Physical parameters of Kepler target

Atmospheric parameters and pulsational properties for a sample of  Sct,  Dor, and hybrid Kepler targetsthanks: This work is based on spectra taken at the Loiano (INAF - OA Bologna) and Serra La Nave (INAF - OA Catania) Observatories.

G. Catanzaro, V. Ripepi, S. Bernabei, M. Marconi, L. Balona, E-mail: gca@oact.inaf.it    D. W. Kurtz, B. Smalley, W. J. Borucki, H. Bruntt, J. Christensen-Dalsgaard,    A. Grigahcène, H. Kjeldsen, D. G. Koch, M. J. P. F. G. Monteiro,    J.C. Suárez, R. Szabó, K. Uytterhoeven
INAF-Osservatorio Astrofisico di Catania, Via S.Sofia 78, I-95123, Catania, Italy
INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131, Napoli, Italy
INAF-Osservatorio Astronomico di Bologna, Via Ranzani 1, I-40127, Bologna-Italy
South African Astronomical Observatory, P.O. Box 9, Observatory 7935, Cape Town, South Africa
Jeremiah Horrocks Institute of Astrophysics, University of Central Lancashire, Preston PR1 2HE, UK
Astrophysics Group, Keele University, Keele, Staffordshire ST5 5BG, UK
NASA Ames Research Center, MS 244-30, Moffett Field, CA 94035, USA
Observatoire de Paris, LESIA, 5 place Jules Janssen, 92195 Meudon Cedex, France
Department of Physics and Astronomy, Building 1520, Aarhus University, 8000 Aarhus C, Denmark
Centro de Astrofísica and Faculdade de Ciências, Universidade do Porto, Rua das Estrelas, 410-762 Porto, Portugal
Instituto de Astrofísica de Andalucía (CSIC). Rotonda de la Astronomía S/N. Granada, Spain
Konkoly Observatory of the Hungarian Academy of Sciences, PO Box 67, 1525 Budapest, Hungary
Laboratoire AIM, CEA/DSM-CNRS-Université Paris Diderot; CEA, IRFU, SAp, centre de Saclay, 91191, Gif-sur-Yvette, France
Accepted 2010 September 21. Received 2010 September 21; in original form 2010 June 4
Abstract

We report spectroscopic observations for 19  Sct candidates observed by the Kepler satellite both in long and short cadence mode. For all these stars, by using spectral synthesis, we derive the effective temperature, the surface gravity and the projected rotational velocity. An equivalent spectral type classification has been also performed for all stars in the sample. These determinations are fundamental for modelling the frequency spectra that will be extracted from the Kepler data for asteroseismic inference. For all the 19 stars, we present also periodograms obtained from Kepler data. We find that all stars show peaks in both low- ( Dor; g mode) and high-frequency ( Sct; p mode) regions. Using the amplitudes and considering 5 c/d as a boundary frequency, we classified 3 stars as pure  Dor, 4 as  Dor -  hybrid, Sct, 5 as  Sct -  Dor hybrid, and 6 as pure  Sct. The only exception is the star KIC 05296877 which we suggest could be a binary.

keywords:
Stars: fundamental parameters – Stars: oscillations (including pulsations) – Stars: early-type
pagerange: Atmospheric parameters and pulsational properties for a sample of  Sct,  Dor, and hybrid Kepler targetsthanks: This work is based on spectra taken at the Loiano (INAF - OA Bologna) and Serra La Nave (INAF - OA Catania) Observatories.Referencespubyear: 2002
KIC ID    Other ID Observ. S.T.
mag mag
(1)      (2)   (3) (4) (5) (6)
03219256 HD 178306 L,OACT 8.31 0.020.01 A3
03429637 HD 178875 OACT 7.72 0.040.02 A9,Am
03437940 HD 181569 L,OACT 8.45 0.060.01 F0
04570326 HAT 199-01905 L 9.77 0.000.02 A2
05296877 HAT 199-27597 L 12.50 0.000.02
05724440 HD 187234 L,OACT 7.90 0.060.01 A5
05965837 HAT 199-00623 L 9.23 0.010.02 F2
05988140 HD 188774 L 8.83 0.070.01 F0
07119530 HD 183787 L 8.45 0.020.01 A3
07798339 HD 173109 L,OACT 7.87 0.000.01 F0
08197788 NGC6866-V1 L 12.98 0.120.02
08264404 NGC6866-V3 L 12.22 0.120.02
08264698 NGC6866-V2 L 12.38 0.120.02
08583770 HD 189177 L 10.16 0.170.03 B9
09655114 NGC6811-RH35 L 12.09 0.120.02 A4
09775454 HD 185115 L,OACT 8.19 0.010.01 F1IV
11402951 HD 183489 L,OACT 8.14 0.030.01 A9,Am
11445913 HD 178327 L,OACT 8.46 0.030.01 A9,Am
11973705 HD 234999 L 9.10 0.000.02 B9

a) from photometry; b) from () photometry; c) from () photometry; d) Dutra & Bica (2000); e) Glushkova et al. (1999).

1) SIMBAD; 2) Abt (1984); 3) Fehrenbach & Burnage (1990); 4) Nordstrom et al. (1997); 5) Couteau & Gili (1994); 6) Lindoff (1972); 7) Duflot et al. (1995)

Table 1: List of studied Kepler  Sct candidates. Columns (1) and (2) show the Kepler and other identifications; Column (3) reports the origin of the spectrum: L = Loiano, OACT = INAF - OACT; Columns (4), (5), and (6) report the magnitudes, the colour excess, and the spectral types taken from the literature.

1 Introduction

Stellar pulsations offer a unique opportunity to constrain the intrinsic parameters of stars and, by using asteroseismology, to unveil their inner structure. In particular, the classical  Sct variables are late A-type and early F-type stars that populate the instability strip between the zero-age main sequence and terminal-age main sequence, with . They pulsate in mode of low radial order with periods ranging from about 20 min to 8 h (see Breger, 2000, for a review).  Sct stars pulsate in both radial and non-radial p modes and g modes, driven by the -mechanism, in particular in the He ii ionization zone. The  Dor variables, with periods between about 0.3 and 3 d, are mostly located near the cool edge of the  Sct instability strip (Kaye et al., 1999). Their pulsations are driven by convective blocking at the base of their envelope convection zone (Guzik et al., 2000; Dupret et al., 2004; Grigahcène et al., 2004). The distinction between the two classes is clearer if we consider the value of the pulsation constant, Q (Handler & Shobbrook, 2002). However, the location of the  Dor stars in the Hertzsprung-Russell (HR) diagram suggests some relationship with the  Sct variables. Indeed, stars exist which show simultaneously both  Sct and  Dor pulsations (Henry & Fekel, 2005; King et al., 2006; Rowe et al., 2006; Uytterhoeven et al., 2008a; Handler, 2009). These hybrid objects are in principle of great interest, because they offer additional constraints on stellar structure. Indeed, the  Dor stars pulsate in g modes which have high amplitudes deep in the star and allow us to probe the stellar core, while the p modes, efficient in Sct stars, have high amplitudes in the outer regions of the star and probe the stellar envelope. Moreover, since  Dor stars pulsate in g modes of high radial order, the asymptotic approximation predicts regular patterns in the periods which, in principle, can be used to determine the spherical harmonic degree. Hybrids thus provide a unique opportunity for asteroseismology which is not available in pure  Sct stars (Handler & Shobbrook, 2002). Recently, a large separation-like feature has been discovered in the  Sct star HD 174936 by García Hernández et al. (2009) using CoRot data. In that work, such a regularity was used to constrain the modelling of this star. It is extremely interesting to search for such regularities in hybrid stars, for which the presence of other frequency regimes definitely may help the overall comprehension of the pulsational behaviour of these objects.

The Kepler satellite111 http://kepler.nasa.gov/ was launched on 2009 March 6 and will continuously monitor the brightness of over 100 000 stars for at least 3.5 yr in a 105 square degree fixed field of view near the plane of the Milky Way between Deneb and Vega. The main aim of the mission is to detect extrasolar planets, particularly Earth-sized planets in the habitable zone of their stars, where water may be liquid, by the transit method (Borucki et al., 1997). To accomplish this goal, Kepler is capable of measuring the stellar brightnesses to mag precision (Gilliland et al., 2010) which, together with the long duration of the observations, make the data ideal for asteroseismology. Most of the observations are long-cadence (29.4-min) exposures, though a small allocation is available for short-cadence (1-min) exposures. The long-cadence as well as some short-cadence data released to the Kepler Asteroseismic Science Consortium (KASC) have been surveyed for  Sct and/or  Dor stars. The long-cadence data are not always suitable for a detailed study of  Sct oscillations because many of these stars have frequencies higher than the Nyquist frequency (24.5 c/d) for 29.4-min sampling. These data are, however, suitable for the detection of  Sct –  Dor hybrids.

The early KASC data releases led to the discovery of the nineteen candidate  Sct stars listed in Table 1; many more have been found in subsequent data releases, and ground-based studies of these stars are now in progress. Interestingly, many objects show periodograms with frequencies both in the p mode  Sct and g mode  Dor domains, i.e., they are candidate hybrid pulsators (Grigahcène et al., 2010). Dedicated short-cadence Kepler data for the most promising hybrid candidates will be exploited for seismic studies of these stars. To this end it is extremely important to constrain the fundamental parameters of the stars (effective temperature , surface gravity , projected rotational velocity , luminosity ) in order to limit the range of models. Measurement of is essential to constrain the rotational velocity of the models. Stellar fundamental parameters can be obtained by using photometry, e.g., in the Strömgren system, or by means of mid- or high-resolution spectroscopic observations. Very few of the 19 Kepler  Sct stars have previously been observed spectroscopically and no reliable estimates of the stellar parameters can be derived from the existing data. For this reason, we undertook a systematic spectroscopic study of these Kepler targets and report our results here. This work fits in the ground-based observational efforts of KASC with the aim to characterize all Kepler pulsators (Uytterhoeven et al., 2010a, b).

KIC ID E. S.T.
km s K K K K cm/s cm/s cm/s
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
03219256 A8V 905 7500150 7450150 7650250 7450150 7300250 3.60.1 4.10.3 3.60.3
03429637 F0III 505 7100150 7650200 7400150 6950250 3.00.2 3.40.3
03437940 A7.5V 1205 7700120 7800150 7850250 7900150 7400250 4.10.2 3.70.3 3.90.3
04570326 F1V 8020 7000150 6600200 6900150 4.00.3
05296877 F4.5IV 20020 6500200 6000400 6500150 6650250 3.80.3 4.10.3
05724440 A9IV 2205 7350120 7700150 8150250 7850150 7300250 3.60.3 4.20.3 3.60.3
05965837 F1V 2010 6975200 6700200 6850150 6500250 4.00.4 4.10.3
05988140 A9IV 7020 7400150 7750150 7900250 7900150 7450250 3.70.3 3.70.3 3.50.3
07119530 A8IV 20020 7500200 7750150 7800250 7850150 7800250 3.60.3 3.30.3 3.50.3
07798339 F3IV 155 6700200 6900150 6800250 6900150 6700250 3.70.3 3.70.3 3.40.3
08197788 A8V 23020 7500150 7700200 7950150 8000250 4.00.3 4.00.3
08264404 A8IV 25020 7500200 7500200 7950150 7900250 3.70.3 3.70.3
08264698 A8V 21020 7500200 7650200 8000150 8000250 3.90.2 3.80.3
08583770 A2III 13010 9000200 8200300 8750200 7650250 3.00.2 3.50.3
09655114 A9V 15020 7400200 7850250 7700150 7750250 3.90.3 3.80.3
09775454 F1V 705 7050150 7150150 7300250 7050150 4.00.3 4.00.3
11402951 F0IV 1005 7150120 7450150 7450150 3.50.1
11445913 F0IV 505 7200120 7150150 7150150 6950250 3.50.2 3.90.3
11973705 A9.5V 12020 7300300 7350200 7400150 7400250 4.20.3 4.00.3
Table 2: Comparison of fundamental parameters obtained from spectroscopy and photometry, columns (2)-(6). In column (2) we report the Equivalent Spectral Type, i.e., the spectral type assigned to the stars by comparing the spectroscopic with the table in Schmidt-Kaler (1982)

2 Observations and data reduction

The spectra used in our analysis were acquired with two different instruments:

  1. Loiano Observatory: We used the Bologna Faint Object Spectrograph & Camera (BFOSC) instrument attached to the 1.5-m Loiano telescope222http://www.bo.astro.it/loiano/index.htm. We adopted the echelle configuration with Grism #9 and #10 (as cross dispersers). The typical resolution was . Spectra were recorded on a back-illuminated (EEV) CCD with pixels of 20 m size, typical readout noise of 1.73 e and gain of 2.1 e/ADU. Observations were carried out during the nights of 2009 September . The exposure times ranged from 1200 to 3600 s for the brightest and faintest targets respectively.

  2. INAF - OACT: the 91-cm telescope of the Istituto Nazionale di Astrofisica – Osservatorio Astrofisico di Catania (INAF–OACT) was used to carry out spectroscopy of eight of the targets. The telescope is fibre linked to a REOSC333REOSC is the Optical Department of the SAGEM Group. echelle spectrograph, giving R  20000 spectra in the range  Å. The resolving power was checked using the Th-Ar calibration lamp. Spectra were recorded on a thinned, back-illuminated (SITE) CCD with pixels of 24 m size. The typical readout noise was 6.5 e at a gain of 2.5 e/ADU. Observations were carried out during five nights: 2009 September 28, 29, 30 and November 19 and 28. Exposure times were fixed for all the stars at 1 h.

The reduction of spectra, which included the subtraction of the bias frame, trimming, correcting for the flat-field and the scattered light, the extraction of the orders, and the wavelength calibration, was done by using the NOAO/IRAF package444IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc.. The amount of scattered light correction was about 10 ADU. The S/N ratio of the spectra was at least  130 and 80 for Loiano and OACT observatories, respectively.

3 Physical parameters

3.1 Parameters from photometry: and

Complete Strömgren-Crawford photometry is available for seven objects in our sample (stars with an “” in column 5 of Table 1) while data are present for three additional objects (stars with a “” in column 5 of Table 1). The source of both the Strömgren and Strömgren-Crawford data is Hauck & Mermillod (1998). For the other six objects (identified with a “” in column 5 of Table 1) plus the three stars in NGC 6866, only Johnson photometry is available, mainly in filters. For these stars we used the values reported by SIMBAD. In the near-infrared, photometry of good quality is present in the 2MASS catalogue (Skrutskie et al., 1996) for all the targets.

For the seven stars with photometry, can be estimated by using the calibration by Moon (1985), using the IDL code uvbybeta. The result is reported in Table 1, where we have used the transformation (Cardelli et al., 1989). For the three stars without indices we used the equivalent spectral type derived in Section 3.2 to derive the intrinsic from the relation between and spectral type (Voigt, 2006). Similarly, for five stars with colours, we adopted the intrinsic colours as a function of spectral type (Schmidt-Kaler, 1982). We assigned a larger error to these values than those based on photometry. The remaining four variables are cluster members, three belong to NGC 6866 and one to NGC 6811. The reddenings of these two clusters were adopted from Dutra & Bica (2000) for NGC 6866 and Glushkova et al. (1999) and Luo et al. (2009) for NGC 6811.

Values of and were estimated from and using the data grid by Moon & Dworetsky (1985). Typical photometric errors (0.015 and 0.03 mag in and , respectively) have been assumed. The derived values of and are reported in Table 2 (columns 6 and 10, respectively). In calculating the uncertainties, we conservatively assumed an error of 250 K and 0.3 dex for and , respectively. The values of and derived from spectroscopy (see Section 3.2 below) and are in good agreement, with all the differences less than 3. Only KIC 05724440 (HD 187234) shows a difference in temperature close to the edge of this limit. We discuss this object in Section 3.3.

Figure 1: Examples of the fitting procedure for two stars of our sample. The top panel shows three spectral regions of KIC 11402951 (HD 183489) observed with the OACT equipment, while the bottom panel shows the same spectral range, but for KIC 05988140 (HD 188774) observed with the Loiano spectrograph. Both synthetic spectra have been computed with synthe based on LTE atlas9 atmospheric models with solar ODF and metallicity.

An additional photometric estimate of can be obtained from the calibrations by Masana et al. (2006). These are based on the colour as well as on and []. The and band were taken from the SIMBAD and 2MASS catalogues, respectively. For we use the value from our spectroscopy. For the metallicity, following Bruntt et al. (2008), we adopted . This arbitrary value has only a small impact on the results because varying by gives an error of only 40 K in . To de-redden the observed colours we adopted the reddening reported in Table 1, using the relation (Cardelli et al., 1989) for the stars with Strömgren photometry, and for the other stars. The resulting and the relative errors are reported in Table 2 (column 5). In general, there is good agreement between the photometric and spectroscopic values.

Near infrared photometry from 2MASS, complemented by the one in the optical, can be used to derive an alternative estimate of by means of the Infrared Flux Method (IRFM, Blackwell & Shallis 1977). In particular, broad-band photometry (this work, plus TASS4 I-mag, NOMAD R-mag, CMC14 r’ mag and 2MASS photometry) was used to estimate the total observed bolometric flux (). The photometry was converted to fluxes and the best-fitting Kurucz (1993b) model flux distribution was found and integrated to determine . The Infrared Flux Method (Blackwell & Shallis, 1977) was then used with 2MASS fluxes to determine the T reported in Table 2 (column 7).

Finally, we inspected the Kepler Input Catalogue (KIC555accessible via http://archive.stsci.edu/kepler/kepler_fov/search.php, Latham et al. (2005)) where additional estimates for and based mainly on 666Note, however, that only 25% of the KIC stars have photometry, and less than 0.1% have (see http://nsted.ipac.caltech.edu/data/NStED/kic_columns.html) are present. These value are reported in columns (8) and (11) of Table 2. It is worth noticing that the KIC catalogue was mainly aimed at separating dwarfs from giants, therefore the and are not expected to be very precise. Since no errors are present in the KIC catalogue, we assumed uncertainties of 250 K and 0.3 dex in and , respectively.

3.2 Parameters from spectroscopy: , and rotational velocities

We determined and of the stars by minimizing the difference between the observed and the synthetic H profiles. For the goodness-of-fit parameter we used defined as


where is the total number of points, and are the intensities of the observed and computed profiles, respectively, and is the photon noise. The errors have been estimated from the variation in the parameters required to increase by one. As starting values of and , we used and derived from the photometry, as described in the previous section. At the same time, we determined the projected rotational velocity by matching the Mgii 4481 Å profile with a synthetic profile. The synthetic profiles are computed with synthe (Kurucz & Avrett, 1981) on the basis of atlas9 (Kurucz, 1993a) LTE atmosphere models. All models are calculated using the solar opacity distribution function (ODF), solar metallicity and a microturbulence velocity of  = 2 km s. The atomic parameters for the spectral lines were taken from Kurucz & Bell (1995).

The derived values of , and are reported in Table 2 (columns 4,9, and 3, respectively). The table also shows the equivalent spectral types and luminosity classes derived by comparing these values of and with the tables in Schmidt-Kaler (1982). In Fig. 1, we show the spectra in three different wavelength ranges for two stars observed with both telescopes. The following lines are plotted: Mg ii 4481 Å, Mg i 5167 Å, 5172 Å and the 5183-Å triplet, and H. The Mg i triplet was also used to check the derived values of for the coolest stars.

Figure 2: Comparison of obtained spectroscopically and photometrically via IRFM (top panel), (middle panel) and KIC (bottom panel). Filled circles, pentagons and open circles represent variables classified as pure Sct, pure Dor, and hybrids, respectively; the cross shows the candidate W Uma variable (see section 6 and Table  5). Symbols surrounded by circles refer to stars for which Strömgren photometry is available in the literature (i.e. more precise reddening estimate). Note that for the sake of clarity, the of the three stars in NGC 6866 have been shifted by  25 K. Note also that the star KIC 08583770 (HD 189177) is not visible in the figure because it lies outside the boundaries of the plots.
Figure 3: HR diagram for the nineteen stars investigated in this paper. Symbols are as in Fig. 2. Note that the of KIC 05965837 (HAT199-00623) was artificially lowered by 25 K to avoid a complete overlap with the star KIC 04570326 (HAT 199-01905). The black solid line is the ZAMS from Pickles (1998); the red solid lines show the  Sct instability strip by Breger & Pamyatnykh (1998); the blue dashed and dotted-dashed lines show the empirical and theoretical red edge of the  Dor instability strip by Handler & Shobbrook (2002) and Warner et al. (2003), respectively.

3.3 Comparison between astrophysical parameters derived by different methods

For the 15 stars with spectral types available in the literature (see column 6 of Table 1)777KIC 05296877 (HAT 199-27597) and the three objects in NGC 6866 have no spectral type known before. we can compare these values with those derived in the present paper (column 2 of Table 2). For seven stars there is agreement. For the three stars classified as metallic-lined (Am stars) by Abt (1984), our inferred spectral type agrees with that from Balmer lines derived by this author on the basis of 1 Å resolution spectra. For the remaining five stars, the discrepancy is large, with differences of more than three or four spectral sub-types. This is not surprising because the nature of several classifications in the literature is uncertain or based on photometry. For these stars we adopt the values from our spectroscopic analysis. The only high-resolution study in the literature is by Nordstrom et al. (1997) for the star KIC 07798339 (HD 173109). These authors analysed echelle spectra in the narrow wavelength range  Å to obtain  = 7000 K,  = 3.5 and  = 15.4 km s (no errors available). The difference of 300 K in is not significant within the errors, and the and values are in good agreement with our results.

It is useful to compare the values of derived spectroscopically with those obtained via photometric methods (IRFM, (V - K) calibration, KIC). Inspection of Fig. 2, which illustrates such a comparison, shows a general good agreement among all these values. Quantitatively, a weighted mean of such differences gives: =200200; =130200; =50300, non significant to the 1 level. Similarly a very good agreement is found between and estimated through photometry (see Table 2). However there are two exceptions to this trend:

KIC 05724440 (HD 187234) - This star shows a large difference between the spectroscopic T and that estimated from uvby photometry (800  300 K). This difference is at a level of  2.9 , and deserves some comments. Indeed, there is no a clear explanation for such a large difference. The Loiano and INAF - OACT spectra give exactly the same values for and , suggesting that there could be a problem with the photometry. The values reported for this star by Hauck & Mermillod (1998) are the average of the measurements by Olsen (1983) and Jordi et al. (1996), while the value, on which the depends, was measured only by the latter authors. The two quoted values are slightly discrepant, but the difference is not large enough to change significantly the derived value of . We also considered the possibility that a close companion is affecting the photometric measurements. We visually inspected both POSS II and 2MASS images of KIC 05724440 (HD 187234), where the star appears to be isolated in the near infrared. In the optical it is surrounded by a few very close faint stars whose contribution can hardly be considered significant. By using the calibration by Masana et al. (2006), the discrepancy is reduced to only 350 K, reinforcing our suspicion that there is something wrong with the photometry of this star.

KIC 08583770 (HD 189177) - The =9000200 K derived spectroscopically for this star is in good agreement with the value derived from IRFM, and consistent within the errors with the derived from color. However there is a large discrepancy with respect to the KIC estimate. This occurrence could perhaps be explained in terms of a visual binary, with a companion star dimmer by 3 mag at a distance of 0.9 arcsec. Even if nothing is known about the companion, due to the small separation, it is likely that the photometric values are affected by the secondary star flux.

KIC Luminosity Mass Can. Mass NonCan.
/L /M /M
03219256 19.0 2.20 2.20
03429637 20.0 3.6 3.2
03437940 12.5 1.80 1.80
04570326 7.8 1.70 1.65
05296877 7.9 1.60 1.70
05724440 17.0 2.20 2.30
05965837 7.4 1.70 1.65
05988140 16.3 2.00 2.20
07119530 18.8 2.20 2.40
07798339 9.0 1.80 1.90
08197788 12.7 1.85 1.80
08264404 17.4 2.30 2.20
08264698 14.3 2.00 1.90
08583770 65.0 4.80 4.40
09655114 13.5 1.90 1.90
09775454 8.5 1.70 1.65
11402951 15.5 2.30 2.20
11445913 16.3 1.95 2.20
11973705 8.6 1.60 1.60
Table 3: For each star the luminosity estimated on the basis of Schmidt-Kaler (1982) tables, the masses estimated from the evolutionary tracks with canonical and non- canonical (i.e. with overshooting) physics, respectively. The errors on the mass and luminosity correspond to the relative precision obtained using the BaSTI database using non-rotating models. These errors are expected to be different when rotation is considered in the modeling (more details in the text).
Figure 4: - diagram for the investigated stars. Symbols are as in Fig. 2. For comparison the instability strip for  Sct stars by Breger & Pamyatnykh (1998) is shown as straight (blue) lines. The evolutionary tracks for the canonical (left panel) and non-canonical (right panel) physics are also shown. Each track is labelled with the mass (blue number) expressed in M.

4 The HR and diagrams

The stellar parameters and determined in the previous section allow us to estimate the luminosity of the investigated objects by interpolating the tables by Schmidt-Kaler (1982). The result is reported in Table 3. Note that the errors on the luminosity were evaluated through the same tables by taking into account the errors on and . Figure 3 shows the HR diagram for the nineteen stars studied in this work, in comparison with the zero-age main sequence (ZAMS) (Pickles, 1998), the observed instability strip for  Sct stars (Breger & Pamyatnykh, 1998) as well as the empirical and theoretical red edge of the  Dor instability strip (Handler & Shobbrook, 2002; Warner et al., 2003). We note that the pulsating variables (see Section 6) are in the expected position, i.e. inside the instability strip, except for KIC 08583770 (HD 189177) and KIC 05296877 (HAT 199-27597) which are hotter and cooler than the instability strip, respectively. The former was discussed in the previous section, the latter is not a pulsating star (see Section 6).

We can use the values of and to estimate the mass of the target stars. For this purpose we used the evolutionary tracks in the BaSTI database888http://albione.oa-teramo.inaf.it/ which are based on the franec evolutionary code (Chieffi & Straniero, 1989). We retrieved tracks with both canonical and non-canonical (i.e. with convective overshooting: ) physics in the mass range  M with , , , and mixing lenght = 1.913 (Pietrinferni et al., 2004). In Fig. 4 we show the diagram. The left and right panels in the figure show canonical and non-canonical tracks, respectively. The resulting masses for the two cases (listed in Table 3) are very similar and agree well within 1. On other hand,  Sct stars are typically fast-rotating objects, and the rotation effects on the structure and evolution might modify the estimates of global parameters of the stars (see e.g. Goupil et al., 2005; Suárez et al., 2005; Fox Machado et al., 2006). To verify if this effect is important in our case, we considered a typical case for a star with mass 1.7-1.8 M☉. According to Suárez et al. (2005), even in case of vi150-200 km/s, the effect on the mass estimate from the HR diagram is of few %, well within the uncertainty due to the errors on the empirical estimates of luminosity and effective temperature (see table 3).

KIC (mas) /L /L
Hipp. Spect.
03429637 (HD 178875) 3.750.58 56.2 20.0
05724440 (HD 187234) 8.020.51 11.1 17.0
07798339 (HD 173109) 6.860.48 13.4 9.0
11402951 (HD 183489) 5.910.63 14.9 15.5
Star D (pc) /L /L
Cluster Spect.
08197788 (NGC6866-V1) 1200120 10.3 12.7
08264404 (NGC6866-V3) 1200120 20.6 17.4
08264698 (NGC6866-V2) 1200120 17.9 14.3
09655114 (NGC6811-RH35) 103050 17.2 13.5
Table 4: Comparison between the luminosity derived from present spectroscopy and Schmidt-Kaler (1982) tables and the one obtained from the HIPPARCOS parallaxes or Cluster distance (see text).

5 Checks of the results by means of Parallaxes and Cluster stars

We used the parallaxes measured by the HIPPARCOS satellite (Perryman et al., 1997) to verify the luminosities derived in the present work. We also estimated independently the luminosity of cluster stars by adopting the distances found in the literature obtained through e.g. isochrone fitting.

Only four stars in our sample are sufficiently bright for inclusion in the HIPPARCOS parallax catalogue. These are listed in Table 4 together with the parallaxes from the van Leeuwen (2007) revised catalogue. To derive the luminosity we used the and values listed in Table 1 as well as the bolometric correction as a function of spectral type from Pickles (1998). The resulting luminosities and errors are listed in Table 4 where our spectroscopic results are also shown for comparison purposes. An inspection of the table reveals that there is agreement within the errors. The only obvious discrepancy is found for the star KIC 03429637 (HD 178875). The difference in luminosity is , and deserves some discussion. We did not find any significant difference between the spectroscopic and the photometric estimates of for this star. Furthermore, the HIPPARCOS parallax (van Leeuwen, 2007) is very small relative to the parallax estimated from its spectral type and apparent magnitude. In our opinion, KIC 03429637 (HD 178875) is very likely a double star (Dommanget & Nys, 1994). The binary nature can significantly affect the estimated parallax, colour, and . As mentioned in Section 3, our spectroscopic determination of is in agreement with that derived by Abt (1984).

As for cluster stars, we have to estimate the distances to the host clusters NGC 6866 and NGC 6811 first. NGC 6866: as reported by Molenda-Żakowicz (2009), both the distance modulus and E(B-V) vary significantly from author to author. Here we decided to assume a distance D=1200120 pc as in Molenda-Żakowicz (2009) (no error on distance is available in the literature, we assumed conservatively an uncertainty of 10%). As for the reddening we adopted , according to Dutra & Bica (2000) who made a study of the foreground and background dust in the direction of the cluster. The resulting luminosities for the three variables in NGC 6866 are shown in Table 4 in comparison with our estimates. The agreement is good within the errors. NGC 6811: distance modulus and of this cluster were measured by Glushkova et al. (1999) and Luo et al. (2009). They found , =0.120.02, and , =0.120.05, respectively. To estimate the distance, we made a weighted mean of these results, obtaining D=103050 pc. Then, we calculated the luminosity for the star KIC 09655114 (NGC6811-RH35) which is reported in the last row of Table 4. Again, we note the good agreement within the errors with the spectroscopic result.

Figure 5: Periodograms of stars of Table 1. The precision in amplitude of the peaks in these periodograms is typically in the range of mag.

6 Kepler observations

Information on Kepler observations for the stars studied here is given in Table 5. For 15 out of 19 stars short cadence observations are available. From these data we calculated the periodograms (by using L. Balona’s custom software, based on a combination of FFT and normal periodogram) shown in Fig. 5. We note that practically all stars show peaks in both the low-frequency ( Dor; g mode) and high-frequency ( Sct; p mode) regions. In this sense, practically all  Sct stars observed by Kepler are hybrids. This is a surprising finding which has been discussed in Grigahcène et al. (2010). To make a distinction, we followed the classification scheme proposed by latter author. We visually classified the stars as  Sct if most of the peaks are in the  Sct region and as  Sct –  Dor if most of the peaks are in the  Sct region but with a significant contribution from the  Dor region. The frequency 5 c/d was taken as the boundary between the two regions. Following similar arguments, we classify a star as  Dor or  Dor –  Sct. There appears to be physical significance to such a scheme, as discussed by Grigahcène et al. (2010). We applied these classification criteria to the stars of this study, and classified six targets as  Sct stars, five stars as  Sct- Dor hybrids, four stars as  Dor- Sct hybrids, and three stars as pure  Dor pulsators (see also Table 5). Below we discuss the targets that show particularities in their periodogram (Fig. 5).

KIC 03429637 (HD178875): As noted above, this star shows a difference between the luminosity values derived from the HIPPARCOS parallax and from spectroscopy (see Table 4). Binarity is a possible explanation for this discrepancy. The frequency spectrum shows two dominant peaks near 10 and 12 d-1. A model in terms of  Sct pulsations, rotation and/or binarity needs to be investigated.

KIC 05296877 (HAT 199-27597): This star is the coolest star in the sample and lies outside the instability strip. The periodogram shows a single strong peak at  c/d. KIC 5296877 is probably a contact binary with an orbital period of  d. The late spectral type of F4.5IV and the large value  km s suggest that it is a high amplitude ellipsoidal variable.

KIC 07119530 (HD 183787): this star has been classified as pure Dor as the frequencies are predominantly in the Dor range and those in the Sct region have low amplitude. However the star lies in the middle of the Sct instability strip. All the temperature indicators adopted in this paper agree very well one each other and indicate a 7500 K, i.e. a bit too hot for a pure Dor variable. We conclude that the variability classification of this star is uncertain since it could be a Dor – Sct Hybrid.

KIC 08583770 (HD 189177): This star is the hottest star in the group, and lies outside the instability strip (see Fig 4). The periodogram shows significant power at very low frequency. The light curve of KIC 08583770 is presented in Fig. 6. No specific period can be deduced, but it is clear that there is something peculiar about this star, which needs further investigation.

KIC 09775454 (HD185115): The frequency spectrum of KIC 09775454 shows one dominant peak in the  Sct region, and several - seemingly equidistant - peaks at lower frequencies. Further investigation of the Kepler light curves will clarify if this star is a  Sct star with rotational modulation effects.

KIC 11973705 (HD 234999): The light curves of KIC 11973705 show a periodic long-term behaviour, with  d (Fig. 6). The spectral type B9, recorded in the Henry Draper catalogue, is a full spectral class too early compared to our classification of A9.5V. It is most likely a  Sct star in a binary system.

KIC ID Type N Cad (d)
03219256  Sct 43974 SC 30.03
03429637  Sct 9870 LC 217.98
03437940  Sct 43989 SC 30.03
04570326  Dor–  Sct 44010 SC 29.97
05296877 - 14245 SC 9.72
05724440  Sct 43093 SC 30.34
05965837  Dor 14204 SC 9.70
05988140  Sct -  Dor 2099 LC 44.44
07119530  Dor 10340 LC 228.95
07798339  Dor 43254 SC 29.97
08197788  Dor –  Sct 43370 SC 29.97
08264404  Sct –  Dor 43375 SC 29.97
08264698  Dor –  Sct 43348 SC 29.97
08583770  Sct –  Dor 41807 SC 30.79
09655114  Sct 38340 SC 27.11
09775454  Sct –  Dor 10341 LC 228.95
11402951  Sct 14240 SC 9.72
11445913  Sct –  Dor 14244 SC 9.72
11973705  Dor –  Sct 14212 SC 9.72
Table 5: Information on Kepler photometry. The first column is the KIC identification. In the second column the proposed classification is given. The third column gives the number of photometric observations, . In the fourth column SC signifies short-cadence (1-min exposures) and LC long cadence (29.4-min exposures). The last column gives the length of the data set, , in days.

7 Summary

We presented a spectroscopic analysis of 19 candidate  Sct variables observed by Kepler both in long and short cadence mode. The analysis is based on medium- to high-resolution spectra obtained at the Loiano and INAF - OACT observatories. For each star we derived , and by matching the observed spectra with synthetic spectra computed from the SYNTHE code (Kurucz & Avrett, 1981) and using the LTE atmospheric models calculated by ATLAS9 (Kurucz, 1993a). The typical errors are about 200 K, 0.2 dex, and 10 km s for , , and , respectively. Equivalent spectral types and luminosity classes were also derived. The luminosities of the stars were obtained using the tables of Schmidt-Kaler (1982).

Figure 6: Top panel: light curve of K8583770 (HD 189177). Bottom panel: light curve of K11973705 (HD 234999). The time is expressed in days starting from HJD = 2454950.5 and the brightness is given in mmag.

For ten stars we used Strömgren photometry from the literature to estimate the reddening. For seven stars for which photometry was also available, and could be obtained for comparison with our spectroscopic values. In addition, colours, the IFRM method and values listed in the KIC were used to obtain independent estimates of . We find a general good agreement between photometric and spectroscopic results. Four stars with significant parallaxes and four cluster member objects were used to check our estimate of the luminosities. We obtain consistent results for all the stars, with the exception of KIC 03429637 (HD 178875), which is a wide binary and may have an erroneus parallax determination. Moreover, for KIC 05724440 (HD 187234) we suspect a problem with the photometry, since derived from the index is in agreement with our estimate within the errors.

Finally, we present the periodograms for the 19 investigated stars, based on the Kepler satellite photometry. These beautiful data allowed us to classify the type of variability of each star, including KIC 05296877, which is a high amplitude ellipsoidal variable candidate. As a result, we find six pure Sct, 3 pure Dor and nine hybrid pulsators. This classification is consistent with the derived physical parameters and their position in the HR diagram. As already noted by Grigahcène et al. (2010), we were surprised by the large number of hybrid pulsators. An asteroseismic study of these objects will have a strong impact on our knowledge of the evolution and internal structure of A/F stars. A more in depth study of the pulsational behaviour of the 18 pulsators is out of the scope of this paper, and will be presented in a forthcoming paper.

The stellar parameter estimates for the 18 investigated pulsating stars, presented in this work, will be a fundamental starting point for building proper asteroseismic models aimed at interpreting the frequency spectra extracted from the exceptionally good Kepler data.

Acknowledgments

This work was supported by the Italian ESS project, contract ASI/INAF I/015/07/0, WP 03170 and by the European Helio- and Asteroseismology Network (HELAS), a major international collaboration funded by the European Commission’s Sixth Framework Programme.
Funding for the Kepler mission is provided by NASA’s Science Mission Directorate. We thank the entire Kepler team for the development and operations of this outstanding mission.
This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This work has made use of BaSTI web tools. RSz. has been supported by the National Office for Reseach and Technology through the Hungarian Space Office Grant No. URK09350 and the ‘Lendület’ program of the Hungarian Academy of Sciences. MJPFGM and AG are co-supported by project PTDC/CTE-AST/098754/2008 from FCT-Portugal.

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