Fundamental M-dwarf parameters from high-resolution spectra using PHOENIX ACES models: I. Parameter accuracy and benchmark stars

2.8 MB·

by  Vera Maria Passegger

Astronomy&Astrophysicsmanuscriptno. Mdwarf_ACES_corr (cid:13)cESO2016
January11,2016
Fundamental M-dwarf parameters from high-resolution spectra
using PHOENIX ACES models (cid:63)
I. Parameter accuracy and benchmark stars
V.M.Passegger1,S.Wende-vonBerg1 andA.Reiners1
InstitutfürAstrophysik,Georg-August-UniversitätGöttingen,Friedrich-Hund-Platz1,D-37077,Germany
e-mail:[e-mail]
6
ABSTRACT
1
0 M-dwarfstarsarethemostnumerousstarsintheUniverse;theyspanawiderangeinmassandareinthefocusofongoingandplanned
2 exoplanetsurveys. Toinvestigateandunderstandtheirphysicalnature,detailedspectralinformationandaccuratestellarmodelsare
n needed.Weuseanewsyntheticatmospheremodelgenerationandcomparemodelspectratoobservations.Totestthemodelaccuracy,
a wecomparedthemodelstofourbenchmarkstarswithatmosphericparametersforwhichindependentinformationfrominterfero-
J metric radius measurements is available. We used χ2-based methods to determine parameters from high-resolution spectroscopic
observations. OursyntheticspectraarebasedonthenewPHOENIXgridthatusestheACESdescriptionfortheequationofstate.
8
Thisisamodelgenerationexpectedtobeespeciallysuitableforthelow-temperatureatmospheres. Weidentifiedsuitablespectral

] tracers of atmospheric parameters and determined the uncertainties in Teff, logg, and [Fe/H] resulting from degeneracies between
SR pσa[Frae/mH]et=ers0a.1n1d.frTohmesnheowrtcmoomdienlgsspoefcttrhaeamchoideevleaatmreolsipabhleerems.aTtchhetionhoeurrenotbsuenrcveerdtadinattiae;sowuerfirensdulatrsefσorTeTffeff=a3n5dKlo,gσglogagre=c0o.n1s4i,staenndt
withliteraturevaluestowithin1σ. However,metallicitiesreportedfromearlierphotometricandspectroscopiccalibrationsinsome
.
h casesdisagreewithourresultsbymorethan3σ. Apossibleexplanationaresystematicerrorsinearliermetallicitydeterminations
p thatwerebasedoninsufficientdescriptionsofthecoolatmospheres. Atthispoint,however,wecannotdefinitelyidentifythereason
- forthisdiscrepancy,butouranalysisindicatesthatthereisalargeuncertaintyintheaccuracyofM-dwarfparameterestimates.
o
r Keywords. line:formation,profiles-stars:low-mass,browndwarfs,atmospheres-techniques:spectroscopic
t
s
a
[
1. Introduction metricfluxesfromphotometry. Alluncertaintiesliebelow80K.

1 ThesameapproachwasusedbyvanBelle&vonBraun(2009).
vDeterminingatmosphericparametersinMdwarfsisverydiffer- Theycalculatedeffectivetemperaturesforawiderangeofspec-
7entfromthesituationinSun-likestars. Thecomplexityofcool tral types, including two main-sequence M dwarfs. Gaidos &
7atmospheresisdramaticallyenhancedbecausethemainopacity Mann(2014)usedPHOENIXmodelatmospheres((Allardetal.
8sourcesaremoleculesandnotatoms. Theformationandabun- 2001;Hauschildtetal.1997))todeterminetheeffectivetemper-
1dance of these molecules is a complex process, and molecular
aturefromspectraobservedinthevisiblewavelengthrange. For
0absorptionbandsconsistofthousandsofindividuallinesthatare
spectra taken in near-infrared K band they used spectral curva-
1.notatallorsometimesonlypoorlyknown.Forexample,Fischer tureindices. Differentmethodshavebeenusedtodeterminethe
0&Valenti(2005)determinedeffectivetemperature,surfacegrav- surface gravity. Ségransan et al. (2003) used interferometry to
6ity,andmetallicityinasampleof1040F-,G-,andK-typestars. determinetheangulardiameterofthestars: togetherwithmass-
1Theprecisiontheyachievedintermsof1σuncertaintiesis44K
luminosity relations, the mass can be derived and the surface
v:forTeff,0.06dexforlogg,and0.03dexforabundances. Accu- gravity can be easily calculated. Other authors, for example,
ratedeterminationsoflow-massstaratmosphericparameters,on
i Rice et al. (2015) and del Burgo et al. (2013), used model fits
Xtheotherhand, stilldonotprovideaclearpicture, inparticular
todirectlydeterminethesurfacegravity,whichavoidsassump-
rwhenmetallicityisconcerned. tionsaboutradius,mass,andage.Determiningthemetallicityin
a
Previousworktryingtodeterminestellarpropertiesforlow- Mdwarfsismoredifficultthandeterminingtemperatureandsur-
massstarsgenerallydealtwitheachparameterseparately.Rojas- facegravity.Afterseveraldecadesofresearch,differentmethods
Ayalaetal.(2012)investigatednear-infraredK-bandspectraof andmodelscanstillgivecontradictingresults,hencewedecided
133Mdwarfs. Theydeterminedeffectivetemperaturesbyusing todiscussthistopicinmoredetailbelow.
theH2O-K2indexthatquantifiesabsorptionduetoH2Oopac-
ity.ForcalibrationtheyusedBT-Settlmodels(Allardetal.2011) ThemeasurementofmetallicitiesinMdwarfsisdifferentto
of solar metallicity. The uncertainties in temperature lie below the determination in Sun-like stars because the dense forest of
100K. Another approach was used by Boyajian et al. (2012), spectralfeaturescomplicatesaline-by-lineapproach. Instead,a
who calculated the effective temperature for nearby K and M fullspectralsynthesisoftheconsideredspectralrangeisprefer-
dwarfs through interferometrically determined radii and bolo- able, which is generally much more complex than computing
individual lines. Early attempts to measure metallicities for M
(cid:63) BasedonobservationscarriedoutwithUVESatESOVLT. dwarfs date back to Mould (1976), who performed a line-by-
Articlenumber,page1of9
line analysis of atomic near-IR lines. Jones et al. (1996) used manyfollowingstudiessince,forexamplebyCasagrandeetal.
PHOENIX model spectra (Allard et al. 2001; Hauschildt et al. (2008) and for the calibration applied in Neves et al. (2013).
1999) to follow a similar approach, and Gizis (1997) matched However,Rojas-Ayalaetal.(2012)foundthattheresultsofBon-
low-resolution optical spectra to the same models. One of the filsetal.(2005)showlowermetallicityvaluesforstarswithso-
first analyses of a high-resolution M dwarf spectrum was per- lar and super-solar metallicities. Gaidos & Mann (2014) used
formedbyValentietal.(1998)andZboril&Byrne(1998),try- empiricalrelationsbetweenmetallicityandatomiclinestrength
ing to fit high-resolution spectra to PHOENIX models. They in the H and K band calibrated with FGK+M binary systems
concludedthattheirM-dwarfmetallicitieswereonlyindicative, asdescribedbyMannetal.(2013). Theirresultsinmetallicity
a conclusion that is probably valid for all previous references. agree excellently well with those of Rojas-Ayala et al. (2012),
AsanexamplefortheproblemsinherenttoM-dwarfmetallicity withmeandifferencesof0.03dex.ArecentworkbyMaldonado
determinations, we can compare the values for one star found etal.(2015)usedpseudo-equivalentwidthsofopticalspectrato
withdifferentanalyses; forthemid-MobjectGl725B(M3.5), determine effective temperature and [Fe/H]. They showed that
Valenti et al. (1998) reported [Fe/H] = −0.92, while Zboril & the calibration of Casagrande et al. (2008) underestimates tem-
Byrne(1998)found[Fe/H]=−0.15.Theresultsfortheprobably peraturesbecauseCasagrandeetal.(2008)assumedMdwarfsto
best-known mid-M dwarf, Barnard’s star (GJ 699, M4), which beblackbodies,butMdwarfshavemorefluxintheinfraredthan
we also investigated here, are spread in the literature between predicted for a blackbody. For metallicities, however, Maldon-
[Fe/H]=−0.39±0.17fromRojas-Ayalaetal.(2012)and−0.75 ado et al. (2015) reported good agreement of their results with
fromJonesetal.(1996). Rojas-Ayalaetal.(2012)analysedthe Nevesetal.(2012)andNevesetal.(2014).
equivalentwidthsofNaIandCaIandcalibratedtheirscaleusing A surprising result that arose from the comparison be-
metallicitiesof18FGK+Mbinarysystems. tweenmetallicitiesinSun-likeplanet-hostingstarsandM-dwarf
Animportantindicationthatmetallicityseverelyaffectsthe planet-hosting stars was made by Bean et al. (2006b), who
energydistributioninlow-massstarswasprovidedbyDelfosse claimedthatSun-likeplanethoststendtohavehighmetalabun-
etal.(2000). Theauthorsuseddirectmassdeterminationsfrom dances, but this is not the case for M-dwarf planet hosts. This
measurements in binary systems to derive an empirical mass- result was disproved by several subsequent works (e.g.Gaidos
luminosity relation. They found that while this relation shows & Mann (2014); Johnson & Apps (2009); Rojas-Ayala et al.
relativelylittlescatterintheKband,thescatterintheV ishuge. (2012)), whichshowedthatM-dwarfplanethostsalsohaveso-
Morespecifically,thecolourindexV −K showslargescatteras lartosuper-solarmetallicities. Onewaytoexplainthediscrep-
afunctionofmass,whichcanbeexplainedbyascatterinmetal- ancyfoundbyBeanetal.(2006b)isthatmetallicitydetermina-
licities,aswasshownusingpredictionsofV −K colourscalcu- tionsforMdwarfsaresystematicallyunderestimatingthemetal
lated from the PHOENIX models. Clearly, metallicity plays a abundance,implyingthatthecolour-metallicityrelationsarenot
crucialroleforthespectraatvisualwavelengths,whileitisnot generallyapplicableeither. ThisalternativewastestedbyJohn-
asimportantatnear-IRwavelengths. son & Apps (2009), who compared metallicity measurements
AquantitativeimprovementtometallicitycalculationsinM inSun-likestarsandMdwarfsintheoverlappingregionwhere
dwarfswasachievedwhenSégransanetal.(2003)reportedinter- different calibration methods are valid. They showed that the
ferometricradiusmeasurementsofMdwarfs.Directradiusmea- metallicitiesofthehigh-metalMdwarfsintheirsampleareun-
surementstogetherwiththeluminosityofandthedistancetoa derestimatedbyasmuchas0.32dexin[Fe/H]onaverage.Neves
starprovideindependentconstraintstoeffectivetemperatureby etal.(2012)reportedthatthemethodofJohnson&Apps(2009)
removingonefreeparameter. Furthermore,themass-luminosity is a good predictor for high metallicities, but tends to overesti-
relation from Ségransan et al. (2003) can estimate the mass as matelow-metallicityMdwarfsbyabout0.14dex. Rojas-Ayala
afunctionofthenear-IRluminosityreasonablywell,sothatto- etal.(2012)cametothesameconclusion.Schlaufman&Laugh-
gether with the radius, the surface gravity is known as well. In lin(2010)inferredaphotometricmetallicitycalibrationandalso
systems with direct radius measurements, measurements of the found that Johnson & Apps (2009) overestimated metallicities.
apparentluminosity,andaccuratedeterminationsofthedistance, Rojas-Ayala et al. (2012) reported that Schlaufman & Laugh-
metallicityremainstheonlyfreeparameterinthedescriptionof lin(2010)underestimatedvaluesforsomesolarandsuper-solar
a stellar atmosphere. This concept was applied to two nearby metallicitystars,butforstarswithsub-solarmetallicitytheyei-
M dwarfs by Woolf & Wallerstein (2004) and Dawson & De therunder-oroverestimatebyupto0.6dex. Amethodsimilar
Robertis(2004)usingNextGenmodelatmospheres(Hauschildt totheonewedescribeinthisworkwasusedbyRajpurohitetal.
et al. 1999). Woolf & Wallerstein (2005) measured metallici- (2013). Theycomparedlow-andmedium-resolutionspectraof
ties in 15 M dwarfs for which no direct radius measurements 152 M dwarfs to BT-Settl models and applied a χ2-method to
were available. Bonfils et al. (2005) enriched this sample with determine effective temperatures. Rajpurohit et al. (2014) im-
20 systems consisting of an F-, G-, or K-dwarf primary and an proved this work by additionally determining logg and metal-
M-dwarfsecondary. Thesebinariesarebelievedtohaveformed licityandinterpolatingbetweenthemodelgridpointsforthese
togethersothattheirmetalabundanceisexpectedtobeidentical, two parameters. This was done for high-resolution spectra of
which provides the only independent test of M-star metallicity. 21 M dwarfs. A comparison of available metallicity determi-
A similar approach was chosen by Bean et al. (2006a,b), who nations was carried out by Neves et al. (2012). In their recent
usedfivebinariestodeterminethemetalcontentoftheprimary work, Mann et al. (2015) presented their temperature determi-
andfromthisdeducedthemetalcontentoftheM-dwarfsecon- nation using optical spectra and BT-Settl models following the
daries. The model they developed was then used to determine approachofMannetal.(2014). Formetallicitytheyusedequiv-
the metallicity of three planet-hosting M dwarfs. Bonfils et al. alentwidthsofatomicfeaturesinnear-infraredspectratogether
(2005) also provided a colour-metallicity relation, from which with the empirical relation from Mann et al. (2013) and Mann
themetalabundanceofMdwarfscanapparentlybederivedsim- etal.(2014). Theyfoundonlyslightdifferencestothemetallic-
ply from their colours. This reduces the complex problem of itiesreportedbyRojas-Ayalaetal.(2012), Nevesetal.(2013),
atmosphericphysicsinMdwarfstoatwo-dimensionalrelation and Neves et al. (2014). In this paper we aim for a fresh at-
between infrared and visual luminosities and has been used in tempttodeterminetheatmosphericparametersofcoolstars. We
Articlenumber,page2of9
Passegger,Wende-vonBergandReiners:FundamentalM-dwarfparameters
Table1.Parameterspaceofthespectralgrid. (seeWendeetal.(2009)forFeHasanexample). Moresensitive
tosurfacegravityarealkalilines(Fig.1),whichshowlargealter-
Range Stepsize ationsoftheirlinewingsthatareduetopressurebroadening(in
Teff [K] 2300–5900 100 caseoftheKlinesitismorepronouncedtowardscoolertemper-
log(g) 0.0–+6.0 0.5 atures).WechosetheK-andNa-linepairsataround7680Å and
[Fe/H] −4.0–−2.0 1.0 8190Å, respectively. To determinethemetallicity, we can use
−2.0–+1.0 0.5 all these regions as well because the (cid:15)-TiO band and the alkali
lines are strongly dependent on this quantity (see Fig. 2). Ra-
jpurohitetal.(2014)alsousedtheK-andNa-linepairsbecause
takeadvantageofthenewPHOENIXmodelgrid(Husseretal. of their sensitivity to gravity and metallicity, as well as several
2013),whichmakesuseofsignificantlyadvancedmicrophysics TiO-bandsfortemperaturedetermination. Theyalsoillustrated
relevanttoM-dwarfatmospheres.InSect.2wedescribethenew the dependency on the different stellar parameters. The chosen
model, andinSect.3weintroduceourmethodtoderiveatmo- spectral regions are also affected by lines of the Earth’s atmo-
spheric properties from comparison between synthetic spectra sphere. EspeciallytheK-andNa-linepairsarecontaminatedby
andobservations. Observationaldatafrombenchmarkstarsare O2andH2Obands,respectively. Weusedmaskstoexcludethe
describedinSect.4,andananalysisofthesestarsiscarriedout atmospheric lines from the fit. The contamination of the TiO
inSect.5,beforewesummariseourresultsinSect. 6. bandsaround7050Å and8430Å isveryweakandcanbene-
glected. The degree of sensitivity on a certain parameter for a
particular line (band) also varies. In Fig.3 we show how the
2. PHOENIXACESmodelatmospheres width of a χ2-level in a χ2-map changes with varying effective
ForthespectralfittingweusedthelatestPHOENIXgridACES temperature (i.e. the Teff of the synthetic spectrum from which
(see Husser et al. 2013)1. It makes use of a new equation of the χ2-map is produced is varied) for a fixed surface gravity of
logg=5.0cgsandmetallicityofz=0.0cgs. Thechangeisalso
state, whichaccountsespeciallyfortheformationofmolecules
measured in terms of discretion elements in the χ2-maps, since
at low temperatures. Hence it is ideally suited for the syntheti-
thisdeterminesthegivenresolution(leftaxis). Allinvestigated
sation of cool stars spectra. The 1D models are computed in
plane-parallelgeometryandconsistof64layers. Convectionis regionsbecomelessgravitysensitivetowardshigherTeff ,which
isprobablyduetotheincreasingthermalbroadening,whichbe-
treatedinmixing-lengthgeometry, andfromtheconvectiveve-
locityamicroturbulentvelocityisdeducedviav = 0.5·v comesstrongerthanthepressurebroadening(seealsoSect.3.3).
mic conv
Atthispointwehavetokeepinmindthatthesensitivitycurves
(see Wende et al. (2009)). Both are used to compute the high-
only represent the behaviour for the chosen parameter values.
resolutionspectra. Anoverviewofthemodelgridparametersis
They look different for other metallicities or surface gravities,
showninTable1. Inallmodelstheassumptionoflocalthermal
which are not shown in detail here. Nevertheless, it becomes
equilibriumisused.
clearthatthecombinedχ2-mapofallregionsisthebestchoice
First comparisons of these models with observations show
formosttemperaturesandprovidesthehighestsensitivity. Even
that the quality of the computed spectra is greatly improved in
thoughthesensitivityoftheKlinesisbetterformosttempera-
comparisontoolderversions. EspeciallytheregionsoftheTiO
turesthanthecombinedone, wewouldnotsuggesttouseonly
bandsintheopticalarenowwellfitted. Theseregionsaresome
of the key regions to determine effective temperatures (see be- these lines because the results would then only depend on two
lines. Experience in fitting real observations showed that the
low). OneprobleminpreviousPHOENIXversionswasthatthe
resultsdeducedfromtheKlinesalonecandifferfromthecom-
(cid:15)-andγ-TiObandsinobservationscouldnotbereproducedwith
thesameeffectivetemperature(Reiners2005). Thisproblemis binedsolutionwherethelattermatchestheactualparametersto
ahigheraccuracy.
nowsolvedinthecurrentversionofthecode(seebelow).
3. Parameterdeterminationmethod 3.2. χ2-method
Sincetheparameters,Teff,logg,andmetallicityinM-typestars
can be strongly degenerate, it is necessary to use spectral re- To determine the stellar parameters, we basically used a χ2 re-
gionsthataresensitivetooneormorestellarparameterssimul- duction. We started with the χ2 determination using a low-
taneously to break the degeneracies. To determine the best set resolution grid of atmospheres in a wide range around the ex-
ofparametersforagivenstar, aχ2-methodisappropriate. The pectedparametersoftheobjectofinterest. Inthisstep,themod-
detailsofthemethodusedherearedescribedinthefollowing. els were first convolved to match the observed spectral resolu-
tion. Then we normalised the average flux of the models and
theobservedspectratounity. Afterthis,themodelswereinter-
3.1. Spectralregions
polatedtothewavelengthgridoftheobservedspectra. Finally,
We chose several spectral regions that exhibit different depen- everymodelofthegridwascomparedtotheobservedspectrum
denciesonthethreestellarparameters. Wechosethemolecular ateachwavelengthpoint,andtheχ2wascalculatedtodetermine
TiObandsaround7050Å and8430Å (γ-and(cid:15)-electronictran- a rough global minimum. To obtain more pronounced minima
sitions, respectively) since these oxide bands are very sensitive in the χ2-map, a dynamical mask was applied to every model
toeffectivetemperature,butalmostinsensitivetosurfacegravity spectrum. Figures1and2showtheχ2-mapsafterthisfirststep
(Fig.1). For cooler stars, as shown here, a dependence on sur- for the different wavelength ranges we used. In the next step
facegravityisintroducedbytheincreasingmicro-turbulentve- we used the IDL curvefit-function to determine accurate stellar
locities,whichenhancethelinewidthtowardslowerloggvalues parametersaroundanarrowrangeoftheminimumusinglinear
interpolationinsidethemodelgrid. Todothis,weusedthethree
1 http://phoenix.astro.physik.uni-goettingen.de/ smallestlocalminimafromthecombinedχ2-mapasstartvalues
Articlenumber,page3of9
Fig. 1. χ2-maps of the used oxygen bands and alkali lines for the
M dwarf GJ551 with logg = 5.02, Teff = 2927K, Fe/H = −0.07,
andS/N ∼ 100. WeshowthefitqualityintheTeff -loggplaneafter
calculatingaroughglobalminimumonthelow-resolutiongrid.
Fig.3. Changesinsensitivityoncertainparametersfordifferentlines
with increasing temperature. The ciel-function is used because only
discretenumberscanberesolved.
model spectrum, which should be applied to the observations,
was determined by dividing the model by the mean spectrum.
Thoseregionsshowingawidedifference(i.e. ratiosverydiffer-
entfrom1)indicatewavelengthregionsthatareverysensitiveto
theactualparameterconfiguration. Theseregionsweremasked
and used as weighting in the χ2 calculation. Applying such a
maskhasnobasicinfluenceonfindingthebestfit,butresultsin
morepronouncedminimaintheχ2-maps. Toaccountforslight
Fig.2. χ2-mapsoftheusedoxygenbandsandalkalilinesfortheM differencesofthecontinuumlevelandpossiblelineartrendsbe-
dwarf GJ551 with logg = 5.02, Teff = 2927K, Fe/H = −0.07, and tween the already normalised observed and computed spectra,
S/N ∼ 100. We show the fit quality in the Teff - [Fe/H] plane after weappliedare-normalisation. Weused
calculatingaroughglobalminimumonthelow-resolutiongrid.
continuumfit
Fobs = Fobs· model , (1)
re−norm continuumfit
forthefittingalgorithmtosearchforaglobalminimumthatmay observation
belocatedbetweenthegridpointsoftheχ2-map. where the continuum fits are linear. This has no significant in-
fluenceonthepositionsoftheminima,butimprovestheoverall
accuracy.
3.2.1. Dynamicalmask andre-normalisation
As already mentioned, not all parts of the spectrum show the
3.2.2. Fitalgorithm
same dependence on the stellar parameter. In certain parame-
ter regions, certain lines react stronger or weaker to variations. TheIDLcurvefit-functionturnedouttobethemoststable,accu-
Toweighttheverysensitivelinesmoreintheχ2-determination, rate,andfastestalgorithmtodeterminethesetofparameters.We
we applied a dynamical mask that depends on the model spec- also tested the IDL powell- and amoeba-algorithms. Since the
trumcurrentlyappliedtotheobservedspectrum. Inafirststep, curvefit-functionrequirescontinuousparameters,weperformed
we produced a synthetic mean spectrum, constructed from all athree-dimensionallinearinterpolationinthecomputedspectra
model spectra within the parameter range used for χ2 calcula- on the grid shown in Table 1. The interpolation was made for
tion. Then the difference between the mean spectrum and the eachwavelengthpointintherequiredwavelengthrange.
Articlenumber,page4of9
Passegger,Wende-vonBergandReiners:FundamentalM-dwarfparameters
Fig.5. ComparisonofthenewPHOENIXmodels(grey)tofourstarswithknowntemperatureandsurfacegravity(colour;fromtoptobottom:
GJ411,GJ551,GJ667C,andGJ699). Thenewmodelsprovideasubstantialimprovementovertheoldmodelgeneration(seeReiners2005). In
particular,thetwoTiObandsyieldconsistentresults,althoughtheremightstillbesomeproblemsfittingtheK-andNa-lines(e.g.seespectrumof
GJ551andGJ699).ThedatawerenotcorrectedforabsorptionlinesfromEarth’satmosphere,thereforemanysharplinesseenintheobservations
arenotcapturedbythemodels.Theselineswerenotincludedinthefit.
3.3. Precisionofthemethod means that the determined parameters are slightly higher than
theactualones.
To test the precision of our method, we produced a set of
Wefindstandarddeviationsfromthemeanvalueof35Kfor
1400 spectra with uniformly distributed random parameters
(Teff, logg, [Fe/H], and vsini) and different resolutions of R = Teff, 0.14dex for logg, 0.11dex for [Fe/H], and 0.5kms−1 for
vsini. No Gaussian FWHM was used since the residual distri-
100000, 44000, and 10000. We added Poisson noise to simu-
late a S/N of ∼ 100. The starting values differ from the actual butionsarenotsymmetric. Thereasonfortheasymmetryinthe
p[Faera/Hm]e,taenrsdi±n1akrmansg−e1ofofr±r5o0taKtiofnoarlTberffo,a±de0n.2in5gd.eWxefoarlsloogugseadnda ltoergogfatnhde[qFuea/Hnt]itpy.lotFiosrplroowbaebfflyecdtuiveetotemthpeelroagtaurrietshmthiecdcherairvaecd-
continuum normalisation different to the one used in the fitting temperatures are systematically lower. This changes towards
routine to simulate normalisation effects. We used the method hightemperaturesintotheopposite. Thisislikelyrelatedtothe
temperature-sensitive TiO bands, which are hardly present for
describedabovetodeterminetheparametersandshowthedevi-
high temperatures and start to saturate towards the cooler end.
ations from input to output parameters in the set of histograms
inFig.4forR=100000. However,theaveragedeviationsatbothendsareabout50Kand
agreewiththefinalprecision.
The deviation from a mean residual value of zero probably
stems from the fitting algorithm, since we observe a change in In the plot for the rotational velocities, the largest scatter is
sign between the curvefit-function and the amoeba-algorithm. foundforvaluesbelow3km.Thisisexplainedbytheinstrumen-
Thetwoalgorithmsusedifferentconvergencecriteria,whichwe talresolutionthatwesettoR = 100000,whichequalsabroad-
believe results in the offset. In the presented case all values eningof∼ 3km. Hencelowervelocitiescannotbeexpectedto
except for the resolving power (or v sini) are positive, which beresolved.
Articlenumber,page5of9
chips. For GJ411 and GJ551 the ESO PHASE3 data products
were used. The data for GJ667C and GJ699 were reduced us-
ing the ESOREX pipeline for UVES. The wavelength solution
is based on the Th-Ar calibration frames. All orders were cor-
rectedfortheblazefunctionandalsonormalisedtounitycontin-
uumlevel. Thenallordersweremerged. Foroverlappingorders
(at shorter wavelengths) the red sides were used because their
qualityisbetter. Someofourspectracontainordersmergedinto
a one-dimensional spectrum; this merging of orders can poten-
tially lead to artefacts caused by incorrect order merging, such
aslinedeformationoralterationoflinedepths,whichispartic-
ularlyproblematicifspectralfeaturesusedtodeterminethepa-
rameterareinfluenced. OurexperienceisthattheESOpipelines
perform order merging very carefully with little systematic in-
fluence. Moreover,weusedanumberofdifferentfeaturesinour
fitting procedure that are unlikely to systematically fall into re-
gions close to order edges. We therefore believe that potential
defects from individual lines and order merging are negligible.
Inalaststepweremovedbadpixelsandcosmics.
4.2. Objects
WewishtotesttheresultsdeterminedfromourPHOENIXmod-
els in stars with well-studied parameters. We used four objects
forthesebenchmarktests. Thefirstthreearestarsforwhichin-
terferometricradiusdeterminations(Ségransanetal.2003)allow
anindependentestimateoftheirsurfacegravityandtemperature
togetherwithinformationonluminosityanddistance(Table3).
Ourfourthbenchmarkobject,GJ667C,wasusedforacompar-
isonofmetallicitythatisknownforitsbinarycompanions. This
fourthobjectmainlyservesasanadditionalconsistencycheck,a
moresystematicinvestigationconsideringalargersampleofbi-
narycomponentswillbecarriedoutinasubsequentpaperwhen
alargersampleofM-dwarfspectraisanalysed. Allfourbench-
Fig.4. Comparisonanddeviationsbetweenoutputandinputparam-
eters. Leftcolumns:Input(notstarting)parametersagainstdetermined markstarsareveryslowrotatorswithnoindicationforrotational
parameters. Thediagonallinerepresentsaone-to-onecorrespondence. linebroadening. Thefirstthreeobjectsalsohavemeasuredrota-
Rightcolumns:Histogramsofthedeviationsbetweenoutputandinput tionperiodsconsistentwithveryslowrotationandlowactivity
parameters. (seeReinersetal.2012).
– GJ411(M2): Thisisthehotteststarweinvestigated. With
For lower resolutions the standard deviations will increase its slow rotation and no signs of high magnetic activity, it
becausethespectracontainlessinformationandcloselinesbe- is an ideal target for testing the new model atmospheres
gintooverlap. ForresolutionsaroundR = 44000(likeourob- at the warm end of M-dwarf temperatures. Radius mea-
servedspectrafromGJ441andGJ551,seenextsection)thede- surements and a determination of logg are taken from Sé-
viationsare40KforTeff,0.18dexforlogg,0.14dexfor[Fe/H], gransan et al. (2003). Temperature estimates derived from
afonrdT1effk,m0s.4−16fdoerxvfosirnloi.gFgo,r0R.36=d1ex00fo0r0[Fthee/Hd]e,vaiantdio7n.5skarmes1−214foKr i(nvtaenrfeBroelmleet&ricvraodniuBsraanudnlu2m00in9o)siatyndarTeeTffeff==33456903±±3670KK
vsini. However, because of the resolution we do not expect to (Boyajian et al. 2012). Results from spectroscopy yielded
raensdol∼ve3r0oktamtiso−n1aflovreRloc=it1ie0s0lo0w0.erthan∼7kms−1forR=44000 etetmapl.er2a0tu1r2e),eTsteiffma=te3s6o9f7±T1eff10=K35(G26a±id1o8s K&(MRoanjans-2A0y1a4la)
and Teff = 3563±60 K (Mann et al. 2015). The metal-
licity of this star was reported as [Fe/H] = −0.4 (Woolf
4. Observationaldata & Wallerstein 2005), [Fe/H] = −0.41±0.17 (Rojas-Ayala
et al. 2012), [Fe/H] = −0.35±0.08 (Neves et al. 2013),
4.1. Observeddata
[Fe/H] = −0.3±0.08 (Gaidos & Mann 2014), and most re-
The observational data used to determine the spectral parame- cently[Fe/H]=−0.38±0.08byMannetal.(2015).
ters are UVES spectra. The spectrum of GJ411 was taken un- – GJ699 (Barnard’s star, M4): Barnard’s star is of the
dertheprogramID74.B-0639witharesolutionofR ∼ 46000. most frequently observed and well-studied stars. It is clas-
GJ551 was observed under the program ID 73.C-0138 with a sified as an M4 dwarf and shows no indications for en-
resolving power of R ∼ 42300. The spectra of GJ667C and hanced magnetic activity in the spectra. Radii measure-
GJ699weretakenundertheprogramID87.D-0069. Thehigh- ments are reported in Ségransan et al. (2003) together
resolution mode with a slit width of 0.3” was used, leading to with logg. Boyajian et al. (2012) derived a temperature
a resolving power of R ∼ 100000. The observations cover of Teff = 3230±10 K from radius and luminosity data.
a wavelength range from 640nm to 1020nm on the two red Spectroscopic temperatures reported are Teff = 3266±29 K
Articlenumber,page6of9
Passegger,Wende-vonBergandReiners:FundamentalM-dwarfparameters
Table2.MetallicitiesmeasuredforGJ667AB 5.1. Effectivetemperatureandsurfacegravity
Reference [Fe/H] Our results for temperature and surface gravity are consistent
Perrinetal.(1988) −0.59 withmostoftheliteraturedatawithin1σuncertainties(seetop
Marsakov&Shevelev(1988) −0.52 panel in Fig.6). For GJ 551, the temperature from Neves et al.
Thevenin(1998) −0.55 (2013) is significantly cooler than our result and the one from
Santosetal.(2005) −0.43 Ségransanetal.(2003). Thisdiscrepancymaybecausedbythe
Taylor(2005) −0.66 TiO bands starting to saturate at cooler temperatures, as men-
tioned in Sect. 3.3. This consistency is crucial for our test of
theaccuracyofthenewPHOENIXACESmodelgeneration. It
(Rojas-Ayala et al. 2012), Teff = 3338±110 K (Neves et al. shows that with the new model set we are able to obtain phys-
2014), Teff = 3247±61 K (Gaidos & Mann 2014), and ically meaningful parameters of very cool stars. Furthermore,
Teff = 3228±60 K (Mann et al. 2015). Metallicities re- the fact that the synthetic spectra match the TiO bands as well
ported for this star are spread between [Fe/H] =−0.39
asatomiclineswithoneconsistentparameterset(seeFig.5)in-
and −0.75, recent examples are [Fe/H] = −0.39±0.17
dicates that the microphysics used for the new PHOENIX at-
(Rojas-Ayala et al. 2012), [Fe/H] = −0.52±0.08 (Neves
mosphere grid has improved significantly with respect to older
et al. 2013), [Fe/H] = −0.51±0.09 (Neves et al. 2014),
modelgenerations(Reiners2005). ForGJ411andGJ699our
[Fe/H] = −0.32±0.08 (Gaidos & Mann 2014), and
results perfectly agree with those of Mann et al. (2015) within
[Fe/H]=−0.40±0.08(Mannetal.2015).
10K.
– GJ551(M6): ThisM6staristhecoolestobjectinoursam-
ple. Like the other stars, no indications of enhanced ac-
tivity were found and the spectra are consistent with slow 5.2. Metallicity
rotation. Teff and logg from Ségransan et al. (2003) are Forthethreebenchmarkstarsusedabove,GJ411,GJ699,and
shown in Table3. Neves et al. (2013) derived a tempera-
ture of Teff = 2659K, which is significantly lower than the GmJat5io5n1,odnirteecmtrpaedriautusrmeeaansdurseumrfeanctespgrroavviitdye.inTdheepetnhdiredntcrinufcoiar-l
value from interferometry. Reports of metallicity include
[Fe/H] = 0.19 (Edvardsson et al. 1993), [Fe/H] = 0.0±0.08 atmospheric parameter, metallicity, is not independently con-
(Nevesetal.2013),[Fe/H]=0.16±0.20(Nevesetal.2014), strained, but can only be determined from spectroscopic anal-
and[Fe/H]=−0.03±0.09(Maldonadoetal.2015). ysis. Literature values given in Table3 are also based on spec-
– GJ667C (M1.5): This M1.5V dwarf also is a slow rota- troscopic models, which are often calibrated using components
tor without signs of strong magnetic activity; it shows no of binary stars, as discussed in the introduction. For the three
Hα emission, for example. The star hosts several low- starsGJ411,GJ699,andGJ551,ourmetallicitiesarenotfully
mass planets. Atmospheric parameters were reported in consistent with the literature values of Neves et al. (2013); on
Anglada-Escudé et al. (2013). The star has no interfer- average, our results are ∆[Fe/H] = 0.22dex higher. As an in-
ometric radius constraints, hence we lack independent in- dependent test of our metallicity results, we consider the M1.5
formation on temperature and gravity. Because it is part dwarfGJ667C,whichispartofatriplesystemandoftenusedto
of a multiple star system, we have constraints on metallic- anchorM-dwarfmetallicityscales.Forthebrightercomponents,
ity assuming that the three components of the triple share [Fe/H]isveryaccuratelydeterminedwithameanliteraturevalue
similar metallicities. For the K3V component of the sys- of[Fe/H]=-0.55(Sect.4.2). Thislow-metallicitystarshouldbe
tem, we found five independent metallicity determinations agoodindicatorforwhetherourmodelscandeterminemetallic-
that we collect in Table2. The mean and median val- ities in M dwarfs with sub-solar metal abundances. Our result
ues of the sample are [Fe/H] = −0.55 with a standard de- is[Fe/H]=−0.56±0.11,whichagreesverywellwiththemetal
viation of σ[Fe/H] = 0.08. For the temperature, liter- abundanceofcomponentsAandBandalsowiththeresultfrom
a2t0u1r3e),dTateaff a=re33T5e1ff (=Ne3v3e5s0e±t5a0l. 2K01(3A)n,gTleaffda=-E3s4c4u5d±é1e1t0aKl. Avanlugeladreap-EorstceuddébyetNale.v(e2s01e3t)a(l.w(h2o01u4se)disth[eFsea/Hm]e=me−th0o.5d±).0T.0h9e,
(Neves et al. 2014), and Teff = 3472±61 K (Gaidos & which is also consistent with the system’s higher mass compo-
Mann2014). Spectroscopicdeterminationofmetallicityfor nents.
theCcomponentare[Fe/H]=−0.55±0.1(Anglada-Escudé We conclude from this first test that the new PHOENIX
et al. 2013), [Fe/H] = −0.53±0.08 (Neves et al. 2013), ACES models provide reliable results in logg and Teff. For
[Fe/H] = −0.50±0.09 (Neves et al. 2014). Gaidos & Mann metallicity, the situation is more difficult. Our models indi-
(2014)reportedavalueof[Fe/H]=−0.3±0.08fromanem- cate higher metallicities than other methods in the three stars
piricalrelationbetweenmetallicityandatomiclinestrength, forwhichtemperatureandgravityareconstrainedfromknowl-
describedinMannetal.(2013). edgeaboutthestellarradii.Inthefourthobject,whichhasinfor-
mation on metal abundance from its higher mass companions,
ourmethodsprovideresultsthatareconsistentwithothermeth-
5. Results ods. Furtherinvestigationincludingcomparisonofmetallicities
inotherbinarysystemswillbecarriedoutinasubsequentpaper
whenalargerM-dwarfsamplewillbeinvestigated.
Figure 5 shows the spectra of all four stars together with
the best-fit models. The atmospheric parameters derived from
6. Summaryanddiscussion
the comparison between our observational data and the new
PHOENIXmodelsaresummarisedinTable3. Wevisualiseour We have determined atmospheric parameters from high-
resultsincomparisontoliteraturedataforeffectivetemperature resolution optical spectroscopy in a few benchmark M dwarfs
in the top panel of Fig.6, logg in the middle panel, and metal- withthenewPHOENIXACESmodels. Themodelsincludean
licityinthebottompanelofFig.6. improved description of physical processes in low-temperature
Articlenumber,page7of9
Table3.Parametersforbenchmarkstarswithinterferometricradii. Columns3–5: literaturevalues;Cols. 6–9: parametersdeterminedfromour
modelfit.
Object Sp Teff [K]b loggb [Fe/H]a Tefffit loggfit [Fe/H]fit
GJ411 M2.0 3570±42 4.85±0.03 −0.35±0.08 3565±40 4.84±0.18 +0.00±0.14
GJ699 M4.0 3163±65 5.05±0.09 −0.52±0.08 3218±35 5.25±0.14 −0.13±0.11
GJ551 M5.5 3042±117 5.20±0.23 +0.00±0.08 2927±40 5.02±0.18 −0.07±0.14
aNevesetal.(2013)
bSégransanetal.(2003)
atmospheres and are expected to provide a better fit to spectro- Toaddressouroffsetinmetallicity,weinvestigatedafourth
scopic observations and accurate atmospheric parameters. We star that is a member of a multiple system with known metal-
identified useful spectroscopic indicators with which the three licities. In thiscase, ourresult agrees withthe literature values
parameterscanbeconstrainedwithinsmallstatisticaluncertain- reportedforthemoremassivecomponents,inwhichdetermina-
ties. Uncertaintiesduetodegeneraciesbetweenspectrawithdif- tions of metallicity are better established. While this compari-
ferentparametersareσ = 35K,σ = 0.14,andσ = son supports the interpretation that the new models accurately
Teff logg [Fe/H]
0.11. describe cool atmospheres, it does not solve the puzzle of why
ourmetallicitiesdisagreewithotherM-dwarfmetallicityscales
The main purpose of the paper was a comparison of the
becauseinthisparticularstarotherdeterminations(aredesigned
model spectra to stars with independent information on atmo-
to)agreeaswell.
sphericparameters. Temperature, surfacegravity, andmetallic-
High-resolutionspectraoflow-massstarscanpotentiallybe
ityweredeterminedforfourstars.Forthreeofthefour,wecom-
used to determine atmospheric parameters and even individual
paredourmodelresultstotemperatureandgravityknownfrom
element abundances to high accuracy. We have shown that the
interferometric radius measurements, luminosity, and parallax.
newPHOENIXgridprovidesagoodsetofmodelstostartsuch
In all six parameters, the agreement is excellent (within 1σ).
acomparison. Weplantouseourmethodtoderiveatmospheric
Metallicity measurements are also available for the three stars,
parametersfrommanyM-dwarfspectra,andthisanalysisshould
buttheyareinconsistentwithourresults.Onaverage,ourmodel
also include a comparison to other metallicity scales. If the
fitsare0.31dexhigherthanliteraturevalues,whichissimilarto
realmetallicitiesofMdwarfsareindeedseveraltenthsofadex
theoffsetfoundbyJohnson&Apps(2009). Acomparisonwith
higher than currently assumed, this would have serious ramifi-
resultsintheNIR(Rojas-Ayalaetal.2012)showedanaverage
cations for our understanding of planet formation and the local
deviation of 0.33 dex for GJ411 and GJ699. The same differ-
stellar population. Therefore, a consistent understanding of all
encewasfoundwhencomparingourresultsforthesetwostars
spectralfeaturesincoolatmospheresismandatory.
toMannetal.(2015). Atthispoint, wecannotclearlyidentify
thereasonforthisdiscrepancy. Onepossibleexplanationisthat Acknowledgements. We thank Barbara Rojas-Ayala and Andreas Schweitzer
ourimprovedmodelsprovideabetterdescriptionofthecoolat- forfruitfuldiscussionsaboutlow-massstaratmospheresandmetallicityscales.
VMPacknowledgesfundingfromtheGrK-1351ExtrasolarPlanetsandtheir
mospheres and therefore more accurate metallicities than other
HostStars. SWvBacknowledgesDFGfundingthroughtheSonderforschungs-
methods. However, we cannot exclude the possibility that our bereich963AstrophysicalFlowInstabilitiesandTurbulence,andtheGrK-1351
metallicitiessystematicallyoverestimatethemetalabundances. ExtrasolarPlanetsandtheirHostStars. ARacknowledgesfundingfromthe
DFGasaHeisenberg-ProfessorunderRE-1664/9-2andsupportbytheEuropean
Rajpurohit et al. (2014) determined stellar parameters of M ResearchCouncilundertheFP7StartingGrantagreementnumber279347.
dwarfsusingBT-Settlmodels. Theyreportedgoodfittingofthe
TiO-bands, but rather poor fitting of the K- and Na-line pairs
for later-M dwarfs, with the observed lines being broader and
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