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\renewcommand{\@evenfoot}{\hbox to \textwidth {Astron. Tsirkulyar No.~1652\hfil\thepage\hfil October 2022}}
\renewcommand{\@oddfoot}{\hbox to \textwidth {Astron. Tsirkulyar No.~1652\hfil\thepage\hfil October 2022}}
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{ISSN 0236-2457}\hfill {DOI:10.24412/0236-2457-2022-1652-1-4}
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\centerline{ASTRONOMICHESKII TSIRKULYAR}}
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\centerline{Published by the Eurasian Astronomical Society}
\centerline{and Sternberg Astronomical Institute}
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\centerline{No.1652, 2022 October 24}
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\centerline{\textbf{FAST LINE PROFILE VARIATIONS FOR $\gamma\,$Cas TYPE STARS: CASE $\pi\,$Aqr}}
% \centerline{\textbf{Capitalize All the Words,}}
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\centerline{\textbf{A.F.~Kholtygin$^1$, M.A.~Burlak$^2$, Yu.V. Milanova$^1$, A.V.~Dementyev$^1$, and O.A.~Tsiopa$^3$}}
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\centerline{\textit{$^1$Saint-Petersburg University}}
\centerline{\textit{E-mail: afkholtygin@gmail.com}}
\centerline{\textit{$^2$Sternberg Astronomical Institute, Moscow University}}
\centerline{\textit{$^3$Main (Pulkovo) Astronomical observatory}}
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\centerline{\small Received May 23, 2022, after revision October 20, 2022}
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\textbf{Abstract.} Fast spectral variations of $\gamma\,$Cas type stars $\pi\,$Aqr (a $\gamma\,$Cas analogue star) are analysed.
Regular line profile variations (LPVs) at the short-time scale with periods from 4 to 136 minutes are detected.
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\section*{Introduction}
The $\gamma\,$Cas type stars is a special subclass of Be stars [1]. These stars possess by the hard and strong thermal X-ray emission [1, 2] with high plasma temperature up to 20-30 keV.
Their X-ray luminosities $L_\mathrm{X}>10^{31}$\,erg\,cm$^{-2}$s$^{-1}$ and are intermediate between those of normal massive stars and those of X-ray binaries and
are characterized by short- and long-term variations in the [2--10]\,keV energy range [2].
The origin of these peculiar X-ray emission remains badly known with two leading scenarios: accretion on to a compact object [3] or star-disc interactions [1].
To shed light on the nature of these enigmatic objects, we started a program of searching for their fast spectral variations [4, 5].
In the present paper our recent observations of the B1III-IVe $\gamma\,$Cas type stars $\pi\,$Aqr made at the 1.25-m telescope in the Crimean station of
Sternberg Astronomical Institute by Moscow State University are analysed.
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\section*{Observations and data reduction}
The Be star $\pi\,$Aqr (HD\,212571) is the fast rotating ($V\sin i=215\pm 4$\,km\,s$^{-1}$) massive ($M=10.7\pm0.7M_{\odot}$) binary stellar system [6, 7].
The orbital period of the binary system is 84.1 days and the mass of the component ($2-3\,M_{\odot}$) corresponds to the main sequence A-F stars~[8].
Our observations of $\pi\,$Aqr were made with the 1.25-m telescope on the night of October 10/11, 2021. All spectra were obtained with an exposure time 5\,s and time resolution 8\,s
including SSD reading-out time. Totally 1250 spectra in the range $\lambda\lambda\,4420-6860\,$\AA\ with a spectral resolution $\sim\,$1000 are obtained.
The full duration of observation is $\sim\!$165~min.
The data reduction was made using the code CCDops\footnote{http://company7.com/library/sbig/sbwhtmls/ccdopsv5.html}. %
One-dimensional spectra were obtained by summing the counts within a 40-pixel ($79''$) aperture, at a mean FWHM of 26 pixels, with the subtraction of the sky
background from a region of 60--120 pixels from the centre of the stellar spectrum. The wavelength calibration was made with a Ne-Ar lamp.
The spectra are normalized to the continuum. The normalization procedure is described by Kholtygin et al.~[9]. The normalized spectra averaged
over all 1250 spectra is given Fig.~\ref{Fig.MeanSpGamCas}.
%*******************************************************************************************Fig.01
\begin{figure}[!ht]
\begin{center}
\includegraphics*[height=0.225\textheight]{AC1652-Figure1.eps}
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\caption{Averaged over all obtained spectra the mean spectrum of $\pi\,$Aqr}
\label{Fig.MeanSpGamCas}
\end{figure}
%*******************************************************************************************Fig.01
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\section*{Fast LPVs}
Analysing the difference profiles we will use the Doppler shifts $V$ from the laboratory wavelength $\lambda_0$ of the line instead of the wavelength $\lambda$, where
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$$
V=c\cdot \left( \frac{\lambda-\lambda_0}{\lambda_0}\right),
$$
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and $c$ is the speed of light. The difference line profile
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\begin{equation}
\label{Eq.DiffProf}
d(V,t)=F(V,t) - \overline{F}(V) .
\end{equation}
%
where $N$ is the total number of the analysed spectra, $F(V,t)$ is the continuum normalized line flux for the spectrum obtained at time $t$, and $\overline{F}(V)$
is the mean normalized line flux at the velocity $V$. Dynamical spectra $d(V,t)$ for H and HeI lines are given in Fig.~\ref{Fig.DynSpectra}.
One can see the similarity of LPVs for H$_\beta$, HeI\,5107, and H$_\alpha$ lines. Fast variations at the minute time scale may be seen.
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\begin{figure}[!ht]
\begin{center}
\includegraphics*[height=0.25\textheight]{AC1652-Figure2.eps}
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\caption{Dynamical spectra of lines H$_\beta$ (left panel), HeI\,5017 (middle panel), and H$_\alpha$ (right panel)}
\label{Fig.DynSpectra}
\end{figure}
%*******************************************************************************************Fig.02
%=====================================================================================================================================2.
\section*{Regular components of LPVs}
For looking for the periodic components of the line profile variations in the spectrum of $\pi\,$Aqr the CLEAN method of Fourier analysis~[10] for difference profiles $d(V,t)$ of HeI and
H~lines are used. The errors of the regular component frequency and the errors of the corresponding periods in the Fourier spectrum are calculated using the expression
$\Delta\nu \le 1/T$~[11], where $T= 165.4\,$minutes is the total duration of observations.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Table.01
\begin{table}[!ht]
\label{Table.LPVperiods}
\begin{center}
\caption{Periods of regular LPV's components}
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\begin{tabular}{lccccc}
\hline
No. & 1 & 2 & 3 & 4 & 5 \\ \hline
P, min & $4.02\pm0.10$ & $23.08\pm3.22$ & $27.78\pm4.67$ & $42.86\pm11.11$ & $62.51\pm23.63$ \\ \hline
No. & 6 & 6 & 8 & 9 & 10 \\ \hline
P, min & $75.01\pm34.02$ & $88.25\pm47.09$ & $107.15\pm69.43$ & $115.39\pm80.52$ & $136.39\pm112.49$ \\ \hline
\end{tabular}
\end{center}
%%% {\bf Notes to Table 1.} Here you can insert some comments to the above Table.
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%==Table.01
The detected periods together with their errors are given in Table~1. Given short-time LPVs are firstly detected in spectra of $\pi\,$Aqr was not known before but they
are similar to those calculated by us for $\gamma\,$Cas~[4].
The period $P_9=115.39\pm80.52$ of LPVs is close to period $P_\mathrm{opt}=113\,$min detected from an analysis of spectral observations and
to period $P_\mathrm{phot}=122\,$min from the photometric observations of $\pi\,$Aqr~[2].
The similar short time scale periods we detected in the X-ray light curve of the $\gamma\,$Cas type star HD\,110432 and in the optical
spectra of the $\gamma\,$Cas type star HD\,45995 from 30 to 150 min~[12]. Resuming we can conclude that the minute time scale optical and photometric variations can be
typical for the $\gamma\,$Cas type stars.
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\section*{References}
\hspace{6.5mm}
{\small
1. Smith M.A., Lopes de Oliveira R., Motch C., Adv. Space Res., \textbf{58}, 782 (2016)
2. Naze Y., Pigulski A., Rauw G., Smith M.A., MNRAS, \textbf{494}, 958 (2020)
3. Postnov K., Oskinova L., Torrejon J.M., MNRAS, \textbf{465}, L119 (2017)
4. Kholtygin A.K., Burlak M.A., Tsiopa O.A., Astron. Tsirk., No. 1649, 1 (2021)
5. Kholtygin A.F., Moiseeva A.V., Yakunin I.A. et al., Geom.\& Aeron., \textbf{61}, 923 (2021)
6. Tetzlaff N., Neuhauser R., Hohle M.M., MNRAS, \textbf{410}, 190 (2011)
7. Arcos C., Kanaan S., Chavez J. et al., MNRAS, \textbf{474}, 5287 (2018)
8. Bjorkman K.S, Miroshnichenko A.S., McDavid D., Pogrosheva T.M., ApJ, \textbf{573}, 812 (2002)
9. Kholtygin A.F., Burlakova T.E., Fabrika S.N., Astron. Rep. \textbf{50}, 887 (2006).
10. Roberts D.H., Lehar J., Dreher J.W., Astron. J. \textbf{93}, 968 (1987).
11. Vityazev V.V., Analiz neravnomernykh vremennykh ryadov (SPbSU Press, St. Petersburg, 2001, in Russian).
12. Kholtygin A.F., Moiseeva A.V., Yakunin I.A. et al., Geom.\& Aeron., in press (2022)
}
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\centerline{\textbf{�.�.~��������$^1$, �.�.~������$^2$, �.�.~��������$^1$, �.�.~���������$^1$ � �.�.~�����$^3$}}
\centerline{\textit{$^1$�����-������������ ��������������}}
\centerline{\textit{E-mail: afkholtygin@gmail.com}}
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\centerline{\textit{$^2$��������������� ��������������� �������� ����� �.�. ���������� ���}}
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\centerline{\textit{$^3$������� (����������) ��������������� ������������}}
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\textbf{������.} ���������������� ������� ������������ ������������ �������� ����� � ������� $\pi\,$Aqr. ���������� ���������� �������� �������� � ��������� �� 4 �� 136 �����.
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