A&A 480, 811-823 (2008)
DOI: 10.1051/0004-6361:20077834
T. Ryabchikova1,2 - O. Kochukhov3 - S. Bagnulo4
1 - Department of Astronomy, University of Vienna, Türkenschanzstraße 17, 1180 Vienna, Austria
2 -
Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya 48, 109017 Moscow, Russia
3 -
Department of Physics and Astronomy, Uppsala University, 751 20 Uppsala, Sweden
4 -
Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland
Received 9 May 2007 / Accepted 31 December 2007
Abstract
Aims. We have completed an accurate investigation of the Ca isotopic composition and stratification in the atmospheres of 23 magnetic chemically peculiar (Ap) stars of different temperature and magnetic field strength.
Methods. With the UVES spectrograph at the 8 m ESO VLT, we have obtained high-resolution spectra of Ap stars in the wavelength range 3000-10 000 Å. Using a detailed spectrum synthesis calculations, we have reproduced a variety of Ca lines in the optical and ultraviolet spectral regions, inferring the overall vertical distribution of Ca abundance, and have deduced the relative isotopic composition and its dependence on height using the profile of the IR-triplet Ca II line at 8498 Å.
Results. In 22 out of 23 studied stars, we found that Ca is strongly stratified, being usually overabundant by 1.0-1.5 dex below
,
and strongly depleted above
.
The IR-triplet Ca II line at
8498 Å reveals a significant contribution of the heavy isotopes 46Ca and 48Ca, which represent less than 1 % of the terrestrial Ca isotopic mixture. We confirm our previous finding that the presence of heavy Ca isotopes is generally anticorrelated with the magnetic field strength. Moreover, we discover that in Ap stars with relatively small surface magnetic fields (
4-5 kG), the light isotope 40Ca is concentrated close to the photosphere, while the heavy isotopes are dominant in the outer atmospheric layers. This vertical isotopic separation, observed for the first time for any metal in a stellar atmosphere, disappears in stars with magnetic field strength above 6-7 kG.
Conclusions. We suggest that the overall Ca stratification and depth-dependent isotopic anomaly observed in Ap stars may be attributed to a combined action of the radiatively-driven diffusion and light-induced drift.
Key words: stars: abundances - stars: atmospheres - stars: chemically peculiar - stars: magnetic fields
After the pioneering work by Michaud (1970), atomic diffusion in stellar envelopes and atmospheres has been recognized as the main process responsible for the atmospheric abundance anomalies in the peculiar stars of the upper main sequence. Due to their unique characteristics, such as an extremely slow rotation, strong, global magnetic fields, and the absence of convective mixing, magnetic, chemically-peculiar (Ap and Bp) stars exhibit the most clear manifestation of diffusion effects and thus represent privileged laboratories for investigation of chemical transport processes and magnetohydrodynamics.
Detailed diffusion calculations performed for a set of chemical elements in the atmospheres of
magnetic peculiar stars predict separation of chemical elements over the stellar surface and with
height in stellar atmosphere (abundance stratification). These theoretical predictions can be
directly tested through the comparison with empirical maps of chemical elements inferred from
observations. For a small number of elements, including Ca, an effect of the vertically-stratified
element distribution on the spectral-line profiles was demonstrated in early studies (Borsenberger
et al. 1981). However, the absence of high-resolution, high signal-to-noise spectroscopic
observations did not allow a robust comparison between observations and theoretical diffusion
modelling. This step was achieved by Babel (1992), who calculated the Ca abundance
distribution in the atmosphere of magnetic Ap star 53 Cam and showed that the unusual shape of
Ca II K line - a combination of the wide wings and extremely narrow core
(Babel 1994; Cowley et al. 2006) - is a
result of a step-like Ca distribution with an abundance decrease at
.
Following Babel, the step-function approximation for the abundance distributions was employed in
many stratification studies based on the observed profiles of spectral lines
(Savanov et al. 2001;
Bagnulo et al. 2001; Wade et al. 2003;
Ryabchikova et al. 2002,2005,2006; Glagolevskii et al. 2005;
Cowley et al. 2007).
Table 1: Fundamental parameters of the program stars.
Ca has been found to be stratified in almost the same way as in 53 Cam (enhanced concentration of Ca
below
and its depletion above this level) in all stars for which
stratification analyses have been performed:
CrB (Wade et al. 2003),
Equ
(Ryabchikova et al. 2002), HD 204411 (Ryabchikova et al. 2005), HD 133792
(Kochukhov et al. 2006a) and HD 144897 (Ryabchikova et al. 2006). In addition to
remarkable diffusion signatures, recently another Ca anomaly was detected, first in the spectra of
the Hg-Mn stars by Castelli & Hubrig (2004) and then in Ap stars by Cowley & Hubrig
(2005). These authors found a displacement of the lines of Ca II IR triplet due to
a significant contribution from the heavy Ca isotopes.
Ryabchikova, Kochukhov & Bagnulo (see review paper by Ryabchikova 2005) were
the first to apply spectrum synthesis calculations to investigate the effects of Ca isotopes on the
calcium-line profile shape in magnetic CP stars.
In particular, we have demonstrated the general anticorrelation
between the presence of heavy Ca and magnetic field strength: in Ap stars the
contribution of heavy Ca isotopes decreases with the increase of the field modulus, and disappears
when the field strength exceeds
3 kG.
Cowley et al. (2007) have come to a similar conclusion, but with reservations.
In the present paper we summarise our detailed analysis of the vertical stratification of Ca
abundance in the atmospheres of magnetic Ap stars of different temperatures and
magnetic field strengths. We combine this vertical Ca mapping with the analysis
of the Ca isotopic anomaly and its dependence on height, based on the spectrum synthesis modelling
of the IR triplet Ca II line at 8498 Å. Our study is the first to present a
homogeneous and systematic determination of the vertical stratification of a given element in
the atmospheres of a large number of stars, enabling us to study the signatures of
atmospheric atomic diffusion in the presence of strong magnetic field as a function of stellar
parameters and magnetic field intensity.
Our paper is organized as follows. In Sect. 2 we describe spectroscopic observations and the data reduction. Determination of the stellar atmospheric parameters is detailed in Sect. 3. Sections 4-6 present our methodological approach to magnetic spectrum synthesis, determination of Ca stratification and the study of Ca isotopic composition. Our findings are summarised in Sect. 7 and are discussed in Sect. 8.
Twenty-three slowly rotating Ap stars were chosen for the Ca stratification analysis. The list of program stars is given in Table 1. In addition, three stars, Procyon (=HD 61421, spectral type F5), HD 27411 (=HIP 20106, spectral type A3m), and HD 73666 (=40 Cnc, spectral type A1 V) were used as standards for the Ca isotopic study. Of the 23 magnetic Ap stars included in our study, 12 stars show high-overtone acoustic p-mode pulsations and thus belong to the group of rapidly oscillating Ap (roAp) stars.
We note that metallic-line stars show signatures of strong turbulence and convection in their atmospheres (Landstreet 1998; Kochukhov et al. 2006b). Theoretical diffusion models for Am stars (e.g. Michaud et al. 2005) achieve reasonable success in reproducing the surface abundance patterns assuming full mixing of the outer envelope. Thus, despite non-solar abundances, strong mixing inhibits development of the vertical chemical gradients in the line-forming region and for this reason Am star HD 27411 can be considered as a comparison object in the context of the present investigation.
For the majority of our targets, high-resolution, high signal-to-noise-ratio spectra were obtained
with the UVES instrument (Dekker et al. 2000) at the ESO VLT in the context of program
68.D-0254. The observations were carried out using both available dichroic modes (standard
settings 346+580 nm and 437+860 nm). In both the blue arm and the red arm the slit width was set
to 0.5
,
for a spectral resolution of about 80 000. The slit was oriented along
the parallactic angle, in order to minimize losses due to atmospheric dispersion. Almost the full
wavelength interval from 3030 to 10 400 Å was studied except for a few small gaps, the largest of which was at 5760-5835 Å and 8550-8650 Å. In addition, there are several gaps, approximately 1 nm wide, due to the lack of overlap between the échelle orders in the 860U setting.
Spectra of HD 24712 and HD 61421 (Procyon) were acquired with the UVES at VLT as part of the
UVESpop project (Bagnulo et al. 2003a).
The UVES observations of the magnetic Ap star
HD 66318 employed in our paper were described by Bagnulo et al. (2003b). All three stars
were observed using the same instrumental settings as the Ap targets from our main data set.
A spectrum of HD 73666 was obtained with the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii
Telescope and analysed to determine chemical abundances by Fossati et al. (2007). A reduced spectrum was kindly provided to us by these authors.
The UVES spectra have been reduced with the automatic pipeline described in Ballester et al. (2000). For all settings, science frames are bias-subtracted and divided by the extracted flat-field, except for the 860 nm setting where 2D (pixel-to-pixel) flat-fielding was applied to better correct for the fringing effects. Because of the high flux of the spectra, we used the UVES pipeline average extraction method.
Due to the gaps in spectral coverage, only one line of the Ca II IR triplet,
8498 Å, was observable for all stars and can be used for modelling. This line is
generally the weakest of the three IR triplet transitions, which facilitates quantitative
analysis, especially in cooler stars where the triplet Ca II lines become particularly
strong.
All three lines of the Ca II IR triplet overlap with the hydrogen Paschen lines, which become very prominent in the spectra of hotter Ap stars (see Fig. 1). The 8498 Å line is located further away from the centre of the nearest Paschen line (P16) than the other two lines of the IR triplet. The hydrogen line blending for this Ca II transition is also weaker than for the other two Ca II lines. Moreover, being the weakest among three IR triplet lines the 8498 Å line is less dependent on the accuracy of Stark and Van der Waals broadening parameters. These circumstances suggest that the Ca II 8498 Å line is most suitable for detailed modelling.
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Figure 1:
Synthetic spectra calculated with different treatment of the overlapping hydrogen-line opacity. Usual calculation ( HLINOP routine, dashed line) is compared with
spectrum synthesis based on the occupation probability formalism
( HBOP routine, solid line). In both cases, ATLAS9 model atmosphere with
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The studied Ca II line is close to the gap in the wavelength coverage of the UVES setting employed. An additional difficulty arises due to the broad overlapping absorption produced by the Paschen lines. These properties of the data complicate continuum normalization in the region around Ca II 8498 Å. In fact, with the available data, we are generally unable to rectify the spectra in the usual manner. For each star, observations were instead adjusted to match calculated Paschen line spectrum in a small region close to the P16 line. This procedure was completed in two stages. First, a high-order spline function was employed to trace the wings of the hydrogen line, and observations were divided by this fit. Secondly, observed spectra were multiplied by the theoretical hydrogen line spectrum calculated using individual stellar atmospheric parameters and hydrogen line opacity described in Sect. 4.
For most program stars spectral coverage of our UVES spectra precluded analysis of the two stronger lines of the IR triplet, Ca II 8542 and 8662 Å. However, for one of the targets, HD 24712, we have investigated these lines using complementary observations obtained with the ESPaDOnS instrument at CFHT. The ESPaDOnS spectrum HD 24712 is the average of 81 time-resolved observations of this star analyzed by Kochukhov & Wade (2007). We refer to this paper for the details of reduction of these data. Unlike the UVES spectrum of HD 24712, the ESPaDOnS data were collected close to the phase of magnetic maximum (JD 2 453 744.71-2 453 744.83).
Fundamental parameters of the program stars are provided in Table 1. For most stars
effective temperatures
and surface gravities
g were taken from the most recent studies
(references are provided in the last column of Table 1). For HD 965, HD 47103,
HD 118022 and HD 134214 atmospheric parameters were derived using the Strömgren photometric
indices extracted from the catalogue of Hauck & Mermilliod (1998). We used calibrations
by Moon & Dworetsky (1985) and by Napiwotzki et al. (1993) as implemented in the
TEMPLOGG code (Rogers 1995). For HD 111133 the effective temperature was taken from Kochukhov & Bagnulo (2006), while other parameters were derived in the present study. For HD 75445, HD 176232 and
HD 203932 effective temperatures were further refined by fitting the H
profile.
This resulted in a small correction relative to the published
values.
The mean surface magnetic fields
were derived using spectral lines which exhibit resolved and
partially-resolved Zeeman splitting patterns. In all stars, rotational velocities were estimated
by modelling profiles of the magnetically-insensitive Fe I lines at
5434.5
and 5576.1 Å. Model atmospheres for all program stars were calculated with the ATLAS9
code (Kurucz 1993), employing opacity distribution functions (ODFs) with an enhanced
metallicity. For stars with especially strong magnetic fields we used ODFs with a non-zero
pseudo-microturbulence velocity in order to simulate the modification of the line opacity due to
magnetic intensification of spectral lines. All spectrum synthesis for
magnetic stars employed zero microturbulence. For comparison stars, we have adopted the following
values:
km s-1 for Procyon (Allende Prieto et al. 2002),
1.9 km s-1 for HD 73666 (Fossati et al. 2007) and 2.5 km s-1 for HD 24711 (determined in this paper).
Analysis of the Ca stratification and isotopic composition was based on detailed magnetic spectrum synthesis calculations with the SYNTHMAG code (Kochukhov 2007a). This program allows the polarized, radiative-transfer equation to be solved, and theoretical stellar spectra to be calculated in four Stokes parameters, for the prescribed model atmosphere and vertical distribution of any number of chemical elements. The SYNTHMAG calculations performed in this paper are based on a simplified model of the stellar magnetic field topology, characterized by a single value of the field modulus and a homogeneous field distribution over the surface of the star. When rotation-broadening is significant or the field is too weak, we assume purely radial-field orientation. In other cases the effective field orientation is inferred from the profiles of magnetically-sensitive lines and is parameterized with the ratio of the radial to azimuthal field components (see Table 1). Although undoubtedly rather simplified, this magnetic model is quite successful in explaining the shapes of resolved Zeeman split lines in the Stokes I spectra of many Ap stars (Kochukhov et al. 2002; Nielsen & Wahlgren 2002; Leone et al. 2003; Ryabchikova et al. 2006) and, in some cases, performs even better than low-order multipolar field geometries (Kochukhov 2007b).
In all spectrum synthesis calculations in this paper, we use zero microturbulence because the SYNTHMAG code models magnetic intensification by directly including magnetic-field effects in the solution of the polarized radiative transfer equation. The true microturbulence is thought be absent in Ap stars because kG-strength magnetic field is quite efficient in suppressing convective motions.
Here we analyse the target stars assuming a homogeneous distribution of Ca over their surfaces. This assumptions appears to be reasonable given a slow rotation of the majority of the targets. Moreover, no evidence of substantial horizontal Ca abundance gradients exist for any of the studied stars, although many of them were observed at high resolution more than once (e.g., Mathys et al. 1997; Ryabchikova et al. 2004b). The only star from our sample for which the Ca surface inhomogeneity was investigated previously, is HD 24712 (Lüftinger et al. 2007). The full range of the horizontal Ca abundance variation in this star is only 0.2 dex. The resulting effect on the Ca line profiles is negligible compared to the vertical abundance jump of more than 3 dex (see below). We also note that, even if hypothetical high-contrast Ca spots exist on the surface of some of our stars, their effect will be to weight our modelling results to specific surface areas. But none of the potential horizontal inhomogeneity effects can possibly mimic the stratification or isotopic anomaly studied here.
An important modification to the SYNTHMAG treatment of the hydrogen-line opacity was
introduced to improve analysis of the IR Ca II triplet lines. These Ca II
transitions blend with the high members of the Paschen series, which become prominent in Ap stars
with
K. The usual calculation of the overlapping hydrogen line wings, which
adds linearly opacities due to bound-free and bound-bound hydrogen opacity, becomes increasingly
inaccurate as one approaches the series limit. As illustrated in Fig. 1, this leads to a
spurious reduction in calculated fluxes. The correct treatment of the overlapping hydrogen-line
and continuous opacity should be done according to the occupation probability formalism (Daeppen
et al. 1987; Hubeny et al. 1994). This technique was implemented in SYNTHMAG
with the help of HBOP procedure, developed by P. Barklem at Uppsala Observatory
. This hydrogen opacity code, which also
incorporates previous developments in the hydrogen-line broadening theory
(Stehlé & Hutcheon 1999; Barklem et al.
2000), was applied for the spectrum synthesis of all stars in our sample. Figure 1
shows that correct treatment of the hydrogen opacity significantly reduces predicted Paschen-line
absorption at the position of the Ca II 8498 Å line analysed here.
Magnetic spectrum synthesis with SYNTHMAG was coupled with the vertical abundance mapping procedure DDAFIT, described by Kochukhov (2007a) and used previously by Ryabchikova et al. (2005,2006). This routine provides a graphical and optimization interface to SYNTHMAG, allowing the user to find parameters of a simple stratification model by fitting a large number of spectral lines of a given element.
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Figure 2: Comparison between the observed line profiles (symbols) of HD 176232 (10 Aql) and theoretical spectra calculated with the best-fitting stratified Ca abundance distribution (solid line) and with the homogeneous Ca abundance (dashed line). The plotted spectral windows show segments of the HD 176232 spectra used for determination of Ca stratification; symbols show actual observed points. |
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Before completing a detailed study of the IR Ca II 8498 Å line profile, one has to derive the vertical distribution of Ca abundance in the
atmospheres of Ap stars. Without this step, a quantitative analysis of the isotopic
anomaly is practically impossible because profiles of all strong Ca lines,
including the IR triplet, are dramatically affected by the vertical
stratification of this element. In all program stars Ca stratification was
derived using a set of spectral lines in the optical region, for which no
indication of the significant isotopic shifts exists.
In this way, we are able to decouple the stratification analysis from the study
of isotopic shifts. At this stage, we avoid using the Ca II 8498 Å line
because of the sensitivity to effective temperature error due to the
normalization method used (see Sect. 2).
Atomic parameters of the Ca lines are given in
Table 2. Stratification analysis requires high accuracy not
only for the oscillator strengths but also for the damping parameters, because
Ca has a tendency to be concentrated close to the photospheric layers where the
electron density is high. Accurate treatment of damping wings is particularly
important for the lines of ionized Ca. For the Ca II lines at
3158, 3933, 8248, 8254, 8498, 8912, 8927 Å the Stark damping constants
were taken from the paper by Dimitrijevic & Sahal-Bréchot (1993),
where semi-classical calculations as well as a compilation of the experimental
data was presented. For the rest of Ca lines the Stark damping constants
calculated by Kurucz (1993) were adopted. The oscillator strengths were
taken mostly from the laboratory experiments - these data were thoroughly
verified by the recent NLTE analysis of calcium in late-type stars (Mashonkina
et al. 2007). Because of the large range in effective temperatures and
magnetic field strengths, we could not use the same set of lines for all
stars.
Table 2: Atomic parameters of the spectral lines employed in the Ca stratification analysis.
The Ca stratification analysis was performed using the step-function approximation of the abundance distribution (for details see, e.g., Ryabchikova et al. 2005). This parameterized model of the vertical stratification is characterized by the upper and lower abundance values, as well as by the position and width of abundance jump. In each star these parameters are constrained by simultaneous fit to the profiles of many lines. These observational data are sufficient to constrain stratification parameters with a good precision.
We begin the stratification analysis of Ca by computing the optimal homogeneous
Ca abundance for a chosen set of spectral lines. In the DDAFIT
procedure, we then allow the parameters of the step-function to vary until a suitable fit of the
observed line-profiles is achieved. The outcome of this procedure is illustrated in
Fig. 2, where results of the stratification analysis for the set
of optical lines in HD 176232 (10 Aql) are displayed.
Figure 3 shows that stratified Ca distributions obtained for
HD 176232 and other cool Ap stars also dramatically improve the fit to
the strongest Ca II 3933 Å line compared to the spectrum synthesis with a
homogeneous Ca distribution. In Figs. 2 and 3
synthetic profiles
calculated with the uniform Ca distribution
are
shown by dashed lines while those calculated with the best-fitting stratified Ca
distribution are shown by the solid lines. Clearly, even the schematic Ca
stratification model used here provides a substantial improvement in the
agreement between observations and theoretical calculations.
We use a measure of standard deviation to characterize the quality of the fit. This
parameter is defined as the root-mean-square of the observed minus calculated spectrum, evaluated
on the wavelength grid of observations within the spectral windows covering
lines of interest (see Fig. 2). For HD 176232 and most other stars
the stratified Ca abundance yields roughly two times smaller value of
standard deviation than the homogeneous Ca distribution.
The final
Ca stratification model inferred for HD 176232 is illustrated in Fig. 4.
To verify that the step-function approximation provides a realistic description of the Ca distribution, we performed, for a few stars with weak magnetic fields (HD 133792, HD 176232, HD 203932), a stratification analysis using the Vertical Inverse Problem code, VIP. This program does not use any a priori assumptions about the shape of the vertical element abundance profile but currently cannot be applied to stars with a strong magnetic field (Kochukhov et al. 2006a). A comparison between the Ca distributions derived for HD 176232 with DDAFIT and with VIP is shown in Fig. 4. The same level of agreement was obtained for the two other stars.
However, despite general success of the DDAFIT modelling, in a few stars the step-function approximation could not provide an adequate description of the full set of spectral lines. The obvious reason is the use of normal non-magnetic stellar model atmosphere with a homogeneous element distribution for a star with abundance stratification, and a deviation of the Ca abundance distribution from the simple step-function form.
In cooler stars we do not systematically use the strongest Ca II 3933 Å line in the stratification analysis due to the difficulties of treating blends in the extended
wings and establishing continuum. The range of the formation depths of the remaining weaker
optical lines is different from the IR triplet lines of interest, therefore Ca abundance in
the upper atmospheric layers is poorly-constrained by the optical lines and may not be
accurate enough for the description of the cores of the IR Ca II triplet lines.
This is often reflected by a rather large formal error of the abundance in the upper layers
compared with
the corresponding error of the abundance in the lower layers. For several stars
(see Table 4) a less than 3
change of the Ca abundance in the upper layers
was introduced to fit the overall intensity of the IR triplet line cores.
In addition, for a few other stars further
improvement of the fit quality was possible by introducing a more complicated stratification
profile starting from the results obtained with DDAFIT. This step was performed
manually for 5 out of 23 Ap stars. In all the cases, when we have modified Ca stratification
determined with DDAFIT, the consistency of the altered vertical abundance profile with
all Ca diagnostic lines was verified.
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Figure 3: Comparison between the observed profiles (symbols) of the Ca II 3933 Å line and calculations with the stratified (solid line) and homogeneous (dashed line) Ca distributions for 3 program stars. The spectra of HD 24712 and HD 176232 are shifted downwards for display purpose. |
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The formal stratification analysis of the Am star HD 27411 (whose
is identical to that of HD 176232) and normal star HD 73666 (
= 9382 K) yields a 0.2 dex abundance jump,
which we consider to be insignificant.
The average Ca abundance
in both stars represents very well most of the lines, including the resonance Ca II 3933 Å line.
In both stars 0.1 dex lower abundance is required to fit the Ca II 3933 Å profile compared to
Ca II 8498 Å line.
This internal agreement is excellent considering difficulties in
continuum normalization. It confirms that the Ca abundance variation by several
dex over the vertical span of the Ap-star atmospheres is real.
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Figure 4: Vertical stratification and isotopic separation of Ca derived for HD 176232. The overall Ca abundance profile, inferred from the stratification analysis of optical lines, is shown with the solid line. The hatched areas demonstrate vertical separation of the light and heavy Ca isotopes required to fit the Ca II 8498 Å line. The dashed line shows the Ca distribution derived the with VIP code using the same set of lines. |
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Ca has six stable isotopes with atomic numbers 40, 42, 43, 44, 46, 48. In the terrestrial matter Ca mixture consists mainly of 40Ca (96.9 % according Anders & Grevesse 1989). Table 3 provides wavelengths of all Ca isotopes in the Ca II 8498 Å transition based on the isotopic shifts measured by Nörtershäuser et al. (1998). We list fractional oscillator strengths corresponding to the terrestrial isotopic mixture.
Isotopic shifts were also measured for the Ca II resonance lines at
3933 and 3968 Å (Mårtensson-Pendrill et al. 1992).
The wavelength shift between the 48Ca and
40Ca isotopes is -0.009 Å, and can be observed only for the Ca II 3933 Å line
core in hot stars with an especially significant contribution from the 48Ca isotope.
One star from our sample, HD 133792, shows an isotopic shift in the Ca II 3933 Å line.
Table 3:
Atomic data for the isotopic components of Ca II
8498 Å.
Using the terrestrial isotopic mixture, we calculated the profile of the Ca II 8498 line in the spectra of our reference stars, Procyon, HD 27411 and HD 73666. Comparison of the theoretical spectra and observations is illustrated in Fig. 5. Although in the Procyon spectrum our LTE calculations cannot provide a very good fit to the deepest part of the core, no wavelength shifts are detected in either star. At the same time, the observed profile of the Ca II line in the spectrum of one of our program stars, HD 217522, presented in Fig. 5 exhibits a complex structure and is clearly redshifted, with the strongest component coinciding in wavelength with the expected position of the heaviest Ca isotope. This is a signature of the Ca isotopic anomaly and, as we will show below, of the vertical separation of Ca isotopes.
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Figure 5: Comparison between the observed line profiles (symbols) of the Ca II 8498 Å line and calculations for the normal Ca isotopic mixture (solid line) in the spectra of Procyon, Am star HD 27411, and A1 V star HD 73666. The observed spectrum of the cool (HD 217522) and tepid (HD 133792) Ap stars, presented in the middle and bottom, clearly shows a displaced Ca II line core. The spectra are shifted downwards for display purpose. |
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Figure 6: Derivation of the isotopic composition and its height dependence for the Ca II 8498 Å line in HD 176232 (10 Aql). The three panels show the UVES observations (full circles) compared to various modelling attempts, as follows. a) Dashed line: theoretical spectrum obtained with a homogeneous Ca distribution. Solid line: theoretical spectrum calculated for a stratified Ca abundance. A terrestrial mixture of Ca isotopes is adopted for these computations. b) Solid line: theoretical spectrum obtained for a terrestrial Ca isotopic composition (same as panel a); Dashed line: theoretical spectrum obtained for a 50:50 ratio of 40Ca to 46Ca+48Ca. c) Solid line: the Ca II line profile computed for the best-fitting model of vertical isotopic separation (see Fig. 4). Dashed and dash-dotted lines show contributions of 40Ca and 46Ca+48Ca, respectively. The wavelength position of 40Ca and 48Ca is indicated in each panel. These plots show that an acceptable fit to the observations can only be achieved with a depth-dependent Ca isotopic mixture. |
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The core of the IR Ca II 8498 Å line is formed higher than any of the optical
lines, except Ca II 3933 Å. For most stars the Ca II
3933 Å line was not modelled in our stratification calculations. Therefore, Ca
abundance in the upper atmosphere of some stars may be somewhat uncertain, as all other optical lines are not
sensitive to the abundance variations above
to -2.5.
However, for the majority of our targets the Ca abundance in the
upper atmosphere, responsible for the strength of the Ca II 8498 Å line core, is
defined by the slope of the abundance gradient in the jump region. If the Ap atmospheric
structure is close to the normal ATLAS9 atmosphere adopted in our analysis, then the
Ca II 8498 Å line should be well-described by the Ca abundance distribution
derived from optical lines. Our calculations show that while it is correct for the observed total
intensity, in many of the program stars we cannot fit the line cores, which are often redshifted.
This situation is illustrated in Fig. 6a, where we compare the observed
spectrum of HD 176232 with the synthetic spectrum calculated for the terrestrial Ca isotopic
mixture and Ca abundance distribution (Fig. 4) derived from optical lines. One
immediately notices that while the line wings are explained by our calculations, the line core
cannot be fitted with the terrestrial Ca isotopic mixture.
Cowley & Hubrig (2005) showed that the red-shift of the Ca IR line core arises due to the heavy Ca isotopes and claimed that ``in extreme cases the dominant isotope is the exotic 48Ca''. A simple interpretation of the anomaly observed in the Ca II 8498 Å line core is to suggest that heavy Ca isotopes are strongly enhanced and even dominant throughout the atmospheres of some magnetic Ap stars. However, our magnetic spectrum synthesis calculations demonstrate that this hypothesis is incorrect. On the example of HD 176232 we can show that using a model with stratified Ca distribution found previously and assuming a depth-independent enhancement of 46Ca and 48Ca relative to 40Ca, the centre-of-gravity of the Ca II 8498 Å line core is shifted to the red, but the overall fit to the line profile does not improve considerably (Fig. 6b). In disagreement with observations, a constant overabundance of the heavy Ca isotopes gives rise to the red-shifted long-wavelength wing of the Ca II line.
Here we propose a different explanation of the Ca II 8498 Å line shape. Observations of HD 176232 and other stars with displaced Ca line core show a shallow line with wide wings at the position of 40Ca isotope, which means that this line component is formed in the lower atmospheric layers. On the other hand, at the position of 48Ca we see a sharp deep line, which is responsible for a characteristic steep intensity gradient in the red wing of the Ca II 8498 Å line. We derive the same result for all cool Ap stars with significant isotopic shifts of the Ca II line core. Given the Ca stratification inferred for all Ap stars, this deep component lacking developed wings can be explained by the absorption in the upper atmosphere, above the Ca abundance jump or in the outermost part of the transition region. Thus, observations of the Ca II 8498 Å line in Ap stars should be interpreted in terms of vertical separation of Ca isotopes in the stellar atmosphere.
If we separate 40Ca and the sum of 46Ca and 48Ca isotopes in the atmosphere of
HD 176232 as indicated in Fig. 4 (the boundary between heavy and light Ca is at
), a satisfactory agreement between the observed and calculated
spectra is obtained (see Fig. 6c). The dominant atmospheric constituent is
still the normal isotope 40Ca, but the shape of the Ca II 8498 Å line core is
influenced by the high-lying cloud of heavy Ca, in which 46Ca and 48Ca contribute
35% and 65%, respectively.
Thus, in our modelling of the Ca isotopic anomaly in Ap stars we adopt an initial model in which the total element abundance is given by the stratification profile obtained previously, while the vertical separation of the light and heavy Ca isotopes occurs nearly instantaneously and is characterized by a single transition depth, deduced from the Ca II 8498 Å line. Relative contributions of 46Ca and 48Ca to the heavy Ca layer in the upper atmosphere are also adjusted based on the Ca II IR triplet line.
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Figure 7: Comparison of the observed IR triplet lines (symbols) in the ESPaDOnS spectrum of HD 24712 and theoretical spectrum synthesis for the best-fitting stratified Ca abundance distribution (solid line) with Ca isotopic separation and with the stratified distribution of 48Ca only (dashed line). |
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Parameterization of the vertical separation of Ca isotopes that we adopt here is just one of several models possible. For instance, we find that an acceptable fit to the Ca II 8498 Å line in some of the target stars could be obtained with a model where 48Ca is homogeneously distributed while 40Ca is stratified. Such a model is achieved by placing the border between Ca isotopes horizontally rather than vertically in Fig. 4. We note that formally 48Ca is not anomalous: its relative-to-hydrogen abundance in all stars does not exceed an abundance in the normal solar Ca mixture. This model turns out to be nearly equivalent to the one we use because the boundary between the heavy and light Ca layers is usually located very close to the position of the Ca abundance jump. The 40Ca contribution still dominates in the lower atmosphere, whereas 48Ca contributes to the light absorption in the upper layers. However, for several stars where we need Ca enhancement in the uppermost layers, the model with homogeneously-distributed, heavy Ca isotopes clearly yields worse agreement with observations in comparison with the vertical separation model adopted in here.
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Figure 8: Ca stratification in the atmospheres of selected program stars. Upper panel: distribution of Ca in HD 66318, HD 75445, HD 134214, HD 166473 and HD 111133. For stars enriched in heavy Ca the filled circle indicates the bottom of the heavy Ca isotope layer. Lower panel: same for stars with complex distribution of Ca abundance with height (HD 965, HD 116114, HD 137909, HD 137949, HD 217522). |
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Our isotopic stratification model is based upon only one of the IR triplet lines. High-quality observations of the two other IR triplet lines are unavailable for the majority of our targets. For one of the cool Ap stars, HD 24712, we assessed the quality of the fit to all three Ca II lines using the spectrum obtained with ESPaDOnS at CFHT. These data were collected at the rotational phase different from that of UVES observations, therefore we have performed an independent Ca stratification and isotopic analysis for HD 24712 based on the ESPaDOnS spectrum alone. Figure 7 compares calculated and observed Ca II 8498 Å and 8662 Å line profiles. Because the Ca II 8542 Å line is close to the beginning of the spectral order, creating uncertainty in the continuum normalization, we did not include this line in the plot.
Of course, the proposed model of Ca isotopic separation is at best a crude approximation of potentially much more complex isotopic stratifications. However, we find that, for many stars, introducing a combination of stratification and isotopic segregation noticeably improves the fit to the IR triplet lines and provides direct evidence for the Ca isotopic separation in the atmospheres of Ap stars.
Finally, we note that the continuum normalization in the region
around IRT lines is indirectly based on the adopted effective temperatures, which may
introduce an additional uncertainty and sometimes lead to a poor fit in the line
wings. However, we have verified that even considerable
errors in
lead only to a small
change in the overall depth of the Ca II 8498 Å line computed for a given Ca
stratification. Since this line is located sufficiently
far from the H line core, its profile, especially the shape of the inner core region used
in the isotopic analysis, is generally not affected by the
errors.
The Ca stratification analysis described in Sect. 5 was applied to
all Ap stars included in our sample. The presence of a stratified Ca distribution
is inferred for all stars except the hot Ap star HD 170973,
where stratification appears to be negligible.
Table 4 provides parameters of the
step-function model distributions of Ca abundance. These vertical abundance profiles are
characterized by an abundance jump in the atmospheric region
,
a 1-1.5 dex overabundance deep in the atmosphere and a
strong Ca depletion above
.
The formal uncertainty of the stratification parameters is typically 0.3-0.7 dex,
0.1-0.3 dex and < 0.1 dex for
the upper abundance, lower abundance and the position of the Ca abundance jump, respectively.
The Ca stratification in the
atmospheres of selected program stars is shown in Fig. 8.
For several stars, we had to consider a more complex vertical distributions of Ca abundance.
Observations of HD 965, HD 137909, HD 137949 are better reproduced with an increase of Ca
concentration in the upper atmospheric layers above
.
Although seemingly
complicated, this picture does not contradict theoretical Ca diffusion calculations. Both
Borsenberger et al. (1981, Fig. 6) and Babel (1992) inferred an increase in Ca abundance in the uppermost layers that are above the main abundance jump. However, NLTE treatment of the Ca lines
formation is needed to investigate stratification of Ca in the upper atmospheric layers in more
detail. For two other stars, HD 116114 and HD 217522, a structure of the transition zone
somewhat more complex than a linear transition between two constant values is required to fit
observations. Figure 8 (lower panel) illustrates the final chemical stratification
profiles adopted for the five stars where Ca stratification deviates from a step-function profile.
We note that for all stars the DDAFIT inversion was performed on the original
column mass (
)
depth grids of the ATLAS9 models.
Table 4 provides the vertical stratification parameters converted to the
scale. In the cases when the transition zone is wide, extending to the
lower atmospheric layers, transformation between
the column mass and the standard optical depth scale becomes non-linear, which leads to a
distortion of the step-function shape (e.g., Ca distribution for HD 137949 in
Fig. 8).
For the same reason in some of the stars where this problem was encountered (e.g.,
HD 137949, HD 188041) the formal solution for the Ca distribution yields an unrealistically high Ca
abundance in the lower atmosphere. However, we find that in these objects the actual inferred
stratification profile often has a plateau with
in the layers
around
.
This value of the abundance gives the actual element concentration that influences
the Ca line formation. The formal high Ca abundance occurs far below the photosphere (e.g., the
bottom panel of Fig. 8 shows this situation for HD 137949). It does not influence
the observed Ca line profiles. Therefore, for all stars marked by a letter ``c'' in
Table 4 we assumed the Ca abundance at
as
,
modifying the position and the width of the abundance jump
correspondingly.
Table 4: Parameters of the Ca stratification and isotopic anomaly determined for magnetic CP stars.
Homogeneous determination of the calcium vertical distribution in a large number of magnetic
Ap stars allows us to search for possible dependence of diffusion signatures on the stellar
atmospheric parameters and magnetic field strength. However, except for the marginal tendency of
the Ca abundance in the upper layers to be higher in hotter stars, we found no clear
correlations between each of the four stratification parameters on the one hand, and
and
on the other. Although the qualitative form of the Ca stratification is the same in
all stars, indicative of a universal radiative diffusion process, the
observed star-to-star variation in stratification profiles appears to be irregular and unrelated
to any other stellar characteristic.
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Figure 9: Comparison of the observed (full circles) and calculated (lines) profiles of the Ca II 8498 Å line in a subset of program stars. Solid line shows theoretical calculations for the terrestrial Ca isotopic mixture and the Ca stratification derived from optical lines. The dashed line presents spectrum synthesis for the models with vertical separation of the Ca isotopes. The stars are arranged in order of increasing magnetic field strength. |
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The Ca isotopic analysis procedure outlined in Sect. 6 was applied to all stars
included in our paper. Table 4 lists the lower boundary
(uncertain to within 0.1 dex) of the heavy Ca
layer in the atmospheres of magnetic Ap stars for which the Ca II 8498 Å line
could not be reproduced with the terrestrial isotopic mixture. Our estimate of the
dominant contributor among different heavy Ca isotopes is also given. Out of 23 program stars, the
presence of heavy isotopes is established in 17 objects.
For three stars, HD 965, HD 137909, HD 137949, the modelling of the IR triplet line requires an increase of the Ca abundance in the upper atmosphere, above the abundance jump given by the simple stratification analysis. In these cases we attribute the high-lying cloud to heavy Ca.
Figure 9 compares theoretical spectrum synthesis calculations with observations
for a subset of 12 cooler (
9000 K) stars with different effective temperatures
and different magnetic field intensity.
The stars are arranged in order of increasing magnetic field strength. It is evident that
the presence of heavy Ca isotopes inversely correlates with magnetic field strength.
This effect is further illustrated in Fig. 11a, where we quantify
the detection of heavy Ca by the ratio of calculated equivalent widths of the
44Ca +46Ca +48Ca to 40Ca line components. In the stars
with small to moderate magnetic fields we clearly see a significant contribution of the
heavy isotopes 46Ca and 48Ca (large equivalent width ratio). This contribution decreases with the increase in
magnetic field strength. Even in HD 137909 (
CrB), with a mean magnetic field modulus of
= 5.4 kG, one still needs a small contribution of 48Ca, but under the assumption of
a specific Ca distribution shown in Fig. 8.
No evidence for the presence of heavy Ca is found in cool Ap stars with
kG.
Due to the temperature dependence of the Ca line intensity, we used a smaller number of lines for
stratification analysis of hot Ap stars (
> 9000 K). In these stars stratification is
defined mainly by the Ca II lines. Among the neutral Ca lines only the resonance
Ca I 4227 Å line could be utilized. The agreement of calculated and observed line
profiles is poorer for hot stars. However, the general anticorrelation between the presence of the
heavy Ca isotopes and magnetic field strength is still apparent (see Fig. 10). As in
cool stars, no evidence for the presence of heavy Ca is found in hot Ap stars with
kG.
The only exception is HD 170973, which has no observable magnetic field and shows no contribution of
the heavy Ca isotopes. We note that HD 170973 is also the only star for
which we find no evidence of Ca stratification.
This star also possesses the highest Ca abundance among the hot Ap stars in our sample.
Thus, it appears that the mechanism responsible for the accumulation of heavy Ca isotopes in the line-forming atmospheric region works more efficiently in stars with a small magnetic field strength. Figure 11 illustrates several other interesting relations between the Ca isotopic anomaly and stellar parameters that we have revealed in this study. The optical depth of the layer separating the heavy and light Ca clouds depends on the magnetic field strength. In stars with more intense fields heavy Ca isotopes tend to accumulate much higher in the stellar atmospheres (Fig. 11b). There is also an anticorrelation of the heavy Ca contribution and the total equivalent width of the Ca II 8498 Å transition (Fig. 11c), which implies that the efficiency of the isotope separation process depends on the total line intensity in cases where such separation exists.
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Figure 10:
Same as in Fig. 9 but for the stars with
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We find no difference between roAp and non-pulsating Ap stars (shown with different symbols in Fig. 11) regarding the presence of heavy Ca excess in their atmospheres and its correlation with the magnetic field strength and line intensity.
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Figure 11: Results of the analysis of Ca isotopic composition in Ap stars. a) Ratio of calculated equivalent width of the heavy and light Ca components of the 8498 Å line vs. magnetic field strength. b) Position of the boundary between the light and heavy Ca layers vs. magnetic field strength. c) The equivalent width ratio vs. the total equivalent width of the Ca II 8498 Å line. d) The equivalent width ratio vs. the optical depth of the boundary between the light and heavy Ca layers. In all plots different symbols correspond to Ap stars with detected presence of heavy Ca ( filled symbols) and those showing no heavy Ca isotopes ( open symbols), as well as to roAp ( circles) and non-pulsating Ap ( triangles) stars. |
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In this paper we have investigated the vertical stratification and isotopic anomaly of Ca in a large sample of cool magnetic Ap stars. Our study is the first to address the interesting problem of the presence of heavy Ca isotopes in chemically-peculiar stars with detailed polarized radiative-transfer calculations, which take into account the effects of the magnetic field and chemical separation in stellar atmospheres. We derive stratification of Ca for 23 Ap stars using a sample of Ca I and Ca II lines distributed over a broad spectral range. All but one program star clearly show signatures of the Ca stratification, whereas comparison stars reveal no inhomogeneities in the vertical Ca distribution when analysed with the same techniques and atomic data. Although our stratification modelling was based on a simplified step-function approximation and adopted a simplified homogeneous model for the magnetic field geometry, the inferred parameters of the vertical Ca distributions impose important observational constraints on radiation-diffusion process theory in stellar atmospheres.
Analysis of the IR Ca triplet line Ca II 8498 Å provided information on the relative contribution of different Ca isotopes. Spectrum synthesis calculations show that significant isotopic shifts observed in the core of Ca II 8498 Å cannot be attributed to the overabundance of heavy Ca isotopes throughout the whole stellar atmosphere. Instead, we show that the Ca line profile shape is consistent with the vertical separation of different Ca isotopes, with heavy Ca located in a cloud above the most abundant isotope 40Ca. Even though the presence of heavy Ca is prominent in the line core, the normal Ca isotope dominates the line wings and is more abundant in the lower atmosphere where the total Ca abundance is also much larger. Thus, our tentative model calls for a less extreme heavy Ca enrichment than was suspected in previous investigations limited to the centroid measurements of the Ca II 8498 Å line core.
Recently different stratification of He isotopes was found by Bohlender (2005) in the analysis of 3He and related stars. That paper used a similar approach to modelling chemical stratification, but addressed He vertical distribution only in hot non-magnetic, chemically-peculiar stars.
We have successfully used the model with Ca stratification and vertical isotopic separation to explain the appearance of the Ca II 8498 Å in all stars showing an excess of heavy Ca isotopes. The prominent anticorrelation between the presence of heavy Ca and magnetic field strength, first reported by Ryabchikova (2005), is confirmed and strengthened in the present paper. We find that only stars with sufficiently weak fields show traces of heavy Ca. According to our knowledge, this interesting relation is the only case when definite dependence of the chemical abundance characteristic on the magnetic field strength is found for Ap stars. Furthermore, we find that in stars with stronger fields the heavy Ca isotopes tend to accumulate higher in the atmosphere.
According to the results of our study, pulsating (roAp) and non-pulsating Ap stars are not distinguished by the characteristics of their Ca isotopic anomaly. Both groups of stars are equally likely to show an excess of heavy Ca, and follow the same trend of the heavy isotope contribution versus magnetic field strength and Ca II 8498 Å line intensity.
If the overall distribution of Ca abundance in the atmospheres of Ap stars follows the
predictions of radiatively-driven diffusion, our results on the isotopic separation
favour the light-induced drift (LID) as the main process responsible for this separation.
According to Atutov & Shalagin (1988), LID arises when the radiation field is
anisotropic inside the line profile. Such an anisotropy takes place for a line of the trace
isotope, for instance 46Ca and 48Ca in the terrestrial calcium mixture, which is
located in the wing of a strong line of the main isotope 40Ca. The main isotope induces
the drift velocity for other isotopes. If the trace isotope's line is located in the red
wing of the line due to the main isotope, the drift velocity is directed towards the upper
atmosphere and the trace isotopes are pushed upwards. This is in agreement with the observed
vertical distribution of Ca isotopes. The Zeeman splitting changes the line shape and
decreases the flux anisotropy for the line of trace isotope. When magnetic field becomes
sufficiently strong, 5-6 kG, the flux anisotropy disappears and the isotopic separation is
ceasing. Therefore, the observed Ca isotopic anomaly in magnetic stars may be qualitatively
explained by the combined action of the radiatively-driven diffusion and the light-induced
drift. For He, a theoretical study of both radiatively-driven diffusion and LID was
presented by LeBlanc & Michaud (1993). These authors showed
that LID accelerates separation of 3He from 4He in hotter CP
stars.
Detailed theoretical chemical diffusion calculations
(LeBlanc & Monin 2004) should incorporate LID in order to test our hypothesis
that this effect may be important for the chemical transport processes in cool Ap-star
atmospheres.
Acknowledgements
We thank Luca Fossati for letting us use his spectrum of HD 73666. This work was supported by the RAS Presidium Program ``Origin and Evolution of Stars and Galaxies'', by Austrian Science Fund (FWF-P17580N2) and by the grant 11630102 from the Royal Swedish Academy of Sciences. TR also acknowledges partial support from the RFBR grant 06-02-16110a and the Leading Scientific School grant 4820.2006.2. OK acknowledges financial support from the Swedish Royal Physiographic Society in Lund.