A search for SX Phe stars among Kepler δ Scuti stars

Mon. Not. R. Astron. Soc. 426, 2413 2418 (2012) doi:10.1111/j.1365-2966.2012.21957.x A search for SX Phe stars among Kepler δ Scuti stars L. A. Balona 1 and J. M. Nemec 2 1 South African Astronomical Observatory, PO Box 9, Observatory 7935, Cape Town, South Africa 2 Department of Physics & Astronomy, Camosun College, Victoria, BC V8P 5J2, Canada Accepted 2012 August 19. Received 2012 August 15; in original form 2012 May 29 ABSTRACT The SX Phe stars are Population II pulsating variables lying below the horizontal branch. Their pulsation characteristics resemble those of δ Sct stars. Since old stars in the Kepler field situated in the thick disc or halo are likely to have kinematics different from δ Sct stars, we use proper motions and tangential velocities to search for possible SX Phe variables among 1424 Kepler δ Scuti stars. Tangential velocities derived from distances obtained from the photometric calibration in the Kepler input catalogue appear to be an effective method of separation between thin-disc and thick-disc/halo stellar populations. Using this method, 34 candidate SX Phe stars are identified, eight of which are located more than 0.5 kpc above the galactic plane. We find that the light curves of these stars cannot be distinguished from those of normal δ Scuti stars. It is generally thought that field SX Phe stars have high amplitudes and only one or two frequencies, but such light curves are rare among the candidate SX Phe stars in the Kepler field. We suggest that the relatively high amplitudes, which until now have been a defining characteristic of field SX Phe stars, are merely a selection effect. This supports the recent finding of several low-amplitude multiperiodic SX Phe stars in some globular clusters. Key words: stars: kinematics and dynamics stars: oscillations stars: variables: δ Scuti. 1 INTRODUCTION The SX Phe variables are A F type pulsating stars with frequencies in the range of 5 40 d 1 (Nemec et al. 1995; Jeon et al. 2004). There are 14 SX Phe stars in the general field which have characteristics similar to the high-amplitude δ Scuti stars except that they have high proper motions and low metallicity (Fauvaud et al. 2010). In our Galaxy, low metallicity usually indicates a different population type and hence a different evolutionary state than normal metallicity. In this case metallicity is probably a reasonable classification characteristic. The large numbers of low-metallicity high-amplitude δ Scuti (HADS) stars recently discovered in the Large Magellanic Cloud (Garg et al. 2010), however, are clearly main-sequence dwarfs and giants in the same stage of evolution as normal δ Sct stars and do not qualify as SX Phe variables. Therefore low metallicity, by itself, is not a useful characteristic in defining an SX Phe star. One cannot use a measure of low metallicity typical for our Galaxy to classify an SX Phe star in another stellar system. Most of the SX Phe stars are to be found in globular clusters and in dwarf galaxies of the Local Group. These stars are located in the lower part of the instability strip, mixed with the δ Sct stars. The majority of globular cluster SX Phe variables are blue straggler (BS) stars. These stars are bluer and brighter than the main-sequence E-mail: lab@saao.ac.za turn-off of the cluster (Mateo 1993) and their origin is unclear. The BS stars may arise from internal mixing in the atmosphere of single stars or mergers of two stars via mass transfer or direct collisions (Livio 1993; Stryker 1993). The connection between SX Phe stars and the BS phenomenon has been analysed by several authors (e.g. Eggen & Iben 1989; Nemec & Mateo 1990). All field SX Phe stars and most cluster SX Phe stars are of relatively high amplitude and usually consist of a single frequency, but some are double-mode pulsators with a characteristic period ratio which indicates fundamental and first-overtone radial pulsation (McNamara 1995). The simple frequency spectrum and highamplitude characteristic of SX Phe stars may largely be a selection effect. Because most cluster SX Phe stars are faint (typically m V > 16 mag), only those with the largest amplitudes tend to be detected. However, intensive and accurate surveys in globular clusters have provided observational evidence that low-amplitude multiperiodic modes are also excited in the SX Phe stars (Pych et al. 2001; Mazur, Krzemiński & Thompson 2003; Olech et al. 2005). Even in field SX Phe stars, such as BL Cam, careful observations have disclosed a very rich and dense frequency spectrum (Rodríguez et al. 2007). Space observations of SX Phe stars are likely to reveal that most are multiperiodic. Therefore, the high amplitudes and dominance of only one or two frequencies, while very common, cannot be regarded as a defining characteristic of these stars. In short, it is not possible to distinguish between δ Sct and SX Phe stars by amplitude and number of frequencies or by C 2012 The Authors

2414 L. A. Balona and J. M. Nemec metallicity. The distinction between the two classes of stars lies only in their evolutionary status which is very difficult to determine for field stars. Apart from a detailed analysis of the spectrum which may allow age determination, one has to rely on kinematics. Field stars with high proper motion probably belong to the thick disc or halo and may therefore be considered to be in an advanced stage of evolution. Pulsating stars with high spatial velocities resembling δ Sct variables may therefore be SX Phe stars, even if they do not have high amplitudes and few frequencies. The Kepler mission is designed to detect earth-like planets around solar-type stars by the transit method (Koch et al. 2010). Kepler is continuously monitoring the brightness of over 100 000 stars for at least 3.5 yr in a 105 deg 2 fixed field of view with extremely accurate photometry (at the micromagnitude level). Kepler observations of 374 δ Sct stars have been recently discussed by Uytterhoeven et al. (2011). A much larger sample of 1568 δ Sct stars from Kepler has been discussed by Balona & Dziembowski (2011). The Kepler field is centred at Galactic latitude b = 13. 5 and is directed along the Orion spiral arm (l = 76. 32). With this moderately high latitude, it may be expected that the more distant stars with high proper motions are old and evolved and belong to the Galactic thick disc or halo, while the nearer stars are main sequence and giants belonging to the thin disc. In addition to classical main-sequence δ Scuti stars, the Kepler field may therefore be expected to contain SX Phe stars. The aim of this paper is to attempt an identification of SX Phe stars among the Kepler δ Scuti stars and to determine what proportion of these SX Phe stars have light curves similar to the known field SX Phe variables. One method which can be explored is to exploit the differences in kinematics between stars in the thin Galactic disc and those in the thick disc or halo. For this purpose we make use of proper motion measurements of these stars in the UCAC3 catalogue (Zacharias et al. 2010). This catalogue contains proper motions of 100 766 420 stars covering the entire sky. 2 THE DATA The Kepler data used here were obtained during the 418-d interval JD 2455 4953.54 2455 5371.16 (quarters 0 5) and are publicly available. For most stars observations cover one month of continuous data, though a few stars were observed for the full time span. Most of these observations were obtained in long-cadence (LC) mode with exposure times of 29.4 min. A smaller number of stars were observed in short-cadence (SC) mode with sampling times just under 1 min. The data are available in uncalibrated or calibrated form. The calibrated data suffer from artefacts caused by the processing and are not used here. Details of the technique used to correct these data and how the corrections affect the derived frequencies can be found in Balona (2011). The lowest frequency which can be detected in these data is about 0.1 d 1 (period 10 d), while the highest frequency in LC data is 24 d 1 (period 0.04 d). In SC data the highest frequency is in excess of 700 d 1. These are the Nyquist frequencies corresponding to exposure times of 30 and 1 min, respectively. In some δ Scuti stars, all pulsation frequencies may be in excess of 24 d 1. In LC data, a frequency, ν, in the range of 24 <ν< 48 d 1 will be seen as a peak with frequency ν = 2ν Nyquist ν 48 ν d 1. Frequencies higher than 48 d 1 will, of course, be completely suppressed because the exposure time is longer than the equivalent frequency. Frequencies near 48 d 1 will be reflected as low frequencies in the periodograms of LC data, but will be heavily damped in amplitude since the exposure time covers most of the pulsational cycle. Stars with frequencies in excess of 24 d 1 will be detected as δ Scuti stars even in the LC data. Stars with significant peaks at frequencies higher than about 40 d 1 are uncommon. Nearly all δ Sct stars have frequencies lower than 48 d 1. We can thus be confident that we will not miss many of these stars, even if they are observed only in LC mode. Of course, the frequencies in the LC data may possibly be aliases of the true frequencies and the amplitudes will also be affected. As already mentioned, we classified, by visual inspection, the light curves and periodograms of all SC stars with T eff > 5000 K in the Kepler Input Catalogue (KIC). We also classified all LC stars with T eff > 6500 K and all LC stars brighter than Kp = 12 and with T eff > 5000 K. We feel, therefore, that the sample of stars is reasonably representative of the stars in the δ Sct instability strip. Classification of a star as a δ Scuti was based on the presence of peaks in the periodogram with frequencies in excess of 5 d 1 and confirmed by the location of the star in the Hertzsprung Russell (HR) diagram using the derived effective temperatures and radii in the KIC. Of the stars we classified as δ Sct, 37 do not have effective temperatures and radii in the KIC. 3 AGE DISCRIMINATION OF δ SCT STARS From visual classification of the Kepler light curves, all objects classified as δ Sct stars were extracted (1588 stars). The RA and Dec. of these objects were matched with those in the UCAC3 catalogue (Zacharias et al. 2010), resulting in proper motions for 1424 stars. In some cases duplicate entries had to be resolved by matching magnitudes. The bottom panel of Fig. 1 shows the proper motion in Dec. as a function of the proper motion in RA. The mean proper motions for these 1424 stars are μ α = 1.3 ± 0.2 and μ δ = 2.5 ± 0.3 mas yr 1. The standard deviations are σ α = 6.5 and σ δ = 10.1 mas yr 1.Most of the stars are grouped around the mean, but there are outliers which have different kinematics and may belong to the thick disc or halo. One could draw a box around the main distribution to segregate the two populations. Selecting a radius of 30 mas yr 1, which is approximately three standard deviations, gives 34 outliers which are listed in Table 1. The value of log L/L in this table is derived from the log T eff and radii given in the KIC. There are clearly substantial errors in these values. According to Brown et al. (2011), the KIC error in log T eff is about 200 K and in radius about 50 per cent, giving an error of about 0.43 in log L. In the bottom panel of Fig. 1 we also show, for comparison, the proper motions of several Kepler-field RR Lyr stars and all SX Phe stars in the general field. Although there are some outliers in both cases, a significant number of RR Lyr and field SX Phe stars have normal proper motions, so discrimination by proper motion alone is not very efficient. A star may have a large proper motion because it is truly moving at high speed relative to the Sun. On the other hand, it may have a speed similar to stars in the local neighbourhood, but have a large proper motion because it is close to the Sun. Better discrimination between different population groups might be achieved by using the tangential velocity, v T, but this requires the distance. The distance is not tabulated in the KIC, but it can be obtained from the listed visual extinction, A V, and the Galactic latitude, b,using d = h ( ) sin b ln sin b 1 A V k V h

SX Phe stars among Kepler δ Scuti stars 2415 Figure 1. Bottom panel: the proper motions in RA and Dec. (mas yr 1 )for Kepler δ Sct stars (small red filled circles). Larger open (blue) circles are Kepler RR Lyr stars. Plus signs are previously known field SX Phe stars. The dashed circle has a radius of 30 mas yr 1. Top panel: the tangential velocities in RA and Dec. (km s 1 obtained from the proper motions using distances derived from the KIC. The dashed circle has a radius of 60 km s 1.Open circles are RR Lyraes with distances calculated on the basis of log L/L = 1.7 for all stars. (Brown et al. 2011), where h is the dust scale height (assumed to be 150 pc), b is the galactic latitude and k V is the dust opacity in the galactic plane (assumed to be 1 mag kpc 1 ). Multiplying the distance by the proper motion gives the tangential velocity, v T. Since 1 mas yr 1 = 1.536 314 66 10 16 radians s 1 and 1 pc = 3.085 680 25 10 13 km, we have v t = 0.00474 μd km s 1 if the proper motion, μ, is measured in mas yr 1. The top panel of Fig. 1 shows the tangential velocity in Dec. as a function of the tangential velocity in RA. The mean tangential velocities are v Tα = 7.0 ± 1.0 andv Tδ = 11.6 ± 1.4kms 1. The standard deviations are σ α = 36.4 and σ δ = 53.6 km s 1. Selecting a radius of 120 km s 1 gives 51 outliers. We may sharpen the discrimination further by selecting only stars of high proper motion among these 51 stars. If we select those stars with proper motions in excess of 30 mas yr 1, we obtain the 34 stars listed in Table 1. Since we know that RR Lyr stars belong to the halo and old disc population, they should have large proper motions for their distance. In fact, there is very little discrimination between Kepler δ Sct and RR Lyr stars from the proper motions alone, as can be seen from the bottom panel of Fig. 1. This is due to the fact that the stars are generally faint and distant, so that even a large relative velocity translates into a small proper motion. In Table 2 we list data for Kepler RR Lyr stars with known proper motions. The KIC luminosities are not very reliable for RR Lyraes and it is probably prudent to use a typical luminosity log L/L = 1.7 for all these stars. This luminosity is reasonable for all but the most metal-rich RR Lyrae stars and for the evolved metal-poor stars. The tangential velocities thus obtained are listed in Table 2. The tangential velocities are also shown in the top panel of Fig. 1. There is a marked improvement in discrimination between δ Sct stars and the more evolved RR Lyrae stars which clearly have different kinematics. This exercise lends confidence to our assumption that pulsating stars in the halo and the old disc (i.e. SX Phe stars) can be separated from young main-sequence δ Sct stars. Proper motion combined with distance can be an indicator of population type, as described above. We may also consider the distance above the Galactic plane, z, as another indicator of population. Table 1. List of 34 candidate SX Phe stars in the Kepler field. These are δ Sct stars with proper motions differing from the mean by over 30 mas yr 1 and with tangential velocities in excess of 120 km s 1. Stars marked with an asterisk are at more than 0.5 kpc above the galactic plane.the columns show the KIC number,the Kepler magnitude, the effective temperature, luminosity, surface gravity and metallicity (all from the KIC), the proper motion in RA and Dec., the tangential velocity in RA and Dec. and the distance in parsecs. KIC Kp log (T eff ) log(l/l ) log (g) [Fe/H] μ α μ δ v Tα v Tδ d (mag) (K) (dex) (mas yr 1 ) (mas yr 1 ) (kms 1 ) (kms 1 ) (kpc) 1162150 11.240 3.837 1.46 3.46 0.01 33.1 37.6 90 128 0.7 3456605 13.108 3.852 0.98 3.94 0.18 1.3 48.4 4 214 0.9 4168579 13.612 3.877 1.28 3.79 0.09 36.0 39.2 208 292 1.6 4243461 13.786 3.840 0.69 4.15 0.24 74.4 21.4 260 96 0.9 4662336 13.105 3.858 1.07 3.89 0.13 0.0 62.1 0 303 1.0 4756040 13.315 3.881 0.96 4.09 0.01 28.5 31.6 106 153 1.0 5036493 12.553 3.901 1.22 3.95 0.00 1.1 45.1 3 209 1.0 5390069 15.110 3.828 0.09 4.83 0.26 11.9 47.6 29 155 0.7 5705575 13.692 3.879 1.07 3.99 0.16 92.4 78.5 448 504 1.3 6130500 13.869 3.879 0.90 4.14 0.01 59.9 11.0 256 62 1.2 6227118 12.932 3.858 4.01 1.03 0.15 21.8 28.4 322 561 4.2 6445601 13.595 3.856 0.83 4.09 0.17 55.6 18.7 197 89 1.0 6520969 13.422 3.921 1.33 3.96 0.13 42.5 21.0 242 160 1.6 6780873 13.746 3.837 0.46 4.35 1.09 24.5 56.7 61 193 0.7

2416 L. A. Balona and J. M. Nemec Table 1 continued KIC Kp log (T eff ) log(l/l ) log (g) [Fe/H] μ α μ δ v Tα v Tδ d (mag) (K) (dex) (mas yr 1 ) (mas yr 1 ) (kms 1 ) (kms 1 ) (kpc) 7020707 13.433 3.872 1.01 4.00 0.21 32.6 22.6 135 127 1.2 7174372 13.621 3.859 0.84 4.10 0.30 35.7 76.7 133 390 1.1 7300184 15.430 3.813 0.03 4.72 0.08 45.7 46.5 131 182 0.8 7301640 13.862 3.846 0.81 4.07 0.01 44.2 11.2 161 56 1.0 7621759 13.912 3.843 0.82 4.05 0.26 8.9 48.1 33 251 1.1 7765585 13.980 3.827 0.06 4.80 0.15 27.7 81.2 43 173 0.4 7819024 13.799 3.877 0.93 4.10 0.27 11.6 41.1 50 246 1.3 8004558 13.350 3.885 1.19 3.90 0.45 11.1 38.4 53 256 1.4 8110941 13.749 3.835 0.69 4.13 0.09 46.8 17.5 143 74 0.9 8196006 13.810 3.846 0.61 4.25 0.44 24.4 31.2 69 124 0.8 8330910 13.457 3.868 0.93 4.06 0.20 39.0 59.2 135 286 1.0 9244992 13.998 3.819 1.32 3.51 0.14 40.2 28.2 240 240 1.8 9267042 13.424 3.910 1.44 3.80 0.11 79.0 96.5 480 840 1.8 9535881 13.402 3.855 0.74 4.18 0.22 6.9 28.2 19 113 0.8 9966976 13.491 3.883 1.15 3.93 0.05 19.1 53.8 84 346 1.4 10989032 13.866 3.935 1.28 4.07 0.01 68.0 52.8 393 460 1.8 11649497 13.432 3.884 1.05 4.02 0.10 21.4 33.6 85 206 1.3 11754974 12.678 53.2 57.7 172 291 1.1 12643589 13.754 3.813 0.25 4.44 0.26 98.6 72.4 170 201 0.6 12688835 13.801 3.931 1.49 3.86 0.28 9.5 35.2 60 364 2.2 Table 2. Kepler RR Lyr stars. The effective temperature, luminosity and surface gravity are from the KIC. The [Fe/H] values are spectroscopic measurements from Nemec et al. (in preparation). The tangential velocities and distances were calculated using a fixed luminosity log L/L = 1.7 for all stars. KIC Name Kp log (T eff ) log (L/L ) log(g) [Fe/H] μ α μ δ v Tα v Tδ d (mag) (K) (dex) (mas yr 1 ) (mas yr 1 ) (kms 1 ) (kms 1 ) (kpc) 3733346 NR Lyr 12.684 3.807 0.82 3.90 2.54 17.1 3.5 221 45 2.7 3864443 V2178 Cyg 15.593 3.812 1.02 3.74 1.65 13.3 9.8 658 484 10.4 4484128 V808 Cyg 15.363 3.825 1.17 3.67 1.19 22.5 27.9 1000 1241 9.4 5299596 V782 Cyg 15.392 3.734 0.80 3.64 0.42 7.1 9.1 322 410 9.5 5559631 V783 Cyg 14.643 3.769 0.55 3.99 1.2 5.9 10.6 187 338 6.7 6070714 V784 Cyg 15.370 3.800 0.41 4.24 0.05 7.8 1.0 346 44 9.4 6100702 13.458 3.825 0.71 4.07 0.19 3.9 10.3 73 190 3.9 6183128 V354 Lyr 16.260 3.800 0.41 4.24 1.44 14.3 18.6 959 1251 14.2 6763132 NQ Lyr 13.075 3.891 1.38 3.77 1.90 0.9 1.9 14 29 3.3 6936115 FN Lyr 12.876 3.810 0.59 4.11 1.98 3.4 10.2 48 144 3.0 7198959 RR Lyr 7.862 3.797 0.36 4.27 1.19 79.9 7.0 112 9.3 7505345 V355 Lyr 14.080 3.890 1.38 3.76 1.15 4.4 1.1 109 27 5.2 7742534 V368 Lyr 16.002 3.928 1.44 3.89 1.29 6.4 6.1 380 364 12.6 7988343 V1510 Cyg 14.494 3.784 0.63 3.97 2.0 9.6 6.2 287 184 6.3 8344381 V346 Lyr 16.421 3.901 1.09 4.07 1.8 2.3 2.2 170 159 15.3 9578833 V366 Lyr 16.537 3.841 0.76 4.09 1.15 0.3 16.5 21 1261 16.1 9591503 V894 Cyg 13.293 3.789 0.75 3.89 1.66 3.6 9.0 62 154 3.6 9697825 V360 Lyr 16.265 3.824 0.62 4.15 1.50 3.9 10.1 261 681 14.2 9947026 V2470 Cyg 13.300 3.870 1.15 3.88 0.53 1.4 8.0 23 137 3.6 10136240 V1107 Cyg 15.648 3.789 0.75 3.89 1.40 6.3 19.3 317 979 10.7 10789273 V838 Cyg 13.770 3.921 1.45 3.85 1.01 5.5 1.1 117 23 4.5 11125706 11.367 3.789 0.75 3.89 1.05 6.0 12.8 42 90 1.5 11802860 AW Dra 13.053 3.793 0.62 4.03 1.33 7.9 3.9 120 59 3.2 12155928 V1104 Cyg 15.033 3.830 0.71 4.09 1.20 12.9 14.1 492 539 8.1 We expect the young classical δ Sct stars, which belong to the thindisc population, to be close to the Galactic plane, whereas Population II and halo objects are expected to be further above the plane. Once again, the main source of error in determining this distance is the stellar luminosity. Stars with z > 0.5 kpc are marked by an asterisk in Table 1. One could attempt further discrimination of δ Sct stars using a metallicity index such as [Fe/H]. Unfortunately, the [Fe/H] values from the KIC cannot be trusted (Brown et al. 2011), though we note that nearly all the stars in Table 1 do, in fact, have negative [Fe/H] values, suggesting that they are metal poor. These are the stars which we presume are most similar to the SX Phe stars. The location of these stars in the HR diagram is compared with other δ Sct stars in Fig. 2. It is clear that stars with different kinematics cannot be distinguished in this diagram.

SX Phe stars among Kepler δ Scuti stars 2417 Figure 2. The theoretical HR diagram for Kepler δ Sct stars (small filled circles). The large filled circles are δ Sct stars in Table 1 which have large proper motions and large tangential velocities (i.e. SX Phe candidates). Evolutionary tracks from Bertelli et al. (2008) are shown and labelled with the solar mass. 4 SX PHE STARS IN THE Kepler FIELD Kepler δ Scuti stars with large proper motions and large tangential velocities are shown in Table 1. Those stars which, in addition, are far above the Galactic plane are marked with an asterisk in the table. The stars in this table, and especially those marked with an asterisk, are most likely Population II stars and therefore may be classified as SX Phe variables. Fig. 3 shows the periodograms of these stars. All of them except for KIC 9267042 were observed in LC mode and we need to bear in mind that frequencies higher than 24 d 1 will reflect back into the 0 24 d 1 range with diminished amplitude. It is possible that some of the stars may, in fact, be pulsating with higher frequencies. None of the stars has a particularly high amplitude which is so characteristic of field SX Phe stars. Indeed, except for KIC 7174372, 8004558 and 9267042, their amplitudes are too small to be observed from the ground. KIC 11649497 has low-amplitude eclipses, while KIC 12688835 may also be a binary. In short, the light curves of these stars are typical of normal δ Sct stars. The only star whose amplitude is in the range of the field SX Phe stars is KIC 8004558 which has a single dominant mode and also a mode of much smaller amplitude and slightly lower frequency. Since field SX Phe stars all have high amplitudes, it is interesting to determine the proportion of high-amplitude stars among SX Phe stars in the Kepler field. Examination of the 34 stars in Table 1 shows that only four stars have high amplitudes and one or two dominant modes. Table 3 lists light-curve parameters for these stars. KIC 11754974 has by far the largest amplitude. Harmonics up to 6f 1 (f 1 being the dominant frequency) are clearly visible in the periodogram. Moreover, the frequency ratio f 1 /f 2 = 0.764 of the two independent frequencies of largest amplitude is compatible with fundamental and first-overtone radial modes. For KIC 9267042 SC data are also available and harmonics up to 3f 1 can be seen, but the frequency ratio of f 2 /f 1 = 0.91 suggests that at least one mode is non-radial. For the two stars with SC data and for which no ambiguity exists in the frequencies, the frequencies are in the range of 16 24 d 1. We conclude that only about 12 per cent of Kepler SX Phe stars have the high amplitude characteristics of known field SX Phe stars. This conclusion is consistent with recent observations of SX Phe stars which suggest that multiperiodicity is Figure 3. Periodograms of Kepler δ Scuti stars, which are far above the plane of the Galaxy, have large proper motions and transverse velocities (i.e. probable SX Phe stars). more common than generally supposed (Pych et al. 2001; Mazur et al. 2003; Olech et al. 2005). We suspect, therefore, that the characteristic light curves of field SX Phe and globular cluster stars are mostly a selection effect and that the pulsation

2418 L. A. Balona and J. M. Nemec Table 3. The candidate Kepler-field SX Phe variables (high proper motions and high tangential velocities) that most closely resemble large-amplitude field SX Phe stars. The frequencies of the two independent modes of largest amplitude are shown. KIC f (d 1 ) A (mmag) Notes 7300184 11.657 30.5 2f 1 visible. 20.764 5.3 8004558 23.413 13.9 22.605 4.2 9267042 24.664 9.9 SC; 2f 1,3f 1 visible. 22.449 3.9 11754974 16.344 56.3 SC; 2f 1 6f 1 visible. 21.399 15.5 ASAS 143 characteristics of SX Phe stars are no different from those of normal δ Sct stars. 5 CONCLUSIONS Since the Kepler field of view includes a large number of pulsating stars at fairly high Galactic latitude, it would not be surprising if many of these stars are Population II stars in the post-giant stage of evolution. These are therefore SX Phe variables and not δ Sct stars. Since the large majority of SX Phe stars have characteristic light curves with only one or two dominant frequencies and high amplitude, one might expect that Population II pulsating stars in the Kepler field would also show predominantly high amplitudes. We have attempted to identify Population II stars in the thick disc or halo by means of their high proper motions and tangential velocities. Of the 1424 δ Sct stars in our sample, 34 stars have high proper motions and tangential velocities (Table 1). These 34 stars are likely to be Population II SX Phe stars. Of these SX Phe stars, only four stars with high proper motion have reasonably high amplitudes (Table 3). Therefore, we conclude that only about 12 per cent of field SX Phe stars have high amplitudes. In the Kepler field there is only one δ Sct star out of more than 1600 with a peak-to-peak amplitude in excess of 0.3 mag (which is usually taken as the lower amplitude limit for HADS stars). It is therefore not surprising that none of the 34 high proper motion stars has amplitudes similar to those in SX Phe or HADS stars. We suspect that the large number of SX Phe stars with high amplitudes is a selection effect. We find that it is impossible to distinguish between δ Sct and SX Phe stars on the basis of the light curve alone. It seems that there is no difference in the pulsational characteristics of the two classes of stars. If this is the case, then careful observations of high proper motion field stars within the instability strip should reveal some of them to be low-amplitude multiperiodic SX Phe stars similar to the δ Sct stars. ACKNOWLEDGMENTS This paper is based on data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. The authors wish to thank the Kepler team for their generosity in allowing the data to be released and for their outstanding efforts which have made these results possible. LAB wishes to thank the National Research Foundation and the South African Astronomical Observatory for financial support. Some/all of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-hst data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. This research has made use of the SIMBAD data base, operated at CDS, Strasbourg, France. REFERENCES Balona L. A., 2011, MNRAS, 415, 1691 Balona L. A., Dziembowski W. A., 2011, MNRAS, 417, 591 Bertelli G., Girardi L., Marigo P., Nasi E., 2008, A&A, 484, 815 Brown T. M., Latham D. W., Everett M. E., Esquerdo G. A., 2011, AJ, 142, 112 Eggen O. J., Iben I., Jr, 1989, AJ, 97, 431 Fauvaud S. et al., 2010, A&A, 515, A39 Garg A. et al., 2010, AJ, 140, 328 Jeon Y.-B., Lee M. G., Kim S.-L., Lee H., 2004, AJ, 128, 287 Koch D. G. et al., 2010, ApJ, 713, L79 Livio M., 1993, in Saffer R. A., ed., ASP Conf. Ser. Vol. 53, Blue Stragglers. Astron. Soc. Pac., San Francisco, p. 3 McNamara D. H., 1995, AJ, 109, 1751 Mateo M., 1993, in R. A., ed., ASP Conf. Ser. Vol. 53, Blue Stragglers, Saffer. Astron. Soc. Pac., San Francisco, p. 74 Mazur B., Krzemiński W., Thompson I. B., 2003, MNRAS, 340, 1205 Nemec J., Mateo M., 1990, in Cacciari C., Clementini G., eds, ASP Conf. Ser. Vol. 11, Confrontation Between Stellar Pulsation and Evolution. Astron. Soc. Pac., San Francisco, p. 64 84 Nemec J. M., Mateo M., Burke M., Olszewski E. W., 1995, AJ, 110, 1186 Olech A., Dziembowski W. A., Pamyatnykh A. A., Kaluzny J., Pych W., Schwarzenberg-Czerny A., Thompson I. B., 2005, MNRAS, 363, 40 Pych W., Kaluzny J., Krzeminski W., Schwarzenberg-Czerny A., Thompson I. B., 2001, A&A, 367, 148 Rodríguez E. et al., 2007, A&A, 471, 255 Stryker L. L., 1993, PASP, 105, 1081 Uytterhoeven K. et al., 2011, A&A, 534, A125 Zacharias N. et al., 2010, AJ, 139, 2184 This paper has been typeset from a TEX/LATEX file prepared by the author.