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Studies of line spectra of G- and K-type stars

van Paradijs, J.A.

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Citation for published version (APA):van Paradijs, J. A. (1975). Studies of line spectra of G- and K-type stars. Amsterdam: Universiteit vanAmsterdam.

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Download date: 16 Apr 2020

Astron.. & Astrophys. 23, 369 379(1973)

Ann Analysis of the Line Spectra of Some G and K lb Supergiants J.. van Paradijs Astronomicall Institute, University of Amsterdam

Receivedd September 12, revised November 7, 1972

Summary.. In this paper we present the results of an ana-lysiss of the line spectra of seven supergiants of type G and KK lb. This analysis is based on observations of line strengthss on spectrograms of 1.6 and 6.5 A/mm, in the wavelengthh region between 5000 A and 6650 A, and on calculationss of weak line strengths for a grid of model atmospheres.. Curves of growth have been made using solarr 0/-values. Fromm the condition of minimum scatter in the curve off growth effective temperatures are derived. These temperaturess favour the lower temperature scale of Böhm-Vitensee (1972), and support the suggestion of Frickee et ai. (1972) that the discrepancy between mass determinationss of cepheids from evolution theory and fromm pulsation theory may be removed by lowering thee previously adopted temperature scale of Rodgers (1970)) and Parsons (1971) by a few hundred de-grees. . Thee gravity of the stars has been obtained from the requirementt that two ionisation states of one element

shouldd give the same abundances. The agreement be-tweenn these spectroscopic gravities with gravities deri-vedd from calculations of stellar evolution is excel-lent. . Thee supergiants in our program have solar abundances forr most elements, except 3 Cet, which shows a general overabundancee by a factor of 1.6. Na is overabundant inn all the stars, extending the results of Cayrel de Strobell et al (1970) for late type stars of luminosity classs III . Sr and Ba are systematically overabundant, butt this effect is neither very large nor very certain. Inn order to check the result of Bakos (1971) that there iss a correlation between the abundances of heavy ele-mentss and the luminosity of the star we have also analyzedd five early K type giants, using the equivalent widthss of Cayrel and Cayrel (1963) and of Koel bloed (19722 b). No indication of such an effect is found.

Keyy words: supergiants - effective temperature - spec-troscopicc gravity - abundances

Introductio n n

AA study of the line spectra of G and K type supergiants iss of interest for a number of reasons. From the point off view of the theory of stellar structure data on chemi-call composition, effective temperature and gravity are important,, as these are part of an observational basis forr theoretical mass and luminosity calculations, theo-riess of nucleosynthesis etc. Moleculee formation, convection and turbulence have a smalll influence on the structure of this type of stellar atmospheress (Böhm-Vitense, 1972). These fortunate circumstancess make the use of model atmospheres in ann analysis of spectral lines feasible. The study of the linee spectra may indicate to what extent the various approximationss made in the calculations of the model atmospheress are justified. Inn the present paper we will be concerned especially withh the following subjects. 1.. The effective temperatures of lb supergiants. 2.. The comparison of spectroscopic gravity with gra-vityy as determined from mass and radius. 3.. The chemical composition of late type supergiants; inn particular the abundances of heavy elements, which

somee authors recently found to be enhanced (Warren, 1970;; Bakos, 1971; Warren and Peat, 1972). Inn the main part of this study we analyse seven super-giantss with spectral types between G 0 lb and K 5 lb. Forr purposes of comparison we also present at the end off the paper an abridged account of an analysis of fivefive K giants.

Observationall Data

Thiss study is based on spectrograms of seven super-giantss with spectral types between G 0 lb and K, 5 lb. Thesee spectrograms were taken by Dr. D. Koelbloed withh the 100 inch telescope of Mount Wilson Observa-toryy during 1965-1966. The dispersions of the plates aree 1.6 and 6.5 A/mm. The wavelength region covered runss from 5000-6650 A. Basicc observational data are given in Table 1. These dataa were taken from the Bright Star Catalogue (Hoffleit,, 1964) and from the list of Iriarte et ai (1965). .

33 33

370 0 J.. van Paradijs

Tablee 1. Fundamental data for program stars

Name e

HH Per att Aqr 99 Peg ee Gem ee Peg 3Cet t £Cyg g

BS S

1303 3 8414 4 8313 3 2473 3 8308 8 9103 3 8079 9

HD D

26630 0 209750 0 206859 9 48329 9

206778 8 225212 2 200905 5

sp. . type e

GOO lb G2Ib b G5Ib b G8Ib b K2I b b K3I b b K5I b b

at t

(1900) )

4h07,,,33, ,

222 00 39 211 39 47 66 37 47

211 39 16 233 59 23 211 01 18

Ö Ö

(1900) )

++ 48°09' - 000 48 ++ 16 53 ++ 25 14 ++ 09 25 - 111 04 ++ 43 32

V V

4.14 4 2.92 2 4.31 1 2.98 8 2.38 8 5.16 6 3.70 0

B-V B-V

0.95 5 0.98 8 1.18 8 1.40 0 1.53 3 1.68" " 1.65 5

U-B U-B

0.64 4 0.79 9 0.96 6 1.47 7 1.68 8

1.80 0

B-VB-V taken from Kraf t and Hiltner (1961).

AA full account of the reduction of these spectro-grams,, together with a table of the observed equivalent widths,, is published separately in the Supplement Seriess of this Journal.

Modell Atmospheres

Thee model atmospheres used in this investigation are ann extension of the grid of models (for Te{[ ^ 5500 °K) publishedd by Carbon and Gingerich (1969). These are fluxx constant, plane parallel L.T.E. models, including thee effects of line blanketing. A convenient property of thesee models is that the relation between the tempera-turee and the optical depth T5 0 00 (at 5000 A) is nearly independentt of the value of the gravity. In the region off the formation of the weak spectral lines the varia-tionn of the temperatures at equal optical depth is of the orderr of a few tens of degrees. In the deeper layers the variationn is larger, but regular. These deep layers hardly affectt the visible line or continuous spectrum. Wee have extrapolated the T(T5 0 0 0) relations of Carbon andd Gingerich to lower gravities in two ways. Firstly byy extrapolating the temperature at every optical depth point,point, and alternatively by simply taking the average off the temperatures in the higher gravity models. The differencess between these two approaches are signifi-cantt only for logT5000>0.2, as expected. The results off weak line strength calculations, to be mentioned below,, are completely insensitive to these differences. Inn the following we have used the average of the temperaturee distributions of the higher gravity models. Inn a sense this extrapolation can be regarded as an improvedd version of scaling solar models. The error inn the temperature, arising from this method of extra-polationn only, is smaller than 25 °K in all interesting partss of the model atmospheres. Systematic errors arisingg from different line blocking as a function of wavelengthh in these lower gravity atmospheres, changing thee backwarming and the boundary temperature of thee atmosphere, may be present. From the data of Carbonn and Gingerich (1969) and Rodriguez (1969) it appearss that the line blocking does not change abruptly whenn going to lower values of \ogg. Furthermore, it willl appear below that the extrapolation of the log#

valuess is not too large (A log# * — 1). So this extra-polationn to lower gravity models probably does not introducee serious systematic errors in the temperature stratification. . Withh these temperature distributions we have integra-tedd the equation of hydrostatic equilibrium, using a standardd Runge-Kutta integration scheme. Values of thee effective temperature are 5500, 5000, 4500 and 40000 °K; for logg we have taken the values 0.5, 1.0, 1.55 and 2.0. Thee continuous absorption coefficient has been inter-polatedd in the tables of Bode (1965). The ratio of elec-tronn pressure to gas pressure was obtained with the ionizationn equilibria of the elements used by Carbon andd Gingerich, and the dissociation equilibria of H2, Hjj and H~. In the calculation of these equilibria wee have made use of the data of Mihalas (1967). Inn order to check the accuracy of our integrations we havee compared our results for identical input para-meterss (Teff, logg, chemical composition) with the re-sultss of Carbon and Gingerich. The largest differences, fromm ten models, in the most important interval - 11 < logT5000 < 0 are A logP, = 0.028, A logPe = 0.022 andd A logxcont = 0.044. These results satisfy our pur-poses. . Itt may be useful to mention here the most important implicitt assumptions underlying the calculations of the modell atmospheres. Firstly, we have assumed that the atmospheress are stable. It has however been found that supergiantss sometimes show small erratic variations in magnitudee and radial velocity (Abt, 1957). The only signn of variability which we found from our spectro-gramss is the remarkable change of the Ha profile of 3Cett (see Fig. 1). The two spectra of 3Cet which weree first taken (with a time interval of one day) both showw a blue shifted extra absorption superposed on the "normal"" profile as it is observed five months later. Thee NaD lines on these spectrograms also show profiless which are distorted on the blue side. This suggestss an outflow of matter from the atmosphere off this star. A rough order of magnitude of the velocity off this matter can be obtained from the Doppler shift off the blue side of the Ha profile; we find a velocity off 30 km/s. From the effective temperature, the gravity

J * *

Linee Spectra of G and K lb Supergiants 371 1

Fig.. 1. Line profiles of Ha in the spectrum of 3 Cet at three different times,, showing the variation of the violet side of the line core. The verticall lines indicate the position of the line centre relative to neighbouringg spectral lines

andd an evolutionary track in the Hertzsprung-Russell diagramm the mass and radius of the star can be obtained. Thee escape velocity found with these data is of the order off 100 km/s. In view of the small time interval which the exposuress of the spectrograms cover and the uncer-taintyy in the estimates of both velocities, these observa-tionss should be considered seriously as an indication forr instabilities in these atmospheres causing non-violentt mass loss now and then. This changing Ha profilee reflects changing conditions in layers high above thee photosphere. Furthermore, the line strengths on differentt spectrograms show that the physical conditions inn the photospheric region do not vary much in time. Forr these reasons the assumption of stability appears aa reasonable approximation. Furtherr assumptions made in the calculations are the neglectt of turbulent pressure and of H 20 formation. Thee reasons for not taking turbulence into account inn the equation of hydrostatic equilibrium are the fact thatt microturbulence is small in supergiants later than GOO (Rosendhal, 1970), and the lack of an observa-tionall basis regarding macroturbulence. Inn order to check the effect of the formation of H 2 0 onn the temperature stratification we have compared

ourr lowest temperature models (where the effect is largest)) with the models of Auman (1969). After trans-formingg the T 1 1 7 00 scale of Auman into a T 5 0 00 scale it appearss that the temperature differences near t50oo = 0-5 aree smaller than 100 K.. For the hotter models the in-fluencee of H 20 formation will of course be still smaller.. We conclude that the neglect of H 2 0 does nott lead to unacceptable errors in our models.

Weakk Line Strengths

Ourr knowledge of the structure of the atmospheres of latee type supergiants is limited with regard to para-meters,, like microturbulence (as a function of optical depth),, which determine the detailed form of the curves off growth. Therefore we have based our analysis on empiricall curves of growth. These curves are made by plottingg the observed logF = \ogW//. + 6 against the weakk line strength logX = \oggfA + logF. W is the equivalentt width of the spectral line in mA, A is the abundancee relative to hydrogen. T is the weak line strengthh for unit abundance, which we calculated usingg the theory of weighting functions (Unsold, 1955, p.. 400).

F = 1 06 ^ - j G ( T ) P ( T ) d T / xc o n t , , mcmc J0

'ogFweakk = logNelem/NH + \oggf + logF.

G(T)) is the weighting function, for flux (stars) or intensity (sun),, and P{x) is the function which gives the population off the lower level of the transition. These populations havee been calculated assuming L.T.E., and neglecting secondd ionization of all elements. Data on the ioniza-tionn potential and partition functions have been taken fromm Shore and Menzel (1968), Cayrel and Jugaku (1963),, Aller (1963) and Righini and Rigutti (1966). Thee calculations have been performed for excitation potentialss ^exc between 0 and 5 eV in steps of 0.5 eV. Thee slope of the relation between log F and #exc equals öexc.. It is slightly dependent on xtxc. Thee values of log F have been calculated for all the models.. For a particular (Feff, logg) combination the logg F values are interpolated in the grid of calculated values. . Sincee F depends on wavelength we have repeated the calculationss for X = 7000 A, after transforming the tem-peraturee distribution F ( T5 0 0 0) into F ( T7 0 0 0) . The differ-entiall behaviour with respect to the wavelength varia-tionn of log F in the star and in the sun - assumed to bee linear - was taken into account by applying the correctionss appropriate to the average wavelength and excitationn potential of each element. In all cases the magnitudee of the effect is very small. The differential variationn with wavelength of log F for different values off the excitation potential can be neglected, and we havee used only log F at I = 5000 A in the determina-tionn of the stellar temperatures.

372 2 J.. van Paradijs

Oscillatorstrengths s

Thee use of oscillatorstrengths is an indispensable step inn the process of transforming a set of observed line strengthss into statements about the physical properties off stars. A good example is the temperature determina-tion,, which is based on the requirement that the abundancee of an element should not depend on the excitationn potential of the transition from which it is derived.. Stated otherwise, one requires a minimum scatterr in the curves of growth. The temperature ob-tainedd in this way is in fact the excitation temperature. Thee effective temperature, which is more interesting fromm other points of view, e.g. evolutionary theory, iss related to this excitation temperature by a model atmosphere. . Thee problem associated with this method of tempera-turee determination is that a systematic error of the oscillatorstrengths,, depending on the excitation poten-tiall of the lines, results in a systematic error in the derivedd temperatures. Since Fei has by far the largest weightt in the temperature determination we centre the followingg discussion on this element. It is well known thatt it is difficult to free laboratory ^/-values from thiss effect. The Fe I #/-values of Corliss and Bozman (1962)) and Corliss and Warner (1964) provide a good example.. More recent determinations of Fei gf-valuess (Wolnik et al, 1970, 1971; Garz and Kock, 1969;; Bridges and Wiese, 1970; Richter and Wulff, 1971)) show some large differences. The scale of Wolnik etet al shows a temperature difference J0«O.O8 with the otherr sets mentioned. The latter values were all obtained fromm stabilised iron arcs, and agree closely, with a differencee Ad<0.025. Unfortunately the number of weakk lines in the yellow and red parts of the spectrum, onn which we wish to base our study, for which data aree available is very small. In view of this it was decidedd to use solar ^/-values. These are derived from thee strength of solar spectral lines. Data on most solar equivalentt widths were taken from Moore et al. (1966); dataa on many weak Til lines were kindly put at our disposall by Dr. N. Grevesse. From the solar curve of growthh we read off the abscissa, which may be put equall to the logarithm of the unsaturated equivalent width,, written as logX = logr + \oggf AQ. T is calcula-tedd from a model of the solar atmosphere, so the pro-ductt of the oscillatorstrength and the solar abundance iss at once obtained. For the solar atmosphere we have adoptedd the Harvard Smithsonian Reference Atmo-spheree (Gingerich et al, 1971).

Byy this method temperature errors may get into the scalee of 0/-values by the following causes.

1.. The solar model atmosphere may give the wrong excitationn temperature. This seems improbable, in vieww of the very small differences in the temperature distributionss of recent solar model atmosphere (Ginge-richh and De Jager, 1968; Peytremann, 1970; Gingerich

eiei al, 1971) in the interval - 1 < logi<0, which deter-miness the excitation temperature. 2.. In case there is a correlation between line strength andd excitation potential, systematic errors as a function off excitation potential in the set of ^/-values used to makee the solar curve of growth will change the shape off this curve. This correlation does exist in the blue and greenn regions of the solar spectrum for Fe i lines with logFQQ = log WQ/X + 6 > 1.0. W0 is the equivalent width off the solar spectral line in mA. The importance of thiss effect is clear from the fact that the microturbulence inn the sun, derived with the same line strengths and modell atmosphere, depends on the ^/-values used (Garzz et al, 1969). This effect is strengthened in the casee of Fei, since different multiplets show different upperr parts of their curves of growth, due to different dampingg constants. Since the damping constant is correlatedd with excitation potential the use of an Fe i curvee of growth with only one average damping part introducess serious temperature errors in the ^/-values off these strong lines. We have taken the splitting of thee Fe l curve of growth into account by using the data ofPagel(1964). . Thee correlation between line strengths and excitation potentiall may also cause a temperature error in the solarr ^/-values when there exist systematic errors, as aa function of line strengths, in the measurements of thee equivalent widths of solar spectral lines. A compari-sonn of the data of Muller and Mutschlecner (1960) withh those of Moore et al (1966) reveals that such systematicc deviations, up to about 10%, exist. It seems thatt facts like this set a limit to the accuracy attainable forr solar #/-values. Fortunately,, in supergiant spectra the lines are much strongerr than in the solar spectrum. The lines which wee use for the temperature determination of the super-giantss are all weaker than logFQ = 1.1 in the sun. So thee dangerous effects mentioned will not affect the solar #ƒ-valuess of the lines which are needed for the temperaturee determinations of the program stars. Thee oscillatorstrengths of lines of other elements have beenn obtained with the average Fe i curve of growth. Itt is thus assumed that for all elements the same curve off growth applies. (Exceptions are mentioned below). Thee analysis of some elements however, depends on strongg lines. Examples are Ban and Cut. For these elementss we have used that damping branch which fittedd the observations of these elements best. Of course errorss in the ^/-values do not disappear in this way. Thee abundances of elements which have been derived fromm strong lines only must be considered very un-certain. . Sincee the microturbulence in the solar atmosphere is quitee small, differences in thermal velocity of the ele-mentss will change the total Doppler velocity, derived fromm the curve of growth appreciably. Values of the microturbulencee recently derived differ substantially,

Lin ee Spectra of G and K lb Supergiants 373 3

mainlyy by the use of different sets of gƒ-values. Cowley andd Cowley (1966) derived a value of 1.5km/s, Powell (1969)) and Garz el al. (1969) got 1.0km/s, whereas Foyy (1972) obtained a microturbulence of only 0.5 km/s. Inn this study we have adopted 1.2 km/s. The solar curve off growth of all elements has been shifted vertically overr the distance A\ogV=\ogVtlcment-\ogVFe. V is thee total Doppler velocity entering the profile of the absorptionn coefficient, including microturbulence and thermall velocity. Na is the element of our list most sensitivee to this effect. Using the value 0.5 km/s for the microturbulencee instead of 1.2 km/s changes JlogFNa byy +0.04 and logöf/Na by less than 0.15. Thee elements V, Mn, Co and Cu are much affected byy hyperfine structure line broadening (HFS). It is out-sidee the scope of the present study to calculate the solarr and stellar curves of growth including this effect properly,, and we have considered HFS in a first approximationn as an extra turbulent velocity KHFS, withh the method given by Unsold (1955). We use only onee value of VH¥S per element, and in this way introduce moree scatter in the curves of growth of these elements. Especiallyy for Cu the approximation is poor. The values off VHFS were obtained using the data of Abt (1951) and Holl weger and Oertel (1971); the results are given in Tablee 2.

Tablee 2. Microturbulen t velocity KHFS representing the effect of hyper-finestructur e e

Element t

VHFS{km/s) )

V V

1.9 9

Mn n

3.3 3

Co o

2.5 5

Cu u

3.6 6

Temperaturess of lb Supergiants

Thee effective temperature of the program stars have beenn derived from the curves of growth of Fe I and Ti I byy the requirement that the scatter in these curves shouldd be minimal. Preliminary curves of growth were madee using a starting value of the effective temperature, obtainedd from the color indices V-R, V-I, V-J andd V-K (Johnson et al, 1966), together with the temperature-colorr relations of Johnson (1966). An empiricall curve of growth was drawn through mean pointss of groups of lines. From the correlation between thee horizontal shift to this curve and the excitation potentiall the correction to the (excitation) temperature iss found. Only weak and medium strong lines have beenn used in these determinations. The corrections A6A6tKtK are not too large, so we may set A6eff = A0txe. Thee internal accuracy of the Fe I and Ti I temperatures aree o{A0Ttl) = 0.025 and ff(40Til) = O.O6, varying only byy a small amount from star to star. There is a margin-allyy significant systematic difference of 0.025 7 (m.e.)) between A6¥cl and A6Tii, in the sense that the

Tablee 3. Effective temperature and gravity of lb supergiants

Star r

HH Per a.a. Aqr 99 Peg ee Gem ££ Peg 3Cet t ÉCyg g

TÏK <Fe«) )

4650 0 4625 5 4350 0 4100 0 3825 5 3750 0 3650 0

TTtft tft

5100 0 5075 5 4850 0 4600 0 4225 5 4100 0 3900 0

log(7,p p

1.30 0 1.45 5 1.75 5 1.00 0 1.10 0 1.10 0 0.75 0.75

\o%Jf/Jt\o%Jf/JtQ Q

0.85 5 1.00 0 0.80 0 0.97 7 0.91 1 0.96 6 0.90 0

logtf* . .

1.27 7 1.06 6 1.44 4 1.07 7 0.89 9 0.74 4 0.78 8

Fee i temperatures are lower. In Table 3 the weighted meann values of the effective temperature determinations aree given for the program stars. Since the effective temperaturess are model dependent, we also give the Fee i excitation temperatures, on the basis of 0 eV to 33 eV, which depend only on the observed line strengths. . Previouslyy effective temperatures of lb supergiants, as aa function of an intrinsic color index or spectral type, havee been given by Johnson (1966), Rodgers (1970), Parsonss (1971), Böhm-Vitense (1972) and Schmidt (1972).. The temperature relation of Johnson is based on aa calibration using interferometrically observed radii off a few stars, combined with bolometric corrections obtainedd from multicolor photometry. The results of Parsonss are derived from a comparison of observed colorr indices in the system of Stebbins and Kron (1964) withh flux distributions calculated from line blanketed modell atmospheres. Böhm-Vitense has computed the theoreticall color indices of a number of model atmo-spheres,, in which the effects of depth dependent line blanketingg are taken into account. The basis of the temperaturee calibration of Schmidt is provided by a comparisonn of observed and theoretical line widths of Haa at 90% continuum intensity. In Fig. 2 the results of thesee authors are shown as a function of the intrinsic {B{B — V)0. It is at once clear that mutually very large differencess occur. An extreme example is provided by thee temperatures at {B — V)0 = 0.9, as given by Schmidt andd by Böhm-Vitense, which differ by some 800 °K. Alll these effective temperature determinations are to somee extent model dependent, since the quantities fromm which they are derived reflect the conditions at ann optical depth of, say, 0.5. So different model atmospheress will yield different relations between the effectivee temperature and the temperature indicator whichh is used. Anotherr source of difficulties is the apparent dis-agreementt on the intrinsic colors and color excesses of thee supergiants. As an example of the errors which may bee expected, take the assertion of Schmidt (1972) that hiss values of the color excesses EB„ V agree best with thosee of Sandage and Tammann (1968). The latter authorss use the results of Kraft (1961) and Kraft and Hiltnerr (1961) to obtain the color excesses. However, comparingg the values of EB_V, which Schmidt (1972)

374 4 J.. van Paradijs

7000 0

'eff f

6000 0

5000 0

«000 0

_L L

Q40 0 Q60 0 080 0 1000 1.20

CB-VL L

1.40 0 1.60 0

Fig.. 2. Effective temperature as a function of (B -Johnsonn (1966) A ; by Böhm-Vitense (1972) -

V)V)00,, as established by Schmidt (1972) ;; and the present study

byy Parsons (1971) and Rodgers (1970) —-; by

andd Kraft (1961) give for the stars aAqr, s Peg and £,£, Cyg, we find differences of +0.02, —0.30 and ++ 0.15 mag. Inn principle it is possible to derive the color excesses of ourr program stars by shifting them along the reddening linee in the U — B, B—V diagram onto the intrinsic twoo color relation. In practice, however, the method iss liable to large errors since the reddening line and the intrinsicc U — B, B—V relation run nearly parallel in thee two color diagram (cf. Fernie, 1963). In order to obtainn the intrinsic (B — V)0 we have simply taken the averagee of the spectral type - (B — V)0 relations of Ferniee (1963), Schmidt-Kaler (1965) and FitzGerald (1970),, which mutually are in good agreement. Judging fromm the differences between these relations and the variationn of (B — V)0 within one spectral subtype, the accuracyy of these color indices is not better than 0.11 mag. The adopted relation between spectral type andd (B — V)0 is given in Table 4. Inn Fig. 2 the effective temperatures of the program starss are plotted against this intrinsic (B— V)0. It is clearr from this figure that for the G type supergiants

Tablee 4. Adopted relation between spectral type and intrinsic (B— V)0

forr lb supergiants

Spectral l type e

GO O G2 2 G5 5 G8 8 K 0 0 K.2 2 K 3 3 K 5 5

[B-n, [B-n,

0.75 5 0.86 6 1.01 1 1.11 1 1.23 3 1.32 2 1.44 4 1.61 1

ourr results favour the lower temperature scale found byy Böhm-Vitense (1972). For the later type stars our temperaturess lie just between those of Böhm-Vitense andd Johnson (1966). Itt is particularly interesting that these results confirm aa conclusion of Fricke et al. (1971). According to these authorss the temperature scale of Rodgers (1970), which iss nearly identical to that of Parsons (1971), should be

38 8

Linee Spectra of G and K. lb Supergiants 375 5

Tablee 5. Effective temperature and gravity of comparison stars of luminosityy Class II I and IV

Star r HD D Spectrall Type Tef logs s

eVir r <55 Dra cCyg g qCep p JJ Cep

113226 6 180711 1 197989 9 198149 9 216228 8

G9I I I I GG 9 III KOII I I KOIV V KK 1 II I

4970 0 4940 0 4890 0 4980 0 4970 0

2.85 5 3.00 0 2.85 5 2.95 5 3.35 5

'eff f 50000 -

48000 -

0.40 0 0.50 0 R-l l

0.60 0

Fig.. 3. Relation between R — I and effective temperature for giant stars.. The straight line represents the theoretical relation for the loggg = 3 models of Carbon and Gingerich (1969)

loweredd by some 500 K around (B — V)0 = 0.8, in order too get agreement between the masses of classical cepheidss as derived from pulsation theory and from evolutionn theory. Accordingg to Johnson (1966) the problems with intrinsic colorr indices are not present for normal giants of luminosityy class III . Since these stars can provide us withh a check on the temperature scale of the solar ^/-valuess which we use, we have obtained effective temperaturess for some giants in the same way as for thee supergiants. We have taken equivalent width data fromm Cayrel and Cayrel (1963) for the star £ Vir (G 9 III) , andd from Koelbloed (1972b) for the stars ö Dra (G 9 III) , fiCygfiCyg (KOIII) , i Cep (K l III ) and rj Cep (KOIV) . Thee latter are based on 3.3 A/mm spectrograms taken withh the 48" telescope of the Dominion Astrophysical Observatory,, Victoria. The results are given in Table 5. Inn Fig. 3 we have plotted these temperatures against thee color index R-l, taken from Dickow et al. (1970). Thiss color index has also been calculated as a function off effective temperature, using the flux distributions of thee logg = 3 models of Carbon and Gingerich (1969). Itt will be shown below that this is a reasonable gravity forr these stars. The R and I sensitivities and effective wavelengthss were taken from Johnson (1966). The reasonn for taking R — I in comparing the observed and calculatedd temperature-color relations is the severe difficultyy with line blocking in the blue region of the spectraa of these stars. From Fig. 3 it appears that a systematicc temperature error in the solar g/-values is smallerr than 50 °K.

Griffi nn (1969) and Koelbloed (1972a) found that forr K giants there is a systematic difference in the temperaturess derived from Fe I and Ti i lines. For

thee average difference ,d0exc(Fei) minus J0eIC(Tii ) Griffi nn finds -0 .04 + 0.006 (m.e.), Koelbloed gets -0.0622 +0.013 (m.e.). Contrary to this we find a systematicc difference which is not very significant: —— 0.018 3 (m.e.), i.e. the Fei temperature is some-whatt higher than the Ti i temperature. It is remarkable thatt this is opposite to what was found for the super-giants.. This difference between supergiants and giants cannott be attributed to relative temperature errors in thee ^/-values of these elements. If it is real, it may showw the breakdown of the assumption of L.T.E.

Gravity y

Inn the atmospheres of the kind of stars we study here thee elements of the iron group are almost completely ionized,, and the second ionisation stage can be completelyy neglected. It follows that the relative numberr of singly ionized atoms is constant, and, usingg the Saha equation, the relative number of neutral atomss is proportional to the electron pressure. Although Rayleighh scattering by neutral hydrogen gains in importance,, H~ provides the dominant continuous absorptionn mechanism for which the proportionality too electron pressure also holds. Since line strengths are determinedd by the ratio of the line absorption coeffi-cientt (proportional to number of absorbers) to the continuouss absorption coefficient, the line strengths off neutral atoms of the iron group are approximately constantt with varying gravity, whereas those of the correspondingg ions get stronger for lower gravity. This effectt is the basis for our logg determinations. Fromm the definition of the curve of growth (observed logFF versus logr + loggr/ 0̂) it follows that the horizontall shift to the congruent curve going through thee origin equals log A/A 0, yielding the abundance of thee element relative to the sun. Assuming a trial value off the gravity, at already fixed effective temperature, wee will not derive the same abundance from the I and III spectra of an element. The condition that these abundancess should be equal determines the gravity. Thiss method has been applied to the elements Sc, Ti,, V, Cr and Fe.

Thee weak side of the method is the sensitivity of the gravityy to the adopted effective temperature. This dependencee has been determined graphically. It appears thatt A logg/A6ef{» —13, essentially constant with ef-fectivee temperature. Anotherr systematic effect influencing our gravities is the recentt large change in the iron abundance, which was nott included into the models of Carbon and Gingerich. Thee introduction of the new solar iron abundance of Garzz et al. (1969) alters the ionization equilibria of all elements.. Of course the blanketing effects on the atmospheress are unaffected, since the product gfA, andd thus the line strengths, are the same. So the use of

39 9

376 6 J.. van Paradijs

thee same T{z) relations is justified. We have estimated thee influence on the gravity by the calculation of logff values for a number of models with the old and withh the new iron abundance. Relative to the "iron poor"" models the abundances of the elements change byy less than 0.02 dex, which can be neglected. The logt/ changess by about -0.15 dex; this amount somewhat dependss on the effective temperature. All our results aree based on models with the iron abundance of Garzz et al. (1969). Inn Table 3 we present the values of log*/. The mean error,, which measures only the agreement of the results ass obtained from different elements, not including the systematicc uncertainty due to temperature errors, varies betweenn 0.15 and 0.35. It is of considerable interest to comparee these data with the results of stellar structure calculations,, assuming that the stars are in a common evolutionaryy stage. In view of their position in the Hertzsprung-Russelll diagram it is reasonable to assume thatt G and K lb stars are in the stage of He core burningg and H burning in a shell around the core. It is thenn possible to derive a relation between the mass M andd the absolute bolometric magnitude M^,. From the evolutionaryy tracks of Iben (1967) we obtain the relationn MM = 8.65 \o%MIJi0 +0.68. A comparison withh the data of Hofmeister (1967) and Paczyriski (1970) showss that the use of Iben's tracks is not very critical. Thee radius of the stars is derived from the absolute visuall magnitudes (Kraft et al., 1964; Blaauw, 1963), thee bolometric correction (Schlesinger, 1969) and the effectivee temperature. The gravity gM R obtained from thesee data is given in Table 3. Onn the average we find

log0spp - log^,R = 0.16 0.19 (p.e.).

Inn view of the scatter of the absolute magnitude determinationss the agreement between spectroscopic andd theoretical gravity is better than might have been hopedd for. This excellent agreement contrasts sharply withh earlier investigations (Pannekoek, 1937; Koelbloed, 1953)) where discrepancies up to a factor of 100 were found.. The present results show that large scale outflow off matter and turbulence are not important factors in thee pressure equilibrium of these stellar atmosperes.

Abundances s

Withh the effective temperatures and gravities found already,, curves of growth have been made for 22 elements.. The microturbulence was obtained from a comparisonn with Wrubel's (1949) theoretical curves off growth. The use of these curves may introduce some inconsistencyy because the models underlying them aree not identical with our models. Hunger (1956) has shownn that errors in the microturbulence due to differentt assumptions concerning the models are rather

Tablee 6. Microturbulenc e in G and K lb stars

Starr K. t(km/s)

HH Per 3.6 aa Aqr 3.9 99 Peg 3.4 r.r. Gem 3.3 ££ Peg 3.5 33 Cet 3.0 ££ Cyg 2.8

small.. More important in the determination of the microturbulencee is how well the linear part of the curve off growth is reached. We find that for the stars earlier thann K 0 this does not give much trouble, whereas for thee later type stars the situation is less satisfactory. Thee results, given in Table 6, confirm the low values of thee microturbulence found earlier for late lb stars (Rosendhal,, 1970). Afterr application of the corrections for different total Dopplerr width, due to different atomic weight and hyperfinee structure, the abundances of the elements are att once obtained. These are given in Table 7, together withh the maximum number of lines available for each element.. The elements for which the abundances suffer mostt from the assumption of identical shape of all curvess of growth are marked by a colon. Thee results of Table 7 can be summarized as follows. Exceptt 3 Cet, which shows a general overabundance byy a factor of 1.6, all stars have a solar chemical composition,, apart from enhancements of the elements Na,, Sr and Ba. Inn view of the possibility that the overabundances of Naa and Ba are caused by the use of an inappropriate Fee i curve of growth, it was investigated in a rather crudee manner whether, due to different damping constants,, the shape of the curves of growth of Na i andd Ba n should have to be changed so much, that the abundancess will change significantly. As a first step wee have compared the mean Fe i damping constant, as derivedd from the fitting to one of Wrubel's (1949) curves,, with the calculated mean damping constant. Radiativee and Van der Waals damping have been included.. In the calculation the physical conditions at xx = 0.1 in the log0=1.5 models were assumed. This givess logFjr = 3.0, hardly dependent on the effective temperature.. For the lines populating the damping partt of the curve of growth we find with the data of Warnerr (1969) an average collision damping constant logVww = 7.4 0.3. The uncertainty derives from the approximativee character of Pg and the intrinsic varia-tionn of logyw between different multiplets. The mean radiativee damping constant of these Fei lines was calculatedd with the lifetimes of Fei levels given by Corlisss and Tech (1967), corrected to the scale of Bridgess and Wiese (1970). Absorption and stimulated emissionn have been neglected. We get an average

Lin ee Spectra of G and K lb Supergiants 377 7

Tablee 7. Abundances of the elements for supergiants

II lemcnt

Nai i Mg i i Sii i Cai i Sci i Sen n Ti l l Ti n n V i i Vi l l Cr i i C m m Mnl : : Fei i Fen n Coi i Ni l l Cui : : Sri i Y i i Y n n Z n n Ban: : Lai l l Cen n Pri i i Ndn n Euu u

Maximum m number r off lines

4 4 4 4

32 2 27 7 22 2 16 6

117 7 10 0 63 3 5 5

56 6 10 0 18 8

331 1 21 1 29 9 88 8 2 2 1 1 5 5 8 8

25 5 3 3 4 4 9 9 4 4

16 6 2 2

/iPcr r

++ 0.51 ++ 0.25 ++ 0.09 ++ 0.02 -0.02 2 -0.01 1 ++ 0.04 ++ 0.12 -0.10 0 -0.29 9 ++ 0.01 -0.07 7 -0.17 7 +0.07 7 ++ 0.05 +0.01 1

0.00 0 -0.16 6 +0.60 0 ++ 0.47 -0.14 4 ++ 0.26 ++ 0.40 -0.02 2 -0.06 6 -0.14 4

0.00 0 -0.24 4

aa Aqr

++ 0.20 ++ 0.28 ++ 0.18 -0.02 2 ++ 0.16 -0.06 6

0.00 0 +0.10 0 -0.04 4 ++ 0.02 ++ 0.09 -0.12 2 -0.24 4 +0.05 5 -0.04 4 ++ 0.05 -0.03 3 -0.30 0 +0.51 1 ++ 0.27 -0.13 3 ++ 0.25 ++ 0.36 -0.02 2 ++ 0.02 -0.14 4 -0.04 4 -0.17 7

99 Peg

++ 0.38 ++ 0.29 ++ 0.21 -0.01 1 ++ 0.02 -0.15 5 -0.08 8 ++ 0.12 ++ 0.05 ++ 0.04 ++ 0.05 -0.01 1 ++ 0.03 ++ 0.02 ++ 0.04 -0.05 5 -0.02 2 -0.10 0 ++ 0.58 -0.02 2 ++ 0.04 ++ 0.04 +0.54 4 ++ 0.33 ++ 0.16 ++ 0.30 ++ 0.16 -0.36 6

[N/H ] ]

<:Gcm m

-0.01 1 -0.04 4 ++ 0.08 -0.07 7 -0.02 2 -0.12 2 +0.13 3

0.00 0 -0.09 9 +0.08 8 -0.04 4 -0.02 2 -0.01 1 -0.12 2 -0.02 2 -0.04 4 -0.30 0

— — -0.08 8 -0.02 2 ++ 0.11

— — +0.04 4 +0.12 2 ++ 0.25

0.00 0 — —

«Peg g

++ 0.37 +0.22 2 ++ 0.13 -0.10 0 -0.23 3

0.00 0 +0.10 0 +0.10 0 -0.07 7 -0.07 7 +0.02 2 ++ 0.04 -0.04 4 ++ 0.01 -0.18 8 +0.03 3 -0.02 2 +0.22 2 +0.48 8 -0.06 6 +0.04 4 -0.25 5 +0.21 1 +0.37 7 ++ 0.26 ++ 0.13 ++ 0.10 +0.10 0

3Cet t

+0.70 0 ++ 0.09 +0.22 2 +0.08 8 +0.15 5 +0.22 2 +0.32 2 +0.37 7 +0.10 0 ++ 0.46 ++ 0.32 +0.42 2 +0.01 1 +0.28 8 +0.08 8 +0.04 4 +0.28 8 ++ 0.20 +0.88 8 -0.18 8 ++ 0.22 -0.06 6 +0.50 0 ++ 0.78 +0.64 4 +0.45 5 ++ 0.55 +0.16 6

^('y * *

++ 0.63 ++ 0.18 +0.19 9 -0.14 4 +0.07 7

0.00 0 +0.06 6

0.00 0 -0.03 3 +0.51 1 ++ 0.10 +0.31 1 -0.15 5 +0.06 6 +0.04 4 +0.04 4 ++ 0.08 ++ 0.40 ++ 0.48 -0.18 8 +0.17 7 +0.05 5 ++ 0.23 ++ 0.46 ++ 0.30 ++ 0.38 ++ 0.52 ++ 0.11

log?r.dd = 805. F or t ne t o t al damping constant we find logytott = 8.13. It is clear that radiative damping prevails. Fromm the fitting of the Fei curve of growth to the Wrubell curves we derive log2a = \o$y/Ao>D= -2.3, withoutt much variation from star to star. In view of the accuracyy of this determination it is justified to work withh one average value for the Doppler parameter Ja>D. Withh \o%A(Ovl<»= -4.96 we get logy = 8.24, in good agreementt with the theoretical value. Forr Nai and Ban the damping constants have been determinedd in the same way, using for both elements thee calculated gf-values of Warner (1968) in the radiativee damping constant, and the Coulomb ap-proximationn (Unsold, 1955, p. 333) in the collisional dampingg constant. Holweger (1971) found that in order too derive the same Na abundance from all solar Na i lines,, the damping constant yw should formally be increasedd by 0.32 dex over the value predicted by the Coulombb approximation. We have included this cor-rection,, and in the case of Ba n we have looked into the effectt of taking such a correction into account. The resultss are logytot = 8.60 for Nai and logylot = 8.12 for Baa n (logy(ol = 8.22 including the correction). Itt may be concluded that for Ba n the use of the mean Fee i curve of growth cannot explain the overabundances. Forr Na i the shape of the curve of growth should be changed.. It turns out however, that the Na i lines used

inn this study, are not strong enough to feel much of thiss effect. Thee Sr i lines, expected from the tables of Meggers et al. (1961)) to be most useful for an abundance analysis, are alll blended with much stronger absorption features of otherr elements. The solar equivalent width of the one linee which we used in our analysis may easily be in errorr by a factor of two, giving a spurious abundance differencee in all the supergiants. If,, in spite of the observational difficulties, the en-hancementt of Sr and Ba is a real abundance effect, an explanationn in terms of s-processes is not without problems:: neighbouring elements of Sr and Ba, also possessingg magic neutron number isotopes - so ex-pectedd to be sensitive to the same process - do not showw the same systematic abundance anomalies (Y, Zr, La,, Ce, Nd). Bakoss (1971), using equivalent width data obtained fromm 12 A/mm spectrograms in the region from 3900 too 4600 A, concluded that the abundances of the heavy elementss relative to Fe are correlated with luminosity, inn the sense that they are overabundant in the more luminouss stars. He chose Sr and Ba to represent the heavyy elements. Inn order to see whether we could confirm this result, wee have derived the gravity and the abundances of thee K giants for which the effective temperature had

VI I

378 8 J.. van Paradijs

Tablee 8. Abundances of the elements for giants Tablee 10. Mean abundances of elements relative to Fe for supergiants

Element t

N a i i M g i i S il l Cat t Sci i S en n T i l l T i n n V i i V n n Cr i i C m m M m m F ei i F en n C oo i N i l l Sr i i Y i i Y u u Z n n B an n L aa ii C en n N d n n

fiVir fiVir

++ 0.32 ++ 0.20 - 0 . 04 4 - 0 . 01 1 - 0 . 10 0 ++ 0.03 - 0 . 06 6 - 0 . 06 6 - 0 . 08 8 ++ 0.08 ++ 0.05 - 0 . 07 7 - 0 . 22 2 ++ 0.05 ++ 0.02 - 0 . 07 7

0.00 0 ++ 0.27 ++ 0.12 - 0 . 20 0 - 0 . 16 6 ++ 0.06 ++ 0.02 ++ 0.12 ++ 0.06

<5Dra a

++ 0.13 - 0 . 03 3 ++ 0.05 ++ 0.05 ++ 0.20 ++ 0.20 ++ 0.26 ++ 0.35 ++ 0.08 ++ 0.24 ++ 0.23 ++ 0.11 - 0 . 14 4 ++ 0.09 ++ 0.11 ++ 0.15 ++ 0.11 ++ 0.14

— — ++ 0.20 ++ 0.10 ++ 0.12 ++ 0.12 ++ 0.30 ++ 0.30

[ N / H ] ]

cCyg g

++ 0.20 ++ 0.46 ++ 0.06 ++ 0.20 ++ 0.20 +0.16 6 ++ 0.29 ++ 0.56 ++ 0.20 ++ 0.34 ++ 0.21 ++ 0.11 - 0 . 12 2 ++ 0.11 ++ 0.04 ++ 0.17 ++ 0.04 ++ 0.54 ++ 0.22 ++ 0.05 ++ 0.03 +0.18 8 ++ 0.12

++ 0.25 ++ 0.37

f C ep p

- 0 . 02 2 - 0 . 08 8 - 0 . 17 7 - 0 . 13 3 - 0 . 03 3 - 0 . 26 6

0.00 0 ++ 0.05 - 0 . 06 6

— — - 0 . 09 9 ++ 0.02 - 0 . 28 8 - 0 . 10 0 - 0 . 20 0 - 0 . 05 5 - 0 . 13 3 ++ 0.32 +0.12 2

— — ++ 0.03 - 0 . 10 0 - 0 . 08 8

++ 0.07 ++ 0.28

iCep p

++ 0.28 ++ 0.54 ++ 0.03 ++ 0.03 ++ 0.21 ++ 0.18 ++ 0.32 ++ 0.33 ++ 0.26 ++ 0.49 ++ 0.15 ++ 0.24 ++ 0.04 ++ 0.08 ++ 0.11 ++ 0.12 ++ 0.15 ++ 0.33

— — ++ 0.24 ++ 0.19 ++ 0.13 ++ 0.10

++ 0.39 ++ 0.52

andd giants

Element t

Nai i Mg i i Sii i Cai i Sci i Sen n Ti i i Ti n n V i i V n n C n n C m m M m m Coo i Ni l l Sri i Y i i Y u u Z n n Ban n Laa II

Cen n Ndn n

l b b

++ 0.37 3 ++ 6 ++ 0.07 9 - 0 . 088 0 - 0 . 066 3 - 0 . 077 6 - 0 . 022 7 ++ 0.06 7 - 0 . 077 6

0.000 5 ++ 0.03 5 - 0 . 011 6

4 4 - 0 . 077 8 - 0 . 033 4 ++ 0.52 6 - 0 . 044 1 - 0 . 044 1 - 0 . 011 1 ++ 0.33 2 ++ 0.20 9 ++ 0.14 + 0.17 ++ 0.12 0

II I I

++ 0.14 9 ++ 0.17 3 - 0 . 066 2 - 0 . 022 6 +0.055 2 ++ 0.01 4 ++ 0.11 4 +0.200 0 ++ 0.03 4 ++ 1 ++ 0.06 6 ++ 0.04 1 - 0 . 199 9 ++ 0.02 8 - 0 . 011 6 ++ 0.28 6 ++ 0.13 8 - 0 . 011 8 - 0 . 011 4 ++ 0.03 3 ++ 0.01 3 ++ 0.18 7 ++ 8

Difference e

+0 .23 3 - 0 . 05 5 ++ 0.13 - 0 . 06 6 - 0 . 11 1 - 0 . 08 8 - 0 . 13 3 - 0 . 14 4 - 0 . 10 0 - 0 . 14 4 - 0 . 03 3 - 0 . 05 5 ++ 0.01 - 0 . 09 9 - 0 . 02 2 ++ 0.24 - 0 . 17 7 - 0 . 03 3

0.00 0 +0 .30 0 ++ 0.19 - 0 . 04 4 - 0 . 04 4

Tablee 9. Comparison of abundance determinations using the same equivalentt width data

Star r

eV i r r <5Dra a e C yg g ii Cep rjCep rjCep

AA [ N / F e] thi ss study

- 0 . 099 7 ++ 0.08 6 - 0 . 022 5

5 5 - 0 . 155 1

Ref. .

Cayrell et al. (1963) Koelbloedd (1972b) Koelbloedd (1972 b) Koelbloedd (1972b) Koelbloedd (1972b)

alreadyy been obtained. The results are given in Tables 55 and 8. This is also of interest, since a comparison of independentt abundance analyses using the same equiva-lentt widths gives a clear idea of the accuracy of the resultss of this kind of work. In Table 9 we give the resultss of the comparison of our abundances with thosee of Cayrel and Cayrel (1963) and by Koelbloed (1972b),, for the elements with the best curves of growth (Caa i, Si i, Ti i, Cr i, Fe i, Co i, Ni i). It appears that the abundancess obtained from 3.3 A/mm plates, apart from systematicc errors arising from temperature errors etc., aree accurate to about 0.15 dex. Forr the comparison of the abundances in class III and lb starss we have for each element taken the average abundancee within each group. These are given in Tablee 10, together with the scatter of the individual abundances.. Judging from the expected accuracy of ann individual abundance determination, as obtained

above,, most elements have the same abundance within thee two groups, so a comparison of the average abundancess makes sense. From the last column of Tablee 10 we see that most elements do not have significantlyy different abundances in the two groups. Baa and Sr are enhanced in the supergiants relative to thee giants, but other heavy elements do not show this. Thee extent of this overabundance is a factor of two smallerr than was found by Bakos. A closer inspection off Table III in Bakos' paper shows some large discrepanciess with our results. For example, Bakos givess for the difference in the ratio Zr/Fe between eGemm and e Peg the value 1.36 dex, whereas we find 0.38.. For Y/Fe the numbers are 0.76 and 0.08 re-spectively.. Perhaps difficulties with line blending and thee location of the continuum in the violet region of thesee spectra must be blamed for these large devia-tions. . Fromm the present discussion it is clear that as yet there existt no firm grounds for the conclusion that the heavyy elements are generally overabundant in the supergiants. .

Acknowledgements.Acknowledgements. It is a pleasure to thank Dr. D. Koelbloed for his interestt and advice, and for his permission to use his unpublished resultss of an analysis of K giants. I am indebted to Dr. N. Grevesse forr putting his equivalent width measurements of solar Ti i lines at myy disposal. I thank Mr . H. de Ruiter and Mr . E. Faverey for their helpp in the reductions and at the microphotometer. The calculations havee been performed with the CDC 3200 and CDC 6400 of the Foundationn for Fundamental Research on Matter (F.O.M.), placed att the Zeeman Laboratory of the University of Amsterdam.

42 2

Linee Spectra of G and K lb Supergiants 379

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k3 k3