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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
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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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