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40Peremennye Zvezdy (Variable ¡Stars) 38, No. 1, 2018 Received 15 January; accepted 12 April.
A Study of Double-Mode Variables
A. V. Khruslov
Sternberg Astronomical Institute, Moscow State University, Universitetskij pr. 13, Moscow 119992, Russia; [email protected]
Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya str. 48, Moscow 119017, Russia
I present a detection of 44 new double-mode variable stars, of which 25 variables are highamplitude S Scuti stars, HADS(B) type, and 19 stars are RR Lyrae variables, RR(B) type. For two of the HADS(B) stars, their detection was the variability discovery. We analyzed all observations available for these stars in the Catalina Surveys and SuperWASP online public archives using the period-search software developed by Dr. V.P. Goranskij for Windows environment. In two cases, we also used data of the ASAS-SN archive. According to these data, one star, GSC 02900-00317, is possibly pulsating in the first- and second-overtone modes; the other stars are pulsating in the fundamental and first-overtone modes.
1 Introduction
I studied 44 double-mode variable stars using the available photometric archive data: the Catalina Sky Surveys1 (CSS, Drake et al. 2009) and the Wide Angle Search for Planets2 (1SWASP, Butters et al. 2010). Additionally, in two cases, I used data of the All-Sky Automated Survey for Supernovae3 and its catalog of new variables4 (ASAS-SN, Shappe et al. 2014, Kochanek et al. 2017).
The SuperWASP observations are available as FITS tables, which were converted into ASCII tables using the OMC2ASCII5 program as described by Sokolovsky (2007).
I performed my search for candidate double-mode stars using the Catalina surveys periodic variable star catalog (Drake et al. 2014) and the Catalina surveys southern periodic variable star catalog (Drake et al. 2017). I studied the variables designated as HADS and RRC type stars in these lists and made a sample of stars with the phased light curve showing a somewhat enhanced scattering. For double-mode candidates, I analyzed all the observations using Deeming's method (Deeming 1975) implemented in the WinEfk code6 written by V.P. Goranskij. Besides, I confirmed variability of one previously suspected star and detected its double periodicity: RR_13 was suspected as an RR Lyrae star by Ivezic et al. (2000) on the base of its colors and variability properties. In addition, I discovered variability of two stars using the 1SWASP data and APASS catalog7.
1 http://nunuku.caltech.edu/cgi-bin/getcssconedb_release_img.cgi
2 http://wasp.cerit-sc.cz/form
3 https://asas-sn.osu.edu
4 https://asas-sn.osu.edu/variables
5 http://scan.sai.msu.ru/swasp_converter/
6 http://www.vgoranskij.net/software/
7 http://www.aavso.org/download-apass-data
In five cases (DS_07, DS_16, DS_18 and RR_08, RR_15), the periods presented in the Catalina surveys periodic variable star catalog were found to be wrong.
Most of the double-mode variables we studied experience radial pulsations in the firstovertone and fundamental modes. One star is possibly pulsating in the first- and second-overtone modes. For two HADS stars, I detected possible additional non-radial pulsations.
In this paper, the following designation are used for the variables: for the stars in the HADS(B) section, DS_01 ... DS_24 (see Tables 1-3); for the stars in the RR(B) section, RR_01 ... RR_19 (see Tables 5-7); one star, GSC 02693-00926, is called by its catalog name.
For RR(B) stars, this paper is a continuation of our publication series (Khruslov 2014a, 2015ab). For HADS(B) stars, this paper supplements our previously published articles (Khruslov 2009, 2011, 2014b, 2015c).
The light curves, finding charts, and data (from CSS, SSS, MLS, 1SWASP, ASAS-SN surveys) are available online in the html version of this paper as a zip-archive. The light curves are given in the format displayed in Fig. 1. Top panels present data folded with the fundamental-mode and first overtone periods (in the case of GSC 02693-00926, the first and second overtone periods). Bottom panels show the same curves after prewhitening the other oscillation (if fx + f0, fx — f0 and other interaction frequencies or non-radial frequencies were excluded, it is also noted). These light curves are given for all data series. Along with the light curves, we present power spectra of the double-mode variables, for the raw data and after subtraction of the dominant mode (fundamental or first-overtone oscillations). The structure of the power spectra shows that the secondary periods are real.
The radial pulsation modes were identified by the period ratio (Pshort/Plong). The typical period ratio of pulsations in the fundamental and first-overtone modes (F/1O) is Px/P0 = 0.74 for RR(B) stars and P1/P0 = 0.75 — 0.78 for HADS(B) stars. The typical period ratio of pulsations in the first- and second-overtone modes (1O/2O) is P2/P1 = 0.80.
The stars were identified in the USN0-B1.0 (Monet et al. 2003) and GSC (Morrison et al. 2001) catalogs. The tabulated coordinates of the variables were drawn from either the GSC2.3 (Lasker et al. 2008) or 2MASS (Skrutskie et al. 2006) catalogs. In the case of RR_19, the coordinates are from the UCAC4 catalog (Zacharias et al. 2012).
2 New HADS(B) stars, F/1O
I detected 24 HADS(B) stars pulsating in the fundamental and first-overtone modes. Their magnitudes are between 12m7 and 17^7 in the CV system. The highest peak-to-peak amplitude of light variations is 0m99 (DS_17). The fundamental-mode periods are between 0d074 and 0d 138.
Information on these stars is presented in Tables 1-3. The light curves and power spectra for one of the stars (DS_04) are displayed in Fig. 1. Table 1 contains equatorial coordinates (J2000); magnitudes at maximum and minimum in the Catalina surveys photometric system; star numbers from the USN0-B1.0 or GSC catalogs; information on the source of data used in this study (c: CSS; m: MLS; s: SSS, w: 1SWASP, a: ASAS-SN). For magnitudes at maximum and minimum in the 1SWASP system, see Comments to Table 1.
In most cases, I derived light elements from Catalina surveys data. 1SWASP data were helpful for improving the light elements and detecting additional oscillations. An example
of 1SWASP light curves is displayed in Fig. 2 (DS_11).
Table 2 presents light elements of fundamental and first-overtone oscillations: the fundamental period P0, the first-overtone period P1, the fundamental and first-overtone mode epochs of maxima, the period ratio P1/P0. Additional information on some of the stars can be found in Comments to Table 2.
Table 2a contains periods of the interaction frequencies f1 + f0 (P1+0), f1 — f0 (P1-0), ¡1 + 2f0 (P1+20), 2f1 — f0 (P21-0), 2f0 — f1 (P20-1), 2f1 + f0 (P21+0), f1 + 3f0 (P1+30).
Table 3 presents semi-amplitudes of the oscillations, separately for Catalina surveys and 1SWASP data: semi-amplitudes of the fundamental mode (A0) and first-overtone (A1) oscillations, and of their interaction frequencies.
Figure 1.
The light curves and power spectra of DS_04 (USNO-B1.0 1217-0037791) from CSS data.
GSC 06042-01379 - 1SWASP J093025.53-215631.6
mag
126
127
128
12.3
130
131
132
13.3
134
135
136
A mag
-0.4
-0.3
-02
-01 00 01 02 0.3 04 0.5
HJD(max) = 2454245 3590 + 0 0958519 xE
HJD(max) = 2454245.3690 + 0.0742366 xE
ISWASPdata 1SWASP data
(ÎSWMSP data) -ff - ft + f0)--- (2f0- f,) (1SWASP data) - f0- ft+ f0) -... - (2f0- f,) IMMMjjiiiMiiirt
1.5
Phase
Figure 2.
The light curves of DS_11 (GSC 06042-01379) from 1SWASP data.
For DS_02, DS_03, DS_11 and DS_14, we improved the light elements and detected additional interaction frequencies using 1SWASP data. The variability discovery of DS_06 used data from the 1SWASP survey and APASS catalog. In this case, only 1SWASP data are available.
Table 1. HADS(B) stars: positions, magnitudes, and identifications
No. Coordinates (J2000) CV mag Name Data
1 02h11 m45!13 +37°10' 38'! 3 15m 81 - 16m 38 USN0-B1.0 1271-0037436 c
2 02 24 38.93 +26 21 01.6 13.36 - 13.83 GSC 01774-01236 cw
3 02 37 22.96 +38 28 47.2 14.40 - 14.98 GSC 02832-01221 cw
4 02 55 39.90 +31 45 18.7 16.20 - 16.78 USN0-B1.0 1217-0037791 c
5 03 44 52.19 +17 16 34.6 15.27 - 15.76 USN0-B1.0 1072-0051636 c
6 04 28 53.38 +43 15 10.9 (see Comments) USN0-B1.0 1332-0126848 wa
7 05 13 46.48 +06 59 24.2 16.09 - 16.66 USN0-B1.0 0969-0055157 c
8 07 26 43.58 +41 35 23.1 16.71 - 17.41 USN0-B1.0 1315-0187511 c
9 08 22 37.42 +03 04 41.8 13.31 - 13.83 GSC 00201-01923 c
10 08 56 36.42 -02 25 35.2 14.32 - 14.85 GSC 04869-01051 c
11 09 30 25.52 -21 56 31.6 12.67 - 13.21 GSC 06042-01379 csw
12 11 49 44.16 +18 51 28.1 16.89 - 17.60 USN0-B1.0 1088-0197927 c
13 12 00 37.39 +12 28 05.3 16.76 - 17.66 USN0-B1.0 1024-0244792 c
14 13 06 36.82 -35 46 23.0 13.99 - 14.74 GSC 07262-00111 sw
15 15 45 18.61 +16 40 51.6 15.98 - 16.42 USN0-B1.0 1066-0249103 c
16 16 22 43.63 +00 05 03.1 14.73 - 15.31 GSC 00369-01308 c
17 16 28 18.88 +03 26 51.1 16.52 - 17.51 USN0-B1.0 0934-0280421 c
18 17 46 43.81 +28 55 33.3 14.60 - 15.17 GSC 02089-01468 c
19 18 44 25.40 -56 36 46.2 13.58 - 13.99 GSC 08766-01800 s
20 19 41 49.54 -53 32 46.6 15.70 - 16.14 USN0-B1.0 0364-0811436 s
21 20 55 40.03 -02 03 21.2 15.67 - 16.40 USN0-B1.0 0879-0781144 c
22 20 59 10.15 -03 28 20.7 14.45 - 15.11 GSC 05183-01938 c
23 21 26 09.20 +14 53 18.7 13.99 - 14.74 USN0-B1.0 1048-0604416 c
24 23 56 59.35 +06 31 32.5 14.91 - 15.39 GSC 00593-01336 c
Comments to Table 1:
DS_02. From 1SWASP data, 13m27 - 13m74. DS_03. From 1SWASP data, 14m2 - 14m9. DS_06. From 1SWASP data, 14m4 - 15m0;
from ASAS-SN data, 14m23 - 15m08 (V). DS_11. From 1SWASP data, 12m80 - 13m41. DS_14. From 1SWASP data, 14m 1 - 15m 1.
Table 2. HADS(B) stars: light elements
No. Po,d Pi, d Epoch0, HJD Epoch1, HJD Pi/Po
1 0.1052902 0.0815073 2455500.0183 2455500.0520 0.7741
2 0.1015792 0.0801161 2455500.0440 2455500.0700 0.7887
3 0.11067530 0.08543985 2455500.0669 2455500.0217 0.7720
4 0.1289001 0.0995168 2455500.1110 2455500.0123 0.7720
5 0.0748235 0.0578434 2455500.0555 2455500.0587 0.7731
6 0.1371462 0.1055856 2454100.2017 2454100.2135 0.7699
7 0.1029720 0.0797190 2455500.0610 2455500.0130 0.7742
8 0.0903166 0.0702281 2455500.0515 2455500.0260 0.7776
9 0.0905480 0.0702981 2455500.0380 2455500.0110 0.7764
10 0.0882723 0.0683850 2455500.0686 2455500.0572 0.7747
11 0.0958519 0.0742366 2454245.3590 2454245.3690 0.7745
12 0.0896816 0.0702105 2455500.0300 2455500.0083 0.7829
13 0.0903184 0.0708550 2455500.0350 2455500.0432 0.7845
14 0.1379871 0.1063876 2455500.1150 2455500.0450 0.7710
15 0.0865396 0.0686981 2455500.0204 2455500.0017 0.7938
16 0.1051553 0.0812981 2455500.0995 2455500.0785 0.7731
17 0.1253521 0.0985880 2455500.1155 2455500.0320 0.7865
18 0.0815316 0.0634601 2455500.0548 2455500.0150 0.7780
19 0.0943743 0.0728273 2455500.0950 2455500.0585 0.7717
20 0.1110649 0.0857819 2455500.0980 2455500.0063 0.7724
21 0.0839438 0.0655573 2455500.0654 2455500.0550 0.7810
22 0.0762165 0.0590200 2455500.0193 2455500.0090 0.7744
23 0.0904151 0.0705390 2455500.0123 2455500.0060 0.7802
24 0.0946992 0.0732698 2455500.0363 2455500.0190 0.7737
Comments to Table 2:
DS_05. Double periodicity is confirmed in MLS data.
DS_07. Strong scattering of the phased light curve towards brighter magnitudes.
DS_15. The variability was discovered by Palaversa et al. (2013), LINEAR 15289666. The variable was classified as a 8 Sct or SX Phe star with the period 0"?086539. Drake et al. (2014) independently detected the star's variability and gave the type HADS with the period 0?0865394. The variable is actually a HADS(B) star. It is difficult to determine the correct periods because the frequencies are close to the relation fi & f0 + 3. The ratio of the detected most probable periods (Pi/P0 = 0.7938) is typical not of the p and P0 periods but of the P2 and Pi periods. The one-day alias periods P0 = 0?0947630 and Pi = 0?0737655 are not excluded; their period ratio, Pi/P0 = 0.7784, is more typical.
DS_21. An additional non-radial pulsation, fN (PN = 0? 126514, AN = 0.033), is possible.
DS_22. Two additional non-radial pulsations (quasi-equidistant triplet) are possible: fo-m (Po-m = 0d0762248, Ao_m = 0.022) and fo+m (Po+m = 0d0762082, Ao+m = 0.019); m = 0.001429; beat period n = 700d; interaction frequency 2f0 -m (P20-m = 0d03811026, A20-m = 0.016). This result needs an independent verification.
A.V. Khruslov: A Study of Double-Mode Variables Table 2a. HADS(B) stars: periods of interaction frequencies
No. Pi+o, d Pi-o, d P1+20 j d P21-0, d P20-1, d P21+0j d P1+30j d
1 0.04594235 0.360844 - - - - -
2 0.0447901 0.379181 0.0310840 - - - -
3 0.0482170 0.374715 - 0.0695756 - - -
4 0.0561592 0.436562 - - - - -
5 0.0326234 0.254889 - - - - -
6 0.0596571 0.458810 - - - - -
7 0.0449329 0.353021 - - - - -
8 0.0395077 0.315741 - - - - -
9 0.0395742 0.314342 0.02753848 - 0.127185 - -
10 0.0385332 - - - - - -
11 0.0418354 0.329194 0.0291237 - 0.135225 0.0267566 -
12 0.03938024 0.323378 - - - - -
13 0.0397057 0.328798 0.0275807 - - - -
14 0.0600722 0.464556 0.0418521 - - - 0.0321122
15 0.03829673 0.333222 - - - - -
16 0.0458502 0.358335 - - - - -
17 0.0551854 0.461743 0.0383168 - - - -
18 0.03568483 0.286310 0.02482110 - - - -
19 0.04110613 - - - - - -
20 0.0483999 - - - - - -
21 0.0368099 0.299299 - - - - -
22 0.03326248 0.261581 - - - - -
23 0.0396249 0.320878 0.0275507 - - - -
24 0.04130874 0.323789 - - - - -
Table 3. HADS(B) stars: semi-amplitudes
No. Ac Ai CSS Al+c Ai_o A1+20 Ac Ai WASP A1+0 Ai_c Ai+2c
1 0.067 0.103 0.027 0.013 - - - - - -
2 0.111 0.040 0.023 0.023 0.011 0.104 0.046 0.023 0.018 0.009
3 0.053 0.129 0.026 0.022 - 0.056 0.130 0.027 0.031 -
4 0.086 0.113 0.031 0.040 - - - - - -
5 0.111 0.053 0.016 0.019 - - - - - -
6 - - - - - 0.097 0.091 0.040 - -
7 0.083 0.100 0.033 0.044 - - - - - -
8 0.142 0.063 0.036 0.035 - - - - - -
9 0.123 0.069 0.032 0.038 0.012 - - - - -
10 0.137 0.049 0.020 - - - - - - -
11 0.128 0.068 0.029 0.036 - 0.146 0.080 0.033 0.037 0.012
12 0.132 0.067 0.041 0.043 - - - - - -
13 0.127 0.107 0.046 0.045 0.021 - - - - -
14 0.247 0.038 0.034 - 0.015 0.295 0.054 0.038 0.024 0.025
15 0.107 0.041 0.022 0.023 - - - - - -
16 0.134 0.067 0.031 0.023 - - - - - -
17 0.203 0.108 0.051 0.056 0.031 - - - - -
18 0.165 0.054 0.032 0.034 0.016 - - - - -
19 0.139 0.030 0.017 - - - - - - -
20 0.089 0.050 0.021 - - - - - - -
21 0.126 0.073 0.033 0.046 - - - - - -
22 0.209 0.033 0.018 0.024 - - - - - -
23 0.157 0.085 0.046 0.042 0.024 - - - - -
24 0.124 0.060 0.021 0.017 - - - - - -
Comments to Table 3:
DS_03. According to CSS data, A21-0 = 0.015.
DS_06. According to ASAS-SN data, A0 = 0.124, A1 = 0.114, A1+0 = 0.046, A1-0 = 0.040 in V-band.
DS_09. According to CSS data, A20-1 = 0.017.
DS_11. According to 1SWASP data, A21+0 = 0.008 and A20-1 = 0.009. DS_14. According to 1SWASP data, AW0 = 0.013.
3 GSC 02900-00317, a 1O/2O HADS(B) star
I discovered variability of GSC 02900-00317 (a = 05h 16m 25151, 8 = +41° 03' 56'.'8, J2000) from 1SWASP data and the APASS catalog. According to 1SWASP data (1SWASP J051625.48+410356.1), GSC 02900-00317 is a double-mode HADS star probably pulsating in the first- and second-overtone modes. The variability range in the 1SWASP data is 12m63 — 13m00. The light curves and power spectra of GSC 02900-00317 are displayed in Fig. 3. The M — m parameter for the first-overtone pulsation is 0?34.
Figure 3.
The light curves and power spectra of GSC 02900-00317 from 1SWASP data.
Additionally, I studied ASAS-SN data for this variable (GSC 02900-00317 was included in the list of the new ASAS-SN variables as a HADS star). My analysis of these data
confirmed double periodicity with the detected periods. These data made it possible to improve the light elements of the two oscillations. The variability range in the ASAS-SN data is 12m62 - 12m98 (V).
The light elements of the detected pulsation modes are presented in Table 4. The columns contain: the pulsation mode identification; period (P); epoch; and semi-amplitude (A) according to 1SWASP and ASAS-SN data.
Table 4. The light elements of GSC 02900-00317
Mode P, days Epoch, HJD A, mag (1SWASP) A, mag (ASAS-SN)
fi 0.1604573 2454410.025 0.116 0.138
¡2 0.1306435 2454410.113 0.027 0.020
fl + ¡2 0.072006 2454410.068 0.011 -
The period ratio is P2/P1 = 0.8143, somewhat higher than usual for HADS 1O/2O stars. All known HADS(B) variables pulsating in the first and second overtone modes (6 stars included in the GCVS, Samus et al. 2017: VZ Cnc, V798 Cyg, V1719 Cyg, VY Equ, V1553 Sco, V0526 Vel, and also 0GLE-GD-DSCT-0044, see Pietrukowicz et al. 2013) have smaller period ratios, 0.797 < P2/P1 < 0.806. Besides, the low galactic latitude of GSC 02900-00317, b = +1?7, suggests its membership, together with V798 Cyg, V1719 Cyg, and V0526 Vel, in a special group that should probably be considered together with the short-period (P < 1d) 10/20 Cepheids.
4 New RR(B) stars, F/1O
I detected 19 RR(B) stars pulsating in the fundamental and first-overtone modes. Their magnitudes are between 14m2 and 19m6 in the Catalina surveys CV system. The fundamental-mode periods are between 0d. 469 and 0d. 594.
Information on these stars is presented in Tables 5-7. The light curves and power spectra for one of the stars (RR_11) are displayed in Fig. 4.
Figure 4.
The light curves and power spectra of RR_11 (USNO-BI.O 0684-0313652) from CSS and SSS data.
Table 5 contains: equatorial coordinates (J2000); magnitudes at maximum and minimum in the Catalina surveys photometric system; name in the USNO-BI.O catalog (in two cases, GSC or UCAC4 designations are given); data source (cf. explanations to Table 1). The asterisk marks non-system magnitudes (see Comments).
Table 5. RR(B) stars: positions, magnitudes and identifications
No. Coordinates (J2000) CV mag. Name Data
1 00h16 m25S98 + 16°28/43//6 15m 42 - 15m99 USN0-B1.0 1064 0003260 c
2 00 56 10.67 + 19 20 44.5 16.14 - 16.81 USN0-B1.0 1093 0010992 c
3 01 19 10.06 +09 50 43.0 16.71 - 17.48 USN0-B1.0 0998 -0017969 c
4 01 32 26.59 + 19 16 52.2 16.82 - 17.52 USN0-B1.0 1092 -0017592 c
5 03 22 18.38 -06 24 12.5 16.90 - 17.56 USN0-B1.0 0835 0031093 c
6 03 50 10.72 -14 32 21.1 17.1 - 17.7 USN0-B1.0 0754- 0038907 c
7 04 07 58.09 -01 05 40.4 17.7 - 18.5 USN0-B1.0 0889 -0041400 c
8 10 22 59.45 -26 28 27.1 15.48 - 16.23 USN0-B1.0 0635 0260183 s
9 12 08 43.42 -25 51 50.8 15.59 - 16.26 USN0-B1.0 0641- 0273182 sc
10 12 44 26.99 -36 51 16.6 16.31 - 17.05 USN0-B1.0 0531- -0317052 s
11 13 26 55.62 -21 31 27.0 15.71 - 16.29 USN0-B1.0 0684 -0313652 sc
12 13 27 46.05 -25 26 53.2 17.07 - 17.91 USN0-B1.0 0645 -0292159 sc
13 14 15 54.97 +01 10 03.2 18.8 - 19.6 USN0-B1.0 0911- 0230636 cm
14 16 04 42.89 +01 39 57.9 16.08 - 16.63 USN0-B1.0 0916- 0269667 c
15 16 05 38.92 +00 59 57.6 16.74 - 17.49 USN0-B1.0 0909 0258003 c
16 16 10 58.64 -26 00 31.9 17.1 - 18.0 USN0-B1.0 0639 0370202 s
17 16 17 40.50 +03 13 10.2 16.61 - 17.22 USN0-B1.0 0932 0295381 c
18 16 21 44.14 +02 32 18.5 15.85 - 16.42 USN0-B1.0 0925 0362680 c
19 20 06 03.42 -30 42 18.5 14.21 - 14.64* UCAC4 297-225560 s
Table 6 presents light elements of the oscillations: the first-overtone period P1, the fundamental period P0, epochs of maxima for the first-overtone and fundamental modes, period ratio P1/P0, periods of the interaction frequencies f1 + f0 (P1+0) and f1 — f0 (P1-0).
Table 7 presents semi-amplitudes of all the oscillations, for Catalina surveys data only: semi-amplitudes of the first-overtone (A1) and fundamental-mode (A0) oscillations, plus those for the f1 + f0 (A1+0) and f1 — f0 (A1-0) frequencies. Asterisks mark non-system magnitudes.
Additional information about some of the stars can be found in Comments.
A.V. Khruslov: A Study of Double-Mode Variables Table 6. RR(B) stars: light elements
No. Pi, d Po, d Epoch1, HJD Epoch0, HJD Pi/Po Pi+o, d Pi-o, d
1 0.366502 0.491483 2455000.720 2455000.676 0.7457 - -
2 0.382973 0.514406 2455000.016 2455000.513 0.7445 0.2195303 -
3 0.373757 0.501374 2455000.527 2455000.692 0.7455 0.2141272 -
4 0.405567 0.543824 2455000.538 2455000.692 0.7458 - 1.59528
5 0.392303 0.525648 2455000.032 2455000.330 0.7463 - -
6 0.361584 0.486163 2455000.170 2455000.012 0.7438 - -
7 0.401199 0.537884 2455000.192 2455000.205 0.7459 - -
8 0.364036 0.488910 2455000.229 2455000.152 0.7446 0.2086668 1.4255
9 0.378950 0.508272 2455000.065 2455000.347 0.7456 0.2170927 -
10 0.374799 0.502687 2455000.161 2455000.503 0.7456 0.2147115 1.4733
11 0.370470 0.497699 2455000.143 2455000.016 0.7444 0.2123791 1.4492
12 0.380228 0.509824 2455000.134 2455000.013 0.7458 - -
13 0.349210 0.469574 2455000.180 2455000.105 0.7437 - -
14 0.355046 0.476957 2455000.143 2455000.296 0.7444 0.2035345 -
15 0.443102 0.594485 2455000.408 2455000.222 0.7454 0.2538750 -
16 0.372812 0.500750 2455000.375 2455000.405 0.7445 - -
17 0.394849 0.528949 2455000.352 2455000.463 0.7465 0.2260829 -
18 0.421655 0.565145 2455000.307 2455000.490 0.7461 0.2414845 1.66081
19 0.375104 0.503422 2455000.220 2455000.453 0.7451 0.2149447 -
Comments to Tables 5 and 6:
RR_08. The close companion USNO-BI.O 0635-0260181 = SSS_J102259.0-262834 (d = 9. 0) is constant according to SSS data.
RR_11. There is a faint close redder companion USN0-B1.0 0684-0313650, d = 5'2.
RR_18. Additional non-radial pulsation fN, PN = 0d476790, AN = 0.020.
RR_19. The magnitudes in the SSS data correspond to the combined brightness of two stars (d = 4"5), thus the amplitude is underestimated. The pair is not resolved in the GSC, GSC2.3, or USN0-B1.0 catalogs (GSC 07441-00826, GSC2.3 SCHK000551, USN0-B1.0 0592-0877865) but resolved in the 2MASS and UCAC4 catalogs: 2MASS 20060341-3042184 = UCAC4 297-225561 (J - K = 0.49) and 2MASS 20060326-3042225 = UCAC4 297-225560 (J - K = 0.37); possibly, it is UCAC4 297-225560 that varies: it has a bluer color index and maybe shows variability in the P-band DSS archive plates.
Table 7. RR(B) stars: semi-amplitudes
No. Ai Ao Ai+o Ai_o
1 0.174 0.049 - -
2 0.167 0.074 0.027 -
3 0.149 0.089 0.038 -
4 0.134 0.074 - 0.042
5 0.181 0.059 - -
6 0.175 0.107 - -
7 0.144 0.086 - -
8 0.178 0.139 0.061 0.037
9 0.168 0.072 0.037 -
10 0.161 0.077 0.033 0.033
11 0.142 0.082 0.026 0.029
12 0.169 0.090 - -
13 0.161 0.102 - -
14 0.161 0.050 0.023 -
15 0.153 0.088 0.039 -
16 0.170 0.132 - -
17 0.160 0.044 0.028 -
18 0.139 0.065 0.026 0.022
19 0.093* 0.050* 0.034* -
5 The Petersen diagram
The Petersen diagram for double-mode HADS and RR Lyrae variables studied in the present paper is displayed in two figures of this section. In both diagrams, the doublemode stars detected in this paper are marked with red circles.
The HADS(B) Petersen diagram is displayed in Fig. 5. Open squares and triangles represent respectively the known double- and triple-mode HADS variables. The figure shows different sequences of HADS(B) stars: stars pulsating in the fundamental and first overtone modes (10/F), in the first and second overtones (20/10), and a possible sequence for the third and second overtones (30/20).
The RR(B) Petersen diagram is displayed in Fig. 6. 0pen circles represent the known Galactic double-mode RR Lyrae stars; filled circles are the RR(B) variables in the 0GLE-IV survey (Galactic bulge stars).
Acknowledgments: The author wishes to thank Dr. V.P. Goranskij for providing his software. Thanks are due to Dr. N.N. Samus for helpful discussion. This study was supported by the sub-programme "Astrophysical 0bjects as Space Laboratories" in the Programme P-28 of the Presidium of Russian Academy of Sciences.
Figure 5.
The Petersen diagram for the HADS(B) stars.
Figure 6.
The Petersen diagram for the RR(B) stars.
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