Synthetic photometry for M and K giants and stellar evolution: hydrostatic dust-free model atmospheres and chemical abundances

2.8 MB·

by  Bernhard Aringer

MNRAS000,1–21(2015) Preprint27January2016 CompiledusingMNRASLATEXstylefilev3.0
Synthetic photometry for M and K giants and stellar
evolution: hydrostatic dust-free model atmospheres and
chemical abundances
B. Aringer,1,2⋆ L. Girardi,2 W. Nowotny,3 P. Marigo,1 and A. Bressan,4,2
1Dipartimento di Fisica e Astronomia Galileo Galilei, Universita`di Padova, Vicolo dell’Osservatorio3, I-35122 Padova, Italy
6 2Osservatorio Astronomico di Padova – INAF, Vicolo dell’Osservatorio5, I-35122 Padova, Italy
1 3Department of Astrophysics, Universityof Vienna, Tu¨rkenschanzstraße 17, A-1180 Wien, Austria
0 4SISSA, viaBonomea 265, I-34136, Trieste,Italy
2

n
a
Accepted2016January25.Received2016January24;inoriginalform2015October26
J

6
2 ABSTRACT

Based on a grid of hydrostatic spherical COMARCS models for cool stars we have
]
R calculatedobservablepropertiesof these objects,which will be mainly used in combi-
nationwithstellarevolutiontracksandpopulationsynthesistools.Thehighresolution
S
opacity sampling and low resolution convolved spectra as well as bolometric correc-
.
h tionsfor alargenumberoffilter systemsaremadeelectronicallyavailable.We exploit
p those data to study the effect of mass, C/O ratio and nitrogen abundance on the
-
photometry of K and M giants. Depending on effective temperature, surface gravity
o
r andthechosenwavelengthrangesvariationsoftheinvestigatedparameterscausevery
t weak to moderate and, in the case of C/O values close to one, even strong shifts of
s
a the colours. For the usage with stellar evolution calculations they will be treated as
[ correction factors applied to the results of an interpolation in the main quantities.

When we compare the synthetic photometry to observed relations and to data from
1
the Galactic Bulge, we find in general a good agreement. Deviations appear for the
v
5 coolestgiantsshowingpulsations,masslossanddustshells,whichcannotbedescribed
2 by hydrostatic models.
0
Keywords: stars:late-type–stars:AGBandpost-AGB–stars:atmospheres–stars:
7
0 evolution – molecular data – Hertzsprung-Russelland colour-magnitude diagrams
.
1
0
6
1 1 INTRODUCTION For the more massive galaxies observed in the infrared
: alargefractionofthedetectedbrightpointsourcesarecool
v As more infrared facilities allowing photometric measure-
i M stars with very red colours. In general, these objects are
X ments of faint sources become available, stellar popula- situatedintheHRDontheasymptoticgiantbranch(AGB),
tionsinclosegalaxiesarebeingincreasinglyobservedinthe
r intheregionofredsupergiants(RSG)andinmetal-richen-
a corresponding passbands. Our direct neighbours, the Mag-
vironments often close to the tip of the red giant branch
ellanic Clouds, have their evolved red stars almost com-
(RGB). They may be confused with carbon stars, if only
pletely sampled by surveys such as 2MASS (Cutri et al.
broad band photometry is available (Boyeret al. 2013). In
2003),IRSF(Katoet al.2007)andVMC(Cioni et al.2011)
order to study their behaviour in colour-colour and colour-
in the near infrared and by SAGE (Meixner et al. 2006),
magnitudediagramsofgalaxies,oneneedsspectrallibraries
S3MC (Bolatto et al. 2007), AKARI IRC (Itaet al. 2008)
to convert stellar isochrones into the corresponding observ-
and WISE (Nikuttaet al. 2014) in the mid infrared. There
able properties. These should cover the relevant ranges in
arealsodataforM31andafewdozensofothergalaxies in
effective temperature, surface gravity and chemical compo-
ourvicinity.Theyhavebeenpartiallycoveredbyhighresolu-
sition.
tion near infrared imaging from the HST (Dalcanton et al.
2012a,b). The amount of available photometry for distant Libraries of synthetic spectra have the advantage that
stellar populations will increase a lot, when new space tele- they may cover a wide range of well-defined stellar param-
scopes like JWST or WFIRSTstart to operate. eters. There are several grids of hydrostatic models, which
can be or could be used to study K and M giants. Due to
thelowtemperaturesoftheseobjectstheopacitiescausedby
⋆ E-mail:[email protected] manymolecularandatomiclinesdominatetheatmospheres.
(cid:13)c 2015TheAuthors
2 B. Aringer et al.
Examples are the work of Bessell et al. (1989), Flukset al. computedwiththeCOMARCSprogram.Thelatterisbased
(1994) and Levesqueet al. (2005) or large libraries based on theversion of theMARCS code(Gustafsson et al. 1975,
ontheMARCS(Gustafsson et al.2008)andthePHOENIX 2008)describedinJørgensen et al.(1992)andAringer et al.
code (Allard et al. 2012; Husseret al. 2013). For warmer (1997). The models are calculated assuming spherical sym-
stars onemayalso takethespectrafrom Castelli & Kurucz metry and local thermodynamic and chemical equilibrium
(2003).Allofthosemodelscoverdifferentvaluesoftheeffec- (LTE).Thecontinuousandatomic or molecular absorption
tive temperature, surface gravity, [Fe/H] and in some cases at the frequencies used for the opacity sampling in our cal-
even [α/H]. Results obtained with modified abundances of culations is taken from external tables generated with the
C, N and O typical for RSG objects were published by COMA program. The formation of dust is not included.
Lan¸con et al. (2007). The current approach is identical to the one described in
In a considerable number of cases hydrostatic models Aringeret al. (2009) for a grid of carbon star models. For
werealsousedtogeneratetablescontainingsyntheticvisual furtherdetails we refer tothis work.
andnearinfrared photometryfor cooloxygen-richgiantsas The COMA (Copenhagen Opacities for Model At-
a function of stellar parameters. Examples are the works mospheres) program is an opacity generation code that
of Gustafsson & Bell (1979), Bell & Gustafsson (1989), was originally developed by Aringer (2000) to com-
Plez et al. (1992), Bessell et al. (1998), Houdashelt et al. pute wavelength dependent absorption coefficients for cool
(2000),VandenBerg& Clem (2003) andClem et al.(2004). model atmospheres. It has also been used to deter-
The results of Worthey& Lee (2011) are partly based on mine weighted mean opacities for stellar evolution cal-
observations. culations (Lederer& Aringer 2009; Cristallo et al. 2007).
Thementionedhydrostaticmodelscannotincludedevi- In combination with an attached radiative transfer mod-
ations from sphericalsymmetry ordynamicalprocesses like ule COMA was applied in a considerable number of in-
pulsationcreatingshockwaves,andmasslosswithdustfor- vestigations to obtain synthetic photometry and spec-
mation, which become important in the cooler AGB and tra at very different resolution (e.g. Aringeret al. 2009;
RSG objects. A grid for M-type AGB variables covering Eriksson et al. 2014; Nowotny et al. 2010; Lebzelter et al.
a limited parameter range was produced by Bladh et al. 2014; Uttenthaleret al. 2015). In the central routines the
(2015).Becauseofpossibleuncertaintiesofthemodels,they abundances of many important ionic and molecular species
may be complemented with empirical spectral libraries like areevaluatedassumingchemicalequilibrium.Subsequently,
the ones from Flukset al. (1994), Lan¸con & Wood (2000) the resulting partial pressures can be used to compute the
and Rayneret al. (2009, IRTF). continuousandlineopacityateachselectedfrequencypoint
InthisworkwediscussagridofhydrostaticCOMARCS (inLTE).Atthemoment,uptomorethan175milliontran-
modelsforcoolstars,whichwasmainlydesignedtoprovide sitions are included in a calculation covering the complete
librariesofsyntheticspectraandphotometryusableincom- COMARCS wavelength range. This number,which is dom-
binationwiththePARSEC(Bressan et al.2012)andCOL- inatedbymolecular specieswithmorethantwoatoms(e.g.
IBRI (Marigo et al. 2013) evolutionary codes to obtain ob- H2O,HCN,CO2)orelectronictransitions(e.g.TiO,CN)de-
servablepropertiesofstellarpopulations.Inadditiontothe pendsonthechosenlinelists.Inaddition,COMAisalsoable
primary parameters effective temperature, surface gravity, toproduceopacitiesforaconsiderableamountofdusttypes,
mass and metallicity, we have also varied the abundances ifinformation concerningthedegreeof condensationispro-
of elements like carbon or nitrogen to take the impact of vided(e.g.Bladh et al.2015;Nowotny et al.2011,2015).It
dredge-up processes into account. This includes new im- shouldbenotedthatequilibriumabundancesofsolid parti-
proved calculations for C-type giants, which replace to an cles are not computed,since such a situation neverappears
ever-increasing extent the data published by Aringeret al. in astrophysical environments.
(2009),butarenotreviewedhere.Inthecurrenttextwefo- More information concerning the COMA code can be
cusonKandMstars.Wefirstdescribethemodelstogether found in Aringeret al. (2009). In comparison to that work
with their synthetic spectra and photometry in Section 2. we haveadded some new opacity sources mainly important
ThenwediscussinSection 3theinfluenceofC/O ratio, ni- for the structures and spectra of dwarf stars. Line lists for
trogen abundance, mass and the used water opacity on the the hydrides MgH (Weck et al. 2003b; Skory et al. 2003),
atmospheric structures and energy distributions as well as TiH(Burrows et al.2005)andCaH(Wecket al.2003a)are
on various colour indices. In Section 4 the predicted pho- now taken into account. Their features appear primarily
tometric properties are compared to observed relations and in the visual range. For CaH and MgH the data for the
to stars in theGalactic Bulge. Moreover, theapplication of chemical equilibrium constantscome from Sauval& Tatum
the COMARCS data in combination with isochrones is re- (1984) with a revised dissociation energy of 1.285 eV for
viewed. The appendix contains a table with the abundance MgH (Shayesteh et al. 2007). The corresponding values for
sets, which are at the moment available in thegrid. TiH were taken from Burrows et al. (2005). At this point
it should also be noted that we have changed the dissocia-
tionenergyofCrHfrom2.86to2.17eV(Bauschlicher et al.
2001)resultinginsignificantlylowerabundances(uptotwo
2 MODEL ATMOSPHERES AND SYNTHETIC ordersofmagnitude)andweakerbandsofthemoleculecom-
SPECTRA pared to Aringeret al. (2009).
Other species which have been added to the line opac-
2.1 Opacities and Hydrostatic models
ity calculations are CS (Chandra et al. 1995) and CH4. In
In order to study the spectra and photometric properties the case of methane COMA can currently only process the
of K and M giants we used hydrostatic model atmospheres HITRAN2008data(Rothmanet al.2009)withaquitelim-
MNRAS000,1–21(2015)
Synthetic photometry for M and K giants 3
itednumberoftransitions.Thisisnoproblemfortheresults since higher pressures favour the formation of polyatomic
presentedhere,sincethehydrostaticmodelatmospheresdo molecules. An interesting trend visible in Fig. 1 is that the
notextendintothecooltemperaturerangeswhereCH4 be- features of H2O get stronger with decreasing metallicity.
comes important. At the moment the following molecules Thisbehaviourcanmainlybeexplainedbythereducedheat-
are included in COMA and the line opacities used for this ingoftheatmospheresduetoTiO.Inordertoobservesuch
work: CO, CH, C2, CS, CN, H2O, C2H2, HCN, C3, SiO, aneffect,starswithidenticalparameters(Teff,log(g)) need
OH, TiO, VO, YO, ZrO, CO2, SO2, CH4, HF, HCl, FeH, to be compared. However, this is not so easy, if one studies
CrH, MgH, TiH and CaH. different stellar populations.
Line lists from the HITRAN database may be se- In Fig. 1 it is also obvious that at cooler temperatures
lected in COMA as an option for CO, H2O, CO2, OH, HF thereexistsnopointinthespectra,whichisnotaffectedby
and C2H2, while they represent the only available source intensemolecularoratomicabsorption.Duetotheimpactof
for SO2, HCl and CH4. In the case of OH they are the lineopacitiesontheatmosphericstructuresandmeasurable
preferred choice. In comparison to the computations de- pseudo-continua the relation between chemical abundances
scribed in Aringeret al. (2009), where only the 2004 ver- and the apparent depth of spectral features may become
sion of HITRAN (Rothman et al. 2005) could be used, it quitecomplicated.
is now also possible to take the data from HITRAN 2008 There are still some uncertainties concerning theopac-
(Rothmanet al. 2009). For the work presented here we ex- ity data, especially for species with a large numberof tran-
tractedthetransitionsofSO2,HClandCH4 fromHITRAN sitions and at higher spectral resolutions. This can already
2008, while we kept HITRAN 2004 for OH (better agree- be seen in Fig. 17 where we compare the results from dif-
ment with observed mid IR spectra). In addition, COMA ferenthydrostaticmodelapproaches.Theeffectofchanging
canprocesstheHITEMP2010dataforH2O,CO2,OHand the selected line list for TiO and H2O in COMA is shown
CO (Rothmanet al. 2010), which may improve the results in Figs. 2 and 3. Nevertheless, in the case of the K and M
for the first three of the molecules. However, since that op- giantsstudiedherewe donotexpect thatanyuncertainties
tion was not available when the work on the COMARCS oftheuseddataorpossiblemissingopacitieswillhaveasig-
gridwasstarted,theHITEMP2010listsarenotconsidered nificantinfluenceontheoverallabsorptionandatmospheric
here.Thisisnotabigproblem,becauseforH2OandOHthe structures.
changesoftheoverallabsorptionandmediumorlowresolu- InFig.2wecomparesyntheticspectraforaCOMARCS
tion spectra are small, if one compares to calculations with model with T = 2800 K, log(g [cm/s2]) = 0.0, one so-
eff
thecurrentstandarddata(HITRANfor OHandBT2 from lar mass and solar metallicity, which were calculated us-
Barber et al. (2006) for water). The update of HITEMP to ing different TiO data. The computations presented here
the2010versionproducessomedifferencesintheCO2bands are normally done with the NASA-AMES list (Schwenke
around4.4 µm.But evenin thecoolest COMARCS models 1998). In addition, we have included results obtained with
thefeatures of carbon dioxide remain always very weak. the Plez (Plez 1998) and the SCAN list (Jørgensen 1994,
It should be mentioned that the changes discussed in 1997). The spectra, which do also contain the features of
the previous paragraphs do not have a significant effect on the other species, cover the wavelength range up to 1.2 µm
the overall opacity and atmospheric structure in the mod- ataresolutionofR=200.Itshouldbenotedthatthesame
els. As in Aringeret al. (2009) Doppler profiles including COMARCS model calculated with the NASA-AMES data
the thermal and the microturbulent contribution were as- wasusedinallthreecases.Thisinconsistencyisnoproblem,
sumed for the molecules, while the atomic transitions are sincethestudiedlistsproducequitesimilaroverallopacities
broadened with Voigt functions, if damping constants are andatmosphericstructures.Thereareonlysomedifferences
available. In Fig. 1 we show absorption spectra of different on smaller scales.
species important for K and M stars, which are calculated A similar comparison is done in Fig. 3 where we in-
from COMARCS atmospheres with log(g [cm/s2]) = 0.0, vestigate the effect of using different H2O data. The stel-
M/M⊙ =1.0andscaledsolarabundances.Fourmodelshav- lar parameters of the corresponding COMARCS model are
ing solar (Z/Z⊙ = 1.0) or ten times lower (Z/Z⊙ = 0.1) thesame as in Fig. 2. We present results obtained with the
metallicity and Teff =2800 K or 3600 K are included. The BT2(Barber et al.2006),SCAN(Jørgensen et al.2001)and
spectra were normalized using a computation without any NASA-AMES (Partridge & Schwenke 1997) list. HITEMP
lineopacitiesandhavearesolutionofR=200.Speciesshow- 2010 (Rothman et al. 2010), which may be regarded as the
ing similar behaviour are combined in groups: atoms, CO, most recent and complete collection of water lines, is not
CH&CN,SiO&OH,TiO,VO&ZrO&YO,H2O,FeH& includedintheplot.However,attheselectedlowresolution
CrH & MgH & CaH & TiH. ofR=200thedifferencesbetweenBT2andHITEMP2010
As one can see in Fig. 1, TiO and atoms dominate arerathersmall.ItshouldbenotedthatHITEMPispartly
theopacitiesbelow1µm.Thecorrespondingabsorptionin- basedontheworkofBarber et al.(2006).Theatmospheres
creases with higher metallicity and lower temperature. Es- intheCOMARCSgridarecomputedusingtheSCANdata,
peciallyincoolerobjectsthestellarradiationisalmostcom- which represent therefore the prime choice for the calcu-
pletelyblocked inbroad regionsof thespectrum,whichhas lation of the synthetic spectra. For all oxygen-rich models
a severe impact on the atmospheric structure. The strong with temperatures cool enough that water absorption may
heating effect caused by TiO is discussed in Aringeret al. becomeimportanttheaposterioriradiativetransferhasalso
(1997). At low temperatures water becomes an impor- been done involving the BT2 list. The limit was in most of
tant absorber in the whole infrared range. For solar abun- thecasessettoT =4000K,butmaybecomehigherthan
eff
dances this happens in giants cooler than 3200 K, while in 5000 K for dwarfs. In the plots of this paper we show usu-
dwarfsintenseH2Obandsappearalreadyataround4200K, allytheresultsobtainedwiththeBT2dataifavailable.Like
MNRAS000,1–21(2015)
4 B. Aringer et al.
1.0
0.8
0.6
0.4
0.2
0.0 Atoms CO
1.0
0.8
0.6
0.4
0.2
Cont 0.0 CH & CN SiO & OH
F
F/ 1.0
0.8
0.6
0.4
0.2
TiO VO & ZrO & YO
0.0
1.0
0.8 [Z/H] = +0.0, 2800K
0.6 [Z/H] = +0.0, 3600K
[Z/H] = -1.0, 2800K
0.4
[Z/H] = -1.0, 3600K
0.2
H O FeH & CrH & MgH & CaH & TiH
0.0 2
0.5 1 5 10 0.5 1 5 10
λ [µm] λ [µm]
Figure 1. Continuum normalized spectra for important molecular species and atomic lines based on COMARCS models with
log(g [cm/s2]) = 0.0, M/M⊙ = 1.0 and scaled solar abundances. Two different metallicities (Z/Z⊙ = 1.0 → [Z/H] = 0.0,
Z/Z⊙=0.1→[Z/H]=−1.0)andtemperatures (Teff =2800K,fulllines,Teff =3600K,dashedlines)areshown.
for TiO, the inconsistent treatment of opacities in the cal- consistent usage of theBT2 opacities for thedetermination
culation of COMARCS atmospheres and synthetic spectra ofthemodelstructureandtheaposterioriradiativetransfer.
will not cause problems, since the different lists give quite It is obvious that the differences between the two spectra
similarstructures.Itshouldbenotedthatthisistrueforhy- remaininallregionsverysmall.Thisconclusionisalsovalid,
drostaticmodelsandtherangeofparameterscoveredbythe if one plots the absolute intensities without normalization.
COMARCS grid. If a significant part of the computed at- Therelativedeviationsofthefrequencyintegratedradiative
mosphereextendstogastemperaturesbelow1000K,SCAN fluxes in the various layers up to the surface caused by the
and BT2 producedeviating results. Thereason for thisis a inconsistent treatment of thewater opacity in thefirst case
systematic difference in the overall absorption above 6 µm do never exceed values around 2 %. This confirms that our
as one can see in Fig. 3. A discussion of the behaviour of approachconcerningtheBT2spectraisnottooproblematic.
SCANandNASA-AMESinthemidinfraredandacompar-
isontoISO-SWSobservationsarepresentedinAringeret al. In addition to the new and updated line lists we have
(2002). also revised the continuous opacities by including the colli-
sion induced absorption (CIA) of H2 – H2 (Borysow et al.
In Fig. 3 we compare two different spectra obtained 2001; Borysow 2002), H2 – H (Gustafsson & Frommhold
with the BT2 line list. The first one is based on a standard 2003), H2 – He (Jørgensen et al. 2000) and H – He
COMARCSatmosphere,whichhasbeencalculatedwiththe (Gustafsson & Frommhold 2001). This is especially impor-
SCAN data. The second energy distribution results from a tant for the very cool and dense dwarf atmospheres at low
MNRAS000,1–21(2015)
Synthetic photometry for M and K giants 5
2.2 Model parameters
The COMARCS grid, which was mainly designed to trans-
fer the results of stellar evolution calculations into observ-
TiO - SCAN
able properties of the various objects (e.g. Aringer et al.
TiO - Plez
1 TiO - NASA 2009), aims at cool stars. The typical range of effective
2800K, log(g)=0.0 temperatures covered by the models is between 2500 and
5000 K with values of log(g [cm/s2]) extending from 5.0
Fmean0.1 ptoac−t1(.l0o.g(Sgom[cemh/so2t]t)erup(Tteoff5u.3p2)toco7m17p0utKa)tioannsdamreoraelscoomin--
F/ cluded. An overview of the COMARCS grid can be found
in the appendix in Table A1, where we list the opacity
0.01
sets available at the moment. They correspond to an in-
put file produced by COMA and are characterized by a
certain selection of elemental abundances, microturbulent
0.001 velocity (ξ) and source data for the absorption. Each of
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
λ [µm] them may contain models with different effective temper-
ature,surfacegravityormass.TherangeinT andlog(g)
eff
covered by the various sets is also listed in the table. Since
Figure2.SpectracalculatedwithdifferentTiOdatabasedona theCOMARCS grid is constantly growing, theinformation
COMARCSmodelwithTeff =2800K,log(g[cm/s2])=0.0,one givenintheappendixrepresentsonlyasnapshotatthetime
solar mass and solar metallicity. The NASA-AMES(black, used when this paper was produced. An updated and complete
inthisworkasstandard),Plez(red)andSCAN(green)linelists catalogue of the available models may be obtained from
arecompared. Theintensities νLν arenormalizedto their mean http://starkey.astro.unipd.it/atm.
value.
The central part of the COMARCS database are sev-
eralsubgridsofdifferentmetallicitywheretherelativeabun-
dancesofallelementsheavierthanHe(Z)havebeenscaled
in the same way. The values with reference to the Sun
log (Z/Z⊙) or [Z/H] range from −2 to +1 separated by
steps of 0.5. The corresponding solar chemical composition
10 is based in essence on Caffau et al. (2009a,b) resulting in
H O - NASA a C/O ratio close to 0.55. In this work Z/Z⊙ and [Z/H]
2
H O - SCAN represent the relative abundance of the bulk of metals. A
2 variationoftheamountofoneormoreelementslikecarbon
H O - BT2
2 or nitrogen will not change these numbers. Since the cur-
BT2 consistent
mean 1 2800K, log(g)=0.0 raenspteCcOiaMl sAcaRliCnSgdfoartaibroanse,d[Zo/eHsn]oitsianlcwluadyseoepqaucailtytose[tFsew/Hith].
F
F/ The subgrids of different metallicity cover effective temper-
atures between 2600 and 5000 K with steps of 100 K or
smaller, while the values of log(g [cm/s2]) range from 5.0
to −1.0 with a maximum increment of 0.5. Models with
0.1 log(g [cm/s2]) < 0.0 were usually only computed for stars
coolerthanabout3500K.Thestandardmicroturbulentve-
1 2 3 4 5 6 7 8 9 10 locity of the calculations was set to ξ = 2.5 km/s, which is
λ [µm]
in agreement with our previous work (Aringer et al. 2009,
1997) and high resolution observations of M giants (e.g.
Smith & Lambert 1985, 1990). For other groups of objects
Figure3.SpectracalculatedwithdifferentH2Odatabasedona covered by the COMARCS grid different typical ξ values
COMARCSmodelwithTeff =2800K,log(g[cm/s2])=0.0,one
will be appropriate. An example are dwarfs or red super-
solar mass and solar metallicity. The SCAN (black, used in this
work as standard), BT2 (green, used in this work as standard) giants, which are not discussed in this paper. However, the
and NASA-AMES (red) linelists are compared. The intensities influence of the microturbulence on the atmospheric struc-
νLν arenormalizedtotheirmeanvalue.Wealsoshowtheresult ture and low resolution spectra remains for most of the
obtained with a consistent usage of the BT2 data for the com- coolermodelsquitelimited,ifthedeviationsdonotbecome
putation of the atmospheric structure and the spectrum (green too large. This is due to the huge number of weak over-
dashed), which is very similar to the one, where BT2 was only lapping lines that dominate the opacity. For solar metallic-
takenfortheaposterioriradiativetransfer(greenfull).
itytheCOMARCSdatabaseincludesalsocalculationswith
ξ = 1.5 and 5.0 km/s. In general, the model atmospheres
in the central subgrids were computed assuming the mass
of the Sun. Especially for the more extended objects with
log(g [cm/s2]) ≤ 0.0, where sphericity effects may become
metallicity,whileithasnoeffectonthestructuresandspec- important, different selections of this parameter have been
tra of thegiants studied here. considered.
MNRAS000,1–21(2015)
6 B. Aringer et al.
Concerning the evaluation of the convective fluxes
we follow the approach described and applied by
Gustafsson et al. (1975, 2008) for their MARCS models
-1
as we use the mixing length formalism from Henyeyet al.
(1965) with the same parameters (α = 1.5, ν = 8.0,
0
y = 0.076). For the calculation of the turbulent pressure
we have adopted β = 1.0. The velocity of the convec- 1
tive elements from the equations was taken. According to
)
Gustafsson et al. (2008) this may result in values being too g 2
(
high. However, the influence of the chosen turbulent pres- g
o
sure on our synthetic spectra and photometry is limited, l 3
since only theinnermost layers are affected.
4
In Fig. 4 we show the subgrid of T and log (g) val-
eff
ues for the solar chemical composition. Models of different
5
masses and microturbulent velocities are included without
any further distinction. Up to 3800 K the calculations have 5500 5000 4500 4000 3500 3000 2500
been extended to log(g [cm/s2])< 0.0. The high density of Teff [K]
grid pointsin that region and constraintsof thelower limit
forthesurfacegravityaround3000Karepartiallycausedby
Figure4.Valuesofeffectivetemperatureandlog(g[cm/s2])cov-
convergence problems (Aringeret al. 2009). In the domain
ered by the current COMARCS grid in the case of solar abun-
ofthecompactobjectsthereisasequenceofCOMARCSat-
dances (crosses). Models of different mass are not distinguished.
mosphereswitheffectivetemperaturesfrom5000to3000K, Inaddition,evolutionarytracksforstarswithonesolarmassand
whichcrossesthelog(g[cm/s2])=5.0line.Thiscorresponds Z/Z⊙ = 1.0 (full line, red) as well as Z/Z⊙ = 0.1 (dashed line,
to the ZAMS of dwarfs having solar chemical composition green)aredisplayed.
asderivedfrom thePARSECcode(Bressan et al.2012) for
stellar evolution.
the end of Table A1. The models therein will replace the
Figure 4 contains also two sequences of models con- database of Aringer et al. (2009).
nected by lines, which have been placed along evolutionary TheCOMARCSdataallowalsotoinvestigatetheeffect
tracksforstarswiththemassoftheSun.Thecorresponding ofanincreasednitrogenabundance.Modelswith[N/Z]=+1
valuesofTeff andlog(g)werecomputedusingPARSECand exist for two different metallicities: [Z/H] = 0 and −1. At
forthelateststagestheCOLIBRIcode(Marigo et al.2013). the moment sequences with log(g [cm/s2]) = 0.0 and +2.0
TheycoverthewholeperiodbetweentheZAMSandthefi- covering temperatures between 2600 and 5000 K as well as
nalphaseoftheAGB.Thesequences,whichextendtomuch COMARCSatmospheresplacedalonganevolutionarytrack
highertemperaturesthantherestoftheshownCOMARCS of a star with one solar mass (see Fig. 4 & text above) are
subgrid (5940 & 7170 K), differ by their chemical composi- available. The effects of enhancing nitrogen and changing
tion. The first one is compatible with the other models in C/O will bediscussed in thenext sections.
the figure, since it has also solar abundances. The second
track, which is considerably hotter, was calculated assum-
ing[Z/H]=−1.Becauseofintensestellar windsat thelate 2.3 Synthetic Spectra and Photometry
stages of the AGB evolution that are included in the COL-
For the complete grid of hydrostatic COMARCS atmo-
IBRI computations, the mass of the last few objects in the
spheres we computed synthetic opacity sampling spectra
sequences is reduced (0.74 & 0.79 M⊙ at the final point). coveringtherangebetween400and29814.7cm−1(0.3354to
We have taken this effect into account when producing the
25.0 µm) with aresolution of R = 10000. Following theap-
COMARCS models.
proach described in Aringer et al. (2009) or Nowotny et al.
As one can see in Table A1, the COMARCS database (2011) for carbon stars, we used theCOMA codein combi-
contains also opacity sets where the abundances of individ- nationwithanattachedsphericalradiativetransferprogram
ualelementshavebeenchangedseparately.Themostimpor- (Windsteiget al.1997).Exceptforthedenserdistributionof
tantexampleistheamountofcarbon,whichisspecifiedhere frequency points, the treatment of the continuous and line
bythe C/O ratio. This varies duringthelate stages of stel- absorption was in general consistent with the input data
lar evolution due to several nucleosynthesis and dredge-up for the production of the models. As it is discussed in Sec-
processes (e.g. Busso et al. 1999; Cristallo et al. 2011). The tion 2.1, that is not valid for the spectra, which have been
dataincludeanumberof subgridsand sequencescomputed calculated involving the BT2 list for water. However, this
with C/O values different from the one associated with the doesnotcreateasevereproblem,sincethedifferentapplied
solar composition (0.55), which cover the interval between H2O data result in similar hydrostaticstructures.
0.25and10.0.Modelswereusuallyproducedforthosecom- Because of the statistical nature of the opacity sam-
binationsofeffectivetemperatureandsurfacegravitywhere pling approach, only the average over a larger number of
thecorrespondingintrinsicmodificationsoftheabundances frequency points (about 20 to 100) ensures a realistic rep-
are expected. As an example, there was no need to take resentation of the observed stellar spectra (Nowotny et al.
dwarfs into account. This results in subgrids much smaller 2011). Thus, we decreased the resolution of the output of
than the ones with a metallicity scaled solar composition. theradiativetransfercodetoR=200byconvolvingitwith
The opacity sets for carbon stars (C/O > 1) are listed in aGaussian function.Wedidnotincludeanyadditionalline
MNRAS000,1–21(2015)
Synthetic photometry for M and K giants 7
broadening induced for example by a macroturbulent ve-
locity. The wavelength grid has been done with a spacing
corresponding to R = 2000 resulting in a smooth appear- 6000
ance of the final spectra. The same procedure was already
C/O = 0.55
used by Aringer et al. (2009) to obtain their low resolution C/O = 0.30
data. Examples for theoutputcan be found in Figs. 1, 2, 3 5000 C/O = 0.70
C/O = 0.80
& 17. The spectra are electronically available as described
C/O = 0.90
in Section 3.2.
4000
We also produced synthetic bolometric corrections for K]
a large set of filters following the same formalism as de- T [ green: 4400K, log(g)=2.0
scribedinGirardi et al.(2002,eq.7&8).Firstweconvolved 3000
thetransmissioncurvewiththecalculatedopacitysampling red: 3600K, log(g)=0.0
spectra. This was done with an integration of the energy
or the number of detected photons depending, if amplifiers 2000 black: 2800K, log(g)=0.0
or counting devices were used for the definition of the in-
vestigated photometric system. Subsequently, the obtained
0.01 0.1 1 10 100 1000 10000
magnitudes were scaled with respect to a reference inten- 2
p [dyn/cm ]
sity in order to consider the zero points. This quantity was gas
determinedfrom aconvolution with thefiltercurveapplied
to a constant flux per unit wavelength (frequency) in the Figure 5. The effect of the C/O ratio on the atmospheric
caseofSTmag(ABmag)systemsortoaVega(αLyr)spec- temperature versus gas pressure structure is shown for differ-
ent COMARCS models with solar mass and metallicity. Three
trumfor Vegamag data.Wetook theenergy distribution of
thestandardstarfromtheworkofBohlin(2007).Thecorre- examples are included: Teff = 2800 K, log(g [cm/s2]) = 0.0
spondingvaluesareexpectedtobeaccuratetowithinabout (black) with C/O = 0.30, 0.55, 0.70, 0.80, 0.90, Teff = 3600 K,
log(g [cm/s2]) = 0.0 (red) with C/O = 0.30, 0.55, 0.70 and
2% in the optical and near infrared range. The latest table Teff = 4400 K, log(g [cm/s2]) = 2.0 (green) with C/O = 0.30,
ofsyntheticbolometriccorrectionsiselectronicallyavailable 0.55.C/O=0.55correspondstothesolarvalue.Theplotsymbols
as described in Section 3.3. placed along the different curves mark steps of ∆log(τRoss) = 1
startingwith−5attheouteredge.
3 RESULTS
In this section we want to present some results obtained
using the COMARCS grid with special emphasis on theef- 6000
fectsofC/Oratio,nitrogenabundanceandstellarmass.The [N/Z] = +0.0
impact of these quantities on the atmospheric structures, [N/Z] = +1.0
5000
spectra and colours will bediscussed. It can beregarded as
acorrectionthathastobeappliedtothepropertiesofastar
predictedfromthemainparameters,whicharetemperature, 4000
]
surface gravity andoverall metallicity (see Section 4.3).We K
[
investigate, wherethementioned effectsbecomeimportant. T green: 4400K, log(g)=2.0
Asitwasalreadystated,thevaluesofC/Oand[N/Z]change 3000
red: 3600K, log(g)=0.0
during the late stages of stellar evolution. If the C/O ratio
exceedsone,aseveremodificationoftheatmosphericstruc-
2000 black: 2800K, log(g)=0.0
tureandspectralappearancehappens,sincetheobjectturns
intoacarbonstar.However,thiscasewillnotbeconsidered
here, because we focus on K and M giants. The evolution- 0.01 0.1 1 10 100 1000 10000
ary tracks for one solar mass shown in Fig. 4 that are used p [dyn/cm2]
gas
for some plots of this paper do also not reach C/O ≥ 1.0.
An enhancement of s-process elements like Y or Zr, which
Figure 6. The effect of the nitrogen abundance on the atmo-
is often connectedtoan increased C/O value,is as well not
spheric temperature versus gas pressure structure is shown for
discussed, since we do not cover S stars in our study. The
different COMARCS models with solar mass and metallicity.
properties of thelatter group of objects are investigated by Three examples are included: Teff = 2800 K, log(g [cm/s2]) =
van Eck et al. (2011). 0.0 (black), Teff = 3600 K, log(g [cm/s2]) = 0.0 (red) and
Teff = 4400 K, log(g [cm/s2]) = 2.0 (green). [N/Z] = 0.0 (full)
corresponds to the solar value of log(εN/εH)+12 = 7.90 and
3.1 Atmospheric Structure
[N/Z] = +1.0 (dashed) to N enhanced by a factor of 10. The
plot symbols placed along the different curves mark steps of
In Fig. 5 we present the atmospheric temperature pressure
structureofvarioushydrostaticmodelstakenfrom theCO- ∆log(τRoss)=1startingwith−5attheouteredge.
MARCS grid, which have the mass and overall metallicity
of the Sun. For three different combinations of T and
eff
log (g) the effect of changing the C/O ratio is shown. Val-
ues between 0.3 and 0.9 are covered including 0.55 for the
MNRAS000,1–21(2015)
8 B. Aringer et al.
solar composition. Models with a high C/O exceeding 0.7
are only available for the coolest set with T = 2800 K
eff
and log(g [cm/s2]) = 0.0. Such a large relative enhance-
ment of carbon can appear during and after the AGB
1.40
phaseas aconsequenceof thethirddredge-up(Busso et al.
T=2800K, log(g)=0.0
1999;Cristallo et al.2011).Theadditionalcombinationsare 1.20
T =3600 K with log(g [cm/s2])=0.0 and T =4400 K
eff eff 1.00
with log(g [cm/s2]) = 2.0. The figure shows that there is a
C/O = 0.30
clear trend of colder structures with increasing C/O ratio, 0.80
C/O = 0.70
but significant changes happen solely above 0.7. The lat- 0.60 C/O = 0.80
ter may be partly explained by thefact that theamount of C/O = 0.90
oxygen atoms not bound in CO gets more crucial for the 0.40 [N/Z] = +1.0
)
formation of other species like TiO or H2O, if it becomes 0.00.20
verylow.However,oneshouldalwayskeepinmindthatthe +
= 1.15 T=3600K, log(g)=0.0
relations can be quite complicated, if molecules important ]
for theoverallopacity are involved.Forexample,theabun- N/Z1.10
dspahnecreeso,fdTeciOre,aswehsiicnhtchaeuisnensearrsetgroionngshoefatthinegmoofdtehlsehaatvminog- 5, [1.05
51.00
T =2800 K and log(g [cm/s2])= 0.0 at higher C/O val- 0.
eff = 0.95
ues, while it grows in theouter areas below Tgas =2400 K. O
In Fig. 6 we demonstrate, how increasing the nitrogen C/0.90
abundance by a factor of ten affects the atmospheric tem- F(0.85
perature pressure structure. This enhancement can be re- F /
garded as typical for the late stages of stellar evolution, 1.10 T=4400K, log(g)=2.0
sincethemaximumvaluespredictedbycodeslikeCOLIBRI
(Marigo et al.2013)rangebetweenabout2and100depend- 1.00
ingonmassandcomposition.Weshowthreesetsofmodels
0.90
with thesame parametersastheonesusedin Fig.5for the
C/O ratio. It is obvious that the impact of changing [N/Z]
0.80
remains in general small. It disappears almost completely
forthecoolest objects, wheretheCNbandsbecomeweaker 0.70
and theirimportance is additionally reducedby theintense 0.3 1 3 10
absorption of otherspecies like TiO orwater. λ [µm]
3.2 Spectra
The complete grid of our R = 10000 opacity sampling Figure 7. Relative spectral changes due to different C/O ra-
and convolved low resolution R = 200 spectra com- tiosandanincreasednitrogenabundanceforCOMARCSmodels
puted from the COMARCS models can be found in withsolarmassandmetallicity.Thespectraarenormalizedtoa
http://starkey.astro.unipd.it/atm. The corresponding calculation with solar composition (C/O = 0.55, log(εN/εH)+
tables consist of three columns: wavelength [A˚], contin- 12 = 7.90). Three examples are included: Teff = 2800 K,
uumnormalizedfluxandspecificluminositytimesfrequency log(g [cm/s2])=0.0(upper panel) withC/O = 0.30, 0.70, 0.80,
(ν·Lν [erg/s]). Thesecondquantityisobtainedfrom divid- 0.90, [N/Z] = +1.0, Teff = 3600 K, log(g [cm/s2]) = 0.0 (mid-
ing the result of a full radiative transfer calculation by one dle panel) with C/O = 0.30, 0.70, [N/Z] = +1.0 and Teff =
4400 K, log(g [cm/s2]) = 2.0 (lower panel) with C/O = 0.30,
wheretheatomicandmolecularlineabsorptionistotallyne-
[N/Z]=+1.0.
glected.Thisallowstoevaluatetheapparentintensityofthe
variousspectralfeatures.However,suchcontinuumnormal-
ized data should be interpreted with care, since the optical
with a calculation where the investigated parameters have
depthscalechangeswhenopacitiesareremoved.Anexample
solar values.
canbeseenin Fig.1,whereweinvestigatethecontribution
of different species to the total absorption. In this case a
calculationincludingonlythecorrespondingtransitionswas
3.2.1 C/O Ratio & Nitrogen Abundance
divided by one without any lines. The resolution is again
R=200.WewanttoemphasizethattheR=10000opacity In Fig. 7 one can see what happens, if the nitrogen abun-
sampling spectra must not be directly compared to obser- danceincreasesbyafactoroftenandtheC/Ovaluechanges
vations as it was explained in Section 2.3. The parameters to 0.3, 0.7, 0.8 or 0.9. In order to emphasize the effects,
usedtocharacterizethedifferententriesinourdatabasecan the spectra are normalized using a calculation with solar
be found in Section 3.3, where we describe the tables with chemical composition implying C/O = 0.55 and [N/Z] = 0.
thesyntheticphotometry. The figure has three panels with different combinations of
In the following sections we study the changes of the temperature and surface gravity. The corresponding sets of
R = 200 spectra caused by different C/O ratios, nitrogen COMARCS models are equal to the ones described in Sec-
abundances and masses. This is done by normalizing them tion 3.1 and appearing in Figs. 5 and 6. Only the compu-
MNRAS000,1–21(2015)
Synthetic photometry for M and K giants 9
tations with solar abundances are missing, since they have
been used for the normalization. Thus, they would get a
constant valueof onein theplot.
For the coolest of the shown sets with T = 2800 K
eff
and log(g [cm/s2])=0.0 there exists a clear trend. The ab- 2.5 0.74
sorptionatshortwavelengthsdominatedbyTiOandatoms 2.00
5.00
increases with higher C/O values, while the water bands
10.0
above 1.8 µm become weaker. Considerable differences ap- 2
99.0
pear especially in theoptical range. The fluxin the V filter
varies by a factor of about three, if C/O grows from 0.3
to 0.9. But even a moderate change from solar composition 1.5
to C/O = 0.3 or 0.7 causes deviations of ±20%. The re-
lation between atmospheric structure, chemical equilibrium
)
and molecular absorption is often not simple. As it has al- Msol 1
readybeenmentionedinSection3.1,theabundanceofTiO, 0
which produces a strong heating, decreases in the inner re- 1. 2761K, log(g) = -0.6
(
gions of the models at higher C/O ratios, while it grows in m 0.5
theouter areas below 2400 K. nor
F
An enhancement of nitrogen has almost no effect on / m 2.5 21.00.00
or
thespectra of thecoolest set. As one can see in Fig. 1, this Fn 90.0
is mainly due to the weakness of the CN bands appearing 2
at lower temperatures. Also the large opacities of TiO and
water in the outer regions of the cold atmospheres play a
role.InKandMgiantsCNisthemost importantmolecule 1.5
contributingtotheabsorption,whichincludesnitrogen.The
situation becomes quite different in the warmer sets with
1
3600 and 4400 K, where [N/Z] has some influence. In these
casesanincreasedvaluecausesdeeperCNbandsandweaker
atomic features. In general the variations produced by the 3600K, log(g) = 0.0
0.5
investigated changes of the composition are smaller at the
0.3 1 3 10
highertemperatures.Apartfromafewexceptionstheynever λ [µm]
exceed ±10% in the two warmer sets. However, one should
not forget that at 3600 and 4400 K the C/O ratios above
0.7 are not covered.
Concerning the behaviour as a function of the C/O Figure 8. Relative spectral changes due to different stellar
value there is a clear trend in the spectra of the warmer mass for COMARCS models with solar abundances. The spec-
sets. The depth of the CO bands in the near and mid in- tra are normalized to a calculation with M/M⊙ = 1.0. The ef-
frared increaseswithahigherratio, whichcanbeexplained fects are shown for parameters typical for a late AGB object
bythefact thatmorecarbon becomesavailabletoform the (Teff =2761K,log(g [cm/s2])=−0.6,upper panel)andaRSG
molecule. This effect appearsalready at 2800 K,where it is orRGBstar(Teff =3600K,log(g [cm/s2])=0.0,lowerpanel).
less pronounced due to the contamination with the opacity
of water. In themodels with 3600 K theabsorption around 3.2.2 Mass
0.6µm,whichisdominatedbyTiO,getsweaker,iftheC/O
valuegrows. This is the opposite of the behaviourobserved InFig.8weinvestigatetheimpactofthestellarmassonour
forthecoolest set andanexampleforamore complexrela- COMARCS spectra. If the effective temperature and sur-
tion,wheretrendsmaybereversedwhenchangingthebasic face gravity are fixed, this parameter represents the degree
stellar parameters. Thus, one should always be careful, if ofsphericityinahydrostaticatmosphere.Itcauseschanges,
abundance corrections to synthetic spectra or photometry which are in general much smaller than the ones connected
determined for a certain combination of effective tempera- tothetwoothermentionedquantities.Thus,thecorrespond-
ture and surface gravity are transferred to models with dif- ingdeviationscanalsobetreatedasacorrectionappliedto
ferent properties. At 2800 and 3600 K the intensity of the the result of an interpolation in the main variables, when
atomicabsorptionbelow0.5µmincreaseswithahigherC/O using the COMARCS grid to determine observable prop-
ratio. Also this trend does not appear in all places, as one erties of stars (see Section 4.3). In Fig. 8 we show spectra,
can see looking at the4400 K set in theplot. whicharenormalizedrelativetoacalculationwithonesolar
mass. This helps to identify the changes caused by the in-
The significance of the excess of oxygen compared to vestigatedparameter.Twosetsofmodelswiththechemical
carbon (O−C) for the spectra and atmospheric structures composition of the Sun are presented, which are character-
at a changing C/O ratio is discussed in the second part of ized bytheireffectivetemperatureandsurface gravity.The
theappendix.Especiallyincoolermodelsthisparameterwill firstonewastakenfromthestellarevolutiontrackdescribed
beimportant,sincemostoftheCatomsformCOmolecules. in Section 2.2 and displayed in Fig. 4. With T = 2761 K
eff
MNRAS000,1–21(2015)
10 B. Aringer et al.
and log(g [cm/s2]) = −0.6 it is typical for a very extended
lateAGBstar.Massesbetween0.74and99M⊙ arecovered.
The smallest value corresponds to the result from the evo-
12
lutionarytrack,ifthelossofmaterialduetostellarwindsis log(g) = 0.0, 1.0M , C/O = 0.55, [N/Z] = +0.0
11 sol
considered.ItshouldbenotedthatintheusedPARSECand HO - SCAN
2
COLIBRImodelsthiseffectplaysonlyasignificantroledur- 10 [N/Z] = +1.0
ingthelaststagesoftheAGBphase.Theparametersofthe 9 CC//OO == 00..3700
second set having Teff = 3600 K and log(g [cm/s2]) = 0.0 8 C/O = 0.90
are close to the regions, where one can find RSG or RGB K) 90.0Msol
- 7
stars, with the latter being typically a bit more compact. V
(
In this case masses between 2 and 90 M⊙ are shown. The 6
very high values were chosen to simulate a plane-parallel 5
environment.
4
ForbothsetsshowninFig.8weobservethesametrend.
3
TheintensityoftheTiObandsintheopticalrangeincreases
with lower mass, while themolecular absorption in themid 2
4500 4000 3500 3000 2500
and far infrared becomes smaller. This weakening affects T [K]
eff
in the cooler models mainly the water opacity and in the
warmeronesthefeaturesofCOandSiO.Itcanbeexplained
by a geometric phenomenon. A lower mass causes a larger Figure 9. (V−K) as a function of the effective temperature for
contributionoftheopticallythinedgesofastartothetotal COMARCS models with solar metallicity and log(g [cm/s2]) =
flux, which produces more intense emission components in 0.0.ThestandardparametersareM/M⊙=1.0,solarabundances
(C/O=0.55,[N/Z]=0.0)andusageoftheBT2linelistforwater
the lines. These may be directly observed in the profiles of
below4000K(black). Theresultofchanging C/Oto0.3(blue),
differenttransitionsespecially in theinfrared,ifonestudies
0.7(magenta)and0.9(orange),ofincreasingnitrogenbyafactor
highresolutionspectraofpulsatinggiantswitharadialand
of ten ([N/Z] = +1.0, green) or the mass to 90 M⊙ (cyan) is
temporalvariationofthevelocityfields(e.g.Nowotny et al. shown.Inaddition,wedemonstratetheeffectoftakingtheH2O
2010;Alvarezet al.2001).Duetoanincreasedatmospheric opacitiesfromtheSCANdata(red).
extension the effect will become very pronounced in dy-
namical objects with significant stellar winds. It is usually
strongeratthelongerwavelengths,whereonemightinsome
cases evenget broad emission features(e.g. Matsuura et al.
2002; Gautschy-Loidlet al. 2004). In our hydrostatic CO-
MARCS models with no mass loss or velocity fields we ob- ratedintodifferentfilescontainingthevaluesofallincluded
tain only thementioned weakening of thelines. filters and COMARCS models. This wealth of information
The changes of the TiO bands visible in Fig. 8 are may be exploited by the users of the database. In the cur-
caused by differences of the atmospheric structure. As one rent work we will only discuss the visual and near infrared
would expect, all effects of mass are much larger for the magnitudesthatweredeterminedaccordingtothedefinition
more extended cooler set, since they depend a lot on the fromBessell(1990)andBessell & Brett(1988).TheV,I,J,
surface gravity.Iflog(g [cm/s2]) grows abovezero, theybe- H and K values and corresponding colours, which appear
come quickly very weak. Thus, the sphericity needs only in thefollowing sections and figures, are based on thispho-
to be taken into account during the last (and maybe first) tometric system (Bessell). The mentioned filters have been
stages ofstellar evolution.However,suchstarsare often far used for a large numberof observations.
away from hydrostaticequilibrium. The observed colours of many cool and variable stars
areseverelyaffected byreddeningduetocircumstellar dust
(Nowotnyet al.2011).Sincehydrostaticmodelatmospheres
3.3 Synthetic Photometry
do not take this process into account, the corresponding
The synthetic photometry computed for the complete grid corrections have to be applied a posteriori to the results
of our hydrostatic COMARCS models can be found in (Marigo et al. 2008). However, in such cases it is preferable
http://starkey.astro.unipd.it/atm. The tables contain tousedynamicalcalculationsdescribingpulsationandmass
the bolometric corrections (BC) described in Section 2.3 as loss.
afunctionofthestellarproperties.Thecorrespondingmain In Figs. 9, 10, 11 and 12 the colours (V−K), (V−I),
parameters are Teff, log(g [cm/s2]), M/M⊙, [Fe/H], [O/H], (J−K)and(J−H)arepresentedasafunctionoftheeffective
[C/H], ξ [km/s] and a flag for the used water absorption temperature for COMARCS atmospheres with solar metal-
data (SCAN or BT2, see Section 2.1). [Fe/H] which repre- licity.WecompareresultsobtainedwithaC/Oratioof0.3,
sents[Z/H]aswellas[O/H]and[C/H]whichdeterminethe 0.7and0.9,[N/Z]=+1.0,90M⊙aswellaslog(g[cm/s2])=
C/O ratio are listed with the absolute abundances scaled 2.0toastandardmodelhavinglog(g[cm/s2])=0.0,1.0M⊙
relative to hydrogen log(εFe,O,C/εH)+12. Other quantities and the chemical abundances of the Sun. In addition, we
like [N/H], [Y/H] or [Zr/H] were included, if they deviate show the consequences of using the SCAN water data in-
from the standard values. The opacity sets available at the stead ofBT2 for starscooler than4000 K (seeSection2.1).
moment in theCOMARCS grid can befound in Table A1. Calculations with log(g [cm/s2])=2.0 are only included in
Thecompletesetoftablescoversthebolometriccorrec- theplotsfor(J−K)and(J−H),sincethesecoloursaremore
tionsformorethan40photometricsystems,whicharesepa- affected by thesurface gravity.
MNRAS000,1–21(2015)