Effective temperature scale and bolometric corrections from 2MASS photometry

1.1 MB·English

by  E. Masana

Astronomy&Astrophysicsmanuscriptno.masana February5,2008
(DOI:willbeinsertedbyhandlater)
Effective temperature scale and bolometric corrections from
⋆
2MASS photometry
6
0 E.Masana1,2,C.Jordi1,2,3,andI.Ribas3,4
0
2
1 Departamentd’AstronomiaiMeteorologia,UniversitatdeBarcelona,Avda.Diagonal647,08028Barcelona,Spain

n 2 CERforAstrophysics,ParticlePhysicsandCosmology,associatedwithInstitutdeCie`nciesdel’Espai-CSIC
a 3 Institutd’EstudisdeEspacialsdeCatalunya(IEEC).Edif.Nexus,C/GranCapita`2-4,08034Barcelona,Spain
J
4 InstitutdeCie`nciesdel’Espai,CSIC,CampusUAB,Fac.Cie`ncies,TorreC5parell,2aplanta,08193Bellaterra,Spain
3

Received/Accepted
1
v
9 Abstract.Thispaperpresentsamethodtodetermineeffectivetemperatures,angularsemi-diametersandbolometriccorrections
4 forpopulationIandIIFGKtypestarsbasedonV and2MASSIRphotometry.Accuratecalibrationisaccomplishedbyusing
0 asampleofsolaranalogues,whoseaveragetemperatureisassumedtobeequaltothesolareffectivetemperatureof5777K.
1 Bytakingintoaccountallpossiblesourcesoferrorweestimateassociateduncertaintiesbetterthan1%ineffectivetemperature
0 and in the range 1.0–2.5% in angular semi-diameter for unreddened stars. Comparison of our new temperatures with other
6
determinationsextractedfromtheliteratureindicates,ingeneral,remarkablygoodagreement. Theseresultssuggest thatthe
0
effectivetemperaurescaleofFGKstarsiscurrentlyestablishedwithanaccuracybetterthan0.5%–1%.Theapplicationofthe
/
h methodtoasampleof10999dwarfsintheHipparcoscatalogueallowsustodefinetemperatureandbolometriccorrection(K
p band)calibrationsasafunctionof(V K),[m/H]andlogg.BolometriccorrectionsintheVandKbandsasafunctionofT ,
- [m/H]andloggarealsogiven.Wepr−ovideeffectivetemperatures,angularsemi-diameters,radiiandbolometriccorrectionseiffn
o
theVandKbandsforthe10999FGKstarsinoursamplewiththecorrespondinguncertainties.
r
t
s
a Key words.stars:fundamental parameters–stars:late-type–stars:sub-dwarfs–infrared:stars–techniques: photometric–
: methods:analytical
v
i
X
r 1. Introduction rectmethodsaremainlybasedontheuseofphotometry,spec-
a
troscopy,or a combinationof both.In the case of thetemper-
Effectivetemperatureandluminosityaretwofundamentalstel-
atures, although many of the published calibrations claim to
lar parametersthat are crucial to carry out tests of theoretical
haveuncertaintiesof theorderof severaltensof degrees,val-
models of stellar structure and evolution by comparing them uesobtainedbydifferentauthorscaneasilyhavediscrepancies
with observations.Theaccuracyin the determinationofother of 100 K or even larger. The reason for such nagging differ-
stellar properties,suchasmetallicity,ageorradius,hingeson
encesmustbefoundsomewhereintheingredientsofthemeth-
ourabilitytoestimatetheeffectivetemperaturesandluminosi-
ods: atmosphere models, absolute flux calibrations, oscillator
ties.
strengths,calibrationstars,etc.
There are several approaches in the literature to compute Inthispaperwepresentasemi-empiricalmethodtodeter-
effective temperature and/or luminosity.Except when applied mine effective temperatures (T ) and bolometric corrections
eff
to the Sun, very few of them are direct methods that permit (BC)from2MASS1 JHK2 photometry(Cutrietal.2003)that
anempiricalmeasurementoftheseparameters.Usually,semi- is applicable to FGK type stars. As all others, our method is
empirical or indirect methods are based to a certain extent susceptible to problems derived from the uncertainties in the
on stellar atmosphere models. Among the direct approaches ingredientsmentionedabove.However,ourapproachbenefits
we find the remarkable work by Code et al. (1976), which is from two major features: First, it provides a way to evaluate
basedoninterferometricmeasurementsofstellarangularsemi- realistic individual uncertainties in T , θ and luminosity by
eff
diameters(θ)andtotalfluxes(Fbol)atEarth,andthemorere- considering all the involved errors; and second, as it is cali-
cent works of Mozurkewich et al. (2003) and Kervella et al. bratedtousethe2MASSphotometry,itallowsthecalculation
(2004),alsobasedoninterferometry.Ontheotherhand,indi- ofconsistentandhomogeneousT andBCforseveralmillion
eff
stars in the 2MASS catalogue. This paper also provides T ,
eff
⋆ Table 3 is only available in electronic form at the CDS via
anonymousftptocdsarc.u-strasbg.fr (130.79.128.5)orvia 1 http://www.ipac.caltech.edu/2mass
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?]/A+A/ 2 Throughoutthepaper,KreferstoK band.
s
2 E.Masanaetal.:Effectivetemperaturescaleandbolometriccorrections
angular semi-diameters, radii and BCs for 10999 dwarfs and However,theIRfluxbecomesverysensitivetometallicityand
subdwarfsintheHipparcoscatalogueESA(1997).Suchlarge surfacegravityforstarshotterthan8000Ksothatsmalluncer-
samplehasallowedusto constructsimpleparametriccalibra- taintiesintheseparameterstranslateintolargeuncertaintiesin
tions as a function of (V K) , [m/H] and logg. Note that a theeffectivetemperature.InsuchsituationtheSEDFapproach
0
−
preliminaryversionofthemethodpresentedherewasalready becomes inadequate. At the cold end, the accuracy of stellar
successfullyappliedtothecharacterizationofthepropertiesof atmospheremodelslimitstheuseofthemethodtostarshotter
planet-hostingstars(Ribasetal.2003). than4000K(molecularopacityplaysanimportantrolebelow
The present paper is organized as follows. Section 2 thistemperature).Theselimitationsrestricttheapplicabilityof
presentsthemethodandexplainsindetailtheproceduretoob- the SEDF to FGK type stars. Fortunately,these stars are very
tain T and angular semi-diameters, including the fitting al- common in the Galaxy and dominate the content of most of
eff
gorithm,zeropointcorrectionsanderrorestimates. Thecom- surveycatalogues.Theyarecrucialforseveralkeyastrophys-
parisonofourtemperatureswithseveralpreviousworks,both icaltopics, suchasthe studyofthe structureandevolutionof
based on photometric and spectroscopic techniques, is de- theGalaxy,boththediskandthehalo,andthecharacterization
scribed in Sect. 3. In Sect. 4 we present simple parametric ofplanet-hostingstars,amongothers.
calibrations of T and BC as a function of (V K) , [m/H]
eff 0
−
and logg valid for dwarf and subdwarf stars. The sample of
2.1.Calculationofsyntheticphotometry
10999 stars used to build the calibrations is also described in
thissectiontogetherwithadetailedexplanationofthedifferent The calculation of the synthetic photometry requires a well-
contributors to the final uncertainties. Finally, the results are characterized photometric system, an accurate flux calibra-
discussed in Sect. 5 and the conclusions of the present work tion and suitable synthetic spectra. The work by Cohen et al.
arepresentedinSect.6. (2003a,b)providesconsistentabsolutefluxcalibrationsinboth
thevisible(V)(Landoltsystem)andIR(2MASSJHK)bands.
The calibration given by Cohen et al. is computed from a set
2. TheSpectralEnergyDistributionFit(SEDF)
of calibrated templates, using the synthetic Kurucz spectrum
method
of Vegaof Cohenetal. (1992).Inthe case of theIR photom-
Theuseofinfrared(IR)photometrytodetermineeffectivetem- etry, they consider the transmission of the camera and filters,
peratureswasinitiallyproposedbyBlackwell&Shallis(1977). the detector properties and the Earth’s atmosphere character-
Theirso-calledInfraredFluxMethod(IRFM)usestheratiobe- istics. From the comparison between observed and synthetic
tween the bolometric flux of the star and the monochromatic photometryfora set of 9 A-typestars and 24 coolgiants,the
flux at a given infrared wavelength, both measured at Earth, authorsinfertheneedtointroduceazeropointoffsetinthesyn-
as the observable quantity. This ratio is then compared with theticphotometrytomatchtheobserved2MASSphotometry:
a theoreticalestimate derivedfromstellar atmospheremodels 0.001 0.005 mag (J); 0.019 0.007 mag (H); 0.017 0.005
± − ± ±
tocarryoutthedeterminationoftheeffectivetemperature.The mag(K).Thecalculationofsuchvaluesisnotexemptofsome
IRFMhasbeenwidelyusedbyanumberofauthors,beingmost difficultysincethedispersionsofthedifferencesbetweenboth
noteworthytheworkbyAlonsoetal.(1995,1996a,b). photometries(syntheticandobserved)areofthesamemagni-
The Spectral Energy Distribution Fit (SEDF) method that tudeasthezeropointoffsetsthemselves.
we propose here follows a somewhat different approach, To computethe syntheric magnitudeswe made use of the
namelythefitofthestellarspectralenergydistributionfromthe no-overshoot Kurucz atmosphere models grid (Kurucz 1979)
optical(V) to the IR(JHK) usingsynthetic photometrycom- takenfromhttp://kurucz.harvard.edu/grids.html:
putedfromstellaratmospheremodels.UnliketheAlonsoetal.
Fi
(1996a)implementationoftheIRFM,whichaveragestemper- mi (T ,logg,[m/H])=2.5log cal (1)
syn eff F(T ,logg,[m/H])
aturesderivedindividuallyforeachIRband,ourmethodtakes i eff
into account the four bands simultaneously (and naturally). whereFi istheabsolutefluxcalibrationgivenbyCohenetal.
cal
In addition, and also unlike the IRFM, the bolometric flux is (2003b)(formi = 0) and F(T ,g,[m/H])is theflux inthe
cal i eff
not required a priori by the SEDF method but results self- ibandcomputedfromtheintegrationofthemodelatmosphere
consistently with the temperature. The fitting algorithm (see convolved with the transmission function (filter, detector and
Sect.2.2)minimizesthedifferencebetweenobservedandsyn- Earth’satmosphere)fromCohenetal.(2003b):
theticphotometrybytuningthevaluesoftheeffectivetemper-
ature andthe angularsemi-diameter.The BC can be obtained F(T ,logg,[m/H])= ∞φ(T ,logg,[m/H],λ) (λ)dλ(2)
i eff eff i
Z T
fromthesetwoparameters,andthen,whenthedistancetothe 0
starisknown,theluminosityiscomputedfromtheBCandthe where φ(Teff,logg,[M/H],λ) is the flux given by the stellar
absolute magnitude in a given photometric band. The uncer- atmospheremodeland (λ)theeffectivetransmissionfunction
i
T
taintiesofthederivedparameters(T ,angularsemi-diameter intheibandnormalizedtoapeakvalueofunity.
eff
andBC)areestimatedfromtheerrorsintheobservedandsyn-
thetic photometryas well as in the assumed[m/H],logg and
2.2.Fittingalgorithm
A .
V
From a theoreticalpointof view, the SEDF methodcould The fitting algorithm is based on the minimization of the χ2
be applied to stars of any spectral type and luminosity class. function defined from the differences between observed (cor-
E.Masanaetal.:Effectivetemperaturescaleandbolometriccorrections 3
rected forinterstellar extinction)and synthetic VJHK magni- theyare ofno use to calibratethe SEDFmethod.As analter-
tudes,weightedwiththecorrespondingerror: native, we have used the list of photometric solar analogues
compiled by CayreldeStrobel (1996).We assume that, as an
V A V 2 J A J 2
χ2 = − V − syn + − J− syn + ensemble, the average of the effective temperatures of these
σV ! σJ ! photometric solar analogues should be equal to the effective
H A H 2 K A K 2 temperatureoftheSun(i.e.,5777K).
H syn K syn
+ − − + − − (3)
After selecting a subsample of 50 unreddened stars
σ ! σ !
H K
with non-saturated 2MASS photometry from table 1 of
This function depends (via the synthetic photometry)on T ,
eff CayreldeStrobel(1996),we computedtheirtemperaturesus-
logg,[m/H]andamagnitudedifference ,whichistheratio
ingtheSEDFmethod.Weobtainedanaveragetemperatureof
A
betweenthesynthetic(star’ssurface)andtheobservedflux(at 5832 14 K, i.e., 55 K (or 1%) higherthan the solar effec-
Earth)( = 2.5logF /F ). isdirectlyrelatedtothe ± ∼
star Earth tivetemperature.Exactlythesamevalueisobtainedifweuse
A − A
angularsemi-diameterbythefollowingexpression: the subset of solar “effectivetemperatureanalogues”fromta-
θ=10 0.2 (4) ble 5 of CayreldeStrobel. Withouta profoundanalysis of all
− A
theingredientsinvolved–fromthestellaratmospheremodelto
Althoughthesyntheticphotometrydependsimplicitlyongrav- the absoluteflux calibration,– itis verydifficultto assess the
ityandmetallicity,inpractice,thespectralenergydistribution reasons for such difference. However, it seems clear that the
in the optical/IRfor ourrangeof temperaturesis onlyweakly temperature scale as obtained from the synthetic photometry
dependent on these quantities. This fact makes it possible to aloneneedsacorrectiontoagreewiththeaverageofthesolar
obtainaccuratetemperaturesevenforstarswithpoordetermi- analogues.Fromaformalpointofview,thiscorrectioncanbe
nationsofloggand[m/H]. computedfromthesyntheticphotometrythatresultsfromforc-
As canbeseen,the χ2 functiondependsalsoonthe inter- ingavalueofT =5777Ktotheentiresample.Afterdoingso,
eff
stellarabsorptionAV (theabsorptionintheotherbandscanbe wereplacedthezeropointsgivenbyCohenetal.(2003b)(see
computedusingtheextinctionlawofSchaifers&Voigt(1982): Sect.2.1)bytheaveragedifference(foreachband)betweenthe
AJ = 0.30AV, AH = 0.24AV and AK = 0.15AV). In principle, observedandsyntheticphotometrycomputedforthesolarana-
itispossibletoconsiderAV asafreeparameter.However,the logues.AssumingthatthereisnooffsetontheV band,theoff-
strongcorrelationbetweenTeffandAV,especiallyforthehotter setsfortheotherbandsare:0.027 0.003mag(J);0.075 0.005
± ±
stars, decreasesthe precisionin the determinationof both pa- mag (H); 0.022 0.005 mag (K). It is interesting to note that
±
rameters,withresultingtypicaluncertaintiesof4%inTeff and both in the case of Cohen et al. (2003a) and in our case, the
0.25maginAV.Thus,forbestperformance,AV shouldonlybe valueoftheoffsetinthe H banddifferssignificantlyfromthe
consideredasafreeparameterwhenitsvalueissuspectedlarge offsetsin J andK.Itshouldbestressedthattheeffectivetem-
andnoothermethodforitsestimationisavailable.Ingeneral, peraturesgivenbyCayreldeStrobel(1996)havenotbeenused
thebestapproachis tofix thevalueof AV inEq.(3)fromthe here.Wehaveonlyusedthepropertyofthestarsinbeingclas-
estimationbyphotometriccalibrations,forinstance. sifiedassolaranalogues,and,consequently,weassumedtheir
Therefore,theonlytwoadjustableparametersbytheSEDF averagetemperaturetobeequaltothesolareffectivetempera-
method in the present work are Teff and , whereas logg, ture.
A
[m/H] and AV are fixed parameters. To minimize Eq. (3) Inourprocedure,we are implicitlyassumingthatthe cor-
with respect to these two parameters we use the Levenberg- rectionin our temperaturescale is just a zero pointoffsetand
Marquardtalgorithm(Press etal. 1992),which isdesignedto that no dependence on temperature or metallicity is present.
fita setofdatato anon-linearmodel.Inallourtests, conver- These assumptionsare justified a posteriori in Sect. 3, where
gence towards the minimum value of χ2 was reached rapidly several comparisonsof SEDF temperatureswith other photo-
andunequivocally. metricandspectroscopicdeterminationsareshown.
The angular semi-diameters computed from Eq. (4) were
used to check the consistency of the new zero points in our
2.3.CalibrationoftheSEDFmethodusingsolar
temperature scale. These angular semi-diameters were com-
analogues
pared with the direct values compiled in the CHARM2 cata-
The standard procedure for the calibration of an indirect logue(Richichi&Percheron2005).Werestrictedthecompar-
method to determine effective temperatures is based on the isontostarswith accurateVLBIorindirect(spectrophotome-
comparisonoftheresultswith accuratetemperaturesfromdi- try)measurementsofthesemi-diameter.Only10ofthesestars
rectmethodsforasetofstars.Inthisway,thelistofstarswith fulfill the conditions for applicability of the SEDF method.
empirical effective temperatures and angular semi-diameters Figure1showsthecomparisonofthesemi-diametersforthese
from Code et al. (1976) has been widely used for calibration 10 stars. The agreement is excellent, with an average differ-
purposes. This list has been recently increased with the the ence (θ θ ), weighted with the inverse of the square
dir SEDF
−
worksofMozurkewichetal.(2003)andKervellaetal.(2004). of the error, equal to 0.3% with a s.d. of 4.6% (see Table
−
Otherauthorsuse well-studiedstars,suchastheSun,Vegaor 1). All the direct values used in the comparison correspond
Arcturus,tocalibratetheirmethods. to an uniform stellar disk. A crude comparison of both uni-
Unfortunately, the few stars with empirical values of form disk and limb darkened values for about 1600 F, G and
T are too bright to have accurate 2MASS photometry and K stars in the CHARM2 catalogue indicates a 4% positive
eff
∼
4 E.Masanaetal.:Effectivetemperaturescaleandbolometriccorrections
2.4.Errorestimation
One ofthe featuresofthe SEDFmethodisthatityieldsindi-
vidualuncertaintiesofbothT andθ.Thetotaluncertaintycan
0.5 eff
be calculated by combining the contributions from the spec-
tral energy distribution fit and also from the uncertainties in
thefixedparameters,i.e.,logg,[m/H],andA .Assumingnull
V
0.4 correlationbetweenthesedifferent(and,inprinciple,indepen-
M2 (mas) (dTeenfft)osrour)ceisstohfeeqrruoard,rtahteictostuamluonfcethrteaidnitffyeorefnttheerYrokrpcaoranmtriebtuer-
R A
A tions:
H
meter C0.3 (∆Yk)2 = (∆YkSEDF)2+ ∂[∂mY/kH]!2(σ[m/H])2
a
di
mi ∂Y 2 ∂Y 2
Se0.2 + ∂logkg! (σlogg)2+ ∂Ak ! (σAV)2
V
(5)
Asmentionedabove,theminimizationofχ2iscarriedoutwith
HD 209458
0.1 respecttothefourmagnitudesVJHK,withtheparametersA ,
0.1 0.2 0.3 0.4 0.5 V
Semidiameter (SEDF) (mas) [m/H]andloggbeingheldfixed.Thefirsttermoftheequation
(∆Y SEDF)istheerrorin theparameterY comingfromthe fit
k k
tothespectralenergydistribution,whichiscomputedfromthe
covariance matrix (∆Y SEDF √C ). The derivatives in the
k kk
≡
Fig.1. Comparison of angular semi-diameters computed from the otherthreetermsoftheequationaredeterminednumerically:
SEDFmethod(withthenewzeropointinthetemperaturescale)and
∂Y Y (+∆[m/H]) Y ( ∆[m/H])
fromtheCHARM2catalogue.InthecaseofHD209458,thecompar- k k − k − (6)
∂[m/H] ≈ 2
isonofthesemi-diameterisbetweentheSEDFmethodandanempir-
icaldeterminationfromahigh-precisiontransitlightcurve. inthecaseofthemetallicity,andinananalogouswayforthe
surfacegravityandtheinterstellarabsorption.
TheerrorinT isobtaineddirectlyfromEq.(5),whereas
eff
Table1.ComparisonofdirectandSEDFangular semi-diameters. theerrorinθmustbecalculatedfromtheerrorinthe param-
θdirareVLBIandspectrophotometricvalues(Richichi&Percheron eter: A
2005).ForHD209458,θ isderivedfromaplanetarytransitlight
dir σ =0.2 ln10θσ (7)
curve. θ
A
The adopted values for the errors in the magnitudes (σ ),
Star θ (mas) θ (mas) ∆θ(%) mi
dir SEDF metallicity (σ ) and surface gravity (σ ) are discussed
[M/H] logg
HIP6702 0.190 0.050 0.189 0.004 0.5
± ± inSect.4.1.1.
HIP8433 0.225 0.050 0.286 0.005 27.1
± ± −
HIP48113 0.405 0.005 0.402 0.006 0.7
HIP50786 0.260±0.010 0.265±0.004 1.9 3. Comparisonwithothermethods
± ± −
HIP51056 0.290 0.030 0.306 0.005 5.5
± ± − Five samples of FGK stars with accurate determinations of
HIP85365 0.380 0.015 0.410 0.036 7.9
± ± − effective temperatures (both photometric and spectroscopic)
HIP91237 0.210 0.015 0.251 0.004 19.5
± ± − wereselectedfromtheliterature(Alonsoetal.1996a,Ram´ırez
HIP96895 0.270 0.015 0.278 0.004 3.0
HIP96901 0.260±0.015 0.255±0.003 −1.9 & Mele´ndez 2005, Fuhrmann 1998, Santos et al. 2003 and
HIP113357 0.365±0.010 0.352±0.006 3.6 Edvardsson et al. 1993) to carry out a comparison with our
± ±
HD209458 0.113 0.010 0.115 0.002 1.8 results. We put special attention in correcting for the effects
± ± −
of interstellar reddening, which could lead to systematic dif-
ferences.FortheAlonsoetal.andRam´ırez&Mele´ndezsam-
ples(the mostreddened),interstellarreddeningwas corrected
using the values of E(B V) given by the authors so that
−
the two temperature estimations would be directly compara-
ble. For the other three samples, composed of stars at closer
correctionforlimbdarkening,ofthesameorderofthedisper- distances, we restricted our comparisonsto unreddenedstars.
sion of the relative differencesshown in Table 1. In addition, Anyhow,thismeantrejectingveryfewstarsfromfurtheranal-
we compared the radius of HD 209458 – obtained with the ysis. Among several papers in the literature, we chose these
HubbleSpaceTelescopefromahighprecisionplanetarytran- five samples because they have a minimum of 25 stars with
sitlightcurve(Brownetal.2001)–withourestimationfrom non-saturated2MASSphotometryandthevaluesof[m/H]and
SEDF, obtainingvery goodagreement:1.146 0.050R and logg – needed for a consistent comparison– are providedby
± ⊙
1.160 0.058R ,respectively. theauthors.
± ⊙
E.Masanaetal.:Effectivetemperaturescaleandbolometriccorrections 5
3.1.MethodsbasedonIRphotometry:Alonsoetal.
(1996a)andRam´ırez&Mele´ndez(2005)
8000
Asmentionedabove,theIRFMisthemostpopularmethodto
computeeffectivetemperaturesfromIRphotometry.Thework 7000
by Alonso et al. (1996a) is undoubtedly the widest applica- K)
tionoftheIRFMtoFGKstars.Theauthorscomputedeffective M) (
temperaturesfor 462starswith knowninterstellarabsorption, RF 6000
surfacegravityandmetallicity.Afterselecting thestars inthe T(Ieff
Alonso et al. sample in the range 4000 < Teff < 8000 K and 5000
witherrorsinthe2MASSphotometrybelow0.05mag,weob-
tainedeffectivetemperaturesfromtheSEDFmethodforasub-
4000
setof315stars.Thecomparisonbetweenbothdeterminations
ofT isshowninFig.2.Theaveragedifference∆T (IRFM 300
eff eff K)
−SEDF)wasfoundtobe−67K,withastandarddeviationof EDF( 150
81K.Thedependenceofthisdifferenceonthetemperatureis STeff 0
nbootttsoimgnpifiacnaenlto:fTFeIRffigF.M2=,th1e.0re30isTneSoffEDdFe−pe2n3d9enKc.eAosfsthheowtenmipnetrhae- RMF - -150
turedifferencewithmetallicity. ITeff-300
4000 5000 6000 7000 8000
In a recent work, Ram´ırez & Mele´ndez (2005) have re- T (SEDF) (K)
eff
computed the IRFM temperatures of almost all the stars in
Alonso et al. (1996a) using updated input data. According to K) 300
the authors, the difference between the old and new temper- EDF ( 150
ature scales is not significant. They also compare their effec- ST eff 0
tivetemperatureswithsomedirectdeterminations.Theauthors MF - -150
csoolnacrlutedmeptheraatttuhreer(einisthaesysesntesmeaIRticFMdifferenc–ethoefirabvoaulute4s0).KThaet IRT eff-300
Alonso -4 -3 -2 -1 0
comparisonbetweenthetemperaturesofRam´ırez&Mele´ndez [m/H]
andourdeterminationsisshowninFig.3.For385starsincom-
Fig.2.ComparisonoftheeffectivetemperaturesfromtheIRFMand
mon we find ∆Teff (IRFM −SEDF) equal to −58 K (σTeff=67 theSEDFmethodfor315starsinthesampleofAlonsoetal.(1996a).
K), and TIRFM = 1.061 TSEDF 403 K. Unlike in the case Thebottom panel shows the temperature difference asafunction of
eff eff −
ofAlonso etal. (1996a),thedependenceof∆Teff in [m/H]is themetallicity.
relevant (Fig. 3, bottom panel). For [m/H] < 2.0 the tem-
−
peratures from Ram´ırez & Mele´ndez are clearly hotter than
ourtemperatures.ThesametrendwasfoundbyCharbonnel&
Primas (2005)when comparingtheir temperaturesof 32 halo
dwarfs( 3.5< [Fe/H]< 1.0)withthevaluesofRam´ırez&
− −
Mele´ndez. halo. Effective temperatures were determined from fits to the
wings of the Balmer lines. Of those stars, 24 have accurate
3.2.Othermethods 2MASSphotometrysothatreliableSEDFtemperaturescanbe
derived. The comparison is shown in Fig. 4. The mean aver-
Besides the IRFM, which uses IR photometry, we have also age difference ∆T (Fuhrmann SEDF) is 12 K, (σ =45
comparedtheeffectivetemperaturesobtainedusingtheSEDF K), with a slight deeffpendenceon−the temperature:TFuhrTmeaffnn =
eff
method with other determinations. Two of these (Fuhrmann 0.895TSEDF+618K.Nodependencewasfoundbetween∆T
eff eff
1998 and Santos et al. 2003) are spectroscopic works, while and[m/H](Fig.4,bottompanel).
in another case (Edvardssonet al. 1993) the temperaturesare
basedonuvby βphotometry.Thechiefprobleminthecaseof
−
spectroscopicdeterminationsisthat,ingeneral,theyaremostly 3.2.2. Santosetal.(2003)
applied to bright stars, which have poor 2MASS photometry
(the 2MASS detectors saturate for stars brighter than K 4 Tostudythecorrelationbetweenthemetallicityandtheprob-
≈
mag). This fact reduces the number of stars in the Fuhrmann ability of a star to hosta planet,Santoset al. (2003)obtained
(1998)andSantosetal.(2003)samplesthatcanbecompared spectroscopic temperatures for 139 stars based on the analy-
withSEDFmethod. sis of several iron lines. Effective temperatures for a total of
101 stars in the sample of Santos et al. can be obtained us-
ing the SEDF method.In this case, ∆T (Santos SEDF) is
3.2.1. Fuhrmann(1998) eff −
28 K, with σ = 68 K, and practically independent of the
Teff
This sample is composed of about 50 F and G nearby stars, temperature:TSantos = 1.053TSEDF 270K(Fig.5).Thereis
eff eff −
both main sequence and subgiants, of the Galactic disk and nodependenceof∆T with[m/H](Fig.5,bottompanel).
eff
6 E.Masanaetal.:Effectivetemperaturescaleandbolometriccorrections
6500
8000
6250
7000
6000
K) K)
MF) ( 6000 ec.) ( 5750
T(IReff T(Speff
5500
5000
5250
4000
SEDFT (K) eff 1350000 SEDFT(K)eff 50100000
IRMF - T eff--310500 Spec.T - eff --210000
4000 5000 6000 7000 8000 5000 5250 5500 5750 6000 6250 6500
T (SEDF) (K) T (SEDF) (K)
eff eff
K) 300 K) 200
SEDF T( eff 1500 SEDF T( eff 1000
IRMF - T eff--310500 Spec. T - eff--210000
-4 -3 -2 -1 0 1 -2.5 -2 -1.5 -1 -0.5 0 0.5
[m/H] [m/H]
Fig.3.ComparisonoftheeffectivetemperaturesfromtheIRFMand Fig.4.Comparisonof theeffectivetemperaturesfromfitstoBalmer
theSEDFmethodfor386starsinthesampleofRam´ırez&Mele´ndez linesandtheSEDFmethodfor24starsincommonwiththesampleof
(2005).Thebottompanelshowsthetemperaturedifferenceasafunc- Fuhrmann(1998).Thebottompanelshowsthetemperaturedifference
tionofthemetallicity. asafunctionofthemetallicity.
3.2.3. Edvardssonetal.(1993)
tobepreferredoverthebestpossibleaccuracy.Inthissection
ThesampleofEdvardssonetal.iscomposedby189nearbyF we present calibrations for both Teff and BC as a function of
andGtypestars.Incontrastwiththeprevioustwo,theeffective (V K)0, [m/H]and logg. To calculate the calibrations, the
−
temperatureisnotderivedfromspectroscopybutfromuvby β SEDFmethodwasappliedtoasampleofstarsintheHipparcos
−
photometry. To do so, the authors built a grid of synthetic catalogue,asdescribedbelow.Notethatthesecalibrationsare
photometryusing the atmospheremodels of Gustafsson et al. subjecttotwolimitationswithrespecttothefullSEDFmethod:
(1975) and further improvedit by adding several new atomic First, theyare simplificationssince notallthe available infor-
and molecular lines. Effective temperatures for 115 stars in mationisused,andsecond,individualuncertaintiescannotbe
their sample could be derived using the SEDF method. The determined.
average difference ∆T (Edvardsson SEDF) is 10 K, with
eff
−
a dispersion of 70 K and no dependence on the temperature:
4.1.Thestellarsample
TEdvardsson = 1.006TSEDF 27K(Fig.6).Asinthetwoprevi-
eff eff −
ouscases,thebottompanelofFig.6showsthatthetemperature We collected a sample of FGK dwarfs and subdwarfs in the
differenceisnotcorrelatedwith[m/H]. Hipparcos catalogue, and therefore with measured trigono-
metric parallaxes. Their V magnitudescome mainly from the
Hauck & Mermilliod (1998) catalogue, except for those stars
4. Parametriccalibrations
withlessthantwoobservations,whereweusedtheHipparcos
ThepracticaluseoftheSEDFmethodasithasbeendescribed catalogue. The entire sample has complete and non-saturated
in Sect. 2 is not straightforward since it requires the calcula- JHK photometry in the 2MASS catalogue. The metallicity
tion of synthetic photometry from stellar atmosphere models wasextractedfromthecompilationofCayreldeStrobeletal.
and then use a numerical algorithm to minimize the χ2 func- (2001) or computed from uvby β photometry– either mea-
−
tion.Parametriccalibrations(asafunctionofoneormorepa- sured fromour own observationsor obtainedfrom the Hauck
rameters) may offer a suitable means to estimate reliable ef- &Mermilliod(1998)catalogue–,usingaslightlyrevisedver-
fective temperatures in cases where simplicity and speed are sionoftheSchuster&Nissen(1989)calibration.Therangeof
E.Masanaetal.:Effectivetemperaturescaleandbolometriccorrections 7
6500 7000
6000
6500
K) K)
pec.) ( 5500 hot.) (
S P
T(eff T(eff 6000
5000
5500
K)4500 K) 300
DF ( 150 DF ( 150
SETeff 0 SET eff 0
Spec.- Teff --310500 Phot.T - eff--310500
4500 5000 5500 6000 6500 5500 6000 6500 7000
T (SEDF) (K) T (SEDF) (K)
eff eff
K) 300 K) 200
SEDF T( eff 1500 SEDF T( eff 1000
Spec. - T eff--310500 Phot. T - eff--210000
-1 -0.5 0 0.5 -1.5 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5
[m/H] [m/H]
Fig.5.Comparisonoftheeffectivetemperaturesfromironlinefitsand Fig.6. Comparison of the effective temperatures from photometry
theSEDFmethodfor101starsincommonwiththesampleofSantos and the SEDF method for 115 stars in common with the sample of
etal.(2003).Thebottompanelshowsthetemperaturedifferenceasa Edvardsson et al. (1993). The bottom panel shows the temperature
functionofthemetallicity. differenceasafunctionofthemetallicity.Thestandarddeviationfor
asinglestarinEdvardssonetal.(1993)is81K.
metallicities covered by the sample is 3.0 . [m/H] . 0.5.
−
Values of logg were computed from uvby β photometry a few measurements(and with no evaluationof systemat-
−
(Masana 1994; Jordi et al. 1996). Originally, the sample was ics),wehavesetaminimumerrorinV equalto0.015mag.
builttostudythestructureandkinematicsofthediskandhalo Theuncertaintiesintheabsolutefluxcalibrationaregiven
oftheGalaxy(Masana(2004))andafulldescriptionincluding by Cohen et al. (2003a,b) and are in the range 1.5–1.7%
thephotometryandacompletesetofphysicalparameterswill (0.016–0.019mag),dependingontheband.Forthosestars
beprovidedinaforthcomingpaper(Masanaetal.2006). affectedbyinterstellarreddening,theuncertaintyin A as
V
Inspiteoftheproximityofthestars(90%ofthemarecloser derived from photometric calibrations based on uvby β
−
than 200 pc), we computedindividualinterstellar absorptions photometry (Jordi et al. 1996) is expected to be of about
fromuvby β photometryandcorrectedthe observedmagni- 0.05mag,or 1.5%inT .
eff
− ∼
tudes.Asdiscussedbelow,interstellarabsorptionisoneofthe – Errors in [m/H] and logg: As mentioned above,
mostimportantsourcesofuncertaintyintheT determination. [m/H] was obtained, whenever possible, from spectro-
eff
scopicmeasurements,andotherwise we used photometric
calibrations, with assigned uncertainties of 0.10 dex and
4.1.1. Errors
0.15 dex, respectively. We assigned uncertainties of 0.18
For our sample, the errors in the magnitudes, metallicity and dex to logg values determined from photometric calibra-
surfacegravitywereestimatedinthefollowingmanner: tions. The effecton the final effectivetemperaturesdueto
the uncertainties of both [m/H] and logg is very small:
– Errors in the VJHK magnitudes: The total error in each an error of 0.5 dex in [m/H] has an effect in T of less
eff
magnitude was computed as the quadratic sum of the ob- than 0.5%, whereas the same error in logg has an effect
servational error, the error in the absolute flux calibration
thatrangesbetween0%and1%,dependingonthevalueof
and the error in the determination of the interstellar ex-
T andlogg.
eff
tinction. The first one comes from the photometric cata-
logues.However,topreventtheunderestimationoftheer- No error was attributed to the flux in the stellar atmosphere
ror in the V band, usually computed from the average of models. Comparisonscarried out by using other stellar atmo-
8 E.Masanaetal.:Effectivetemperaturescaleandbolometriccorrections
Fig.7.Relativeerror(%)ineffectivetemperatureassumingσ = 0.015mag,σ = 0.2,σ = 0.2andtheerroroftheabsoluteflux
VJHK [m/H] logg
calibration.Topleft:[m/H]=0.0.Topright:logg=4.5.Bottomleft:[m/H]= 2.0.Bottomright:logg=2.0.
−
sphere models such as those by Castelli et al. (1997) and the keptinmindthatmostofthestarsinoursampleareessentially
NextGenmodelsbyHauschildtetal.(1999)showresultingdif- unreddened,thusyieldingthebestpossibleaccuracy.
ferencesintemperaturebelow 0.3%inallcases(Ribasetal. Table 3 lists effective temperatures, angular semi-
∼
2003). diameters, radii and bolometric corrections in the V and K
AnestimationofthefinalerrorsinT asfunctionofT , (2MASS) bands with the corresponding uncertainties for the
eff eff
[m/H] and logg is shown in Fig. 7. As can be seen, the fi- entire sample. Using these values, we calculated simple para-
nalerrorisalmostindependentof[m/H]andlogg,butnotof metriccalibrationsofeffectivetemperatureandbolometriccor-
T . Hotter stars have greater uncertainties (slightly >1% for rectionasdescribedbelow.
eff
T = 7500 K) than cooler stars (0.6% for T = 5000 K).
eff eff
It is important to note that, in the case of reddened stars, an
4.2.Effectivetemperaturecalibration
uncertaintyof0.05maginA candoubletheerrorinT com-
V eff
pared to the values in Fig. 7. For the angular semi-diameter Although the effective temperature for FGK type stars is
the behaviour of the errors is very similar to those of the ef- strongly correlated with the (V K) index (see for instance
0
−
fectivetemperature,withvaluesforunreddenedstarsofabout Alonsoetal.(1996a)),italsodependsweaklyonthemetallicity
1.0–2.5%.ThismeansthatforHipparcosstarswithgoodparal- andsurfacegravity,aswementionedinSect.2.Therefore,an
laxes,weareabletodeterminethestellarradiiwithremarkable empiricalcalibrationofT shouldincludetermsinall(V K) ,
eff 0
−
uncertaintiesofabout1.5–5.0%. [m/H]andlogg.Furthermore,inourcasethecalibrationswere
Figure 8 shows the cumulative histograms of the relative constructedseparatelyintwo(V K)0intervals.Starsdeparting
−
errorsin effectiVetemperature,angularsemi-diameterandra- morethan3σfromthefitwererejected.Theresultingexpres-
dius for the 10999stars of the sample. As can be seen, about sionsare:
85%ofthestarshavedeterminationsofT betterthan1.1%.
eff
The relative error in the angular semi-diameter is also better – 0.35<(V K)0 <1.15(4954stars):
−
than1.5%for about85%ofthe stars. In thecase ofthe radii,
θ = 0.5961+0.1567(V K) +0.0309(V K)2+
themaincontributortotheerroristheuncertaintyintheparal- eff − 0 − 0
lax.Evenso,50%ofthestarshaveradiusdeterminationsbetter + 0.009[m/H]+0.0022[m/H]2
than 10%, and 85%of the stars better than 25%. It shouldbe + 0.0021(V K) [m/H] 0.0067logg
0
− −
E.Masanaetal.:Effectivetemperaturescaleandbolometriccorrections 9
11
nn
ctioctio00..7755
aa
ar’s frar’s fr00..0022..5555
StSt
00
00 0.25 00..55 0.75 11 1.25 11..55 1.75 22 2.25 22..55 2.75 33
Relative error in T (%)
eff
11
nn
ctioctio00..7755
aa
ar’s frar’s fr00..0022..5555
StSt
00
00 0.25 00..55 0.75 11 1.25 11..55 1.75 22 2.25 22..55 2.75 33
Relative error in θ (%)
11
nn
ctioctio00..7755
aa
ar’s frar’s fr00..0022..5555
StSt
00
00 5 1100 15 2200 25 3300 35 4400 45 5500
Relative error R (%)
Fig.8. Cumulative histograms of the relative error in effective tem-
perature,angularsemi-diameterandradiusforthe10999starsinthe
sample.
Fig.9. Residuals of the T fit as function of effective temperature,
eff
metallicityandsurfacegravity.
σ = 0.0028 (8)
θeff
getfromMKclassification.Theerrorineffectivetemperature
– 1.15 (V K) <3.0(5820stars):
0
≤ − causedbyanerrorinloggwillbe:
θ = 0.5135+0.2687(V K) 0.0174(V K)2+
eff + 0.0298[m/H] 0.00−09[m0/−H]2 − 0 ∆Teff = 50a40Te2ff∆logg (11)
−
0.0184(V K) [m/H] 0.0028logg
0 whereaisthecoefficientoftheloggtermsinEqs.(8)and(9).
− − −
σθeff = 0.0026 (9) In the worst case, that of the hotter stars, ∆Teff = 85 ∆logg.
Thus,eveniftheuncertaintyinloggisasmuchas0.5dex,the
whereθ = 5040.ThestandarddeviationofEqs.(8)and(9)is
eff Teff errorinducedinTeff isjust40K.
about20 K and 25 K, respectively.As shown in Fig. 9, there
The fits for four different metallicities and logg = 4.5 to-
isnoresidualtrendasafunctionof(V K) ,[m/H]orlogg.
0 getherwiththestellarsampleareshowninFig.10.Figure11
−
Equation(8)isaplicableintherange3.25 . logg . 4.75and
showsthe empiricalT -(V K) relationshipsasa function
eff 0
eq.9intherange3.75.logg.4.75.Furthermorethecalibra- −
ofthemetallicity.
tionsarevalidintherangesofcoloursandmetallicitiesofthe
sample:
4.3.Bolometriccorrectioncalibration
3.0<[m/H]< 1.5 for 1.0<(V K) <2.9
0
− − − Since the SEDF method provides both effective temperature
1.5 [m/H]< 0.5 for 0.5<(V K) <2.9
− ≤ − − 0 andangularsemi-diameter,italsonaturallyallowsforthede-
0.5 [m/H]<0.0 for 0.4<(V K)0 <3.0 termination of the bolometric correction in a specific band.
− ≤ −
0.5 [m/H]<0.5 for 0.35<(V K) <2.8 (10) From this, if the distance is known, one can compute the lu-
0
≤ −
minosityofthestar.Thebolometriccorrectioninagivenband
While(V K) isanobservationalquantityand[m/H]can
0 isdefinedasthedifferencebetweenthebolometricmagnitude
−
be obtained from photometric and/or spectroscopic measure-
andthemagnitudeinthatband:
ments, a good determination of logg is usually unavailable
for the most of the stars. This could severely restrict the ap- BC = M M =m m (12)
i bol i bol i
− −
plicability of the above calibrations. However, some photo-
where m and m are assumed to be corrected of interstellar
metricindexes,astheStro¨mgrenδc (see Crawford(1975)or bol i
1
reddening. M can be easily expressed as a function of the
Olsen(1988)),aregoodsurfacegravityindicatorsand,ifavail- bol
radiusandeffectivetemperature:
able,canhelptoestimatelogg.Ontheotherhand,catalogues
ofspectroscopicmetallicitiesusuallyprovideanestimationof R T
M = 5log 10log eff +4.74 (13)
thesurfacegravity.Finally,acrudeestimationofloggcanbe bol
− R − Teff
⊙ ⊙
10 E.Masanaetal.:Effectivetemperaturescaleandbolometriccorrections
riccorrection:
BC = M M =
x bol x
−
θ T
= 5log 10log 0.26 m (14)
x
− KR !− T − −
⊙ ⊙
where is the factor correspondingto the transformation of
K
units.Oncethebolometriccorrectionforabandiisknown,the
bolometriccorrectionforanyband jcanbedeterminedfrom:
BC =(m m )+BC (15)
j i j i
−
The error in the bolometric correction can be expressed as a
functionoftheuncertaintiesinT ,θ(or )andm,asinSect.
eff i
A
2.4:
5 σ 2 10 σ 2
(σ )2 = θ + Teff +(σ )2 =
BCi ln10 θ ! ln10 Teff ! mi
10 σ 2
= (σ )2+ Teff +(σ )2 (16)
A ln10 Teff ! mi
The procedure described here was used to compute the
Fig.10. T -(V K) fits for four groups of stars with different bolometric correction in the K (2MASS) band for the stars
metallicitieeffs.The−empir0icalrelationshipscorrespondtologg=4.5and in our sample. In the same way as for the effective tempera-
[m/H]= 2.0, 1.0, 0.25and+0.25. ture, we calibrated BC as a function of (V K) , [m/H] and
0
− − − −
loggwiththefollowingresults:
– 0.35<(V K) <1.15(4906stars):
0
−
BC = 0.1275+0.9907(V K) 0.0395(V K)2+
K − 0− − 0
+0.0693[m/H]+0.0140[m/H]2
8000 +0.0120(V K) [m/H] 0.0253logg
[m/H] = -3.0 − 0 −
[m/H] = -2.0 σ = 0.007mag (17)
BC
[m/H] = -1.0
7000 [m/H] = 0.0 – 1.15 (V K)0 <3.0(5783stars):
≤ −
BC = 0.1041+1.2600(V K) 0.1570(V K)2+
) K − − 0− − 0
K +0.1460[m/H]+0.0010[m/H]2
T (eff6000 −0.0631(V−K)0[m/H]−0.0079logg
σ = 0.005mag (18)
BC
5000
Therangeofvalidityofthesecalibrationsisthesameasinthe
caseoftheeffectivetemperature.Thebolometriccorrectionin
4000 anybandcanbeobtainedfromBCK viaEq.(15).
Figure12showsthefitsforfourdifferentmetallicities,to-
0 1 2 3 4 gether with the stars in the sample used to obtain the calibra-
(V-K) tions. The BC (V K) relationships as a function of the
0 K − − 0
metallicity are shown in Fig. 13. The calibration is tabulated
inTable2andcomparedwiththecalibrationsbyAlonsoetal.
(1995)andFlower(1996)inFig.14,showinggoodagreement.
Fig.11.T -(V K) relationshipsforlogg=4.5andfourdifferent
eff − 0
metallicities.
5. Discussion
whereR =6.95508108mandT =5777K.FortheSunwe Theproceduredescribedinthispaperyieldsthreebasicstellar
eff
adopt V(⊙ ) = 26.75 mag and m⊙ ( ) = 26.83 mag, and parameters: the best-fitting effective temperature and angular
bol
⊙ − ⊙ −
thereforeBC ( )= 0.08(Cox2000). semi-diameterand,fromthem,thebolometriccorrection.Ifthe
V
⊙ −
Using the definition of the absolute magnitude at a given distance is known, θ can be transformed into the true stellar
band (M = m + 5logπ + 5) and expressing the radius as radius. The accuracies of the parameters for the stars in our
x x
function of the parallax (π) and the angular semi-diameter sampleare0.5–1.3%inT ,1.0–2.5%inθand0.04–0.08mag
eff
(R = θ/π), we obtain the following formula for the bolomet- fortheBC.