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Peremennye Zvezdy (Variable Stars) 41, No. 2, 2021 Received 4 March; accepted 12 March. |
Article in PDF |
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DOI: 10.24412/2221-0474-2021-41-6-10
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CCD Observations of AS Cas
L.N. Berdnikov1, A.A. Belinskii1, E.N. Pastukhova2, M.A. Burlak1, N.P. Ikonnikova1, E.O. Mishin1, N.I. Shatskii1
- Sternberg Astronomical Institute, Moscow State University,
Universitetskij pr. 13, Moscow 119992, Russia
- Institute of Astronomy, Russian Academy of Sciences, ul. Pyatnitskaya 48, Moscow, 119017, Russia
1665 magnitude measurements in the  ,  ,  , and
 filters were acquired for the double-mode Cepheid AS Cas. The
light curves for both fundamental and first-overtone modes were
constructed.
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We performed CCD observations of the Cepheid AS Cas in October
2020-February 2021 (the JD range 2459126-2459265) at the
Caucasus Mountain Observatory (CMO, Russia) with the 60-cm
telescope using the Andor iKon-L camera, 2048
2048 pixels,
with a pixel size of 13.5 microns. The Johnson 
-band filters
and 
-band filters of the ZTF survey system (Masci et al.,
2019) were used. Information about the CMO and description of the
observing data reduction technique can be found in our previous
paper (Berdnikov et al., 2020). We obtained a total of 1665
magnitude measurements with photometric errors close to 0.01 mag.
Observations are available in a text file in the html version of the paper (Table 1). The light curves, constructed with the fundamental period, are shown in Fig. 1.
observations (Table 1) phased
with the fundamental period.
Using the Period04 code (Lenz and Breger, 2004), we determined the
frequencies for the fundamental, 
, and first-overtone, 
,
modes. Then we used 17 combinations of these frequencies (Table 2;
amplitudes in filter are given for information) to approximate
our observations by Fourier series. For this purpose, we converted
all observations to intensities and, for each 
th observation,
set up conditional equations in the form:
 |
(1) |
is the observed intensity; 
is the
mean intensity; 
and 
are the amplitudes; 
is the
Julian Date of observation; 
is the frequency. The system of
linear equations (1) is solved by the least-squares method for
unknowns , , and .
Clearly, the difference between observed intensity, , and the
sum (1) without harmonics of any particular mode gives us the
intensity for this mode. These intensities, converted back to
magnitudes, form the light curves of AS Cas for the fundamental
and first-overtone modes given in Table 3 and
Table 4 (in the html
version of the paper), respectively. They are shown in Fig. 2 and
Fig. 3, constructed with the light elements:
 |
(2) |
 |
(3) |
Table 2. Frequencies for equations (1). Amplitudes for the filter are given
are given | Name of frequency | Frequency, d |
Amplitude, mag |
|
0.33067805 | 0.3366 |
| 2 |
0.66135610 | 0.0961 |
| 3 |
0.99203415 | 0.0361 |
| 4 |
1.32271220 | 0.0062 |
| + |
0.79471209 | 0.1209 |
| 2+ |
1.12539014 | 0.0723 |
| - |
0.13335599 | 0.0686 |
| +2 |
1.25874613 | 0.0421 |
| 2(+) |
1.58942418 | 0.0288 |
| 2- |
0.19732206 | 0.0143 |
| 3+ |
1.72278017 | 0.0127 |
| 3- |
0.52800011 | 0.0080 |
| 2(-) |
0.26671198 | 0.0022 |
|
0.46403404 | 0.2197 |
| 2 |
0.92806808 | 0.0414 |
| 3 |
1.39210212 | 0.0079 |
| 4 |
1.85613616 | 0.0054 |
The sum (1) for harmonics of any particular mode gives the
template light curve for this mode; these are shown in Fig. 4 and
Fig. 5 (for the fundamental and first-overtone modes,
respectively) and presented in the html version of the paper as
Table 5 and Table 6, which list the , , , and -band
magnitudes for phases from 0 to 0.995 with a step of 0.005. We
plan to use these templates to study the behavior of pulsating
periods of AS Cas.
Acknowledgments: This work was supported by the Russian
Foundation for Basic Research (project No. 19-02-00611).
References:
Berdnikov, L.N., Belinskii, A.A., Shatskii, N.I., et al., 2020, Astron. Rep., 64, 310
Masci, F.J., Laher, R.R., Rusholme, B., et al., 2019, Publ. Astron. Soc. Pacif., 131, 018003
Lenz, P. and Breger, M., 2004, Proceedings IAU Symposium, No. 224, 786