Kepler observations of Am stars★

Abstract

We present an analysis of high-resolution spectra for two pulsating Am stars in the Kepler field. The stellar parameters derived in this way are important because parameters derived from narrow-band photometry may be affected by the strong metal lines in these stars. We analyse the Kepler time series of ten known Am stars and find that six of them clearly show δ Scuti pulsations. The other four appear to be non-pulsating. We derive fundamental parameters for all known pulsating Am stars from ground-based observations and also for the Kepler Am stars to investigate the location of the instability strip for pulsating Am stars. We find that there is not much difference between the Am-star instability strip and the δ Scuti instability strip. We find that the observed location of pulsating Am stars in the HR diagram does not agree with the location predicted from diffusion calculations.

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Mon. Not. R. Astron. Soc. 414, 792–800 (2011) doi:10.1111/j.1365-2966.2011.18454.x
Kepler observations of Am stars?
L. A. Balona,1† V. Ripepi,2G. Catanzaro,3D. W. Kurtz,4B. Smalley,5P. De Cat,6
L. Eyer,7A. Grigahc` ene,8S. Leccia,2J. Southworth,5K. Uytterhoeven,9
H. Van Winckel,10J. Christensen-Dalsgaard,11H. Kjeldsen,11D. A. Caldwell,12
J. Van Cleve12and F. R. Girouard13
1South African Astronomical Observatory, PO Box 9, Observatory 7935, Cape Town, South Africa
2INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Napoli, Italy
3INAF-Osservatorio Astrofisico di Catania, Via S. Sofia 78, I-95123 Catania, Italy
4Jeremiah Horrocks Institute of Astrophysics, University of Central Lancashire, Preston PR12HE
5Astrophysics Group, Keele University, Staffordshire ST5 5BG
6Koninklijke Sterrenwacht van Belgie, Brussels, Belgium
7Observatoire de Gen´ eve, 51 ch. des Maillettes, CH-1290 Sauverny, Switzerland
8Centro de Astrofisica, Faculdade de Ciˆ encias,, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
9Laboratoire AIM, CEA/DSM CNRS-Universit´ e Paris Diderot, Paris, France
10Instituut voor Sterrenkunde, K.U. Leuven, Celestijnenlaan 200B, 3000 Leuven, Belgium
11Department of Physics and Astronomy, Building 1520, Aarhus University, 8000 Aarhus C, Denmark
12SETI Institute/NASA Ames Research Center, Moffett Field, CA 94035, USA
13Orbital Sciences Corporation/NASA Ames Research Center, Moffett Field, CA 94035, USA
Accepted 2011 January 29. Received 2011 January 27; in original form 2010 December 17
ABSTRACT
We present an analysis of high-resolution spectra for two pulsating Am stars in the Kepler
field. The stellar parameters derived in this way are important because parameters derived
from narrow-band photometry may be affected by the strong metal lines in these stars. We
analyse the Kepler time series of ten known Am stars and find that six of them clearly show δ
Scutipulsations.Theotherfourappeartobenon-pulsating.Wederivefundamentalparameters
for all known pulsating Am stars from ground-based observations and also for the Kepler Am
stars to investigate the location of the instability strip for pulsating Am stars. We find that there
is not much difference between the Am-star instability strip and the δ Scuti instability strip.
We find that the observed location of pulsating Am stars in the HR diagram does not agree
with the location predicted from diffusion calculations.
Key words: stars: chemically peculiar – stars: fundamental parameters – stars: oscillations –
stars: variables: δ Scuti.
1 INTRODUCTION
The study of pulsating stars in the δ Scuti instability strip has been
rapidly developing over the last few years. Previous to space mis-
sions such as MOST, CoRoT and Kepler, we could separate the δ
Sct stars from the cooler γ Dor stars purely on the basis of the
frequencies. Ground-based observations of δ Sct stars showed that
?Based on observations made with the Italian Telescopio Nazionale Galileo
(TNG) operated on the island of La Palma by the Fondaci´ on Galileo Galilei
of the Istituto Nazionale di Astrofisica (INAF), at the Spanish Observatorio
del Roque de los Muchachos of the Instituto de Astrofisica de Canarias,
and with the Mercator Telescope operated on the island of La Palma by the
Flemish Community.
†E-mail: lab@saao.ac.za
all have frequencies higher than about 5 d−1. These are predomi-
nantly p modes driven by the κ mechanism operating in the partial
ionization zone of He II. γ Dor stars are located near the red edge
of the δ Sct instability strip and have frequencies lower than 5 d−1.
These are g modes driven by the convective blocking mechanism.
A few stars showing characteristics of both types of variable
were discovered and labelled as hybrid δ Sct/γ Dor pulsators. The
presenceofbothtypesofmodesinsomemodelsofthesestarsshows
thatconvectiveblockingandκ mechanismcansimultaneouslydrive
low-frequency g modes and high-frequency p modes and explains
the existence of the hybrids (Dupret et al. 2005). A significant
part of the δ Sct instability strip overlaps the γ Dor instability
strip and it is in this region where models show both low and
high frequencies. The gap between the two frequency regimes is
explained by radiative damping.
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Kepler observations of Am stars
793
Results from CoRoT and particularly from Kepler have com-
pletely changed this picture. The lower detection limit from space
observations shows that both high and low frequencies are present
in almost all stars in the δ Sct instability strip (Grigahc` ene et al.
2010). This means that it is no longer possible to distinguish be-
tween δ Sct and γ Dor stars on frequencies alone. The frequency
gap predicted by the models does not exist. This problem remains
unresolved at this stage.
The Ap stars are magnetic stars where the effect of diffusion in
a magnetic field has left surface patches of different abundances.
Vertical segregation of elements is also present. Our current under-
standing of diffusion is that He should drain from the ionization
zone. When insufficient He remains in the driving region, the star
cannot pulsate. On this basis, we would not expect to observe Ap
stars with pulsations in the δ Sct frequency range. Furthermore,
since Ap stars have strong magnetic fields, damping of pulsations
due to magnetic slow wave leakage is also expected. The lack of
δ Sct pulsations in Ap stars is indeed supported by ground-based
observations where so far only one Ap star is known to be a δ Sct
variable (Koen et al. 2001). However, Kepler observations of Ap
stars indicate that pulsation in Ap stars may be more common than
expected (Balona et al. 2011).
Note that driving of the high-frequency pulsations in roAp stars
is not connected with helium, but appears to be due to the opacity
bumpinthehydrogenionizationzone.Pulsationalinstabilityoccurs
whenconvectioninthiszoneissuppressedbyamagneticfield.Thus
the effect of diffusion is quite different in this case.
Closely related to the Ap stars are the metallic-lined A stars,
the Am stars. These are A-type stars (judging by the strength of
the Balmer lines), but with strong absorption lines of some met-
als such as Zn, Sr, Zr and Ba and weaker lines of other met-
als such as Ca and/or Sc (Preston 1974). The strengths of these
metal lines are more typical of an F star rather than an A star.
It is thought that these anomalies are a result of diffusion in a
non-magnetic star. A peculiarity of Am stars is that their pro-
jectedrotationalvelocitiesaregenerallysmallerthannormalAstars
(v sini typically less than 100 km s−1) and that the vast majority
of Am stars are known to be members of close binary systems.
Rotational braking by tidal friction in a binary system is regarded
as a possible explanation for the low rotational velocities of Am
stars. Slow rotation further assists the segregation of elements by
diffusion.
For many years it was thought that Am stars did not pulsate, in
accordance with the expectation of diffusion which depletes helium
from the driving zone. More intensive observations have revealed
that this picture is not correct and several Am stars are known
to pulsate from ground-based observations. The diffusion scenario
has been modified to include diffusion of heavy elements (Turcotte
et al. 2000). This new model makes certain predictions regarding
the location of pulsating Am stars in the HR diagram which can be
tested.
In this context, data from the Kepler satellite can provide impor-
tant information on the incidence of pulsation in Am stars. Because
Kepler photometry attains a precision of only a few µmag even
for rather faint stars, lack of variability due to pulsation cannot be
attributed to insufficient detector sensitivity. It may then be possible
to falsify current theories regarding diffusion in Am stars if pulsa-
tion is detected outside the region in the HR diagram where theory
dictates that pulsation should not occur. There are 10 known Am
stars in the Kepler field of view, which is a reasonable sample for
thispurpose.AnoverviewoftheKepler scienceprocessingpipeline
is presented by Jenkins et al. (2010).
Of course, it is necessary to place these stars in the HR diagram,
and for this purpose high-resolution spectroscopy is the best tool.
Because of the blanketing caused by the chemical peculiarities in
the atmospheres of Am stars, fundamental stellar parameters based
on photometric indices may not be appropriate for Am stars. This
problem can only be resolved by matching synthetic spectra to the
observed spectra of Am stars. For this purpose, we present an anal-
ysis of two Kepler Am stars: KIC11402951 and KIC11445913.
The only previous investigation of these two Am stars is the recent
preliminary analysis by Catanzaro et al. (2011) and observations
by Abt (1984) who obtained photographic spectra with 1 Å resolu-
tion for classification purposes. A spectroscopic analysis of a third
Kepler star, KIC 7548479, is already available (Antoci et al., in
preparation).
Using these results, we discuss how the ten pulsating and non-
pulsating Am stars observed by Kepler can help us understand
the diffusion process in these stars. We supplement these results
with data from all known pulsating Am stars from ground-based
observations and compare the instability region for these stars with
that calculated from recent Am star models incorporating heavy-
element diffusion.
2 SPECTROSCOPIC OBSERVATIONS
SARG is a high-resolution cross-dispersed echelle spectrograph
(Gratton et al. 2001) that operates in both single-object and longslit
modes (with up to 26 slits). The spectra cover the wavelength range
from 3700 Å up to about 10000 Å with a resolution ranging from
R = 29000 to 164000.
Spectra were obtained on 2009 November 51at R = 57000 with
exposure times of 600 s using two grisms (blue and yellow) and
two filters (blue and yellow). These were used in order to obtain a
continuous spectrum from 3600 to 7900 Å with significant overlap
inthewavelengthrangebetween4620and5140Å.Weanalysedthe
spectral region 4600–6100 Å where the signal-to-noise ratio (S/N)
is largest (60 < S/N < 140). In the region centered around the Mg I
triplet at 5170 Å the measured S/N is about 80.
One spectrum of KIC11445913 was acquired on 2010 April
22 with the HERMES@Mercator Telescope. The spectral range is
4000–9000ÅwithS/Natleast150andresolvingpowerR≈85000.
Five further spectra of this star were obtained with the Sandiford
Cassegrain Echelle Spectrometer mounted on on the 2.1-m Otto
Struve Telescope at McDonald Observatory, Texas, USA. Spectra
wereobtainedbetween2010June22and28,witharesolvingpower
of R ≈ 60000. Depending on conditions, the S/N varies from 80
to 250. The reduction of all spectra was done using the NOAO/IRAF
packages.2The IRAF package rvcorrect was used to correct times to
the heliocentric rest frame.
Since quite a few spectra taken at different times are available
for KIC11445913, we decided to investigate the radial velocity
variation using the fxcor cross-correlation code in IRAF. For this
purpose, we also included a spectrum obtained at the INAF-Catania
Astrophysical Observatory which was previously used in the anal-
ysis of Catanzaro et al. (2011). The resulting radial velocities are
shown in Table 1. These are clustered in two groups spanning about
10km s−1, suggesting that KIC11445913 is probably a single-lined
1Director discretionary time, proposal ID: A20DDT5.
2IRAF is distributed by the National Optical Astronomy Observatory, which
is operated by the Association of Universities for Research in Astronomy,
Inc.
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794
L. A. Balona et al.
Table 1. Radial velocities (km s−1) for KIC11445913.
The truncated heliocentric Julian day (HJD - 245000.0) is
given. The last column shows the observatory where spectra
were obtained as follows: Catania Astrophysical Observa-
tory (OAC), Telescopio Nazionale Galileo (TNG), Hermes
(Her), McDonald Observatory (McD).
HJD
Vrad
Obs
5104.4784
5141.3271
5309.5687
5370.7018
5371.6582
5372.6497
5373.7117
5376.6495
−35.0±1.7
−34.1±1.3
−26.2 ±0.5
−21.9±2.5
−21.3±3.1
−21.8±3.6
−22.6±3.0
−24.3±6.7
OAC
TNG
Her
McD
McD
McD
McD
McD
Table 2. Data for two Kepler Am stars discussed in this
paper. Teff(lit) (in K) is from Catanzaro et al. (2011) and
Teff(TNG) is from the Hβ observations with SARG@TNG.
Teffis the finally adopted effective temperature, while log g
and v sini are the surface gravity (cgs units) and projected
rotational velocity (km s−1) derived from the spectra.
QuantityKIC11402951 KIC11445913
V (mag)
Teff(lit)
Teff(TNG)
Teff
log g
v sini
8.148.46
7150 ± 120
7400 ± 150
7250 ± 100
3.5 ± 0.1
100 ± 2
7200 ± 120
7400 ± 200
7250 ± 100
3.5 ± 0.2
51 ± 1
spectroscopic binary. Nearly all Am stars are members of binary
systems so this result is not surprising.
3 PHYSICAL PARAMETERS
We determined the effective temperature, Teff, and surface gravity,
logg,ofthestarsbyminimizingthedifferencebetweentheobserved
andthesyntheticHβ lineprofiles.Forthegoodness-of-fitparameter,
we used χ2defined as
??
where N is the total number of points, Iobsand Ithare the intensities
of the observed and computed profiles, respectively, and δIobsis the
photon noise. The standard deviation of a particular quantity can
be calculated from the deviation which will increase χ2by unity.
The values of Teff, log g and v sini in Catanzaro et al. (2011) were
used as starting values for the solution. The projected rotational
velocity was estimated by matching the metallic line profiles in the
range 5160–5200 Å with synthetic profiles. In this spectral range,
the Mg I triplet at 5167.321, 5172.684 and 5183.604 Å is a very
useful diagnostic for surface gravity. The value of log g from these
lines was used to check the reliability of log g determined from the
Hβ line profile fit.
Wehaveadoptedtheweightedmeanoftheeffectivetemperatures
and gravities determined in this study and in Catanzaro et al. (2011)
as final values. These results are shown in Table 2. Note that the
projected rotational velocity of 100 km s−1for KIC11402951 is
among the highest for an Am star. In Fig. 1, we show the match
between the data and the synthetic Hβ line profiles. The synthetic
line profiles were computed with SYNTHE (Kurucz & Avrett 1981)
using ATLAS9 (Kurucz 1993) atmospheric models. All models
were calculated using the solar opacity distribution function and a
microturbulence velocity ξ =3 km s−1. This value was determined
fromtheξ = ξ(Teff,logg)calibrationinAllendePrietoetal.(2004).
High-dispersion spectroscopy gives values of log Teffand log g,
but we need log L/L?to place the star in the HR diagram. One
way to do this is simply to use log g as an indicator of spectral class
and use a calibration of spectral type as a function of luminosity
to obtain log L/L?. This is the method used in Catanzaro et al.
(2011). Evolutionary models give us log Teff, log L/L?and log g
for a given mass and composition, so one can select a model which
matches the log Teff, log g value to directly obtain log L/L?with
much better precision.
Wecanalsodispensewithevolutionarymodelsaltogetheranduse
a purely empirical mass–luminosity relationship. We use L/L?=
(R/R?)2(Teff/Teff?)4together with g/g?= (M/M?)/(R/R?)2
to eliminate the stellar radius, R. This leaves us with a relationship
expressing the luminosity in terms of the effective temperature,
gravity and mass. The mass can be eliminated using a suitable
mass–luminosity relationship, giving log L/L?in terms of log Teff
χ2=
1
N
Iobs− Ith
δIobs
?2
,
Figure 1. Observed and synthetic Hβ line profiles for two Kepler Am stars. Fundamental parameters for the synthetic line profiles are given in Table 2.
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Kepler observations of Am stars
795
and log g. We used the relationship in Torres, Andersen & Gim´ enez
(2010).
SincereliabledeterminationoftheatmosphericparametersofAm
stars can be somewhat problematical (Smalley & Dworetsky 1993),
wehaveusedavailablebroad-bandphotometryandStr¨ omgrenuvby
photometry as an independent check on our spectroscopic determi-
nations. Spectral energy distributions constructed using broad-band
photometry from the literature were fitted using Kurucz (1993)
model fluxes to estimate values of Teff, which are generally in
reasonable agreement with the values listed in the Kepler Input
Catalogue (KIC) and those from spectroscopy. For the four Kepler
Am stars that have uvby photometry we have used the calibration of
Balona (1994) and the grids of Smalley & Kupka (1997) to deter-
mine Teffand log g, with luminosity estimated using the calibration
of Torres et al. (2010). These luminosity values are in accord with
those determined for stars with measured parallaxes (van Leeuwen
2007), but somewhat discrepant with those from spectroscopy due
to differences in log g of up to 0.5 dex.
4 METAL ABUNDANCES
The spectral lines in the two Kepler Am stars are relatively broad
and it is difficult to find unblended lines. To overcome this problem,
the stellar abundance was estimated by matching a rotationally
broadened synthetic spectrum to the observed spectrum. For this
purposewedividedthespectrumintoseparatewavelengthsegments
eachcoveringarangeof25Å.Foreachsegment,theabundancewas
determined by χ2minimization. We used the spectral line list and
atomic parameters in Castelli & Hubrig (2004) which are updated
from Kurucz & Bell (1995).
One can calculate the mean abundance of a particular element
from the individual abundances in each segment. The standard de-
viation of the mean can also be calculated. The standard deviation
of the mean calculated in this way was taken as the overall standard
deviationfortheabundanceoftheelementinquestion.Forelements
whose lines occurred in only one or two segments, the error in the
abundance was evaluated by varying the effective temperature and
gravity within their uncertainties (as given in Table 2) and com-
puting the abundance for Teffand log g values within these ranges.
We found a variation of ≈0.1 dex in abundance due to temperature
variation, but no significant variation when log g was varied. Thus
the uncertainty in temperature is probably the main source of error
intheabundance.InFigs2and3weshowexamplesofthematching
between synthetic and observed spectra. The abundances are given
in Table 3.
In Fig. 4 we show a comparison between the abundances derived
for our targets and the solar values in Grevesse et al. (2010). A
comparisonwiththeabundancesofnormalstarsofthesamespectral
type is also shown. To do this, we extracted a homogeneous sample
of abundances for A-type stars with 7000 ≤ Teff ≤ 8000 K and
3.5 ≤ log g ≤ 4.0 from the list of Erspamer & North (2003) (a total
of 42 stars). We used the average abundance for each element in
these stars as a representative abundance. The standard deviation
of the representative abundance was determined from the scatter in
abundances.
Classical Am stars are defined as A-type stars in which the spec-
tral type from the Ca K line and the spectral type from other metal
lines differ by five or more spectral subclasses. In the two Am
stars, KIC11402951 and KIC11445913, we find a slight overabun-
dance of iron-peak elements such as Ti, Fe and Ni (≤0.8 dex). In
KIC11445913 there is also an overabundance of Ba (≈1 dex). The
Figure 2. Spectral interval between 5160 and 5400 Å of KIC11402951 ob-
served with the SARG spectrograph superimposed on the computed model.
Figure 3. As Fig. 2 but for KIC11445913.
abundances of Ca and Sc appear to be normal. This is unusual, but
not unknown among Am stars.
Abt (1984) classifies KIC11402951 as kF3hA9mF5 and
KIC11445913 as kA7hA9mF5, indicating that while the strength
of the Balmer lines indicates a spectral type of A9, the metal lines
indicate a spectral type of F5 in both stars. Indeed, we find that the
metal lines can be quite well matched in a solar abundance model
witheffectivetemperatureofabout6500KwhichcorrespondstoF5
(though the fit to the Hβ line is very poor, of course). This supports
the classification of these two stars as classical Am stars.
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L. A. Balona et al.
Table 3. Abundances inferred for the two stars of our sample expressed in
the form log N/Ntot. For comparison we report the abundances of the Sun
(Grevesse et al. 2010) and of the A-type stars (Erspamer & North 2003).
El.KIC11402951 KIC11445913 Sun A type
C
Na
Mg
Si
Ca
Sc
Ti
Cr
Mn
Fe
Ni
Sr
Y
Ba
–
−3.52 ± 0.20
−5.50 ± 0.20
−4.05 ± 0.10
−4.40 ± 0.20
−5.70 ± 0.20
−8.80 ± 0.20
−6.75 ± 0.10
−6.15 ± 0.20
−6.10 ± 0.15
−4.00 ± 0.20
−5.60 ± 0.10
−9.25 ± 0.10
−9.25 ± 0.10
−8.85 ± 0.10
−3.62 ± 0.05
−5.79 ± 0.04
−4.43 ± 0.04
−4.52 ± 0.03
−5.69 ± 0.04
−8.88 ± 0.04
−7.08 ± 0.05
−6.39 ± 0.04
−6.60 ± 0.04
−4.53 ± 0.04
−5.81 ± 0.04
−9.16 ± 0.07
−9.82 ± 0.05
−9.85 ± 0.09
−3.54 ± 0.08
−5.35 ± 0.12
−4.33 ± 0.13
−4.42 ± 0.06
−5.69 ± 0.09
−8.60 ± 0.15
−7.05 ± 0.10
−6.40 ± 0.12
−6.59 ± 0.13
−4.56 ± 0.11
−5.81 ± 0.13
−8.89 ± 0.34
−9.39 ± 0.15
−9.48 ± 0.18
−5.50 ± 0.10
−4.00 ± 0.10
−4.50 ± 0.10
−5.70 ± 0.20
−8.70 ± 0.10
−6.30 ± 0.25
−6.10 ± 0.20
−6.65 ± 0.20
−4.00 ± 0.10
−4.95 ± 0.15
–
−9.30 ± 0.20
−9.40 ± 0.10
Figure4. AbundancepatternsderivedfortwoKeplerAmstars(seeTable3).
Filled circles (black) show abundances relative to the solar values, while
open circles (red) show abundances relative to a sample of A-type stars.
5 Kepler OBSERVATIONS OF Am STARS
The Kepler Mission is designed to detect Earth-like planets around
solar-type stars using the transit method (Koch et al. 2010). To
achieve that goal, Kepler is continuously monitoring the brightness
of over 150000 stars for at least 3.5yr in a 105 deg2fixed field of
view.Theresultingphotometryallowsthedetectionofpulsationam-
plitudesofjustafewµmag.TheKepler observationsconsistmostly
of exposures of approximately 30 min duration (long cadence), but
a small allocation for short-cadence (1 min) exposures is available.
Long-cadence exposures are only able to detect frequencies lower
than about 24 d−1making them less useful for studying pulsations
in the δ Sct frequency range. As an indication of the quality of the
data, we show in Fig. 5 part of the light curves of the two Kepler
Am stars for which we obtained high-resolution spectroscopy.
Figure 5. Selected portion of light curves for the two Kepler Am stars for
which we obtained high-resolution spectra. Note the very high S/N of the
data.
The known Am stars which are accessible to Kepler are listed
in Table 4. All stars except KIC 3429637 were observed in short-
cadence mode. Most of the stars were observed during the survey
phaseandtheshort-cadencerunshavedurationsofabout10or30d,
but some of the stars have been observed for a much longer time in
long-cadence mode. There are, no doubt, a great many Kepler stars
which may be Am stars but for which no spectroscopy is available.
One such star for which high-dispersion spectroscopy has recently
been obtained is KIC 7548479 (Antoci et al. 2010, in preparation).
The periodograms of these stars are shown in Fig. 6. We notice
that while some stars definitely show pulsations in the δ Sct region,
others only show variability at much lower frequencies. We note
that the two Am stars that we have studied with high-resolution
spectroscopy both have very rich frequency spectra. KIC 11445913
would be classified as a δ Sct/γ Dor hybrid. On the other hand
KIC 11402951 has only very low amplitude signals in the low-
frequency range. Of the other stars, KIC 3429637, KIC 7548479,
KIC 9204718 and KIC 5219533 (another hybrid) show clear δ Sct
pulsations. The other Am stars do not show anything significant in
the δ Sct range, though clear low-frequency variability is present
in most cases. Some of this low-frequency variability may be of
instrumental origin as long-term trends in Kepler data are not fully
corrected. However, intrinsic variability could arise as a result of
rotational modulation, for example. While no Am star is known to
vary in this way from ground-based observations, it cannot be ruled
out in Kepler photometry due to the extraordinary high precision.
What we want to do is to place the Am stars in the HR diagram as
accurately as possible to see if there is a particular region for Am-
star pulsation. As already mentioned, the most reliable parameters
are those from high-dispersion spectroscopy, but there are only
five pulsating Am stars where such parameters are available. Other
pulsating Am stars have good Hipparcos parallaxes and these too
areimportantsincetheirluminositiescanbereliablyestimatedeven
if the effective temperatures are less certain. The stars in these two
categories are listed in Table 5.
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Table 4. Am stars observed by Kepler. The spectral classification from the literature is given in the third column. The columns marked
Long and Short give the time span of the observations in days for long- and short-cadence exposures. The last two columns give the
derived effective temperatures and luminosities.
KICNameClassificationLong Shortlog Teff
log L/L?
1.54a, 1.67b, 1.50d
1.08a
1.31c
1.15a
1.36a
0.90b
1.01a
1.32d
1.68c, 1.11c, 1.07d
1.01a, 1.68c, 0.90d
3429637
5219533
7548479
8323104
8703413
9117875
9204718
9272082
11402951
11445913
HD 178875
HD 226766
HD 187547
HD 188911
HD 187254
HD 190165
HD 176843
HD 179458
HD 183489
HD 178327
kF2hA9mF3
kA2hA8mA8
Am
kA2mF0
kA2mF0
kA2mF2
kA3mF0
Am?
kF3hA9mF5
kA7hA9mF5
310.6
9.7
44.4
44.4
44.4
33.4
44.4
44.4
228.9
228.9
–3.843a
3.870a
3.875a
3.880a
3.887a
3.865e
3.854a
3.929d
3.860c
3.842a, 3.860c
33.4
30.4
30.4
25.9
9.7
25.9
29.9
9.7
9.7
aFrom the KIC catalogue.bFrom Hipparcos parallaxes.cFrom high-dispersion spectroscopy.dFrom uvbyβ and Balona (1994) and
Smalley & Kupka (1997).eFrom broad-band photometry.
The KIC lists effective temperatures and radii for most stars
derived from the Sloan-like filters. The resulting values of
log Teffand log L/L?are shown in Table 4. For stars with available
Str¨ omgren photometry (Table 6), the temperature and luminosity
can be derived using the calibrations in Balona (1994). The stars
in these two categories have less reliable parameters and should be
given less weight than the stars in Table 5.
Duetotheextraordinaryphotometricprecisionof Kepler,wecan
be practically certain that the non-pulsating Kepler stars are indeed
non-pulsating. This is not the case for ground-based observations
of Am stars. Non-detection of pulsation in this case could just mean
that the pulsational amplitude is below one millimag, the typical
threshold for ground-based photometry. Therefore, the location in
the HR diagram of Am stars which are deemed to be non-pulsating
from ground-based observations is not very useful.
It is, however, important to include ground-based data of pulsat-
ing Am stars to improve the statistics. For this purpose, we show
in Table 6 pulsating Am stars with uvbyβ photometry and derive
the effective temperatures and luminosities using the Balona (1994)
calibration. Note that HD 114839 in this table was observed by the
MOST satellite (King et al. 2006). We have also included some
preliminary results from (Smalley et al., in preparation) who iden-
tified around 200 pulsating Am stars using the photometry from the
SuperWASP Exoplanet Survey (Pollacco et al. 2006).
The typical standard deviation of Teff obtained from spectro-
scopic measurements is about 200 K which contributes to a stan-
dard deviation of about 0.01 in log L/L?. The spectroscopic value
of log g has a typical standard deviation of about 0.1–0.2 which
leads to a standard deviation of 0.2–0.3 in log L/L?. The standard
deviation of Tefffrom Str¨ omgren photometry is in the range 100–
400 K (Balona 1994), but there might be a unknown systematic
error for Am stars, of course. The standard deviation in the absolute
magnitude derived for A-F stars is typically 0.3–0.4 mag which is
about 0.15–0.20 in log L/L?. Overall, we may attach a standard
deviation of about 0.01 in log Teffand 0.2–0.3 in log L/L?.
We show the resulting location of the constant and pulsating Am
stars in Fig. 7. Whenever possible we use parameters from Table5,
failing this we use parameters from Table6 and lastely the KIC
parameters in Table4. There does not appear to be a systematic
difference between stars with spectroscopic or parallax measure-
ments and those whose parameters were determined from the KIC
or uvbyβ photometry. Besides the Am stars, we show in this dia-
gram all known Kepler δ Sct stars (using parameters in the KIC) as
well as δ Sct stars from ground-based observations for which the
parameters can be derived using uvbyβ photometry and the Balona
(1994) calibration.
6 DISCUSSION
The question of why the atmospheres of Am stars are enriched in
metals is not fully understood. In Am and Ap stars, the observed
abundance anomalies are thought to develop as a consequence of
diffusion in which He sinks and metals rise. In A and F stars there
are two thin convective regions just below the photosphere in which
H and He II are partially ionized. In non-magnetic stars these two
convective zones merge to form a single convective layer. As He
drains from the envelope due to diffusion, the opacity in this joint
convective layer drops, resulting in a much thinner layer supported
by ionization of hydrogen. As a consequence, the opacity bump
is modified and pulsation can no longer be driven. The study of
pulsation among Am stars can tell us about the opacity in envelope,
providing information and a probe of diffusion in these stars.
Itturnsoutthatifonlythediffusionofheliumisconsidered,mod-
els predict a much larger over-abundance of heavy elements than
actually observed. This problem appears to be solved if diffusion
of heavy elements is also taken into account (Turcotte et al. 2000).
As heavy elements settle, the deeper iron-bump opacity region at
about 2 × 105K is enriched by these elements, which increases the
opacity. As a result, a convective zone develops in this region. This
new convective zone, which lies below the thin convective zone of
partial hydrogen ionization, is assumed to mix with the hydrogen
convection zone by overshooting. The result is a single, thicker,
convective zone in which the abundance anomalies are diluted. In
this way, the calculated abundances are in better agreement with
observations.
Theinclusionofheavyelementdiffusionalsoleavesasubstantial
amount of helium in the He II driving region and increases the iron-
bumpopacity.Thuspulsationaldrivingmayresultincertainregions
of the HR diagram. In this scenario, the effect of diffusion on
pulsation is to reduce the width of the instability strip, with the
blue-edge shifting towards the red edge, eventually leading to the
disappearance of instability when helium is sufficiently depleted
from the He II ionization zone (Turcotte et al. 2000). The amount
of driving is related to the amount of helium still present in the
convective envelope and therefore to the depth of the convective
envelope. The cooler the star, the deeper the convective envelope
and the larger the driving. This is the physical reason why the blue
edge moves towards cooler temperature in these Am star models.
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798
L. A. Balona et al.
Figure 6. Periodograms of Am stars from Kepler photometry. The numbers in the panels refer to the KIC identifications.
Another effect of diffusion is that driving from the ionization of
iron-group metals increases relative to driving from He II ioniza-
tion. As a consequence, it turns out that the pulsation frequency
depends on the depth of the He II ionization zone. As the star
evolves, the depth of this zone increases and the frequencies de-
crease (Turcotte et al. 2000). It is found that models of young
Am stars near the zero-age main-sequence (ZAMS) are stable,
while those of δ Sct stars of the same age pulsate. Models of Am
stars eventually become pulsationally unstable as the star evolves,
whereas standard δ Sct models remain pulsationally unstable
throughout.
According to the hypothesis described above, one may expect to
find pulsating Am stars near the cool edge of the instability strip.
Neither hot Am stars nor Am stars near the ZAMS should pul-
sate (Turcotte et al. 2000). The blue edge of the instability strip
for Am stars depends on the over-abundance factor. In models rep-
resentative of Am stars, turbulence is high enough to prevent the
development of convection in the Fe-bump opacity region while
allowing a significant increase of the Fe-bump opacity. This has the
marginal effect of destabilizing some high radial overtone g modes.
The higher frequency modes depend mostly on the He abundance
and to a lesser extent on the H abundance as well. Fig.7 shows
the approximate maximum extent of the instability region for Am
stars according to Turcotte et al. (2000). At that time, it was thought
that the majority of Am stars do not pulsate, but that evolved Am
stars (the δ Del stars) do pulsate. Reasonable agreement between
the location of pulsating δ Del stars and the predicted instability
strip was found.
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Kepler observations of Am stars
799
Table 5. Am stars which have very good trigonometric parallaxes (P) or good spectroscopic parameters (S).
Effective temperatures, Teffare in K and surface gravity, g, in cm s−2.
HDClassification log Teff
log g
log L/L?
TypeReference
8801
27628
71297
98851
102480
104513
178327
183489
187547
199434
204188
kA5hF1mF2
kA5hF0mF2
A5III-IV
kF1hF1IVmF3
kF2hF4mF4
A7m
kA7hA9mF5
kF3hA9mF5
Am
F5II-III
kA6hA9mF0
3.855
3.864
3.900
3.845
3.843
3.879
3.860
3.860
3.875
3.825
3.898
4.20
4.00
4.19
3.50
3.11
4.24
3.50
3.50
3.90
0.80
1.04
1.14
1.67
2.18
0.88
1.75
1.75
1.30
1.57
0.89
S
P
P
S
S
P
S
S
S
P
P
Henry & Fekel (2005)
Burkhart & Coupry (1989)
Allende Prieto & Lambert (1999)
Joshi et al. (2003)
Robinson et al. (2007)
Allende Prieto & Lambert (1999)
KIC 11445913
KIC 11402951
Antoci et al. (2010)
Hohle, Neuhauser & Schutz (2010)
Allende Prieto & Lambert (1999)
–
4.34
Table 6. Pulsating Am stars not in the Kepler field. The effective tempera-
turesandluminositiesarederivedfrompublisheduvbyβ photometryandthe
Balona (1994) calibration. References to the pulsational nature are shown
in the last column.
HD Classificationlog Teff
log L/L?
Reference
1097
8801
13038
13079
27628
71297
104513
113878
114839
118660
204188
A3/5mF0-F5
kA5hF1mF2
A4m
Am
kA5hF0mF2
A5III-IV
A7m
kA5hF0mF3
kA5mF0
A1 IV
kA6hA9mF0
3.880
3.868
3.911
3.874
3.872
3.907
3.879
3.865
3.879
3.883
3.898
0.11
0.75
0.76
0.62
0.81
0.81
0.87
0.91
0.72
0.96
0.74
Kurtz (1989)
Henry & Fekel (2005)
Martinez et al. (2001)
Martinez et al. (2001)
Zhiping (2000)
Kurtz (1984)
Kurtz (1978)
Joshi et al. (2006)
King et al. (2006)
Joshi et al. (2006)
Kurtz (1978)
From Fig.7 we see that the pulsating Kepler Am stars occupy
more or less the same region as normal δ Sct stars. There are several
pulsating Am stars with parameters determined by spectroscopy or
parallaxesthatarewelloutsidethepredictedinstabilitystrip.Infact,
themoreevolvedAmstars,whichincludesbothKIC11402951and
KIC 11445913, are quite close to the theoretical radial fundamental
blue edge. On the other hand, the two non-pulsating Am stars in
Kepler do seem to be hotter than the pulsating Am stars, but we
are dealing here with very small numbers. It would be important
to obtain the physical parameters for the other two non-pulsating
Kepler Am stars.
What is certainly clear from Fig.7 is that there is no relationship
between the predicted Am instability strip based on our current
understanding of diffusion in these stars, and the actual location of
pulsatingAmstars.Itistruethat,asTurcotteetal.(2000)found,the
locationofthemoreevolvedpulsatingδ Delstarsareconsistentwith
the predicted instability strip. What we find here is that pulsation
in relatively unevolved Am stars appears to be quite common (six
of the ten Kepler Am stars pulsate) and that this is not currently
explained in the context of diffusion.
7 CONCLUSION
We obtained high-resolution spectra of two pulsating Am stars in
the Kepler field. Such measurements are very important because
physical parameters derived from narrow-band photometry may be
unreliable. We also find that six of the ten Am stars observed by
Kepler show δ Sct pulsations (with two showing low-amplitude
Figure7. LocationofAmstarsinthetheoreticalHRdiagram.Filledcircles
are Kepler pulsating Am stars and filled squares are other pulsating Am
stars.Thelargersymbolsarethestarsforwhichparametersweredetermined
fromspectroscopyorparallaxes.Crossedopencirclesaretwonon-pulsating
Kepler Am stars (KIC 188911 and KIC 187254). The asterisks are pulsating
Am stars from SuperWASP observations. The gray area is the approximate
location of pulsating Am-star models incorporating heavy-metal diffusion.
The small background points are known δ Sct stars from ground-based
observationsandfromKepler.Evolutionarytracks(fromDupretetal.2004)
are shown for the indicated masses. Also shown are the fundamental radial
mode red and blue edges from Dupret et al. 2004. Typical errors of 0.01 in
log Teffand 0.25 in log L/L?are indicated by the cross on the bottom left
hand corner.
γ Dor pulsations as well). The other four Am stars do not show any
δ Sct pulsations to a level of a few µmag.
We used the spectroscopic estimates of three pulsating Kepler
Am stars to place these stars in the theoretical HR diagram. The
location of most of the other Kepler Am stars could be estimated
either from the KIC parameters or from uvbyβ photometry and the
Balona (1994) calibration. We also investigated all other observa-
tions of pulsating Am stars, particularly those with good spectro-
scopic parameters or with luminosities which could be estimated
from the parallax. It is found that the spectral energy distributions
constructed using broad-band photometry lead to effective temper-
atures which are generally in reasonable agreement with the values
listed in the Kepler Input Catalogue and those from spectroscopy.
The location of these stars in the HR diagram was compared to
that of normal δ Sct stars and to the instability strip calculated by
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L. A. Balona et al.
Turcotte et al. (2000) from diffusion and pulsation models. We find
that there is no obvious difference in the location of the pulsating
Am stars and δ Sct stars, though the two constant Kepler Am stars
that could be placed in the diagram are somewhat hotter than most
of the pulsating Am stars. Whereas diffusion models predict that
there should be no pulsating Am stars near the ZAMS, we find that
many of these stars are, in fact, relatively unevolved. There are also
severalpulsatingAmstarswithwell-determinedparametersthatare
considerably more luminous and hotter than predicted by pulsating
Am-star models. The discrepancy between the observed and calcu-
lated instability strips for these stars suggest that our concept of the
interaction between pulsation and diffusion in these stars needs to
be revised.
ACKNOWLEDGMENTS
The authors wish to thank the Kepler team for their generosity
in allowing the data to be released to the Kepler Asteroseismic
Science Consortium (KASC) ahead of public release and for their
outstandingeffortswhichhavemadetheseresultspossible.Funding
for the Kepler mission is provided by NASA’s Science Mission
Directorate.
This work was partially supported by the Italian ESS project,
contract ASI/INAF I/015/07/0, WP 03170. We wish to thank the
director of Telescopio Nazionale Galileo for the observing time
provided us under the Director Discretionary Time programme.
LAB wishes to thank the South African Astronomical Observa-
tory for financial support.
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C ?2011 The Authors, MNRAS 414, 792–800
Monthly Notices of the Royal Astronomical Society C ?2011 RAS