Peremennye Zvezdy (Variable Stars) 38, No. 1, 2018 Received 15 January; accepted 12 April.

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A Study of Double-Mode Variables

A. V. Khruslov

Sternberg Astronomical Institute, Moscow State University, Universitetskij pr. 13, Moscow 119992, Russia; khruslov@bk.ru Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya str. 48, Moscow 119017, Russia

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 Supernovae³and 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 OMC2ASCII⁵program 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 code⁶written 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.

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 first-overtone 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 , 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 ( ). The typical period ratio of pulsations in the fundamental and first-overtone modes (F/1O) is for RR(B) stars and for HADS(B) stars. The typical period ratio of pulsations in the first- and second-overtone modes (1O/2O) is .

The stars were identified in the USNO-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 127 and 177 in the system. The highest peak-to-peak amplitude of light variations is 099 (DS_17). The fundamental-mode periods are between 0074 and 0138.

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 USNO-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 , the first-overtone period , the fundamental and first-overtone mode epochs of maxima, the period ratio . Additional information on some of the stars can be found in Comments to Table 2.

Table 2a contains periods of the interaction frequencies (), (), (), (), (), (), ().

Table 3 presents semi-amplitudes of the oscillations, separately for Catalina surveys and 1SWASP data: semi-amplitudes of the fundamental mode () and first-overtone () oscillations, and of their interaction frequencies.

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.

Comments to Table 1:

DS_02. From 1SWASP data, 1327 - 1374.

DS_03. From 1SWASP data, 142 - 149.

DS_06. From 1SWASP data, 144 - 150;

          from ASAS-SN data, 1423 - 1508 ().

DS_11. From 1SWASP data, 1280 - 1341.

DS_14. From 1SWASP data, 141 - 151.

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  Sct or SX Phe star with the period . Drake et al. (2014) independently detected the star's variability and gave the type HADS with the period . The variable is actually a HADS(B) star. It is difficult to determine the correct periods because the frequencies are close to the relation . The ratio of the detected most probable periods ( ) is typical not of the and periods but of the and periods. The one-day alias periods and are not excluded; their period ratio, , is more typical.

DS_21. An additional non-radial pulsation, ( , ), is possible.

DS_22. Two additional non-radial pulsations (quasi-equidistant triplet) are possible: ( , ) and ( , ); ; beat period ; interaction frequency ( , ). This result needs an independent verification.

Comments to Table 3:

DS_03. According to CSS data, .

DS_06. According to ASAS-SN data, , , , in -band.

DS_09. According to CSS data, .

DS_11. According to 1SWASP data, and .

DS_14. According to 1SWASP data, .

3. GSC 02900-00317, a 1O/2O HADS(B) star

I discovered variability of GSC 02900-00317 ( , 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 . The light curves and power spectra of GSC 02900-00317 are displayed in Fig. 3. The parameter for the first-overtone pulsation is .

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 ().

The light elements of the detected pulsation modes are presented in Table 4. The columns contain: the pulsation mode identification; period (); epoch; and semi-amplitude () according to 1SWASP and ASAS-SN data.

The period ratio is , 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 OGLE-GD-DSCT-0044, see Pietrukowicz et al. 2013) have smaller period ratios, . Besides, the low galactic latitude of GSC 02900-00317, , 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 ( ) 1O/2O 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 142 and 196 in the Catalina surveys system. The fundamental-mode periods are between 0469 and 0594.

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.

Table 5 contains: equatorial coordinates (J2000); magnitudes at maximum and minimum in the Catalina surveys photometric system; name in the USNO-B1.0 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 6 presents light elements of the oscillations: the first-overtone period , the fundamental period , epochs of maxima for the first-overtone and fundamental modes, period ratio , periods of the interaction frequencies () and ().

Table 7 presents semi-amplitudes of all the oscillations, for Catalina surveys data only: semi-amplitudes of the first-overtone () and fundamental-mode () oscillations, plus those for the () and () frequencies. Asterisks mark non-system magnitudes.

Additional information about some of the stars can be found in Comments.

Comments to Tables 5 and 6:

RR_08. The close companion USNO-B1.0 0635-0260181 = SSS_J102259.0-262834 ( ) is constant according to SSS data.

RR_11. There is a faint close redder companion USNO-B1.0 0684-0313650, .

RR_18. Additional non-radial pulsation , , .

RR_19. The magnitudes in the SSS data correspond to the combined brightness of two stars ( ), thus the amplitude is underestimated. The pair is not resolved in the GSC, GSC2.3, or USNO-B1.0 catalogs (GSC 07441-00826, GSC2.3 SCHK000551, USNO-B1.0 0592-0877865) but resolved in the 2MASS and UCAC4 catalogs: 2MASS 20060341-3042184 = UCAC4 297-225561 () and 2MASS 20060326-3042225 = UCAC4 297-225560 (); possibly, it is UCAC4 297-225560 that varies: it has a bluer color index and maybe shows variability in the -band DSS archive plates.

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 double-mode 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 (1O/F), in the first and second overtones (2O/1O), and a possible sequence for the third and second overtones (3O/2O).

The RR(B) Petersen diagram is displayed in Fig. 6. Open circles represent the known Galactic double-mode RR Lyrae stars; filled circles are the RR(B) variables in the OGLE-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 Objects as Space Laboratories" in the Programme P-28 of the Presidium of Russian Academy of Sciences.

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