High-resolution spectroscopy of \delta Scuti stars

# High-resolution spectroscopy and abundance analysis of δ Scuti stars near the γ Doradus instability strip

F. Kahraman Aliçavuş, E. Niemczura, M. Polińska, K. G. Hełminiak, E-mail: filizkahraman01@gmail.com/filizkahraman@comu.edu.tr    P. Lampens, J. Molenda-Żakowicz, N. Ukita, E. Kambe
Canakkale Onsekiz Mart University, Faculty of Sciences and Arts, Physics Department, 17100, Canakkale, Turkey
Instytut Astronomiczny, Uniwersytet Wrocławski, ul. Kopernika 11, 51-622 Wrocław, Poland
Astronomical Observatory Institute, Faculty of Physics, A. Mickiewicz University, Słoneczna, 36, 60-286, Poznań, Poland
Subaru Telescope, National Astronomical Observatory of Japan, Hilo, HI 96720, USA
Department of Astrophysics, Nicolaus Copernicus Astronomical Center, ul. Rabiańska 8, PL-87-100 Toruń, Poland
Royal Observatory of Belgium, Ringlaan 3, B-1180 Brussel, Belgium
Department of Astronomy, New Mexico State University, Las Cruces, NM 88003, USA
Okayama Astrophysical Observatory, National Astronomical Observatory of Japan, 3037-5 Honjo, Kamogata, Asakuchi,
Okayama 719-0232, Japan
The Graduate University for Advanced Studies, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
Accepted … Received …; in original form …
###### Abstract

Scuti stars are remarkable objects for asteroseismology. In spite of decades of investigations, there are still important questions about these pulsating stars to be answered, such as their positions in  diagram, or the dependence of the pulsation modes on atmospheric parameters and rotation. Therefore, we performed a detailed spectroscopic study of  Scuti stars. The selected objects are located near the  Doradus instability strip to make a reliable comparison between both types of variables. Spectral classification, stellar atmospheric parameters (, , ) and  values were determined. The spectral types and luminosity classes of stars were found to be A1  F5 and III  V, respectively. The  ranges from to  K, whereas the obtained  values are from to . The  values were found between and  km s. The derived chemical abundances of  Scuti stars were compared to those of the non-pulsating stars and  Doradus variables. It turned out that both  Scuti and  Doradus variables have similar abundance patterns, which are slightly different from the non-pulsating stars. These chemical differences can help us to understand why there are non-pulsating stars in classical instability strip. Effects of the obtained parameters on pulsation period and amplitude were examined. It appears that the pulsation period decreases with increasing . No significant correlations were found between pulsation period, amplitude and .

###### keywords:
stars: general – stars: abundances – stars: chemically peculiar – stars: rotation – stars: variables:  Scuti
pagerange: High-resolution spectroscopy and abundance analysis of  Scuti stars near the  Doradus instability stripLABEL:lastpagepubyear: 2017

## 1 Introduction

Asteroseismology provides a great opportunity to probe the internal structures of stars by modelling their pulsation modes. Many pulsating stars have been examined in detail to determine their pulsational properties. One of the remarkable objects for asteroseismology are  Scuti ( Sct) variables because of their large number of pulsation modes, amplitude regimes, which ranges from low () to high () amplitudes, and their positions in the Hertzsprung-Russell (H-R) diagram.

The  Sct stars range from dwarf to giant stars and have spectral types between A0 and F5 (Chang et al., 2013). These stars oscillate in radial and non-radial, low-order pressure (p), gravity (g) and mixed modes excited by the -mechanism. Most  Sct stars pulsate in the frequency range from to  d. Their masses vary between and (Chang et al., 2013). The coolest  Sct stars in the  Sct instability strip are in the transition region, where the convective envelope gradually turns into a radiative one, and the energy is transferred by convection in the core (Aerts, Christensen-Dalsgaard, & Kurtz, 2010, Section 3.7.3). Investigations of  Sct stars will help us to understand processes occurring in the transition region.

Sct variables are located in the lower part of the classical instability strip where the theoretical instability strips of  Sct and  Doradus ( Dor) variables partially overlap. In this overlapping area,  Sct/ Dor hybrids were predicted observationally (Breger & Beichbuchner, 1996; Handler & Shobbrook, 2002) and theoretically (Dupret et al., 2004). The number of these variables increased with the discoveries based on space telescopes observations. Thanks to the high precision photometry obtained by the Kepler space telescope, many  Sct,  Dor, and candidate hybrid stars have been discovered (Uytterhoeven et al., 2011; Grigahcène et al., 2010). Uytterhoeven et al. (2011) showed the position of  Sct,  Dor, and candidate hybrid stars in the H-R diagram mainly by using the photometric atmospheric parameters taken from the Kepler input catalog (KIC) (Brown et al., 2011). It turned out that  Sct and  Dor stars can be found outside their theoretical instability strips. The candidate hybrid stars have been discovered in the instability strip of the  Sct as well as  Dor stars. To find out the exact positions of  Sct and the other A-F type pulsating stars, spectroscopic studies are essential.

Some detailed spectroscopic studies dealing with these variables have been carried out (Catanzaro et al., 2011; Tkachenko et al., 2013; Niemczura et al., 2015; Kahraman Aliçavuş et al., 2016). The atmospheric parameters and the abundance patterns of  Sct,  Dor, and hybrid stars were derived and their accurate positions in the  have been determined. According to these studies,  Sct stars were found mainly inside their theoretical instability strip. A detailed abundance pattern of the  Sct stars was investigated by Fossati et al. (2008) to check whether the assumption of solar abundance in the pulsation models was correct. They found that generally the elements Y and Ba  are overabundant. The abundance pattern of  Sct stars were also compared with the non-pulsating A-F type stars and no significant differences were found. However, it should be kept in mind that only few  Sct stars were used in this study.

On the other hand, a lot of studies based on the frequency analysis of  Sct stars were presented. For instance, Balona & Dziembowski (2011) and Balona (2014) examined the pulsation frequencies of  Sct stars using the Kepler data. They showed that the  Sct stars beyond the blue edge of their instability strip pulsate in high-radial and non-radial overtones as suggested by Breger & Bregman (1975). The authors tested the working hypothesis that rotation in connection with stellar spots (i.e. rotational modulation) could explain the low frequencies but conclude that “rotational splitting, by itself, cannot account for the number of low frequencies nor their distribution”. In the study of Balona & Dziembowski (2011) a gap between zero age main sequence (ZAMS) and the position of  Sct stars in the H-R diagram was also found. It was shown that the gap increases with growing effective temperature.

Although much is already known about their stellar properties, several big issues concerning  Sct stars are still unanswered. For example, the exact position of  Sct stars in the H-R diagram and borders of their instability strip need to be checked observationally. Additionally,  Sct stars in the red border of their instability strip have almost the same atmospheric parameters as  Dor stars but pulsate in different modes. It is known that chemical composition influences the opacity in stars and opacity is related to the mechanism. Additionally, it is known that the chemical composition affects the pulsation modes (Miglio et al., 2008). Therefore, this situation could be explained by a possible chemical abundance differences between  Sct and  Dor stars. The other question concerns the relation between the pulsation quantities and rotation and metallicity of  Sct stars.

To answer all these questions detailed spectroscopic studies of  Sct stars are necessary, preferably using high-resolution observations. Hence, in this study, we aim to obtain fundamental atmospheric parameters and chemical composition of a sample of  Sct stars based on high-resolution spectra taken with different instruments. We have selected a sample of  Sct stars from the catalogue of Rodríguez, López-González, & López de Coca (2000). 31 of these stars are confirmed  Sct variables and the others are suspected  Sct variables which show pulsation but do not have realiable photometric studies to confirm  Sct type variability.

Stars were selected considering their position in the H-R diagram. The  Sct stars located in/near the overlapping region of  Sct and  Dor instability strips were chosen. In Sect. 2 details of the observations and data reductions are given. Spectral classification of stars is presented in the Sect. 3. Determinations of initial atmospheric parameters from photometric indices of several systems and from spectral energy distribution are introduced in Sect. 4. In Sect. 5, the spectroscopic determination of atmospheric parameters and chemical abundances are given. Discussion of the results and conclusions are presented in Sect. 6 and Set. 7, respectively.

## 2 Observations

In our analysis, we used high-resolution spectra taken with four spectrographs: ARCES, ELODIE, HERMES and HIDES. The information about the spectroscopic survey is given in Table 1. The signal-to-noise (S/N) ratios of the spectra near the wavelength  Å are listed in Table 2.

The ARC Échelle Spectrograph (ARCES) is a high-resolution, cross-dispersed optical spectrograph mounted at the -m telescope of the Apache Point Observatory (USA). It captures the entire spectrum between and  Å in a single exposure. ARCES provides spectra with a resolving power of . For the reduction of the data, we used the NOAO/IRAF package and the procedure described in the ARCES data reduction cookbook222The ARCES Data Reduction Cookbook by Karen Kinemuchi is available at the website http://astronomy.nmsu.edu:8000/apo-wiki/wiki/ARCES no1.. The reduction process included the bias subtraction, bad pixels fixing, trimming, scattered light correction, removal of the cosmic rays, flat-field correction and calibration in wavelength done on the basis of the exposures of the ThAr calibration lamps. The spectra were extracted with the use of the apall task also provided by IRAF.

ELODIE is a cross-dispersed échelle spectrograph used at the -m telescope of Observatoire de Haute Provence (OHP, France) between late 1993 and mid 2006. The spectra cover the wavelength range from to  Å with a resolving power of . The standard data reduction of the ELODIE data was performed automatically with the dedicated pipeline. The reduced archival ELODIE data were taken from the public archive (Moultaka et al., 2004).

The High Efficiency and Resolution Mercator Échelle Spectrograph (HERMES) is a high-resolution fibre-fed échelle spectrograph attached to the -m Mercator telescope at the Roque de los Muchachos Observatory (ORM, La Palma, Spain) (Raskin et al., 2011). The spectra acquired in the high-resolution fiber have a resolving power and cover the spectral range from to  Å. The data have been reduced with a dedicated pipeline, which includes bias subtraction, extraction of scattered light, cosmic ray filtering, wavelength calibration by a ThArNe lamps and order merging.

The HIgh-Dispersion Échelle Spectrograph (HIDES Izumiura, 1999) is attached to the -m telescope of the Okayama Astrophysical Observatory (Japan). The spectra cover the visual wavelength range with the resolving power with its high-efficiency fiber-link (Kambe et al., 2013). The reduction was made using dedicated IRAF-based scripts that deal with all chips simultaneously, and included bias, flat-field, and scattered light subtraction, corrections for bad pixels and cosmic rays, aperture extraction, and wavelength calibration. The last step was done on the basis of ThAr lamp exposures. Spectra from three chips were later merged into one file. Due to crowding of the apertures and sudden drop in the signal from the bluest chip, we have extracted only the reddest orders. The final product is composed of spectral orders, spanning from to  Å. A more detailed description of the data reduction process is given in Hełminiak et al. (2016).

The normalisation of spectra was performed manually using the continuum task of the NOAO/IRAF package. The spectra were divided into several parts and each part was normalised individually. The normalisation was checked by comparing the observed spectrum with a synthetic spectrum assuming an approximate effective temperature (), surface gravity () and projected rotational velocity () values. Because of limited observation time, typically one spectrum was obtained per star. However, line profiles in each spectrum were checked carefully to be sure whether the spectroscopic double-lined binary (SB2) stars are present in our sample. A few suspect SB2 stars were found (GW Dra, EE Cam, V1162 Ori, and GX Peg) and excluded from the further analysis. In the case of multiple spectra available for a star, we investigated the averaged spectrum. The averaging process was applied after normalisation.

## 3 Spectral classification

Stellar spectral types and luminosity classes were obtained by using the classical spectral classification method (Gray & Corbally, 2009) of comparison spectra of the studied stars with those of standards (Gray et al., 2003). Our sample consists of A and F stars, so the spectral types are typically derived from hydrogen H and H, Ca ii K, and metal lines. For non-chemically peculiar (non-CP) objects, all these lines provide the same spectral type. These lines are available only in the spectra taken with HERMES. In addition, the hydrogen lines are an excellent tool to derive luminosity types of A stars, but the sensitivity to the luminosity decreases in late A type stars and the ionised metal lines become useful (Gray & Corbally, 2009). Therefore, the luminosity class was obtained from the hydrogen lines for early A stars, whereas for later types the lines of ionised Fe  and Ti  were used.

Spectral types of the analysed stars were derived in the range from A1 to F5, and luminosity classes from III to V. For some objects, spectral classification was difficult because of the available spectral range and normalisation problems occurring typically in broad Balmer lines. The normalisation problem was caused by the merging of short orders in the ARCES and HIDES spectra. Additionally, the spectral range of HIDES data starts around  Å, therefore the analysis of Ca II H and K lines, as well as the H line was impossible for the spectra taken with this instrument. The literature and new spectral classes of the investigated stars are shown in Table 2.

## 4 Atmospheric parameters from Photometry and Spectral energy distribution

Initial atmospheric parameters,  and   were obtained from the photometric indices and the spectral energy distribution (SED). These parameters were used as inputs in the subsequent spectral analysis.

The interstellar reddening, , has a notable influence on the values of atmospheric parameters determined by photometric indices. Hence, the value should be taken into account in the analysis. First, we derived values using an interstellar extinction map and Na D interstellar line. The values were first determined from the interstellar extinction map (Amôres & Lépine, 2005) using the Galactic coordinates and distances of targets. We used the Hipparcos parallaxes (van Leeuwen, 2007) for the stars which have distances less than parsec and Gaia parallaxes (Casertano et al., 2017) for the stars which have distances greater than parsec. The Gaia parallaxes are more accurate for the distances greater than parsec. For the member of Pleiades cluster V624 Tau, we used the cluster distance to calculate the , because the parallax of this star has not been measured. The errors of mainly come from the uncertainty of targets’ distances. The largest error of value was found to be  mag. In the second method, we calculated values from photometry. The values were firstly calculated utilizing the method of Moon & Dworetsky (1985). Using the transformation 1.4 (Cardelli, Clayton, & Mathis, 1989), the values were found and the average error of these values was obtained to be  mag. In the last method, the was derived by using the relation between equivalent width of Na D line ( Å) and (Munari & Zwitter, 1997). In this method uncertainties of the values were adopted to be  mag (Kahraman Aliçavuş et al., 2016) (hereafter KA16). The obtained values are listed in Table 3. As can be seen, determined with all methods are generally in agreement with each other within error bars. In the photometric analysis, the more accurate values determined from the Na D line were used.

In the next step, the atmospheric parameters,  and , were derived using the de-reddened indices of Johnson, 2MASS, uvby Strömgren and Geneva photometric systems. The photometric data were gathered from the General Catalogue of photometric data (GCPD) (Mermilliod, Mermilliod, & Hauck, 1997), the 2MASS catalogue (Cutri et al., 2003), and the updated catalogue of Strömgren - Crawford photometry (Paunzen, 2015). The  and  parameters were derived using the methods described by Moon & Dworetsky (1985), Künzli et al. (1997), Sekiguchi & Fukugita (2000) and Masana, Jordi, & Ribas (2006) for the Strömgren, Geneva, Johnson and 2MASS systems, respectively. The  parameters were determined using all mentioned photometric systems, while  parameters were obtained from Strömgren and Geneva photometric systems only. In the calculations of  from Johnson, and 2MASS photometry, and solar metallicity were assumed. The uncertainties of determined  and  parameters were calculated taking into account errors of and used indices. It turned out that the error on contributes most to the uncertainty ( %). The calculated atmospheric parameters and their uncertainties are given in Table 3.

In the last step, the  parameters were determined by using SED. In the analysis, the code written by Dr. Shulyak (private information) was used. The code automatically scans some spectrophotometric and photometric catalogues and offers the possibility to manually add some photometric data (for more information see KA16). In these calculations, solar metallicity and were fixed. Final parameters are derived by comparing input data with the calculated theoretical spectra (Kurucz, 1993, ATLAS9 code). The obtained  values and their errors are given in Table 3.

## 5 Spectroscopic atmospheric parameters and chemical abundance analysis

Stellar atmospheric parameters have been determined from Balmer and metal lines analysis. Atmospheric chemical abundances were obtained using the spectral synthesis method. The hydrostatic, plane - parallel, and line - blanketed local thermodynamic equilibrium (LTE) atmosphere models were calculated with the ATLAS9 code (Kurucz, 1993), whereas the synthetic spectra were obtained with the SYNTHE code (Kurucz & Avrett, 1981).

### 5.1 Analysis of Balmer lines

To obtain  values, H, H, and H lines were used. The HIDES spectra are in the range from to  Å, hence the H line profiles were not used in their analysis. The procedure described by Catanzaro, Leone, & Dall (2004) was applied to derive  values from the analysis of Balmer lines. For stars with initial  lower than  K, the  values were adopted to be , as the Balmer lines are not sensitive to  for such temperatures (Smalley et al., 2002; Smalley, 2005). For stars with estimated  values higher than  K, both  and  were derived simultaneously. Additionally, metallicities of the stars were assumed to be  dex. The analysis was performed separately for each Balmer line. Final averaged  and  (for stars with   K) values are given in Table 4.

To estimate the uncertainties of  and  values determined from the Balmer lines analysis, we checked both, errors caused by the normalisation process and introduced by the assumed parameters such as , metallicity, and . The correct normalisation of Balmer lines is difficult, especially in the case of broad Balmer lines, which can be spread over more than one échelle order. The error of  caused by inaccurate normalisation has been estimated as approximately  K by checking the standard deviation of the different Balmer line’s determinations. When we took into account the effects of wrongly assumed values of , metallicity, and , an average uncertainty of  was found to be  K. The uncertainties of  were obtained in a similar way, taking into account normalisation problems and effects of assumed parameters. The total uncertainties of  and  parameters were obtained using the squared sum of the individual contributions. The obtained parameters and their uncertainties are given in Table 4.

### 5.2 Analysis of metal lines

The final atmospheric parameters, , , and microturbulent velocities () were obtained using the neutral and ionised iron lines. Previously determined atmospheric parameters were used as input values. The analysis was performed in the following steps:

The normalised spectra were divided into shorter spectral parts taking into account  values of the stars. For fast rotating objects ( km s) long parts covering many blended spectral lines were analysed, whereas for slowly rotating objects ( km s) short parts with one or few lines were taken into account.

The line identification for each part was performed using the line list of Kurucz 666kurucz.harvard.edu/linelists.html.

Analysis of the metal lines was performed for a range of , , and by using the spectrum synthesis method. The detailed information about the method can be found in Niemczura & Połubek (2006). The analysis was carried out in steps of  K, , and  km s for , , and , respectively.

The atmospheric parameters were obtained using the excitation potential (for ) and ionisation balance (for ) of neutral and ionised iron lines. The parameters were derived checking the correlation between the iron abundances and depths of iron lines (for more details see KA16). Simultaneously,  parameters were adjusted.

The final atmospheric parameters are listed in Table 4. The  values derived from different photometries and SEDs were compared with the spectroscopic  values in Fig. 1. As can be seen, these values are generally in agreement within 1- level. In Fig. 2, the distributions of the spectroscopic atmospheric parameters are presented.

The uncertainties of the spectroscopic atmospheric parameters were determined considering relations between the iron abundances and both, excitation potentials of neutral or ionised iron lines, and lines depths. For the accurate parameters, there is no correlation between them. It means that we have similar iron abundances, regardless of line excitation potential or line depth. To find the errors of , , and we check how these parameters change for correlation differences of about  %. Using this method the maximum uncertainties of , , and were obtained to be  K,  dex, and  km s, respectively.

After the determination of accurate atmospheric parameters, the abundance analysis was performed with the spectrum synthesis method. An example of fitting of the synthetic spectrum to the observed one is shown in Fig. 3 for the slowly rotating star HD 161287.

The  values and the chemical abundances are shown in Table 4 and Table 5, respectively. The distribution of the  values is given in Fig. 4. The obtained  range from to  km s.

In Table 5 chemical abundances and their standard deviations are given for five analysed stars. The full table is given in the electronic form. The total errors of the determined abundances are due to the uncertainties of , , , and , assumptions adopted to calculate atmospheric models and synthetic spectra, quality of the data (resolving power, S/N), and the normalisation of spectra.

The assumptions adopted in the atmospheric model calculations (e.g. LTE, plane-parallel geometry, and hydrostatic equilibrium) cause an error of about  dex in chemical abundances (Mashonkina, 2011). The uncertainties due to the resolving power and the S/N ratio of a spectrum were examined by KA16 and Ryabchikova et al. (2016). KA16 found uncertainties of about  dex and  dex for the iron abundance, resulting from the resolving power difference (R =  and R = ), and the S/N ratio difference (S/N =  and S/N = ), respectively. In our study, such introduced uncertainties in chemical abundances cannot be checked, as we do not have even one star observed by different instruments. Therefore these uncertainties were adopted from KA16.

To find the uncertainties of chemical abundances introduced by possible errors in atmospheric parameters , , and , we have selected a few stars with effective temperatures typical for the analysed sample. We were changing values of their atmospheric parameters to check how such changes will influence the determined abundances of chemical elements. If the error of  equals  K, the abundance of iron will change of  dex. Smaller differences, and  dex, are caused by the 0.1 error of  and the  km suncertainty of . The  effect on chemical abundances was examined as well. We found that the uncertainties in abundances caused by  are in a range of  dex. The higher error values were obtained for stars with the higher  values.

The combined errors calculated taking into account all mentioned effects are given in Table 4 for the iron abundances.

## 6 Discussion of the results

### 6.1 Atmospheric parameters of δ Sct stars

The  range of investigated  Sct stars was found to be  K. The typical  values of  Sct stars vary from to  K (Uytterhoeven et al., 2011). As can be seen, the derived  range is in agreement with the characteristic  values of  Sct stars. However, there are two hot stars (HD 213272 and HD 214698) that are located beyond the  range. These stars are suspected  Sct variables (see Table 2) and the nature of their variability should be checked.

We compared the determined range and average values of  for  Sct stars with those for  Dor’s obtained by KA16. The average  ( 260 K) of  Sct stars is slightly higher than this calculated for  Dor’s ( 130 K), as expected. However,  ranges of both variables overlap. This gives us an opportunity to check whether there is a chemical difference between both types of pulsating stars located in the same area of H-R diagram, close to the blue edge of the  Dor instability strip (see Sect. 6.4).

The distribution of  determined from the iron lines analysis is shown in the middle panel of Fig. 2. The  values were found between and . The obtained  values are in good agreement with the luminosity range (V-III) of  Sct stars. Previous studies of  Sct stars (e.g. Fossati et al., 2008; Catanzaro et al., 2011) give  between and which are also in agreement with our results. For  Dor stars  ranges from to (KA16). It seems that  Sct stars are more evolved than  Dor stars, as expected.

The distribution of the derived is shown in the right-hand panel of Fig. 2. The ranges from to  km s with the average value  0.23 km s. The values for  Dor stars were found in the range from to  km swith the average value  0.2 km s (KA16). The values of  Sct stars are higher than determined for  Dor stars within errors. It is consistent with the relation between the and  (see e.g. Niemczura et al., 2015, and references therein). This relation was examined by Landstreet et al. (2009), Gebran et al. (2014), Niemczura et al. (2015) and KA16. It turned out that the value is inversely proportional to  for  higher than 7400 K. This relation for our stars is shown in Fig. 5. As can be seen from the figure, there is no difference between microturbulence values for CP and normal stars. Similar results were found by Niemczura et al. (2015) and KA16.

The  values of the analysed stars range from to  km s, with the average value  5 km s. According to the previous studies (Fossati et al., 2008; Royer, 2009; Catanzaro et al., 2011; Chang et al., 2013; Niemczura et al., 2015), the  values of A-F stars are in a range from to  km s. Our results are in agreement with the  distributions given in the literature. The  values of  Dor stars are from to  km s and the average value is  3 km s (KA16), similar to these obtained for  Sct stars.

### 6.2 Correlations between the atmospheric and pulsation parameters of δ Sct stars

The possible correlations between the pulsation quantities (pulsation period and amplitude ) and the obtained parameters were examined. For this purpose, the of the highest and these values in -band were taken from Rodríguez, López-González, & López de Coca (2000). Four high-amplitude  Sct stars (HADS)777The stars are signed in Table 2. are available in our sample. These stars were discarded in the following analysis. All the other objects represent typical values of classical  Sct stars.

In Fig. 6, the relations between  and pulsation quantities are shown. As can be seen, there is an obvious correlation between  and and . These pulsation parameters have lower values for the hotter  Sct stars. As known, changes in  are related to the stellar radii () and the changes in determine the position of helium ionisation zone which drives the  Sct type pulsations (Cox, 1980). Additionally, this negative correlation between and  can be explained taking into account basic equations. Using the luminosity () – mass () relation (), the mean density (), and the pulsation constant (), we can obtain that ( / ). Breger (1990) also showed that the depends on , , and the bolometric magnitudes of pulsation stars. Balona & Dziembowski (2011) found similar relationships between , and  for  Sct stars in the Kepler field. The relation was also found for  Sct stars in eclipsing binaries (Kahraman Aliçvuş et al., in preparation). The same relations for  Dor stars were checked by KA16. They did not find any significant correlation between  and , while a weak and negative correlation was found between  and . This weak correlation is probably caused by the narrow  range of the analysed  Dor stars which were used to check relations (from to  K).

The correlations of  values with the pulsation quantities were examined as well. The suitable relations are shown in the Fig. 7. As can be seen, there are no significant correlations between , and . On the other hand, Claret et al. (1990) and Breger (1990) found a relation between and . According to them, decreases with increasing  values.  Sct stars in our study were selected considering their positions in the  –  diagram. Most stars in our sample have  values from to . Only three stars have  below and the values for them are clearly higher than the average period of stars with higher  values. So, the chosen sample of stars can be the reason why the is not observed. The same relation was examined for  Dor stars by KA16 and a weak and negative correlation was found between  and , while no correlation was found between  and .

Next, the possible correlations of values with the pulsation quantities were checked. These relations are demonstrated in Fig. 8. As can be seen, there are no significant correlations between and pulsation quantities. In general, higher values of correspond to higher values of . The same correlation were examined in KA16 for  Dor stars. They found that a positive relation between and can occur.

The relations between  and pulsation quantities are shown in Fig. 9. As can be seen, there are no significant correlations. A weak negative correlation may exist for  and . Similar relations between  and were also found in the literature (e.g. Rodríguez, López-González, & López de Coca, 2000; Breger, 2000; Tkachenko et al., 2013). For  Dor stars a strong correlation between  and and a weak correlation between  and were found as well (Van Reeth et al. (2015), KA16).

Relations between the metallicity and pulsation quantities are presented in Fig. 10. No correlations were found. However, the stars generally have metallicities lower than the solar one. There is no significant difference between the average iron abundance of  Sct ( dex) and  Dor ( dex) stars (KA16).

### 6.3 Positions of δ Sct stars in the logTeff−logg diagram

Positions of  Sct stars in the  diagram have been examined in detail since new  Sct stars have been discovered by the space telescopes (MOST Walker et al. 2003, CoRoT Auvergne et al. 2009, Kepler Borucki et al. 2010). Uytterhoeven et al. (2011) showed positions of these variables in the  diagram mainly based on the photometric atmosphere parameters from the KIC catalogue (Brown et al., 2011). They found that Kepler  Sct stars are located both in their instability strip and outside of it. In the most recent study (Niemczura et al., 2015) accurate parameters of a few  Sct stars were obtained and some of them were found outside of their domain. However, the theory cannot explain this.

In Fig. 11 we show the positions of the analysed  Sct stars in the  diagram. As can be seen, most stars are located inside the  Sct instability strip. However, there are a few stars placed outside of the  Sct instability strip. HD 213272 and HD 214698 are located beyond the blue edge, while HD 90747 is located outside the red edge. The stars beyond the blue edge have the lowest amplitudes ( mmag), while the star on the cold side of the  Sct instability strip does not show differences in pulsation quantities in comparison with the other  Sct stars considered. However, all these stars are suspected Sct variables (see Table 2) and the verification of their variability types is necessary.

The positions of CP stars in the  diagram were also shown. In a recent study, metallic stars with  Sct pulsations were found in the  range of  K (Smalley et al., 2017).  of CP stars analysed here are also in this range (within error) and are located in the  Dor instability strip.

### 6.4 Chemical abundances of δ Sct stars

During the spectral classification and abundance analysis, a few chemically peculiar stars were found. HD 37819, HD 79781 and HD 154225 have overabundant iron-peak and heavy elements (Zn , Sr , Zr , and Ba ). The chemical abundance patterns of the discovered chemically peculiar stars are given in Fig 12.

We compared the chemical abundance pattern of  Sct stars with the non-pulsating and  Dor stars’ patterns. Atmospheric parameters and chemical abundances of eighteen non-pulsating stars were taken from Niemczura et al. (2015). The stars used in the comparisons were analysed using exactly the same as in the present work. We divided  Sct stars into two groups: one contains all analysed  Sct stars and second contains stars located only in the  Dor area (, KA16) to check whether there are any differences between their abundance patterns. The comparisons are shown in Fig. 13. It is clearly seen that  Sct stars in  Dor area and the other  Sct stars have abundance patterns similar to  Dor stars. However, abundance patterns of  Sct and  Dor stars show small differences in comparison with the abundance patterns of non-pulsating stars. The Na  is overabundant in non-pulsating stars in comparison with  Sct and  Dor variables. Additionally, abundances of Si  and Cu  are slightly lower in  Sct and  Dor stars than in the non-pulsating stars. On the other hand, Fe  abundances are similar in the investigated types of stars. When we compare the abundance patterns of  Sct and  Dor stars, it turned out that Zn  abundance is lower in  Dor stars than in  Sct stars, and Sr  abundance is higher in  Sct stars than in the non-pulsating and  Dor stars. Fossati et al. (2008) found Y  and Ba  are over-abundant in  Sct stars in comparison to the non-pulsating stars. However, we did not find any difference in abundances of these elements for  Sct and non-pulsating stars.

## 7 conclusions

This study presents the detailed spectroscopic investigation of a sample of  Sct stars. The initial atmospheric parameters ( and ) were derived from the photometric indices, SED and Balmer lines. The accurate spectroscopic atmospheric parameters (,  and ),  values, and chemical abundances were obtained with the spectrum synthesis method.

and  values of  Sct stars were found in ranges of  K and , respectively. The  values were derived from to  km s. Additionally, these parameters of  Sct stars were compared with the parameters of  Dor derived by KA16. As expected the average  value of  Sct stars is higher than the average  value of  Dor stars. We showed that  Sct stars are more evolved than the  Dor stars. No significant difference was found between the average values and ranges of .

The correlations between derived parameters and pulsation quantities were examined. As shown by Breger (1990), the varies depending on the , , and bolometric magnitudes. In our study, we found that a strong correlation between  and exists. The correlation was also obtained for  Dor stars (KA16) but this correlation was not as strong as for  Sct stars. Additionally, although we did not find a significant correlation, it is obvious that the hotter stars in our sample have the lowest values. In the case of hotter stars, pulsation mechanism occurs very close to the stellar surface and it is not significantly effective to drive pulsations. This could explain the lower values in hotter stars.

The relation for pulsating stars has been known before (e.g. Claret et al., 1990; Breger, 1990; Liakos & Niarchos, 2017). However, because our sample consists of stars in a narrow  range, we did not find relations between , and . Similarly, no correlation between and was found for the analysed  Sct stars. On the other hand, a weak positive correlation was obtained for  Dor stars (KA16). Furthermore, the effect of  on pulsation quantities was checked. Although a strong negative correlation between  and was obtained for  Dor stars in the previous study (KA16), the similar correlation was not obtained for  Sct stars analysed here. The  Sct stars pulsate in shorter periods and with higher in comparison with the  Dor stars. Because of the range of values of investigated Sct stars, the effect of  on could not be obtained. Additionally, weak negative correlations between  and were found for both types of variables.

We examined the positions of  Sct stars in  diagram and we conclude that most of our stars are located in  Sct instability strip. Only three stars were found outside of their domain. The stars located beyond the blue edge of  Sct domain, have the lowest values in comparison with the other analysed variables. Additionally, some of investigated stars are placed in an overlapping area of  Sct and  Dor instability strips and the others are in  Sct domain. When we compare pulsation properties of these two groups, we notice that the stars in overlapping area have higher values. This result is in agreement with the relation shown in Fig. 6. The stars in  K area have higher values comparing the hotter ones.

Comparison of the abundance patterns of  Sct,  Dor, and non-pulsating stars were considered. We found that  Sct stars have abundance pattern very similar to  Dor stars. However, Na  was obtained overabundant in non-pulsating stars in comparison with  Sct and  Dor stars, and Si , Cu  were found underabundant in  Sct and  Dor stars in comparison with the non-pulsating ones. Additionally, Zn  is slightly less abundant in  Dor stars comparing with  Sct stars, and Sr  was obtained more abundant in  Sct stars than in the non-pulsating and  Dor stars. The Fe  abundance was determined to be almost the same in all types of stars. The suggested chemical differences between  Sct,  Dor and non-pulsating stars can help us to understand why some stars in classical instability strip do not pulsate. However, such a chemical abundance comparison needs a bigger sample.

Accurate atmospheric parameters and chemical abundance patterns of Sct variables were derived. These parameters are important ingredients for a reliable seismic modelling of pulsating stars. Thus, the examination of the internal structure of stars in any evolutionary stage can be derived more accurately. Additionally, obtained abundance differences between  Sct,  Dor, and non-pulsating stars may give us a first approach of understanding why some stars located in the classical instability strip do not show pulsations.

## Acknowledgments

The authors would like to thank the reviewer for useful comments and suggestions that helped to improve the publication. This work has been partly supported by the Scientific and Technological Research Council of Turkey (TUBITAK) grant numbers 2214-A and 2211-C. EN, MP, JMŻ and KH acknowledges support from the NCN grant No. 2014/13/B/ST9/00902. The calculations have been carried out in Wrocław Centre for Networking and Supercomputing (http://www.wcss.pl), grant No. 214. We are grateful to Dr. D. Shulyak for putting the code for calculating SEDs at our disposal. We thank to Dr. G. Catanzaro for putting the code for Balmer lines analysis at our disposal. This research has made use of the SIMBAD data base, operated at CDS, Strasbourq, France. This work has made use of data from the European Space Agency (ESA) mission Gaia (http://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, http://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

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