The Teffcomparisons between IRFM and YREC for stars in
the Hyades (red circles) and Praesepe (blue triangles). Top: IRFM Tefffrom
V − IC. Bottom: Mean IRFM Tefffrom B − V,V − IC, andV − Ks. The YREC
Teffwas estimated from the luminosity (MV) of each star. Black line in the
bottom panel shows a moving averaged trend of the Teffdifference.
for cool stars are mostly subgiants and giants, while the bulk
of the dwarf sample is hotter than 6000 K. The B11 sample is
similarly distributed,with the transitionfromthe coolevolved
to the hot unevolved sample occurring at 5500 K.
All comparisons below are for the corrected photometric
scale, adjusted for concordance with the IRFM at the hot
end. We compare spectroscopic methods both with the fixed-
metallicity ([Fe/H]=−0.2) temperatures in the catalog and the
refined temperatureestimates made possible with the addition
of metallicity information and theoretical metallicity correc-
tions. We excluded outliers in the following statistical com-
parisons using a 3σ outlier rejection.
As demonstrated below, we find that the two spectroscopic
samples have different zero-points with respect to both the
SDSS and KIC samples, indicating the importance of system-
atic errors in such comparisons. The photometricscale for the
cool dwarfs and giants are in good agreement with the B11
scale, while both are offset relative to MZ11. The situation
is different for hot dwarfs. The IRFM scale was cooler than
the uncorrected SDSS scale. The spectroscopic samples are
cooler than both. We interpret this as evidence of additional
systematic uncertainties for the F stars, and discuss possible
The stellar parameters for the MZ11 sample were de-
rived using the Molenda-˙Zakowicz et al. (2007) template ap-
stars. The surfacegravity,effectivetemperature,andmetallic-
ity were derived from a weighted average of the five closest
spectral matches in the catalog. B11 used asteroseismic sur-
face gravities and derived effective temperatures from tradi-
tional Boltzmann-Saha consistency arguments.
We compare the spectroscopic and photometric tempera-
ture estimates in Figure 14. The top, middle, and bottom pan-
els compare spectroscopic temperatures to those of the KIC,
IRFM (J − Ks), and SDSS, respectively. Left panels show
els show those for giants (KIC logg ≤ 3.5). Filled circles are
the B11 data, while open circles are the MZ11 data. In total,
83 out of 93 sample stars in B11 were used in this compari-
son; the remaining 10 stars do not have griz photometry in all
passbands, so were not included in our KIC subsample. For
g − r >1.0. Triangles in the bottomtwo panels represent stars
estimates (Section 4.2.4). Error bars show the expected ran-
dom errors, with a 70 K error adopted in the temperature for
the individual B11 sample stars.
In the above comparisons, we corrected the IRFM tem-
perature estimates for the spectroscopic metallicity measure-
ment of each sample, although the Teff corrections in C10
were negligible (∆Teff≈ 18 K) in J − Ks. We also used in-
dividual stellar isochrones at each spectroscopic metallicity
to estimate SDSS Tefffrom griz, assuming a constant age of
1 Gyr at all metallicity bins. However, the net effect of these
corrections was small (∆Teff≈ 25 K), because griz-Teffrela-
tions are insensitive to metallicity and the mean metallicities
of the spectroscopic samples are close to our fiducial value
(?[Fe/H]? = −0.07±0.02 and −0.11±0.03 for the B11 and
MZ11 samples, respectively). The SDSS Teffvalues for giants
were correctedfor the logg differencefrom the dwarf temper-
ature scale as described in Section 3.2.
Both spectroscopic samples for dwarfs are systematically
average difference between the B11 sample and the KIC, in
the sense of the KIC minus spectroscopic values, is −170 K
with a dispersion of 116 K, after a 3σ outlier rejection. The
MZ11 sample is closer to the KIC, with a −82 K mean dif-
ference and a dispersion of 172 K. This difference of 88 K is
a reflection of the systematic errors in the spectroscopic tem-
perature scales. In the above comparisons, we did not include
stars with inconsistent SDSS temperature measurements (tri-
angles in Figure 14).
The weighted average difference between the B11 sample
and the SDSS (in the sense SDSS − Spec) for dwarfs is 85 K
with a 95 K dispersion, after excluding those flagged as hav-
ing discrepant Teff(YREC) values. If the metallicity correc-
tions to the SDSS values were not taken into account (i.e.,
based on models at [Fe/H]= −0.2), the mean difference be-
comes 73 K, but the dispersion increases to 111 K.
However, there is a strong temperature dependence in the
offset. Below 6000 K the mean difference is 50 K with a
dispersion of 47 K. For the hotter stars the mean difference
is 101 K with a dispersion of 118 K. The blue line in Fig-
ure 13 shows a moving averaged difference between the B11
spectroscopic values and SDSS Teffwithout the hot-end Teff
corrections (equations 6–8).
Although the size of the dwarf sample in MZ11 is small,
it is found that the effective temperatures are systematically
cooler than the SDSS values, with a weighted mean offset of
152 K (SDSS − Spec) and a dispersion of 175 K. The dif-
ference is temperature dependent, being 53 K for the stars
below 6000 K and 178 K above it. These differences are
3 K and 77 K larger, respectively, than the results from the
B11 sample. The temperature differences between photome-
between the spectroscopic measurements and the KIC, while
14Pinsonneault et al.
FIG. 13.— Systematic differences of various Teffestimates with respect to the YREC scale. Grey line shows the mean trend for the main KIC sample discussed
in this work. The red line represents the difference with the (J − Ks)-based IRFM Tefffor the open cluster sample (Hyades and Praesepe), while the orange line
shows that with respect to the mean IRFM values from B − V, V − IC, V − Ks. The blue line shows the trend for the B11 spectroscopic sample. Error bars in
all cases represent ±1σ error in the mean difference. Our adopted hot-Teffcorrections are shown with a black dashed line. Note that the empirical color-Teff
corrections in YREC are defined at 4000 ≤ Teff≤ 6000 K in SDSS colors.
there is a real difference at the hot end even when system-
atic differences between the two spectroscopic samples are
but their spectroscopic temperatures are consistent with both
IRFM and SDSS temperatures (see middle and bottom right
panels in Figure 14). On the other hand, the MZ11 sample
shows a large offset from IRFM (∆Teff= 245 K) and SDSS
(∆Teff= 206 K), while the KIC and the MZ11 values agree
with each other (∆Teff= 9 K).
The cool MZ11 stars are mostly subgiants and giants, while
the B11 cool sample includes a large dwarf population be-
tween 5000 K and 6000 K. The difference between the two
cool end results - good agreement with B11 for cool dwarfs,
but not with MZ11 - is real. This could reflect systematic
differences between the dwarf and corrected giant results for
the SDSS or the templates adopted by MZ11 for the evolved
and unevolved stars. The scatter between the MZ11 results
and the photometric ones is substantially larger than that be-
tween B11 and photometric temperature estimates. It would
be worth investigating the zero-point of the templates used in
the former method, as well as the random errors, in light of
the results reported here.
In the section above we have focused on differences be-
tween the scales; it is fair to ask how both might compare to
the true temperatures. The photometric scale is at heart sim-
ply an empirical relationship between color and the definition
of the effective temperature itself (L = 4πR2σT4
fore the scale itself should be sound where the photometric
relationsare well-defined. However,the photometricmethods
can fail if there is more than one contributor to the photome-
try, or if the reddeningis incorrectlymeasured. Spectroscopic
temperatures measure physical conditions in the atmosphere,
and are only indirectly tied to the fundamental flux per unit
area, which defines the effective temperature. There are also
systematic uncertainties between different methods for infer-
ring effective temperatures, for example, fitting the wings of
eff), and there-
strong lines, or the use of Boltzmann-Saha solutions based on
ionization and excitation balance. Finally, both photometric
and spectroscopic estimates are only as good as their assump-
tions; stars with large surface temperature differences will be
poorly modeled by both methods.
Our primary conclusion is therefore that the various dwarf
temperature methods, spectroscopic and photometric, are in
good agreement for the cooler stars. Systematic effects are
at or below the 50 K level. The hotter stars in the sample
have real systematic differences between spectroscopic and
photometric temperatures, and similar discrepancies are also
present between the photometric methods themselves. This is
further evidence that work is needed to tie down more pre-
cisely the temperature scale above 6000 K, and that larger
systematic errors should be assigned in this domain until such
an analysis is performed. We have less data for the giants,
but there does appear to be a real difference between the pho-
tometric results and the temperatures inferred for the MZ11
3.5. Effects of Binaries on Colors
Unresolved binaries in the sample could bias a color-based
Teff estimate.Unless the mass ratio of the primary and
secondary components in the binary system is close to ei-
ther unity (twins) or zero (negligible contributions from the
secondary), composite colors of the system are redder than
those from the primaries alone, leading towards systemati-
cally lower Teff. It is difficult to directly flag potential bina-
ries given the filters available to us, and as a result we do not
include star by star corrections in the table. However, such
a systematic bias will be important when evaluating the bulk
properties of the KIC sample. In this section, we therefore
estimate the size of the bias due to unresolved binaries in the
KIC, and provide statistical corrections for the effect of un-
resolved binary companions on average effective temperature
Binary contamination effects on the color-Teff relations
A Revised Effective Temperature Scale for the Kepler Input Catalog15 Download full-text
FIG. 14.— Comparisons of spectroscopic Teffwith KIC (top), IRFM from J − Ks(middle), and SDSS estimates from griz (bottom). Filled and open points are
from Bruntt et al. (2011) and Molenda-˙Zakowicz et al. (2011), respectively. Left panels show dwarf comparisons (KIC logg > 3.5), while the right panels show
giant comparisons (KIC logg ≤ 3.5). Triangles in the bottom two panels represent stars flagged as having internally inconsistent effective temperature estimates
were derived by performing artificial star tests. We used a
1 Gyr old Padova models at solar abundance (Girardi et al.
2004). Thesemodelsincludestellar masses downto 0.15M⊙,
allowing us to include low-mass systems outside the formal
range of the SDSS color calibration. The absolute color-Teff
relations in these models are not exactly the same as in our
base calibration. However, our main purpose is to evaluate
the relative temperature errors induced by companions,so the
effect of this offset is small.
We assumed a 50% binary fractions with 10,000 single
stars and 10,000 binary systems. Primary masses were ran-
domly drawn from a Salpeter mass function, while we ex-
plored three different choices for the relative masses of the
secondaries: Salpeter, flat, and one drawn from the open clus-
ter M35 (Barrado y Navascués et al. 2001). A flat mass func-
tion is expected for short-period binaries, which will be a mi-
nority of the sample; this is thus a limiting case. In the ar-
tificial star simulations, we derived empirical color-color se-
quences in g − i, g − z, and J − Kswith g − r as the principal
colorindex. We simulatedphotometricerrorsbyinjectingdis-
persions of 0.01 mag in gri, 0.03 mag in z, 0.024 mag in J,
and 0.028 mag in Ks. These 2MASS errors are median values
of the actual photometric errors in the KIC sample.
The result of these binary simulations is presented in Fig-
ure 15, which shows the mean deviations in g − i, g − z, and
J − Ksfrom those with primaries alone. For Figure 15 we fit-
ted a Gaussian for each g − r bin to estimate the mean color
offset and the uncertainty as shown by circles and error bars.
The three curves indicate results from three different relative
mass functions for secondaries.
The sizes of these color shifts are shown in Table 6.
The systematic color shift due to unresolved binaries is less
strongly dependent on the choice of secondary mass func-
tions. Typical sizes of these color shifts are ∼ 0.003 mag,
0.008 mag, and 0.010 mag in g − i, and g − z, and J − Ks, re-
spectively. To correct for the unresolved binaries in the KIC,
the above color shifts should be subtracted before estimating
Teff. The last four columns in Table 6 list the average Teffdif-
ference between a population with a 50% unresolved binary
fraction and that of primaries alone. The sense is that un-