Peremennye Zvezdy (Variable Stars) 44, No. 6, 2024 Received 3 June; accepted 23 September.	Article in PDF
	DOI: 10.24412/2221-0474-2024-44-56-77

Catalog of Multi-mode Radially Pulsating Variables: II

A. V. Khruslov^1,2

1. Sternberg Astronomical Institute, Moscow State University, Universitetskij pr. 13, Moscow 119992, Russia; khruslov@bk.ru

2. Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya str. 48, Moscow 119017, Russia

1. Introduction

The second part of the catalog of Multi-Mode Radially Pulsating (MMRP) variables is the continuation of my previous paper (Khruslov 2023), the first part of the MMRP catalog, and presents my detection of 60 new double- and multi-mode variables. The star numbers in the second part of the catalog are from MMRP-051 to MMRP-110.

Among these stars, there are RR Lyrae variables and high-amplitude Scuti (HADS) variables. These are stars that pulsate in the fundamental mode, the first-, second-, or third-overtone mode.

The method I apply to search for multi-periodicity, the photometric data used, identification names of stars included in the catalog, classification system, and multi-row structure of the tables, with a set of sub-rows, each of them corresponding to a individual detected radial pulsation mode, are the same as those described in the first part of the MMRP catalog.

Searching for double periodicity, I mainly used data available in the photometric archives of the All-Sky Automated Survey for Supernovae (ASAS-SN¹, Shappee et al. 2014; Kochanek et al. 2017) and the Zwicky Transient Facility (ZTF, Bellm et al. 2019; Masci et al. 2019). The ZTF data were taken from the SNAD ZTF viewer², Malanchev et al. (2021). The light elements are based on data from these two surveys. The magnitude ranges and amplitudes of brightness variations are given in the tables according to these data. Additionally, in individual cases, I analyzed available data from other archives: the Wide Angle Search for Planets (SuperWASP³, Butters et al. 2010; 7 variables), the Catalina Sky Surveys (CSS⁴, Drake et al. 2009; 6 variables). The SuperWASP observations are available as FITS tables, which were converted into ASCII tables using the OMC2ASCII⁵program as described by Sokolovsky (2007).

In some cases, continuous data series from ZTF, with duration of a whole night of observations, were recalculated as average values that were used for subsequent analysis; they are presented in the data files below the main data series.

The survey data used in this study for the program stars are available online in the html version of this paper as a zip archive. The archive also contains light curves of all variables and a cross-identification table for all stars.

2. Format of presentation

2.1. Identification names

The MMRP catalog uses two types of variable-star identification names:

 

(1) the format for designating stars whose multiperiodicity was first discovered in this study is:

(2) and the format for designating known multiperiodic stars, for which new light elements are presented, is:

(equatorial coordinates for equinox 2000.0).

Designations of the type (2) appeared only in the first part of the MMRP.

2.2. Classification

New original MMRP classification of multiperiodic variables is somewhat more detailed than that used in the General Catalog of Variable Stars, GCVS (Samus et al. 2017), but is based on the principles presented by N.N. Samus and the GCVS team at the XXVI IAU General Assembly in Prague, 2006⁶. The studies that have resulted in the MMRP catalog are a part of the program aimed at inclusion of new variables into the GCVS.

The MMRP classification consists of the variability type designated with a single letter (C - Classical Cepheids; W - W Virginis type II Cepheids; R - RR Lyrae stars; D -  Scuti stars) and the numerical identification of pulsation modes (0 - fundamental mode; 1 - first overtone; 2 - second overtone; 3 - third overtone). Extra characteristics are introduced with an additional index (n - additional non-radial mode; m - amplitude modulation with a slow variation from season to season). An arrow indicates the cases of mode switching. Examples: C01, C12m, D0123, D01n, R01, R01R0.

The radial pulsation modes were identified on the base of the period ratio ( ); see the study of this problem in Petersen (1973), Petersen & Christensen-Dalsgaard (1996), Smolec & Moskalik (2010), etc.

2.3. Tables

We use a multi-row format in the Tables of the MMRP catalog. For a complete description of the format, see the first part of the MMRP catalog (Khruslov 2023).

The main table (Table 1) contains general information on the star: number in the MMRP Catalog; equatorial coordinates J2000; magnitude range; type of multi-periodicity; and then, information about individual modes is presented in sub-rows (light elements, period and epoch of maximum; semi-amplitude; asymmetry parameter of the phased light curve, -). The period ratio (shorter period / longer period) is given for each pair of adjacent sub-rows (in the sub-row for the longer period).

The equatorial coordinates are given according to the Gaia DR3 catalog. The tabulated magnitude range is for the photometric band indicated in brackets (a and a are ASAS-SN and magnitudes; z and z are ZTF and magnitudes). Semi-amplitudes are given in the photometric band indicated in the “Magn.” column.

In addition to the notation used in the MMRP-I catalog, the second part (this paper) contains epochs in the following three formats:

;

;

.

In the second part of the MMRP, I do not present separate tables of comments in the format of coded numbers (Tables 2 and 2a in MMRP-I). After Table 1, I present comments for individual stars. I excluded information about the history of variability studies for individual stars that was included in the Comments of the first MMRP catalog. This information can be found in the web sources of the photometric surveys: the ASAS-SN catalogs of variable stars⁷(Jayasinghe et al. 2018, 2019a, 2019b, 2020, 2021); the ZTF catalog of periodic variable stars⁸, Chen et al. (2020); Gaia DR2 and Gaia DR3, and others. Identifications with these catalogs can be found in the cross-identification table available online in the html version of this paper (see the link in Section 1).

The supplementary Tables 2 and 3 (corresponding respectively to Tables 3 and 4 in MMRP-I) contain semi-amplitudes and magnitude ranges in all bands used in the ASAS-SN and ZTF surveys and known information from catalogs and photometric surveys: color indices and Galactic latitudes.

2.4. Light curves

An example of light curves for one of the stars, MMRP-075, is displayed in Fig. 1. The star is classified as a D13 type variable. The top panels present data folded with the first- and third-overtone periods. The bottom panels show the same curves after prewhitening the other oscillation (also, the , , , and interaction frequencies were excluded). 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 (the first-overtone oscillation in the case of MMRP-075). The structure of the power spectra shows that the secondary periods are real.

The light curves for all studied stars are available online in the html version of this paper as a zip archive (see the link in Section 1). The light curves are given in the format displayed in Fig. 1. A similar and more complete format is used for triple- and quadruple-mode variables.

3. Results

Among the 60 stars presented in this paper, there are 10 RR Lyrae stars of the R01 type, 50 high-amplitude Scuti stars (double-mode: 22 stars of the D01 type; 8 D12 stars; 3 D02 stars; 10 D13 stars; triple-mode: one D012 star and 5 D123 stars; one quadruple-mode D0123 star). Stars of the D02 and D13 types have not been studied by me before. Double-mode or multi-mode Cepheids are not presented in this paper.

In addition, one of the previously studied stars, MMRP-010, was reclassified as a D01 star.

Comments to Table 1.

 

MMRP-054. A blend in the ASAS-SN data is possible, amplitude underestimated. Due to large errors, this data is not included in the table.

 

MMRP-062. The third-overtone period varies. The elements in the Table are given for the ASAS-SN and and ZTF data time interval. The elements for the -band ASAS-SN time interval are:

HJD(max) = 2457777.0115 + 00533036 .

The first-overtone period also possibly varies.

 

MMRP-064. Amplitude modulation with slow variation from one season to another is possible for the second-overtone oscillation . Type D12m is not excluded.

 

MMRP-067. A blend in the ASAS-SN data is possible, amplitude underestimated.

 

MMRP-069. The period varies. Elements for are given for the whole time interval covered with observations. The Table gives light elements for the first time interval in ZTF data, JD 2458287-2459150. The light elements for the second time interval in ZTF data, JD 2459150-2459995, are:

: HJD(max) = 2459600.0530 + 00841481 ;

: HJD(max) = 2459600.0160 + 00566891 ;

= 0.155 and = 0.014 in the z band, = 0.219 and = 0.021 in the z band.

 

MMRP-075. Data from 1SWASP and CSS were used to improve the light elements. Magnitude range and semi-amplitude according to 1SWASP data: 1432-1534 (1SWASP mag); = 0.234, = 0.097. According to CSS data: 1315-1356 (C); = 0.123, = 0.046. In the 1SWASP data, the oscillation amplitude is the largest.

 

MMRP-076. A blend in ASAS-SN data is possible, amplitude underestimated.

 

MMRP-078. Other period ratios: = 0.6214, = 0.6709.

 

MMRP-081. The first overtone period possibly varies. In the ASAS-SN -band data (earlier time interval), the second-overtone oscillation is not detected, amplitude of the third-overtone mode is the largest. Amplitude modulation is not excluded.

 

MMRP-082. Amplitude modulation of the second overtone oscillation. The photometry was studied in three time intervals:

I. JD 2455970-2458452. Only a data. The first overtone elements are:

: HJD(max) = 2457777.0710 + 00915920 ; - = 0.35.

The semi-amplitude is = 0.190 (a).

The detection of the second-overtone mode is very uncertain, the possible period = 0737833, .

II. JD 2458034-2458994. The analysis made use of the a, z, and z data. The light elements and amplitudes for this time interval are presented in the Tables.

III. JD 2459076-2460373. The light elements are the following:

: HJD(max) = 2460000.0290 + 00915930 ; - = 0.37;

The semi-amplitudes are: (a), 0.160 (z), 0.240 (z).

: HJD(max) = 2460000.0360 + 007378 ; - = 0.50:.

The semi-amplitudes are: (a), 0.006 (z), 0.007 (z).

 

MMRP-083. There is an additional non-radial pulsation with the following light elements:

HJD(max) = 2458888.0432 + 005668265 ;

The semi-amplitudes are 0.009 (a), 0.008 (a). - = 0.49.

 

MMRP-085. Amplitudes and magnitude range in the -band of ZTF data: = 0.102, = 0.113; 1689-1744.

 

MMRP-086. Data from 1SWASP were used to improve the light elements. Magnitude range and semi-amplitudes according to 1SWASP data: = 0.078, = 0.013; 1259-1285 (1SWASP mag).

An additional, possibly non-radial, pulsation was found with certainty in the -band ASAS-SN data; in the -band ASAS-SN and 1SWASP data, it is uncertain. Its light elements are the following:

HJD(max) = 2458888.0410 + 007345498 .

The semi-amplitudes are 0.007: (a), 0.008 (a), 0.003: (1SWASP mag). The period ratio = 0.7857 possibly corresponds to the ratio, but = 0.7766 does not correspond to the ratio.

 

MMRP-088. The amplitudes and magnitude range in the band of ZTF data: , ; 1926-1983.

 

MMRP-090. The amplitude and magnitude range in the band of ZTF data: , ; 1712-1771.

 

MMRP-091. Type D01D0 is not excluded. ASAS-SN data were analyzed in four separate time intervals:

I, JD 2457400-2458100, band;

II, JD 2458100-2458800, and bands;

III, JD 2458800-2459500, band;

IV, JD 2459600-2460400, band.

In the data for time interval I, double periodicity was detected, the light elements are given in the Table. In the data for time interval II, the first-overtone oscillation in the -band data was possibly detected (very uncertainly) with a small amplitude and a different period. The possible period :, = 0.014 (a). In -band data for the time interval II, was not detected. In the data for the time intervals III and IV, was not detected.

The fundamental-mode period varies, the following light elements were derived for separate time intervals:

II: HJD(max) = 2458500.0423 + 00707801 ; = 0.201 (a), 0.167 (a);

III: HJD(max) = 2459200.0544 + 00707797 ; = 0.201 (a);

IV: HJD(max) = 2460000.0212 + 00707817 ; = 0.199 (a).

In the earlier time interval of 1SWASP data, JD 2453860-2454275, double-mode periodicity was detected with the following elements:

: HJD(max) = 2454054.0025 + 00707800 ; - = 0.40,

: HJD(max) = 2454054.0025 + 00545125 ; - = 0.45.

The semi-amplitudes are = 0.186, = 0.055 (1SWASP mag).

In the 1SWASP data, after removing the radial frequencies and as well as interaction frequencies ( and ), a possible non-radial oscillation with the period is detected, = 0.018 (1SWASP mag). In the -band ASAS-SN data for all time intervals (I and II), this frequency is not detected. In the -band ASAS-SN data for all time intervals (II, III and IV), this oscillation is detected:

II: :, = 0.015;

III: , = 0.020;

IV: , = 0.012.

 

MMRP-092. The magnitude range according to CSS data: 1706-1761 (C). In CSS data, is not detected.

 

MMRP-093. The amplitudes and magnitude range in the band of ZTF data: = 0.081, = 0.115; 1704-1752.

 

MMRP-094. Data from 1SWASP were used to improve the light elements. The amplitudes and magnitude range in the 1SWASP data: = 0.146, = 0.016; 1308-1354 (1SWASP mag).

 

MMRP-095. The amplitudes and magnitude range in the band of ZTF data: = 0.091, = 0.119; 1731-1782. The amplitudes and magnitude range according to CSS data: = 0.099, = 0.137; 1704-1793 (C). Data from CSS were used to improve the light elements.

 

MMRP-098. The amplitudes and magnitude range in the band of ZTF data: = 0.054, = 0.130; 1879-1934. In CSS data, the fundamental mode period is not detected, magnitude range 187-196 (C).

 

MMRP-099. In ASAS-SN -band data, the second-overtone frequency is not detected. Amplitude modulation is not excluded.

 

MMRP-100. An additional non-radial pulsation with the period , or Blazhko effect of the second-overtone oscillation with . Semi-amplitude is 0.022 (a), 0.023 (a).

Data from 1SWASP were used to improve the light elements. The semi-amplitudes are , , , . Blend in 1SWASP data.

 

MMRP-103. According to 1SWASP data, the light elements are:

: HJD(max) = 2454150.0410 + 00706180 ;

: HJD(max) = 2454150.0124 + 00546466 .

The magnitude range and semi-amplitudes according to 1SWASP data: 1375-1415, , .

 

MMRP-104. A possible non-radial oscillation with the period ; the semi-amplitude is 0.021 (z), 0.016 (z). , identification with the second overtone is not excluded.

 

MMRP-105. A blend in ASAS-SN data, amplitude underestimated.

 

MMRP-106. A blend in ASAS-SN data, amplitude underestimated. In the data for z, z, and a bands, the brightening trend was excluded before the amplitude analysis, its full amplitude being 0.018 (z), 0.021 (z), and 0.110 (a). In the a-band data (an earlier time interval), the trend was not detected.

 

MMRP-107. An additional non-radial pulsation with the following light elements (ASAS-SN and ZTF data):

HJD(max) = 2458888.032 + 005108950 ;

the semi-amplitude is 0.012 (a), 0.012 (a), 0.007 (z), 0.010 (z); - = 0.45.

Light elements for the CSS (JD 2453568-2456446) and 1SWASP (JD 2453860-2454615) time intervals:

: HJD(max) = 2455055.0333 + 00767249 ;

: HJD(max) = 2455055.0225 + 00515180 ;

: HJD(max) = 2455055.0406 + 00510897 .

The magnitude ranges and semi-amplitudes according to 1SWASP and CSS data: 1352-1382 (C), 1385-1418 (1SWASP mag); is 0.068 (C), 0.058 (1SWASP mag); is 0.018 (C), 0.015 (1SWASP mag); is 0.013 (C), 0.007 (1SWASP mag).

 

MMRP-108. The first-overtone period possibly varies. Light elements for the CSS time interval:

: JD(max) = 2455055.0276 + 00644806 ;

: JD(max) = 2455055.0075 + 00502488 .

The magnitude range and semi-amplitudes: 1518-1561 (C), , .

 

MMRP-109. The amplitude of the first-overtone oscillation varies from season to season, the mean estimates of the amplitude are given in the Table.

 

MMRP-110. A blend in ASAS-SN data, results of this analysis are not given in the Tables. In these data, the second-overtone frequency is not detected (as a result of possible large errors of observations).

4. Discussion

4.1. Re-classification of MMRP-010

In the first part of the MMRP catalog (Khruslov 2023), I made a wrong classification of MMRP-010 as a quadruple-mode D0123-type variable. For this star, the frequencies of the supposed radial modes are equidistant, . Frequencies and are not in doubt, but the frequencies and of this equidistant quadruplet can be considered interaction frequencies of the two main oscillations: and .

Thus, in this case, we have two main frequencies and ; in addition to them, interaction frequencies , , , and are also detected (in the order of decreasing amplitude).

Usually, the frequencies and especially have very small amplitudes and are very rarely detected in data analysis. It is possible that the oscillations in these interaction frequencies are amplified when they coincide with the expected frequencies of the second and third overtones.

For this reason, we re-classified MMRP-010 as a D01-type star. The real D0123 quadruplets (see 14 Galactic-bulge cases in Netzel et al. 2022) are not equidistant. In this paper, I also present a new real case of a D0123 type star, MMRP-078.

Among other features of MMRP-010, the inverted asymmetry (- = 0.55) of its first-overtone light curve is worth noting.

4.2. Pulsation modes of MMRP-086

MMRP-086 was classified as a Scuti star pulsating in the fundamental and second overtone modes with an additional non-radial pulsation (D02n type). In this case, the additional non-radial pulsation was found with certainty in the -band ASAS-SN data, but it is not detected or uncertain in the other photometric data (-band ASAS-SN and 1SWASP). The period ratio = 0.7857 may correspond to the ratio, but = 0.7766 does not correspond to the ratio. Therefore, I do not consider as a pulsation in the first overtone and do not classify the star as D012 type. The light curves and power spectra of the star MMRP-086 are displayed in Fig. 2.

4.3. Variables with amplitude modulation

For 4 variables, amplitude modulation with slow changes (from one season to another) was detected. The variability type of these stars contains the index "m". Among these variables, there are two D01m stars (MMRP-091 and MMRP-109), one D12m star (MMRP-082 = V611 Cam), and one D13m star (MMRP-069).

In some cases, a periodic amplitude variation is possible; however, also in a number of cases, it can represent mode switching. For example, in the case of MMRP-091, during the last time interval, the first-overtone oscillation was not detected, mode switching is possible, type D01D0 is not excluded. Follow-up monitoring of the object is necessary.

4.4. The Petersen diagram

The Petersen diagram for all detected MMRP variables is displayed in Fig. 3. The diagram shows sequences corresponding to individual types of multi-periodic radially pulsating variables.

4.5. A note to this paper

When this paper was already submitted to Peremennye Zvezdy, Jia et al. (2024) published a catalogue of multimode  Sct stars from the Zwicky Transient Facility Survey. A number of stars from our publication were included in this work. These are objects MMRP 051-057, 059, 060, 062, 064, 066, 067, 070, 071, 074, 076-079, 082, 104, 105, and 110. In most cases, the results (classification of pulsation modes and light elements) are almost identical. However, MMRP-104 was classified by Jia et al. (2024) as a triple-mode pulsating star that varied in the fundamental, first- and second-overtone modes, while I identified the third pulsation as a non-radial mode (because of the period ratio ) and gave the star the D01n type; MMRP-105 was classified by Jia et al. (2024) as a double-mode  Scuti star pulsating in the first and second overtones, while I give the type D123 (the third-overtone mode is real, see power spectra in the z and z bands). Also, the cited authors did not detect the amplitude modulation of MMRP-082.

Additionally, for seven of these stars (MMRP-054, 056, 062, 067, 076, 082, and 105), I used data from ASAS-SN to improve their light elements.

Acknowledgments: The author wishes to thank Dr. V.P. Goranskij for providing his software.

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4.6. Supplement Tables

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