Abundances in HD27411 and the helium problem in Am stars
aa r X i v : . [ a s t r o - ph . S R ] D ec Mon. Not. R. Astron. Soc. , 1–10 (2002) Printed 13 October 2018 (MN L A TEX style file v2.2)
Abundances in HD 27411 and the helium problem in Amstars
G. Catanzaro ⋆ , L. A. Balona INAF - Osservatorio Astrofisico di Catania, Via S. Sofia 78, I–95123, Catania, Italy South African Astronomical Observatory, P.O. Box 9, Observatory 7935, Cape Town, South Africa
Accepted . Received ; in original form
ABSTRACT
We analyze a high-resolution spectrum of the A3m star HD 27411. We compareabundances derived from ATLAS9 model atmospheres with those using the morecomputationally-intensive ATLAS12 code. We found very little differences in the abun-dances, suggesting that ATLAS9 can be used for moderate chemical peculiarity. Ourabundances agree well with the predictions of diffusion theory, though for some el-ements it was necessary to calculate line profiles in non-thermodynamic equilibriumto obtain agreement. We investigate the effective temperatures and luminosities ofAm/Fm stars using synthetic Str¨omgren indices derived from calculated spectra withthe atmospheric abundances of HD 27411. We find that the effective temperatures ofAm/Fm stars derived from Str¨omgren photometry are reliable, but the luminositiesare probably too low. Caution is required when deriving the reddening of these starsowing to line blanketing effects. A comparison of the relative proportions of pulsat-ing and non-pulsating Am stars with δ Scuti stars shows quite clearly that there isno significant decrease of helium in the driving zone, contrary to current models ofdiffusion.
Key words: stars: chemically peculiar – stars: individual: HD 27411 – stars: abun-dances
The “metallic-lined” or Am stars are A-type stars whichhave strong absorption lines of some metals such as Zn,Sr, Zr and Ba and weaker lines of other metals such asCa and/or Sc relative to their spectral type as determinedby the strength of the hydrogen lines (Preston 1974). Thestrong metallic lines are more typical of an F star ratherthan an A star. The work of Michaud (1970) established ra-diative diffusion in a strong magnetic field as the likely causeof the chemical peculiarities in Ap stars. When the magneticfield is absent, diffusion leads to the Am/Fm stars (Watson1971). The presence of magnetic fields in Am stars has beeninvestigated, but with negative results, (e.g. Fossati et al.(2007)). A peculiarity of Am stars is that their projectedrotational velocities are generally much smaller than nor-mal A stars and they are nearly always members of closebinary systems. Rotational braking by tidal friction in a bi-nary system is regarded as a possible explanation for thelow rotational velocities in Am stars. Slow rotation furtherassists the segregation of elements by diffusion. ⋆ E-mail: [email protected]
The abundance anomalies predicted by the dif-fusion hypothesis are usually much larger than ob-served. Richer, Michaud & Turcotte (2000) developed de-tailed models of the structure and evolution of Am/Fm starsusing OPAL opacities, taking into account atomic diffusionand the effect of radiative acceleration. These models de-velop a convective zone due to ionization of iron-group el-ements at a temperature of approximately 200,000 K. Inaddition to this convective zone, these stars also have a thinsuperficial convective zone in which H and He i are partiallyionized. By assuming sufficient overshoot due to turbulence,these separate convective zones become one large convec-tive zone. The resulting mixing dilutes the large abundanceanomalies predicted by previous model, leading to abun-dances which closely resemble those observed in Am/Fmstars.A detailed abundance analysis of eight Am starsbelonging to the Praesepe cluster (Fossati et al.2007) show good agreement with the predictions ofRicher, Michaud & Turcotte (2000) for almost all thecommon elements except for Na and possibly S. The modelsof Richer, Michaud & Turcotte (2000) assume a certainad-hoc parametrization of turbulent transport coefficients c (cid:13) G. Catanzaro, L. A. Balona which are adjusted to reproduce observations. Other pa-rameterizations of turbulence have been proposed for othertypes of stars. Talon et al. (2006) have investigated to whatextent these are consistent with the anomalies observedon Am/Fm stars. They find that the precision of currentabundances is insufficient to distinguish between models.More recently, Michaud et al. (2011) have studied theabundance anomalies of the mild Am star Sirius A. Theyfind that except for B, N and Na, there is good agreementwith the predicted anomalies but turbulent mixing or massloss is required. It is not clear whether it is turbulenceor mass loss which competes with diffusion to lower theabundance anomalies. For example, Vick et al. (2011) findthat diffusion in the presence of weak mass loss can explainthe observed abundance anomalies of pre-main-sequencestars. This is in contrast to turbulence models which donot allow for abundance anomalies to develop on thepre-main-sequence.Most of the pulsational driving in δ Scuti stars is causedby the κ mechanism operating in the He ii ionization zone.Diffusion tends to drain He from this zone and thereforepulsational driving may be expected to be weaker or ab-sent in Am/Fm stars (Baglin 1972). In fact, for many yearsit was thought that classical Am/Fm stars did not pul-sate, though claims were made for some stars (Kurtz 1989).Recently, intensive ground-based observations by SUPER-WASP (Smalley et al. 2011), and also from the Kepler mis-sion (Balona et al. 2011) have shown that many Am/Fmstars do pulsate. Smalley et al. (2011), for example, foundthat about 200 Am/Fm stars out of a total of 1600 (12.5percent) show δ Sct pulsations, but with generally loweramplitudes. They found that the pulsating Am/Fm starsare confined between the red and blue radial fundamentaledges, in agreement with Balona et al. (2011). While thereare many δ Sct stars hotter than the fundamental blue edge,this does not seem to be the case for pulsating Am/Fm stars.The significance of this result remains to be evaluated.The effect of draining of He from the He ii ionizationzone is to reduce the width of the instability strip, the blueedge moving towards the red edge, eventually leading to thedisappearance of the instability strip when He is sufficientlydepleted (Cox et al. 1979). Turcotte et al. (2000) has dis-cussed the effect of diffusion on pulsations in Am/Fm starsusing the models by Richer, Michaud & Turcotte (2000).One significant difference with earlier models is that a sub-stantial amount of He remains in the He ii ionization zone.The blue edge of the instability strip for Am/Fm stars issensitive to the magnitude of the abundance variations andis thus indicative of the depth of mixing by turbulence.Turcotte et al. (2000) predict that pulsating Am/Fm starsshould lie in a confined region of the HR diagram close to thered edge of the δ Sct instability strip. However, Balona et al.(2011) show that there is no relationship between the pre-dicted Am/Fm instability strip and the actual location ofthese stars in the HR diagram.A particularly interesting result of the pulsation analy-sis of Turcotte et al. (2000) is the prediction of long-periodg modes in A-type stars. As the star evolves, the drivingregions shift deeper into the star and the g modes becomegradually more and more excited. Whereas p modes are sta-bilized through diffusion, g modes tend to be excited as aresult of that process. It appears that diffusion may act to enhance driving of long-period g modes due to a significantincrease in opacity due to iron-group elements. This mayhave a bearing on the fact that nearly all A-type stars ob-served by
Kepler have unexplained low-frequencies (Balona2011).When dealing with objects with non-standard chemi-cal composition, such as Am stars, it is crucial that theopacities are correctly calculated. This question has beeninvestigated by several authors in recent years. These stud-ies show that a non-standard chemical composition of thestellar atmosphere alters the flux distribution of the star ormodifies the profiles of the Balmer lines (Leone & Manfr´e(1997), Catanzaro, Leone & Dall (2004)). Therefore a deter-mination of T eff and log g based on a comparison betweenobserved and computed Balmer-line profiles will not be cor-rect unless one takes into account the metallicity of the star.Thus, even estimates based on standard analysis of the spec-tra may be in error when applied to Am/Fm stars.In this paper, we investigate the determination ofeffective temperature and surface gravity of the Amstar HD 27411 (HR 1353, A3m) using spectra in theESO archives. The purpose is to determine whetherthe stellar parameters of this star agree with thoseobtained from Str¨omgren photometry and hence totest the reliability of the effective temperature calibra-tion applied to Am/Fm stars. The star was used byRyabchikova, Kochukhov & Bagnulo (2008) as a compari-son in their study on the calcium stratification in Ap stars.HD 27411 is not known to pulsate. However, as we knowfrom Kepler observations, pulsations in A and F stars withamplitudes too low to be detected from the ground are com-mon.Atmospheric models obtained with ATLAS9 (Kurucz1993) use precomputed line opacities in the form of opacitydistribution functions (ODFs). These are tabulated for mul-tiples of the solar metallicity and for various microturbulentvelocities. This approach allows very fast computation ofmodel atmospheres, but with very little flexibility in choiceof chemical profile and microturbulent velocity. While thisis satisfactory for most applications, it fails for chemicallypeculiar stars where a non-standard chemical compositionprofile is required. This can be done with ATLAS12 (Kurucz1997), which is essentially identical to ATLAS9, but uses theopacity sampling (OS) method to evaluate line opacities. Inthis study we compare the abundances of HD 27411 obtainedwith both codes to determine if the use of ATLAS12 is es-sential.The result that Am stars are not confined to particularregion of the δ Sct instability strip depends, to a large ex-tent, on effective temperatures and luminosities estimatedfrom Str¨omgren photometry (Smalley et al. 2011). It is notclear whether the calibration, derived from normal AF stars,can be applied to Am/Fm stars. In this paper we use syn-thetic Str¨omgren photometry applied to models of Am/Fmstars to investigate the reliability of fundamental parame-ters estimated from the photometry. Finally, we discuss therelative numbers of pulsating and non-pulsating Am starsand compare these to the relative numbers of δ Scuti andconstant stars in the instability strip. From this comparison,one can deduce the effectiveness of pulsational driving in theHe ii ionization zone and compare the He abundance to thatexpected from diffusion calculations. c (cid:13) , 1–10 bundances in HD 27411 Figure 1.
Comparison between the observed (crosses) and computed (solid red line) hydrogen line profiles. From top to bottom: theBalmer line profiles from H δ to H α . The synthetic profiles were computed with SYNTHE using an ATLAS12 model atmosphere withT eff = 7400 ±
150 K, log g = 4.0 ± ξ = 4.2 ± − , v e sin i = 20.5 ± − and individual abundances shown in Table 2. Table 1.
Ions used to determine the microturbulent velocity inHD 27411. The number of spectral lines used, the microturbulentvelocity, ξ , the derived abundance and the radial velocity, RV, arelisted.Elem N ξ Abundance RVkm s − log N el /N Tot km s − Fe i
71 3.9 ± − ± ± ii
15 4.4 ± − ± ± i
24 4.4 ± − ± ± ± ± The spectrum of HD 27411 is available in the ESO archiveas a part of the UVES Paranal Observatory Project (UVESPOP), which aims to create a library of high-resolution spec-tra across the HR diagram (Bagnulo et al. 2003). The spec-trum was obtained in 2002, September 18 with a resolvingpower of R = 80 000.In order to determine the optimal parameters, we mini-mize the difference between the observed and synthetic spec-trum. Thus we minimize χ = 1 N X (cid:16) I obs − I th δI obs (cid:17) where N is the total number of points, I obs and I th are theintensities of the observed and computed profiles, respec-tively, and δI obs is the photon noise. Synthetic spectra weregenerated in three steps. Firstly, we computed a model at-mosphere using the ATLAS9 code. The stellar spectrum wasthen synthesized using SYNTHE (Kurucz & Avrett 1981). Finally, the spectrum was convolved with the instrumentaland rotational profiles.As starting values of T eff and log g , we used the val-ues derived from Str¨omgren photometry: V = 6 . ± . b − y = 0 . ± . m = 0 . ± . c = 0 . ± . β = 2 . ± .
005 (Hauck & Mermilliod 1998). Using the al-gorithm in Moon (1985) to obtain the reddening, we ob-tain V = 5 . b − y ) = 0 . m = 0 . c =0 . eff = 7820 K and log g = 4.12, while the cal-ibration of Balona (1994) gives T eff = 7760 K, log g = 4.11.Again, because of increased line blanketing, these must betaken merely as provisional values. We adopt T eff = 7800 K,log g = 4.12.To decrease the number of parameters, we computed the v e sin i of HD 27411 by matching synthetic line profiles fromSYNTHE to a number of metallic lines. The Mg i triplet at λλ v e sin i = 20.5 ± − . Thisvalue is in good agreement with v e sin i = 20.4 ± − by Diaz et al. (2011).To determine stellar parameters as consistently as pos-sible with the actual structure of the atmosphere, we per-formed the abundance analysis by the following iterativeprocedure:(i) T eff is estimated by computing the ATLAS9 modelatmosphere which gives the best match between the ob-served H δ , H γ , H β , and H α line profiles and those com-puted with SYNTHE. log g is estimated by matching the ob-served and calculated profiles of the Mg i triplet at λλ c (cid:13) , 1–10 G. Catanzaro, L. A. Balona
Figure 2.
Comparison between observed (crosses) and com-puted (solid red line) spectra in the region of the Mg i b triplet, λλ eff = 7400 K, log g = 4.0, and log Mg/N tot = − ± eff = 7600 ±
150 K, log g = 4.0 ± ξ , is determined inde-pendently from three sets of spectral lines: 71 lines fromFe i , 15 lines from Fe ii , and 24 lines from Ni i . For this pur-pose we used all lines with equivalent width (EW) > ξ is computed by requiring that the de-rived abundances do not depend on the measured equiva-lent widths. To convert equivalent widths to abundances weused the WIDTH9 code (Kurucz & Avrett 1981). Values of ξ , the abundance and the radial velocity obtained for eachion are listed in Table 1. The adopted microturbulence is inagreement with Landstreet et al. (2009) (see Fig. 2 of theirpaper). The effective temperature is in agreement with theequilibrium condition between Fe i and Fe ii , since the ironabundances derived separately from these two different ion-ization stages are in good agreement.(iii) The projected rotational velocity is relatively high.To overcome line blending problems, we divided the spec-trum into a number of sub-intervals ≈
25 ˚A wide. For eachinterval we performed a separate synthesis analysis. We usedthe abundances of Fe and Ni given in Table 1 as starting val-ues in this procedure. The atomic parameters adopted in thisanalysis are from Kurucz & Bell (1995) with line lists subse-quently updated by Castelli & Hubrig (2004). The adoptedabundances, shown in the second column of Table 2, areweighted averages expressed in the usual form log N el /N Tot .Values of T eff , log g , ξ and individual abundances es-timated in this way were then used as initial guesses forstarting another iterative procedure based on the ATLAS12code. The best fit was obtained after three iterations and ledto the following parameters: T eff = 7400 ±
150 K, log g = 4.0 ± ξ = 4.2 ± − and v e sin i = 20.5 ± − .The corresponding abundances are shown in the secondcolumn of Table 2. Ryabchikova, Kochukhov & Bagnulo(2008) analyzed HD 27411 in a study of Ap stars and de-rived the following parameters: T eff = 7650 K, log g = 4.0, v e sin i = 18.5 km s − , and ξ = 2.5 km s − . Considering theexperimental errors, these values are in agreement with ours.The fits between the observed and synthetic Balmerlines are shown in Fig. 1. The determination of surface grav- Figure 3.
Location of HD 27411 in the HR diagram together withevolutionary tracks and isochrones for log t ranging from 8.87 to8.95 (step 0.02 and t in yrs). Asterisks are the pulsating AmFmstars taken from Smalley et al. (2011). The gray area is the ap-proximate location of pulsating Am star models incorporatingheavy-metal diffusion (Turcotte et al. 2000). ity was constrained by using the Mg i triplet at λλ eff and log g were estimatedby the change in parameter values which leads to an increaseof χ by unity (Lampton et al. 1976). If we adopt T eff = 7400 ±
150 K and log g = 4 . ± .
10 fromour spectroscopic analysis, we may use the relationships byTorres et al. (2010) to derive log
L/L ⊙ = 0 . ± .
12. Theserelate the mass and radius of a star to the effective temper-ature and gravity through empirical calibrations. The great-est source of uncertainty is the surface gravity determina-tion.The
Hipparcos parallax for HD 27411, π = 11.13 ± V = 6 . M V = 1 . ± .
08 where the error is derived fromthe error in the parallax. If we adopt the bolometric cor-rection BC = 0.051 derived from Balona (1994), we have M bol = 1 . ± .
09. Using M bol , ⊙ = 4.74 (Drilling & Landolt1999), we obtain log( L/L ⊙ ) = 1 . ± .
07. From the luminos-ity and using T eff = 7400 K, we obtain R/R ⊙ = 2 . ± . . ± . M ⊙ is log g ≈ . ± .
1. All the astrophysicalquantities derived here are summarized in Table 3.The location of the star in the HR diagram, to-gether with some evolutionary tracks computed for non-solar metallicity Z = 0.03 (Girardi et al. 2000), is shown inFig. 3. Also shown are isochrones computed by Marigo et al.(2008) for the same Z and for five ages, i.e. log t = 8.87, 8.89,8.91, 8.93 and 8.95 ( t in years). The non-solar metallicity fol-lows from our abundance analysis, and Z=0.03 is the nearest c (cid:13) , 1–10 bundances in HD 27411 Table 2.
Comparison among atmospheric parameters and abun-dances derived by ATLAS9 modeling and by ATLAS12 approach.The measurement without error is to be considered only as upperlimit. In the last column we reported abundances derived withNLTE approach. All the abundances are expressed in the usualform log N el /N Tot .A9 A12 A12+SYNSPECT eff ±
150 7400 ±
150 7400 ± g ± ± ± − ± − ± − ± − ± − − − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± − ± metallicity in the models computed by Girardi et al. (2000)and Marigo et al. (2008). The location of the star indicatesa mass M ≈ ⊙ and an age of t ≈ ±
40 Myrs.In Table 3 we summarized all the astrophisical quanti-ties for HD 27411.It is well known that the vast majority of Am starsare binaries. There are few radial velocity measurements ofHD 27411 in the literature. We could only find three mea-surements in Buscombe (1963): +17, +34 and −
53 km s − . From our spectrum, we derived a radial velocityRV = +40.6 ± − , which is a weighted av-erage of the single velocities derived by convertingthe shift between observed and theoretical λ c fromthe species reported in Tablle 1. The scatter in thesevalues does, indeed, suggest that HD 27411 is a binary. Ifso, then the companion is probably much fainter than theprimary, otherwise one may expect to see some evidence inthe spectrum.
Table 3.
Astrophysical quantities for HD 27411. The second col-umn are quantities derived from the parallax. The third columnare quantities derived from Str¨omgren photometry and the lastcolumn from spectroscopy.Paramerter Parallax Str¨omgren Spectroscopy π . ± . V . ± .
007 5 . ± . V . ± . bol . ± . eff ±
200 7400 ± L/L ⊙ ) 1 . ± .
07 0 . ± .
15 0 . ± . g . ± . . ± .
10 4 . ± . ⊙ . ± .
10 1 . ± .
27 1 . ± . M/M ⊙ . ± .
05 1 . ± .
07 1 . ± . In Fig. 4 we compare the LTE abundances derived frommodel atmospheres computed using ATLAS9 and AT-LAS12. It is evident that there is good agreement in theabundances derived with the two different codes. There aresome very small differences for Na, V, Zr and Nd, but theseare only 0.1 dex or less. Thus we may use the faster ATLAS9code with confidence. In Fig. 5 we show the abundances rel-ative to solar standard abundances (Grevesse et al. 2010).The chemical pattern displayed here is typical of that ob-served in Am stars, i.e. an underabundance of C, N, O, Caand Sc and a general increasing overabundance for heavyelements.The atmospheric abundance of Li is interestingin the context of diffusion. Burkhart & Coupry (1991)and Burkhart et al. (2005) find that, in general, the Liabundance in Am stars is close to the cosmic value(log N Li /N Tot ≈ − .
04 dex), although some Am/Fmstars appear to have an underabundance of Li. Nor-mal A-type stars in the range 7000 < T eff < N Li /N Tot ≈ − .
64 dex, (Burkhart & Coupry 1995).To determine the Li abundance, we used the Li i λ N Li /N Tot = − ± eff up to a maximum age of ≈
670 Myrs.We find that age of HD 27411 to be about 810 ±
40 Myr,which is considerably older than the maximum age of modelsin Richer, Michaud & Turcotte (2000), but we will assumethat models of 670 Myr still give a fair approximation of theabundances. For T eff = 7400 K, which is our best estimatefor HD 27411, the models by Richer, Michaud & Turcotte(2000) predicts underabundances ranging from -0.3 dex to-0.1 dex for C, N, O, Na, Mg, K, and Ca. For Si and Sthe abundances are normal, while overabundances of about0.1–0.8 dex are found for for Li, Al, Ti, Cr, Mn, Fe, and c (cid:13) , 1–10 G. Catanzaro, L. A. Balona
Figure 4.
Comparison between abundances computed using AT-LAS9 and ATLAS12 model atmospheres. The differences in abun-dance given by the two models are shown as a function of atomicnumber.
Ni. Inspection of their figure reveals that for Na, Mg, Al,Si, S, Ca, Ti, Cr, Mn, and Fe, the abundance anomaly isapproximately constant with age and depends only on theturbulence. The abundances of Li, C, N, and O vary withage. Fig. 5 shows the abundances of the elements at 670 Myrpredicted by Richer, Michaud & Turcotte (2000) comparedwith our abundances. There is indeed good agreement for Li,C, N, O, Mg, K, Ca, Ti, Mn, Fe, and Ni, but abundances ofNa, Al, Si, S, and Cr are somewhat discrepant. Similar dis-crepancies for Na and S were found by Fossati et al. (2007)for the Am star HD 73730. From the NLTE analysis of the Sabundance by Kamp et al. (2001), Fossati et al. (2007) con-cluded that NLTE effects should be taken into account todetermine whether this resolves the discrepancy with diffu-sion predictions.Following this idea, we performed a NLTE analysis onNa, Al, Si, S, and Cr, to derive their abundances. We usedthe same technique of matching predicted and observed lineprofiles, but in this case the NLTE line profiles were com-puted with version 43 of SYNSPEC (Hubeny & Lanz 2000).This code reads the same input model atmosphere previ-ously computed using ATLAS12 and solves the radiativetransfer equation, wavelength by wavelength in a specifiedspectral range. SYNSPEC also reads the same Kurucz listof lines that we used for determining metal abundances.SYNSPEC allows one to compute the line profiles by us-ing an approximate NLTE treatment, even for LTE models.This is done by means of second-order escape probabilitytheory (for details see Hubeny, Harmanec & Stefl (1986)).The results of these calculations are shown in Table 2.All the NLTE abundances are lower than the LTE abun-dances by factors ranging from 0.23 dex (S) to 0.39 dex(Al). As can be seen from Fig. 5, the NLTE calculations
Figure 5.
Abundances in HD 27411 as a function of atomicnumber. Filled circles represent our abundances. Open boxes(red) are abundances predicted by the diffusion model ofRicher, Michaud & Turcotte (2000) for 670 Myr. Starred sym-bols represent the elements for which NLTE abundances havebeen calculated. bring the observations closer to the diffusion predictionsby Richer, Michaud & Turcotte (2000). In fact, there is nolonger any discrepancy in abundances within the observa-tional errors.
In order to investigate the effect of line blanketing on theStr¨omgren colour indices, we used the method of syntheticphotometry. For this purpose we computed the spectrumof a star at different effective temperatures with abun-dances shown in Table 2. We used the abundances givenby the ATLAS12 models modified by NLTE where neces-sary. The spectra were calculated using
SPECTRUM , version2.76e (Gray & Corbally 1994). Synthetic spectra with nor-mal and peculiar abundances were calculated for 6000 T eff <
10 000 K and log g = 4 .
00. In all cases the micro-turbulence velocity was set to ξ = 4 km s − . These spectrawere convolved with standard uvbyβ transmission functionsto calculate synthetic Str¨omgren indices.It should be noted that not all Am/Fm stars will havethe same abundance anomalies as HD 27411. Hence the re-sults described here are only indicative of what might betypical in Am/Fm stars. Individual Am/Fm stars will havedifferent abundances and different line blanketing.In computing these synthetic Str¨omgren indices, it isnecessary to identify a particular model with a real star inorder to determine the zero points. We chose a model of Vega c (cid:13) , 1–10 bundances in HD 27411 Table 4.
Synthetic Str¨omgren indices for normal stars andAm/Fm stars with the abundances of Table 2. T eff b − y m c β Normal:6000 0.365 0.251 0.372 2.6306250 0.323 0.210 0.425 2.6456500 0.296 0.183 0.482 2.6636750 0.264 0.168 0.544 2.6847000 0.232 0.162 0.608 2.7077250 0.200 0.163 0.677 2.7337500 0.150 0.186 0.846 2.7927750 0.121 0.191 0.914 2.8198000 0.092 0.196 0.976 2.8418250 0.063 0.199 1.030 2.8588500 0.041 0.196 1.062 2.8708750 0.026 0.189 1.076 2.8759000 0.013 0.180 1.077 2.8759250 0.003 0.172 1.071 2.8729500 -0.005 0.163 1.058 2.8669750 -0.012 0.156 1.038 2.857Am/Fm:6000 0.434 0.351 0.202 2.6376250 0.392 0.315 0.251 2.6496500 0.352 0.288 0.312 2.6656750 0.312 0.268 0.382 2.6837000 0.274 0.255 0.459 2.7057250 0.236 0.247 0.542 2.7307500 0.183 0.267 0.705 2.7867750 0.148 0.263 0.790 2.8128000 0.114 0.258 0.870 2.8358250 0.079 0.251 0.944 2.8528500 0.053 0.239 0.995 2.8658750 0.034 0.223 1.027 2.8719000 0.019 0.207 1.042 2.8729250 0.007 0.193 1.046 2.8699500 -0.002 0.180 1.042 2.8639750 -0.010 0.168 1.027 2.855 ( b − y = 0 . , m = 0 . , c = 1 . , β = 2 . b − y as a function of β with the standard relations of Crawford (1975) shows thatthe β zero point required a further correction of -0.04. Thesynthetic colours for normal and Am/Fm stars are listedin Table 4. Comparison of indices for models with standardsolar abundance and the abundances of Table 2 are shownin Fig. 6.Various colour–colour diagrams derived from the syn-thetic colours are shown in Fig. 7 together with reddeninglines. The reddening lines are from Crawford (1976): E ( u − b ) E ( b − y ) = 1 . E ( c ) E ( b − y ) = 0 . E ( m ) E ( b − y ) = − . . Also shown are the locations of HD 27411. It is clearthat the star lies nicely on the synthetic relations given bythe enhanced abundances and that the star is unreddenedor only very slightly reddened. It is also clear that indetermining the reddenings of Am/Fm stars it is wiseto avoid using m and u − b . The c /b − y relations forAm/Fm abundances is almost the same as for normalabundances and it is preferable to use this diagram to Figure 6.
Relation between synthetic Str¨omgren indices for nor-mal stars (horizontal axis) and for Am/Fm stars (vertical axis).The straight line represents equality between the indices. deduce the reddening correction. Assuming that HD 27411is unreddened and matching the observed indices with thosefor modified abundances in Table 4 gives T eff = 7600 K.The β index is correlated well with effective tempera-ture for T eff < b − y is correlated with effec-tive temperature but is affected by blanketing for the coolerstars. As can be seen from Fig 6, the m index is severely af-fected by blanketing. The c index for Am/Fm stars is nearlyalways smaller than for normal stars. This index measuresthe strength of the Balmer discontinuity (and hence the sur-face gravity), but it is clearly not entirely free of blanketingeffects.In estimating the absolute magnitudes, M V , of F stars,Crawford (1975) defines, first of all, a relationship for starson the ZAMS as a function of b − y , M V = M V ( ZAMS, b − y ) . The absolute magnitude for a star above the ZAMS is cal-culated from the value of δc = c − c ( ZAMS ), i.e. thedifference between the measured c and the value of c onthe ZAMS at the given b − y . Since there are significantline blanketing effects on c for Am/Fm stars, their abso-lute magnitudes derived in this way are probably not free ofsystematic errors. We derived M V using the data of Table 4for stars with solar abundance and with the Am abundanceusing the calibration of Crawford (1975). We find that on av-erage the Am stars are estimated to be about 1.2 magnitudesfainter than normal stars of the same effective temperatureand gravity. This is due to the systematically lower valuesof c in the Am star models. Table 5 lists Am stars whichhave good parallaxes. The general trend of lower luminosi-ties derived from Str¨omgren photometry is apparent.From this exercise we conclude that although the effec-tive temperatures of Am/Fm stars derived from Str¨omgrenphotometry are probably reliable, the absolute magnitudes c (cid:13) , 1–10 G. Catanzaro, L. A. Balona
Figure 7.
Synthetic colour–colour diagrams for stars with normalabundance (open circles) and with abundances of Table 2 (filledcircles). The asterisk shows the observed location of HD 27411and the arrows are the reddening lines from Crawford (1976).
Table 5.
Am stars which have very good trigonometric paral-laxes. The luminosities calculated from the parallaxes and fromStr¨omgren photometry are shown. Parallax Str¨omgrenHD Class log T eff log g log LL ⊙ log LL ⊙ may be systematically too faint. For example, if we ap-ply the Crawford (1975) calibration to HD 27411,assuming no reddening, we obtain M V = 2 . or log L/L ⊙ = 0 . (using BC = 0.035 derived fromBalona (1994)), whereas the most reliable estimate(Hipparcos parallax) gives log L/L ⊙ = 1 . . This effectcan be seen in Fig 3 where many of the Am stars are belowthe line defining the ZAMS. The luminosities of these starswere derived using the standard calibration and hence havebeen under-estimated.
The diffusion models of Richer, Michaud & Turcotte (2000)are the best models presently available for Am/Fm stars.The models seem to be able to predict the abundances inthese stars rather well, but we need to bear in mind that this
Table 6.
The numbers of all stars in the given effective temper-ature range, N (All), and the number of δ Sct stars in that range, N ( δ Sct), and the corresponding percentage is given. The firstblock refers to
Kepler δ Scuti stars with maximum amplitude ex-ceeding 1.5 mmag. The second block refers to all Am stars andthe pulsating Am stars in the given temperature range. T eff N (All) N ( δ Sct) Percent
Kepler :5500 - 6500 1509 33 2.196500 - 7000 3842 174 4.537000 - 7500 1412 263 18.637500 - 8000 811 172 21.218000 - 8500 512 51 9.968500 - 9000 297 11 3.709000 - 10000 263 1 0.38Am stars:5500 - 6500 16 2 12.506500 - 7000 75 21 28.007000 - 7500 307 52 16.947500 - 8000 489 9 1.848000 - 8500 185 1 0.548500 - 9000 32 2 6.259000 - 10000 7 0 0.00 is achieved because of adjustable free parameters to describethe turbulence. We still do not know if the mechanism com-peting with diffusion is turbulence, mass loss or some otherfactor. What we do know is that the current description ofAm stars is in trouble because it fails to account for thewide distribution of pulsating Am stars in the δ Sct insta-bility strip (Balona et al. 2011; Smalley et al. 2011).One question that is of interest is the fraction of Amstars that pulsate. To answer this question we have to de-fine what we mean by “non-pulsating”. Clearly, a star couldbe pulsating but with amplitudes too small to be visiblefrom the ground. Balona & Dziembowski (2011) discussedthis issue in the context of
Kepler observations which, ofcourse, allow pulsations to be detected at the micromagni-tude level. They deduced that the fraction of pulsating starsin the δ Sct instability strip is surprisingly low. There isclearly some damping mechanism which is currently not un-derstood. The fraction of δ Sct stars in the instability stripvaries with effective temperature, but does not exceed about50 percent.We can answer this question for Am stars only in partbecause we do not have a sufficient number of Am starsobserved at the micromagnitude level. In order to comparethese ground-based observations with the extensive
Kepler observations of δ Sct stars, we need to degrade the
Kepler data by considering as pulsating only those δ Sct stars withamplitudes over 1.5 mmag. We chose this minimum ampli-tude as roughly representative of the detection limit in thecatalogue of pulsating Am stars in Smalley et al. (2011). Thepercentage of
Kepler δ Sct stars with this minimum ampli-tude relative to all stars in a particular temperature rangeis shown in Table 6.We can now compare this distribution of ordi-nary δ Sct stars with the distribution of pulsating Amstars in Smalley et al. (2011). We used the catalogue of c (cid:13) , 1–10 bundances in HD 27411 Figure 8.
The percentage of δ Scuti stars relative to all stars inthe given effective temperature range is shown as the solid linehistogram. The dashed line histogram is the percentage of pul-sating Am stars relative to all Am stars in the given temperaturerange.
Renson & Manfroid (2009) and estimated the effective tem-peratures of the Am stars using the Balona (1994) calibra-tions. Results are shown in Table 6 and Fig. 8. It is evidentthat the pulsating Am stars are cooler than normal δ Sctstars, a fact already mentioned by Smalley et al. (2011).This conclusion still holds even if the amplitude thresholdin
Kepler data is lowered to a few micromagnitudes.From this comparison, we may deduce that there is cer-tainly a tendency for pulsating Am stars to be confined moretowards the red edge, but that this effect is far smaller thanpredicted by Turcotte et al. (2000). In fact, Table 6 showsthat the percentage of pulsating Am stars among the Amstars is about the same as the percentage of δ Scuti starsin the instability strip. This tells us that driving in the He ii ionization zone is practically unaffected. We may thereforeconclude that there is no significant reduction of He in theionization zone, contrary to the prediction of current diffu-sion models. We analyzed the spectrum of the Am star HD 27411 fromthe UVES POP archive. Our aim was to investigate if theATLAS12 model atmosphere code provides more reliable re-sults than the ATLAS9 code for chemically peculiar stars.We found that there is very little difference in the abun-dances derived from ATLAS9 and from ATLAS12. SinceATLAS12 demands considerably greater resources, it seemssafe to use ATLAS9, at least for moderate metallic enhance-ment. We find that the derived abundances in HD 27411 arein good agreement with the predictions of diffusion modelsby Richer, Michaud & Turcotte (2000). There were discrep-ancies for Na, Al, Si, S, and Cr, but these are resolved byusing NLTE model atmospheres.We investigated the reliability of effective temperaturesand luminosities of Am/Fm stars determined by Str¨omgrenphotometry by synthesizing spectra having the abundancesof HD 27411 for a range of effective temperatures. The re-sulting synthetic colours indicate that effective temperaturescan be reliably determined from photometry, but owing to line blanketing in the c passband, the resulting surface grav-ities are systematically to high, leading to lower luminosities.This result appears to be verified by comparing luminositiesof Am/Fm stars obtained from their parallaxes and fromphotometry. Determination of reliable luminosities for Amstars remains a difficult problem. At this stage, par-allaxes offer the best results, but this can only bedone for very few stars. As we have seen, lumi-nosities obtained from Str¨omgren photometry aresubject to a systematic bias which depends on theoverabundances of metals. The error in the surfacegravity from high-resolution spectroscopy is typi-cally 0.1 in log g . For A–F main sequence and giants,this translates into an error of about 0.12 in log L/L ⊙ when using the calibration of Torres et al. (2010).For HD 27411, for example, we derive log g = 4 . ± . from spectroscopy, whereas the value derived fromthe parallax is log g = 3 . ± . (Table 2), Althoughthe two values only differ by two standard devia-tions, this is enough to cause a difference of 0.36 in log L/L ⊙ . Although spectroscopic determinations ofluminosities may lead to quite large errors in theluminosity, they should at least not be biased. By far the most serious problem confronting the diffu-sion model is that there seems to be no appreciable settlingof He in the He ii ionization zone, as predicted by the mod-els. This is demonstrated by the fact that pulsating Am/Fmstars occur throughout the δ Scuti instability strip, thoughthey tend to be cooler than normal δ Sct stars. In fact, therelative proportions of pulsating Am stars to non-pulsatingAm stars is no different from the proportion of δ Sct stars toconstant stars in the δ Sct instability strip. There is clearlya need to revise current ideas of diffusion to explain the Amphenomenon.
ACKNOWLEDGMENTS
LAB wishes to thank the National Research Foundation andthe South African Astronomical Observatory for financialassistance.
REFERENCES
Andersen J., Gustafson B., Lambert D. L., 1984, A&A,136, 65Baglin A., 1972, A&A 19, 45Balona L. A., 1994, MNRAS, 268, 119Balona L. A., 2011, MNRAS, 415, 1691Balona L. A., Dziembowski W. A., 2011, MNRAS, 417, 591Balona L. A., Ripepi V., Catanzaro G. et al., 2011, MN-RAS, 414, 792Bagnulo et al., 2003, Messenger, 114, 10Burkhart C., Coupry M. F., 1991, A&A, 249, 205Burkhart C., Coupry M. F., 1995, Mem. Soc. Astron. It.,66, 357Burkhart C., Coupry M. F., Faraggiana R., Gerbald, M.,2005, A&A, 429, 1043Buscombe W., 1963, MNRAS, 126, 299Castelli F., Hubrig S., 2004, A&A, 425, 263 c (cid:13) , 1–10 G. Catanzaro, L. A. Balona
Catanzaro G., Leone F., Dall T. H., 2004, A&A, 425, 641Cox A. N., King D. S., Hodson S. W., 1979, ApJ, 231, 798Crawford D. L., 1975, AJ, 80, 955Crawford D. L., Mandwewala, N., 1976, PASP, 88, 917D´ıaz, C. G., Gonz´alez, J. F., Levato, H., Grosso, M., 2011,A&A, 531, A143Drilling J. S., Landolt A. U., 1999, in
Allen’s AstrophysicalQuantities , Fourth Edition, p. 381, Edited by Arthur N.Cox, Los Alamos, NMFossati L., Bagnulo S., Monier R., et al., 2007, A&A, 476,921Girardi L., Bressan A., Bertelli G., Chiosi C., 2000, A&AS,141, 371Gray R. O., Corbally, C. J., 1994, AJ, 107, 742Grevesse N., Asplund M., Sauval A. J., Scott P., 2011,Ap&SS, 328, 179Hauck B., Mermilliod M., 1998, A&AS, 129, 431Hubeny I., Lanz T., 2000, SYNSPEC - A user’s guideHubeny I., Harmanec P., Stefl S. 1986, Bull. Astron. Inst.,Czechoslovakia, 37, 370Kamp I., Iliev I. K., Paunzen E. et al., 2001, A&A, 375,899Kurtz D. W., 1989, MNRAS 238, 1077Kurucz R. L., 1997, Model Atmospheres for IndividualStars with Arbitrary Abundances. In: The Third Con-ference on Faint Blue Stars, A. G. D. Philip, J. Liebert,R. Saffer and D. S. Hayes (eds.), Published by L. DavisPress, p.33Kurucz R. L., Bell B., 1995, Kurucz CD-ROM No. 23. Cam-bridge, Mass.: Smithsonian Astrophysical Observatory.Kurucz R.L., 1993, A new opacity-sampling model atmo-sphere program for arbitrary abundances. In: Peculiar ver-sus normal phenomena in A-type and related stars, IAUColloquium 138, M.M. Dworetsky, F. Castelli, R. Farag-giana (eds.), A.S.P Conferences Series Vol. 44, p.87Kurucz R.L., Avrett E.H., 1981, SAO Special Rep. 391Lampton M., Margon B., Bowyer S., 1976, ApJ, 208, 177Landstreet J. D., Kupka F., Ford H. A., et al., 2009, A&A,503, 973Leone F., Manfr´e, 1997, A&A, 320, 893Marigo P., Girardi L., Bressan A., Gronewegen M. A. I.,Silva L., Granato G. L., 2008, A&A, 482, 883Michaud G., 1970, ApJ, 160, 641Michaud G., Richer J., Vic, M., 2011, A&A, 534, A18Moon T. T., 1985, Comm. from the Univ. of London Obs.,78Moon T. T., Dworetsky M. M., 1985, MNRAS, 217, 305Ryabchikova T., Kochukhov O., Bagnulo S., 2008, A&A,480, 811Preston G. W., 1974, ARA&A, 12, 257Renson P., Manfroid J., 2009, A&A, 498, 961Richer J., Michaud G., Turcotte S., 2000, ApJ, 529, 338Smalley B., et al., 2011, A&A, 535, A3Torres G., Andersen J., Gim´enez A., 2010, A&ARv, 18, 67Talon S., Richard O,, Michaud G., 2006, ApJ, 645, 634Turcotte S., Richer J., Michaud G., Christensen-DalsgaardJ., 2000, A&A, 360, 603Van Leeuwen F., 2007, A&A, 474, 653Vick M., Michaud G., Richer J., Richard O., 2011, A&A,526, A37Watson W. D., 1971, A&A, 13, 263 c (cid:13)000