Eclipsing binary stars with a \delta Scuti component

Eclipsing binary stars with a  Scuti component

F. Kahraman Aliçavuş, E. Soydugan, B. Smalley and J. Kubát
Faculty of Sciences and Arts, Physics Department,Canakkale Onsekiz Mart University, 17100, Canakkale, Turkey
Astrophysics Research Centre and Ulupınar Observatory, Çanakkale Onsekiz Mart University, 17100 Çanakkale, Turkey
Astrophysics Group, Keele University, Staffordshire ST5 5BG, UK
Astronomický ústav, Akademie ved České republiky, CZ-251 65 Ondřejov, Czech Republic
E-mail: filizkahraman01@gmail.com / filizkahraman@comu.edu.tr
Accepted … Received …; in original form …
Abstract

Eclipsing binaries with a  Sct component are powerful tools to derive the fundamental parameters and probe the internal structure of stars. In this study, spectral analysis of 6 primary  Sct components in eclipsing binaries has been performed. Values of , , and metallicity for the stars have been derived from medium-resolution spectroscopy. Additionally, a revised list of  Sct stars in eclipsing binaries is presented. In this list, we have only given the  Sct stars in eclipsing binaries to show the effects of the secondary components and tidal-locking on the pulsations of primary  Sct components. The stellar pulsation, atmospheric and fundamental parameters (e.g., mass, radius) of 92  Sct stars in eclipsing binaries have been gathered. Comparison of the properties of single and eclipsing binary member Sct stars has been made. We find that single  Sct stars pulsate in longer periods and with higher amplitudes than the primary  Sct components in eclipsing binaries. The of  Sct components is found to be significantly lower than that of single  Sct stars. Relationships between the pulsation periods, amplitudes, and stellar parameters in our list have been examined. Significant correlations between the pulsation periods and the orbital periods, , , radius, mass ratio, , and the filling factor have been found.

keywords:
Stars: binaries: eclipsing – stars: fundamental parameters – stars: variables: Scuti
pagerange: Eclipsing binary stars with a  Scuti componentEclipsing binary stars with a  Scuti componentpubyear: 2017

1 Introduction

The  Scuti ( Sct) stars are remarkable objects for asteroseismology particularly because of their pulsation mode variability. The  Sct stars oscillate in low-order radial and non-radial pressure and gravity modes and most of them have frequency range of d (Breger, 2000). Pulsations are driven by the -mechanism in these variables (Houdek et al., 1999). The  Sct stars are dwarf to giant stars with spectral types between A0 and F0 (Chang et al., 2013). These variables have masses from 1.5 to 2.5  and are located on or near the main sequence (Aerts, Christensen-Dalsgaard, & Kurtz, 2010). Therefore, they are in a transition region where the convective envelope turns to a radiative envelope, while energy starts to be transferred by convection in the core of the star (Aerts, Christensen-Dalsgaard, & Kurtz, 2010). The  Sct stars allow us to understand the processes occurring in this transition region by using their pulsation modes.

Approximately 70% of stars are binary or multiple systems (Mason et al., 2009; Sana & Evans, 2011; Alfonso-Garzón et al., 2014). Therefore, it is likely to find a  Sct variable as a member of a binary system. The existence of a pulsating variable in an eclipsing binary system makes this variable more valuable. Using the pulsation characteristic, the interior structure of the star can be probed and, using the eclipsing characteristic, the fundamental parameters (e.g.  mass, radius) of the pulsating component can be derived by modelling the light and radial velocity curves of a binary system. These fundamental parameters are important to make a reliable model of a pulsating star. Thus, the interior structures and the evolution statuses of stars can be examined in detail.

Many  Sct stars in eclipsing binary systems have been discovered (e.g. Lee et al., 2016; Soydugan et al., 2016). A group of eclipsing binaries with a  Sct component was defined as oscillating eclipsing Algol (oEA) systems by Mkrtichian et al. (2004). The oEA systems are B to F type mass-accreting main-sequence pulsating stars in semi-detached eclipsing binaries. Because of mass-transfer from the secondary components onto the primary pulsating stars and also due to the tidal distortions in oEA systems, the pulsation parameters and the evolution of primary pulsating components can be different.

There have been several studies on the effect of binarity on  Sct type pulsations. Firstly, Soydugan et al. (2006a) showed the effect of orbital period on the pulsation period. The relation between orbital and pulsation periods was theoretically revealed by Zhang, Luo, & Fu (2013). They showed that pulsation periods vary depending on the orbital period, mass ratio of binary system and filling factor of the primary pulsating component. It was also shown that the gravitational force applied by secondary components onto their primary components influences the pulsation periods of primary  Sct components (Soydugan et al., 2006a). Because of the effects of mass-transfer and tidal distortions in semi-detached binaries, the primary  Sct components also evolve more slowly through the main sequence than single  Sct stars (Liakos & Niarchos, 2015).

The number of known binaries with a  Sct component constantly increases. Additionally, hybrid stars, which show both  Sct and  Dor type pulsations, have been discovered in eclipsing binary systems (Schmid et al., 2015; Hambleton et al., 2013). In a recent study, an updated list of  Sct stars in binaries was presented by Liakos & Niarchos (2017). In their study, all known  Sct stars and also  Sct -  Dor hybrids in binaries were collected, including the non-eclipsing ones. Although 199 binary systems are given in their list, there are only 87 detached and semi-detached eclipsing binaries containing a  Sct variable. The others are mostly visual binaries, ellipsoidal variables, and spectroscopic binaries in which the fundamental parameters cannot be derived as precisely as in eclipsing binary systems.

As listed by Lampens (2006), some open questions about the eclipsing binaries with a pulsation component exist. The effect of binarity on pulsation quantities (period and amplitude), possible connections between orbital motion, rotation, chemical composition, and pulsation are some of these questions. Therefore, we have focused on the eclipsing binary systems with  Sct components in this study. To obtain the stellar atmospheric parameters, a spectroscopic analysis of six  Sct stars in eclipsing binary systems has been performed. A revised list of  Sct stars in eclipsing binaries is presented to show the effects of secondary components and fundamental stellar parameters on the pulsations of the primary pulsating components.

Information about the spectroscopic observations and data reduction are given in Sect 2. The spectroscopic analysis of the stars is presented in Sect 3. The revised list of eclipsing binary systems with a  Sct component, general properties of these systems, and the relations between pulsation periods, amplitudes and fundamental parameters of the stars are introduced in Sect 4. In Sect 5 we present a discussion on the correlations found, the positions of  Sct stars in eclipsing binaries in the  –  diagram, and a comparison of the properties of single and eclipsing binary members  Sct stars. The conclusions are given in Sect 6.

Name Observation S/N Number of Light
dates spectra Contribution
XX Cep 2015-06/09 50 2 3.7 
UW Cyg 2015-07/09 35 2 5.1 
HL Dra 2015-06/07 120 2 4.4 
HZ Dra 2015-06/07/09 80 3 0.5 
TZ Dra 2015-06/09 60 2 7.6 
CL Lyn 2015-09&2001 50 2 4.2 

Percentage of light contribution of secondary component in band. [1] Koo et al. (2016), [2] Liakos et al. (2012), [3] Liakos & Niarchos (2013)

Table 1: Information about the spectroscopic survey. S/N gives the values for combined spectra apart from CL Lyn. The S/N of CL Lyn is the value for ELODIE spectrum.

2 Observations

Spectroscopic observations of six eclipsing binaries with a primary  Sct component were carried out. The stars were selected taking into account the secondary components’ light contributions, in order to obtain spectra which are less influenced by the light of secondary components. The light contributions of the stars from literature photometric analyses are given in Table 1.

The observations were carried out using the 2-metre Perek Telescope at the Ondřejov Observatory (Czech Republic). We acquired spectra with the coudé slit spectrograph at its 700-mm focus, in which the PyLoN 2048512 BX CCD chip was used (for details, see Šlechta & Škoda, 2002). The resolving power of the instrument is about 25 000 at 4300 Å. The spectra were taken in the wavelength range of 4272–4506 Å, which covers the H line. This wavelength region was also selected because metal lines (e.g. Ti , Mg and Fe ) are more numerous in this range of effective temperature.

To further minimise the light contribution of secondary components in the spectra, spectra of each star were taken at approximately 0.5 orbital phase when the primary is covering the secondary. The individual spectra were combined to increase the signal-to-noise (S/N) ratio. For CL Lyn an ELODIE111http://atlas.obs-hp.fr/elodie/ spectrum, taken in 2001, was used in addition to our observation. Information about the spectroscopic survey is given in Table 1. The stars are semi-detached eclipsing binaries with a primary  Sct component, except for HZ Dra which is a detached binary with a primary  Sct component (Liakos et al., 2012).

The reduction and normalisation of the spectra were performed using the NOAO/IRAF package222http://iraf.noao.edu/. In the reduction process, bias subtraction, flat-field correction, scattered light extraction and wavelength calibration were applied. The reduced ELODIE spectrum for CL Lyn was used. The standard reduction was performed by the dedicated reduction pipeline of ELODIE. The spectra of each star were manually normalised using the continuum task of the NOAO/IRAF package.

3 Spectroscopic analysis

Prior to detailed spectroscopic analysis, spectral classifications of the stars were obtained. The effective temperature () of the primary components were derived using the spectral energy distribution (SED) and the H line. The metallicities were obtained using the spectrum fitting method.

Name V Sp type Sp type
(mag) (mag) (literature) (This Study) (SED) (Spec) (km s)
 0.023 (K) (K)
HL Dra 7.36 0.040 A5 A6 IV 7786  174 7800  200 4.22 107  10 0.12  0.17
HZ Dra 8.14 0.016 A0 A8/A7 V 7926  250 7700  200 4.07 120  10 0.09  0.20
XX Cep 9.18 0.026 A6 V A7 V 7160  152 8200  300 4.09 54  5     0.59  0.23
TZ Dra 9.32 0.020 A7 V A7 V 7382  173 7800  200 4.26 86  8 0.01  0.22
CL Lyn 9.77 0.181 A5 A8 IV 7699  189 7600  300 3.98 75  3 0.16  0.20
UW Cyg 10.86 0.101 A6V A7/A6 IV 7550  176 7800  350 4.06 45  10      

Calculated using the stars’ masses and radii which are given in Table 1. Could not be calculated because of the low S/N ratio. [1] ESA (1997), [2] Koo et al. (2016), [3] Herbig (1960), [4] Liakos et al. (2012)

Table 2: The stellar parameters of the six  Sct stars in eclipsing binaries.

3.1 Spectral classification

Preliminary information about the atmospheric parameters (, surface gravity ) and surface peculiarities of stars can be obtained by spectral classification (Niemczura, Smalley, & Pych, 2014).

The spectral and luminosity types of stars are identified by comparing their spectra with a group of well-known standard stars’ spectra. The A–F type standard stars were used in our classification (Gray et al., 2003), because the  Sct variables are A and F type stars. The spectral types of the stars were derived primarily using H and neutral metal lines ( Fe, Ti) in the 4400–4500 Å wavelength region. The luminosity types were also derived by using the ionised metal lines.

The spectral and luminosity types obtained for the stars are given in Table 2. Only for HZ Dra, newly determined spectral classification (A8/A7 V) was found to be significantly different than the previous classification (A0, Heckmann 1975), while the other spectral types are mostly in agreement with the literature.

3.2 Determination of , , and metallicity

The of the primary  Sct components were obtained from the H line and metallicities were determined using metal lines in the 4400–4500 Å wavelength region.

Prior to the spectral analysis, we determined from the SED. The SEDs were constructed from literature photometry and spectrophotometry, using 2MASS , and magnitudes (Sktrutskie et al., 2006), Tycho and magnitudes (Høg et al., 1997), USNO-B1 magnitudes (Monet et al., 2003), TASS magnitudes (Droege et al., 2006), and data from the Ultraviolet Sky Survey Telescope (TD1) (Boksenberg et al., 1973). However, TD1 data are only available for HL Dra and HZ Dra. To remove the effect of interstellar reddening on the SED, values were calculated from the Galactic extinction maps (Amôres & Lépine, 2005), with distances obtained from Gaia parallaxes 333https://gea.esac.esa.int/archive/ (Casertano et al., 2016). The values are given in Table 2. The average uncertainty in was found to be 0.023 mag. The SEDs were de-reddened using the analytical extinction fits of Seaton (1979) for the ultraviolet and Howarth (1983) for the optical and infrared.

The stellar  (SED) values were determined by fitting solar-composition Kurucz (1993) model fluxes to the de-reddening SEDs. The model fluxes were convolved with photometric filter response functions. A weighted Levenberg-Marquardt non-linear least-squares fitting procedure was used to find the solution that minimised the difference between the observed and model fluxes. Since is poorly constrained by our SEDs, we fixed  = 4.0 for all the fits. The uncertainties in  (SED) includes the formal least-squares error and uncertainties in (0.023) and (0.2) added in quadrature. In Fig. 1, we show the SED fit for HL Dra.

Figure 1: SED fit for HL Dra.

By using the initial values of  (SED), fundamental atmospheric parameters were determined for each star. Before the hydrogen line analysis and metallicity determinations of the stars, the projected rotational velocity () values were derived. A theoretical spectrum of each star was calculated using the initial atmospheric parameters. The metal lines in the spectrum of each star were matched to the theoretical spectrum by adjusting (Gray, 2008). Final values of were obtained by minimising the difference between the observed and theoretical spectra. The values are given in Table 2.

Hydrogen lines are good temperature indicators, since they are insensitive to for stars with   8000 K (Gray, 2008; Heiter et al., 2002). In our analysis, we adopted value of which were calculated using the stars’ masses and radii values given in the literature (see Table A1). Additionally, and metallicity (, assumed to be solar) were fixed. In our analysis, the hydrostatic, plane-parallel, local thermodynamic equilibrium ATLAS9 models (Kurucz, 1993) were used and the SYNTHE code (Kurucz & Avrett, 1981) was used to produce theoretical spectra. was determined by minimising the difference between the theoretical and observed hydrogen line, as described by Catanzaro, Leone, & Dall (2004). The  (Spec) values obtained are listed in Table 2 and comparison of the calculated and observed spectra for one of the stars is shown in Fig. 2.

Figure 2: Comparison of the calculated (red line) and observed spectra of H line of HL Dra.

The values were derived using the  (Spec), and values given in Table 2. The analysis was executed using version 412 of the Spectroscopy Made Easy (SME) package (Valenti & Piskunov, 1996), which determines atmospheric parameters, and elemental abundances using the spectrum fitting method. In this analysis, atmosphere models produced by ATLAS9 code (Kurucz, 1993) were used. The line list was taken from the Vienna Atomic Line Database444http://vald.astro.uu.se/ (VALD Piskunov et al., 1995). The  Å wavelength range was used in the metallicity analysis. The values obtained are given in Table 2. However, could not be determined for UW Cyg because of the low S/N ratio of the spectra. The comparison of the theoretical and observed spectra used in the analysis is demonstrated in Fig. 3. Uncertainties of the spectroscopic parameters comprise the least-squares error and the uncertainties caused by the fixed parameters in each analysis. Additionally, the error due to low S/N ratio was included, using the value from Kahraman Aliçavuş et al. (2016).

The values of the analysed stars were also compared with those used in the literature. In this comparison, we noticed that if had been obtained from spectral classifications, the used in previous studies are in agreement with our spectroscopic results to within the errors. Others, however, have completely different values. We determined values of HZ Dra and XX Cep to be 7700 and 8200 K, respectively. However, their previously used values are 9800 K for HZ Dra (Liakos et al., 2012) and 7300 K for XX Cep (Hosseinzadeh, Pazhouhesh, & Yakut, 2014). However, a newer spectral analysis of XX Cep was recently presented by Koo et al. (2016). They obtained = 7946  240 K and = 48.6  6.8 km s, which are in good agreement with our results.

Figure 3: Upper panel: comparison of the theoretical (red lines) and observed spectra of HL Dra. Lower panel: difference between the observed and theoretical spectra.

4  Sct stars in Eclipsing Binary systems

The properties of  Sct stars in eclipsing binaries can be different from single  Sct stars. Especially, the pulsating primary components in close binary systems evolve differently than single ones (Liakos & Niarchos, 2015). In close binary systems, the primary component can gain mass from the secondary and can be covered by material from the secondary. Additionally, tidal distortion is present in these systems. Mass-transfer and tidal distortion will affect the pulsation period () and amplitude () of  Sct stars in close binaries. How much the binarity affects the  Sct pulsations in binaries is one of the open questions.

To show the effect of binarity on pulsation, the correlations between , and the orbital and atmospheric parameters of eclipsing binary member  Sct stars have been examined. Firstly, a correlation between and orbital period () for 20  Sct stars in eclipsing binaries was found by Soydugan et al. (2006a). The  –  correlation was improved by newer discoveries (Liakos et al., 2012). Then, a theoretical explanation for the  –  correlation was given by Zhang, Luo, & Fu (2013) who expressed mainly as a function of the pulsation constant (Q), the filling factor (), , and the mass ratio (, where denotes the mass) with the following equation:

(1)

where and are the gravitational constant and effective radius (radius divided by semi-major axis), respectively. shows how much a star fills its Roche potential () and it is expressed by:

(2)

Zhang, Luo, & Fu (2013) tested whether this theoretical approach is compatible with the observed correlation of  –  using 69 eclipsing binaries with  Sct stars. They found that the theoretical correlation is in agreement with the observed one. This correlation was also confirmed by Liakos & Niarchos (2017). They obtained a similar correlation using 66 semi-detached and 25 detached systems which have 13 days. They also showed that for binaries with 13 days, there is no significant effect of binarity on pulsations. In their study, the known correlation between and was also shown for 82 systems which contained semi-detached, detached and unclassified stars with 13 days. However, it should be kept in mind that in their study, both eclipsing and non-eclipsing binaries were used and some of these stars were assumed to be detached systems. Additionally, a negative correlation between of primary  Sct components and gravitational force applied by secondary components onto the pulsating stars has been found (Soydugan et al., 2006a; Liakos et al., 2012; Liakos & Niarchos, 2017).

The known and possible correlations between the fundamental absolute parameters (e.g., masses, radii), atmospheric parameters, and the pulsation quantities (, ) of  Sct components in eclipsing binary systems give us an opportunity to understand these stars in detail and show the effect of secondary components, mass transfer and tidal locking on pulsation quantities. Therefore, we have prepared a revised list of eclipsing binaries with a primary  Sct component. The list includes 67 semi-detached and 25 detached eclipsing binaries. Seven of these stars (WX Dra, GQ Dra, KIC 06669809, KIC 10619109, KIC 1175495, KIC 10686876 and KIC 6629588) were taken from Liakos & Niarchos (2016, 2017). In these studies, the stars were found to be  Sct variables in eclipsing binaries for the first time. In our study, we did not include any stars which have unclassified Roche geometry.

The parameters of the primary and secondary components of our sample of 92 eclipsing binary systems with a primary  Sct component were gathered from the literature. In this revised list, values of , , masses (), radii (), luminosities (), bolometric magnitudes (M), semi-major axis () of the primary and secondary components and , , , peak-to-peak in and -band of primary pulsating components and the parallaxes, orbital inclinations (), and the of binary systems were collected, as well as the basic parameters of the systems such as visual magnitudes (), spectral types (SP) and binary types. This updated list contains more stars and a wider variety of stellar parameters compared to the previous list (Liakos & Niarchos, 2017). The updated list is given in Table 1.

4.1 General properties of  Sct components in eclipsing binaries

In our list, there are only two eclipsing binaries that show  Sct type pulsations in both components (RS Cha and KIC 09851944). In the other eclipsing binaries, only the primary components exhibit  Sct type pulsations. Therefore, in all our examinations we only took into account the properties of the primary  Sct components.

Figure 4: The distributions of and -band of the primary  Sct components in eclipsing binary systems.

The and -band distributions of primary  Sct components in eclipsing binaries are shown in Fig. 4. The pulsation periods of the highest amplitudes were collected in the list and only -band of the stars was used in any comparisons and analyses in this study. It is clearly seen that  Sct type primary pulsating components mainly oscillate in periods between 0.016 and 0.195 days, with an average amplitude of 21 mmag. In the list, there is also a high-amplitude  Sct star (HADS) (V1264 Cen) which is not used in Fig. 4 and excluded in the next steps. The average values for semi-detached and detached systems were found to be 0.049 and 0.073 days, respectively. Although the number of detached systems is lower than the semi-detached ones, there is a clear distinction between the pulsation periods of both systems. However, we did not find a significant difference in the -band of  Sct components of both type of eclipsing binary. The reason for lower pulsation periods of primary  Sct components in the semi-detached systems can be the effects of tidal locking and mass-transfer from the secondary non-pulsating component to the primary pulsating component (Liakos et al., 2012; Soydugan et al., 2006b, 2003). The primary component gains mass from the secondary component and this can change the surface composition and internal structure of the primary pulsating component and also the angular momentum of both components changes during this process (Aerts, Christensen-Dalsgaard, & Kurtz, 2010). Hence, mass-transfer could affect the oscillations.

Figure 5: The distributions of , , and values of primary  Sct components in eclipsing binaries. The gray histograms show the distributions of whole sample, while slanted lines represent the distributions of the stars that have and values derived by the spectroscopic analyses
Figure 6: The distributions of and values of primary  Sct components in eclipsing binaries.

The , , and ranges of  Sct components in eclipsing binary systems are illustrated in Fig. 5. In the figure, the distributions of parameters obtained from photometric and spectroscopic studies are shown. Both photometric and spectroscopic and values have similar ranges, which are 6750 – 9660 K and 3.40 – 4.38, respectively. The values of semi-detached and detached systems are in the range of 3.80 – 4.38 and 3.50 – 4.20, respectively, while ranges of these eclipsing binary types are similar. One semi-detached system, QY Aql, has a value of 3.40 (Liakos & Niarchos, 2013), which is low for the primary component of a semi-detached system, since they are generally main-sequence stars. The values of the primary  Sct components were found to be in the range from 12 to 130 km s. The values of and for the primary  Sct components were also found in the ranges of and 4.24 , respectively, as shown in Fig. 6. No significant difference was obtained between the range of and values for detached and semi-detached systems.

4.2 Correlations between the collected parameters and the pulsation quantities

The known and possible correlations between the collected fundamental, atmospheric and orbital parameters, and the pulsation quantities of the primary  Sct components in eclipsing binary systems were examined. Firstly, the known correlation between and was checked for semi-detached and detached systems. These correlations are demonstrated in Fig. 7. Average errors in and are about 10 and 10 days, and the error bars are smaller than the size of the symbols. Therefore, the error bars of and are not shown in this and subsequent figures. Additionally, for some stars, the errors of the parameters were not given in the literature. Therefore, the average uncertainties of the parameters are shown in all figures.

Significant positive  –  correlations were found for both semi-detached and detached systems. The relationships for these correlations are given in the top of each panel in Fig. 7. The correlation for semi-detached systems was found to be stronger than for the detached systems. As can be seen from Fig. 7, all stars are mainly inside the 1- level. The -band pulsation relation with was examined as well. As a result, a correlation was found between these parameters as shown in Fig. 8. However, the correlation is not strong, because of the scatter and number of data of points.

Figure 7: The correlations between and for detached (lower panel), semi-detached (middle panel) and all systems (upper panel). The filled circles, diamonds and red lines represent the semi-detached, detached and 1- levels, respectively. The equations in each panel were obtained from the correlations. R constant shows the spearman rank which gives the strength of correlation (number before the comma in the R constant) and the deviation amount of points from the correlation (number after the comma in the R constant).
Figure 8: The correlation between the V-band pulsation and of primary  Sct stars in eclipsing binary systems. The symbols, lines, and the R constant are the same as in Fig. 7.

The correlations between the atmospheric parameters (, ) and and -band of primary  Sct components were examined. While no correlation between and the atmospheric parameters was found, there are significant correlations between , , and . As shown in Fig. 9, these correlations were found for all types of eclipsing binaries’ primary  Sct components and they show a negative variation in with increasing and . However, as can be seen from the upper panel of Fig. 9, the log  –  relation is stronger for the pulsating primary components of detached systems than for semi-detached systems. Therefore, only the relationship for the correlation for detached systems is given in Fig. 9. The  –  relationship and the correlation for the primary  Sct components in all types of eclipsing binary systems are also shown in Fig. 9.

Figure 9: The  –  (upper panel) and  –  (lower panel) correlations. Green line in upper panel illustrates the correlation only for detached systems, while black line shows the correlation of semi-detached systems. The equations in upper and lower panels are given for detached and all systems’ primary  Sct components considering the correlations, respectively. The symbols, red lines, and R constant are the same as in Fig. 7.

The existence of  –  correlation offers us other probable connections between , , and . Given that , a positive correlation for  –  and a negative correlation for  –  should exist. Hence, these were examined and the expected correlations were obtained as demonstrated in Fig. 10. The positive  –  correlation is stronger than the negative  –  correlation. Additionally, no meaningful and correlations with -band were detected for all types of binaries with primary  Sct components.

Figure 10: The  –  (upper panel) and  –  (lower panel) correlations. The equation in lower panel was derived from the correlation for both detached and semi-detached systems. The symbols, red lines, and R constant are the same as in Fig. 7.

According to Eq. 1, theoretically a correlation between and should exist. When this relation was examined, it turned out that a correlation is present for detached systems, although no significant correlation is found for semi-detached systems. These are shown in the upper panel of Fig. 11. The  –  correlation was examined as well. This correlation is also not significant for semi-detached systems, while there is a strong correlation between and for detached systems. This relation is shown in the lower panel of Fig. 11.

Figure 11: The  –  (upper panel) and  –  (lower panel) correlations. Green lines illustrate the correlations for detached systems, while black lines show semi-detached systems’ correlations. The equations in each panel were derived from the correlations of detached systems. The symbols, red lines and R constant are the same as in Fig. 7.

The other important factor that theoretically affects according to Eq. 1, is the filling factor () of primary  Sct components. A direct proportional relation between and should exist. When this relation was examined for semi-detached systems, was found to be inversely related to as shown in the upper panel of Fig. 12. This result conflicts with Eq. 1. We also investigated the  –  correlation. As shown in the lower panel of Fig. 12, regularly decreases with increasing .

Figure 12: The correlation between , , and . The equations in the panels were derived from the correlations for semi-detached systems. No errors of values were given in the literature, hence we could not show the error bars of values. The symbols, red lines, and R constant are the same as in Fig. 7

Additionally, we calculated the gravitational force () which is applied by the secondary component to the primary pulsating  Sct star. The effect of this force causes a decrease in . This result was first obtained by Soydugan et al. (2006a). They found the same result as we show in the right-hand, upper panel of Fig. 13. The relation between and -band pulsation was examined as well and a negative correlation was found. The relationships for these correlations were found to be:

(3)
(4)

In the left-hand of Fig. 13 we show the correlations between orbital separation (), , and -band values. These correlations are opposite to the correlations found for as expected, because .

Figure 13: The correlations of a and with the and V-band pulsation values. The symbols, red lines, and R constant are the same as in Fig. 7.

5 Discussion

5.1 Comparison of single and eclipsing binary member  Sct stars

In this section, we compare the properties of single and eclipsing binary member  Sct stars. All parameters of single  Sct stars were taken from Rodríguez, López-González, & López de Coca (2000) (R2000, hereafter).

The values of  Sct components in eclipsing binaries were found between 0.016 and 0.147 days, while the range for single  Sct stars extends to 0.288 days (R2000). Hence, values of single  Sct stars are significantly longer than those in eclipsing binaries. Additionally, highest -band value of single  Sct stars is 250 mmag (R2000), compared to only 80 mmag for  Sct stars in eclipsing binaries555HADS stars were omitted in the comparison.. This difference was mentioned in the study of Soydugan et al. (2006b). Furthermore, the binarity effect was found when the average values of of semi-detached and detached systems were compared. Oscillations of  Sct stars in detached systems were found to be slower (0.073 d) than for semi-detached systems (0.045 d). Because semi-detached systems have generally lower values than detached systems, tidal locking is more effective in these systems. Additionally, in semi-detached systems the secondary components are evolved stars and they transfer mass onto the primary pulsation components. However, no difference was found between the -band pulsation of detached and semi-detached systems. The reason of this could also be the effect of mass-transfer in semi-detached systems.

The and of  Sct components in eclipsing binaries were found in the ranges of 6750 – 9660 K and 3.40 – 4.38, respectively. All types of eclipsing binary member  Sct stars have the same ranges, although the evolved stars, which have values lower than 3.80, are generally detached type eclipsing binary systems, except for QY Aql which probably has an incorrect value. The of  Sct stars is typically in the range of 6300 – 8600 K (Uytterhoeven et al., 2011). The values of  Sct stars in eclipsing binaries are in a good agreement with this range. However, there are some hotter stars and the of these stars should be re-examined. Comparisons of and for single and eclipsing binary member  Sct stars were not made, owing to a lack of these parameters for single  Sct stars in R2000.

The values of primary  Sct components in eclipsing binary systems were found between 12 and 130 km s, but extends to 285 km s for single  Sct stars (R2000). The average values for single and binary member  Sct stars are 90 and 64 km s, respectively. As a whole, the single  Sct stars rotate faster than those in eclipsing binary systems.

5.2 Correlations

A positive correlation between and was found for both detached and semi-detached eclipsing binaries’ primary  Sct components. According to this correlation, of primary  Sct components increase with the growing . Growing values relate to increasing ( a). Therefore, the effect of the secondary component on the primary pulsating component decreases with increasing and the pulsations of the primary  Sct stars are less influenced by binarity.

The  –  correlation was shown in the recent study of Liakos & Niarchos (2017) for all known  Sct stars in binaries, including the non-eclipsing ones. They found that there is a 13-days limit in and for longer values binarity has less of an effect on pulsations. However, our result is different. In our  –  correlation, there are detached stars (GK Dra, KIC 3858884 and KIC 8569819) which have  days and agree with the  –  correlation to within the 1- level. The 13-days limit for the binarity effect on pulsations appears to be underestimated. Our results show that binarity still influences the pulsations of primary  Sct components with  days. Although Liakos & Niarchos (2017) did not include stars having  days in their  –  correlation, our correlation is in agreement, as can be seen from Fig. 14. However, the theoretically calculated  –  relationship by Zhang, Luo, & Fu (2013) is different than ours. The reason of this difference could be the negative effects of some parameters ( and in semi-detached systems) on the pulsations, contrary to the expected positive effects of these parameters according to Eq. 1, which were used to derive the theoretical  –  relationship.

The -band of primary  Sct components in eclipsing binary systems increases with increasing . No  –  correlation was found in previous studies (Soydugan et al., 2006a; Liakos et al., 2012; Zhang, Luo, & Fu, 2013; Liakos & Niarchos, 2017). The gravitational force applied by secondary components onto the surface of primary pulsation stars appears to cause a decrease in .

Figure 14: Comparison of  –  correlations for eclipsing binaries with a primary  Sct component. Square symbols illustrate the stars have 13 d. The other symbols are the same as in Fig. 7.

A significant negative correlation was found between and . Balona & Dziembowski (2011) also showed the same relation and Kahraman Aliçavuş et al. (in preparation) also found it for single  Sct stars. The and relation is an expected result. When the pulsation constant (), mean density () and the luminosity-mass relation () are taken into account, a negative relation between and is found (). Additionally, changes in bears on the changes in , which affect the region of He ionization which is responsible from the pulsations (Cox, 1980).

The known negative correlation between and was demonstrated using the data of newly discovered stars. The correlation shows that main-sequence  Sct components in eclipsing binaries pulsate in shorter periods than evolved stars. Using the pulsation constant, mean density and surface gravity (), a relationship between and can be found (). According to this rough approach, our  –  correlation was found as expected.

The  –  correlation was also examined by Liakos & Niarchos (2017) for  Sct components in binary systems. Additionally, Claret et al. (1990) obtained the same relation for single  Sct stars. In Fig. 15, we compare the correlations of  –  found for single and binary  Sct stars. Our correlation is approximately parallel to the correlation found for single  Sct stars, but there is a significant difference between our correlation and that of Liakos & Niarchos (2017). In our study, we only used  Sct stars in eclipsing binaries, whereas Liakos & Niarchos (2017) used all binaries containing  Sct components. In eclipsing binaries, the values of pulsating components can be derived more accurately, which is probably the reason for the difference between the two correlations.

Figure 15: Comparison of  –  correlations of single and eclipsing binary member  Sct stars. The symbols are the same as in Fig. 7.

Positive  –  and negative  –  correlations were obtained, as expected. From the  –  correlation we know that both and values have effect on pulsation. Therefore, combining both equations we obtain:

(5)

A similar equation was found for Cepheid stars by Fernie (1965). As can be seen from the equation, is more influenced by changes in than changes in . In Fig. 10, the weak effect of and the stronger effect of on the pulsation of primary  Sct components can be seen.

We found that the binary mass ratio () has no significant effect on of primary  Sct components in semi-detached systems, although there is a correlation between and for primary  Sct components in detached systems. According to Eq. 1, should be directly proportional to . The lack of any correlation in semi-detached systems might be due to the lack of systems with .

The variation of with was also found only for detached systems. The decreases with increasing . Since semi-detached systems are generally close binaries, rotation synchronisation is present. Therefore, owing to the  –  correlation, we expected to find a correlation between and in the semi-detached systems. However, mass-transfer in these systems is very effective and this changes the and of the primary  Sct components, and these affect the rotation and angular momentum. The altered angular momentum also results in a change of which can change the rotation (). All these effects can be the reason why we did not find a  –  correlation for semi-detached systems. A correlation between and was also found by Tkachenko et al. (2013) using the values of some  Sct stars taken from Uytterhoeven et al. (2011) and R2000. In their work they found a weak  –  relation, but, contrary to our results, with increasing with declining . The rotation of stars causes changes in their stellar structure, hence the reason why can be different for different values of (Soufi, Goupil, & Dziembowski, 1998).

According to Eq. 1, should be directly proportional to . However, in our study, we have obtained the opposite result. When the correlation between and was examined, we noticed that increases with decreasing . The gravitational force applied on the primary pulsating component grows with increasing value. Thus, we can say has a significant effect on and we, therefore, obtained a negative relation between and instead of a positive correlation. Additionally, we found that the strength of applied by the secondary component to the primary pulsation star affects and in a negative way. The same correlation between and was also obtained by Soydugan et al. (2006a).

5.3 Positions in HR Diagram

The positions of the analysed primary  Sct components in this study and the other primary  Sct components given in the updated list in the Hertzsprung-Russell (HR) Diagram are shown in Fig. 16. Our analysed  Sct components and the  Sct components given in the revised list are located in the  Sct instability strip. However, there are a few stars (RR Lep, V2365 Oph, VV UMa and V346 Cyg) placed beyond the blue edge of  Sct instability strip. The and values of these stars were taken from literature spectral classification and photometric analyses (see Table A1 for references). Therefore, these stars should be re-analysed with new data.

In our study, the primary  Sct components in eclipsing binaries were mostly located inside the theoretical  Sct instability strip to within the error bars. However, in the study of Liakos & Niarchos (2017), there are more stars located beyond the blue border of  Sct instability strip compared to our results. Liakos & Niarchos (2017) showed positions of  Sct stars in all binaries, whereas we only showed the positions of  Sct in eclipsing binaries. The fundamental parameters of stars can be obtained more accurately in the eclipsing binary case. Probably because of this reason Liakos & Niarchos (2017) found more stars located beyond the blue edge of  Sct instability strip.

Figure 16: Positions of analysed and collected  Sct stars in eclipsing binary systems. The symbols are the same as in Fig. 7. Solid lines represent the theoretical instability strips of  Sct stars (Dupret et al., 2005). Triangle and square symbols illustrate the stars analysed spectroscopically in this study and the stars have 13 d, respectively. The evolutionary tracks were taken from Kahraman Aliçavuş et al. (2016)

6 Conclusions

In this study, we present an updated list of  Sct stars in eclipsing binaries and the spectroscopic analysis of six of  Sct components in eclipsing binary systems.

In the spectroscopic analysis of six primary  Sct components in eclipsing binaries, we obtained the spectral classification, , , and of the stars. XX Cep was found to be metal-rich, while others have approximately solar metallicity.

In the updated list of  Sct components in eclipsing binaries, we collected the atmospheric and orbital parameters of the primary  Sct components. We examined the properties of the primary  Sct components and compared them with the properties of single  Sct stars. Liakos & Niarchos (2017) stated that the single and binary member  Sct stars have similar pulsational behaviour. However, when and -band of single and eclipsing binary member  Sct stars were compared, we found that eclipsing binary member  Sct stars oscillate with shorter and lower comparing to single ones. These differences in pulsation quantities of single and binary  Sct stars are thought to be caused by the effects of gravitational force applied by the secondary component on the primary and mass-transfer in these binaries. Additionally, binarity effects were also found when of detached and semi-detached member  Sct stars were compared. We showed that  Sct stars in detached systems pulsate in longer periods.

The of single and eclipsing binary member  Sct stars was also compared. We found that, on average, single  Sct stars rotate faster than those in eclipsing binary systems.

We examined the relations between the orbital and atmospheric parameters of primary  Sct components. Firstly, the known  –  correlation was checked and we obtained that increases with increasing . Liakos & Niarchos (2017) found that binarity does not have a significant effect on pulsation if 13 days. However, we showed that the  –  correlation is still significant even if is 26 days. Therefore, it appears that the 13-days limit for the binarity effect is too low. When our  –  correlation was compared with the previously found correlations we obtained similar trends except for the theoretically calculated relationship of Zhang, Luo, & Fu (2013). The difference between the theoretical relation and our correlation is caused by some parameters (, ) having adverse effects on pulsation, whereas these parameters were found to be directly proportional to pulsation in the theory. We also found that -band of primary  Sct components increases with increasing .

Significant negative relations between and atmospheric parameters and were found. The  –  correlation was already known, however the  –  correlation for the primary  Sct components was shown the first time. The  –  correlation was compared with those in the literature. We find that our correlation is almost in agreement with that found for single  Sct stars. However, the correlation found by Liakos & Niarchos (2017) is incompatible with ours.

A positive  –  and a negative  –  correlations were found. As both parameters influence the pulsation, we gave a new equation for in terms of and (Eq. 5). Additionally, we showed that increasing caused increasing in for detached systems, while has no effect on in semi-detached systems. According to theory should be directly proportional to . The relationship between and of primary  Sct components was also examined. No relationship was obtained for semi-detached systems. However, for detached systems, of the primary  Sct components decreases with increasing . The suggested positive and correlation by Zhang, Luo, & Fu (2013) was also checked. However, we found that is inversely proportional to . When the relationship between and was checked, we also obtained a negative correlation. Components in binaries come closer to each other with decreasing and the Roche lobes of the components become smaller, therefore increases with decreasing . This effect is rather dominant in binaries. Hence, we still see this effect in the  –  relationship. Therefore, a negative correlation between these parameters was obtained contrary to suggested relation. Additionally, we found that the gravitational force applied by the secondary components onto the primary  Sct components changes and of  Sct stars.

The positions of the primary  Sct components in the  -  diagram were shown. The primary  Sct components in detached and semi-detached systems are located inside the  Sct instability strip. However, there are some semi-detached member  Sct components located beyond the blue edge of  Sct instability strip, but the and of these stars may not be reliable.

In this study, we show the importance of  Sct components in eclipsing binaries. The differences between the single and binary member  Sct stars were emphasised. The effects of the fundamental and orbital parameters on pulsation and the correlations between the pulsation quantities and some fundamental parameters were given. These relationships allow us to infer the initial values of the fundamental parameters of pulsating  Sct components. This is important for the theoretical examination of pulsating stars and understanding the internal structures and evolutionary statuses of stars. Additionally, utilizing the found  –  correlation, the lower frequencies in  Sct stars can be examined to see if they are related to binarity.

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. We thank Çanakkale Onsekiz Mart University Research Foundation (Project No. FDK - 2016 - 861) for supporting this study. This article is a part of the PhD thesis of FKA. JK thanks to the grant 16-01116S (GAČR). We thank Dr. G. Catanzaro for putting the code for Balmer lines analysis at our disposal. We are grateful to Dr. D. Shulyak for putting the code for calculating at our disposal. We thank Dr. J. Ostrowski for helping us for the evolution tracks. 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. This research has made use of the SIMBAD data base, operated at CDS, Strasbourq, France.

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HD Name V Spectral Parallaxes Type Amp Amp
(mag) Type (mas) (days) (days) (mmag) (mmag) (K) (K) (km s)
354963 QY Aql 11.89 F0 1.74 (87) SD 7.2296 0.0938 9.4 (2) 11.8 (2) 7300 4244 (122) 3.4 (10)
193740 XZ Aql 10.18 A2/3 II/III 2.03 (44) SD 2.1392 0.0326 6.8 (2) 8.6 (2) 8770 (150) 4720 (150) 4.10 (03)
V729 Aql 13.76 SD 1.2819 0.0357 4.2 (4) 6900 4300 (175) 4.00 (10)
V1464 Aql 08.68 A2V 4.12 (48) SD 0.6978 0.0171 24.0 (3) 30.0 (2) 7420 (192) 6232 (161)
CZ Aqr 11.10 A5 SD 0.8627 0.0282 3.7 (5) 8200 5650 (12) 4.21 42
211705 DY Aqr 10.49 A1/2 III 1.83 (75) SD 2.1597 0.0428 9.4 7625 (125) 3800 (200) 4.25 (25) 50 (10)
203069 RY Aqr 9.25 A7V 6.48 (28) SD 7650 4520 (122) 4.25 (60)
V551 Aur 14.27 F D 1.1732 0.1294 19.1 (3) 15.7 (3) 7000 6085 (34)
EW Boo 10.26 A0 2.23 (26) SD 0.9063 0.0191 12.4 (2) 14.4 (2) 7840 4515 (35) 4.1 (10)
YY Boo 11.58 A4+K4IV 1.17 (23) SD 3.9330 0.0613 79.2 (2) 116.8(2) 4650 (10)
Y Cam 10.60 A9IV+K1IV 0.82 (30) SD 3.3058 0.0665 12.2 8000 (250) 4629 (150) 3.79 51 (4)
194168 TY Cap 10.36 A5 III 1.95 (55) SD 1.4235 0.0413 15.6 (7) 18.5 (7) 8200 4194 (30) 3.98
AB Cas 10.32 A3 V 2.91 (22) SD 1.3669 0.0583 19.6 (9) 22.2 (1) 8000 4729 (24)
IV Cas 11.34 A2 1.06 (40) SD 0.9985 0.0306 3.4 (2) 8500 (250) 5193 (7) 4.0 (50) 115 (5)
017138 RZ Cas 6.26 A3 V 14.99 (34) SD 1.1952 0.0156 5.4 (3) 2.7 (3) 8907 (15) 4797 (20) 4.35 66 (1)
V389 Cas 11.09 D 2.4948 0.0370 9.2 (4) 7673 (31) 4438 (22) 3.87
V1264 Cen 11.95 A7V 0.97 (39) SD 5.3505 0.0734 350.0 7500 4200 4.00
222217 XX Cep 9.18 A7V 3.17 (23) SD 2.3374 0.0310 2.6 (2) 2.9 (2) 8000 (250) 4280 (36) 4.09 50
WY Cet 9.28 F0V 4.64 (73) SD 1.9396 0.0757 7.7 (3) 7500 4347 (7) 4.02
075747 RS Cha 6.07 A7V D 1.6699 0.0473 7640 (76) 7230 (72) 4.05 64 (6)
057167 R Cma 5.70 F2 III/IV 23.3 (59) SD 1.1359 0.0471 7300 4350 4.19 82 (3)
UW Cyg 10.86 A7/A6 IV 1.60 (30) SD 3.4507 0.0359 1.9 (2) 7800 (250) 4347 (4) 4.06 45
V346 Cyg 12.22 A5 1.11 (22) SD 2.7433 0.0502 30.00 8353 6620 3.68
V469 Cyg 12.33 B8+F0 SD 1.3124 0.0278 20.0 4.13
099612 AK Crt 11.28 A5/9 II/III 1.81 (48) D 2.7788 0.0680 8-35
BW Del 11.28 F2 SD 2.4231 0.0398 1.8 (2) 2.9 (2) 7000 4061 (30) 4.00
152028 GK Dra 8.77 F0 3.03 (22) D 16.960 0.1138 7100 (70) 6878 (57) 3.83 (03)
GQ Dra SD 0.7659 0.0335
172022 HL Dra 7.36 A6IV 6.24 (24) SD 0.9443 0.0372 2.8 (3) 3.0 (2) 7800 (250) 5074 (8) 3.80 88
173977 HN Dra 8.07 F2 3.88 (23) D 1.8008 0.1169 7.6 6918 6309 3.83 73
187708 HZ Dra 8.14 A8/A7 V 4.89 (29) D 0.7729 0.0196 4.0 (4) 7600 (250) 5015 (68) 4.22 120
OO Dra 11.39 1.54 (29) D 1.2384 0.0239 4.2 (2) 4.9 (3) 8500 6452 (8) 4.15
238811 SX Dra 10.40 A7V+ K7IV 1.16 (27) SD 5.1696 0.0440 23.6 (3) 34.6 (4) 7762 4638 (200) 3.99
139319 TW Dra 7.46 A5+K0III 5.90 (24) SD 2.8069 0.0530 10.00 8160 (15) 4538 (11) 3.88 (02) 47 (1)
TZ Dra 9.32 A7V 3.96 (25) SD 0.8660 0.0196 2.8 (2) 3.7 (2) 7600 (250) 5088 (55) 4.20 (10) 80
021985 AS Eri 8.30 A1V 5.06 (51) SD 2.6641 0.0169 8500 4790 4.35 40
TZ Eri 9.61 A5 3.27 (34) SD 2.6061 0.0534 7.3 8.30 9307 (20) 4562
336759 BO Her 11.14 A7 1.51 (30) SD 4.2728 0.0745 50.8 (3) 68.0 (3) 7800 4344 (68) 3.90 (10)
CT Her 11.32 A3V 0.83 (46) SD 1.7864 0.0189 3.3 (1) 8700 4651 (7) 4.17 (02) 50
EF Her 11.53 A0 1.14 (26) SD 4.7292 0.0310 51.0 69.0 9327 4767
151973 LT Her 10.55 A1 1.71 (81) SD 9400 5063 (25)
TU Her 11.14 A5 1.84 (22) SD 2.2669 0.0556 9-10
V948 Her 8.91 F2 6.15 (26) D 2.0831 0.0947 31.0 7000 4310 (63) 4.20 (10)
AI Hya 9.35 F2m+F0V 1.88 (35) D 8.2897 0.1380 20.0 7100 6750 4.10
078014 RX Hya 9.56 A5 III 3.80 (33) SD 2.2817 0.0516 7.0
AU Lac 11.81 A5 1.60 (20) SD 1.3926 0.0172 5.00 8200 3784 (15) 4.26
WY Leo 10.89 A2 1.51 (49) SD 4.9858 0.0656 11.0 (1) 3.79
Y Leo 10.07 A3V 2.50 (26) SD 1.6861 0.0290 8.12 (15) 8855 4276 (23) 4.27
033789 RR Lep 10.14 A4 III 2.20 (35) SD 0.9154 0.0300 7.6 (4) 9.6 (4) 9300 4904 (106) 4.00 (10)
CL Lyn 9.77 A8 IV 2.82 (25) SD 1.5861 0.0434 5.7 (4) 7.3 (3) 7200 (250) 4948 (14) 3.98 75
198103 VY Mic 9.54 A4 III/IV 1.66 (36) SD 4.4364 0.0817 19.4 (2) 8705 5301 4.15
V577 Oph 11.19 A 1.29 (26) D 6.0791 0.0695 57.8
155002 V2365 Oph 8.86 A2 3.54 (29) SD 4.8656 0.0700 50.0 9500 6400 (27) 4.05
293808 FL Ori 11.42 A2 2.05 (40) D 1.5510 0.0550 8232 5243 4.28
248406 FR Ori 10.64 A7 2.53 (86) SD 0.8832 0.0259 5.8 7830 4583 (10) 4.21
252973 V392 Ori 10.49 A5V 2.56 (25) SD 0.6593 0.0246 8300 5065 (11) 4.15
MX Pav 11.35 A5+K3IV 1.56 (38) SD 5.7308 0.0756 76.9 (3)
BG Peg 11.35 A2 SD 1.9527 0.0391 30.6 (5) 36 (6) 8770 5155 (200) 4.20
275604 AB Per 9.72 F0 SD 7.1603 0.1954
IU Per 10.56 A4 1.62 (45) SD 0.8570 0.0232 3.08 (07) 8450 4900 (250) 4.29
AO Ser 11.04 A2 2.19 (41) SD 0.8793 0.0465 20.00 8860 4547 (512) 4.30
Table 1: The list of  Sct stars in eclipsing binaries. The fundamental, orbital, and atmospheric parameters of primary  Sct and secondary components. The subscripts, p and s represents primary and secondary components, respectively.
HD Name V Spectral parallaxes Type Amp Amp
(mag) Type (mas) (days) (days) (mmag) (mmag) (K) (K) (km s)
UZ Sge 11.40 A0 SD 2.2157 0.0214 8700 4586 (60) 4.20 (10)
AC Tau 11.09 A8 1.65 (43) SD 2.0434 0.0570 6.0
IZ Tel 12.20 A8+G8 IV 0.52 (26) SD 4.8802 0.0738 45.9 (4)
12211 X Tri 9.00 A7V 4.85 (22) SD 0.9715 0.0220 20.0 8600 5188 (4)
115268 IO Uma 8.21 A3 1.05 (43) SD 5.5202 0.0454 10 (2) 13.0 (2) 7800 (150) 4260 (30) 3.84 (05) 35 (2)
VV Uma 10.28 A2V 2.45 (45) SD 0.6874 0.0205 28.0 (1) 9660 (30) 5579 (20) 4.38
AW Vel 10.70 A7 1.69 (41) SD 1.9925 0.0658 58.0 (1)
BF Vel 10.62 A3 1.92 (30) SD 0.7040 0.0223 26.0 (2) 8550 4955 (4) 4.27
CoRot 105906206 12.21 0.96 (25) D 3.6946 0.1062 6750 (150) 6152 (162) 3.57 48 (1)
172189 GSC 455-1084 8.73 A6V-A7V D 5.7017 0.0510 7600 (150) 8100 (150) 3.48 78 (3)
232486 GSC 3671-1094 9.64 A5 3.07 (25) D 2.3723 0.0409 20.0
GSC 3889-202 10.39 A7 V-IV 1.27 (24) SD 2.7107 0.0441 50.0 70.0 7750 4500 3.90 60
GSC 4293-432 10.56 A7+K3 SD 4.3844 0.1250 35.0 40.0 7750 4300 40
GSC 4588-883 11.31 A9 IV+K4III 0.94 (48) SD 3.2586 0.0493 7650 4100 3.90 60
062571 GSC 4843-2140 8.83 F0-F2 SD 3.2087 0.1141 41.7 7762 5719 (150)
220687 GSC 5825-1038 9.60 A2 III 2.31 (42) D 1.5943 0.0382 12.8 (14)
KIC 3858884 9.28 F5 1.78 (22) D 25.952 0.1383 6810 (70) 6890 (80) 3.60 32 (2)
181469 KIC 4150611 08.00 A2 7.73 (46) D 94.090 7400 (100) 3.80 (20) 128 (5)
KIC 4544587 10.83 1.36 (41) D 2.1891 0.0208 8600 (100) 7750 (180) 4.12 (02) 87 (13)
KIC 4739791 14.63 A7V D 0.8989 0.0482 7778 (28) 5447 (17) 4.20 (02)
KIC 6220497 SD 1.3232 0.1174 7279 (54) 3907 (22) 3.78 (30)
KIC 6629588 D 2.2645 0.0746 6787 (247) 4405 (621)
KIC 8569819 D 20.849 7100 (250) 6047 (253)
KIC 9851944 11.42 D 2.1639 0.0962 7026 (50) 6950 (50) 3.96 53 (7)
KIC 10619109 11.90 SD 2.0452 0.0234 7138 (284) 3824 (571)
KIC 10661783 9.53 A2 1.94 (26) SD 1.2314 0.0355 7764 (54) 5980 (72) 3.90 79 (4)
KIC 10686876 11.54 F0V D 2.6184 0.0476 8167 (285) 6475 (817)
KIC 11175495 SD 2.1911 0.0155 8293 (290) 6999 (790)
KIC 11401845 D 2.2000 7590
TYC 7053-566-1 11.51 1.09 (23) SD 5.1042 0.0743 7000 (200) 4304 (9) 3.91 (02)
USNO-A2.0 1200-03937339 14.53 SD 1.1796 0.0326 5.1 (4) 7250 4320 (108) 3.90 (10)
Table 1: Continuation.
HD Name References
() () () () () () () (mag) (mag) () ()
354963 QY Aql 88.6 (5) 0.250 (200) 0.403 1.6 (2) 0.4 (1) 4.1 (2) 5.4 (2) 43.0 (3.0) 8.0 (1) 4.0 (2) 16.3 (7) 6, 42
193740 XZ Aql 84.8 (1) 0.204 (2) 0.500 2.5 (1) 0.5 (03) 2.3 (04) 2.5 (04) 6.0 (04) 0.5 (07) 1.1 (1) 3.6 (2) 10.1 (1) 6, 73
V729 Aql 77.3 (2) 0.440 (10) 0.723 1.5 (2) 0.7 (1) 2.0 (01) 2.0 (01) 7.8 (1) 1.3 (2) 2.0 (1) 4.6 (1) 43
V1464 Aql 38.4 (2) 0.710 (20) 1.000 2.1 (05) 1.8 (01) 12.0 (3) 4.4 (02) 4.8 6, 11, 84
CZ Aqr 89.7 (1) 0.490 (100) 0.780 2.0 1.0 (1) 1.9 (1) 1.8 (1) 15.3 (9) 2.9 (2) 1.8 (6) 3.6 (6) 1.9 (2) 3.8 (1) 41
211705 DY Aqr 75.4 (5) 0.310 (200) 0.489 1.8 (2) 0.6 (4) 2.1 (1) 2.7 (1) 9.4 (5) 9.4 (5) 2, 6
203069 RY Aqr 83.2 (4) 0.204 (6) 1.3 (1) 0.3 (02) 1.4 (07) 1.9 (1) 56.0 (9) 1.4 (3) 4.4 (2) 2.8 (2) 7.6 6, 55
V551 Aur 74.3 (1) 0.725 (6) 0.539 52
EW boo 76.5 (1) 0.130 (2) 0.708 1.8 (2) 0.2 (02) 1.8 (1) 1.1 (04) 10.9 (5) 0.4 (1) 5.0 (2) 6, 83, 84
YY Boo 81.7 (1) 0.290 (10) 0.303 6, 24
Y Cam 85.6 (1) 0.241 0.535 2.1 (1) 0.5 3.1 (05) 3.3 (05) 1.4 (06) 0.5 (06) 1.3 (2) 3.6 (2) 6, 25, 34, 41, 61, 84
194168 TY Cap 80.4 (2) 0.520 (100) 0.706 2.0 (1.1) 1.1 2.5 (1) 2.5 (1) 24.3 (8) 1.8 (2) 1.3 (1) 4.1 (1) 2.7 (3) 5.2 (1) 6, 41
AB Cas 88.3 (1) 0.190 0.535 6, 67, 84
IV Cas 87.5 (5) 0.408 (1) 0.781 2.0 (1) 0.8 (04) 2.1 (04) 1.8 (03) 1.3 (05) 0.3 (05) 1.4 (1) 3.9 (1) 6, 30, 31
017138 RZ Cas 82.0 (3) 0.342 (1) 0.494 2.0 (2) 0.7 (1) 1.6 (1) 1.9 6.6 (3) 6, 69, 74, 84
V389 Cas 81.8 (2) 1.5 (01) 1.5 (01) 2.5 (02) 2.6 (05) 1.6 3.9 (1) 0.1 6, 37
V1264 Cen 86.5 (1) 0.220 (20) 0.350 1.5 (02) 0.3 (02) 2.4 (02) 4.0 (01) 6.7 (03) 3.9 (03) 1.8 3.5 6, 8
222217 XX Cep 81.6 (1) 0.173 (5) 0.387 2.5 (1) 0.4 (01) 2.3 (02) 2.4 (02) 20.0 (3.0) 2.1 (4) 1.5 (2) 3.9 (4) 6, 26, 36, 84
WY Cet 81.8 (1) 0.260 (10) 0.514 1.7 0.4 (01) 2.2 (1) 2.3 (1) 14.0 (9) 1.7 (1) 1.9 (8) 4.2 (8) 1.8 (3) 6.9 (1) 6, 41, 84
075747 RS Cha 83.4 (3) 0.709 1.9 (01) 1.9 (01) 2.2 (06) 2.4 (06) 1, 3, 84
057167 R Cma 81.7 (2) 0.140 0.542 1.7 (1) 0.2 (1) 1.8 (03) 1.2 (07) 8.2 (2) 0.5 (01) 5.7 5.7 4, 6, 56, 84
UW Cyg 87.1 (1) 0.140 (100) 0.316 1.9 0.3 (1) 2.2 (1) 2.9 (1) 18.0 (9) 2.6 (1) 1.6 (4) 3.7 (6) 1.5 (2) 11.2 (1) 6, 41
V346 Cyg 2.3 1.8 3.8 4.7 61.8 39.9 6, 68, 84
V469 Cyg 81.0 0.430 3.3 2.7 5, 41, 68
099612 AK Crt 6, 60
BW Del 78.6 (4) 0.160 (20) 0.416 1.5 (2) 0.3 (1) 2.1 (1) 2.2 (1) 10.0 (1) 1.2 (1) 1.3 (1) 8.0 (4) 42
152028 GK Dra 86.1 (2) 1.244 (20) 0.356 1.5 (1) 1.8 (1) 2.4 (04) 2.8 (05) 2.0 (1) 1.8 (1) 6, 19, 84, 89
GQ Dra 51
172022 HL Dra 66.5 (1) 0.370 (100) 0.859 2.5 (2) 0.9 (1) 2.5 (4) 1.8 (3) 24.3 (7) 1.9 (1) 1.3 (2) 4.1 (2) 1.7 (3) 4.4 (1) 6, 41, 84
173977 HN Dra 67.0 0.931 1.9 1.3 2.9 1.4 6, 7, 84
187708 HZ Dra 72.0 (3) 0.120 (40) 0.773 3.0 (3) 0.4 (1) 2.3 (1) 0.8 (1) 45.0 (3.0) 0.4 (2) 0.6 (4) 5.9 (4) 0.6 (1) 4.7 (1) 6, 41, 84
OO Dra 85.7 (1) 0.097 (2) 0.558 2.0 (3) 0.3 (03) 2.0 (1) 1.2 (05) 6, 86
238811 SX Dra 85.3 (1) 0.373 (2) 0.320 1.8 0.5 2.3 4.3 16.4 6, 72
139319 TW Dra 86.8 (3) 0.411 (4) 0.581 2.2 (1) 0.9 (05) 2.6 (02) 1.3 (1) 3.2 12.2 (2) 6, 33, 75, 84
TZ Dra 77.6 (1) 0.310 (30) 0.665 1.8 (2) 0.6 (1) 1.7 (1) 1.5 (1) 9.0 (1.0) 1.3 (1) 1.2 (1) 4.0 (2) 6, 42
021985 AS Eri 0.277 1.9 1.6 6, 41, 58, 84
TZ Eri 87.7 (07) 0.177 (5) 0.306 6, 39
336759 BO Her 85.4 (4) 0.220 (200) 0.324 1.8 (2) 0.4 (1) 2.5 (1) 3.8 (1) 20.0 (1.0) 4.6 (4) 2.7 (1) 12.1 (5) 6, 42
CT Her 81.9 (01) 0.141 0.432 2.3 (02) 0.3 (04) 2.1 (06) 1.9 (08) 17.4 (2.4) 1.2 (2) 1.7 (2) 4.5 (2) 1,6, 44
EF Her 77.80 0.210 0.421 6, 64
151973 LT Her 75.6 (2) 0.200 (3) 0.840 2.5 0.5 2.7 1.6 49.5 1.7 6, 62
TU Her 6, 45
V948 Her 84.4 (6) 0.270 (30) 0.574 1.5 (2) 0.4 (07) 1.6 (1) 0.7 (3) 6.0 (1.0) 0.2 (1) 2.9 (2) 7.0 (1.0) 1.3 (7) 4.9 (2) 6, 40, 41
AI Hya 89.9 (1) 1.9 2.1 2.1 3.8 1.5 1.2 6,29, 61, 68
078014 RX Hya 6, 33, 84
AU Lac 83.0 (1) 0.300 (10) 0.490 2.0 0.6 (1) 1.8 (1) 2.1 (1) 12.6 (7) 0.8 (1) 2.0 (6) 5.0 (7) 1.7 (2) 5.7 (1) 6, 41, 58
WY Leo 2.3 3.3 5, 6, 15
Y Leo 86.1 (2) 0.324 (3) 2.3 0.7 1.9 2.5 8.6 6, 75, 76, 84
033789 RR Lep 80.5 (6) 0.287 (21) 0.802 2.5 (3) 0.7 (1) 2.4 (1) 1.5 (2) 15.6 (4) 1.0 (1) 0.8 (4) 4.6 (8) 5.1 (1) 5.9 (1) 6, 16, 42
CL Lyn 78.7 (1) 0.190 (20) 0.606 2.0 0.4 2.5 (1) 1.9 (1) 25.2 (9) 2.0 (7) 1.2 (9) 4.0 (8) 1.3 (3) 6.6 (1) 6, 41, 84
198103 VY Mic 2.4 2.0 2.2 4.4 26.0 14.0 6, 60, 68
V577 Oph 0.939 (6) 1.6 6, 9, 88
155002 V2365 Oph 87.4 (1) 0.538 (3) 0.346 2.0 (02) 1.1 (01) 2.2 (01) 35.0 (4.0) 1.3 (03) 0.9 (1) 4.4 17.5 17.5 6, 27, 41, 84
293808 FL Ori 84.5 0.900 0.549 2.9 1.9 2.1 2.2 18.6 3.2 6, 41, 68, 83
248406 FR Ori 83.2 (1) 0.325 (2) 0.735 1.8 0.6 1.8 1.6 5.2 6, 83
252973 V392 Ori 79.8 (03) 0.247 (1) 0.951 2.0 (2) 0.5 (05) 2.0 (07) 1.3 (04) 16.9 (8) 0.5 (02) 3.6 (1) 6, 85
MX Pav 77.0 0.150 5, 6, 60
BG Peg 83.2 (1) 0.233 (3) 0.582 2.2 0.5 2.0 2.4 9.2 70
275604 AB Per 31, 32, 84
IU Per 78.8 (4) 0.273 (50) 0.762 2.2 0.6 2.0 1.5 19.1 1.1 5.4 5.4 6, 35, 83
AO Ser 87.0 (1) 0.396 (82) 0.846 2.4 1.0 1.8 1.5 17.5 0.8 1.6 5.0 5.8 6, 22
Table 1: Continuation.
HD Name References
() () () () () () () (mag) (mag) () ()
UZ Sge 88.8 (1) 0.140 (100) 0.396 2.1 (2) 0.3 (2) 1.9 (2) 2.2 (2) 19.0 (4) 1.9 (4) 1.6 (2) 4.0 (1) 1.2 (8) 8.6 (6) 40
AC Tau 0.0 6, 16, 41
IZ Tel 0.0 6, 60, 81
12211 X Tri 87.9 (1) 0.599 (200) 0.724 2.1 1.3 6, 51, 84
115268 IO Uma 78.3 (1) 0.135 (3) 0.342 2.1 (1) 0.3 (02) 3.0 (04) 3.9 (05) 1.5 (04) 0.7 (07) 1.1 (1) 3.1 (2) 17.6 (1) 6, 71, 84
VV Uma 80.9 (03) 0.337 (2) 0.722 1.7 1.4 4.9 6, 20, 46,84
AW Vel 6, 57
BF Vel 86.2 (1) 0.424 (19) 0.814 2.0 (2) 0.8 (08) 1.8 (01) 1.5 (01) 15.2 (4) 1.8 (02) 1.8 4.1 4.7 6, 54
CoRot 105906206 81.4 (1) 0.574 (8) 0.720 2.3 (04) 1.3 (03) 4.2 (02) 1.3 (01) 15.3 (1) 6, 10
172189 GSC 455-1084 73.2 (6) 0.960 (1) 0.621 1.8 (2) 1.7 (2) 4.0 (1) 2.4 (07) 52.4 (2.9) 22.2 (1) 20.3 (1) 9, 41
232486 GSC 3671-1094 6, 17, 41, 84
GSC 3889-202 6, 12
GSC 4293-432 14
GSC 4588-883 78.5 (2) 6, 13
062571 GSC 4843-2140 73.0 0.662 (16) 28, 41
220687 GSC 5825-1038 6, 60
KIC 3858884 0.999 (5) 0.213 1.9 (03) 1.9 (04) 3.5 (01) 3.1 (01) 57.2 (2) 6, 53, 84
181469 KIC 4150611 6, 65, 84
KIC 4544587 87.9 (03) 0.810 (12) 0.689 2.0 (1) 1.6 (06) 1.8 (03) 1.6 (03) 1.6 6, 23
KIC 4739791 72.6 (02) 0.070 0.740 1.8 (1) 0.1 (06) 1.7 (03) 0.9 (02) 10.0 (1.0) 0.6 (1) 2.3 (1) 5.2 (2) 48
KIC 6220497 77.3 (3) 0.243 (10) 0.871 1.6 (8) 0.4 (2) 2.7 (6) 1.7 (4) 18.0 (2) 0.6 (1) 1.6 (1) 5.3 (2) 47
KIC 6629588 1.2 (3) 1.8 (7) 51, 79
KIC 8569819 89.9 (1) 0.588 1.7 1.0 44.6 38
KIC 9851944 74.5 (02) 1.010 (30) 0.432 1.8 (1) 1.8 (07) 2.3 (03) 3.2 (04) 10.7 (1) 10.7 (1) 21
KIC 10619109 1.5 (3) 2.1 (8) 51, 79
KIC 10661783 82.4 (2) 0.091 0.744 2.1 (03) 0.2 2.6 (02) 1.1 (02) 1.4 4.3 (1) 6, 49, 66
KIC 10686876 1.9 (2) 2.4 (8) 51, 79
KIC 11401845 18
KIC 11175495 2.0 (3) 3.1 (5) 51, 79
TYC 7053-566-1 71.13 0.236 (4) 0.337 1.7 (1) 0.4 (03) 2.4 (07) 4.2 (11) 6, 59
USNO-A2.0 1200-03937339 84.6 (2) 0.190 (20) 0.760 1.6 (2) 0.3 (1) 2.2 (04) 1.4 (03) 12.4 (5) 0.7 (1) 1.0 (1) 5.0 (1) 43

1 - Alecian et al. (2005), 2 - Alfonso-Garzón et al. (2014), 3 - Bohm et al. (2008), 4 - Budding & Butland (2011), 5 - Budding et al. (2004), 6 - Casertano et al. (2016), 7 - Chapellier et al. (2004) 8 - Christiansen et al. (2007), 9 - Creevey et al. (2010), 10 - Creevey et al. (2009), 11 - da Silva et al. (2014), 12 - Dal & Sipahi (2013), 13 - Dimitrov, Kraicheva, & Popov (2008), 14 - Dimitrov, Kraicheva, & Popov (2009), 15 - Dimitrov, Kraicheva, & Popov (2009), 16 - Dvorak (2009), 17 - Erdem & Öztürk (2016), 18 - Escolà-Sirisi et al. (2005), 19 - Gaulme & Guzik (2014), 20 - Griffin & Boffin (2003), 21 - Gunsriwiwat & Mkrtichian (2015) 22 - Guo et al. (2016), 23 - Hambálek (2015), 24 - Hambleton et al. (2013), 25 - Hambsch et al. (2010), 26 - Hong et al. (2015), 27 - Hosseinzadeh, Pazhouhesh, & Yakut (2014), 28 - Ibanoǧlu et al. (2008) 29 - Kacar (2012), 30 - Khaliullin & Kozyreva (1989), 31 - Kim et al. (2010), 32 - Kim, Lee, & Lee (2006), 33 - Kim et al. (2004), 34 - Kim et al. (2003), 35 - Kim et al. (2002), 36 - Kundra, Hric, & Gális (2013), 37 - Koo et al. (2016), 38 - Korda, Zasche, & Kučáková (2015), 39 - Kurtz et al. (2015), 40 - Liakos et al. (2008), 41 - Liakos & Niarchos (2012), 42 - Liakos et al. (2012), 43 - Liakos & Niarchos (2013), 44 - Liakos & Cagaš (2014), 45 - Lampens et al. (2004), 46 - Lázaro et al. (2001), 47 - Lázaro et al. (2001), 48 - Lee et al. (2016), 49 - Lee et al. (2016), 50 - Lehmann et al. (2013), 51 - Liakos & Niarchos (2017), 52 - Liakos, Zasche, & Niarchos (2010), 53 - Liu et al. (2012), 54 - Maceroni et al. (2014), 55 - Manimanis, Vamvatira-Nakou, & Niarchos (2009), 56 - Manzoori & Salar (2016), 57 - Mkrtichian & Gamarova (2000), 58 - Moriarty et al. (2013), 59 - Narusawa (2013), 60 - Norton et al. (2016), 61 - Pigulski & Michalska (2007), 62 - Popper (1988), 63 - Rodríguez et al. (2010), 64 - Russo & Milano (1983), 65 - Senyüz & Soydugan (2008), 66 - Shibahashi & Kurtz (2012), 67 - Southworth et al. (2011), 68 - Soydugan et al. (2003), 69 - Soydugan et al. (2006b), 70 - Soydugan & Soydugan (2007), 71 - Soydugan et al. (2011), 72 - Soydugan et al. (2013), 73 - Soydugan & Kaçar (2013), 74 - Soydugan et al. (2016), 75 - Tkachenko, Lehmann, & Mkrtichian (2009), 76 - Tkachenko, Lehmann, & Mkrtichian (2010), 77 - Turcu, Pop, & Moldovan (2008), 78 - Turcu et al. (2011), 79 - Van Eylen, Winn, & Albrecht (2016), 80 - van Leeuwen (2007), 81 - Yang, Wei, & Li (2014), 82 - Zasche (2011), 83 - Zhang (2008), 84 - Zhang, Luo, & Fu (2013), 85 - Zhang, Luo, & Wang (2015), 86 - Zhang et al. (2015), 87 - Zhang et al. (2014), 88 - Zhou (2001), 89 - Zwitter et al. (2003).

Table 1: Continuation.
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