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1Peremennye Zvezdy ( Variable ¡Stars) 44, No. 6, 2024
Received 3 June; accepted 23 September.
DOI: 10.24412/2221-0474-2024-44-56-77
Catalog of Multi-mode Radially Pulsating Variables: II
A. V. Khruslov1'2
1 Sternberg Astronomical Institute, Moscow State University, Universitetskij pr. 13, Moscow 119992, Russia; [email protected]
2 Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya str. 48, Moscow 119017, Russia
I present the second part of the catalog of newly detected Multi-Mode Radially Pulsating (MMRP) variable stars. For these stars, pulsations in the fundamental, first-, second-, or third-overtone modes were detected. This paper includes 60 double- and multi-mode stars (numbered from MMRP-051 to MMRP-110). Variability types determined for these stars are RR Lyrae variables and high-amplitude s Scuti (HADS) stars. In addition, one of the previously studied stars, MMRP-010, was reclassified.
I analyzed all observations available for these stars in the ASAS-SN and ZTF online public archives using the period-search software developed by Dr. V.P. Goranskij for Windows environment. Light elements and parameters of oscillations were determined.
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 8 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
1 https://asas-sn.osu.edu/
2 https://ztf.snad.space/
3 http://wasp.cerit-sc.cz/form/
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 OMC2ASCII5 program 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:
MMRP-XXX
(2) and the format for designating known multiperiodic stars, for which new light elements are presented, is:
MMRP JXXXXXX.XX+XXXXXX.X
(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 - 5 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, R01^R0.
The radial pulsation modes were identified on the base of the period ratio (Pshort/Piong); see the study of this problem in Petersen (1973), Petersen & Christensen-Dalsgaard (1996), Smolec & Moskalik (2010), etc.
4 http://nunuku.caltech.edu/cgi-bin/getcssconedb_release_img.cgi
5 http://scan.sai.msu.ru/swasp_converter/
6 http://www.sai.msu.su/gcvs/future/classif.htm
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, M-m). The period ratio PS/PL (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 (aV and ag are ASAS-SN V and g magnitudes; zr and zg are ZTF r and g 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:
Ea = aX.XXXX = HJD - 2457777.0;
Eb = bX.XXXX = HJD - 2458888.0;
Ec = cX.XXXX = HJD - 2460000.0.
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 /3+/1, f3-f1, /3+2/1, and 2f1-f3 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.
7 https://asas-sn.osu.edu/variables
8 http://variables.cn:88/ztf/
3 Results
Among the 60 stars presented in this paper, there are 10 RR Lyrae stars of the R01 type, 50 high-amplitude 8 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.
Figure 1. The light curves and power spectra of the star MMRP-075 (D13 type) from g-band ZTF data.
Table 1: MMRP variables
No. J2000 Magn. Type Period, d Epoch Ampl. M-m Ps/Pl
010 04 53 16.75 +39 14 18.2 14.3715.21 ag) D01 0.323070 0.243812 b0.036 b0.100 0.164 0.136 0.37 0.55 0.7547
051 00 06 39.46 +53 13 44.0 17.6718.24 zg) D13 0.0675897 0.0456185 b0.0012 b0.0414 0.210 0.018 0.38 0.50 0.6749
052 00 09 33.51 +56 21 44.4 17.84 18.43 zg) D01 0.0836583 0.0648244 b0.0165 b0.0040 0.139 0.054 0.39 0.44 0.7749
053 00 10 52.50 +56 31 18.5 17.63 18.50 zg) D01 0.1539483 0.1183604 b0.0427 b0.0285 0.140 0.162 0.38 0.35 0.7688
054 00 14 24.72 +53 20 52.7 16.05 16.50 zg) D01 0.0859502 0.0665394 b0.0654 b0.0105 0.183 0.017 0.36 0.50 0.7742
055 00 23 45.18 +64 45 54.9 17.33 17.83 zg) D01 0.1097914 0.0849198 b0.1045 b0.0690 0.060 0.112 0.40 0.40 0.7735
056 00 27 07.81 +57 37 40.7 15.4715.90 zg) D012 0.1165398 0.0897679 0.0719476 b0.0500 b0.0499 b0.0645 0.035 0.140 0.016 0.47 0.39 0.50 0.7703 0.8015
057 00 29 28.85 +54 18 42.6 17.18 17.69 zg) D01 0.06204725 0.0481865 b0.0154 b0.0170 0.170 0.031 0.38 0.48 0.7766
058 00 29 30.75 +50 45 40.7 15.91 16.60 zr) R01 0.465953 0.346377 b0.067 b0.097 0.132 0.159 0.40 0.39 0.7434
059 00 35 42.60 +64 27 12.6 17.76 18.08 zr) D01 0.1457098 0.1123257 b0.127 b0.043 0.053 0.042 0.42 0.39 0.7709
060 00 37 28.27 +55 20 00.3 17.77 18.52 zg) D01 0.0766737 0.0575075 b0.0408 b0.0340 0.245 0.029 0.34 0.46 0.7500
061 00 45 27.68 +58 53 58.9 16.31 17.20 zg) D01 0.0946369 0.0730509 b0.0235 b0.0304 0.154 0.146 0.37 0.35 0.7719
062 00 48 11.14 +47 37 19.0 13.58 14.25 ag) D13 0.0793879 0.0533018 b0.0215 b0.0097 0.245 0.025 0.37 0.50: 0.6714
063 00 50 42.33 +56 51 08.9 17.79 18.30 zg) D13 0.0845786 0.0550910 b0.0470 b0.0260 0.175 0.018 0.40 0.50 0.6514
064 00 51 37.66 +68 45 17.0 17.35 17.95 zg) D12 0.0930969 0.0748047 b0.0701 b0.0738 0.211 0.023 0.40 0.43: 0.8035
Table 1: MMRP variables
No. J2000 Magn. Type Period, d Epoch Ampl. M-m Ps/Pl
065 00 51 41.52 16.88 D01 0.0853045 b0.0130 0.174 0.36 0.7744
+52 43 16.3 17.55 zg) 0.0660640 b0.0406 0.082 0.41
066 01 00 46.09 18.13 D01 0.0653560 b0.0567 0.120 0.37 0.7525
+71 59 36.6 18.54 zr) 0.0491802 b0.0315 0.016 0.44
067 02 37 13.67 15.38 D12 0.0985287 b0.0244 0.140 0.38 0.8035
+63 02 49.9 15.75 zr) 0.0791710 b0.0138 0.010 0.50
068 02 43 26.13 18.00 D12 0.0821909 b0.0283 0.214 0.35 0.8027
+65 21 01.1 18.63 zr) 0.0659757 b0.0205 0.015 0.50
069 02 46 59.99 17.34 D13m 0.0841481 b0.0759 0.221 0.38 0.6736
+61 35 38.7 17.95 zg) 0.0566862 b0.0105 0.042 0.48
070 03 20 12.89 16.62 D13 0.0662601 b0.0240 0.070 0.43 0.6581
+62 34 13.0 16.84 zr) 0.0436084 b0.0097 0.015 0.47
071 03 23 43.84 18.10 D01 0.1094991 b0.0757 0.059 0.47 0.7730
+62 52 47.9 18.45 zr) 0.0846419 b0.0545 0.053 0.48
072 03 34 42.83 17.43 D01 0.1028625 b0.0866 0.099 0.39 0.7715
+60 31 08.3 17.77 zr) 0.0793606 b0.0250 0.026 0.46
073 03 43 18.44 16.34 D13 0.0911844 b0.0530 0.065 0.45 0.6484
+68 31 57.1 16.56 zr) 0.0591228 b0.0183 0.019 0.47
074 03 52 55.98 18.09 D01 0.1074287 b0.0740 0.152 0.35 0.7730
+55 03 33.5 18.63 zr) 0.0830433 b0.0470 0.054 0.39
075 03 58 02.52 13.92 D13 0.1995958 b0.147 0.168 0.48 0.6718
+36 49 09.6 14.45 zg) 0.1340875 b0.044 0.061 0.45
076 04 05 46.65 16.45 D12 0.1301875 b0.0945 0.167 0.43 0.8038
+57 40 21.6 16.90 zg) 0.104641 b0.0592 0.023 0.46
077 04 09 46.34 17.02 D12 0.0740534 b0.0345 0.119 0.37 0.8073
+53 07 47.6 17.37 zr) 0.0597822 b0.0587 0.012 0.44
078 04 18 00.38 16.27- D0123 0.1224802 b0.0825 0.051 0.42 0.7722
+56 08 42.3 16.60 zr) 0.0945762 b0.0225 0.057 0.42 0.8048
0.0761115 b0.0693 0.023 0.47 0.8336
0.0634467 b0.0250 0.029 0.50
079 04 19 16.52 17.41 D01 0.0838792 b0.0404 0.137 0.31 0.7747
+57 14 23.1 17.83 zr) 0.0649833 b0.0145 0.018 0.48
Table 1: MMRP variables
No. J2000 Magn. Type Period, d Epoch Ampl. M-m Ps/Pl
080 05 15 27.80 +70 36 58.8 16.59 17.42 zg) D01 0.0701374 0.0544502 b0.0374 b0.0325 0.234 0.058 0.32 0.46 0.7763
081 05 28 53.05 +48 36 11.8 13.20 13.41 zr) D123 0.1482472 0.1188605 0.0989185 b0.144 b0.105 b0.019 0.076 0.009 0.013 0.43 0.50 0.48 0.8018 0.8322
082 07 14 14.39 +73 27 29.6 13.72 14.33 zg) D12m 0.0915925 0.0737798 b0.0885 b0.0296 0.224 0.035 0.35 0.50 0.8055
083 09 48 09.85 -61 19 30.3 13.36 13.69 ag) D13n 0.08640150 0.05703713 b0.0125 b0.0540 0.101 0.011 0.44 0.53: 0.6601
084 14 01 22.52 +26 39 00.5 18.60 19.40 zg) R01 0.542780 0.405293 b0.245 b0.212 0.058 0.224 0.50: 0.39 0.7467
085 14 03 54.78 +67 08 42.6 16.74 17.73 zg) R01 0.489193 0.363813 b0.160 b0.072 0.194 0.235 0.41 0.39 0.7437
086 14 31 33.52 -44 14 40.3 12.80 13.18 ag) D02n: 0.09348775 0.05704222 b0.0181 b0.0082 0.135 0.013 0.41 0.48 0.6102
087 14 50 44.40 -51 09 56.0 14.29 15.01 ag) D02 0.1817898 0.1088370 b0.071 b0.044 0.235 0.025 0.32 0.43 0.5987
088 15 03 57.99 +67 12 16.7 19.32 20.15 zg) R01 0.58066 0.43331 b0.398 b0.187 0.057 0.216 0.40 0.35 0.7462
089 15 19 31.77 -62 58 21.0 13.61 14.10 ag) D123 0.1691712 0.1352296 0.1124590 b0.068 b0.055 b0.073 0.102 0.037 0.040 0.47 0.49 0.46 0.7994 0.8316
090 15 46 05.81 +79 22 24.7 16.99 18.01 zg) R01 0.473777 0.352505 b0.362 b0.016 0.182 0.220 0.41 0.37 0.7440
091 15 56 32.39 -38 48 02.0 13.90 14.55 aF) D01m 0.0707824 0.0545141 a0.0124 a0.0330 0.141 0.071 0.38 0.50: 0.7702
092 16 07 49.75 +20 16 56.9 17.29 17.89 zg) R01 0.486850 0.362469 b0.070 b0.170 0.033 0.231 0.47 0.40 0.7445
093 16 26 25.26 +69 44 18.3 16.86 17.80 ag) R01 0.481098 0.358113 b0.183 b0.007 0.151 0.222 0.40 0.38 0.7444
094 16 29 16.93 -20 49 49.2 13.14 13.61 ag) D02 0.16514947 0.1005594 b0.0733 b0.0828 0.177 0.020 0.34 0.48 0.6089
Table 1: MMRP variables
No. J2000 Magn. Type Period, d Epoch Ampl. M-m Ps/Pl
095 16 49 42.63 +47 53 42.6 17.11 -18.11 (zg) R01 0.475254 0.353766 b0.060 b0.324 0.169 0.226 0.40 0.38 0.7444
096 17 50 31.00 -28 11 35.6 11.76 -12.00 (ag) D13 0.1239932 0.0817480 b0.1177 b0.0522 0.075 0.015 0.46 0.45 0.6593
097 18 00 55.06 -56 45 32.7 14.48 -15.40 (ag) D01 0.1176389 0.0907838 b0.021 b0.063 0.235 0.063 0.36 0.43 0.7717
098 18 01 23.93 +46 12 26.2 18.70 -19.62 (zg) R01 0.547167 0.408183 b0.435 b0.153 0.097 0.234 0.43 0.37 0.7460
099 18 13 15.97 -16 04 22.1 14.47 -14.72 (zr) D123 0.1163633 0.0930402 0.0771944 b0.0233 b0.0685 b0.0418 0.060 0.023 0.020 0.50 0.49 0.43 0.7996 0.8297
100 18 32 35.84 +23 45 13.1 12.38 -12.83 (ag) D123n 0.1763344 0.1407097 0.1157337 b0.081 b0.065 b0.020 0.099 0.028 0.043 0.46 0.49 0.49 0.7980 0.8225
101 18 41 51.71 + 19 34 59.4 19.2 -19.7 (zr) R01 0.513113 0.382661 b0.135 b0.382 0.045 0.143 0.47 0.43 0.7458
102 18 57 09.54 -29 32 13.2 15.10 -15.60 (ag) D01 0.08030705 0.06228179 b0.0360 b0.0437 0.065 0.062 0.44 0.43 0.7755
103 19 11 49.38 -27 44 44.1 13.60 -14.16 (ag) D01 0.07061797 0.05464646 b0.0125 b0.0336 0.152 0.051 0.38 0.45 0.7738
104 19 45 52.97 + 16 41 58.7 17.58 -18.25 (zg) D01n 0.0815354 0.0640002 b0.0316 b0.0307 0.108 0.110 0.41 0.37 0.7849
105 19 45 53.19 + 19 17 04.3 14.41 -14.87 (zg) D123 0.1565323 0.1247345 0.1039327 b0.0925 b0.0870 b0.0077 0.174 0.018 0.010 0.39 0.50: 0.44: 0.7969 0.8332
106 19 48 42.16 + 18 20 51.4 15.6716.03 (zg) D12 0.1284792 0.1025547 b0.0088 b0.0339 0.128 0.013 0.44 0.45 0.7982
107 19 56 54.19 -22 53 31.5 13.92 -14.24 (ag) D13n 0.07672450 0.05151785 b0.0440 b0.0498 0.093 0.019 0.45 0.50 0.6715
108 20 36 21.97 -50 02 15.3 15.15 -15.80 (ag) D01 0.0644808 0.0502418 b0.0219 b0.0085 0.110 0.115 0.47 0.44 0.7792
109 23 46 17.96 17.54 - D01m 0.0911045 b0.0065 0.104 0.44 0.7772
Table 1: MMRP variables
No. J2000 Magn. Type Period, d Epoch Ampl. M-m Ps/Pl
+53 34 08.9 18.12 (zg) 0.0708039 b0.0327 0.091 0.43
110 23 46 29.54 +64 10 27.3 16.84 -17.52 (zg) D12 0.0892052 0.0716654 b0.0878 b0.0567 0.259 0.024 0.38 0.48 0.8034
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 P3 varies. The elements in the Table are given for the g ASAS-SN and r and g ZTF data time interval. The elements for the F-band ASAS-SN time interval are:
HJD(max) = 2457777.0115 + 0d0533036 xE.
The first-overtone period Pi also possibly varies.
MMRP-064. Amplitude modulation with slow variation from one season to another is possible for the second-overtone oscillation f2. Type D12m is not excluded.
MMRP-067. A blend in the ASAS-SN data is possible, amplitude underestimated.
MMRP-069. The period P3 varies. Elements for P1 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:
f1: HJD (max) = 2459600.0530 + 0d0841481 xE; /3: HJD (max) = 2459600.0160 + 0d0566891 xE; A1 = 0.155 and A3 = 0.014 in the zr band, A1 = 0.219 and A3 = 0.021 in the zg band.
MMRP-075. Data from 1SWASP and CSS were used to improve the light elements. Magnitude range and semi-amplitude according to 1SWASP data: 14m32-15m34 (1SWASP mag); A1 = 0.234, A3 = 0.097. According to CSS data: 13m 15-13m56 ( CF); A1 = 0.123, A3 = 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: P2/P0 = 0.6214, P3/P1 = 0.6709.
MMRP-081. The first overtone period P1 possibly varies. In the ASAS-SN F-band data ( earlier time interval), the second-overtone oscillation f2 is not detected, amplitude of the third-overtone mode A3 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 aF data. The first overtone elements are:
fi: HJD(max) = 2457777.0710 + 0d0915920 xE; M-m = 0.35. The semi-amplitude is A1 = 0.190 (aV).
The detection of the second-overtone mode f2 is very uncertain, the possible period P2 = 0d737833, A2 < 0.010.
II. JD 2458034-2458994. The analysis made use of the ag, zr, and zg 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:
fl: HJD(max) = 2460000.0290 + 0d0915930 xE; M-m = 0.37;
The semi-amplitudes are: A1 = 0.209 (ag), 0.160 (zr), 0.240 (zg).
f2: HJD(max) = 2460000.0360 + 0d07378 xE; M-m = 0.50:. The semi-amplitudes are: A2 < 0.008 (ag), 0.006 (zr), 0.007 (zg).
MMRP-083. There is an additional non-radial pulsation fn with the following light elements:
HJD(max) = 2458888.0432 + 0d05668265 xE; The semi-amplitudes An are 0.009 (aV), 0.008 (ag). M-m = 0.49.
MMRP-085. Amplitudes and magnitude range in the ¿-band of ZTF data: A0 = 0.102, A1 = 0.113; 16m 89-17m 44.
MMRP-086. Data from 1SWASP were used to improve the light elements. Magnitude range and semi-amplitudes according to 1SWASP data: A0 = 0.078, A2 = 0.013; 12m59-12m85 (1SWASP mag).
An additional, possibly non-radial, pulsation fn was found with certainty in the g-band ASAS-SN data; in the V-band ASAS-SN and 1SWASP data, it is uncertain. Its light elements are the following:
HJD(max) = 2458888.0410 + 0d07345498 xE. The semi-amplitudes An are 0.007: (aV), 0.008 (ag), 0.003: (1SWASP mag). The period ratio Pn/P0 = 0.7857 possibly corresponds to the P1/P0 ratio, but P2/Pn = 0.7766 does not correspond to the P2/P1 ratio.
MMRP-088. The amplitudes and magnitude range in the i band of ZTF data: A0 = 0.039, A1 = 0.108; 19m26-19m83.
MMRP-090. The amplitude and magnitude range in the i band of ZTF data: A0 = 0.085, A1 = 0.111; 17m 12-17™71.
MMRP-091. Type D01^D0 is not excluded. ASAS-SN data were analyzed in four separate time intervals:
I, JD 2457400-2458100, V band;
II, JD 2458100-2458800, V and g bands;
III, JD 2458800-2459500, g band;
IV, JD 2459600-2460400, g 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 g-band data was possibly detected (very uncertainly) with a small amplitude and a different period. The possible period P1 = 0d0545112:, A1 = 0.014 (ag). In V-band data for the time interval II, fi was not detected. In the data for the time intervals III and IV, fi was not detected.
The fundamental-mode period P0 varies, the following light elements were derived for separate time intervals:
II: HJD(max) = 2458500.0423 + 0d0707801 xE; Ao = 0.201 (ag), 0.167 (aF); III: HJD(max) = 2459200.0544 + 0d0707797 xE; A0 = 0.201 (ag); IV: HJD(max) = 2460000.0212 + 0d0707817 xE; A0 = 0.199 (ag).
In the earlier time interval of 1SWASP data, JD 2453860-2454275, double-mode periodicity was detected with the following elements:
f0: HJD(max) = 2454054.0025 + 0d0707800 xE; M-m = 0.40, f1: HJD(max) = 2454054.0025 + 0d0545125 xE; M-m = 0.45.
The semi-amplitudes are A0 = 0.186, A1 = 0.055 (1SWASP mag).
In the 1SWASP data, after removing the radial frequencies f0 and f1 as well as interaction frequencies (f1 + f0 and f1 — f0), a possible non-radial oscillation fn with the period Pn = 0d0369620 is detected, An = 0.018 (1SWASP mag). In the F-band ASAS-SN data for all time intervals (I and II), this frequency is not detected. In the g-band ASAS-SN data for all time intervals (II, III and IV), this oscillation is detected: II: Pn = 0d0369614:, An = 0.015; III: Pn = 0d03696196, An = 0.020; IV: Pn = 0d0369631, An = 0.012.
MMRP-092. The magnitude range according to CSS data: 17m06-17"61 (CF). In CSS data, P0 is not detected.
MMRP-093. The amplitudes and magnitude range in the i band of ZTF data: A0 = 0.081, A1 = 0.115; 17m04-17"52.
MMRP-094. Data from 1SWASP were used to improve the light elements. The amplitudes and magnitude range in the 1SWASP data: A0 = 0.146, A2 = 0.016; 13m08-13m54 (1SWASP mag).
MMRP-095. The amplitudes and magnitude range in the i band of ZTF data: A0 = 0.091, A1 = 0.119; 17m31-17m82. The amplitudes and magnitude range according to CSS data: A0 = 0.099, A1 = 0.137; 17m04-17m93 (CF). Data from CSS were used to improve the light elements.
MMRP-098. The amplitudes and magnitude range in the i band of ZTF data: A0 = 0.054, A1 = 0.130; 18m79-19m34. In CSS data, the fundamental mode period P0 is not detected, magnitude range 18m7-19m6 (CF).
MMRP-099. In ASAS-SN F-band data, the second-overtone frequency f2 is not detected. Amplitude modulation is not excluded.
MMRP-100. An additional non-radial pulsation with the period Pn = 0d 1351951, or Blazhko effect of the second-overtone oscillation with n = 3d4496. Semi-amplitude An is 0.022 (aF), 0.023 (ag).
Data from 1SWASP were used to improve the light elements. The semi-amplitudes are A1 = 0.059, A2 = 0.016, A3 = 0.028, An = 0.014. Blend in 1SWASP data.
MMRP-103. According to 1SWASP data, the light elements are: f0: HJD(max) = 2454150.0410 + 0d0706180 xE;
fl: HJD(max) = 2454150.0124 + 0d0546466 xE. The magnitude range and semi-amplitudes according to 1SWASP data: 13m75-14m 15, A0 = 0.101, Ai = 0.026.
MMRP-104. A possible non-radial oscillation with the period Pn = 0t?0520505; the semi-amplitude An is 0.021 (zg), 0.016 (zr). Pn/Pl = 0.8133, 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 zg, zr, and ag bands, the brightening trend was excluded before the amplitude analysis, its full amplitude being 0.018 (zg), 0.021 (zr), and 0.110 (ag). In the aV-band data (an earlier time interval), the trend was not detected.
MMRP-107. An additional non-radial pulsation fn with the following light elements (ASAS-SN and ZTF data):
HJD(max) = 2458888.032 + 0d05108950 xE; the semi-amplitude An is 0.012 (aV), 0.012 (ag), 0.007 (zr), 0.010 (zg); M-m = 0.45.
Light elements for the CSS (JD 2453568-2456446) and 1SWASP (JD 2453860-2454615) time intervals:
fi: HJD(max) = 2455055.0333 + 0d0767249 xE; f3: HJD(max) = 2455055.0225 + 0d0515180 xE; fn: HJD(max) = 2455055.0406 + 0d0510897 xE. The magnitude ranges and semi-amplitudes according to 1SWASP and CSS data: 13m52-13m82 (CV), 13m85-14m 18 (1SWASP mag); Ai is 0.068 (CV), 0.058 (1SWASP mag); A3 is 0.018 (CV), 0.015 (1SWASP mag); An is 0.013 (CV), 0.007 (1SWASP mag).
MMRP-108. The first-overtone period Pi possibly varies. Light elements for the CSS time interval:
f0: JD(max) = 2455055.0276 + 0d0644806 xE; fi: JD(max) = 2455055.0075 + 0d0502488 xE. The magnitude range and semi-amplitudes: 15m 18-15m61 (CV), A0 = 0.072, Ai = 0.070.
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 f2 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, fi — f0 = f2 — fi = f3 — f2 = 1.0062. Frequencies
f0 and fi are not in doubt, but the frequencies f2 and f3 of this equidistant quadruplet can be considered interaction frequencies of the two main oscillations: f2 = 2fi — f0 and f3 = 3fi — 2f0.
Thus, in this case, we have two main frequencies f0 and fi; in addition to them, interaction frequencies fi + f0, 2fi — f0, fi — f0, 3fi — 2f0 and fi + 2f0 are also detected (in the order of decreasing amplitude).
Usually, the frequencies 2fi — f0 and especially 3fi — 2f0 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 (M-m = 0.55) of its first-overtone light curve is worth noting.
4.2 Pulsation modes of MMRP-086
MMRP-086 was classified as a 5 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 fn was found with certainty in the g-band ASAS-SN data, but it is not detected or uncertain in the other photometric data (V-band ASAS-SN and 1SWASP). The period ratio Pn/P0 = 0.7857 may correspond to the Pi/P0 ratio, but P2/Pn = 0.7766 does not correspond to the P2/Pi ratio. Therefore, I do not consider fn 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 D01^D0 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 5 Sct stars from the Zwicky Transient Facility Survey. A number
of stars from our publication were included in this work. These are objects MMRP 051057, 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 P3/P2 = 0.8133) and gave the star the D01n type; MMRP-105 was classified by Jia et al. (2024) as a double-mode 8 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 zg and zr 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.
References:
Bellm, E. C., Kulkarni, S. R., & Graham, M. J. 2019, Publ. Astron. Soc. Pacific, 131, 018002
Butters, O. W., West, R. G., Anderson, D. R., et al. 2010, Astron. & Astrophys., 520, L10
Chen, X., Wang, S., Deng, L., et al. 2020, Astrophys. J., Suppl. Ser., 249, id. 18 Drake, A. J., Djorgovski, S. G., Mahabal, A., et al. 2009, Astrophys. J., 696, 870 Gaia Collaboration, Brown, A.G.A., Vallenari, A., Prusti, T., et al. 2018, Astron. &
Astrophys., 616, id. A1 Gaia Collaboration, 2022, Gaia DR3 Part 4. Variability, VizieR On-line Data Catalog: I/358
Jayasinghe, T., Kochanek, C. S., Stanek, K. Z., et al. 2018, Mon. Notices Roy. Astron. Soc., 477, 3145
Jayasinghe, T., Kochanek, C. S., Stanek, K. Z., et al. 2021, Mon. Notices Roy. Astron. Soc., 503, 200
Jayasinghe, T., Stanek, K. Z., & Kochanek, C. S. 2019a, Mon. Notices Roy. Astron. Soc., 486, 1907
Jayasinghe, T., Stanek, K. Z., & Kochanek, C. S. 2019b, Mon. Notices Roy. Astron. Soc., 485, 961
Jayasinghe, T., Stanek, K. Z., & Kochanek, C. S. 2020, Mon. Notices Roy. Astron. Soc., 491, 13
Jia, Q., Chen, X., Wang, S., et al. 2024, Astrophys. J, Suppl. Ser., 273, id. 7 Khruslov, A. V. 2023, Perem. Zvezdy, 43, No. 7, 55
Kochanek, C. S., Shappee, B. J., Stanek, K. Z., et al. 2017, Publ. Astron. Soc. Pacific, 129, 104502
Malanchev, K. L., Pruzhinskaya, M. V., Korolev, V. S., et al. 2021, Mon. Notices Roy.
Astron. Soc., 502, 5147 Masci, F. J., Laher, R. R., & Rusholme, B. 2019, Publ. Astron. Soc. Pacific, 131, 018003 Netzel, H., Pietrukowicz, P., Soszynski, I., & Wrona, M. 2022, Monthly Notices Roy.
Astron. Soc., 510, 1748 Petersen, J. O. 1973, Astron. & Astrophys., 27, 89
Petersen, J. O., & Christensen-Dalsgaard, J. 1996, Astron. & Astrophys., 312, 463
Samus, N. N., Kazarovets, E. V., Durlevich, O. V., Kireeva, N. N., Pastukhova, E. N.
2017, Astron. Rep., 61, 80 Shappee, B. J., Prieto, J. L., Grupe, D., et al. 2014, Astrophys. J., 788, 48 Smolec, R. & Moskalik, P. 2010, Astron. & Astrophys., 524, A40 Sokolovsky, K. V., 2007, Perem. Zvezdy Prilozh., 7, No. 30
4.6
No.
ÔÏÔ
051
052
053
054
055
056
057
058
059
060
061
062
063
064
065
066
067
068
069
070
071
Supplement Tables
Table 2: Semi-amplitudes and magnitude ranges
Semi-amplitudes
Magnitude ranges
aV ag zr zg aV ag zr zg
0.143 0.164 0.112 0.162 14.00- 14.37- 13.68- 14.32-
0.120 0.136 0.102 0.130 14.74 15.21 14.26 15.17
- - 0.142 0.210 - - 17.32- 17.67-
- - 0.012 0.018 17.71 18.24
- - 0.089 0.139 - - 17.51- 17.84-
- - 0.035 0.054 17.89 18.43
- - 0.095 0.140 - - 17.12- 17.63-
- - 0.117 0.162 17.72 18.50
- - 0.121 0.183 - - 15.85- 16.05-
- - 0.009 0.017 16.15 16.50
- - 0.043 0.060 - - 16.23- 17.33-
- - 0.079 0.112 16.56 17.83
0.033 0.045 0.023 0.035 15.18- 15.44- 14.99- 15.47-
0.115 0.131 0.087 0.140 15.72 16.00 15.32 15.90
<0.016 0.014: 0.012 0.016
- - 0.115 0.170 - - 16.97- 17.18-
- - 0.023 0.031 17.31 17.69
- - 0.132 0.179 - - 15.91- 16.02-
- - 0.159 0.222 16.60 16.97
- - 0.053 0.080 - - 17.76- 19.27-
- - 0.042 0.063 18.08 19.73
- - 0.181 0.245 - - 17.19- 17.77-
- - 0.017 0.029 17.73 18.52
- 0.118 0.103 0.154 16.2:- 16.4- 15.92- 16.31-
- 0.118 0.103 0.146 16.7: 17.2 16.55 17.20
0.225 0.245 0.173 0.239 13.47- 13.58- 13.58- 13.55-
0.015 0.025 0.018 0.031 14.06 14.25 14.03 14.20
- - 0.118 0.175 - - 15.26- 17.79-
- - 0.009 0.018 15.63 18.30
- - 0.142 0.211 - - 16.45- 17.35-
- - 0.016 0.023 16.83 17.95
- - 0.116 0.174 - - 16.63- 16.88-
- - 0.053 0.082 17.12 17.55
- - 0.120 0.162 - - 18.13- 18.44-
- - 0.016 0.016: 18.54 18.98
0.113 0.168 0.140 0.204 15.6- 16.0- 15.38- 16.03-
<0.040 <0.020 0.010 0.011 15.9 16.4 15.75 16.57
- - 0.214 0.308 - - 18.00- 19.3-
- - 0.015 0.019: 18.63 20.2
- - 0.153 0.221 - - 16.52- 17.34-
- - 0.024 0.042 16.96 17.95
- - 0.070 0.105 - - 16.62- 17.59-
- - 0.015 0.018 16.84 17.93
- - 0.059 0.086 - - 18.10- 19.27-
No.
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
090
091
092
Table 2: Semi-amplitudes and magnitude ranges
Semi-amplitudes Magnitude ranges
aF ag zr zg aF ag zr zg
- - 0.053 0.070 18.45 19.85
- - 0.099 0.145 - - 17.43- 18.32-
- - 0.026 0.042 17.77 18.85
- - 0.065 0.093 - - 16.34- 16.94-
- - 0.019 0.028 16.56 17.24
- - 0.152 0.248 - - 18.09- 19.83-
- - 0.054 0.101 18.63 20.85
0.150 0.170 0.101 0.168 13.69- 14.00- 13.56- 13.92-
0.044 0.063 0.042 0.061 14.20 14.59 13.93 14.45
0.097: 0.109: 0.120 0.167 15.65- 16.0- 15.64- 16.45-
0.018: 0.017: 0.017 0.023 16.05: 16.5 15.97 16.90
- - 0.119 0.176 - - 17.02- 17.86-
- - 0.012 0.016 17.37 18.38
- - 0.051 0.068 - - 16.27- 17.11-
- - 0.057 0.083 16.60 17.56
- - 0.023 0.033
- - 0.029 0.042
- - 0.137 0.200 - - 17.41- 18.09-
- - 0.018 0.021 17.83 18.70
- - 0.177 0.234 - - 16.60- 16.59-
- - 0.042 0.058 17.17 17.42
0.090 0.101 0.076 0.106 13.28- 13.55- 13.20- 13.64-
<0.007 0.012 0.009 0.010 13.56 13.91 13.41 13.97
0.021 0.018 0.013 0.018
- 0.232 0.157 0.224 13.67- 13.69- 13.73- 13.72-
- 0.032 0.023 0.035 14.06 14.30 14.15 14.33
0.077 0.101 - - 13.16- 13.36- - -
0.012 0.011 - - 13.43 13.69
- - 0.041 0.058 - - 18.54- 18.60-
- - 0.165 0.224 19.18 19.40
- - 0.136 0.194 - - 16.77- 16.74-
- - 0.152 0.235 17.48 17.73
0.113 0.135 - - 12.64- 12.80- - -
0.010 0.013 - - 12.96 13.18
0.200 0.235 - - 13.94- 14.29- - -
0.023 0.025 - - 14.52 15.01
- - 0.038 0.057 - - 19.27- 19.32-
- - 0.149 0.216 19.85 20.15
0.093 0.102 - - 13.15- 13.61- - -
0.028 0.037 - - 13.55 14.10
0.034 0.040 - -
- - 0.128 0.182 - - 17.00- 16.99-
- - 0.156 0.220 17.79 18.01
0.141 - - - 13.90- 14.33- - -
0.071 - - - 14.55 14.92
- - 0.023 0.033 - - 17.20- 17.29-
Table 2: Semi-amplitudes and magnitude ranges
No. Semi-amplitudes Magnitude ranges
aF ag zr zg aF ag zr zg
- - 0.159 0.231 17.65 17.89
093 - - 0.110 0.151 - - 16.93- 16.86-
- - 0.156 0.222 17.57 17.80
094 0.151 0.177 0.116 0.165 12.83- 13.14- 12.65- 13.13-
0.014 0.020 0.010 0.020 13.23 13.61 12.95 13.55
095 - - 0.112 0.169 - - 17.20- 17.11-
- - 0.159 0.226 17.87 18.11
096 0.062 0.075 - - 11.60- 11.76- - -
0.015 0.015 - - 11.81 12.00
097 0.196 0.235 - - 14.41- 14.48- - -
0.050 0.063 - - 15.18 15.40
098 - - 0.065 0.097 - - 18.76- 18.70-
- - 0.152 0.234 19.35 19.62
099 0.073 0.070 0.060 0.088 14.7- 15.2- 14.47- 15.37-
<0.027 0.027 0.023 0.028 15.2 15.7 14.72 15.72
0.038 0.024 0.020 0.034
100 0.082 0.099 - - 12.17- 12.38- - -
0.023 0.028 - - 12.52 12.83
0.038 0.043 - -
101 - - 0.045 0.062 - - 19.2- 19.5-
- - 0.143 0.217 19.7 20.4
102 0.063 0.065 - - 14.95- 15.10- - -
0.056 0.062 - - 15.37 15.60
103 0.127 0.152 0.104 0.141 13.51- 13.60- 13.60- 13.67-
0.039 0.051 0.028 0.048 14.00 14.16 13.98 14.12
104 - - 0.075 0.108 - - 17.23- 17.58-
- - 0.081 0.110 17.69 18.25
105 0.105 0.128 0.108 0.174 13.75- 14.05- 13.73- 14.41-
0.011 0.014 0.012 0.018 14.08 14.50 14.05 14.87
0.010 0.007 0.007 0.010
106 0.039: 0.041: 0.077 0.128 14.6:- 14.65:- 15.17- 15.67-
0.011: 0.006: 0.010 0.013 14.75: 14.85: 15.41 16.03
107 0.083 0.093 0.050 0.083 13.75- 13.92- 13.73- 13.96-
0.018 0.019 0.013 0.019 14.05 14.24 13.91 14.20
108 0.088 0.110 - - 15.10- 15.15- - -
0.087 0.115 - - 15.65 15.80
109 - - 0.081 0.104 - - 17.18- 17.54-
- - 0.062 0.091 17.61 18.12
110 - - 0.180 0.259 - - 16.06- 16.84-
- - 0.018 0.024 16.53 17.52
A.V.
noT
ölö"
051
052
053
054
055
056
057
058
059
060
061
062
063
064
065
066
067
068
069
070
071
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
090
091
092
093
094
Table 3: Color indices and Galactic latitude
J - K, B - V, g' - r', g - V, g - r b, deg
2MASS APASS APASS ASAS-SN ZTF
0.47 0.91 0.72 0.45 0.82 -2.9
0.24: 0.48 0.50 - 0.46 -9.1
0.46: - - - 0.47 -6.0
0.53 - - - 0.69 -5.9
0.29 0.46 0.25 0.23: 0.29 -9.1
0.69 0.76 1.12 - 1.19 +2.1
0.35 0.75 0.53 0.30 0.55 -5.1
0.55 - - - 0.31 -8.4
0.47: 0.42 0.27 - 0.27 -12.0
0.90 - - - 1.60 + 1.6
0.59 - - - 0.69 -7.5
0.40 0.59 0.57 0.45 0.62 -4.0
0.17 0.39 0.08 0.17 0.11 -15.2
0.33 - - - 0.60 -6.0
0.42 - - - 1.02 +5.9
0.63 - - - 0.37 -10.2
- - - - 0.39 +9.1
0.53 1.09 - 0.46 0.77 +2.6
0.73 - - - 1.41 +5.0
0.58 0.51 0.57 - 0.90 +1.7
0.65 - - - 1.04 +4.5
0.97 - - - 1.30 +5.0
0.37 - - - 0.98 +3.8
0.38 0.68 0.58 - 0.63 +10.7
0.91 - - - 1.99 +0.9
0.36 0.72 0.58 0.36 0.45 -12.5
0.45 0.93 0.76 0.37 0.86 +4.0
0.69 - - - 0.93 + 1.1
0.71 - - - 0.90 +4.1
0.43: - - - 0.78 +5.0
0.16: 0.41 0.20 - 0.19 + 18.1
0.39 0.61 0.44 0.33 0.51 +7.7
0.18 0.27 0.10 0.15 0.11 +27.5
0.20: 0.42 0.28 0.23 - -5.9
- - - - 0.13 +74.4
0.74 - - - 0.14 +48.5
0.21 0.44 0.24 0.21 - + 15.0
0.45 0.89 0.78 0.44 - +7.4
- - - - 0.18 +45.2
0.60 1.06 1.02 0.49 - -4.8
- - - - 0.14 +34.5
0.29 0.61 0.40 0.34 - + 11.2
- 0.03 0.54 - 0.16 +44.8
- - - - 0.10 +37.6
0.39 0.72 0.74 0.35 0.57 +18.7
Table 3: Color indices and Galactic latitude
No. J - K, B - V, g'- r', g - V, g - r b, deg
2MASS APASS APASS ASAS-SN ZTF
095 1.25: - - - 0.11 +39.8
096 0.22 0.60 0.27 0.17 - -0.5
097 0.17 0.40 0.20 0.18 - -15.9
098 - - - - 0.12 +27.6
099 1.23 0.97 0.91 0.45 0.94 +0.9
100 0.23 0.35 0.18 0.27 - + 14.5
101 - - - - 0.53 + 10.8
102 0.23 0.45 0.17 0.20 - -14.1
103 0.15 0.33 0.04 0.16 0.12 -16.4
104 0.84 - - - 0.51 -4.0
105 0.41 0.96 0.71 0.40 0.76 -2.7
106 0.44 0.80 0.50 0.09: 0.58 -3.7
107 0.21 0.44 0.28 0.20 0.24 -24.1
108 0.39 0.21 0.09 0.10 - -37.0
109 - - 0.30 - 0.43 -8.1
110 0.49 - - - 0.91 +2.2
Figure 2. The light curves and power spectra of MMRP-086 (D02n: type) from g-band ASAS-SN data.
Figure 3. The Petersen diagram for the multi-periodic stars of the MMRP catalog: blue - stars of the MMRP-I catalog, red - stars of the MMRP-II catalog (this paper); circles - double-mode stars, triangles - triple-mode stars, squares - quadruple-mode variables.
