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The composition of HB stars RR Lyrae variables

The composition of HB stars  RR Lyrae variables
The composition of HB stars  RR Lyrae variables

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THE COMPOSITION OF HB STARS:RR LYRAE V ARIABLES 1G.CLEMENTINI 2Osservatorio Astronomico di Bologna,CP 596,I-40126Bologna E.CARRETTA Dipartimento di Astronomia,Universit′a di Padova,Vicolo dell’Osservatorio 5,I-35122Padova and Osservatorio Astronomico di Bologna,CP 596,I-40126Bologna R.GRATTON Osservatorio Astronomico di Padova,Vicolo dell’Osservatorio 5,I-35122Padova R.MERIGHI Osservatorio Astronomico di Bologna,CP 596,I-40126Bologna J.R.MOULD M.Stromlo and Siding Spring Observatories,Institute of Advanced Studies,Australian National University,Weston PO,ACT 2611,Australia J.K.McCARTHY Palomar Observatory,California Institute of Technology,Pasadena,CA 91125

ABSTRACT

We have used moderately high-resolution,high S/N spectra to study the chemical composition of10?eld ab-type RR Lyrae stars.Variables having accurate photometric and radial velocity data were selected,in order to derive a precise estimate of the atmospheric parameters independently of excitation and ionization equilibria.A new temperature scale was determined from literature Infrared Flux Method measures of subdwarfs and the Kurucz(1992)model atmospheres,and used to calibrate colors for both dwarfs and RR Lyraes. Photometric reddening estimates for the program stars were carefully examined, and compared with other determinations.The applicability of Kurucz(1992) model atmospheres in the analysis of RR Lyraes at minimum light was analyzed: we found that they are able to reproduce colors,excitation and ionization equilibria as well as the wings of Hα.The comparison solar abundances were carefully determined.From a new analysis of weak Fe I lines with accurate gf s (Bard&Kock1994)we derived log?(F e)⊙=7.52,in agreement with the Fe abundances determined from meteorites and Fe II lines.

We derived abundances for21species.Main results are:

?The metal abundances of the program stars span the range

?2.50<[Fe/H]<+0.17.

?Lines of most elements are found to form in LTE conditions.Fe lines

satisfy very well the excitation and ionization equilibria.A comparison with statistical equilibrium computations shows that rather large collisional cross sections are required to reproduce observations.If these cross sections are then used in the analysis of the formation of Fe lines in subdwarfs and RGB stars,no signi?cant departures from LTE are found for these stars, thus validating the very numerous LTE analyses.

?RR Lyraes share the typical abundance pattern of other stars of similar [Fe/H]:α-elements are overabundant by~0.4dex and Mn is underabundant by~0.6dex in stars with[Fe/H]

extremely metal-poor star X Ari([Fe/H]~?2.5).

?Signi?cant departures from LTE are found for a few species:Nd II,

Ce II,Y II and Sc II are severely underabundant(~0.5dex)in metal-rich variables;Ti I and Cr I are slightly(~0.1?0.2dex)underabundant

in metal-poor stars.These e?ects are attributed to overionization.We suggest that the photoionization of the alkaline earth-like ions is due to

Lyman lines emission produced by the shock waves that propagate in the atmosphere of these variables(Fokin1992).

?Departures from LTE were considered in detail in the derivation of

abundances for the light elements(O and Na).Signi?cant corrections

were required for the O I IR triplet and the Na D lines.The resulting

pattern reproduces that observed in less evolved?eld stars.We did

not?nd any evidence for an O-Na anti-correlation among these?eld

HB-stars,suggesting that the environment is likely to be responsible for the anti-correlation found in metal-poor globular cluster stars(Sneden et al1992).

We used our new[Fe/H]abundances,as well as values from Butler and coworkers(corrected to our system),and from high resolution spectroscopy of globular clusters giants,to obtain a revised calibration of the low-resolution metallicity index?S(Preston1959):

[Fe/H]=?0.194(±0.011)?S?0.08(±0.18)

Our new metallicity scale is stretched on both low and high metallicity ends with respect to Butler’s(1975).The error in[Fe/H]by?S observations is 0.16dex,well of the same order of high resolution metallicity determinations. The slope of the calibration obtained considering only stars with4

The new[Fe/H]values were used to update the metallicity calibration

of the Ca II K line index(Clementini et al1991).Using the present new metallicities,and W′(K)values and relative errors from Clementini et al(1991), a least-squares?t weighted both in W′(K)and[Fe/H]gives:

[Fe/H]=0.65(±0.17)W′(K)?3.49(±0.39)

Finally,our new metallicity scale was used to revise the metallicity dependence of the absolute magnitude of RR Lyrae stars,M https://www.wendangku.net/doc/652171711.html,ing M V values from Fernley(1994)for the?eld stars,and estimates from Liu&Janes(1990b) and Storm et al(1994)for the cluster variables,we found:

M V=0.20(±0.03)[Fe/H]+1.06(±0.04)

and:

M V=0.19(±0.03)[Fe/H]+0.96(±0.04)

the last being obtained by using M V estimates derived for a value of the conversion factor between observed and true pulsation velocity p=1.38(Fernley 1994).The adoption of the new metallicity scale does not yield signi?cant changes in the slope and zero-point of the M V vs[Fe/H]relation.Observations do not rule out the possibility that the slope of the M V vs[Fe/H]relation might be di?erent for metal-poor and metal-rich variables.However,a larger sample of Baade-Wesselink M V determinations is requested to de?nitely settle this question.

Subject headings:Stars:variables(RR Lyrae)-Stars:abundances-

Stars:atmospheres-Clusters:globular-Sun:abundances

1.INTRODUCTION

This is the second in a series of papers dealing with abundance analysis of RR Lyrae stars from high resolution spectroscopy(Clementini et al1994a,hereafter Paper I).In Paper I we successfully applied our technique to derive abundances of three ab?type RR Lyrae variables in the globular cluster M4.Here we extend our study to a larger sample of bright ?eld ab-type RR Lyraes,using high quality observational material explicitly taken for this purpose.

A number of factors make elemental abundance analysis of RR Lyrae stars an extremely worthwhile challenge:

?(a)RR Lyrae variables are powerful tools to study the chemical composition of the halo and disk of our Galaxy,and of the globular clusters.RR Lyraes have been

used to derive the metal abundance of:(i)globular clusters(Smith&Butler1978, Smith1984,Costar&Smith1988),(ii)Baade’s Window(Walker&Terndrup1991), (iii)the Galactic Halo,and to study the metallicity distribution as a function of

the galactocentric distance(Suntze?et al1991,hereinafter SKK91).Since these

variables are generally too distant to allow a direct measure of their metallicity with high resolution spectroscopy,the most commonly used method to derive their metal abundance is via the spectrophotometric index?S(Preston1959).?S measures

the di?erence in tenths of spectral class between the spectral type of an ab?type RR Lyrae at minimum light estimated from the hydrogen lines,and that estimated from the Ca II K line intensity,and it is correlated to the[Fe/H]abundance of the star.Butler(1975)empirically derived the following metallicity calibration for?S:

[Fe/H]=?0.16?S?0.23(1),

using metal abundances measured from curve of growth analysis of13?eld RR Lyrae stars.(We adopt the usual spectroscopic notation,namely:[X]≡log(X)star?log(X)⊙for any abundance quantity X,and logε(X)=log(N X/N H)+12.0for absolute

number density abundances).Butler’s calibration was further con?rmed by the

abundance analysis of Butler&Deming(1979).More recently Clementini et al

(1991)have used the equivalent width of the Ca II K line,W′(K),to derive the metal abundance of?eld RR Lyraes.The W′(K)-[Fe/H]relation([Fe/H]=0.53W′(K)?3.08) is tighter than the one involving the?S index;however,it is again based on the Butler (1975)and Butler&Deming(1979)abundances.Butler’s abundances,however,are now rather old and his work“needs to be redone with high S/N,high dispersion digital data,using modern synthetic spectral codes”(Suntze?et al1994,hereinafter SKK94).

In spite of the large use of RR Lyraes as metallicity indicators,the literature of the last decade contains no modern redeterminations of the original metal abundances on which the?S and Ca II K line indices are based.In this paper we present abundance analysis for10?eld RR Lyraes,4of which taken from Butler original sample,using high S/N(>200),moderately high resolution(~18000)CCD spectra obtained with the Cassegrain echelle spectrograph of the Palomar60-inch telescope(McCarthy, 1988).Our[Fe/H]abundances are used to derive a revised calibration of the?S and Ca II K line indices.The new metallicity scale is then compared with the globular clusters metallicity scale.

?(b)RR Lyrae stars are primary distance indicators for our own and nearby galaxies because they are easily detected even at a large distance and exhibit a relatively small dispersion in their intrinsic luminosities.RR Lyraes have been detected in the Magellanic Clouds(see e.g.Walker1991),in M31(Pritchet&Van den Berg1987), and in a few galaxies of the Local Group(Saha et al1992a,b and references therein). The absolute magnitude of RR Lyraes(M V)is derived with a rather well established accuracy by means of the Baade-Wesselink(B-W)method(Liu&Janes1990a,b, Jones et al1992,Cacciari et al1992),which also de?nes the M V vs[Fe/H]dependence. We have used our[Fe/H]abundances to revise the M V vs[Fe/H]relation.

?(c)RR Lyraes can be used to investigate the origin and evolution of the abundance anomalies found for giants in globular clusters.In a series of papers,Kraft and coworkers have found that in halo giants belonging to the?eld and to globular clusters there is a global anticorrelation of[Na/Fe]and[O/Fe](see e.g.Sneden et al1994).It is not clear if this anticorrelation extends to metal-rich clusters([Fe/H]>?1),since it has not been found for giants in47Tuc(Brown&Wallerstein1992;Carretta& Gratton1992)and M71(Sneden et al1994).The most plausible interpretation for this anticorrelation is that the O decline is the result of deep mixing,in which some 23Na produced by proton captures on22Ne is dredged up to the surface(Denisenkov &Denisenkova1990;Langer et al1993).While the e?ect is primarily correlated to the evolutionary state,it seems to be modulated by some other mechanism,which may be meridional circulation activated by core rotation(Sweigart&Mengel1979). Atmospheric e?ects or departures from LTE are less likely to be important(Drake et al1992,1993).Observations of Na and O abundances in RR Lyrae stars may play an important role,since these stars are in an evolutionary phase following that observed on the giant branch.It should then be possible to observe some RR Lyrae variables which have low O and high Na abundances:this should be explored by means of accurate spectroscopic analyses,taking into account the possibility of departures from LTE.

?(d)Quantitative estimates of statistical equilibrium in late type stars have been

up to now hampered by our poor knowledge of collisional cross sections,mainly

those with neutral H atoms;these last can only be obtained theoretically,owing

to di?culties in the related experiments.Steenbock&Holweger(1984)suggested that this mechanism plays an important thermalizing r?o le in late type stars,on the basis of order-of-magnitude estimates by Drawin(1968,1969).Drawin formulas after Steenbock&Holweger have since been used in various estimates of non-LTE e?ects in late type stars(see e.g.Steenbock1985).However,recently Caccin et al(1993) used more reliable estimates by Kaulakys(1985,1986)to show that at least for Na, Drawin formulas severely overestimate the cross sections for HI collisions.Given the large theoretical uncertainties,a parametric approach may be used,where collisional cross sections are estimated by matching observed non-LTE features in stars where they are expected to be large.These cross sections may then be used to predict

departures from LTE in other stars,where they are expected to be smaller.Due to the combination of atmospheric parameters(gravity g,e?ective temperature T e?and overall metal abundance),and to the presence of shock waves in their atmospheres caused by the pulsation mechanism itself,departures from LTE are expected to be non-negligible in RR Lyrae stars.Since the atmospheric parameters for abundance analysis can be determined from the light and radial velocity curves of these variables without any a priori assumption about excitation and ionization equilibria,any

observed di?erence in abundances derived from neutral and ionized species or among lines of di?erent excitation can be considered,reliably enough,as a hint of departures from the classical LTE assumption.Note,however,that this guess can be misguided by uncertainties existing in the knowledge of the temperature strati?cation for real variable stars compared to the hydrostatic equilibrium model atmospheres adopted in the present analysis.This e?ect may be signi?cant owing to the dynamical character of RR Lyrae atmospheres.Hence,an estimate of the reliability of the adopted model atmosphere must be performed with appropriate tests,such as the ability to predict colors or the pro?les of strong lines.Anyway,if we are able to obtain a quantitative estimate of these e?ects on the derived abundances,we could also put a?rm upper limit on the in?uence of departures from LTE in the derivation of the chemical

composition for stars cooler and less luminous than RR Lyrae stars,e.g.red giant branch(RGB)stars and subdwarfs.

The observational material is presented in Section2,where we describe the star selection,the data reduction procedures,the equivalent width measurements,and the radial velocities determined from the spectra.The adopted atmospheric parameters are discussed in Section3,where emphasis is given to the determination of accurate temperatures

using a new calibration of color indices,and to a discussion on the ability of the new model atmospheres by Kurucz(1992)to reproduce the spectra of RR Lyraes at minimum light.The results of the abundance analysis are given in Section4;care was devoted to a comparison with solar data,and statistical equilibrium computations were performed for Fe,Na,and O lines.Results for all elements are also compared with those obtained for less evolved stars.Section5presents new calibrations of the?S and Ca II K line indices;

a comparison of our results with those obtained from high dispersion spectroscopy of red giants in globular clusters;and?nally a discussion of the impact of our abundances in the M V?[Fe/H]relation for RR Lyraes.Conclusions are summarized in Section6.

2.OBSERVATIONAL MATERIAL

2.1.Star selection and observations

Spectra of the program stars were obtained with the Cassegrain echelle spectrograph of the Palomar60-inch telescope during the four nights:28July-1August1993.The P60echelle spectrograph(McCarthy1988)was operated in echelle grating mode using a52.65lines/mm echelle grating and quartz prism cross-dispersers which yield a resolution R=λ/?λ=38000 per pixel,and large wavelength coverage(3400?A≤λ≤9900?A).Spectra are recorded on a TI800×800pixels backside illuminated CCD(15μm pixel size).The slit width was set at 1.43arcsec,which projects to2.1pixels on the detector.

The FWHM measured from Th-Ar lines is~0.23?A at4300?A.The echelle grating of the P60spectrograph has an o?-plane angle(γ)of about10degrees which produces a variable tilting along each order.In the data reduction phase we have neglected this e?ect in order to simplify the reduction procedure.This results in a mean degradation of the resolution of about10%for stellar sources.However,in our spectra the resolution is limited to about10000by the large amplitude velocity?elds in the atmosphere of the program variable stars.The data cover the spectral range3400-9900?A with65orders,partially overlapping forλ≤7000?A.Exposures of a Th-Ar lamp were taken with the telescope

in the same position of the object to perform the wavelength calibration.Flat?eld and bias exposures were taken routinely at the beginning and end of each night,particularly to monitor slight temperature?uctuations of the CCD Dewar.

We took50spectra of10ab-type RR Lyrae stars close to the minimum light of

the variables.For one of the program star,(namely SW And),we obtained also spectra

around the maximum light phase(see Section4.1.5).Spectra of5candidate red horizontal branch stars(RHB)were also taken for the purpose of making a comparative abundance analysis.Here we will con?ne our study to the RR Lyrae stars;observations are in progress on a larger sample of RHB stars using the1.8m telescope of the Asiago Astrophysical Observatory.A hot bright star was observed at the beginning of each night and used during the reduction phase to locate the echelle orders within the frame.

Since one of the primary purposes of our study was to obtain a new calibration of the ?S and Ca II K line indices we included in our program some of the objects in the Butler (1975)and Clementini et al(1991)original lists.We ensured also that our program stars had known?S and covered a large range in metallicity(?2.2<[Fe/H]<0.1).The sample of objects ultimately observed by us at Palomar had4stars in common with a sample

of bright?eld RR Lyrae variables being studied spectroscopically by Heath et al(1995). The objects in common should allow the two sets of results to be integrated once both independent abundance analyses are complete.

To make an accurate abundance analysis we need knowledge of the atmospheric parameters(gravity and e?ective temperature)of the stars.The gravity can be derived from the radial velocity curves of the stars while the e?ective temperature can be estimated from their color curves by means of a model atmosphere(see Paper I and Section3for

a more detailed discussion of these topics).In our selection we therefore chose objects for which recent BV RI and possibly K light curves and accurate radial velocities were available in the literature(see references in Sections3.2and3.4.1).

The currently available model atmospheres(Kurucz1992;hereinafter K92)are stationary LTE models;however,due to pulsation,the use of a stationary model atmosphere for an RR Lyrae is an approximation not always valid.It has been found,in fact,that shock waves propagate throughout the atmospheres of these variables(Preston& Paczynski1964,Gillet&Crowe1988,Clementini et al1994b).The presence of shocks is associated with the appearance of the bumps and humps in the light curve of the variables. Static model atmospheres are a good approximation for these stars only if the regions of the shocks are avoided.To meet these requirements,our exposures were generally shorter than60minutes and our spectra were all acquired near minimum light(see discussion in Section3.4).Since most of our targets have updated ephemerides,we could safely locate the minimum light and properly phase our exposures.The list of objects is shown in Table1together with the adopted ephemerides for each object(Columns4and5),the Heliocentric Julian Day(HJD)at half exposure of each spectrum(Column6),and the corresponding phase(Column7).Finally,the last column gives the references for the adopted ephemerides.

2.2.Data reduction

The?rst part of the data reduction was performed using the facility ECHELLE in the IRAF3package.

We used spectra of four bright stars(one for each night)to locate the echelle orders within the frame.The position of each order was then traced interactively with a cubic spline.Assigning the bright star as a reference,order?nding and tracing was performed on science frames.Scattered light(and,hence,also the bias)was then eliminated with

a two-dimensional?t of the interorder regions across and along the dispersion axis.The spectra corresponding to the recorded echelle orders were extracted from each of these cleaned frames.

Two-dimensional dispersion solutions were found for the Th-Ar arc spectra.The typical r.m.s.deviation of the arc lines from the?tted wavelength calibration polynomial was~0.02?A.This can be regarded as the internal accuracy in our wavelength calibration. The reduction of the arc spectra con?rmed the spectrograph stability during multiple observations of the same object.Out of65orders found,we retained for further analysis only those52that cover the spectral region between3790and9160?A,because S/N is low outside this range.Further reduction and data analysis were carried out using the ISA (Gratton1988)package,purposely designed for one dimensional high resolution spectra. We found that division by lamp?ats did not yield satisfactory results at long wavelengths due to the presence of rather strong interference fringes which were not well divided out with this technique.Better results were achieved by dividing the spectra by a pseudo-?at ?eld obtained from the spectrum of X Ari,the most metal-poor star in our sample,for which a?ducial continuum may be easily identi?ed by means of cubic spline interpolation through selected spectral points.This technique allowed us to properly correct interference fringes up toλ<7300?A.Beyond this limit the only spectral feature we examined was the permitted O I triplet at7771-7774?A(see Section4.5).Single spectra of each star were compared to eliminate the(very few)cosmic ray spikes,and then summed.Spectra were not shifted before adding them together to account for di?erences in radial velocity because the e?ect of the variation in radial velocity at the observed phases is negligible at our spectral resolution.Giving the brightness of the program stars and the small size of the slit,sky contamination can be safely neglected:therefore no sky subtraction was performed on the spectra.Whenever relevant(5860-5920,6270-6320and7080-7130?A),

telluric lines were divided out still using the spectrum of X Ari;however,regions including strong telluric bands were not used in the analysis.In the case of the D lines region, particular care was taken to prevent the stellar and interstellar absorption lines present in the spectrum of X Ari from producing false emission features on the spectra of the other stars.For this purpose,we used also the spectra of other metal-poor stars,having di?erent radial velocities.Finally,we traced the continuum on the co-added spectra by using a cubic spline interpolation through a few selected spectral https://www.wendangku.net/doc/652171711.html,parison with synthetic spectra showed that the?nal?ducial continuum was correct within0.5%,at wavelengths longer than4500?A,with the exception of the region of the Balmer lines where errors may be as large as1-2%.In Table2we list total exposures and S/N of the co-added spectrum for each star.Small portions of the co-added normalized spectra of X Ari,RR Cet and SW And are shown in Figure1.

2.3.Equivalent widths

Equivalent widths(EW s)for~100lines in the average spectrum of each star were measured by means of a gaussian?tting routine.This procedure works quite well for RR Lyrae stars because damping wings are weak for all measured lines;in a few cases, comparisons with synthetic spectra were also done.The complete list of lines and adopted gf values and their measured EW s is given in Table3a,b,and is available on electronic form from R.Gratton.Errors in these EW s are mainly due to uncertainties in the location of the?ducial continuum:for this reason,EW s were not measured at wavelengths shortward of4500?A in the line rich spectra of SW And and V445Oph,where continuum location is likely to be underestimated.Errors in the EW s are not easy to accurately estimate because the measured EW s should depend on phase and S/N level.A rather realistic estimate can be obtained by comparing the EW s measured for the same lines in the spectra of RR Lyr and RR Cet,which have similar atmospheric parameters at the average observed phases (RR Cet has only a slightly larger value of the microturbulent velocity).This comparison is shown in Figure2,where we have overimposed the best-?t regression line with zero constant value:EW RR Cet=1.052(±0.008)EW RR Lyr from76lines;the regression coe?cient is slightly di?erent from1,mainly due to the di?erent values of the microturbulent velocity. The scatter around this best-?t line is9.3m?A,if we attribute equal errors to the measure of EW s in each star,we obtain an r.m.s.error of6.6m?A.Figure2suggests that this error is fairly independent of the EW itself:hence,10m?A is a reasonable lower limit for reliable estimates of the EW s.RR Cet and RR Lyr spectra have the highest S/N;errors in EW s,

σ(EW),for the other stars likely scale as the inverse of S/N:σ(EW)~2400/(S/N)m?A. The values ofσ(EW)for each star are given in Column6of Table2.

No direct comparison of our EW s with those measured by Butler(1975)and Butler &Deming(1979)is possible,since the spectra used in those analyses were taken close to maximum light.

Carney&Jones(1983)analyzed photographic echelle spectra of VY Ser;their mean phase of observation is0.615,compared to our mean value of0.72.On our scales(see below),T e?and gravity at Carney&Jones phase were T e?=5969K and log g=2.60(their adopted values are T e?=6000K and log g=2.3),compared to the mean values for our observations of T e?=5993K and log g=2.69.These sets of values are very similar,so that no important modi?cations of the EW s are expected.A line-to-line comparison of the EW s indicates that our values are smaller by7±4m?A(σ=16m?A:15lines).This di?erence is small,and a correction of this entity would not a?ect signi?cantly our analysis;however,we can expect that our EW s are more reliable since our CCD echelle spectra have much higher S/N.

2.4.Radial velocities and phases

Radial velocities were measured from the average spectra using a rather large number of lines(~100)for each star.They are listed in Column4of Table2.These values can be used to check the phases of our spectra.Since no radial velocity standard was observed,the zero-point of these radial velocities was determined using the telluric[OI]line at5577.341?A. Internal errors of these radial velocities,as deduced from the line-to-line scatter(reduced by the square root of the number of lines),are±0.3km s?1;star-to-star variations in the radial velocity for the telluric line are similar(σ=0.2km s?1),showing that spectrograph ?exures are small.However,uncertainties in our radial velocities are larger,since errors in the determination of the radial velocity from individual stellar lines are as large as 2.7km s?1,where similar contributions are due to photon noise,residual blending e?ects, and errors in the wavelength calibration;the last source of error(amounting to~0.02?A, i.e.~1.1km s?1)is systematic,and then apply also to the telluric[OI]line.On the other hand,we think that our zero-point error is not very large,as con?rmed by the comparison with the expected radial velocities at the observed phases(Column5of Table2)for those stars for which they may be considered reliable;there are7such variables(no radial velocity curve is available for VX Her;and ST Boo and RR Lyr radial velocities are more uncertain because these stars are a?ected by the Blazhko e?ect).The mean di?erence

between observed and expected velocities is V r(obs)?V r(exp)=?0.4±0.9km s?1.This test con?rms that our ephemerides are reliable.We think that the Blazhko e?ect,more than errors in the adopted ephemerides,might be responsible for the higher discrepancy found for RR Lyr and ST Boo.We discuss in Section3.4the e?ect on the atmospheric parameters adopted for ST Boo and RR Lyr if phases inferred from the radial velocity measures are used in place of phases derived from ephemerides.

Finally,our spectra can be used to test the presence of systematic variations with optical depth,in radial velocities at minimum phase.This problem is of some relevance in the determination of the absolute magnitude of RR Lyrae variables with the B-W method, where the assumption is made that no velocity gradients exist in the region of formation of the lines used to measure the radial velocity(basically weak metal lines),and between this region and the continuum forming region.Jones(1987)and Clementini et al(1994b) measured the velocity of lines at di?erent depths of formation in a sample of?eld and cluster RR Lyraes and reached the conclusion that no signi?cant velocity gradients(≤2km s?1) exist throughout the atmospheric layers where these lines are formed.Here we can repeat their test in a more stringent way.Since the stronger lines measured on our spectra(with EW~300m?A)form at much shallow optical depths(logτRoss~?3)than very weak lines (forming at logτRoss~?1)4,we have checked whether a correlation exists between EW and V rad.The mean value for the linear regression coe?cient a in the EW?V rad plane over all the stars was a=?2.3±1.9km s?1/?A(where the error bar is the standard deviation of the mean over all10program stars).For comparison,in the same observing run we obtained spectra for a sample of non-variable metal-poor giants with4600≤T e?≤6000K: the average value of a for this sample was a=0.2±1.4km s?1/?A.The trend of radial velocity with EW s measured in RR Lyrae variables is only barely signi?cant;we consider it as a marginal indication of a small acceleration of the outward motion throughout the atmosphere at the observed phase(i.e.at minimum).

3.ATMOSPHERIC PARAMETERS

As we have anticipated in Section2.1,to perform abundance analysis we need the e?ective temperature,the surface gravity,the overall metal abundance and the microturbulent velocity of our program stars.E?ective temperatures corresponding to the phases of our

spectra were derived from the B?V,V?R,V?I,and V?K colors of the stars using K92models of appropriate metallicity and gravity.Colors have been previously corrected for reddening.The procedure used to estimate the reddening is described in detail in Section3.1.In Sections3.2and3.3we discuss the derivation of surface gravity and overall metal abundance.In Section3.4we describe our procedure to derive e?ective temperatures from K92model atmospheres.Finally,in Section3.5we discuss the adopted microturbulent velocities.

3.1.Reddening

Reddening is a crucial point in our analysis since an error of0.01mag in the adopted reddening translates into an error of~50K in the derived temperature;this,in turn, translates into an uncertainty in the derived abundance that for instance in the case of Fe I corresponds to~0.05dex.Reddening estimates for the program stars based on photometric indicators have been published by several authors(Sturch1966,Jones1973,Lub1977a,b, 1979,Liu&Janes1990a,Blanco1992and reference therein).Blanco(1992)(hereinafter B92)presents a critical re-evaluation of the reddening of ab-type RR Lyrae stars as derived from photometric indices.He uses a revised version of Sturch(1966)method to evaluate E(B?V)from the observed near-minimum light colors for ab-type RR Lyraes,and derives a formula which gives E(B?V)as a function of the metallicity of the star as inferred from the?S index,the period,and the B?V color during the phase interval0.5<φ<0.8:

E(B?V)=0.5<φ<0.8+0.0122?S?0.00045(?S)2?0.185P?0.356(2)

Equation(2)was established using:(i)mean colors at minimum light taken,when available, from B-W analysis light curves(this is also the photometry used in the present study

to derive temperatures);and(ii)?S values collected from the literature and reduced to Butler’s equivalent values.

B92makes a very extensive comparison with previous reddening determinations, particularly with those by Lub(1977a,b,1979),and Sturch(1966),which are found to

be in good agreement with his results within an accuracy of±0.02mag.A completely independent method to estimate reddening is provided by Burstein&Heiles(1978,1982, hereinafter BH78and BH82)who used H I column densities plus galaxy counts to determine the average reddening as a function of Galactic latitude and longitude,and give values appropriate for the RR Lyraes(taking into account their distances).In Table4we compare B92reddening values for our stars with BH78and BH82.Also listed are reddening values

used in the B-W analysis of the various stars.There is generally good agreement between B92,BH78and BH82with the exception of BH82values for V445Oph and RR Lyr which deviate by a very large amount from both Blanco’s and BH78estimates,and that therefore were not considered(see also the discussion on the reddening of V445Oph in Fernley

et al1990).In conclusion,B92reddening estimates were adopted for our stars with the exception of V445Oph for which a reddening value of0.27mag was found to be more appropriate during the abundance analysis procedure;and of UU Cet,for which a lower metallicity compared to B92was recently found with?S analysis by SKK94(see discussion in Section3.3).E(B?V)for this star was derived from eq.(2),taking into account the new metallicity estimate.The adopted reddening values are listed in Column2of Table5. We associate with these estimates an uncertainty of±0.02mag.

We may compare the adopted photometric estimates of reddening with those derived from interstellar absorption features present in our spectra.We measured the EW s for the Di?use Interstellar Band(DIB)at5780?A,and for the interstellar Na D lines.DIB EW s were transformed into reddening by means of the calibration drawn by Herbig (1993),using only those stars(72)with E(B?V)≤0.4,matching the expected range

of reddening values for the program RR Lyrae variables.The adopted calibration was

E(B?V)=(1.54±0.10)EW5780,where the EW of the DIB is in?A.For the Na D lines, we transformed Na I column densities deduced by means of the doublet ratio method into reddening using the relation:E(B?V)=(3.27±0.19)10?14n(Na I),obtained by Benetti et al(1994)from a compilation of literature data about interstellar lines and reddenings. Table5lists the relevant data.The agreement between the di?erent estimates of the interstellar reddening is good for all stars,excluding X Ari.The Na D lines give slightly larger reddening estimates,but the di?erence is not signi?cant.Mean di?erences are:

E(B?V)Phot?E(B?V)5780=0.00±0.02mag,σ=0.06mag

E(B?V)Phot?E(B?V)Na D=?0.03±0.02mag,σ=0.04mag

E(B?V)5780?E(B?V)Na D=?0.02±0.04mag,σ=0.10mag

If we average the two spectroscopic determinations,the mean di?erence with the photometric reddening(again excluding X Ari)is:

E(B?V)Phot?E(B?V)Spec=?0.01±0.01mag,σ=0.03mag

While this agreement may be fortuitous(given the large spread usually existing in reddening estimates from these spectroscopic features),on the whole it supports the reddening scale adopted in this paper.

Reddening in the(V?R),(V?I)and(V?K)colors was obtained from the

E(B?V)values in Column2of Table5using Cardelli et al(1989)absorption coe?cients: A(R)/A(V)=0.751,A(I)/A(V)=0.479and A(K)/A(V)=0.114,which are valid for a standard value of the total to selective absorption R V=A(V)/E(B?V)=3.1.These coe?cients are very similar to those derived from Howarth(1983)formula.Cardelli et al (1989)coe?cients are calculated for the Johnson photometric system.The V?R and V?I colors used in the present paper are in the Cousins system.Transformation between the two photometric systems is achieved using Bessell(1979)equations:(V?R)C=0.713(V?R)J and(V?I)C=0.778(V?I)J,that lead to the following reddening corrections to apply to the observed colors:E(V?R)C=0.550E(B?V),E(V?I)C=1.257E(B?V),and E(V?K)=2.747E(B?V).The use of Howarth(1983)coe?cients would give reddening corrections in good agreement with those used here even for the most reddened stars,for which we would?nd di?erences≤0.02mag.

3.2.Gravities

Gravity is an input parameter for abundance analysis and it is also needed to select the appropriate K92model to derive the color-temperature transformations.Due to pulsation the gravity of an RR Lyrae star varies during the cycle.The gravity to consider is therefore the e?ective gravity that is described by the formula:

g=GM/R2+d2R/d2t(3)

where M and R are the mass and the radius of the star in solar units.The?rst term in eq.

(3)is the mean gravity of the star(i.e.the gravity that the star would have if it were not pulsating),and may be derived from its mass and mean radius;the second term represents the variation of the gravity along the pulsation cycle due to the acceleration of the moving atmosphere and can be estimated by di?erentiating the radial velocity curve of the variable.

Eight of the objects in our list have recently been the subject of B-W analysis(Liu &Janes1990a,Cacciari et al1989a,b,Cacciari et al1992,Manduca et al1981,Siegel 1982,Jones et al1987,1988,Fernley et al1989,1990).We have used the masses and radii estimated for them with the B-W method to derive the mean gravity term of eq.(3).Radial velocity curves are available for all the variables in our list except VX Her(Liu&Janes 1989,Cacciari et al1987,Clementini et al1990,Sanford1949,Carney&Latham1984, Jones et al1987,Oke1966,Preston&Paczynski1964,Clementini et al1995),and have been di?erentiated to derive the acceleration term in eq.(3).For ST Boo,which does not

have R and M estimates,we have assumed a mean gravity log GM/R2=2.79and derived from eq.(3)log g=2.71as mean value corresponding to our spectra,in good agreement with what found for stars of similar metallicity.Lub(1977b)publishedvalues for RR Lyrae stars estimated from Walraven photometric indices.He noticed that a zero-point error may be present in his gravity calibration.Indeed we found that for the stars we have in common our mean gravities are systematically lower than Lub’s by?0.28±0.09dex.The gravity of VX Her was then obtained from Lub(1977b)converted to our gravity scale and further lowered by0.07dex to take into account that our spectra are taken at minimum light.Mean e?ective gravities corresponding to our average spectra are listed in Column3 of Table10.Given the uncertainties in the adopted masses and radii involved in the above procedure,we assign to our log g estimates a conservative error of0.20dex.

3.3.Metal abundance

In the literature we found a very large collection of metallicity estimates for all the program stars.They include:?S estimates(Preston1959,Butler1975,McDonald1979,Clube et al 1969,Alania1973,Woolley&Savage1971,Smith1990,Kinman&Carretta1991,SKK91, SKK94),Ca II K line estimates(Clementini et al1991),and metallicities from abundance analysis by Butler(1975),Butler&Deming(1979)and Carney&Jones(1983).B92made an extensive review of the various?S values present in the literature which he reduced to a uniform system and averaged for the stars with independent determinations.In Table6we have collected the[Fe/H]values from:

-Columns2,3and4:high resolution spectroscopy(Butler1975;Butler&Deming1979; Carney&Jones1983);

-Column5:Ca II K line index(Clementini et al1991);

-Columns6and7:?S parameter(SKK94;B92);

-Column8:the input values used in the B-W analysis;

-Column9:the input values used in the determination of T e?(see below).

In general the various estimates agree within0.2dex.UU Cet and V445Oph deserve a more extended comment.SKK94?nd for UU Cet a rather low metal abundance compared to other estimates.Since we do not have any reason for preferring one estimate to the others,we have used the average among the available values for this star:[Fe/H]=?1.2.

As it will be discussed in detail in Section3.4,a metallicity[Fe/H]~+0.2was found more appropriate for V445Oph during the abundance analysis.

With the exception of V445Oph the values in Column9agree within±0.10dex with the mean of the other[Fe/H]abundances listed in Table6.A variation of0.2dex in the input metallicity has only a marginal in?uence on the derived temperatures(see Section3.4) and on the derived abundances(see Section4)5.

3.4.K92models and the color-temperature transformations

3.4.1.Intrinsic colors for the program stars

Accurate BV RI photometry is available for all the stars in our sample and K light curves are available for6of them.The observed colors we used are on the Johnson-Cousins system(BV R C I C K J).They are taken from the published works of Liu&Janes(1989), Fitch et al(1966),Siegel(1982),Manduca et al(1981),Carney&Latham(1984),Jones et al(1987,1988),Fernley et al(1989,1990),Burchi et al(1993),Clementini et al(1990, 1995),Cacciari et al(1987,1992),Barnes et al(1988),Stepien(1972),and Sturch(1966). Original photometries were reduced to the Johnson-Cousins system using transformation equations given by Bessel(1979,1983)and Jones et al(1987).A detailed description of the photometric data used in the present analysis and of the procedure used to transform original photometries to a uniform photometric system is given in the Appendix.

Data have then been re-phased according to the ephemerides in Table1,and smoothed curves were drawn through them.Colors read from the smoothed color curves at phases corresponding to those of our spectra were corrected for reddening according to the precepts given in Section3.1.

3.4.2.The color-temperature transformations

E?ective temperatures corresponding to the phases of our spectra were derived from the dereddened colors of the program stars using new color-T e?calibrations we explicitly determined for this purpose.They were obtained using a procedure similar to that recently followed by King(1993).This consists of two steps:?rst,an empirical color-T e?calibration is determined for population I dwarfs,based on T e?derived by means of the Infrared Flux(IF)method(Blackwell&Shallis1977).Second,the appropriate calibration for RR Lyrae stars is obtained by correcting the calibration obtained for population I dwarfs by the corresponding o?sets,due to di?erences in gravities and metal abundances,given by K92model atmospheres.The underlying assumption is that while zero point errors may be present in the K92theoretical colors,these model atmospheres well predict the variations of colors with gravity and metal abundances.

The color-T e?transformations for population I dwarfs

Fernley(1989,hereinafter F89)compared observed V?K colors and e?ective temperatures T e?s derived mainly with the IF method(Saxner&Hammarb¨a ck1985,hereinafter SH85)of population I main sequence stars with synthetic V?K and T e?derived from Kurucz(1979, hereinafter K79)models,and found that theoretical and empirical(V?K)-T e?relations have di?erent slopes.We have repeated Fernley’s procedure on K92models.An approach similar to ours has recently been followed by King(1993);however,this last author used the e?ective temperatures derived from the IF method(SH85)based on the MARCS model atmosphere by Gustafsson et al(1975).A slightly di?erent temperature is derived using the IF method and K92models.Blackwell&Lynas-Gray(1994;hereinafter BLG94)published e?ective temperatures derived with the IF method and the new K92model atmospheres for a large sample of bright solar metallicity stars.They also made a comparison with results from IF method and K79models and give in their Table2the appropriate temperature corrections.Our procedure was the following:a list of Population I main sequence stars of spectral type A-F-G,luminosity class IV-V and with well determined e?ective temperatures was obtained by merging SH85and BLG94lists;temperatures by SH85were systematically corrected upward according to Table2of BLG94.The correction applied was on average ~+52K;BLG94values were adopted for the8stars in common.The resulting sample of population I main sequence stars includes57objects and is shown in Table7.B?V, (V?R)C,(V?I)C,and(V?K)J dereddened colors for these stars were collected from F89,SH85,BLG94and Cousins(1980)data sets;they are shown in Columns7,8,9and 10of Table7,respectively.Separate semi-empirical calibrations were obtained for each color by?tting a second order polynomial to the(V?R)C,(V?I)C,and(V?K)J

-T e?data,and a third order polynomial to the(B?V)-T e?data,in the temperature range 5000

lines).

T e?=?5718.4077(B?V)3+10088.399(B?V)2?9316.128(B?V)+9115.8314(4a)(57objects) T e?=3350.38062(V?R)2C?9445.28906(V?R)C+8757.94727(4b)(22objects)

T e?=753.906677(V?I)2C?4836.16016(V?I)C+8801.4248(4c)(22objects)

T e?=300.313507(V?K)2?2447.8403(V?K)+8768.1709(4d)(54objects) Deviations from the polynomial?ttings are≤±0.02mag in V?R and V?I,and≤±0.05mag in B?V and V?K(with80%of the objects within±0.03mag).

We have compared the coe?cients of our polynomial?tting for the(V?K)-

T e?calibration with BLG94(lower line of BLG94Table8).In the temperature range 5700

40K at T e?=5100and7700K,and of about100K at T e?~9000K,with our temperatures systematically cooler.Our calibration is extrapolated beyond8300K,and hence not reliable. We estimate that equations(4)can be used to derive reliable T e?from observed B?V, (V?R)C,(V?I)C,and(V?K)J colors within the temperature interval5000

The color-T e?transformations for RR Lyrae stars

We have corrected K92synthetic colors to tie them to the semi-empirical calibrations on the assumption that the o?set between synthetic and observed color is independent of gravity and metallicity6.We have calculated the o?sets in color?(B?V),?(V?R),and

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