|
Peremennye Zvezdy (Variable Stars) 43, No. 7, 2023 Received 28 August; accepted 10 September. |
Article in PDF |
|
DOI: 10.24412/2221-0474-43-55-85
|
Catalog of Multi-Mode Radially Pulsating Variables: I
A. V. Khruslov1,2
- 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
I present a catalog of newly detected Multi-Mode
Radially Pulsating (MMRP) variable stars that pulsate in the
fundamental, first, second, or third-overtone modes. This catalog
includes 50 double- and multi-mode stars. Among variability types
of these stars, we find classical Cepheids, RR Lyrae, and
high-amplitude  Scuti (HADS) variables. Additionally, I
studied 14 known multi-periodic variables.
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
In the course of my search for double-mode and multiperiodic
variable stars using available photometric archives, I detected 50
new Multi-Mode Radially Pulsating (MMRP) variables. These stars
pulsate in the fundamental, first-overtone, second-overtone, or
third-overtone modes. This article continued the series of my
previous papers (Khruslov. 2018a, 2021a, 2022, etc.). Among
variability types of these stars, we find classical Cepheids, RR
Lyrae stars, and high-amplitude Scuti variables.
Additionally, I studied 14 known multi-periodic variables (see additional Tables with index 'a') as a part of the program of preparation for their inclusion in the General Catalog of Variable Stars, GCVS (Samus et al., 2017).
Searching for double periodicity, I mainly used data available in the photometric archive of the All-Sky Automated Survey for Supernovae (ASAS-SN, Shappee et al., 2014; Kochanek et al., 2017) and the Zwicky Transient Facility (ZTF, Bellm et al., 2019; Masci et al., 2019)
The method I use to search for multiperiodicity is similar to that described in my earlier paper (Khruslov, 2021). To search for candidate multi-mode variables, I used AAVSO VSX1database, the ASAS-SN catalogs of variable stars2 database (Jayasinghe et al., 2018, 2019a, 2019b, 2020, 2021), ZTF catalog of periodic variable stars3, Chen et al. (2020).
The radial pulsation modes were identified by their period ratio
(
); see the study on this problem by
Petersen (1973), Petersen & Christensen-Dalsgaard (1996), Smolec
& Moskalik (2010), and others.
2. Photometric data
For this study, I used the data of the
ASAS-SN4 database and the ZTF
data available through the SNAD ZTF
viewer5, Malanchev et al. (2021).
The light elements are based on data from these two surveys,
individual cases are described in Comments. The magnitude ranges
and amplitudes in the tables are given according to this data. I
used 
and 
bands of ASAS-SN, and 
and bands of ZTF.
Additionally, in individual cases, I analyzed available data from other archives: the Wide Angle Search for Planets (SuperWASP6, Butters et al., 2010; 8 variables), the Catalina Sky Surveys (CSS7, Drake et al., 2009; 5 variable), the All Sky Automated Survey (ASAS-38, Pojmanski 2002; 2 variables).
The ASAS-3 data used in this paper were downloaded before April 2022, in accordance to requirements of authors of this survey for users located in Russia.
The SuperWASP observations are available as FITS tables, which were converted into ASCII tables using the OMC2ASCII9program, as described by Sokolovsky (2007).
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. This file also includes all light curves of the variables and cross-identification tables for all stars.
In individual cases, the ZTF data contained continuous data series with duration of a whole night of observations. This created some difficulties in the analysis of data. To eliminate these problems, we used averaged values (the mean for about 10 neighboring points) for our analysis. These averaged values are presented in the data files below the main data series. The rows of these supplements contain mean HJD times, mean magnitudes, and number of averaged points.
3. Identification names
In this paper, the following identification names are used for variables.
For new multi-periodic stars, with multi-periodicity first detected in this study, I use designations of the form MMRP-XXX (where MMRP is the name of the present program, aimed at discoveries of Multi-Mode Radially Pulsating variables, and XXX is the sequence number in the catalog). An example: MMRP-010.
For the known multi-periodic stars, for which this paper presents new light elements, I used designations in the form MMRP_JXXXXXX.XX+XXXXXX.X (the abbreviation MMRP followed with equatorial coordinates for the equinox 2000.0). An example: MMRP_J054223.13+275647.6.
4. Classification
In the present paper, I use an original notation for types of multiperiodic variables. The basics of the classification were presented by N.N. Samus and the GCVS team at the XXVI IAU General Assembly in Prague, 200610: classical GCVS types of radial pulsating variables were appended with numbers of pulsation modes (0 - fundamental mode, 1 - first overtone, 2 - second overtone). Double-mode variables are marked with a set of detected modes. For example, RR Lyrae stars can be designated as RR0, RR1, and RRB01 (in the old system, RRAB, RRC, and RR(B), respectively, B meaning "beat"). A similar notation was proposed for classical Cepheids (DCep0, DCep1, DCepB01, and DCepB12).
In the new MMRP classification, the numerical identification of pulsation modes is preserved, and the variability type is designated with a single letter. Additional characteristics are introduced with an additional index. An arrow indicates the cases of mode switching.
I. Types of variable stars:
C - classical Cepheids;
W - W Virginis, or type II Cepheids;
R - RR Lyrae stars;
D - Scuti stars.
II. Numbers of pulsation modes:
0 - fundamental mode;
1 - first overtone;
2 - second overtone;
3 - third overtone.
III. Addition designations:
n - additional non-radial mode;
m - amplitude modulation;
- mode switching.
Examples of designations of multi-periodic variables: C01, C12,
C12m, D01, D123, D23, D12n, D0123, R01, W01, C12C1,
R01R0, R1R01.
The classical GCVS designations of mono-periodic variability types can be converted as follows: DCEP = C0, DCEPS = C1, RRAB = R0, RRC = R1; for multi-mode variable types, RR(b) type can be written as R01 (there are no R12 stars confirmed with certainty); CEP(B) is a group of types designated as C01, C12, C012, C123, and W01; DSCT(B) and SXPHE(B) is a group of all multi-mode D types.
The types from the VSX database are converted as follows: RRd = R01; DCEP(B) = C01; DCEPS(B) = C12; CWB(B) = W01; HADS(B) is a group of all multi-mode D types.
Double-mode type II Cepheids (W Virginis type) and mode-switching
stars are not included in this catalog. An example of a W01 star,
USNO-B1.0 0992-0344981, can be found in Khruslov (2021). An
example of an R01R0 star is USNO-B1.0 1171-0309158, see
Khruslov et al. (2017). Other stars of these types may be included
in later issues of MMPR catalogs.
in addition to type C12, I used type C*12 that includes stars morphologically close to type C12 but with shorter periods characteristic of R1 stars (see Subsection 6.3).
Besides the basic classification, I used two other indices: n for cases of detected additional non-radial modes; m for detected amplitude modulation with slow variation from one season to another.
5. Results
5.1. Tables
For a correct presentation of information on multi-periodic variables in the MMRP catalog Tables, I use a multi-row format, with data presented in several sub-rows, each of them corresponding to an individual detected radial pulsation mode. Modes of pulsations are arranged in order of increasing pulsation frequency: the top sub-row is fundamental mode, the first overtone is below it, still lower are the second overtone, third overtone, and so on.
Each multi-row of the main Table (see Tables 1 and 1a) contains general information on the star: number in the Catalog of Multi-Mode Radially Pulsating (MMRS) stars; equatorial coordinates J2000 (for the earlier known MMRP stars, the coordinates are a part of the name); magnitude range (magnitudes at maximum and at minimum); 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 (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 EDR3
catalog. The tabulated magnitude range is for the photometric band
indicated in brackets (
and 
are ASAS-SN and
magnitudes; 
and 
are ZTF and magnitudes). The
data in these two columns are in two adjacent sub-rows.
Coordinates: top - Right Ascension, bottom - Declination;
magnitude range: top - maximum, bottom - minimum.
Individual mode characteristics: period is expressed in days;
epoch is in one of the following formats:
or
; semi-amplitude in
the photometric band indicated in the "Magn." column; the M-m
parameter is expressed in fractions of the period.
Tables 2 and 2a contain references to comments that supplement the data in the main table, and also provide information about the history of the variability studies for individual stars. The numbers correspond to the list below the tables.
Tables that supplement the main Table (Table 1 with Comments)
follow, they contain general information on the stars. Tables 3
and 3a contain semi-amplitudes and magnitude ranges in all bands
used in the ASAS-SN and ZTF surveys: , , , and .
The data in "Magnitude range" columns is separated between two
adjacent sub-rows: top - maximum, bottom - minimum. These tables
contains amplitudes for four bands, so they partially duplicate
Tables 1 and 1a. Tables 4 and 4a contain the known information
according to catalogs and photometric surveys: color indices 
(2MASS), 
and 
(APASS), 
(ASAS-SN), and 
(ZTF); and Galactic latitude (in degrees). These data are used for
classification of variables.
Table 1. New MMRP variables
| MMRP | J2000 | Magn. | Type | Period | Epoch | Ampl. | M-m |  |
| 001 | 00 02 40.26 | 17.12 - | D12m | 0.221546 | b0.020 | 0.159 | 0.40 | 0.8028 |
| +62 48 07.1 | 17.63 () |
0.177851 | b0.150 | 0.060 | 0.50 | |||
| 002 | 00 14 03.41 | 15.40 - | D123 | 0.2402248 | b0.2335 | 0.149 | 0.44 | 0.7984 |
| +61 51 26.8 | 15.94 () |
0.1917915 | b0.1130 | 0.034 | 0.47 | 0.8339 | ||
| 0.1599293 | b0.0683 | 0.039 | 0.45 | |||||
| 003 | 00 53 46.41 | 17.73 - | R01 | 0.553765 | b0.060 | 0.086 | 0.44 | 0.7465 |
| +16 30 17.6 | 18.47 () |
0.413406 | b0.345 | 0.224 | 0.34 | |||
| 004 | 01 04 59.14 | 16.12 - | C12 | 0.517962 | b0.234 | 0.230 | 0.50 | 0.8022 |
| +63 11 37.9 | 16.70 () |
0.415517 | b0.282 | 0.018 | 0.48 | |||
| 005 | 01 22 26.27 | 12.26 - | C*12 | 0.419811 | b0.347 | 0.140 | 0.50 | 0.7999 |
| +59 12 36.2 | 12.68 () |
0.335806 | b0.069 | 0.035 | 0.46 | |||
| 006 | 01 41 37.16 | 17.66 - | R01 | 0.547006 | b0.148 | 0.059 | 0.44 | 0.7469 |
| +49 06 30.3 | 18.41 () |
0.408560 | b0.132 | 0.238 | 0.35 | |||
| 007 | 02 35 16.88 | 13.94 - | D12 | 0.1171010 | a0.0560 | 0.118 | 0.38 | 0.8161 |
| +45 29 06.0 | 14.32 () |
0.0955676 | a0.0013 | 0.036 | 0.46 | |||
| 008 | 03 28 13.47 | 15.16 - | C12 | 0.76234 | b0.703 | 0.133 | 0.45 | 0.8066 |
| +61 04 11.4 | 15.58 () |
0.61488 | b0.585 | 0.045 | 0.45 | |||
| 009 | 04 50 39.61 | 14.44 - | C12 | 0.481392 | a0.122 | 0.257 | 0.49 | 0.8014 |
| +44 56 33.7 | 15.11 () |
0.385787 | a0.128 | 0.043 | 0.48 | |||
| 010 | 04 53 16.75 | 14.37 - | D0123 | 0.323070 | b0.036 | 0.164 | 0.37 | 0.7547 |
| +39 14 18.2 | 15.21 () |
0.243812 | b0.100 | 0.136 | 0.55 | 0.8030 | ||
| 0.195780 | b0.113 | 0.025 | 0.43 | 0.8354 | ||||
| 0.163560 | b0.147 | 0.023 | 0.50: | |||||
| 011 | 05 55 38.69 | 13.99 - | C*12 | 0.372014 | b0.039 | 0.193 | 0.52 | 0.8016 |
| +27 03 19.9 | 14.48 () |
0.298223 | b0.185 | 0.022 | 0.50 | |||
| 012 | 06 32 45.23 | 12.56 - | D012 | 0.1202966 | a0.1160 | 0.005 | 0.47 | 0.7568 |
| -57 48 19.8 | 13.04 () |
0.0910362 | a0.0660 | 0.187 | 0.36 | 0.8044 | ||
| 0.0732255 | a0.0314 | 0.013 | 0.45 | |||||
| 013 | 06 35 07.25 | 18.12 - | R01 | 0.485603 | b0.415 | 0.127 | 0.44 | 0.7444 |
| -02 24 39.4 | 18.81 () |
0.361474 | b0.370 | 0.155 | 0.38 | |||
| 014 | 07 04 53.11 | 16.53 - | D012 | 0.0990373 | b0.0412 | 0.208 | 0.33 | 0.7822 |
| +72 56 03.8 | 17.61 () |
0.0774669 | b0.0343 | 0.111 | 0.41 | 0.8068 | ||
| 0.0625011 | b0.0240 | 0.036 | 0.43 |
Table 1 (continued)
| MMRP | J2000 | Magn. | Type | Period | Epoch | Ampl. | M-m | |
| 015 | 07 17 06.72 | 14.11 - | D12 | 0.1777760 | b0.1080 | 0.128 | 0.45 | 0.8026 |
| +02 10 06.3 | 14.50 () |
0.1426887 | b0.1100 | 0.032 | 0.48 | |||
| 016 | 07 19 18.34 | 14.01 - | D12m | 0.09090585 | a0.0800 | 0.164 | 0.41 | 0.7991 |
| -57 21 50.8 | 14.50 () |
0.07264440 | a0.0595 | 0.032 | 0.45 | |||
| 017 | 07 34 28.23 | 16.36 - | R01 | 0.517177 | b0.253 | 0.069 | 0.46 | 0.7463 |
| -09 23 48.5 | 17.09 () |
0.385962 | b0.225 | 0.231 | 0.36 | |||
| 018 | 07 41 56.58 | 13.68 - | D12 | 0.1170699 | a0.0088 | 0.141 | 0.48 | 0.8008 |
| -05 35 59.7 | 14.10 () |
0.0937507 | a0.0044 | 0.027 | 0.46 | |||
| 019 | 07 42 26.28 | 12.66 - | D12m | 0.1633818 | b0.1555 | 0.080 | 0.54 | 0.7976 |
| -48 26 25.9 | 12.90 () |
0.1303208 | b0.1240 | 0.007 | 0.48 | |||
| 020 | 08 09 53.53 | 12.66 - | D23 | 0.1894973 | b0.063 | 0.174 | 0.30 | 0.8284 |
| -24 00 01.5 | 13.16 () |
0.1569780 | b0.095 | 0.034 | 0.48 | |||
| 021 | 09 20 33.29 | 13.24 - | C12 | 0.962282 | b0.550 | 0.100 | 0.44 | 0.8041 |
| -53 23 17.3 | 13.57 () |
0.773766 | b0.567 | 0.026 | 0.50: | |||
| 022 | 10 14 19.37 | 14.74 - | D01n | 0.1849927 | b0.0420 | 0.113 | 0.38 | 0.7643 |
| -45 08 07.4 | 15.38 () |
0.1413880 | b0.0640 | 0.108 | 0.55 | |||
| 023 | 10 17 57.49 | 12.99 - | D12 | 0.1604404 | b0.1380 | 0.106 | 0.53 | 0.7925 |
| -43 33 27.5 | 13.30 () |
0.1271510 | b0.0520 | 0.013 | 0.46 | |||
| 024 | 10 20 35.06 | 13.50 - | D012m | 0.1828460 | b0.1275 | 0.103 | 0.40 | 0.7663 |
| -45 27 09.0 | 14.03 () |
0.1401066 | b0.0290 | 0.105 | 0.59 | 0.8001 | ||
| 0.1120996 | b0.1050 | 0.011 | 0.50 | |||||
| 025 | 11 00 35.99 | 17.95 - | D01 | 0.0762403 | b0.0522 | 0.134 | 0.39 | 0.7778 |
| -00 33 15.9 | 18.50 () |
0.0592999 | b0.0572 | 0.057 | 0.49 | |||
| 026 | 12 18 49.01 | 13.73 - | D12 | 0.1206566 | a0.0237 | 0.132 | 0.56 | 0.8004 |
| -40 36 23.7 | 14.11 () |
0.0965767 | a0.0860 | 0.012 | 0.47 | |||
| 027 | 14 00 12.79 | 11.46 - | C*12 | 0.3422644 | b0.886 | 0.086 | 0.47 | 0.7993 |
| -57 59 22.8 | 11.75 () |
0.2735650 | b0.876 | 0.021 | 0.46 | |||
| 028 | 15 23 19.83 | 15.52 - | D01 | 0.06193270 | b0.0094 | 0.184 | 0.40 | 0.7734 |
| -29 23 55.8 | 16.25 () |
0.04790184 | b0.0090 | 0.044 | 0.48 | |||
| 029 | 16 36 55.57 | 14.12 - | D01 | 0.0961730 | b0.0150 | 0.068 | 0.43 | 0.7722 |
| -29 40 06.6 | 14.50 () |
0.0742609 | b0.0387 | 0.044 | 0.45 |
Table 1 (continued)
| ID | J2000 | Magn. | Type | Period | Epoch | Ampl. | M-m | |
| 030 | 16 40 26.77 | 14.76 - | D01 | 0.06017101 | b0.0103 | 0.132 | 0.40 | 0.7760 |
| +02 17 42.7 | 15.34 () |
0.04669287 | b0.0006 | 0.069 | 0.44 | |||
| 031 | 17 22 56.98 | 14.29 - | D23 | 0.1900259 | a0.0420 | 0.143 | 0.44 | 0.8281 |
| -37 09 12.4 | 14.78 () |
0.1573530 | a0.0870 | 0.032 | 0.46 | |||
| 032 | 17 32 05.89 | 13.15 - | D12m | 0.2959543 | a0.0820 | 0.103 | 0.56 | 0.7979 |
| -29 55 58.7 | 13.48 () |
0.2361465 | a0.0824 | 0.022 | 0.45 | |||
| 033 | 18 04 41.13 | 11.49 - | D01m | 0.1929179 | a0.0292 | 0.199 | 0.37 | 0.7680 |
| -28 56 05.0 | 12.12 () |
0.1481671 | a0.1310 | 0.056 | 0.47 | |||
| 034 | 18 29 59.91 | 13.85 - | D01 | 0.06896850 | b0.1162 | 0.119 | 0.44 | 0.7732 |
| +11 23 01.2 | 14.25 () |
0.05332345 | b0.0420 | 0.040 | 0.47 | |||
| 035 | 18 39 23.75 | 14.99 - | D01 | 0.06268663 | b0.0218 | 0.203 | 0.40 | 0.7827 |
| -53 36 50.9 | 15.86 () |
0.04906305 | b0.0077 | 0.076 | 0.44 | |||
| 036 | 19 13 05.48 | 14.97 - | C01 | 5.6242 | b1.36 | 0.195 | 0.42 | 0.6955 |
| +12 38 02.2 | 15.66 () |
3.9115 | b0.49 | 0.104 | 0.49 | |||
| 037 | 19 15 27.55 | 14.93 - | D12 | 0.1738900 | b0.0180 | 0.086 | 0.48 | 0.7996 |
| +09 06 01.1 | 15.28 () |
0.1390354 | b0.0206 | 0.060 | 0.47 | |||
| 038 | 19 22 51.22 | 14.40 - | D12 | 0.06644163 | b0.0434 | 0.071 | 0.46 | 0.7996 |
| -59 07 05.4 | 14.72 () |
0.05312860 | b0.0421 | 0.032 | 0.45 | |||
| 039 | 19 24 06.38 | 14.72 - | D012 | 0.1962641 | b0.057 | 0.070 | 0.42 | 0.7641 |
| +26 48 08.3 | 15.24 () |
0.1499660 | b0.063 | 0.129 | 0.47 | 0.8015 | ||
| 0.1201920 | b0.023 | 0.015 | 0.50 | |||||
| 040 | 19 28 33.27 | 14.87 - | C*12 | 0.345059 | b0.134 | 0.178 | 0.50 | 0.7995 |
| +23 29 20.2 | 15.37 () |
0.275878 | b0.047 | 0.024 | 0.47 | |||
| 041 | 19 40 49.14 | 15.50 - | D23 | 0.1608697 | b0.0444 | 0.153 | 0.35 | 0.8253 |
| +27 36 13.3 | 16.01 () |
0.1327699 | b0.0740 | 0.045 | 0.45 | |||
| 042 | 19 44 01.74 | 11.89 - | C*12 | 0.335738 | a0.268 | 0.161 | 0.50 | 0.7990 |
| +38 14 01.0 | 12.34 () |
0.268255 | a0.102 | 0.026 | 0.47 | |||
| 043 | 19 59 00.10 | 17.26 - | C01 | 0.840380 | b0.410 | 0.127 | 0.34 | 0.7354 |
| +29 28 26.3 | 18.06 () |
0.617996 | b0.460 | 0.117 | 0.40 | |||
| 044 | 20 02 56.86 | 11.73 - | D12 | 0.1769232 | b0.1637 | 0.104 | 0.44 | 0.7945 |
| +23 20 32.1 | 12.05 () |
0.1405731 | b0.0410 | 0.021 | 0.45 |
Table 1 (continued)
| MMRP | J2000 | Magn. | Type | Period | Epoch | Ampl. | M-m | |
| 045 | 20 05 50.64 | 12.73 - | D23 | 0.09904520 | b0.0340 | 0.089 | 0.43 | 0.8333 |
| +30 58 57.3 | 13.02 () |
0.08253105 | b0.0415 | 0.029 | 0.47 | |||
| 046 | 20 08 29.64 | 18.16 - | C12 | 0.662711 | b0.470 | 0.147 | 0.42 | 0.8006 |
| +30 59 48.9 | 18.64 () |
0.530568 | b0.175 | 0.022 | 0.46 | |||
| 047 | 20 35 44.04 | 17.60 - | C12 | 0.702280 | b0.009 | 0.151 | 0.47 | 0.8060 |
| +47 50 35.7 | 18.09 () |
0.566057 | b0.473 | 0.033 | 0.44 | |||
| 048 | 20 57 52.03 | 17.80 - | C12 | 0.533432 | b0.235 | 0.135 | 0.47 | 0.8023 |
| +49 27 23.5 | 18.20 () |
0.427953 | b0.046 | 0.031 | 0.45 | |||
| 049 | 22 38 26.91 | 13.96 - | D01 | 0.1794143 | a0.1080 | 0.047 | 0.45 | 0.7665 |
| +43 52 49.4 | 14.43 () |
0.1375285 | a0.1310 | 0.156 | 0.57 | |||
| 050 | 23 47 49.26 | 16.55 - | C12 | 0.85364 | b0.470 | 0.227 | 0.39 | 0.8050 |
| +64 21 47.4 | 17.34 () |
0.68721 | b0.568 | 0.058 | 0.44 |
Table 1a. Known multi-mode variables
| MMRP_J | Magn. | Type | Period | Epoch | Ampl. | M-m | |
| 044322.93+465703.6 | 14.75 - | C12 | 0.975593 | b0.165 | 0.261 | 0.34 | 0.8022 |
| 15.58 () |
0.782620 | b0.754 | 0.062 | 0.50 | |||
| 054223.13+275647.6 | 12.89 - | C*12m | 0.376512 | b0.217 | 0.251 | 0.49 | 0.7992 |
| 13.61 () |
0.300892 | b0.170 | 0.042 | 0.46 | - | ||
| 074438.61+291222.8 | 11.94 - | D01 | 0.0885372 | b0.0420 | 0.224 | 0.32 | 0.7737 |
| 12.53 () |
0.0684971 | b0.0390 | 0.013 | 0.45 | |||
| 093044.09+320916.8 | 15.67 - | R01 | 0.504562 | b0.165 | 0.141 | 0.41 | 0.7447 |
| 16.53 () |
0.375771 | b0.199 | 0.213 | 0.40 | |||
| 094051.03+345205.2 | 14.44 - | R01 | 0.4598247 | b0.183 | 0.170 | 0.37 | 0.7429 |
| 15.34 () |
0.3415975 | b0.050 | 0.202 | 0.38 | |||
| 105408.01-580421.2 | 14.52 - | D01 | 0.1932659 | a0.0070 | 0.071 | 0.44 | 0.7633 |
| 15.03 () |
0.1475255 | a0.1175 | 0.096 | 0.50 | |||
| 111130.57-632636.4 | 12.66 - | D12n | 0.15607022 | a0.1060 | 0.088 | 0.43 | 0.7994 |
| 13.00 () |
0.1247588 | a0.0460 | 0.046 | 0.48 | |||
| 143130.85+225023.4 | 15.48 - | R01 | 0.4952015 | b0.124 | 0.067 | 0.48 | 0.7454 |
| 16.15 () |
0.3691332 | b0.033 | 0.217 | 0.39 | |||
| 151609.22+320007.3 | 15.70 - | R01 | 0.4706323 | b0.130 | 0.193 | 0.39 | 0.7435 |
| 16.73 () |
0.3499155 | b0.224 | 0.232 | 0.37 | |||
| 160331.49-494754.4 | 13.86 - | D012 | 0.2194880 | b0.0400 | 0.068 | 0.45 | 0.7602 |
| 14.46 () |
0.1668487 | b0.0615 | 0.161 | 0.54 | 0.8000 | ||
| 0.1334800 | b0.1111 | 0.013 | 0.50 | ||||
| 171059.14-351034.8 | 14.09 - | D01 | 0.1232822 | a0.0095 | 0.019 | 0.49 | 0.7715 |
| 14.40 () |
0.09510855 | a0.0040 | 0.083 | 0.66 | |||
| 185513.28+081813.4 | 17.43 - | C01 | 1.86705 | b0.16 | 0.190 | 0.28 | 0.7189 |
| 18.28 () |
1.34230 | b0.46 | 0.084 | 0.43 | |||
| 202946.51+374539.5 | 14.65 - | C01 | 4.2972 | b4.08 | 0.179 | 0.35 | 0.6959 |
| 15.31 () |
2.9905 | b2.07 | 0.070 | 0.45 | |||
| 211839.91+504732.9 | 15.09 - | C01 | 2.99683 | b0.35 | 0.423 | 0.26 | 0.7070 |
| 16.09 () |
2.11870 | b2.07 | 0.023 | 0.50 |
Table 2. Comments for new MMRP variables
| MMRP | Comments | MMRP | Comments |
| 001 | 1,2,3 | 026 | 13,15,29,42 |
| 002 | 1,4,5 | 027 | 4,5,43,44 |
| 003 | 1,2,6 | 028 | 13,16,45,46 |
| 004 | 5,7 | 029 | 13,47,48 |
| 005 | 1,5,8,9,10,11 | 030 | 12,13,15,49 |
| 006 | 1,2,6,12 | 031 | 13,29,35,50 |
| 007 | 13,14,15,16,17 | 032 | 5,13,51 |
| 008 | 5,7,9,12 | 033 | 13,25,52 |
| 009 | 7,9,16,18,19,20 | 034 | 13,14,15,23 |
| 010 | 9,16,21,22 | 035 | 13,53 |
| 011 | 4,5,20,21,23,24 | 036 | 21,34,54,55,56,57 |
| 012 | 13,15,25 | 037 | 10,13,14,15,29 |
| 013 | 1,26 | 038 | 13,15,29 |
| 014 | 12,27 | 039 | 13,14,15,29,31,58 |
| 015 | 13,16,28,29 | 040 | 1,4,5,34 |
| 016 | 13,30 | 041 | 14,15,16,29 |
| 017 | 1,2,6,16 | 042 | 4,5,31,59 |
| 018 | 13,15,29,31 | 043 | 7,18,60 |
| 019 | 13,15,25,29,32,33 | 044 | 13,15,25,61 |
| 020 | 13,15,29,34 | 045 | 10,13,14,15,62 |
| 021 | 29,35,36,37 | 046 | 5,7,63 |
| 022 | 13,15,17,29,38 | 047 | 7,64 |
| 023 | 13,17,29,39 | 048 | 7,18,65 |
| 024 | 13,15,29,40 | 049 | 13,14,15,16,29,66 |
| 025 | 12,41 | 050 | 7,18,67 |
Table 2a. Comments for known multi-mode variables
| MMRP_J | Comments |
| 044322.93+465703.6 | 5,16,68,69 |
| 054223.13+275647.6 | 5,9,16,70,71 |
| 074438.61+291222.8 | 13,14,15,23,72 |
| 093044.09+320916.8 | 1,4,16,45,73,74,75 |
| 094051.03+345205.2 | 4,7,10,17,45,74,76,77 |
| 105408.01-580421.2 | 13,15,79 |
| 111130.57-632636.4 | 13,15,35,79,80 |
| 143130.85+225023.4 | 1,2,4,16,45,73,77,81,82 |
| 151609.22+320007.3 | 1,4,10,45,74,76,77,83 |
| 160331.49-494754.4 | 13,29,35,79,84 |
| 171059.14-351034.8 | 13,29,79,85 |
| 185513.28+081813.4 | 68,69 |
| 202946.51+374539.5 | 55,56,68,69,85 |
| 211839.91+504732.9 | 34,55,68,69,86 |
Comments.
1. Monoperiodic RRC in ZTF Catalog (Chen et al., 2020).
2. Monoperiodic RRC in Gaia DR3 Catalog (Gaia Collaboration, 2022).
3. MMRP-001. Large amplitude modulation of the second-overtone
mode 
. The amplitudes in the Table are for the first interval
of ZTF observations, JD 2458219-2458540; for the next observation
interval, JD 2458607-2459766, the amplitudes of the oscillations
are as follows: 
: A/2 is 0.109 (z), 0.161 (z); :
A/2 is 0.006 (z), 0.011 (z).
4. Monoperiodic RRC in ASAS-SN Catalog (Jayasinghe et al., 2018, 2019a, 2019b, 2020, 2021).
5. Monoperiodic first-overtone DCEP in Gaia DR3 Catalog.
6. Monoperiodic RRC in Gaia DR2 Catalog (Gaia Collaboration, Brown, et al., 2018).
7. Monoperiodic RRAB in ZTF Catalog.
8. Monoperiodic RRc in GCVS (Samus et al., 2017).
9. Monoperiodic RRAB in ASAS-SN Catalog.
10. Variable in ATLAS catalog (Heinze et al., 2018). Class of variability "MSINE" (stars showing modulated sinusoids).
11. Monoperiodic RRC in the Czech Variable Star Catalogue (Skarka et al., 2017).
12. Variable in ATLAS catalog. Class of variability "dubious" (the star might not be a real variable).
13. Monoperiodic HADS in ASAS-SN Catalog.
14. Monoperiodic DSCT in ZTF Catalog.
15. Monoperiodic "main-sequence oscillator", or "DSCT/GDOR/SXPHE" type, in Gaia DR3 Catalog.
16. Variable in ATLAS catalog. Class of variability "MPULSE" (stars showing modulated pulsations).
17. Data from 1SWASP were used to improve the light elements.
18. Monoperiodic RRAB in Gaia DR3 Catalog.
19. MMRP-009. The light elements for the 1SWASP data:
: HJD(max) = 2454420.373 + 0
48136 
;
: HJD(max) = 2454420.240 + 038565 .
20. Blend in 1SWASP data.
21. Monoperiodic variable in ZTF suspected variables catalog (Chen et al., 2020). Type not determined.
22. MMRP-010. Equidistant quadruplet in fact:
,
,
.
23. Variable in ATLAS catalog. Class of variability "PULSE" (pulsating stars showing the classic sawtooth light curve, regardless of period).
24. MMRP-011. Light elements for the 1SWASP data:
: HJD(max) = 2454100.165 + 037202 ;
: HJD(max) = 2454100.011 + 029826 ;
25. Monoperiodic DSCT in ASAS-3 Catalog of Variable Stars, Pojmanski (2002).
26. RR Lyrae star (RR) in Gaia DR3 Catalog.
27. HADS(B) star in VSX database. Period of the dominating mode is given, a second period is not given.
28. Monoperiodic EW star in ZTF Catalog.
29. Monoperiodic "short-timescale source" in Gaia DR3 Catalog.
30. MMRP-016. Amplitude modulation of the second-overtone mode,
. The Tables give mean amplitude (for the whole observation
interval). Mode-switching is not excluded, type D12D1. In
band, three time intervals were studied:
I: JD 2458100-2458700, 
;
II: JD 2458700-2459400, 
;
III: JD 2459400-2459966, 
.
31. Variable in ATLAS catalog. Class of variability "CBF" (close binary, full period).
32. Monoperiodic eclipsing variable in the Catalina Surveys Southern periodic variable star catalogue (Drake et al., 2017).
33. MMRP-019. Amplitide modulation of the second-overtone mode,
. Periods 
and 
possibly vary, the light elements
are given separately for two time intervals, for the band (JD
2456776-2458382) and band (JD 2458031-2460049). Elements for
-band ASAS-SN data:
: HJD(max) = 2457777.1590 + 01633823
;
: HJD(max) = 2457777.1350 + 01303228
.
34. Variable in ATLAS catalog. Class of variability "IRR" (irregular variable).
35. Variability was detected in the GDS catalog (Hackstein et al., 2015).
36. Monoperiodic SR variable in ASAS-SN Catalog.
37. MMRP-021. A second identification in the USNO-B1.0 catalog is possible, USNO-B1.0 0366-0148328.
38. MMRP-022. Additional non-radial pulsation with the following light elements, according to ASAS-SN data:
for -band, JD 2457424-2458326: HJD(max) =
2457878.083 + 0110475 ;
for -band, JD 2458282-2460046: HJD(max) =
2459292.100 + 0110468 ;
, period ratios
,
. Semi-amplitudes 
is 0.029 (a), 0.029 (a).
For the 1SWASP data: magnitude range 14
65-1525;
amplitudes 
, 
, 
.
39. MMRP-023. According to 1SWASP data, semi-amplitudes are 
and 
.
40. MMRP-024. In the ASAS-SN -band data, two possible
non-radial modes with small amplitude are detected, 
and
, periods
and
.
Frequency is also detected in 1SWASP data.
Amplitude modulation of all the radial modes. First overtone mode
period varies. The light elements in the Table are for ASAS-SN
-band, JD 2458282-2460046. Elements for ASAS-SN -band, JD
2457424-2458326:
: HJD(max) = 2457777.1520 + 01828469
;
: HJD(max) = 2457777.1053 + 01401100
;
was not detected.
Elements for 1SWASP data, JD 2453860-2454239:
: HJD(max) = 2454141.083 + 0182847
; 
;
:HJD(max) = 2454141.031 + 0140108
; 
;
: HJD(max) = 2454141.111 + 0112110
; 
.
Magnitude range 1344 - 1398 (1SWASP mag).
41. MMRP-025. Was detected as a candidate RR Lyrae star by Ivezic et al. (2000), [IGF2000] 4.
42. Monoperiodic DSCT star in the Catalina Surveys Southern periodic variable star catalogue (Drake et al., 2017).
43. Monoperiodic RRC star in ASAS-3 Catalog.
44. MMRP-027. Elements for ASAS-3 data:
: HJD(max) = 2453333.307 + 0342260
; ;
: HJD(max) = 2453333.410 + 0273581
; 
;
Magnitude range 1124-1157 ().
45. Data from CSS and SSS were used to improve the light elements.
46. MMRP-028. According to SSS data, semi-amplitude 
, 
. Magnitude range 1485-1536 (C).
47. RS Canum Venaticorum star (RS type) in Gaia DR3 Catalog.
48. MMRP-029. Periods vary. Light elements for ASAS-SN -band
are given in the Table. Elements for ASAS-SN -band:
: HJD(max) = 2457777.0160 + 00961740
;
: HJD(max) = 2457777.0138 + 00742619
.
49. DSCT_SXPHE star in Gaia DR2 Catalog.
50. MMRP-031. According to ASAS-SN -band data, possible
non-radial mode with
, or amplitude modulation
(Blazhko effect) of the third-overtone mode with the period
.
51. MMRP-032. Amplitude modulation of the second-overtone mode
, mean amplitudes (for the full time-interval) are given in
the Table. Three time intervals were studied:
I: JD 2458231-2458777, 
;
II: JD 2458892-2459510, 
;
III: JD 2459610-2460050, 
.
52. MMRP-033. Periodic variable of ambiguous classification, as given in Nataf et al. (2010). In OGLE catalog, possible wrong identification with OGLE-BLG-DSCT-06966.
Amplitude modulation of first overtone mode is detected in
the ASAS-SN data, and bands. The mean amplitudes are given
in the Tables (for the whole observation intervals for individual
bands).
Data from ASAS-3 were used to improve the light elements.
Magnitude range and amplitude according to ASAS-3 data:
1161-1231 (), 
, 
.
53. MMRP-035. Data from SSS were used to improve the light
elements of fundamental mode, . First-overtone period
varies. Magnitude range and amplitude according to SSS data:
1498-1564 (CV), 
; 
.
54. Monoperiodic rotational variable (ROT type) in ASAS-SN Catalog.
55. Monoperiodic fundamental mode Cephei star (DCEP type)
in Gaia DR3 Catalog.
56. MIRA_SR variable in Gaia DR2 Catalog.
57. MMRP-036. Blend in NSVS and ASAS-SN data. Large magnitude
scattering in ZTF -band data. Elements for NSVS data:
: HJD(max) = 2451402.91 + 561 ;
;
: HJD(max) = 2451401.55 + 391 ;
;
Magnitude range 1209-1234 (
).
58. MMRP-039. In -band ASAS-SN data, JD 2456084-2458427
(earliest time-interval), second-overtone mode is not
detected, semi-amplitude 
. Possibly, it is due to large
errors, or amplitude modulation is possible.
59. The variability was detected by Hartman et al. (2004), pulsating type.
60. MMRP-043. In the ZTF catalog, two periods were detected: for
the band,
corresponds to (the most
likely period), or for the -band,
corresponds
to .
61. Variable in ATLAS catalog. Class of variability "SINE" (sinusoidal variables).
62. Monoperiodic DSCT star in GCVS.
63. Monoperiodic RRAB star in Gaia DR2 Catalog.
64. MMRP-047. Amplitude and magnitude range in the 
band of
ZTF data: 
, 
; 1664-1698 ().
65. MMRP-048. Amplitude and magnitude range in the band of
ZTF data: 
, 
; 1673-1704 ().
66. MMRP-049. Elements for 1SWASP data:
: HJD(max) = 2454345.442 + 017941 ; 
;
: HJD(max) = 2454345.531 + 013753 ; 
.
Magnitude range 1400-1446 (1SWASP mag).
67. MMRP-050. Periods and possibly vary.
68. Monoperiodic DCEP variable in ZTF Catalog.
69. Multiperiodicity detected by Shah et al. (2022).
70. Monoperiodic RRAB star in GCVS.
71. MMRP_J054223.13+275647.6 = IY Tau. Double periodicity was
detected by Khruslov
(2018)11.
In this study, I detected amplitude modulation of the
second-overtone mode , according to ASAS-SN data. The Table
gives semi-amplitude for the second -band interval,
JD 2459429-2460055. For the first -band interval,
JD 2458083-2459328, 
, . Period
varies. For the -band, ASAS-SN data gives the following
elements:
: HJD(max) = 2457777.140 + 0376502
;
: HJD(max) = 2457777.283 + 0300891
;
-band amplitudes in Tables are given according to data from the
second -band interval, JD 2457745-2458443. Amplitude for the
first -band interval, JD 2457008-2457720: 
,
( is not detected);
Elements according to 1SWASP data (for light curves see Khruslov, 2018):
: HJD(max) = 2453777.214 + 03764978
; 
;
: HJD(max) = 2453777.096 + 03009072
; 
.
72. MMRP_J074438.61+291222.8. Double periodicity was detected by
Wils et al. (2012), classified as a HADS star of fundamental and
first-overtone modes. Periods varys. Light elements in the Table
are given for the time interval JD 2458033-2459830, ASAS-SN
band and ZTF band.
For ASAS-SN -band, JD 2456905-2458452, light elements are:
: HJD(max) = 2457777.0787 + 00885367
;
: HJD(max) = 2457777.0090 + 00684978
;
Elements for 1SWASP data:
: HJD(max) = 2454120.0653 + 00885370
; 
;
: HJD(max) = 2454120.0228 + 00684974
; 
.
73. Double-mode RR Lyrae star (RRd type) in Gaia DR2 Catalog.
74. Double-mode RR Lyrae star (RRd type) in Gaia DR3 Catalog.
75. MMRP_J093044.09+320916.8. Magnitude range and semi-amplitude
according to CSS data: 1565-1634 (C); 
,
.
76. Double-mode RR Lyrae variable (RRd type) in the Catalina Surveys periodic variable stars catalog (Drake et al., 2014).
77. Double periodicity detected by Huemmerich and Bernhard (2014) corresponds to 2012. Type RRd.
78. MMRP_J094051.03+345205.2 Magnitude range and semi-amplitude:
according to CSS data: 1443-1515 (C); 
,
;
according to 1SWASP data: 146-156 (1SWASP mag), 
, 
.
79. The variable is in the OGLE Scuti stars
database12,
Pietrukowicz et al. (2020).
80. MMRP_J111130.57-632636.4. According to ASAS-SN -band
data, there is additional non-radial oscillation,
; 
.
81. Monoperiodic RRC star in the Catalina Surveys periodic variable stars catalog (Drake et al., 2014).
82. MMRP_J143130.85+225023.4. Magnitude range and semi-amplitude
according to CSS data: 1535-1592 (C), 
,
.
83. MMRP_J151609.22+320007.3. Magnitude range and semi-amplitude
according to CSS data: 1576-1651 (C), 
,
.
84. MMRP_J160331.49-494754.4. Second-overtone mode is not
detected in ASAS-SN -band.
Possible non-radial oscillation detected in ASAS-SN and
bands, 
= 01262036, 
(a); this
frequency is possibly a one-day alias mode to third overtone mode,
.
In ASAS-SN -band, two other oscillation with the periods close
to , 01345739 and 01349735, are possibly detected.
85. Blend in ASAS-SN data.
86. Monoperiodic DCEP star in ASAS-SN Catalog.
5.2. Light curves
An example of light curves for one of the stars, MMRP-049, is
displayed in Fig. 1. Top panels present data folded with the
fundamental-mode and first-overtone periods. Bottom panels show
the same curves after prewhitening the other oscillation (if
, 
and 
interaction frequencies
or non-radial frequencies were excluded, it is also noted). 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 (first-overtone oscillations for MMRP-049). The structure of
the power spectra shows that the secondary periods are real.
The light curves from the ASAS-SN surveys are available online in the html version of this paper as a zip archive (see Section 2). 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.
6. Discussion
6.1. The Petersen diagram
Among the 50 stars with multi-periodicity discovered in this
study, there are 15 Classical Cepheids (two stars of the C01 type,
8 stars of the C12 type, and 5 stars of the C*12 type); four RR
Lyrae stars of the R01 type; 31 high-amplitude Scuti
stars (double-mode: 9 D01 stars, 12 D12 stars, 4 D23 stars;
triple-mode: 4 D012 stars and one D123 star; and one
quadruple-mode star of the D0123 type).
Among the 14 known multi-periodic stars studied in this paper,
there are 5 Classical Cepheids (three of C01 type, one of C12
type, and one of C*12 type); four RR Lyrae stars of R01 type; 5
high-amplitude Scuti stars (3 of D01 type, one of D12
type, one of D012 type).
In this paper, the distribution by variability type is not statistically significant. In fact, in the sample of multi-periodic variable stars, the largest fraction belongs to R01 stars. The number of D01 stars is slightly lower. Next in number are the first- and second-overtone variables of different types (D12 and C12) and C01 Cepheids. For the present paper, I selected the rarest and most interesting objects encountered in my search for multi-periodicity.
The Petersen diagram for all MMRP variables studied in this paper is displayed in Fig. 2.
 |
Fig. 2. The Petersen diagram for the multi-periodic stars of the present study. Blue circles are double-mode variables, green triangles are triple-mode variables, and red squares are quadruple mode variables. |
6.2. Asymmetry inversion for light curves of Scuti stars
In the photometric data of recent surveys, we find more and more
Scuti stars with light-curve asymmetry opposite compared
to brightness variations of typical pulsating stars. Pietrukowicz
et al. (2020) show four examples of phased light curves of
monoperiodic Scuti variables with inversion of asymmetry
(the rising part lasting longer than the fading one), and classify
these stars as likely first-overtone pulsators.
In this paper, I present a confirmation of this assumption using multiperiodic stars. I detected 10 double- and multi-mode variables with one of the modes showing asymmetry inversion. Among these stars, three are of the D01 type (MMRP-22, MMRP-49, and MMRP_J171059.14-351034.8), four stars belong to the D12 type (MMRP-19, MMRP-23, MMRP-26, and MMRP-32), two stars are of the D012 type (MMRP-24 and MMRP_J160331.49-494754.4), and one star is of the D0123 type (MMRP-10). In all these cases, the mode with asymmetry inversion is the first overtone.
An example of the light curves of one of the stars with asymmetry inversion (MMRP-49) is shown in Fig. 1.
The maximal asymmetry inversion was detected for
MMRP_J171059.14-351034.8,
.
All these stars have the longest periods for Scuti stars,
(for four monoperiodic cases by
Pietrukowicz et al., 2020, the periods are within the renge
).
In addition, a slight inversion of asymmetry was detected for
MMRP-011, a star of the C*12 type (
). MMRP-011
(
,
) is similar to the D12 star
MMRP-032 (
,
) and to two known double-mode
first- and second-overtone variables with a slight inversion of
asymmetry, V798 Cyg (
,
) and V1719 Cyg
(
,
). Note both the morphological
similarity of the light curves and the stars' similar position
relative to the Galactic plane.
6.3. C*12 stars
In addition to the C12 type, I used the C*12 type that includes
stars morphologically close to the C12 type (asymmetry parameter
or slightly inverted asymmetry, with a small hump at
the beginning of the brightness increase), but with shorter
periods (
) characteristic of R1 stars
(RRC), bordering Scuti stars. All these stars are located
near the Galactic plane. This classification is based on
OGLE13 and Gaia DR3
catalogs (Gaia Collaboration, 2022), which classified
similar stars as first- and second-overtone Cepheids.
In my study, 6 stars belong to the C*12 type:
MMRPB€“005, MMRPB€“011, MMRPB€“027, MMRPB€“040, MMRPB€“042,
and MMRP_J054223.13+275647.6 = IY Tau.
It should be noted that in the OGLE classification (see Soszyn'ski et al., 2020), a number of stars from the MMRP list with even shorter periods (of δ Scuti type in my classification) are attributed to first-overtone Cepheids (MMRPB€“002 and MMRPB€“032). Some other variables may also be related to this type of stars (MMRPB€“001 and MMRPB€“010).
6.4. Amplitude modulation
For 7 variables, slow amplitude modulation (variations from one
season to another) was detected. For these stars, the tabulated
variability type included the letter "m" (for example, C12m,
D12m, D01m). These are mainly cases of amplitude modulation of the
second-overtone mode for the first- and second-overtone
double-mode Scuti variables (four D12m type stars:
MMRP-001, MMRP-16, MMRP-19, and MMRP-32). One D01m star
(MMRP-33) showed amplitude modulation of the first-overtone mode.
One triple-mode Scuti star of type D012m (MMRP-24)
showed possible amplitude modulation of all its radial pulsation
modes. Also, one C*12m Cepheid star, MMRP_J054223.13+275647.6 =
IY Tau, showed amplitude modulation of the second-overtone mode.
In some cases, a periodic amplitude variation is possible, but, in a number of cases, it also can be mode switching.
Two examples of amplitude modulation are shown in Figs. 3 and 4. MMRP-033 it a possible mode-switching case. MMRP-032 is possibly a case of periodic amplitude variations (during short time intervals of observations, the star shows the "episodic" multiperiodicity; for intervals and variability amplitudes, see Comments to Table 1).
 |
Fig. 3.
The amplitude modulation of MMRP-033. Top
panels: |
in the two time-intervals; Bottom panel: amplitude
variations of the first-overtone mode in the
 |
Fig. 4.
The amplitude modulation of MMRP-032 in
three time intervals (see Comments). Left panels: |
6.5. Triple- and quadruple-mode δ Scuti stars
In my study, 6 triple-mode variables were detected. Five of these stars belong to the D012 type: MMRP-012, MMRP-014, MMRP-024, MMRP-039, and MMRP_J160331.49-494754.4. In the case MMRP_J160331.49-494754.4, the second-overtone mode was not earlier known (in the OGLE database, the star was classified as a variable with two periods, those of the fundamental and first-overtone modes). The sixth star, MMRP-002, belongs to the D123 type.
In all cases of the five D012 stars, with a single exception of MMRP-014, the first-overtone mode dominates. The first-overtone mode also dominates for the D123 star MMRP-002. In two cases, the light curve of the first-overtone oscillation showed asymmetry inversion.
One case, MMRP-010, is a quadruple-mode Scuti star of
the D0123 type. Additionally, it is an equidistant quadruplet with
the frequency differences
.
The light curve of the first-overtone oscillation of this star
also shows inverted asymmetry.
Netzel et al. (2022) presents 14 quadruple-mode Scuti
stars of the D0123 type from the OGLE database (Galactic bulge).
Among them, no one is an equidistant quadruplet. These authors
also presented the discovery of numerous triple-mode
Scuti star of the D013 type (221 variables), their number
considerably exceeding that of the D012 stars (145 variables). In
my study, no D013 stars were detected.
6.6. D23 variables
In this paper, I present my detection of four double-mode
Scuti stars pulsating in the second- and third-overtone modes,
type D23 (MMRP-020, MMRP-031, MMRP-041, and MMRP-045 = V2702
Cyg). Earlier, I found two stars of this type. The first of them
is FH Cir (Khruslov, 2010, first classification as a
Scuti star with nonradial pulsations;
,
; the star was reclassified as a D23 variable by
Khruslov, 2016, PhD dissertation14).
The second of them is V3124 Cyg
(Khruslov, 2014,
,
).
According to my study, the second-overtone periods of D23 stars
range from
to
. The period ratio 
is from 
to 
.
For one of the stars, MMRP-031, I detected an amplitude
modulation of the third-overtone mode that can be interpreted as
Blazhko effect with the period
or as a non-radial
mode with a frequency close to that of the third-overtone mode,
. This case can be possibly classified as a D23n
star, where the letter "m" in the MMRP catalog designates
long-term variations and is not used for stars with Blazhko
effect.
It is particularly interesting that Netzel et al. (2022) did not detect any stars of the D23 type.
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
Drake, A. J., Graham, M. J., Djorgovski, S. G., et al., 2014, Astrophys. J. Suppl., 213, 9
Drake, A. J., Djorgovski, S. G., & Catelan, M., 2017, Monthly Notices Roy. Astron. Soc., 469, 3688
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
Hackstein, M., Fein, Ch., Haas, M., et al., 2015, Astron. Nachr., 336, 590
Hartman, J.D., Bakos, G., Stanek, K.Z., & Noyes, R.W., 2004, Astron. J., 128, 1761
Heinze, A. N., Tonry, J. L., Denneau, L., et al., 2018, Astron. J., 156, id. 241
Huemmerich, S. & Bernhard, K., 2014, Inform. Bull. Var. Stars, No. 6100
Ivezic, Z, Goldston, J., Finlator, K., et al., 2000, Astron. J., 120, 963
Jayasinghe, T., Kochanek, C. S., Stanek, K. Z., et al., 2018, Monthly Notices Roy. Astron. Soc., 477, 3145
Jayasinghe, T., Kochanek, C. S., Stanek, K. Z., et al., 2021, Monthly Notices Roy. Astron. Soc., 503, 200
Jayasinghe, T., Stanek, K. Z., & Kochanek, C. S., 2019a, Monthly Notices Roy. Astron. Soc., 486, 1907
Jayasinghe, T., Stanek, K. Z., & Kochanek, C. S., 2019b, Monthly Notices Roy. Astron. Soc., 485, 961
Jayasinghe, T., Stanek, K. Z., & Kochanek, C. S., 2020, Monthly Notices Roy. Astron. Soc., 491, 13
Khruslov, A. V., 2010, Perem. Zvezdy Prilozhenie (Variable Stars Suppl., 10, 15
Khruslov, A. V., 2014, Perem. Zvezdy Prilozhenie (Variable Stars Suppl., 14, 1
Khruslov, A. V., 2016, Detection and study of pulsating variable stars with multiperiodicity, PhD Dissertation, Moscow: Moscow State University
Khruslov, A. V., Kusakin, A. V., & Reva, I. V., 2017, Acta Astron., 67, 317
Khruslov, A. V., 2018, Proceedings of the 2018 Acad. A. A.`Boyarchuk Memorial Conference, INASAN Science Proceedings. Edited by D. V. Bisikalo and D. S. Wiebe. Moscow: Yanus-K, 2018, p. 57-61
Khruslov, A. V., 2018a, Perem. Zvezdy (Variable Stars, 38, 1
Khruslov, A. V., 2021, Perem. Zvezdy (Variable Stars), 41, 1
Khruslov, A. V., 2021a, Perem. Zvezdy (Variable Stars), 41, 8
Khruslov, A. V., 2022, Perem. Zvezdy (Variable Stars), 42, 5
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, Monthly Notices Roy. Astron. Soc., 502, 5147
Masci, F. J., Laher, R. R., & Rusholme, B., 2019, Publ. Astron. Soc. Paci?c, 131, 018003
Nataf, D. M., Stanek, K. Z., & Bakos, G. Á., 2010, Acta Astron., 60, 261
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
Pietrukowicz, P., Soszynski, I., Netzel, H., et al., 2020, Acta Astron., 70, 241
Pojmanski, G., 2002, Acta Astron., 52, 397
Samus, N. N., Kazarovets, E. V., Durlevich, O. V., Kireeva, N. N., & Pastukhova, E. N., 2017, Astron. Rep., 61, 80
Shah, V., Chen, X., & de Grijs, R., 2022, Astron. J., 164, 162
Shappee B.J., Prieto J.L., Grupe, D., et al., 2014, Astrophys. J., 788, 48
Skarka, M., Mašek, M., & Brát, L., 2017, Open European Journal on Variable Stars, 185, p. 1
Smolec, R. & Moskalik, P., 2010, Astron. & Astrophys., 524, A40
Sokolovsky, K. V., 2007, Perem. Zvezdy Prilozhenie (Variable Stars Suppl.), 7, No. 30
Soszynski, I., Udalski, A., Szymanski, M. K., et al., 2020, Acta Astron., 70, 101
Wils, P., Panagiotopoulos, K., van Wassenhove, J., et al., 2012, Inform. Bull. Var. Stars, No. 6015
7. Supplement Tables
Table 3. Semi-amplitudes and magnitude ranges. New
MMRP stars
| MMRP | Semi- | ampl. | Mag. | range | ||||
|
|
|
|
|
|
|
|
|
| 001 | - | - | 0.102 | 0.159 | - | - | 16.27- | 17.12- |
| - | - | 0.046 | 0.060 | 16.66 | 17.63 | |||
| 002 | 0.125 | 0.147 | 0.100 | 0.149 | 14.87- | 15.34- | 14.55- | 15.40- |
| 0.025 | 0.037 | 0.022 | 0.034 | 15.42 | 16.02 | 14.91 | 15.94 | |
| 0.032 | 0.042 | 0.029 | 0.039 | |||||
| 003 | - | - | 0.058 | 0.086 | - | - | 17.64- | 17.73- |
| - | - | 0.150 | 0.224 | 18.20 | 18.47 | |||
| 004 | 0.139 | 0.155 | 0.150 | 0.230 | 15.15- | 15.77- | 14.74- | 16.12- |
| - | 0.025 | 0.011 | 0.018 | 15.75 | 16.45 | 15.14 | 16.70 | |
| 005 | 0.117 | 0.140 | - | 0.133 | 11.87- | 12.26- | - | 12.27- |
| 0.027 | 0.035 | - | 0.038 | 12.31 | 12.68 | 12.71 | ||
| 006 | - | - | 0.042 | 0.059 | - | - | 17.51- | 17.66- |
| - | - | 0.162 | 0.238 | 18.00 | 18.41 | |||
| 007 | 0.107 | 0.109 | 0.076 | 0.118 | 13.86- | 13.96- | 13.86- | 13.94- |
| 0.034 | 0.038 | 0.025 | 0.036 | 14.27 | 14.37 | 14.11 | 14.32 | |
| 008 | 0.131 | 0.161 | 0.133 | 0.187 | 15.61- | 16.20- | 15.16- | 16.47- |
| 0.051 | 0.061 | 0.045 | 0.066 | 16.38 | 17.08 | 15.58 | 17.09 | |
| 009 | 0.206 | 0.254 | 0.165 | 0.257 | 13.98- | 14.48- | 13.54- | 14.44- |
| 0.027 | 0.040 | 0.029 | 0.043 | 14.63 | 15.25 | 14.00 | 15.11 | |
| 010 | 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 | |
| 0.025 | 0.025 | 0.016 | 0.024 | |||||
| 0.020 | 0.023 | 0.016 | 0.023 | |||||
| 011 | 0.132 | 0.163 | 0.128 | 0.193 | 13.44- | 13.77- | 13.34- | 13.99- |
| 0.014 | 0.022 | 0.015 | 0.022 | 13.83 | 14.30 | 13.68 | 14.48 | |
| 012 | 0.005 | 0.004 | - | - | 12.56- | 12.66- | - | - |
| 0.187 | 0.228 | - | - | 13.04 | 13.24 | |||
| 0.013 | 0.018 | - | - | |||||
| 013 | - | - | 0.127 | 0.155 | - | - | 18.12- | 18.92- |
| - | - | 0.155 | 0.199 | 18.81 | 19.88 | |||
| 014 | - | - | 0.133 | 0.208 | - | - | 16.65- | 16.53- |
| - | - | 0.089 | 0.111 | 17.37 | 17.61 | |||
| - | - | 0.023 | 0.036 |
Table 3 (continued)
| MMRP | Semi- | ampl. | Mag. | range | ||||
|
|
|
|
|
|
|
|
|
| 015 | 0.097 | 0.112 | 0.072 | 0.128 | 13.93- | 14.12- | 14.00- | 14.11- |
| 0.029 | 0.033 | 0.020 | 0.032 | 14.24 | 14.48 | 14.24 | 14.50 | |
| 016 | 0.164 | 0.200 | - | - | 14.01- | 14.14- | - | - |
| 0.032 | 0.015 | - | - | 14.50 | 14.70 | |||
| 017 | - | - | 0.047 | 0.069 | - | - | 16.17- | 16.36- |
| - | - | 0.162 | 0.231 | 16.69 | 17.09 | |||
| 018 | 0.124 | 0.141 | 0.071 | 0.144 | 13.50- | 13.68- | 13.50- | 13.68- |
| 0.015 | 0.027 | 0.013 | 0.023 | 13.86 | 14.10 | 13.74 | 14.05 | |
| 019 | 0.080 | 0.102 | - | - | 12.66- | 12.91- | - | - |
| 0.007 | 0.016 | - | - | 12.90 | 13.22 | |||
| 020 | 0.131 | 0.174 | 0.093 | 0.180 | 12.46- | 12.66- | 12.65- | 12.78- |
| 0.024 | 0.034 | 0.020 | 0.038 | 12.92 | 13.16 | 12.99 | 13.32 | |
| 021 | 0.074 | 0.100 | - | - | 12.76- | 13.24- | - | - |
| 0.019 | 0.026 | - | - | 13.03 | 13.57 | |||
| 022 | 0.092 | 0.113 | - | - | 14.60- | 14.74- | - | - |
| 0.089 | 0.108 | - | - | 15.15 | 15.38 | |||
| 023 | 0.086 | 0.106 | - | - | 12.78- | 12.99- | - | - |
| 0.011 | 0.013 | - | - | 13.04 | 13.30 | |||
| 024 | 0.081 | 0.103 | - | - | 13.25- | 13.50- | - | - |
| 0.121 | 0.105 | - | - | 13.79 | 14.03 | |||
| - | 0.011 | - | - | |||||
| 025 | - | - | 0.103 | 0.134 | - | - | 17.91- | 17.95- |
| - | - | 0.041 | 0.057 | 18.39 | 18.50 | |||
| 026 | 0.095 | 0.132 | - | - | 13.58- | 13.73- | - | - |
| 0.013 | 0.012 | - | - | 13.87 | 14.11 | |||
| 027 | 0.078 | 0.086 | - | - | 11.22- | 11.46- | - | - |
| 0.019 | 0.021 | - | - | 11.48 | 11.75 | |||
| 028 | 0.165 | 0.184 | - | - | 15.20- | 15.52- | - | - |
| 0.036 | 0.044 | - | - | 15.95 | 16.25 |
Table 3 (continued)
| MMRP | Semi- | ampl. | Mag. | range | ||||
|
|
|
|
|
|
|
|
|
| 029 | 0.053 | 0.068 | - | - | 13.76- | 14.12- | - | - |
| 0.042 | 0.044 | - | - | 14.08 | 14.50 | |||
| 030 | 0.116 | 0.132 | 0.090 | 0.141 | 14.66- | 14.76- | 14.84- | 14.83- |
| 0.058 | 0.069 | 0.052 | 0.078 | 15.18 | 15.34 | 15.23 | 15.32 | |
| 031 | 0.126 | 0.143 | - | - | 13.86- | 14.29- | - | - |
| 0.030 | 0.032 | - | - | 14.29 | 14.78 | |||
| 032 | 0.103 | 0.128 | - | - | 13.15- | 13.60- | - | - |
| 0.022 | 0.015 | - | - | 13.48 | 13.97 | |||
| 033 | 0.199 | 0.240 | - | - | 11.49- | 11.69- | - | - |
| 0.056 | 0.036 | - | - | 12.12 | 12.35 | |||
| 034 | 0.098 | 0.120 | 0.084 | 0.119 | 13.63- | 13.78- | 13.73- | 13.85- |
| 0.033 | 0.045 | 0.029 | 0.040 | 14.03 | 14.25 | 13.99 | 14.25 | |
| 035 | 0.162 | 0.203 | - | - | 14.89- | 14.99- | - | - |
| 0.067 | 0.076 | - | - | 15.77 | 15.86 | |||
| 036 | 0.129 | 0.131 | 0.120 | 0.195 | 13.69- | 14.60- | 12.70- | 14.97- |
| 0.067 | 0.064 | 0.061 | 0.104 | 14.15 | 15.21 | 13.26 | 15.66 | |
| 037 | 0.073 | 0.081 | 0.059 | 0.086 | 14.45- | 14.90- | 14.03- | 14.93- |
| 0.049 | 0.056 | 0.041 | 0.060 | 14.80 | 15.35 | 14.26 | 15.28 | |
| 038 | 0.057 | 0.071 | - | - | 14.20- | 14.40- | - | - |
| 0.025 | 0.032 | - | - | 14.50 | 14.72 | |||
| 039 | 0.058 | 0.071 | 0.042 | 0.070 | 14.46- | 14.70- | 14.21- | 14.72- |
| 0.106 | 0.130 | 0.076 | 0.129 | 15.00 | 15.38 | 14.57 | 15.24 | |
 0.014 |
0.018 | 0.011 | 0.015 | |||||
| 040 | 0.130 | 0.161 | 0.117 | 0.178 | 14.08- | 14.67- | 13.59- | 14.87- |
| 0.020 | 0.025 | 0.016 | 0.024 | 14.54 | 15.25 | 13.96 | 15.37 | |
| 041 | 0.094 | 0.121 | 0.091 | 0.153 | 14.85- | 15.35- | 14.71- | 15.50- |
| 0.030 | 0.039 | 0.027 | 0.045 | 15.40 | 16.00 | 15.12 | 16.01 | |
| 042 | 0.136 | 0.161 | - | - | 11.63- | 11.89- | - | - |
| 0.020 | 0.026 | - | - | 12.04 | 12.34 |
Table 3 (continued)
| MMRP | Semi- | ampl. | Mag. | range | ||||
|
|
|
|
|
|
|
|
|
| 043 | - | - | 0.127 | 0.189 | - | - | 17.26- | 19.7- |
| - | - | 0.117 | 0.185 | 18.06 | 21.0 | |||
| 044 | 0.080 | 0.104 | - | - | 11.49- | 11.73- | - | - |
| 0.018 | 0.021 | - | - | 11.73 | 12.05 | |||
| 045 | 0.075 | 0.088 | 0.052 | 0.089 | 12.47- | 12.72- | 12.40- | 12.73- |
| 0.022 | 0.027 | 0.016 | 0.029 | 12.72 | 13.01 | 12.59 | 13.02 | |
| 046 | - | - | 0.147 | - | - | - | 18.16- | 20.9- |
| - | - | 0.022 | - | 18.64 | 21.7 | |||
| 047 | - | - | 0.151 | 0.233 | - | - | 17.60- | 19.5- |
| - | - | 0.033 | 0.058 | 18.09 | 20.2 | |||
| 048 | - | - | 0.135 | 0.201 | - | - | 17.80- | 19.7- |
| - | - | 0.031 | 0.045 | 18.20 | 20.4 | |||
| 049 | 0.042 | 0.045 | 0.029 | 0.047 | 13.77- | 13.90- | 13.84- | 13.96- |
| 0.143 | 0.150 | 0.109 | 0.156 | 14.25 | 14.41 | 14.16 | 14.43 | |
| 050 | - | - | 0.162 | 0.227 | 15.30- | 15.92- | 15.35- | 16.55- |
| - | - | 0.040 | 0.058 | 15.75 | 16.45 | 15.90 | 17.34 |
Table 3a. Semi-amplitudes and magnitude ranges. Known
multi-mode variables
| MMRP_J | Semi- | ampl | Mag. | range | ||||
|
|
|
|
|
|
|
|
|
| 044322.93+465703.6 | 0.245 | 0.270 | 0.185 | 0.261 | 14.15- | 14.79- | 13.55- | 14.75- |
| 0.047 | 0.063 | 0.043 | 0.062 | 14.89 | 15.72 | 14.08 | 15.58 | |
| 054223.13+275647.6 | 0.206 | 0.251 | - | 0.240 | 12.48- | 12.89- | - | 12.99- |
| 0.024 | 0.042 | - | - | 13.08 | 13.61 | 13.53 | ||
| 074438.61+291222.8 | 0.201 | 0.224 | - | 0.233 | 11.92- | 11.94- | - | 11.94- |
| 0.012 | 0.013 | - | 0.013 | 12.42 | 12.53 | 12.50 | ||
| 093044.09+320916.8 | 0.115 | 0.135 | 0.112 | 0.141 | 15.65- | 15.66- | 15.66- | 15.67- |
| 0.186 | 0.206 | 0.157 | 0.213 | 16.70 | 16.75 | 16.30 | 16.53 | |
| 094051.03+345205.2 | 0.147 | 0.188 | 0.125 | 0.170 | 14.37- | 14.40- | 14.50- | 14.44- |
| 0.178 | 0.205 | 0.148 | 0.202 | 15.32 | 15.42 | 15.15 | 15.34 | |
| 105408.01-580421.2 | 0.059 | 0.071 | - | - | 14.24- | 14.52- | - | - |
| 0.074 | 0.096 | - | - | 14.66 | 15.03 | |||
| 111130.57-632636.4 | 0.068 | 0.088 | - | - | 12.40- | 12.66- | - | - |
| 0.036 | 0.046 | - | - | 12.71 | 13.00 | |||
| 143130.85+225023.4 | 0.063 | 0.079 | 0.045 | 0.067 | 15.4- | 15.5- | 15.45- | 15.48- |
| 0.204 | 0.239 | 0.157 | 0.217 | 16.1 | 16.4 | 15.93 | 16.15 | |
| 151609.22+320007.3 | 0.152 | 0.191 | 0.132 | 0.193 | 15.6- | 15.6- | 15.78- | 15.70- |
| 0.150 | 0.216 | 0.151 | 0.232 | 16.5 | 16.8 | 16.47 | 16.73 | |
| 160331.49-494754.4 | 0.058 | 0.068 | - | - | 13.43- | 13.86- | - | - |
| 0.133 | 0.161 | - | - | 13.94 | 14.46 | |||
| - | 0.013 | - | - | |||||
| 171059.14-351034.8 | 0.018 | 0.019 | - | - | 13.54- | 14.09- | - | - |
| 0.069 | 0.083 | - | - | 13.82 | 14.40 | |||
| 185513.28+081813.4 | - | - | 0.190 | 0.316 | - | - | 17.43- | 19.6- |
| - | - | 0.084 | 0.144 | 18.28 | 21.1 | |||
| 202946.51+374539.5 | 0.021 | - | 0.179 | 0.291 | 13.88- | - | 14.65- | 17.40- |
| 0.011 | - | 0.070 | 0.107 | 14.05 | 15.31 | 18.42 | ||
| 211839.91+504732.9 | 0.364 | 0.424 | 0.276 | 0.423 | 14.23- | 15.10- | 13.51- | 15.09- |
| 0.022 | 0.030 | 0.014 | 0.023 | 15.25 | 16.29 | 14.19 | 16.09 |
Table 4. Color indices and Galactic latitudes. New
MMRP-stars
| MMRP | , |
, |
, |
, |
, |
 , deg |
| 2MASS | APASS | APASS | ASAS-SN | ZTF | ||
| 001 | 0.59 | 1.22 | 0.93 | - | 0.92 | +0.5 |
| 002 | 0.59 | 0.86 | 0.62 | 0.53 | 0.97 | -0.7 |
| 003 | - | - | - | - | 0.21 | -46.4 |
| 004 | 0.82 | 1.50 | 1.30 | 0.67 | 1.43 | +0.4 |
| 005 | 0.47 | 0.89 | 0.71 | 0.38 | - | -3.4 |
| 006 | 0.25 | - | - | - | 0.33 | -12.9 |
| 007 | 0.17 | 0.33 | 0.18 | 0.12 | 0.17 | -13.6 |
| 008 | 0.81 | 1.47 | 1.29 | 0.69 | 1.42 | +3.8 |
| 009 | 0.55 | 1.14 | 1.02 | 0.58 | 1.01 | +0.3 |
| 010 | 0.47 | 0.91 | 0.72 | 0.45 | 0.82 | -2.9 |
| 011 | 0.49 | 0.83 | 0.70 | 0.40 | 0.74 | +0.9 |
| 012 | 0.18 | 0.34 | 0.17 | 0.18 | - | -25.1 |
| 013 | - | - | - | - | 0.87 | -4.7 |
| 014 | - | 0.41 | 0.11 | - | 0.16 | +26.8 |
| 015 | 0.23 | 0.46 | 0.25 | 0.19 | 0.22 | +6.7 |
| 016 | 0.25 | 0.42 | 0.27 | 0.17 | - | -19.0 |
| 017 | 0.58 | 0.46 | 0.20 | - | 0.37 | +5.1 |
| 018 | 0.21 | 0.50 | 0.31 | 0.22 | 0.28 | +8.6 |
| 019 | 0.30 | 0.67 | 0.44 | 0.28 | - | -12.2 |
| 020 | 0.26 | 0.44 | 0.28 | 0.22 | 0.32 | +5.0 |
| 021 | 0.92 | 1.14 | 1.06 | 0.51 | - | -2.6 |
| 022 | 0.24 | 0.50 | 0.32 | 0.23 | - | +9.4 |
| 023 | 0.23 | 0.52 | 0.32 | 0.24 | - | +11.0 |
| 024 | 0.28 | 0.55 | 0.41 | 0.24 | - | +9.7 |
| 025 | - | - | - | - | 0.08 | +51.6 |
| 026 | 0.19 | 0.45 | 0.26 | 0.21 | - | +21.8 |
| 027 | 0.29 | -0.14 ? | 0.47 | 0.25 | - | +3.7 |
| 028 | 0.31 | 0.67 | 0.52 | 0.28 | - | +22.8 |
| 029 | 0.58 | 0.71 | 0.57 | 0.38 | - | +11.7 |
| 030 | 0.22 | 0.22 | -0.02 | 0.14 | 0.05 | +30.0 |
| 031 | 0.49 | 0.91 | 0.70 | 0.42 | - | -0.5 |
| 032 | 0.59 | 1.00 | 0.87 | 0.47 | - | +2.0 |
| 033 | 0.32 | 0.60 | 0.54 | 0.24 | - | -3.6 |
| 034 | 0.13 | 0.39 | 0.18 | 0.17 | 0.22 | +9.9 |
| 035 | - | 0.34 | -0.01 | 0.13 | - | -19.8 |
| 036 | 1.04 | 2.39 | 2.18 | 1.01 | 2.36 | +1.0 |
| 037 | 0.51 | 1.07 | 0.93 | 0.53 | 0.99 | -1.1 |
| 038 | 0.25 | 0.49 | 0.29 | 0.22 | - | -27.0 |
| 039 | 0.41 | 0.62 | 0.47 | 0.30 | 0.61 | +5.3 |
| 040 | 0.57 | 1.42 | 1.23 | 0.67 | 1.38 | +2.9 |
| 041 | 0.43 | 1.03 | 0.90 | 0.62 | 0.85 | +2.4 |
| 042 | 0.28 | 0.51 | 0.36 | 0.32 | - | +7.1 |
| 043 | 1.26 | - | - | - | 2.63 | -0.0 |
| 044 | 0.35 | 0.67 | 0.42 | 0.29 | - | -4.0 |
Table 4 (continued)
| MMRP | , |
, |
, |
, |
, |
, deg |
| 2MASS | APASS | APASS | ASAS-SN | ZTF | ||
| 045 | 0.25 | 0.75 | 0.54 | 0.28 | 0.38 | -0.5 |
| 046 | 1.35 | - | - | - | 2.85 | -1.0 |
| 047 | 1.05 | - | - | - | 1.95 | +4.3 |
| 048 | 1.07 | - | - | - | 2.04 | +2.5 |
| 049 | 0.23 | 0.45 | 0.20 | 0.15 | 0.22 | -12.7 |
| 050 | 0.73 | - | 1.52 | 0.67 | 1.36 | +2.3 |
Table 4a. Color indices, and Galactic latitude. Known
multi-mode variables
| MMRP | , |
, |
, |
, |
, |
, deg |
| 2MASS | APASS | APASS | ASAS-SN | ZTF | ||
| 044322.93+465703.6 | 0.81 | 1.58 | 1.42 | 0.70 | 1.37 | +0.6 |
| 054223.13+275647.6 | 0.58 | 1.06 | 0.89 | 0.48 | - | -1.1 |
| 074438.61+291222.8 | 0.20 | 0.27 | 0.06 | 0.09 | - | +23.7 |
| 093044.09+320916.8 | 0.12 | 0.18 | 0.00 | 0.17 | 0.16 | +46.5 |
| 094051.03+345205.2 | 0.26 | 0.20 | 0.19 | 0.11 | 0.11 | +48.8 |
| 105408.01-580421.2 | 0.37 | 0.72 | 0.57 | 0.32 | - | +1.3 |
| 111130.57-632636.4 | 0.44 | 0.69 | 0.55 | 0.31 | - | -2.7 |
| 143130.85+225023.4 | 0.23 | 0.46 | 0.15 | 0.20 | 0.14 | +67.0 |
| 151609.22+320007.3 | 0.19 | 0.17 | 0.03 | 0.15 | 0.13 | +58.3 |
| 160331.49-494754.4 | 0.59 | 0.84 | 0.72 | 0.48 | - | +2.1 |
| 171059.14-351034.8 | 0.53 | 1.13 | 1.06 | 0.57 | - | +2.6 |
| 185513.28+081813.4 | 1.19 | - | - | - | 2.48 | +2.9 |
| 202946.51+374539.5 | 1.41 | - | - | - | 2.99 | -0.8 |
| 211839.91+504732.9 | 1.07 | 1.90 | 1.73 | 0.92 | 1.86 | +0.9 |