KELT-7b: A hot Jupiter transiting a bright V=8.54 rapidly rotating F-star

2.3 MB·English

by  Allyson Bieryla

Draftversion May20,2015
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
KELT-7b: A HOT JUPITER TRANSITING A BRIGHT V=8.54 RAPIDLY ROTATING F-STAR
Allyson Bieryla1, Karen Collins2, Thomas G. Beatty3, Jason Eastman1,4, Robert J. Siverd4, Joshua Pepper6,
B. Scott Gaudi7, Keivan G. Stassun5,8, Caleb Can˜as1, David W. Latham1, Lars A. Buchhave1,9, Roberto
Sanchis-Ojeda10,11, Joshua N. Winn12, Eric L. N. Jensen13, John F. Kielkopf2, KimK. McLeod14, Joao Gregorio15,
Knicole D. Colo´n6, Rachel Street4, Rachel Ross4, Matthew Penny7, Samuel N. Mellon16, Thomas E. Oberst16,
Benjamin J. Fulton17,18, Ji Wang19, Perry Berlind1, Michael L. Calkins1, Gilbert A. Esquerdo1, Darren L.
5 DePoy20, Andrew Gould7, Jennifer Marshall20, Richard Pogge7, Mark Trueblood21, Patricia Trueblood21
1 Draft version May 20, 2015
0
2 ABSTRACT
y WereportthediscoveryofKELT-7b,atransitinghotJupiterwithamassof1.28±0.18MJ,radiusof
a 1.533+−00..004467RJ, andanorbitalperiodof2.7347749±0.0000039days. The brighthoststar(HD 33643;
M KELT-7)is anF-starwith V =8.54,T =6789+50 K,[Fe/H]=0.139+0.075,andlogg=4.149±0.019.
eff −49 −0.081
9 It has a mass of 1.535+−00..006564M⊙, a radius of 1.732+−00..004435R⊙, and is the fifth most massive, fifth
hottest, and the ninth brightest star known to host a transiting planet. It is also the brightest star
1
aroundwhichKELThasdiscoveredatransitingplanet. Thus,KELT-7bisanidealtargetfordetailed

characterizationgivenitsrelativelylowsurfacegravity,highequilibriumtemperature,andbrighthost
]
P star. The rapid rotation of the star (73±0.5kms−1) results in a Rossiter-McLaughlineffect with an
E unusually large amplitude of several hundred ms−1. We find that the orbit normal of the planet is
. likelytobewell-alignedwiththestellarspinaxis,withaprojectedspin-orbitalignmentofλ=9.7±5.2
h
degrees. This iscurrentlythe secondmostrapidlyrotatingstartohaveareflexsignal(andthus mass
p
determination) due to a planetary companion measured.
-
o Subject headings: planetary systems — stars: individual (KELT) techniques: spectroscopic, photo-
r metric
t
s
a
[ 1. INTRODUCTION Transiting planets that orbit bright host stars are

of great value to the exoplanet community. Bright
2
host stars are ideal candidates for follow-up because the
v
5 1Harvard-Smithsonian Center for Astrophysics, Cambridge, higher photon flux generally allows for a wider array
MA02138USA;email: [email protected] of follow-up observations, more precise determination of
6 2Department of Physics and Astronomy, University of physical parameters, and better ability to diagnose and
5 Louisville,Louisville,KY40292,USA control systematic errors. As a result, bright transit-
5 3Department of Astronomy and Astrophysics, Pennsylvania
ingsystemshaveproventobeimportantlaboratoriesfor
0 State University,UniversityPark,PA16801, USA
. 4Las Cumbres Observatory Global Telescope Network, 6740 studying atmospheric properties of the planets through
1 CortonaDrive,Suite102,SantaBarbara,CA93117, USA transmission and emission spectroscopy, for measuring
0 5Department of Physics and Astronomy, Vanderbilt Univer- the spin-orbitalignmentofthe planetorbits,andfor de-
5 sity,Nashville,TN37235,USA
6Department of Physics, Lehigh University, Bethlehem, PA terminingprecisestellarparameters(seeWinn(2011)for
1
18015, USA a review).
v: 7Department of Astronomy, The Ohio State University, 140 The Kilodegree Extremely Little Telescope (KELT)
W.18thAve.,Columbus,OH43210,USA
Xi 8Department of Physics, Fisk University, Nashville, TN transit survey (Pepper et al. 2007) was designed to de-
37208, USA tecttransitingplanetsaroundbright(8<V <10)stars.
r 9Niels Bohr Institute, University of Copenhagen, DK-2100, Very few (∼ 3%) of the known transiting planet host
a Denmark, and Centre for Star and Planet Formation, Natural stars are in this brightness range. This is because this
HistoryMuseumofDenmark,DK-1350Copenhagen
10Department of Astronomy, University of CaliforniaBerke- range spans the gap between radial velocity surveys on
ley,Berkeley,CA94720, USA the bright end, and the saturation limit of the majority
11NASASaganFellow of ground-based transit surveys on the faint end. The
12DepartmentofPhysicsandKavliInstituteforAstrophysics KELT-North (KELT-N) telescope targets this range us-
and Space Research, Massachusetts Institute of Technology,
ing asmall-aperture(42mm) camerawith a awide field
Cambridge,MA02139,USA
13Department of Physics and Astronomy, Swarthmore Col- ofviewof26◦×26◦. Itobserves13fieldsatdeclinationof
lege,Swarthmore,PA19081, USA 31.7 degrees, roughly equally spaced in right ascension,
14WellesleyCollege,Wellesley,MA02481,USA intotalcoveringapproximately40%oftheNorthernsky.
15AtalaiaGroupandCrow-Observatory,Portalegre,Portugal
16Westminster College,NewWilmington,PA16172, USA TheKELT-Nsurveyhasbeeninoperationsince2006and
17Institute of Astronomy, University of Hawaii at Manoa, candidates have been actively vetted since April 2011.
2680WoodlawnDrive,Honolulu,HI96822,USA The KELT-N survey has already announced four
18National ScienceFoundationGraduateResearchFellow
planet discoveries. KELT-1b (Siverd et al. 2012) is a
19YaleUniversity,NewHaven,CT06520,USA
20George P. and Cynthia Woods Mitchell Institute for Fun- 27MJ browndwarftransiting a V =10.7 F-star. KELT-
damental Physics and Astronomy, Texas A and M University, 2Ab (Beatty et al. 2012) is a hot Jupiter transiting the
CollegeStation, TX77843-4242, USA bright (V = 8.77) primary star in a visual binary sys-
21WinerObservaotry,Sonoita, AZ85637, USA
2 Bieryla et al
radial velocity surveys. There is a transition between
0.1 slowly and rapidly rotating stars known as the Kraft
break (Kraft 1970, 1967). Stars hotter than the Kraft
0.075 KELT-North
break around T = 6250K typically have higher rota-
eff
0.05 tion velocities, making precision radial velocities more
s difficult. These higher rotation velocities reflect the an-
t0.025
e gular momentum from formation, which is conserved as
g 0 the stars evolve due to the lack of convective envelope.
r
Ta0.075 California The lack of a convective envelope results in weak mag-
f Planet neticfieldsandineffectivemagneticbreakingfromstellar
o 0.05
winds (e.g., van Saders & Pinsonneault (2013)).
Survey
on0.025 6250K These points are illustrated in Figure 1, which shows
i the distribution of effective temperatures for the KELT-
t 0
c Nstellarsample,the sample ofstarstargetedby Kepler,
a
r0.075 Kepler and a representative radial velocity survey. The KELT-
F
0.05 N targets plotted here are all of the bright (V < 11)
putative dwarf stars in the survey which were selected
0.025
by a reduced proper motion cut and with temperatures
0 calculated from their J-K colors. Approximately 40,000
KELT-North targets (55%) are hotter than 6250K, 28
∗0.3
R of the CPS targets (2.3%) are hotter than 6250K, and
/ 0.2 approximately 20,000 of the Kepler targets (20%) are
Z
RC 0.1 hotter than 6250K.Also shownare theoreticalestimates
of the mass and radius of the convective envelope as a
0.0
function of T for stars with solar metallicity and an
eff
∗0.15 age of 1 Gyr (van Saders & Pinsonneault 2012), as well
M
as the upper envelope of observed rotation velocities as
/ 0.1
Z a function of T based from Reiners & Schmitt (2003).
C eff
M0.05 Hot stars pose both opportunities and challenges for
0.0 transit surveys. On the one hand, hot stars22 have
been relatively unexplored as compared to later spec-
i)s)75 tral types. The first transiting planet was discov-
(/
nm50 eredbyradialvelocitysurveys(Charbonneau et al.2000;
i
sk Henry et al. 2000), which initially targeted only late F,
V(25
G,andiearlyKstars. Duetothemagnituderangeofthe
0 starssurveyedandthe choice ofwhich candidates to fol-
8000 7000 6000 5000 4000
low up, the first dedicated ground-based transit surveys
Effective Temperature (K)
(Alonso et al.2004;McCullough et al.2006;Bakos et al.
2007; Collier Cameron et al. 2007) were also primarily
sensitive to late F, G, and early K stars. As the value
Figure 1. The top three panels show the effective temperature of transiting planets orbiting later stellar types was in-
distributionforthestarstargetedbytheKELT-Northtransitsur-
creasingly recognized, transit surveys began to survey
vey (Siverdetal. 2012), the California Planet Survey (CPS) ra-
dialvelocity(RV)search(Wrightetal.2004),andtheKeplermis- lower-mass stars. Kepler extended the magnitude range
sion (stars observed for all 16 quarters and with logg > 4.0 ac- oftheirtargetsampletofaintermagnitudes(Gould et al.
cording to Kepler Q1-Q16 Stellar Parameters Database a). The
2003; Batalha et al. 2010), in order to include a signifi-
fourth and fifth panels from the top show the relative depth
and mass of outer stellar convective zones at these temperatures cant number of M dwarfs. The Kepler K2 mission will
(vanSaders&Pinsonneault2012),whilethesixth, bottom, panel likely survey an even larger number of M stars than the
shows the observed stellar vsini distribution (Reiners&Schmitt prime mission (Howell et al. 2014). MEarth is specifi-
2003). Thereddashedlineat6250Kshowstheapproximateloca-
cally targeting a sample of some 3,000 mid to late M
tionoftheKraftBreak(Kraft1970).
ahttp://exoplanetarchive.ipac.caltech.edu, NASA Exoplanet dwarfs (Irwin et al. 2014). Finally, HAT-South is sur-
Archive veying even fainter stars than HATNet, in order to in-
crease the fraction of late G, K, and even early M stars
tem. KELT-3b(Pepper et al.2013)isahotJupitertran- (Bakos et al. 2013).
siting a V = 9.8 slightly evolved late F-star. KELT- As a result of this focus on later spectral types, the
6b (Collins et al. 2014) is a mildly-inflated Saturn-mass populationofclose-in,low-masscompanionsto hotstars
planet transiting a metal poor, slightly evolved late F- is relatively poorly assayed. This is particularly true for
star. stars which are both hot and massive; for example, only
Becauseofitsbrightermagnituderange,thesampleof 6 transiting planetary companions are known orbiting
host stars surveyedby KELT has a higher percentage of
luminousstarsthanmosttransitsurveys. Thisluminous
subsample includes giants, as well as hot main-sequence
22 In this paper, we will follow Winnetal. (2010) and define
stars and subgiants. Indeed, all five of the KELT-N dis-
hot stars as those with Teff > 6250K. This is also roughly the
coveries to date (including KELT-7b) orbit F stars with temperature of the Kraft break for stars near the zero age main
T > 6100K. Such hot stars are typically avoided by sequence(seeKraft(1967)andFigure1).
eff
Kelt-7b 3
stars with Teff > 6250K and M > 1.5M⊙.23 Build- However,evenacrudeupperlimitontheDopplerampli-
ing a larger sample is particularly important given ex- tude of a few kms−1 can then be used to exclude essen-
isting claims that the population of planetary and sub- tiallyallcompanionswithmassesinthe stellarorbrown
stellar companions to hot and/or massive stars is dif- dwarf regime. Thus, the Doppler upper limit, combined
ferent than that of cooler and less massive stars. In withthe RM measurement,essentiallyconfirms that the
particular, there is evidence that hot Jupiters orbit- companion is a planet, i.e. that is both mass and radius
ing hot stars tend to have a large range of obliqui- are in the planetary regime. Furthermore, the shape of
ties (Winn et al. 2010; Schlaufman 2010; Albrecht et al. theRMsignalallowsoneto measuretheprojectedangle
2012). Based on surveys of giant stars, whose progeni- between the planet’s orbital axis and the star’s rotation
tors are likely to be massive (Johnson et al. (2013), but axis. This projected obliquity provides clues to the for-
see Lloyd (2013)), there have also been claims that the mation and evolution (Albrecht et al. 2012) history of
distribution of Jovian planetary companions is a strong hot Jupiters and substellar companions. This effect also
function of primary mass (Bowler et al. (2010), but see provides an independent measurement of the rotational
e.g. Maldonado et al. (2013)). Finally, there is anecdo- velocity of the star.
talevidencethatmassivesubstellarcompanionsaremore In this paper, we describe the discoveryand confirma-
commonaroundstarswithT >∼6200K(Bouchy et al. tion of a hot Jupiter transiting the bright V =8.54 star
eff
2011). HD 33643, which we designate as KELT-7b. In Section
Thechallengesposedbyhotstarsareprimarilydue to 2,wesummarizethediscoveryphotometrictransitsignal
the high rotation velocities. The large rotation veloci- and the follow-up photometric and spectroscopic obser-
ties of hot stars result in broad and weak lines, making vations. In Section3, we discuss the analysisofthe data
precision radial velocity difficult. As a result, radial ve- obtained to determine stellar and planetary parameters.
locitysurveys,andtoalesserextenttransitsurveys,have Section 4 considers the false positive scenarios and Sec-
avoidedtargeting, or following up candidates from, such tion 5 discusses the results of this analysis.
stars. Furthermore, for a fixed planet radius, the depths
of planetary transits of hotter stars are shallower. This 2. DISCOVERYANDFOLLOW-UPOBSERVATIONS
is exacerbated by the fact that stars with Teff > 6250K 2.1. KELT Observations and Photometry
have lifetimes that are of order the age of the Galactic
The KELT-N survey has a standard process of data
disk, and thus tend to be significantly evolved.
reduction which will be briefly described in this section.
However, there a number of ways in which these chal-
For more information see Siverd et al. (2012). KELT-7
lenges are mitigated for transit surveys. First, even
is in KELT-N survey field 04, which is centered on (α=
though the transit depths are shallower, they are nev-
05h:54m:14.71s, δ = +31d:39m:55.10s;J2000). Field
ertheless greater than a few millimagnitudes, and thus
04 was monitored from 2006 October 26 to 2011 April 1
readily detectable for Jovian-sized companions. There-
collectingabout7800images. TheKELT-7lightcurvein
fore, identifying such candidate transit signals is possi-
particularhad7745pointsafterasingleroundofiterative
bleevenformain-sequencestarsashotas7000K.Oncea
3σ outlier clipping that occursjust after the trendfilter-
candidatesignalisidentified,itsperiodcanbeconfirmed
ingalgorthm(TFA)(Kov´acs et al.2005). Wereducedthe
with photometric follow-up. With a robustephemeris in
raw survey data using a custom implementation of the
hand, radialvelocity follow-upis greatly eased,as one is
ISIS image subtraction package (Alard & Lupton 1998;
simplylookingforareflexvariationwithaspecificperiod
Alard 2000), combined with point-spread-function pho-
and phase (as opposed to searching over a wide range of
tometry using DAOPHOT(Stetson 1987). Using proper
theseparameters,whichincreasestheprobabilityoffalse
motions from the Tycho-2 catalog (Høg et al. 2000) and
positives). Evenwiththerelativelypoorprecision(afew
J andH magnitudesfrom2MASS(Skrutskie et al.2006;
100 ms−1) of radial velocity measurements of hot stars,
Cutri et al. 2003), we applied a reduced proper motion
itispossibletoexcludestellarcompanionsanddetectthe
cut (Gould et al. 2003) based on the implementation of
reflexmotionofrelativelymassiveplanetaryandsubstel-
methods from Collier Cameron et al. (2007). This al-
lar companions.
lowed us to select likely dwarf and subgiant stars within
Ultimately, however, it is precisely the high rotation
the field for further post-processing and analysis. We
velocities of hot stars that assist in robust confirmation
applied the TFA to each selected light curve to re-
of planetary transits, via the Rossiter-McLaughlineffect
move systematic noise, followed by a search for tran-
(RM) (Rossiter 1924; McLaughlin 1924). The rotating
sit signals using the box-fitting least squares algorithm
host star allows one to measure the spectral aberration
(BLS) (Kov´acs et al. 2002). For both TFA and BLS
of the absorptionlines due to the small blockage of light
we used the versions found in the VARTOOLS package
as the planet transits the rapidly rotating host. The
(Hartman et al. 2008).
magnitude of this effect can be directly predicted by the
Oneofthecandidatesfromfield04wasstarHD33643
rotationvelocitymeasuredfromthespectrum,combined
/2MASS05131092+3319054/TYC2393-852-1,located
with the transit depth and shape. The RM effect can
at(α=05h:13m:10.93s,δ =+33d:19m:05.40s;J2000).
thereforeprovidestrongconfirmationthatthetransitsig-
The star has Tycho magnitudes B = 9.074 and V =
nalisduetoaplanetary-sizedobjecttransitingthetarget T T
8.612 (Høg et al. 2000) and passed our initial selection
star. However, for Jupiter-sized companions, this does
cuts. The discovery light curve of KELT-7 is shown in
not necessarily confirm the planetary nature of the oc-
Figure 2. We observed a transit-like feature at a period
cultor,becauselow-massstars,browndwarfs,andJovian
of 2.7347749days, with a depth of about 8.28 mmag.
planetsallhaveroughly∼R (Chabrier & Baraffe2000).
J
2.2. Follow-up Time Series Photometry
23 Accordingtohttp://exoplanets.org
4 Bieryla et al
We obtained follow-up time-series photometry of
1.04 KELT-7tocheckforfalsepositivesandbetterdetermine
the transit shape. We used the Tapir software package
1.03
(Jensen2013) to predict transitevents,and we obtained
1.02 10 full or partial transits in multiple bands between Oc-
tober 2012 and January 2014. All data were calibrated
1.01
Intensity1.00 CanoWdlliepnrosobectteasaisnle.ed,diunosnipnergefupthl.l)eturAansnltesrsiotsIomoftahKgeEerJwLiTpsae-7cskbtaaigntee2td4h.e(AgI-bJ;anKd.
0.99
onUT2012-10-04atthe University ofLouisville’s Moore
0.98 Observatory. We used the 0.6 m RC Optical Systems
(RCOS)telescopewithanApogeeU16M4Kx4KCCD,
0.97
giving a 26′ x 26′ field of view and 0.39 arcsec pixel−1.
0.96
−0.4 −0.2 0.0 0.2 0.4 WeusedKeplerCamonthe1.2mtelescopeattheFred
Orbital Phase
Lawrence Whipple Observatory (FLWO) to observe two
Figure 2. Discovery light curve of KELT-7b from the KELT-N fullz-bandtransitsonUT2012-10-23andonUT2012-11-
telescope. Thelightcurvecontains7745observationsspanning4.5
03. Wealsoobservedapartialg-bandtransitonUT2012-
years, phase folded to the orbital period of P = 2.7347749 days.
The red line represents the same data binned at 1 hr intervals in 11-22. On the night of UT2013-10-19we observed a full
phase. i-band transit in combination with radial velocity ob-
servations to measure the RM effect (described more in
Section 2.3). KeplerCam has a single 4K x 4K Fairchild
CCD with 0.366 arcsec pixel−1 and a field of view of
′ ′
23.1 x 23.1 . The data were reduced using procedures
outlinedinCarter et al.(2011),whichusesstandardIDL
1.20
routines.
We observeda full transit in g-band on UT2012-11-14
MOR UT 2012-10-04 (g) and a partial transit in i-band on UT2014-01-23 from
the Byrne Observatory at Sedgwick (BOS), operated
by Las Cumbres Observatory Global Telescope Network
KEPCAM UT 2012-10-23 (z)
(LCOGT). BOS is a 0.8 m RCOS telescope with a 3K
1.15 x 2K SBIG STL-6303E detector. It has a 14.7′ x 9.8′
KEPCAM UT 2012-11-03 (z) field of view and 0.572 arcsec pixel−1. Data on the
night of UT2012-11-14 were reduced and light curves
were extracted using standard IRAF/PyRAF routines
BOS UT 2012-11-14 (g) as described in Fulton et al. (2011). Observations from
nt UT2014-01-23wereanalyzedusingcustomroutineswrit-
Consta 1.10 KEPCAM UT 2012-11-22 (g) tenWienoGbDseLrv.2e5dtwo full transits at Canela’s Robotic Ob-
+
ux servatory(CROW)inPortugal. Observationsweremade
fl
d usingthe 0.3mLX200telescopewithaSBIGST-8XME
malize CROW UT 2012-12-08 (V) CCD. The field of view is 28′ x 19′ and 1.11 arcsec
Nor pixel−1. Observations were taken on UT2012-12-08 and
WHITIN UT 2013-01-27 (i) UT2013-01-29in V-band and i-band, respectively.
WeobservedonepartialtransitinI-bandonthenight
1.05
ofUT2013-01-27attheWhitinObservatoryatWellesley
CROW UT 2013-01-29 (i)
College. Theobservatoryusesa0.6mBollerandChivens
telescopewithaDFMfocalreducerthatgivesaneffective
focal ratio of f/9.6. The camera is an Apogee U230 2K
KEPCAM UT 2013-10-19 (i)
x 2K with a 0.58 arcsec pixel−1 scale and a 20′ x 20′
FOV.Reductions were carriedout using standardIRAF
1.00 BOS UT 2014-01-23 (i) packages,with photometry done in AIJ.
Figure 3 shows each transit plotted with the best fit
transit model over plotted in red. Figure 4 shows the
-3 -2 -1 0 1 2 3 combined and binned light curve with all 10 transits.
Time - TC (hrs) Plotsweregeneratedduringthe GlobalFitanalysis(See
Figure 3. Follow-up transit photometry of KELT-7. The Section 3.5) using EXOFAST (Eastman et al. 2013).
red over plotted line is the best fit transit model. The la-
bels are as follows: MOR=University of Louisville Moore Ob- 2.3. Spectroscopic Observations
servatory; KEPCAM=KeplerCam at the Fred Lawrence Whip-
pleObservatory;BOS=BryneObservatoryatSedgwick(LCOGT); WeusedtheTillinghastReflectorEchelleSpectrograph
CROW=Canela’s Robotic Observatory; WHITIN=Whitin Obser- (TRES;Fu˝resz2008), onthe 1.5mtelescope atthe Fred
vatoryatWellesleyCollege
24 http://www.astro.louisville.edu/software/astroimagej
25GNUDataLanguage;http://gnudatalanguage.sourceforge.net/
Kelt-7b 5
servations at an exposure time of 2 seconds and a slight
x defocusoftheimagebecauseofthebrightnessofthestar.
d flu 1.000 2.4. Adaptive Optics Observations
e
aliz 0.995 We obtainedadaptive optics (AO) imageryfor KELT-
m
or 0.990 7 on UT 2014 August 17 using the NIRC2 (instrument
N PI: Keith Matthews) with the Keck II Natural Guide
0.002 Star (NGS) AO system (Wizinowich 2000). We used
C the narrow camera setting with a plate scale of 10 mas
O- 0.000 pixel−1. The setting provides a fine spatial sampling of
-0.002
theinstrumentpointspreadfunction(PSF).Theobserv-
-3 -2 -1 0 1 2 3
Time - T (hrs) ing conditions were good, with seeing of 0.5′′. KELT-7
C
wasobservedatanairmassof1.31. WeusedaBr-γ filter
Figure 4. Top panel: All follow-up light curves from Figure toacquireimageswitha3-pointdithermethod. Ateach
3, combined and binned in 5 minute intervals. This light curve dither position, we took an exposure of 0.5 second per
is not used for analysis, but is shown in order to illustrate the coadd and 20 coadds. The total on-source integration
bestcombinedbehaviorofthelightcurvedataset. Theredcurve
time was 30 sec.
showsthe10transitmodelsforeachoftheindividualfitscombined
and binned in 5 minute intervals the same way as the data, with The raw NIRC2 data were processed using standard
the model points connected. Bottom panel: The residuals of the techniquestoreplacebadpixels,flat-field,subtractther-
binnedlightcurvefromthebinnedmodelinthetoppanel. mal background, align and co-add frames. We did not
find any nearby companions or background sources at
Lawrence Whipple Observatory (FLWO) on Mt. Hop- the 5-σ level (Fig. 5). We calculated the 5-σ detection
kins,Arizona,toobtainspectratotestfalsepositivesce- limit as follows. We defined a series of concentric annuli
narios, characterize radial velocity (RV) variations and centered on the star. For the concentric annuli, we cal-
determine stellar parameters of the host star. We ob- culated the median and the standard deviation of flux
tainedatotalof64TRESspectrabetweenUT2012Jan- for pixels within these annuli. We used the value of five
uary 31 and UT 2014 February 21. The exposure time timesthestandarddeviationabovethemedianasthe5-σ
variedfrom90−2400secondsdepending onthe weather detection limit. The 5-σ detection limits are ∆mag=2.5
conditions and the SNR we were trying to achieve. The mag, 5.4 mag, 6.4 mag, and 7.3 mag for 0.1′′, 0.2′′, 0.5′′,
spectra have a resolving power of R = 44,000 and were and 1.0′′, respectively.
extracted as described by Buchhave et al. (2010).
Initiallyweobtainedobservationsnearphases0.25and 3. ANALYSIS
0.75in orderto checkforlargevelocityvariationsdue to 3.1. Stellar Parameters
asmallstellarcompanionresponsibleforthe lightcurve.
Using the Spectral Parameter Classification (SPC)
Thespectrumappearedtobesingle-lined,andtheveloc-
(Buchhave et al.2012)technique,withT ,logg,[m/H],
ity variation that we saw was much too small to be due eff
and vsini as free parameters, we obtained stellar pa-
toastellarcompanionsowecontinuedobservingtogeta
rameters of KELT-7 from the 64 TRES spectra. SPC
preliminaryorbit. Theorbithadafairamountofscatter
cross correlates an observed spectrum against a grid of
due to the rapid rotation of the host star so we stopped
synthetic spectra based on Kurucz atmospheric mod-
observing spectroscopically and opted instead to follow-
els (Kurucz 1992). The weighted average results are:
upthe starphotometricallyto confirmthe depth, shape,
T =6779±50K,logg=4.23±0.10,[m/H]=0.12±0.08,
and period of the transit, and to search for color-depth eff
andvsini=73.2±0.5kms−1. [m/H]wassubstitutedfor
dependentdepthvariationsindicativeofablendedeclips-
[Fe/H]inthisanalysisbutwedonotbelievethatthiswill
ing binary. Once we had observed multiple transits in
affect the results. The weighted mean values were cal-
differentfilterstodeterminethatthetransitdepthswere
culated by taking an average of the stellar parameters
indeed achromatic, we started obtaining high signal-to-
that were calculated for each spectra individually, and
noise ratio spectra to refine the orbit and to determine
weights them according to the cross-correlationfunction
stellar parameters of the host star. Table 1 lists all of
(CCF) peak height. 26
the RV data for KELT-7.
Of the 64 total spectra, 28 were taken on the night
3.2. Radial Velocity Analysis
of UT 2013 October 19 to measure the RM effect and
determine the projected obliquity of the system. Simul- The relativeRVs were derivedby cross-correlatingthe
taneous data were taken using the TRES spectrograph spectra against the strongest observed spectrum from
on the 1.5 m telescope and photometric data using Ke- the wavelength range 4250 - 5650˚A. Figure 6 shows the
plerCam on the 1.2 m telescope both atop Mt. Hopkins best-fitorbitandcomputedbisectorswithresiduals. The
inAZ.Wecollected28RVspectrawitha9minuteexpo- best-fitorbitisaresultoftheEXOFASTGlobalFit(See
sure cadence and signal-to-noise ratio ranging from 127 Section 3.5) assuming a fixed eccentricity of zero. The
to 165 per resolution element. For the spectroscopic ob- bisector analysis of the RVs taken out of transit showed
servations we began collecting data an hour and a half
before ingress but we only obtained 2 observations after 26 SPCcompares theobserved spectraagainstalibraryofsyn-
egress due to morning twilight. Photometric observa- theticspectra calculated withthesamemixofmetals asthe Sun.
Sinceitusesallthelinesintheobservedspectrainthewavelength
tions were gathered starting two hours prior to ingress
regioncoveredbythelibrary,themetallicity[m/H]isthesameas
until morning twilight which occurred about 10 minutes [Fe/H] only if the mix of metals in the target star is the same as
after egress. We obtained a total of 997 KeplerCam ob- theSun.
6 Bieryla et al
Table 1
RVObservations ofKELT-7
Time RelativeRV RelativeRVerror Bisector Bisectorerror Phase SNRea
BJDTDB (ms−1) (ms−1) (ms−1) (ms−1)
2455957.836103 102 143 −114 209 −0.3053 68.8
2455961.748540 −472 134 −37 143 1.1253 87.4
2455963.607625 −65 144 −35 102 1.8050 122.7
2455964.647614 −387 174 170 137 2.1853 82.2
2455967.702756 −129 73 16 116 3.3024 101.0
2455968.667152 −25 86 −52 61 3.6551 191.2
2455970.667266 −135 136 −79 69 4.3864 106.3
2455971.657526 67 95 −199 77 4.7485 161.3
2455982.637552 −13 83 127 53 8.7633 153.3
2455983.610040 −150 97 55 107 9.1189 174.2
2455984.641133 −197 90 86 76 9.4959 180.2
2455985.610681 94 104 −55 107 9.8504 122.0
2455986.621278 −267 123 −164 156 10.2200 92.1
2456019.663088 −273 115 108 92 22.3017 73.5
2456020.642102 −139 107 −100 88 22.6597 125.5
2456027.643080 −52 89 −262 119 25.2196 141.2
2456310.790708 55 117 144 60 128.7524 296.9
2456340.790829 0 48 97 44 139.7219 297.5
2456584.819001 −45 88 102 131 228.9507 131.4
2456584.826693 81 64 26 71 228.9535 127.1
2456584.835357 62 100 −42 85 228.9567 146.6
2456584.843054 −1 93 75 70 228.9595 148.1
2456584.852250 65 85 8 95 228.9629 144.0
2456584.859959 −62 63 41 87 228.9657 144.5
2456584.867813 13 48 14 78 228.9686 145.7
2456584.875811 7 68 8 104 228.9715 143.5
2456584.884423 96 108 −39 74 228.9746 154.8
2456584.892300 230 96 −130 57 228.9775 154.3
2456584.899864 181 71 −179 70 228.9803 155.7
2456584.907399 265 110 33 112 228.9830 161.2
2456584.915097 86 82 89 61 228.9858 155.4
2456584.923361 146 98 138 62 228.9889 154.1
2456584.930798 93 81 56 43 228.9916 153.1
2456584.938490 −78 65 98 91 228.9944 162.9
2456584.946413 1 76 −9 55 228.9973 162.7
2456584.956825 −87 103 −80 84 229.0011 161.8
2456584.964968 −172 82 −77 78 229.0041 166.5
2456584.972520 −205 109 −70 74 229.0068 165.2
2456584.980362 −255 89 −143 82 229.0097 158.9
2456584.987938 −382 80 −23 56 229.0125 164.0
2456584.996897 −610 118 132 72 229.0158 162.3
2456585.004641 −437 81 240 53 229.0186 165.4
2456585.012118 −223 70 336 79 229.0213 162.9
2456585.019665 −86 80 207 70 229.0241 159.9
2456585.027143 −37 123 243 65 229.0268 156.1
2456585.034609 −226 78 145 70 229.0295 156.2
2456638.901881 26 98 −169 112 248.7261 198.1
2456639.777025 −123 68 −67 73 249.0461 242.0
2456640.913299 −115 80 90 53 249.4616 262.4
2456641.702340 −166 78 6 67 249.7501 169.0
2456642.742449 −347 66 39 92 250.1304 258.3
2456693.611029 72 73 −200 72 268.7305 203.3
2456694.641506 −208 89 −67 68 269.1073 186.2
2456696.631120 11 73 −149 70 269.8348 229.6
2456700.710497 −519 134 −2 75 271.3264 146.0
2456701.756533 −38 67 −206 70 271.7089 238.9
2456702.691941 −207 53 −53 50 272.0509 278.9
2456703.670164 −194 59 −35 42 272.4086 263.7
2456704.671919 −94 77 61 50 272.7749 219.1
2456705.773764 −316 76 −78 75 273.1778 220.1
2456706.652092 −32 68 −41 60 273.4989 254.3
2456707.664631 9 63 −63 37 273.8692 238.4
2456708.711942 −381 84 80 42 274.2521 206.1
2456709.746023 −21 65 −27 59 274.6302 260.8
a Signaltonoiseperresolutionelement(SNRe)whichtakesintoaccounttheresolutionoftheinstrument.
SNReiscalculatednearthepeakoftheechelleorderthatincludestheMgblines.
Kelt-7b 7
Table 2
StellarPropertiesofKELT-7
Parameter Description Value Source Referencea
Names BD+33977
TYC2393-852-1
2MASS05131092+3319054
GSC2393-00852
HD33643
αJ2000 051310.93 Tycho-2 1
δJ2000 +331905.40 Tycho-2 1
NUVGALEX 13.330±0.905 GALEX 2
BT 9.074±0.030 Tycho-2 1
VT 8.612±0.030 Tycho-2 1
V 8.540±0.030 SKY2000 3
B 8.970±0.030 SKY2000 3
U 9.010±0.030 SKY2000 3
IC 8.129±0.051 TASS 4
J 7.739±0.030 2MASS 5
H 7.580±0.042 2MASS 5
K 7.543±0.030 2MASS 5
WISE1 10.179±0.050 WISE 6
WISE2 10.844±0.050 WISE 6
WISE3 12.766±0.180 WISE 6
WISE4 13.741±0.123 WISE 6
µα ProperMotioninRA(masyr-1) 10.40±0.70 UCAC4 7
µδ ProperMotioninDEC(masyr-1) −49.70±0.60 UCAC4 7
Ub kms−1 −33.5±0.2 Thispaper
V kms−1 −9.7±1.8 Thispaper
W kms−1 −8.4±0.9 Thispaper
d Distance(pc) 129±8 Thispaper
Age(Gyr) 1.3±0.2 Thispaper
AV Visualextinction 0.13±0.04 Thispaper
a References: (1)Høgetal. (2000); (2)Martinetal. (2005); (3)Myersetal. (2001); (4)Richmondetal. (2000);
(5)Cutrietal. (2003); Skrutskieetal. (2006); (6)Wrightetal. (2010); Cutri&etal. (2012); (7)Zachariasetal.
(2013)
b PositiveUisinthedirectionoftheGalacticcenter.
8 Bieryla et al
444000000
222000000
m/s)m/s)m/s) 000
V (V (V ( ---222000000
RRR ---444000000
---666000000
O-CO-CO-Cm/s)m/s)m/s) ---222222000000000000000
(((
BisecBisecBisec(m/s)(m/s)(m/s) ---222222000000000000000
000...000 000...222 000...444 000...666 000...888 111...000
OOOrrrbbbiiitttaaalll PPPhhhaaassseee +++ 000...222555
Figure 6. TRESradialvelocitiesofKELT-7. Thegreensquares
representdatatakenonthenightoftheRMevent,whiletheblack
circles are data that were not taken during transit. The phases
have been shifted sothat aphase of 0.25corresponds to the time
oftheprimarytransit,TC. Toppanel: RVobservationsphasedto
thebest orbitalmodel witheccentricity fixedto zeroandwithno
lineartrend, showninred. The predicted RMeffect inthemodel
shownincorporatesthebestfitmodelwhereλ=9.7±5.2degrees.
Middle panel: Residuals of the RV observations to our circular
orbitalfit. Bottompanel: BisectorspanoftheRVobservationsas
afunctionofphase.
the signal, and a slope γ˙ and offset γ to describe
RM RM
the orbital motion of the star. λ is the angle on the
sky measured clockwise from the sky-projection of the
orbitangularmomentumvector,tothesky-projectionof
the stellarangularmomentumvector(Ohta et al.2005).
Theuncertaintyofthemodelparameterswereestimated
usingaMarkovChainMonteCarlo(MCMC) algorithm,
wherethe numberofchains waslargeenoughto guaran-
tee the robustness of the final values.
The results from the analysis show that the sky-
projected obliquity is λ = 4.1+7.9 degrees. The analysis
−7.7
also gives us an independent measure of the projected
rotational velocity, vsini = 66+21 kms−1, which is con-
−19
Figure 5. Top: Br-γ AOimageforKELT-7(HD33643) inBr-γ sistent with the SPC analysis (see Section 3.1). The
(λ=2.1654 mm). North is up, east is left. The horizontal bar is γ offset was determined to be −54+34 ms−1. We
1′′. No nearby companions or background sources were detected. RM −33
can also use the result from the out of transit accel-
Bottom: 5σ detection limit as a function of angular separation.
Detection limits at 0.1′′, 0.2′′, 0.5′′, and 1.0′′ are also given in eration γ˙RM = −671+−334460 ms−1day−1 to estimate the
Section2.4. velocitysemi-amplitude due to the planet. Using the or-
bital period and assuming a circular orbit, we calculate
no indication that the bisector spans were in phase with KRV = 292±146 ms−1. The results from this analysis
are shown in Figure 7.
the photometric ephemeris but the RMS was large due
tothehighvsini. Despitethehighervsiniandresulting
3.4. Time-series Spectral Line Profile
poorer precision, we were ultimately able to detect the
reflex signal at high confidence (roughly 7σ). We do see Theoverallstarlightthatisblockedbytheplanetdur-
acorrelationbetweenthebisectorsandRVstakenduring ingtransitwillappearasabumpintherotationalbroad-
the transit due to the RM effect. The relative RVs and eningfunction(Collier Cameron et al.2010). Eachspec-
bisector values are listed in Table 1. trum taken on the night of the RM event was cross-
correlated against a non-rotating template. The CCFs
3.3. Rossiter-McLaughlin Analysis of the out-of-transit data were median combined to cre-
ateamasterOOTCCF.Themasterwasthensubtracted
We performed an analysis of the RM data separately
from all of the in- and out-of-transit CCFs. Figure 8 is
from the global fit analysis (see Section 3.5). To model
a greyscale plot showing the results. The bright white
the RM effect, we used parameter estimation and model
feature increasing in velocity with time is caused by the
fitting protocols as described in Sanchis-Ojeda et al.
planet as it transits the star. This feature is what we
(2013) and Albrecht et al. (2012). The code implements
would expect to see for a system that has low orbital
formulasfromHirano et al.(2011),usingthelossoflight
obliquity: the planet crosses from the blue-shifted side
calculatedfromtransitparametersandplanetpositionas
of the stellar disk to the red-shifted side, and the center
inputs. The transitdatafromthe nightofthe RMevent
of the transit occurs at a vsininear zero.
were used to determine the time of transit and transit
parametersb, R⋆/a, RP/R⋆. Additional free parameters 3.5. EXOFAST Global Fit
are vsini and λ to describe the amplitude and shape of
Kelt-7b 9
RM prediction for Kelt−7b
666000000
600
400 444000000
nal [m/s] −2200000 V (m/s)V (m/s)V (m/s) 222000000000
Sig −400 RRR ---222000000
---444000000
−600
−800 0.85 0.90 0.95 1.00 1.05 1.10 m/s)m/s)m/s) ---222666000000000000
Time (BJD−2456584) C (C (C ( ---222000000000
O-O-O-
---444 ---222 000 222 444
TTTiiimmmeee --- TTT (((hhhrrrsss)))
1.01 CCC
x
u
ative fl 1.00 Ffleixguvreelo9ci.tyRsMubtrreasuctltesdfrooumt.thTeopglopbaanlelE:XROVFAdaStTafi(tgrweeitnhpthoientrse)-
el from UT 2013 October 19 with the best fit model shown in red.
r 0.99 The two black points were taken on different nights and not in-
cluded in the fit. The shape of the RM signal implies that the
projected obliquity of the host star with respect to the planet is
0.85 0.90 0.95 1.00 1.05 1.10
Time (BJD−2456584) small. Bottompanel: TheresidualsofthedatatotheRMfit.
Figure 7. RM results from our independent analysis. Spectro- As initial inputs for EXOFAST we included as priors
scopic and photometric data are from UT2013 October 19. Top the orbital period P = 2.7347749±0.000004 days from
Panel: RV observations with the best RM fit shown in red. Bot-
theKELT-Ndataandthehoststareffectivetemperature
tom Panel: Photometric transit data with the best fit shown in
red. Dataareplottedintimeforcomparison. Teff =6779±50K,metallicity [Fe/H]=0.12±0.08,and
stellar surface gravity logg = 4.23± 0.10 from TRES
spectroscopy. The priors were implemented as a χ2
penalty in EXOFAST (see Eastman et al. (2013) for de-
tails). In fitting the TRES RVs independently to a Kep-
lerian model we did not detect a significant slope in the
RVs (i.e., due to an additional long-period companion),
andwethereforedidnotinclude thisasafreeparameter
in our final fits.
We used the AIJ package to determine detrending pa-
rameters for the light curves, such as corrections for air-
massandmeridanflip. AIJallowsinteractivedetrending
capabilities. Oncewe determinedthe detrendingparam-
eters for each light curve, we fit the transit light curves
using EXOFAST. All light curves are detrended by air-
mass while the CROW light curve from UT2013 Jan-
uary 29 was also detrended by meridan flip and average
FWHM inthe image. The rawdata with detrending pa-
rameterswereusedastheinputforEXOFAST,andfinal
detrending was done in EXOFAST.
There were a few other considerations when running
Figure 8. Timeseriesoftheresidualaveragespectrallineprofile theglobalfit. First,wehadtochoosewhethertoinclude
fordatatakenonUT2013October19. Thebrightwhitefeatureis
just the full transits, with an ingress and an egress, or
causedbytheplanettransitingthestar.
to include all transits including the partial transits that
We used a custom version of EXOFAST weremissinganingressoranegress. Second,wehadthe
(Eastman et al. 2013) to determine a global fit of the option of allowing the orbital eccentricity and argument
system. EXOFASTdoesasimultaneousMCMCanalysis ofperiastrontofloatfreeortofixthemtozeroandforce
of the photometric and spectroscopic data, including a circular orbit. Third, we had to choose between con-
constraintsonthe stellarparametersofM⋆ andR⋆ from straining the mass-radius relationship using the Torres
the empirical Torres relations (Torres et al. 2010) or relations or by using the Yonsei-Yale stellar models. Fi-
Yonsei-Yale (YY) evolutionary models (Demarque et al. nally, we had the option to include the RM observations
2004), to derive system parameters. This method is and fit the RM RVs as part of the global fit.
similartothatdescribedindetailinSiverd et al.(2012), For the initial runs, we chose to use only the full tran-
but we note a few differences below 27. sits and the non-RM RVs to ensure convergence. We
also chose to fix the eccentricity to zero and set the con-
27 In the EXOFAST analysis, which includes the modeling of straint on the mass-radius relationship using the Torres
filter-specificlimbdarkeningparametersofthetransit,weemploy relations. Once the fit converged, we ran it again but
thetransmissioncurvesdefinedfortheprimedSDSSfiltersrather changed the constraint on the mass-radius relationship
thantheunprimedversions. Weexpectanydifferencesduetothat
totheYYstellarmodels. We foundthefinalparameters
discrepencytobewellbelowtheprecisionofallourobservationsin
thispaperandofthelimbdarkeningtablesfromClaret&Bloemen wereinagreementwithintheuncertainties. Thisgaveus
(2011). confidence to start adding the partial transits. We ini-
10 Bieryla et al
Table 3 6
TransitTimesforKELT-7 BOS
4 CROW
Epoch (BJDTCTDB) Esrercor Ose-cC O-C/Error Observatory min) 2 KMEOPRCAM
WHITIN
(
-55 2456204.817057 64 5.65 0.09 MOR C 0
-48 2456223.959470 31 −83.91 −2.70 KEPCAM -
O
-44 2456234.898861 42 −59.97 −1.42 KEPCAM
-2
-40 2456245.839584 50 79.05 1.56 BOS
-37 2456254.045118 63 182.60 2.88 KEPCAM -4
-31 2456270.451621 55 −4.72 −0.08 CROW
-13 2456319.678871 59 102.16 1.72 WHITIN -150 -100 -50 0 50 100 150
-12 2456322.413721 56 108.34 1.92 CROW Epoch
84 2456584.950978 47 −19.45 −0.41 KEPCAM
119 2456680.667558 87 −77.12 −0.88 BOS
Figure 10. The residuals of the transit times from the best-fit
ephemeris. The transit times are given inTable 3. The WHITIN
observations at epoch -13 are hidden behind the CROW observa-
tially hadtrouble getting the fit to convergewith all the tionsatepoch-12.
lightcurvesandfoundthatweneededtoaddpriorwidth ment with the results from SPC and our independent
constraintonthetransittimingvariation(TTV)andthe RM analysis.
baseline flux for the partial transits. We then released The TTVs for all follow-up transits are shown in Fig-
the prior on eccentricity and let it float free. The result ure 10. The global fit TC and P were constrained only
was e=0.013+0.022 which was consistent with a circular by the RV data and the priors imposed from the KELT
−0.010
orbit. discovery data. Using the follow-up transit light curves
The last step of the process was to include the to constrain the ephemeris in the global fit would artifi-
RM velocities in the combined global fit. The RM cially reduce any observed TTV signal. As part of the
data were modeled using the Ohta et al. (2005) an- globalanalysis,wefitasafreeparameteratransitcenter
alytic approximation. At each step in the Markov timeTC foreachtransitshowninTable3. Astraightline
Chain, we interpolated the linear limb darkening tables was fit to all mid-transit times in Table 3, and shown in
of Claret & Bloemen (2011) based on the chain’s value Figure 10, to derive a separate ephemeris from only the
feonrinloggcgo,effiTecffie,natn,du.[FOe/uHr]gtrooudnedri-vbeastehdeolibnseearrvalitmiobnsdgaernk-- tPra=nsi2t.d73a4ta7.78W5e±fi0n.0d0T00◦0=382,4w5i6t3h55a.2χ2298o0f92±7.05.800a0n1d988,
erallydonotconstrainthetwoquadraticcoefficientswell degrees of freedom. While the χ2 is much larger than
enough to yield unique fits to both parameters. The un- one might initally expect, this is likely due to systemat-
certainties associatedwith this value are not true uncer- ics in the transit data from the ground-based photome-
tainties because they include the covariances with the try. Properlyremovingsystematicsinthe partialtransit
other parameters. For this reason we chose not to in- datawouldbedifficult,sowearethereforenotconvinced
clude the linear limbdarkeningcoefficient, u, inTable 4. thatthisis evidencefor TTVs. We werecarefulto check
The RM RVs were allowed a velocity offset (γRM) sep- thatalltimestampswereinBJDTDB time systemusing
arate from the non-RM RV dataset velocity zeropoint Eastman et al. (2010) to convert timestamps. Further
(γRV). We allowed for this because stars have intrinsic studies would be required to rule out TTVs.
jitter(Albrecht et al.2012;Winn et al.2006)thatcanbe
3.6. Evolutionary Analysis
significant in rapidly rotating stars F-stars. Cegla et al.
(2014) have suggested that F-stars have been found to WeuseT ,logg,stellarmass,andmetallicityderived
eff
have more vigorous convective motions despite being from the EXOFAST global fits (see Section 3.5 and Ta-
magnetically inactive, and that the RV jitter is strongly ble 4), in combination with the theoretical evolutionary
correlatedwith the granulation flicker. We find that the tracksoftheYonsei-Yalestellarmodels(Demarque et al.
offsetbetweenourγRM andγRV valuesof∼100ms−1 is 2004), to estimate the age of the KELT-7 system. We
comparabletotheRMSresidualofthenon-RMRVdata. have not directly applied a prior on the age, but rather
We also find the γRM offset determined in the global fit have assumed uniform priors on [Fe/H], logg, and Teff,
(γRM =−35±−19ms−1)tobeconsistentwiththeγRM whichtranslatesintonon-uniformpriorsontheage. Fig-
offset determined in Section 3.3. The results from the ure 11 shows the theoretical HR diagram (logg vs. T )
eff
EXOFAST RM fit are shown in Figure 9. withevolutionarytracksformassescorrespondingtothe
For our final fits, we included all full and partial tran- ±1σ extrema in estimated uncertainty. We adopt the
sits, all the radialvelocities including the RM velocities, Yonsei-Yale constrained globalfit representedin the top
and we assumed a circular orbit with no RV slope. The panel. The estimated stellar mass (and secondarily the
stellarandplanetaryvalues derivedusing the YY stellar metallicity) define the model stellar evolutionary track
models and using the Torresrelationare shownin Table fromwhichtheageisinferredintheHRdiagram. Within
4 for comparison. We chose to adopt the YY model as the 1σ uncertainties on the observed T , logg, and
eff
ourfiducialvalues. Wefindthatthespin-orbitalignment [Fe/H], the Yonsei-Yale evolutionary track gives an in-
λ = 9.7±5.2 degrees, and our velocity semi-amplitude, ferred age of 1.3±0.2 Gyr. The bottom panel of Figure
KRV = 138±19 ms−1, determined from the global fit 11isshownasacomparisonusingtheTorresconstrained
both agree with our independent solution discussed in global fit values (Torres et al. 2010). The Torres model
Section 3.3. We also find that the resulting vsini from providesempiricalrelationshipsbetweenobservedstellar
the global fit (vsini = 65+6 kms−1) is in close agree- parameters T , logg, and [Fe/H], and stellar mass and
−5 eff