Behaviour of calcium abundance in Am-Fm stars with evolution

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M. Kunzli, P. North

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ASTRONOMY 
AND 
ASTROPHYSICS 
1.2.2008 



Behaviour of calcium abundance in Am-Fm stars with 
evolution 

M. Kunzli and P. North 

Institut d'Astronomie de I'Universite de Lausanne, CH-1290 Chavannes-des-Bois, Switzerland 



Received 7 July 1997/ Accepted 30 September 1997 

Abstract. Calcium abundance in the atmosphere of Am 
stars is examined as a function of their evolutionary 
state within the main sequence. New spectroscopic abun- 
dances as well as abundances abtained photometrically 
by Guthrie (1987) are used, since they are mutually quite 
consistent. 

The main result of this work is that, contrary to ear- 
lier suggestions, calcium abundance does not tend to be 
larger in evolved Am stars than in unevolved ones, for ob- 
jects distributed along a given evolutionary track in the 
HR diagram. The trend appears to be the reverse, if it is 
present at all. 

For our whole sample of Am stars, there is a signif- 
icant correlation between calcium abundance and effec- 
tive temperature, in the sense that the cooler objects are 
the most Ca-deficient, hance have the most pronounced 
Am peculiarity. This implies an apparent correlation be- 
tween calcium deficiency and age, although the lack of Am 
stars younger than logt = 8.6 seems real. Our results are 
fully consistent with the low rate of Am stars observed in 
young clusters and with theoretical predictions of time- 
dependent radiative diffusion (Alecian 1996). 

Key words: Stars: chemically peculiar - stars: abun- 
dances - stars: evolution - stars: fundamental parameters 



1. Introduction 

The Am-Fm stars, whose effective temperature lies be- 
tween 7000 K and 9000 K, are the coolest chemical pe- 
culiar stars on the main sequence (excluding barium or 
carbon dwarfs, which owe their peculiarity to binary evo- 
lution) . Their main characteristics are an underabundance 
of calcium and scandium (about 5 to 10 times lower than 

Send offprint requests to: P. North 

* Based on observations collected at Observatoire de Haute 
Provence (CNRS), France, and on data from the ESA HIP- 
PARCOS astrometry satellite. 



in the Sun), a slight overabundance of iron-peak elements, 
a slow rotational velocity {v smi < 100 km s~^) and a high 
rate of tight binaries (Abt and Levy 1985). 

To explain the emergence of chemical anomalies in Am 
stars, one usually invokes the radiative diffusion theory 
developed by Michaud et al. (1983). This theory predicts 
that, in a slowly rotating star where the large-scale merid- 
ional circulation is weak enough, helium is no longer sus- 
tained and flows inside the star, gradually disappearing 
from the atmosphere. The diffusion process could there- 
fore take place just below the thin Hi convective zone 
where the diffusion time is short with respect to the stellar 
lifetime; as a first approximation, the chemical elements 
whose radiative acceleration is larger than gravity become 
overabundant and, in the opposite case, underabundant. 

The H I convective zone becomes deeper as the star 
evolves on the main sequence; finally, the c.z. may dredge- 
up calcium and scandium, leading to the normalisation of 
the surface abundance. Berthet (1992), using data for Am 
members of three open clusters, provided some evidence 
for a trend between calcium abundance and evolutionary 
stage in agreement with the preceding scenario; Guthrie 
(1987) had already suspected such a trend in a sample of 
field Am stars. Berthet (1992) proposed an evolutionary 
scenario for the Am stars by considering also the S Del 
stars (which have the same abundance anomalies as the 
Am stars except for Ca and Sc which are not deficient) and 
the metallic A and F giants discovered by Hauck (1986) on 
the basis of their enhanced blanketing parameter Am2 of 
Geneva photometry: an Am star would evolve into a 6 Del 
and finally into a metallic F giant, following a sequence 
of increasing Ca abundance. However, a comparison of 
multiplicity and rotational velocities of metallic A-F giants 
and of Am stars has shown that the latter cannot be the 
progenitors of the former, which casts serious doubts upon 
Berthet's scenario (Knzh & North 1997). 

Alecian (1996) has studied theoretically the evolution 
of calcium abundance in the early stages of slowly rotating 
A and F type stars. His work predicts a short phase of cal- 
cium overabundance (before \ogt = 8) followed by a phase 



2 



M. Kiinzli et al.: Calcium abundance in Am-Fm stars 



of underabundance for some depth values of the mixing 

zone which is just below the H i convcctivc zone. Accord- 
ing to this result, all slowly rotating A and F stars go 
through a phase of underabundance of Ca, but only after 
10^ years. This prediction is supported by North (1993), 
who pointed out a deficiency of Am stars in young open 
clusters. 

One goal of the present work is to test the results of 
Berthet (1992) and Guthrie (1987). Another is to deter- 
mine, as far as possible, the evolutionary state at which 
slowly rotating A and F stars become Am stars. The 
knowledge of this parameter may shed some light on the 
formation of Am stars. To this end, we measured at OHP 
some known bright Am stars whose Ca abundance were 
then determined by optimum fit of synthetic spectra to our 
observed ones, taken in the region of the Ca ii K line. To 
this sample we added the 57 stars of Guthrie (1987) whose 
Ca abundance was determined from the photometric k in- 
dex and is well-correlated with ours for the eight common 
stars. For each star, wc dc;tc^rniinc the effective temper- 
ature from Geneva photometry (Knzli et al. 1997) and 
the absolute magnitude (corrected for duplicity) from the 
Hipparcos parallax. Then, in the HR diagram we compute 
the evolutionary state (defined by our i'looo parameter) 
and the age and mass by interpolation in the evolutionary 
tracks of Schaller et al (1992). 



2. The sample and observations 

We have selected Am stars between 1.5 and 2 solar masses 
at different distances from the ZAMS in order to fol- 
low the calcium abundance with evolution. The objects 
selected come from the catalogue of Hauck & Curchod 
(1980) which contains 385 Am stars with known spectral 
type. We have added some metallic giant F stars (Hauck 
1986) and normal A stars as reference stars. Because of 
bad weather, we could observe only 27 Am stars, 2 metal- 
lic giant F stars and 2 normal stars. 

Our observations were made during two sessions of 
a few nights' duration each at Observatoire de Haute- 
Provence (OHP) in May 1994 and in November 1995, 
using the 1.52m telescope equipped with the AURELIE 
spectrograph (Gillet et al. 1995). The detector is a double- 
element TH7832 with sets of 2048 photodiodes of 750 x 
13 /im. We used the grating N° 2 with 1200 lines/mm; 
the spectra were thus obtained at a reciprocal dispersion 
of 8 Amm~^ in the spectral region centered on the Call 
K line [3820A, 4035A]. Using calibration spectra of tho- 
rium, the reduction was made at Geneva with MIDAS 
procedures for the first mission and at OHP with IHAP 
procedures for the second mission. To normalise our spec- 
tra, we simply fitted a straight line to the continuum. For 
most spectra, a signal-to-noise ratio of 150 was achieved 
in the continuum. 



3. Calcium abundance 

For the same reasons as those invoked by Berthet (1992), 
wc use the strong Ca ii K line to determine the abundance 
of this element. In the atmospheres of Am stars, most of 
the calcium is ionised due to a low first ionisation poten- 
tiel, thus the assumption of LTE may fail for the neutral 
calcium lines. However, the wings of the Can K line are 
formed deeper in the atmosphere than the other lines of 
ionised elements, making the LTE assumption more valid 
because the density of this ion is higher and the transi- 
tion comes from the ground state. In addition, this line is 
always visible even when the star rotates rapidly. 





I 1 1 1 1 1 1 1 1 1 






. ...1 JVUnJ/SAif-rN . K 


, , , , 1 


, < 1 , , , < 1 < < , , 1 < , < < 1 



I I I I I I I I I I \ I I I I I I I I I I L 

3920 3925 3930 3935 3940 



A [1] 

Fig. 1. AURELIE spectrum of the Am star HD 74190 in the 
vicinity of the Can K line. The synthetic spectrum (dotted 

line) with Tctf = 7944 K, log^ = 3.84 dcx, [M/H] = -0.22 
dcx, = 3.3 km s^^ and vsini = 58 km s^"'^ is shown to- 
gether with the observed one (continuous line). The ratio (in- 
creased by 0.2 for clarity) of the observed and synthetic spec- 
tra is shown at the top of the figure, while the difference is 
shown at the bottom. The synthetic spectrum is computed 
with log(^) + 12 = 6.28. 

The synthetic spectra are computed using the SYN- 
SPEC code of Hubeny & Lanz (1993) and Kurucz atmo- 
sphere models (1995). The Stark, van der Waals and ra- 
diative widths are those calculated by Kurucz (1989) for 
iron-peak elements lines. The adopted parameters Tes and 
[M/H] for the atmosphere models come from the colours 
obtained in the Geneva photometric system for all stars 
of the sample, using the calibration by Knzli et al. (1997). 
For all Am stars, the surface gravity logg is deduced from 



M. Kiinzli et al.: Calcium abundance in Am-Fm stars 



3 



the HIPPARCOS parallax and from the apparent V mag- 
nitude, while the mass is obtained by interpolation in the 
evolutionary tracks of Schaller et al. (1992). For normal 
and giant metallic stars, logg is determined from Geneva 
photometry (Kiinzli et al. 1997). The microturbulence 
is calculated from Edvardsson et al. (1993) or Coupry & 
Burkhart (1992) according to the effective temperature 
and the surface gravity of the star. The spectra were then 
convoluted by a gaussian with FWHM = 0.379 A rep- 
resenting the instrumental profile and by the appropriate 
rotational profile. The Tcff , log g, [A4 /H] , and v sin i val- 
ues are listed in Table 1 for the stars observed at OHP. 
The Call K spectral type given in this table comes from 
the catalogue of Hauck & Curchod (1980) and the vs'mi 
from Abt & Morrell (1995) or the Bright Star Catalogue 
(HofHeit & Jaschek 1982). In most cases, the vsini values 
taken from the literature are completely compatible with 
our spectra. But in a few instances, the attempt to fit the 
observed spectrum with the synthetic one failed, when the 
latter was convoluted using the v sin i from the literature; 
in such cases (or when v sin i was previously unknown) , 
we used our own estimate, which is quite reliable because 
it is based not only on the Ca K line, but also on many 
metallic lines spread over the 200 A wavelength range. 




5.6 5.8 6 6.2 6.4 



log(Nca/NH) + 12 (OHP) 

Fig. 2. Comparison between Ca abundances obtained by 
Guthrie (1987) and those obtained in this paper. The disper- 
sion of the points from the straight line at 45 degrees is 0.07 
dex. 

When fitting a spectrum, only two parameters remain 
free, that is the rotational velocity and of course the cal- 



cium abundance. The effective temperature, surface grav- 
ity, metallicity and microturbulence are fixed. The photo- 
metrically determined Teg is confirmed by the fit of the 
Balmer lines H^, and in our spectra, so we did not 
attempt to change its value, although these lines are com- 
puted using a simplified broadening theory only and not 
the VCS theory. The calcium abundance essentially affects 
the wings of the K line, because it is saturated. The rota- 
tional velocity acts on the depth of the line, the wings 
being only weakly affected. The quantitative effects of 
the effective temperature, rotational velocity and calcium 
abundance are shown on Figures 3, 4 and 5 of Berthet's 
paper (1992) respectively (he used the ADRS code - see 
Chmielewski 1979, Lanz 1987 - but one sees of course the 
same behaviour with SYNSPEC). For the above reasons, 
we determine the Ca abundance essentially by a fit on the 
wings and then on the depth of the K line. The resulting 
Ca abundances are given in Table 1. The internal preci- 
sion is estimated at about 0.1 dex. As an exemple, Figure 
1 shows the optimal fit of HD 74190 by a synthetic spec- 
trum in the region of the Can K line (3933.663 A). This 
fit leads to a relative abundance log(^^') -|- 12 = 6.28. 

Our determinations were tested with the eight stars we 
have in common (HD 18557, HD 23281, HD 40062, HD 
60652, HD 71297, HD 136403, HD 221675, HD 223461) 
with Guthrie (1987), who measured the Ca abundance 
photometrically by the k index. Figure 2 compares the Ca 
abundances of Guthrie with those determined at OHP. 
Except for HD 23281 which shows a difference of 0.18 dex 
between Guthrie's value and ours, there is an excellent 
correlation. The rms scatter around the straight line at 
45 degrees is only 0.07 dex. For this reason, we include 
Guthrie's sample in our discussion. Guthrie estimates his 
overall error on Ca abundance at about ±0.3 dex, but it 
is probably less. 

4. Discussion 

As part of the discussion will depend on the position of 
Am stars in the HR diagram, it is necessary to present 
their fundamental parameters in more details. 

The effective temperature is photometrically deter- 
mined by the calibration of the Geneva system (Knzli et 
al. 1997) which uses both stars with known fundamental 
parameters and atmosphere models (Kurucz 1993, 1994, 
1996a, 1996b). The only drawback of the Geneva system, 
compared to the uvby(3 one, is its sensitivity to interstellar 
reddening for A and cooler stars. But, as all 76 Am stars 
are bright (m^ < 7 mag.), IS reddening is negligible. The 
fundamental stars used in this range of temperature are 
essentially those of Blackwell & Lynas-Gray (1994), who 
relied on the infrared flux method. These authors give an 
estimated error of about 2%. 

The absolute visual magnitudes are deduced from Hip- 
parcos parallaxes of Am stars (Proposal 55). For the two 
metallic F giants and the two normal stars, the abso- 



4 



M. Kiinzli et al.: Calcium abundance in Am-Fm stars 



Table 1. Abundances of Ca for the sample of Am-Fm stars. The uncertainties on log* are propagated from assumed errors on Tgff and log 5 of 
270 K and 0.18 dex respectively (Asiain et al. 1997), which are comfortably large. An asterisk indicates that Mv was determined not from Hipparcos 
parallaxes, but from Geneva photometry. 



HD 


ST 
Can K 


Rein. 


T 

all 

[K] 


log g 


fM/Hl 


vsin i 
[km s J 


[km s J 


M„ 




M 
[M©] 


log t 


1000 


861 


TT^ 

A2m 


SBl 


7715 


3.90 


0.29 


35 


3.2 


1.49 


5.95 


1.98 


8.934 ± 0.050 


1.285 


2628 


A5m 




7223 


3.77 


-0.14 


20 


2.7 


1.43 


6.15 


1.98 


8.992 ± 0.081 


1.800 


15385 


A5m 


V 


8154 


4.12 


0.00 


21 


3.4 


1.85 


6.61 


1.88 


8.793 ± 0.115 


0.520 


17584 


F2III 


Illm 


6726 


3.56 


-0.09 


149 


3.2 


* 1.26 


6.18 


1.91 


9.112 ± 0.116 


2.026 


18557 


A2m 


V 


7614 


3.90 


0.10 


15 


3.2 


1.57 


5.74 


1.94 


8.958 ± 0.052 


1.267 


21912 


A3in 


SBIO 


8327 


4.31 


0.00 


91 


3.3 


2.30 


6.15 


1.80 


7.089 ± 4.000 


0.026 


23281 


A3m 




7689 


4.20 


-0.02 


81 


3.2 


2.42 


6.12 


1.68 


8.797 ± 0.287 


0.199 


24141 


A5m 




8070 


4.22 


0.35 


54 


3.3 


2.21 


6.38 


1.78 


8.633 ± 0.405 


0.217 


36484 


A2m 


SB 


8711 


4.27 


0.00 


35 


3.2 


1.90 


5.82 


1.93 


8.312 ± 0.674 


0.122 


40062 


A5m 


- 


7030 


3.68 


0.39 


40 


2.6 


1.32 


5.69 


2.02 


9.001 ± 0.076 


2.110 


42954 


A5m 


SB 


7384 


3.70 


0.17 


47 


3.0 


1.10 


5.90 


2.11 


8.934 ± 0.074 


2.087 


44691 


A3m 


SBIO 


7581 


3.76 


0.15 


21 


3.2 


1.13 


5.90 


2.12 


8.911± 0.064 


1.897 


60652 


A5m 




7647 


3.86 


0.44 


63 


3.2 


1.40 


6.15 


2.01 


8.935 ± 0.057 


1.455 


63589 


A2in 


V 


8122 


4.25 


0.00 


35 


3.4 


2.24 


5.85 


1.78 


8.531 ± 0.603 


0.161 


67317 


Aim 




7165 


4.18 


0.43 


35 


2.7 


2.77 


5.42 


1.55 


8.989 ± 0.229 


0.144 


71297 


A5in 




7712 


4.06 


-0.03 


13 


3.2 


1.97 


6.29 


1.81 


8.935 ± 0.060 


0.698 


74190 


A5m 




7944 


3.84 


-0.22 


58 


3.3 


1.13 


6.28 


2.13 


8.868 ± 0.053 


1.568 


83886 


A5m 




8638 


4.18 


0.00 


100 


3.2 


1.69 


6.27 


1.98 


8.613 ± 0.220 


0.375 


84607 


F4III 


Illm 


7050 


3.79 


0.09 


120 


3.0 


*1.66 


6.46 


1.89 


9.052 ± 0.078 


1.642 


88295 


(AO) 


normal 


8594 


4.13 


0.00 


120 


3.3 


*1.58 


6.36 


2.01 


8.683 ± 0.129 


0.515 


1 1 rfiofi 

1 lUOZD 


A3ni 




/ U / D 


4 04 




DO 




2 42 




i.DO 


y.llD iU.UDU 


u.oyz 


135774 


A6m 


V 


6917 


3.80 


0.42 


35 


3.0 


1.79 


5.78 


1.84 


9.091 ± 0.078 


1.579 


136403 


A2in 


SBO 


7670 


4.01 


0.17 


20 


3.2 


1.87 


5.81 


1.84 


8.955 ± 0.047 


0.844 


150557 


F2III-IV 


normal 


6849 


3.85 


-0.18 


95 


2.7 


*2.02 


6.20 


1.75 


9.134±0.068 


1.323 


169885 


A3m 




8050 


3.91 


0.03 


60 


3.4 


1.26 


6.11 


2.08 


8.864 ± 0.042 


1.306 


183262 


A5m 




7055 


4.06 


0.21 


73 


2.6 


2.50 


5.90 


1.61 


9.124 ± 0.065 


0.499 


190401 


A7m 




6877 


3.81 


0.25 


40 


2.8 


1.84 


5.86 


1.82 


9.104 ± 0.077 


1.548 


193472 


A5m 


SB2 


7123 


3.72 


0.23 


93 


2.7 


1.38 


5.68 


1.99 


9.010 ± 0.076 


1.907 


213534 


A5m 


SBO 


7632 


3.74 


-0.31 


48 


2.7 


1.05 


6.22 


2.15 


8.894 ±0.064 


1.968 


221675 


A2m 




7223 


3.84 


0.53 


70 


2.8 


1.67 


5.76 


1.89 


9.031 ± 0.068 


1.472 


223461 


A2in 




7879 


3.91 


0.11 


48 


3.3 


1.38 


5.95 


2.03 


8.899 ± 0.044 


1.282 



lute magnitudes are taken from the calibration of Hauck 
(1973). For these stars, My is preceded by an asterisk in 
Tables 1 and 2. As the stars considered are bright, hence 
near to us, the relative error on the parallax is small, in 
general around 7%, so the error on the absolute magnitude 
is on average 0.15 mag. 

As is well known. Am stars are often members of tight 
binaries, so we have to correct M„ for the flux of the com- 
panion. For this, we apply the following correction: 

- For SB2 systciins, wc compute ^ = ^ and with 
the mass-luminosity relation we obtain Am* = mi — 
mi+2 = 2.51og(l + 10~^^T3^). 

- For SBl systems, Am* = 0.2 is assumed, which corre- 
sponds to a difference of 1.75 magnitudes between the 
components. 

- If the star has a variable radial velocity according to 
the BSC or the catalogue of Renson (1991), Am* = 0.2 
mag is also assumed. 

- If the star is only suspected of having a variable ra- 
dial velocity according to the BSC ("V?" remark), no 
change is made. 

Indications about multiplicity and variabiUty arc given in 
the column "Rem." of Tables 1 and 2. Except for HD 
193472 which is an SB2, all stars are marked SBl, V or 
V? or have no remark. 



We also compute a correction for visual binaries with 
angular separation less than 5 arcscc. This correction is 
applied only to HD 42954 which has a companion of the 
same magnitude at 0.5 arcsec, and to HD 67317 which has 
a faint neighbour at 1.4 arcsec. 

The final HR diagram, where these corrections are 
taken into account, is presented in Figure 3. Stars repre- 
sented by black circles arc those mciasured at OHP, those 
represented by black triangles are from Guthrie (1987). 
We have also plotted the two metallic giant F stars (open 
circles) and one normal star (open triangle). The size of 
each point depends linearly on the logarithmic calcium 
abundance. There is a striking deficiency of young Am 
stars with masses larger than 2 Mq. 

4.1. Behaviour of Ca abundance with logt 

The Barcelona group (Asiain et al. 1997) has kindly trans- 
mitted to us a code which interpolates the age logt and 
mass of a star from its effective temperature and surface 
gravity, in evolutionary tracks from various authors in- 
cluding Schaller et al. (1992). As a first step, logg was 
computed from the absolute magnitude, assuming an ini- 
tal mass of 1 Mq. Then logg was determined by the ab- 
solute magnitude and the mass given in the first interpo- 
lation. This iterative process was stopped as soon as the 
mass converged to — (j^)i| < 10"'^. The num- 



M. Kiinzli et al.: Calcium abundance in Am-Fm stars 



5 




^ I I \ I I I I I \ I I \ I \ \ I I I I I \ I \ \ I 

9000 8500 8000 7500 7000 6500 



Fig. 3. HR diagram of the 76 Am stars included in the dis- 
cussion. The absolute magnitudes are deduced from Hipparcos 
parallaxes and corrected for duplicity. The effective tempera- 
tures arc taken from Knzli ct al. (1997). The stars measured 
at OHP are represented by black circles and those of Guthrie 
(1987) by black triangles. The other stars measured at OHP 
arc represented by open circles for giant metallic F stars and 
by open triangles for normal stars. The size of the points is 
related to the Ca abundance. 



bcr of iterations seldom exceeded 10. The values of logt 
with its internal error and of the mass are given in Tables 
1 and 2. 

When a star is near the ZAMS, the uncertainty on log t 
increases dramatically, because there is a superposition of 
isochrones in this region. Only HD 21912, HD 36484, HD 
63589 and HD 204188 are concerned by this problem. For 
them, the error on logt is larger than 0.5. 

Figure 4 shows the behaviour of log(^^-) + 12 with 
logt. The age of Am stars spreads between 8.6 and 9.15 
with a clear deficiency of Am stars in the lower left part 
of the diagram. It means that A and F stars are really 
deficient in calcium only after logt w 8.8. In order to 
test the significance of this result, a 2 x 2 contingency 
table was built, using a separation at logt = 8.875 and 
log(^) + 12 = 5.88. We get = 9.88 while the value 
for the 99.5% confidence level is 7.88. This dependence 
between Ca abundance and age seems to confirm qualita- 
tively Alecian's theory, which predicts a calcium deficiency 
for slowly rotating A and F stars from log t = 8 on, that is 
0.6-0.8 dex earlier than our observations suggest. However, 
this relation betrays a correlation between Ca abundance 
and effective temperature (Figure 5): since cooler stars are 




8.6 8.8 9 9.2 

log(t) 

Fig. 4. Calcium abundance as a function of log t. See Figure 
3 for the key to symbols. 




9000 8500 8000 7500 7000 6500 

erf 

Fig. 5. Calcium abundance as a function of T^g. See Figure 3 
for the key to symbols. 



6 



M. Kiinzli et al.: Calcium abundance in Am-Fm stars 




6.5 



5.5 



1 

























possible to discuss age effects independently of T^s effects, 
since both parameters are intimately related. When a star 
follows an evolutionary track, the effective temperature 
decreases and the age log t of course increases; if the corre- 
lation between Tcs and Ca abundance found above holds, 
then one may expect that an evolving Am star will be- 
come more and more Ca-deficient. This point is examined 
in more details in the next Subsection. 



9000 8000 7000 



9000 8000 7000 



+ 



o 













\ ' ' ' \ 


1 1 1 1 1 1 1 l_ 


6.5 






+ 


6.5 






6 








6 












z 








5.5 




1 , , , K, -.swe 


log( 


5.5 




, , , 1 , , , 1" 




8.6 


8.8 9 9.2 




8.6 8. 


8 9 9.2 



log(t) 



log(l) 



Fig. 6. Diagram of synthesised Am stars. The two leftmost 
figures reproduce exactly what is observed. If there is no rela- 
tion between Ca abundance and Tes, there is no relation either 
between age and Ca abundance, as shown in both rightmost 
diagrams. Temperature effects closely mimic age effects and 
vice versa, so these two quantities are not independent. 



also older, one will necessarily observes a relation between 
Ca abundance and age. 

We have made some simulations to test the interdepen- 
dence between age, effective temperature and Ca abun- 
dance. First, one has synthesised a population of Am stars 
with masses and ages distributed at random (assuming a 
Salpeter IMF combined with the relative mass distribu- 
tion of North 1993); the age distribution was not imiform, 
but modified so as to mimic the observed one. By inter- 
polation in evolutionary tracks of Schaller et al. (1993), 
we obtain both effective temperatures and absolute mag- 
nitudes. Finally, we determine logt as before and then 
can plot log(^^-) -|- 12 vs logt assuming a relation be- 
tween effective temperature and Ca abimdance. If we im- 
pose the observed relation between T^g and Ca abundance 
given in Figure 5, we recover the relation between logt and 
log(^^^) + 12 shown in Figure 4. The left part of Figure 
6 illustrates this fact, the oblique lines being at the same 
positions as in Figure 5 and 4. On the other hand, if we 
impose no relation between temperature and Ca abun- 
dance, there is no relation either between age and Ca 
abundance (Figure 6, right part). These simulations show 
that temperature effects almost perfectly mimic age effects 
and vice-versa, at least when all stars are considered to- 
gether. Even if one considers only stars distributed along 
an evolutionary path (all having the same mass), it is not 



Z 4 - 



8.6 



9.2 



log(t) 



Fig. 7. Histogram of log t for the Am stars considered in this 
paper. 



Even if the effect of age on Ca abundance can not be 

isolated from that of Tcs, it is interesting to consider the 
histogram of ages. As seen in Figure 7, most of our field 
Am stars are older than logi « 8.8 (in the histogram, we 
do not take into account the four stars having a large er- 
ror on logi). Although our sample should be considered 
as biased because it was defined with the purpose of pop- 
ulating a few evolutionary tracks as uniformly as possible, 
Guthrie's sample is not biased towards young or old ob- 
jects, and it constitutes two thirds of the whole sample. 
Therefore, we think the distribution of Figure 7 shows a 
real lack of young Am stars. This fact is coherent with the 
deficiency of Am stars in young clusters. 

4-2. Behaviour of Ca abundance along an evolutionary 
track 

In order to know how the Ca abundance tends to vary with 
evolution for stars of a given mass, we define the Diooo 
parameter as the difference between the present effective 



M. Kiinzli et al.: Calcium abundance in Am-Fm stars 



7 





12 3 



6.5 

O 



6 - 



5.5 



1 1 1 


1 1 1 1 1 1 1 1 1 1 1 

d - 










1 1 1 





Fig. 8. log(-^^) + 12 as a function of Diooo for different range 
of mass; a: 1.5 < M/Mq < 1.7, b: 1.7 < M/Mq < 1.9, c: 
1.9 < M/Mq < 2.1, d: M/Mq > 2.1. See Figure 3 for the 
signification of symbols. 



temperature of the star and the one it had on the ZAMS, 
divided by 1000 just to have a number close to unity. In 
other words, this parameter represents the "horizontal" 
component of the distance covered by the star in the HR 
diagram along an evolutionary track: 



-Diooo = 



reff-Teff(ZAMS) 

1000 



This parameter therefore measures a kind of age, i.e. the 
time which has expired since the star left the zero-age 
main sequence, although it is of course not on a linear 
scale. 

£'1000 is correlated with the depth of the convective 
zone and consequently with Ca abundance, according to 
the scenario of Berthet (1992). To show this dependence, 
we have defined four mass ranges: 1.5 < M/Mq < 1.7, 
1.7 < M/Mq < 1.9, 1.9 < M/Mq < 2.1 and M/Mq > 
2.1. The Ca abundance was then plotted against Diooo 
for each of these ranges (Figure 8). If Berthct's (1992) 
idea was right, we should see an increasing calcium abun- 
dance with increasing .Diooo because at a constant mass, 
^1000 increases along a given cvohitionary track. Figure 
8 shows that this is definitely not the case: there is no 



correlation between log(^^) and -Diooo- In Figure 8b and 
8c, we rather see the reverse correlation, i.e. an increasing 
calcium deficiency with evolution. This rough correlation 
is in agreement with the preceding result: Tes decreases 
with evolution and Ca gets more depleted. 



If we superimpose Figure 8a and 8d, a positive corre- 
lation appears between log(^^^) and -Dioooj which is due 
to a temperature effect but not to any evolution effects. 
Guthrie (1987) analysed the behaviour of log(^^^) with 
Sc'^ (which is a photometric parameter in the Stromgren 
system similar to -Diooo) without any distinction of mass 
or temperature, and Berthet (1992) did not take into ac- 
count the effect of temperature either; this is probably the 
main reason for the difference between their result and 
ours. 



5. Conclusion 

We have analysed the dependence of Ca abundance with 
evolution in the atmosphere of Am stars. In this paper, 
we put forward the impossibility of isolating the depen- 
dence of Ca abundance on time alone, because when a 
star evolves, time is intimately related to temperature so 
that these two parameters cannot be discussed separately. 

Cool and old Am stars arc more Ca-deficicnt than hot- 
ter and younger ones. So, when an Am star evolves its Ca 
abundance probably decreases. But we can only guess that 
the physical cause for this is the decreasing temperature 
in the star's envelope just below the Hi convective zone, 
which implies a decrease of the radiative acceleration ap- 
plied to the Call ions. However, the parallel decrease of 
the surface gravity acts in the opposite sense and only 
detailed, time-dependent modelling such as Alecian's will 
allow a proper interpretation of the data. 

The Diooo parameter, which measures the evolution- 
ary state of a star, depends on both age and tempera- 
ture. For constant mass, -Diooo follows an evolutionary 
track and so measures directly the effect of evolution. 
We have shown that there is no positive correlation be- 
tween -Diooo &iid Ca abundance, contrary to the claims of 
Berthet (1992) and Guthrie (1987). There is rather a de- 
crease of the calcium abundance as evolution proceeds. In 
their study, Berthet (1992) and Guthrie (1987) have mixed 
stars with different masses and temperatures, which prob- 
ably led them to a wrong conclusion, essentially due to a 
temperature effect. 

Most ages of our field Am stars spread between log t = 
8.6 and 9.2, which agrees well with the lack of Am stars 
in young open clusters (North 1993). 

Acknowledgements. We thank Dr. Simon Jeffery for having 
transmitted to us a file with the continous metallic opacities to 
be used with the SYNSPEC code, and Mrs Barbara Wilhelm 
for the correction of the English text. Constructive criticism by 
the referee is also gratefully acknowledged. This paper received 
the support of the Swiss National Science Foundation. 

References 

Abt H.A., Levy S.G., 1985, ApJS 59,229 
Abt H.A., Morrell N.I., 1995, ApJS 99, 135 
Alecian G., 1996, A&A 310, 872 



8 M. Kiinzli et al.: Calcium abundance in Am-Fm stars 

Table 2. Parameters of age, masse, temperature and absolute magnitude for the stars of Guthrie (1987). 



HR 


HD 


Rem. 


[K] 


M„ 1 


og(-?§-) + 12 


M 
[Mq] 


log(t) 


i'lOOO 


178 


3883 


- 


7279 


0.30 


6.11 


2.34 


8.851 it 0.114 


3.011 


290 


6116 


- 


7964 


0.84 


6.29 


2.25 


8.831 ± 0.062 


1.976 


418 


8801 


- 


7222 


2.69 


6.13 


1.57 


8.988 ± 0.193 


0.192 


540 


11408 


- 


8051 


2.11 


6.26 


1.80 


8.736 ±0.240 


0.325 


976 


20210 


SBO 


7509 


2.32 


5.50 


1.70 


8.951 ±0.111 


0.427 


984 


20320 


SBO 


7530 


2.17 


6.01 


1.74 


8.970 ±0.073 


0.594 


1248 


25425 


V? 


8059 


0.41 


6.05 


2.45 


8.762 ± 0.072 


2.522 


1368 


27628 


SBIO 


7086 


2.82 


5.99 


1.53 


9.023 ±0.215 


0.146 


1414 


28355 


- 


7761 


1.56 


6.30 


1.95 


8.933 ± 0.046 


1.152 


1428 


28546 


V? 


7468 


2.24 


6.31 


1.71 


8.982 ± 0.077 


0.561 


1511 


30121 


- 


7636 


1.81 


5.91 


1.86 


8.964 ± 0.043 


0.951 


1519 


30210 


SBl? 


7960 


0.99 


6.00 


2.19 


8.851 ±0.172 


1.755 


1528 


30453 


SBIO 


7413 


0.98 


6.29 


2.17 


8.909 ±0.074 


2.248 


1627 


32428 


- 


7246 


1.24 


5.78 


2.05 


8.972 ± 0.075 


2.000 


1670 


33204 


- 


7207 


2.24 


6.16 


1.70 


9.070 ± 0.053 


0.738 


1672 


33254 


SBO 


7553 


1.97 


5.70 


1.80 


8.983 ±0.048 


0.819 


1689 


33641 


V 


7868 


1.53 


6.22 


1.97 


8.909 ± 0.043 


1.100 


2566 


50643 


- 


8042 


0.39 


6.30 


2.46 


8.761 ± 0.072 


2.558 


3320 


71267 


- 


7757 


0.91 


6.24 


2.21 


8.862 ± 0.072 


2.046 


3354 


72037 


- 


7814 


2.04 


5.78 


1.80 


8.887 ± 0.098 


0.550 


3619 


78209 


- 


7281 


2.13 


5.78 


1.73 


9.051 ± 0.045 


0.831 


3655 


79193 


SBO 


7556 


1.71 


5.99 


1.89 


8.981 ±0.047 


1.128 


3988 


88182 


- 


7945 


1.74 


6.29 


1.90 


8.886 ± 0.053 


0.800 


4021 


88849 


- 


7074 


1.81 


6.14 


1.83 


9.072 ± 0.067 


1.418 


4237 


93903 


SBIO 


7759 


0.75 


6.14 


2.28 


8.844 ±0.073 


2.271 


4286 


95256 


- 


7985 


1.68 


5.80 


1.93 


8.880 ± 0.050 


0.837 


4424 


99859 


- 


8011 


2.13 


6.19 


1.79 


8.750 ± 0.234 


0.326 


4454 


100518 


- 


7901 


1.26 


5.81 


2.07 


8.886 ± 0.049 


1.427 


4535 


102660 


- 


7329 


2.07 


5.77 


1.76 


9.039 ± 0.045 


0.871 


4543 


102910 


- 


7358 


2.66 


6.04 


1.60 


8.902 ± 0.277 


0.152 


4650 


106251 


- 


7448 


2.37 


5.87 


1.68 


8.969 ± 0.110 


0.406 


4750 


108642 


SBIO 


7884 


1.67 


5.90 


1.92 


8.905 ± 0.044 


1.170 


4751 


108651 


SBO 


7782 


2.34 


5.90 


1.71 


8.780 ± 0.276 


0.243 


4847 


110951 


SBO 


7036 


1.05 


5.92 


2.12 


8.960 ± 0.115 


2.466 


4866 


111421 


- 


7727 


0.49 


6.45 


2.39 


8.813 ± 0.075 


2.648 


5045 


116303 


- 


7366 


0.60 


6.05 


2.20 


8.929 ± 0.109 


2.839 


5405 


126661 


- 


7378 


0.68 


6.38 


2.16 


8.950 ± 0.108 


2.283 


5752 


138213 


SBO 


8369 


0.52 


6.28 


2.41 


8.747 ± 0.061 


2.096 


5845 


140232 


- 


7844 


2.17 


5.91 


1.77 


8.829 ± 0.166 


0.392 


6555 


159560 


SBO 


7321 


2.63 


5.78 


1.60 


8.947 ± 0.211 


0.197 


6813 


166960 


V 


7265 


1.88 


5.86 


1.82 


9.046 ± 0.052 


1.156 


7019 


172741 




7438 


0.52 


6.27 


2.24 


8.908 ± 0.109 


2.445 


7056 


173648 


SBIO 


7748 


1.17 


6.19 


2.10 


8.898 ± 0.058 


1.679 


7833 


195217 




7581 


2.21 


6.01 


1.73 


8.944 ± 0.096 


0.514 


7990 


198743 


SBO 


7018 


1.54 


5.76 


1.93 


9.035 ± 0.089 


1.832 


8210 


204188 


SBO 


7668 


2.76 


6.45 


1.63 


7.283 ± 4.000 


0.008 


8410 


209625 


SBIO 


7583 


1.24 


6.02 


2.07 


8.925 ± 0.061 


1.742 


8970 


222377 




7749 


2.16 


5.93 


1.76 


8.884 ± 0.122 


0.459 


9025 


223461 




7879 


1.39 


6.26 


2.02 


8.900 ± 0.044 


1.351 



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