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Abundances in HD27411 and the helium problem in Am stars

We analyze a high-resolution spectrum of the A3m star HD27411. We compare abundances derived from ATLAS9 model atmospheres with those using the more computationally-intensive ATLAS12 code. We found very little differences in the abundances, suggesting that ATLAS9 can be used for moderate chemical peculiarity. Our abundances agree well with the predictions of diffusion theory, though for some elements it was necessary to calculate line profiles in non-thermodynamic equilibrium to obtain agreement. We investigate the effective temperatures and luminosities of Am/Fm stars using synthetic Stromgren indices derived from calculated spectra with the atmospheric abundances of HD27411. We find that the effective temperatures of Am/Fm stars derived from Stromgren photometry are reliable, but the luminosities are probably too low. Caution is required when deriving the reddening of these stars owing to line blanketing effects. A comparison of the relative proportions of pulsating and non-pulsating Am stars with delta Scuti stars shows quite clearly that there is no significant decrease of helium in the driving zone, contrary to current models of diffusion.


INTRODUCTION
The "metallic-lined" or Am stars are A-type stars which have strong absorption lines of some metals such as Zn, Sr, Zr and Ba and weaker lines of other metals such as Ca and/or Sc relative to their spectral type as determined by the strength of the hydrogen lines (Preston 1974). The strong metallic lines are more typical of an F star rather than an A star. The work of Michaud (1970) established radiative diffusion in a strong magnetic field as the likely cause of the chemical peculiarities in Ap stars. When the magnetic field is absent, diffusion leads to the Am/Fm stars (Watson 1971). The presence of magnetic fields in Am stars has been investigated, but with negative results, (e.g. Fossati et al. (2007)). A peculiarity of Am stars is that their projected rotational velocities are generally much smaller than normal A stars and they are nearly always members of close binary systems. Rotational braking by tidal friction in a binary system is regarded as a possible explanation for the low rotational velocities in Am stars. Slow rotation further assists the segregation of elements by diffusion.
The abundance anomalies predicted by the diffusion hypothesis are usually much larger than observed.  developed detailed models of the structure and evolution of Am/Fm stars using OPAL opacities, taking into account atomic diffusion and the effect of radiative acceleration. These models develop a convective zone due to ionization of iron-group elements at a temperature of approximately 200,000 K. In addition to this convective zone, these stars also have a thin superficial convective zone in which H and Hei are partially ionized. By assuming sufficient overshoot due to turbulence, these separate convective zones become one large convective zone. The resulting mixing dilutes the large abundance anomalies predicted by previous model, leading to abundances which closely resemble those observed in Am/Fm stars.
A detailed abundance analysis of eight Am stars belonging to the Praesepe cluster (Fossati et al. 2007) show good agreement with the predictions of  for almost all the common elements except for Na and possibly S. The models of  assume a certain ad-hoc parametrization of turbulent transport coefficients which are adjusted to reproduce observations. Other parameterizations of turbulence have been proposed for other types of stars. Talon et al. (2006) have investigated to what extent these are consistent with the anomalies observed on Am/Fm stars. They find that the precision of current abundances is insufficient to distinguish between models. More recently, Michaud et al. (2011) have studied the abundance anomalies of the mild Am star Sirius A. They find that except for B, N and Na, there is good agreement with the predicted anomalies but turbulent mixing or mass loss is required. It is not clear whether it is turbulence or mass loss which competes with diffusion to lower the abundance anomalies. For example, Vick et al. (2011) find that diffusion in the presence of weak mass loss can explain the observed abundance anomalies of pre-main-sequence stars. This is in contrast to turbulence models which do not allow for abundance anomalies to develop on the pre-main-sequence.
Most of the pulsational driving in δ Scuti stars is caused by the κ mechanism operating in the Heii ionization zone. Diffusion tends to drain He from this zone and therefore pulsational driving may be expected to be weaker or absent in Am/Fm stars (Baglin 1972). In fact, for many years it was thought that classical Am/Fm stars did not pulsate, 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 mission ) have shown that many Am/Fm stars do pulsate. Smalley et al. (2011), for example, found that about 200 Am/Fm stars out of a total of 1600 (12.5 percent) show δ Sct pulsations, but with generally lower amplitudes. They found that the pulsating Am/Fm stars are confined between the red and blue radial fundamental edges, in agreement with . While there are 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 Heii ionization zone is to reduce the width of the instability strip, the blue edge moving towards the red edge, eventually leading to the disappearance of the instability strip when He is sufficiently depleted (Cox et al. 1979). Turcotte et al. (2000) has discussed the effect of diffusion on pulsations in Am/Fm stars using the models by . One significant difference with earlier models is that a substantial amount of He remains in the Heii ionization zone. The blue edge of the instability strip for Am/Fm stars is sensitive to the magnitude of the abundance variations and is thus indicative of the depth of mixing by turbulence. Turcotte et al. (2000) predict that pulsating Am/Fm stars should lie in a confined region of the HR diagram close to the red edge of the δ Sct instability strip. However,  show that there is no relationship between the predicted Am/Fm instability strip and the actual location of these stars in the HR diagram.
A particularly interesting result of the pulsation analysis of Turcotte et al. (2000) is the prediction of long-period g modes in A-type stars. As the star evolves, the driving regions shift deeper into the star and the g modes become gradually more and more excited. Whereas p modes are stabilized through diffusion, g modes tend to be excited as a result of that process. It appears that diffusion may act to enhance driving of long-period g modes due to a significant increase in opacity due to iron-group elements. This may have a bearing on the fact that nearly all A-type stars observed by Kepler have unexplained low-frequencies (Balona 2011).
When dealing with objects with non-standard chemical composition, such as Am stars, it is crucial that the opacities are correctly calculated. This question has been investigated by several authors in recent years. These studies show that a non-standard chemical composition of the stellar atmosphere alters the flux distribution of the star or modifies the profiles of the Balmer lines (Leone & Manfré (1997), Catanzaro, Leone & Dall (2004)). Therefore a determination of T eff and log g based on a comparison between observed and computed Balmer-line profiles will not be correct unless one takes into account the metallicity of the star. Thus, even estimates based on standard analysis of the spectra may be in error when applied to Am/Fm stars.
In this paper, we investigate the determination of effective temperature and surface gravity of the Am star HD 27411 (HR 1353, A3m) using spectra in the ESO archives. The purpose is to determine whether the stellar parameters of this star agree with those obtained from Strömgren photometry and hence to test the reliability of the effective temperature calibration applied to Am/Fm stars. The star was used by Ryabchikova, Kochukhov & Bagnulo (2008) as a comparison in their study on the calcium stratification in Ap stars. HD 27411 is not known to pulsate. However, as we know from Kepler observations, pulsations in A and F stars with amplitudes too low to be detected from the ground are common.
Atmospheric models obtained with ATLAS9 (Kurucz 1993) use precomputed line opacities in the form of opacity distribution functions (ODFs). These are tabulated for multiples of the solar metallicity and for various microturbulent velocities. This approach allows very fast computation of model atmospheres, but with very little flexibility in choice of chemical profile and microturbulent velocity. While this is satisfactory for most applications, it fails for chemically peculiar stars where a non-standard chemical composition profile is required. This can be done with ATLAS12 (Kurucz 1997), which is essentially identical to ATLAS9, but uses the opacity sampling (OS) method to evaluate line opacities. In this study we compare the abundances of HD 27411 obtained with both codes to determine if the use of ATLAS12 is essential.
The result that Am stars are not confined to particular region of the δ Sct instability strip depends, to a large extent, on effective temperatures and luminosities estimated from Strömgren photometry (Smalley et al. 2011). It is not clear whether the calibration, derived from normal AF stars, can be applied to Am/Fm stars. In this paper we use synthetic Strömgren photometry applied to models of Am/Fm stars to investigate the reliability of fundamental parameters estimated from the photometry. Finally, we discuss the relative numbers of pulsating and non-pulsating Am stars and compare these to the relative numbers of δ Scuti and constant stars in the instability strip. From this comparison, one can deduce the effectiveness of pulsational driving in the Heii ionization zone and compare the He abundance to that expected from diffusion calculations.  Table 2.

OBSERVATION AND DATA ANALYSIS
The spectrum of HD 27411 is available in the ESO archive as a part of the UVES Paranal Observatory Project (UVES POP), which aims to create a library of high-resolution spectra across the HR diagram (Bagnulo et al. 2003). The spectrum was obtained in 2002, September 18 with a resolving power of R = 80 000. In order to determine the optimal parameters, we minimize the difference between the observed and synthetic spectrum. Thus we minimize where N is the total number of points, I obs and I th are the intensities of the observed and computed profiles, respectively, and δI obs is the photon noise. Synthetic spectra were generated in three steps. Firstly, we computed a model atmosphere using the ATLAS9 code. The stellar spectrum was then synthesized using SYNTHE (Kurucz & Avrett 1981).
Finally, the spectrum was convolved with the instrumental and rotational profiles.
To decrease the number of parameters, we computed the ve sin i of HD 27411 by matching synthetic line profiles from SYNTHE to a number of metallic lines. The Mgi triplet at λλ5167-5183Å is particularly useful for this purpose. The best fit was obtained with ve sin i = 20.5 ± 0.5 km s −1 . This value is in good agreement with ve sin i = 20.4 ± 0.4 km s −1 by Diaz et al. (2011).
To determine stellar parameters as consistently as possible with the actual structure of the atmosphere, we performed the abundance analysis by the following iterative procedure: (i) T eff is estimated by computing the ATLAS9 model atmosphere which gives the best match between the observed H δ , Hγ , H β , and Hα line profiles and those computed with SYNTHE. log g is estimated by matching the observed and calculated profiles of the Mgi triplet at λλ 5167- 5183Å which is extremely sensitive to gravity. This leads to T eff = 7600 ± 150 K, log g = 4.0 ± 0.1, and ODF = [+0.5].
(ii) The microturbulent velocity, ξ, is determined independently from three sets of spectral lines: 71 lines from Fei, 15 lines from Feii, and 24 lines from Nii. For this purpose we used all lines with equivalent width (EW) > 10 mÅ. In particular, ξ is computed by requiring that the derived abundances do not depend on the measured equivalent widths. To convert equivalent widths to abundances we used the WIDTH9 code (Kurucz & Avrett 1981). Values of ξ, the abundance and the radial velocity obtained for each ion are listed in Table 1. The adopted microturbulence is in agreement with Landstreet et al. (2009) (see Fig. 2 of their paper). The effective temperature is in agreement with the equilibrium condition between Fei and Feii, since the iron abundances derived separately from these two different ionization stages are in good agreement.
(iii) The projected rotational velocity is relatively high. To overcome line blending problems, we divided the spectrum into a number of sub-intervals ≈25Å wide. For each interval we performed a separate synthesis analysis. We used the abundances of Fe and Ni given in Table 1 as starting values in this procedure. The atomic parameters adopted in this analysis are from Kurucz & Bell (1995) with line lists subsequently updated by Castelli & Hubrig (2004). The adopted abundances, shown in the second column of Table 2, are weighted averages expressed in the usual form log N el /NTot.
Values of T eff , log g, ξ and individual abundances estimated in this way were then used as initial guesses for starting another iterative procedure based on the ATLAS12 code. The best fit was obtained after three iterations and led to the following parameters: T eff = 7400 ± 150 K, log g = 4.0 ± 0.1, ξ = 4.2 ± 0.3 km s −1 and ve sin i = 20.5 ± 0.5 km s −1 . The corresponding abundances are shown in the second column of Table 2. Ryabchikova, Kochukhov & Bagnulo (2008) analyzed HD 27411 in a study of Ap stars and derived the following parameters: T eff = 7650 K, log g = 4.0, ve sin i = 18.5 km s −1 , and ξ = 2.5 km s −1 . Considering the experimental errors, these values are in agreement with ours.
The fits between the observed and synthetic Balmer lines are shown in Fig. 1. The determination of surface grav- Figure 3. Location of HD 27411 in the HR diagram together with evolutionary tracks and isochrones for log t ranging from 8.87 to 8.95 (step 0.02 and t in yrs). Asterisks are the pulsating AmFm stars taken from Smalley et al. (2011). The gray area is the approximate location of pulsating Am star models incorporating heavy-metal diffusion .
ity was constrained by using the Mgi triplet at λλ 5167-5183 A, as shown in Fig. 2. Errors in T eff and log g were estimated by the change in parameter values which leads to an increase of χ 2 by unity (Lampton et al. 1976).

FUNDAMENTAL ASTROPHYSICAL QUANTITIES
If we adopt T eff = 7400 ± 150 K and log g = 4.00 ± 0.10 from our spectroscopic analysis, we may use the relationships by Torres et al. (2010) to derive log L/L⊙ = 0.99 ± 0.12. These relate the mass and radius of a star to the effective temperature and gravity through empirical calibrations. The greatest source of uncertainty is the surface gravity determination. The Hipparcos parallax for HD 27411, π = 11.13 ± 0.38 (Van Leeuwen 2007), is useful in refining the location of the star in the HR diagram. We show below that some caution is required in estimating reddening in Am/Fm stars and that HD 27411 is not significantly reddened. We therefore adopt V0 = 6.075, which gives an absolute magnitude MV = 1.31 ± 0.08 where the error is derived from the error in the parallax. If we adopt the bolometric correction BC = 0.051 derived from Balona (1994), we have M bol = 1.36 ± 0.09. Using M bol,⊙ = 4.74 (Drilling & Landolt 1999), we obtain log(L/L⊙) = 1.35±0.07. From the luminosity and using T eff = 7400 K, we obtain R/R⊙ = 2.88 ± 0.10. The surface gravity obtained by using the parameters derived from the parallax and assuming a mass of about 2.17 ± 0.05 M⊙ is log g ≈ 3.9 ± 0.1. All the astrophysical quantities derived here are summarized in Table 3.
The location of the star in the HR diagram, together with some evolutionary tracks computed for nonsolar metallicity Z = 0.03 (Girardi et al. 2000), is shown in Fig. 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 follows from our abundance analysis, and Z=0.03 is the nearest Table 2. Comparison among atmospheric parameters and abundances derived by ATLAS9 modeling and by ATLAS12 approach. The measurement without error is to be considered only as upper limit. In the last column we reported abundances derived with NLTE approach. All the abundances are expressed in the usual form log N el /N Tot .
It is well known that the vast majority of Am stars are binaries. There are few radial velocity measurements of HD 27411 in the literature. We could only find three measurements in Buscombe (1963): +17, +34 and −53 km s −1 . From our spectrum, we derived a radial velocity RV = +40.6 ± 0.3 km s −1 , which is a weighted average of the single velocities derived by converting the shift between observed and theoretical λc from the species reported in Tablle 1. The scatter in these values does, indeed, suggest that HD 27411 is a binary. If so, then the companion is probably much fainter than the primary, otherwise one may expect to see some evidence in the spectrum.

ABUNDANCES
In Fig. 4 we compare the LTE abundances derived from model atmospheres computed using ATLAS9 and AT-LAS12. It is evident that there is good agreement in the abundances derived with the two different codes. There are some very small differences for Na, V, Zr and Nd, but these are only 0.1 dex or less. Thus we may use the faster ATLAS9 code with confidence. In Fig. 5 we show the abundances relative to solar standard abundances (Grevesse et al. 2010). The chemical pattern displayed here is typical of that observed in Am stars, i.e. an underabundance of C, N, O, Ca and Sc and a general increasing overabundance for heavy elements.
The atmospheric abundance of Li is interesting in the context of diffusion. Burkhart & Coupry (1991) and Burkhart et al. (2005) find that, in general, the Li abundance in Am stars is close to the cosmic value (log NLi/NTot ≈ −9.04 dex), although some Am/Fm stars appear to have an underabundance of Li. Normal A-type stars in the range 7000 < T eff < 8500 K appear to have a higher Li abundance, i.e. log NLi/NTot ≈ −8.64 dex, (Burkhart & Coupry 1995).
To determine the Li abundance, we used the Lii λ6707 A line, taking into account the hyperfine structure (Andersen, Gustafson & Lambert 1984). The abundance that gives the best fit is log NLi/NTot = −8.42±0.10, which is closer to the abundance in normal A stars and agrees with the average Li abundance of three cluster Am/Fm stars observed by Fossati et al. (2007).  predict abundances as a function of stellar age and effective temperature using their models of diffusion. Fig. 14 of their paper allows us to estimate the predicted abundances for a star with a given T 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 models in , but we will assume that models of 670 Myr still give a fair approximation of the abundances. For T eff = 7400 K, which is our best estimate for HD 27411, the models by  predicts underabundances ranging from -0.3 dex to -0.1 dex for C, N, O, Na, Mg, K, and Ca. For Si and S the abundances are normal, while overabundances of about 0.1-0.8 dex are found for for Li, Al, Ti, Cr, Mn, Fe, and Ni. Inspection of their figure reveals that for Na, Mg, Al, Si, S, Ca, Ti, Cr, Mn, and Fe, the abundance anomaly is approximately constant with age and depends only on the turbulence. The abundances of Li, C, N, and O vary with age. Fig. 5 shows the abundances of the elements at 670 Myr predicted by  compared with our abundances. There is indeed good agreement for Li, C, N, O, Mg, K, Ca, Ti, Mn, Fe, and Ni, but abundances of Na, Al, Si, S, and Cr are somewhat discrepant. Similar discrepancies for Na and S were found by Fossati et al. (2007) for the Am star HD 73730. From the NLTE analysis of the S abundance by Kamp et al. (2001), Fossati et al. (2007) concluded that NLTE effects should be taken into account to determine whether this resolves the discrepancy with diffusion predictions.
Following this idea, we performed a NLTE analysis on Na, Al, Si, S, and Cr, to derive their abundances. We used the same technique of matching predicted and observed line profiles, but in this case the NLTE line profiles were computed with version 43 of SYNSPEC (Hubeny & Lanz 2000). This code reads the same input model atmosphere previously computed using ATLAS12 and solves the radiative transfer equation, wavelength by wavelength in a specified spectral range. SYNSPEC also reads the same Kurucz list of lines that we used for determining metal abundances. SYNSPEC allows one to compute the line profiles by using an approximate NLTE treatment, even for LTE models. This is done by means of second-order escape probability theory (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 abundances by factors ranging from 0.23 dex (S) to 0.39 dex (Al). As can be seen from Fig. 5, the NLTE calculations bring the observations closer to the diffusion predictions by . In fact, there is no longer any discrepancy in abundances within the observational errors.

EFFECT OF LINE BLANKETING ON THE PHOTOMETRY
In order to investigate the effect of line blanketing on the Strömgren colour indices, we used the method of synthetic photometry. For this purpose we computed the spectrum of a star at different effective temperatures with abundances shown in Table 2. We used the abundances given by the ATLAS12 models modified by NLTE where necessary. The spectra were calculated using SPECTRUM, version 2.76e 1 (Gray & Corbally 1994). Synthetic spectra with normal and peculiar abundances were calculated for 6000 T eff < 10 000 K and log g = 4.00. In all cases the microturbulence velocity was set to ξ = 4 km s −1 . These spectra were convolved with standard uvbyβ transmission functions to calculate synthetic Strömgren indices. It should be noted that not all Am/Fm stars will have the same abundance anomalies as HD 27411. Hence the results described here are only indicative of what might be typical in Am/Fm stars. Individual Am/Fm stars will have different abundances and different line blanketing.
In computing these synthetic Strömgren indices, it is necessary to identify a particular model with a real star in order to determine the zero points. We chose a model of Vega (b − y = 0.003, m1 = 0.157, c1 = 1.088, β = 2.903) for this purpose. Comparison of the synthetic b − y as a function of β with the standard relations of Crawford (1975) shows that the β zero point required a further correction of -0.04. The synthetic colours for normal and Am/Fm stars are listed in Table 4. Comparison of indices for models with standard solar abundance and the abundances of Table 2 are shown in Fig. 6. Various colour-colour diagrams derived from the synthetic colours are shown in Fig. 7 together with reddening lines. The reddening lines are from Crawford (1976): Also shown are the locations of HD 27411. It is clear that the star lies nicely on the synthetic relations given by the enhanced abundances and that the star is unreddened or only very slightly reddened. It is also clear that in determining the reddenings of Am/Fm stars it is wise to avoid using m1 and u − b. The c1/b − y relations for Am/Fm abundances is almost the same as for normal abundances and it is preferable to use this diagram to deduce the reddening correction. Assuming that HD 27411 is unreddened and matching the observed indices with those for modified abundances in Table 4 gives T eff = 7600 K. The β index is correlated well with effective temperature for T eff < 8000 K and is practically unaffected by line blanketing. It is weakly sensitive to surface gravity, particularly for the hotter stars. b − y is correlated with effective temperature but is affected by blanketing for the cooler stars. As can be seen from Fig 6, the m1 index is severely affected by blanketing. The c1 index for Am/Fm stars is nearly always smaller than for normal stars. This index measures the strength of the Balmer discontinuity (and hence the surface gravity), but it is clearly not entirely free of blanketing effects.
In estimating the absolute magnitudes, MV , of F stars, Crawford (1975) defines, first of all, a relationship for stars on the ZAMS as a function of b−y, MV = MV (ZAM S, b−y). The absolute magnitude for a star above the ZAMS is calculated from the value of δc1 = c1 − c1(ZAM S), i.e. the difference between the measured c1 and the value of c1 on the ZAMS at the given b − y. Since there are significant line blanketing effects on c1 for Am/Fm stars, their absolute magnitudes derived in this way are probably not free of systematic errors. We derived MV using the data of Table 4 for stars with solar abundance and with the Am abundance using the calibration of Crawford (1975). We find that on average the Am stars are estimated to be about 1.2 magnitudes fainter than normal stars of the same effective temperature and gravity. This is due to the systematically lower values of c1 in the Am star models. Table 5 lists Am stars which have good parallaxes. The general trend of lower luminosities derived from Strömgren photometry is apparent.
From this exercise we conclude that although the effective temperatures of Am/Fm stars derived from Strömgren photometry are probably reliable, the absolute magnitudes   (2000) are the best models presently available for Am/Fm stars. The models seem to be able to predict the abundances in these stars rather well, but we need to bear in mind that this Table 6. The numbers of all stars in the given effective temperature range, N (All), and the number of δ Sct stars in that range, N (δ Sct), and the corresponding percentage is given. The first block refers to Kepler δ Scuti stars with maximum amplitude exceeding 1.5 mmag. The second block refers to all Am stars and the pulsating Am stars in the given temperature range. is achieved because of adjustable free parameters to describe the turbulence. We still do not know if the mechanism competing with diffusion is turbulence, mass loss or some other factor. What we do know is that the current description of Am stars is in trouble because it fails to account for the wide distribution of pulsating Am stars in the δ Sct instability strip Smalley et al. 2011). One question that is of interest is the fraction of Am stars that pulsate. To answer this question we have to define what we mean by "non-pulsating". Clearly, a star could be pulsating but with amplitudes too small to be visible from the ground. Balona & Dziembowski (2011) discussed this issue in the context of Kepler observations which, of course, allow pulsations to be detected at the micromagnitude level. They deduced that the fraction of pulsating stars in the δ Sct instability strip is surprisingly low. There is clearly some damping mechanism which is currently not understood. The fraction of δ Sct stars in the instability strip varies with effective temperature, but does not exceed about 50 percent.
We can answer this question for Am stars only in part because we do not have a sufficient number of Am stars observed at the micromagnitude level. In order to compare these 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 with amplitudes over 1.5 mmag. We chose this minimum amplitude as roughly representative of the detection limit in the catalogue of pulsating Am stars in Smalley et al. (2011). The percentage of Kepler δ Sct stars with this minimum amplitude relative to all stars in a particular temperature range is shown in Table 6.
We can now compare this distribution of ordinary δ Sct stars with the distribution of pulsating Am stars in Smalley et al. (2011). We used the catalogue of Figure 8. The percentage of δ Scuti stars relative to all stars in the given effective temperature range is shown as the solid line histogram. The dashed line histogram is the percentage of pulsating Am stars relative to all Am stars in the given temperature range.