Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.astro.spbu.ru/staff/afk/Papers/2006/delOriE.pdf Äàòà èçìåíåíèÿ: Fri Nov 19 16:09:01 2010 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 02:45:27 2012 Êîäèðîâêà: koi8-r Ïîèñêîâûå ñëîâà: ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ï ð ï ð ï ï ð ï ð ï ï ð ï

ISSN 1063-7729, Astronomy Reports, 2006, Vol. 50, No. 11, pp. 887­901. c Pleiades Publishing, Inc., 2006. Original Russian Text c A.F. Kholtygin, T.E. Burlakova, S.N. Fabrika, G.G. Valyavin, M.V. Yushkin, 2006, published in Astronomicheski Zhurnal, 2006, Vol. 83, No. 11, i pp. 990­1005.

Microvariability of Line Profiles in the Spectra of OB Stars: Ori A
A. F. Kholtygin1* , T. E. Burlakova
1

2, 3

, S. N. Fabrika3, G. G. Valyavin2, 3 ,and M. V. Yushkin3

3

Sobolev Astronomical Institute, St. Petersburg State University, Bibliotechnaya pl. 2, Petrodvorets, 198904 Russia 2 Bohyunsan Optical Astronomy Observatory, Jaceon P.O.B., Young-chun, Kyung-pook, 770-820, Republic of Korea Special Astrophysical Observatory, Russian Academy of Sciences, Nizhni i Arkhyz, Karacha i-Cherkessian Republic, 357147 Russia
Received October 20, 2005; in final form, May 14, 2006

Abstract--We have studied variability of the spectral lines of the OBstar Ori A--the brightest component of the Ori triple system. Forty spectra with signal-to-noise ratios 500-800 and a time resolution of four minutes were obtained. We detected variability in the HeII4686, HeI4713, and H absorption and the CIII5696 emission profiles. The amplitude of the variability is (0.5-1)% of the continuum intensity. The dynamical wavelet spectrum of the profile variations reveals large-scale components in the interval 25-50 km/s that move within the -V sin I to V sin i band for the primary star of the system, Aa1 , with a band crossing time of 4h -5h . However, some of the variable features go outside the band, presumably due to either imhomogeneities in the stellar wind from Ori Aa1 or non-radial pulsations of the weaker components of the system, Aa2 or Ab. The detected variability may by cyclic with a period of 4h . We suggest that it is associated with non-radial pulsations of the primary in the sector mode (l, m) = (2, -2). PACS numbers : 97.10.Sj, 97.20.Ec, 97.20.Ec DOI: 10.1134/S1063772906110035

1. INTRODUCTION Spectral observations of hot stars at UV [1, 2], optical [1­6], and X-ray [7, 8] wavelengths indicate the presence of structures in the atmospheres of these stars with various sizes and densities, and with lifetimes from less than an hour to several days. Variations of the line profiles in the spectra of OB stars are mainly regular or quasi-regular. The spectra of B stars and six O stars display regular short-period (3­ 12 h) profile variations for numerous lines (in particular, HeI) associated with the non-radial pulsations of these stars [6]. Weak magnetic fields (several hundred Gauss at the stellar surface) may be one factor favoring the formation of large-scale structures in the atmospheres of O stars [9]. Currently, magnetic fields have been detected with sufficient reliability only in one O star, 1 Ori C [10], and several early B subtype stars [11]. Unlike Bstars, the amplitudes of the line profile variations in the spectra of O stars are relatively small (1%­3%; see, for example, [12]), so it it is more apprpriate to call this line profile microvariability. To detect such variability and to clarify its nature,
*

observations with high time and spectral resolution and high signal-to-noise ratios (300) are needed. Here, we continue our study of the microvariability of hot stars begun in [12], when we analyzed lineprofile variability in the spectra of the supergiants 19 Cep, Cam, and Ori A (O9.5II). We now present the results of spectral observations of the spectral triple system Ori A, whose primary displays the same spectral type as Ori A -- 09.5. Section 2 contains general information about the Ori A system, and Section 3 describes the observations and reduction of the spectra. Section 4 presents the methods used in and the results of our analysis of line-profile variability in the spectrum of Ori A. Our interpretation of the observations is presented in Section 5, followed by a brief conclusion section. 2. THE Ori A SYSTEM Ori is a wide visual triple system containing three components: A (HD 36486), B (Bd­00 983B), and C (HD 36485), with apparent visual magnitudes of 2.23m , 14.0m , and 6.85m , respectively. Components B and C are at distances of 33 and 53 , respectively,
887

E-mail: afk@theor1.astro.spbu.ru


888 Parameters of the Ori A system Parameter Distance to the star, pc Distance to component Aa , R Spectral type Orbital period Radius, R Mass, M Luminosity log(L/L ) T eff ,K log g Contribution to optical radiation in HeI6678 line region, % V sin i,km/s V ,km/s Mass loss M , M /yr
1

KHOLTYGIN et al.

Components Aa1 360 ­ 09.5II ­ 11 11.2 5.26 33 000 3.4 70 157 ± 6 133 2000 1.1 â 10
-6

Aa2 360 33 B0.5III 5.7325 days 4 5.6 4.08 27 000 3.8 7 138 ± 16 ­ 1500 1.2 â 10
-7

References Ab 360 25 000 B(early subtype) 200 yrs ­ 27 ­ ­ ­ 23 300 ­ ­ ­ [15] [8] [14] [14] [8, 14] [14] ­ [16, 17] [16, 17] [14] [14] [18] [19, 20] [19, 20]

from the primary component, A. Our observations refer to the brightest component, Ori A. Ori A (HD 36486, HR 1852) is a physical triple system with the primary Ori Aa, which is an eclipsing binary with orbital period P = 5.73d [13], and the secondary Ori Ab, with an orbital period of 224.5 yrs. Recent detailed Doppler tomography studies [14] have made it possible to refine the parameters of the Ori A triple system, presented in the Table. The brightest component, Ori Aa1 , is a high-mass O9.5II star with an intense stellar wind; the star's mass-loss rate is log M (M /y r ) -6.0 and the limiting velocity of the wind is V 2000 km/s. A value a factor of two lower is given in [21]: log M -6.3. According to [16, 22], V 2300 km/s. The rotational velocities of the star determined by different authors differ appreciably. In [14], a relatively high rotational velocity for the primary was obtained, V sin i = 157 ± 6 km/s, while Abt et al. [18] found V sin i = 133 km/s (see the Table). The study [16] presents a photospheric radius for the primary, Aa1 ,of R = 22R , twice the value R = 11R given in the Table. This discrepancy is probably due to the fact that a larger distance to the star was used in [16] than the distance in the Table, 450 pc. The component Ori Aa2 is a B0.5 III star. Preliminary studies indicate that the third component

of the system, Ori Ab, is an early B-subtype star with broad spectral lines, indicating either a high rotational velocity (V sin i 300 km/s) or binarity of the star [14]. Harvin et al. [14] determined the orbital inclination of the Ori Aa close binary to be i 67 and estimated the mass of the components to be M (Aa1 ) = 11.2 M and M (Aa2 ) = 5.6 M . The secondary, Ori Aa2 , is appreciably weaker than the primary (see Table). Both the primary and secondary, Aa1 and Aa2 , have masses roughly half the mass of main-sequence stars with corresponding positions on the HR diagram [14]. It was suggested in [14] that, in the course of its evolution, the system underwent a commonenvelope stage in which both stars filled their Roche lobe and with intense mass loss. After the system had lost half its total mass, the distance between the components increased and the mass loss ceased. The mass of the third component of the system, Ab, cannot be derived from the radial velocities. The Table presents the value M (Ab) 27 M from [14], which corresponds to a main-sequence star with M bol = -4.2m . A main-sequence star with a mass of 27 M should have spectral type O8.5V [23], which contradicts the spectral classification in the Table. To explain this inconsistency, Harvin et al. [14] suggest that Ab may be a close binary consisting of two mainsequence B0.5V stars with a mass of 19 M .
ASTRONOMY REPORTS Vol. 50 No. 11 2006


LINE PROFILES OF OB STARS

889

3. OBSERVATIONS AND REDUCTION OF THE SPECTRA Our spectral observations of the Ori A system were carried out on January 10/11, 2004 with the 6m telescope of the Special Astrophysical Observatory as part of our program to search for rapid line-profile variability in the spectra of early-type stars [12]. We used the NES quartz echelle spectrograph [24], which is permanently mounted at the Nasmyth focus and equipped with the Uppsala 2048â2048 CCD. To increase the spectrograph's limiting magnitude, we used a three-cut image cutter [25]. The resulting spectral resolution was R 60000 and the dis° persion 0.033 A/pixel. The image size during the observations was about 3 . The reference spectrum was provided by a ThAr lamp. The angular separation between the most distant components, Ori Aa1 and Ab, is about 0.3 (see Table), which means that all components contribute to the resulting spectrum of the Ori A system. Over a total observation time of 2h 50m , we obtained 40 spectra of the star with an exposure time of 180 s. Taking into account the CCD readout, the time resolution was 260 s. The signal-to-noise ratio per pixel ° was 500 in the blue (4500 A) and 800 in the red ° (6000 A). The preliminary reduction of the CCD echelle spectra was done in the MIDAS package [12]. We adapted the standard ECHELLE procedures of the MIDAS package for data obtained with an image cutter. The reduction stages included 1) median filtering and averaging of the bias frames with their subsequent subtraction from the remaining frames; 2) cleaning of cosmic rays from the frames; 3) preparation of the flat-field frame; 4) determination of the position of the spectral orders (using the method of Ballester [26]); 5) subtraction of scattered light (to determine the contribution of scattered light, we distinguished the inter-order space in the frames, and then carried out a two-dimensional interpolation; this function was recorded in individual frames to be subtracted from the initial images); 6) extraction of the spectral orders from the reduced images of the stellar spectrum, the flat fields, and the wavelength reference spectra; flat-field reduction; 7) wavelength calibration using a twodimensional polynomial approximation for the identifications of the lines of the reference spectrum in various spectral orders. When the image cutter is used, each order of the echelle image is represented by three sub-orders
ASTRONOMY REPORTS Vol. 50 No. 11 2006

(cuts). In a given order, the instrumental shift of the upper and lower cuts relative to the middle cut was determined via a cross-correlation with the reference spectra. The three cuts obtained in a given order were summed using median averaging, taking into account the determined instrumental shifts. To study the line profile variability, the processed spectra were normalized to the continuum level reconstructed in each echelle order. We drew the continuum in spectral orders containing narrow spectral lines using the technique developed by Shergin et al. [27], in which spectra are smoothed with a variable ° Gaussian filter with a 25­30 A window, with the same parameters for the entire set of spectra. In orders containing broad (usually hydrogen) spectral lines, the continuum was drawn using the following procedure. In all 40 spectra, broad lines were cut out in fixed wavelength intervals. To determine the position of the continuum, we used a polynomial approximation for all wavelengths of the order, except for the regions of the cut-out broad spectral lines. The approximation parameters remained unchanged for all spectra of the set. This procedure provides stability and reproducibility of our determination of the continuum in all the spectra with an accuracy of up to several tenths of a percent. This makes it possible to reach high accuracy in deriving the differential line profiles and detecting profile variability in broad lines at levels down to 0.1%. 4. LINE PROFILE VARIABILITY

4.1. Contribution from Different Components of the System to the Line Profiles
We selected sufficiently strong unblended lines for detailed studies of the line-profile variations. The selection criterium for absorption lines was that the residual intensity be rmax > 0.1. These criteria led to the selection of the HeII4686, HeI4713, and H lines. In addition, we studied the profiles of the CIII5696 emission line. The Ori A system contains three O and B stars, each of which could have variable line profiles; the observed profiles result from the contributions of all stars. It follows from the Table that above two-thirds of the flux from the system at the wavelength of the HeI6678 line comes from the primary component, Aa1 . The contributions from Aa2 and Ab at these wavelengths are substantially smaller. At other wavelengths, the contributions from Aa2 and Ab may differ from those in the Table. To determine to what extent each of the stars in the system is responsible for line-profile variability, the contribution of each star to the total profiles of the analyzed lines must be clarified. In addition, taking into account the


890

KHOLTYGIN et al.

I/Ic 1.00 0.98 0.96 0.94 0.92 0.90 0.88 0.86 ­ 400

Figure 1 presents the total profile of the photospheric HeII4686 line calculated using these parameters. The observed profiles are reproduced very reasonably. The small discrepancies between the observed and calculated profiles near V =150­250 km/s may be due to the contribution of the stellar wind from Aa1 .

4.2. Variations of the Average Profiles. Differential Profiles
The nightly-average line profiles in O-star spectra are often substantially variable [6]. Line-profile variations on shorter time intervals are insignificant. To make the line-profile variations in the spectra of Ori A in time intervals of 30­40 min more clearly visible, we divided the profiles into four groups with ten profiles in each and calculated the average profiles for these groups. The average profiles for each group presented in Fig. 2 display appreciable variations within an hour. These variations are particularly clearly visible in the HeI4713 line. In the transition from the first group of spectra to the following three groups, the line depth decreases by 1%­1.5%. These variations are correlated with variations in the groups of average profiles for the CIII5696 emission line. In the transition from the first to the fourth group of profiles, the flux in the central region of the line increases by 1%. The amplitude of the flux variations in the H and HeII4686 lines reaches 1%­2%. In the blue wing of the CIII5696 profile, narrow absorption features with depths less than 0.01 of the continuum intensity can be seen. Similar, but less deep, features are also present in the red wing of the line. Our analysis shows that the positions of all of these features coincide with those for atmospheric absorption lines, primarily water vapor [29]. To reveal variable features in the line profiles, we constructed differential profiles by subtracting the average profile obtained using all forty available spectra of Ori A from the individual profiles. Figure 3 presents dynamical differential profiles of the studied lines in the spectrum of Ori. Grey shades indicate deviations of individual profiles from those averaged over the entire set of spectra. For convenience, the wavelength scale is translated into Doppler shifts from the line center. The radial velocity of the center of mass of the Ori A system was used as the zero point of the wavelength scale (see Section 4.1). We show the differential profiles in the "negative", i.e., darker regions in Fig. 3 correspond to regions of the profile that lie above the average value (peaks), while lighter regions correspond to parts of the profile
ASTRONOMY REPORTS Vol. 50 No. 11 2006

­ 200

0

200

400 V, km/s

Fig. 1. HeII4686 synthetic (bold curve) and observed (thin curve) line profiles, plotted in terms of the Doppler shift V from the line center.

substantial scatter of the v sin i values for Aa1 (see the Table), reliable v sin i estimates for the components of the Ori A system are highly desirable. To solve these problems, we modeled the combined profiles for the photospheric HeII4686 and HeI4713 lines in the spectrum of Ori A. We assumed the total line profile to be the sum of the contributions from the components, since Aa1 and Aa2 are not eclipsed at the above orbital phases. We calculated the rotation-broadened line profiles using the standard relations (see, for example, [28]). The radial velocities of the components for the time of the observations were calculated using the ephemeris of Harvin et al. [14]. During our observations, the orbital phase varied in the narrow interval 0.848-0.851. For such small phase variations, the velocities of the components can be considered to be constant over the total observation time. The heliocentric velocities V (Aa1 ) = -21 km/s and V (Aa2 ) = -102 km/s were obtained using the ephemeris [14]. For convenience in comparison, both the calculated and observed line profiles were transformed into the system of the center of mass of the close binary Ori Aa. The velocity V r 23.0 km/s [14] was used as the zero-point of the velocity scale. In this system, the velocity of the third component is V (Ab) 27 km/s [14].


LINE PROFILES OF OB STARS

891

F/Fc 1.010 0.990 0.970 0.950 0.930

1.010 1.000 0.990 0.980 0.970 0.960

0.910 0.890 0.870 0.850 4677 1.000 0.975 0.950 0.925 0.900 0.875 0.850 0.825 0.800 0.775 0.750 0.725 0.700 4850 4854 4858 4862 4866 4872 , å 4680 4683 4886 4689 4692 4695

0.950 0.940 0.930 0.920 4707 4709 4711 4713 4715 4717 4719 1.055 1.050 1.045 1.040 1.035 1.030 1.025 1.020 1.015 1.010 1.005 1.000 0.995 0.990 5687 5690 5693 5696 5699 5702 5705 , å

Fig. 2. Average profiles for spectra 1­10 (thin solid curve), 11­20 (dashed curve), 21­30 (bold solid curve), and 31­40 (dotted curve) for the HeII4686 (top left), HeI4713 (top right), H (bottom left), and CIII5696 (bottom right) lines. The flux in the line frequencies, F , is given as a fraction of the flux in the continuum adjacent to the lines, Fc . The arrows indicate the laboratory wavelengths of the lines.

that lie below the average value (valleys). This makes it easier to identify regular variations of the profiles in Fig. 3. The HeII4686, HeI4713, and H line profiles show that the peaks move from the violet to the red wing of the profile. We can see a broad (50­100 km/s), variable feature in the vicinity of the HeII4686 line. The feaASTRONOMY REPORTS Vol. 50 No. 11 2006

ture appears at a velocity near -100 km/s in the first (lower) differential profiles, and is then gradually shifted towards the line center. In the last (upper) profiles, it is visible in the domain of positive velocities. Such behavior of features in the differential profiles is typical for non-radial pulsations [30]. Virtually no obvious spectrum-to-spectrum profile variations near


892

KHOLTYGIN et al.

2.5 2.0 1.5 1.0 0.5 0

I, r

2.5 2.0 1.5 1.0 0.5 0 ­200 0 200 V, ìî/ð
Fig. 3. Dynamical spectra for the profile variations for the HeII4686 (top left), HeI4713 (top right), H (bottom left), and CIII5696 (bottom right) lines. The interval between consecutive spectra is four minutes. Dark regions in the diagrams correspond to intervals brighter then the average profile (peaks), and light regions to less bright intervals (valleys).

­200

0

200

weaker spectral lines, due to both the short duration of the observations and the low amplitude of the profile variations. We used the technique described in the following subsection to reveal profile variations in such weak lines.

averaged over all the observations. The dispersion of the random Fi () is then equal to D() = TVS() 1 = N -1
n n

(1)
2 i=1

gi Fi () - F i ()
i=1

gi

.

4.3. Analysis of the Spectrum of Time Variations of the Differential Spectra
The method of Fullerton et al. [31] is often used to elucidate the presence of weak line profile variability. We describe here a substantially modified version of this technique, which we used in our analysis. Suppose that N spectra of a studied star have been obtained. We denote Fi ()(i = 1,... ,N ) to be the flux in the ith spectrum at wavelength , normalized to the continuum. Let F i () be the flux at wavelength

Here, gi is the relative weight of the ith observation, c which is inversely proportional to i "-- the standard deviation F i () at wavelengths near the line whose profile variability is being studied. This definition for gi makes it possible to take into account the different qualities of the data in the analyzed set of spectra. TVS(), or the Time Variation Spectrum [31], obeys a 2 /(N - 1) distribution with N - 1 degrees of freedom. In the case of profile variability with a sufficiently
ASTRONOMY REPORTS Vol. 50 No. 11 2006


LINE PROFILES OF OB STARS

893

high amplitude, the TVS() in the vicinity of the corresponding line substantially exceeds its values in the adjacent continuum. To ensure that the increase in the amplitude is due to real variability, we specified asmall significance 1 for the hypothesis that the excess is due to a random variation of the noise component of the profile. The quantiles for the 2 distribution are calculated in the ordinary way for this 1 level (see, for example, [32]). Let 2 be specified so that the probability P (2 /(N - 1) > 2 ) = . If the calculated TVS() value exceeds 2 , the hypothesis that the line profile is variable can be adopted. As was noted in [12], for lines with smallamplitude profile variations or with a small number of spectra, the function TVS() cannot be used to prove whether a given line profile is variable. In the absence of any visible variations, we determined whether a line profile was indeed variable using the following procedure. Before the standard-deviation spectrum was obtained, the differential spectra were pre-smoothed using a filter that is broad compared to the pixel size. If the filter width is on the wavelength scale, then the amplitude of the smoothed random (noise) component of the differential profiles Nj (t) decreases after smoothing by a factor of /, where is the width of an individual pixel on the wavelength scale in the vicinity of the line. If the width of the variable component is not smaller than that of the filter, then smoothing with this filter will not substantially change the amplitude of the variable component, while, after the smoothing, peaks in the standard deviation spectrum that correspond to the variable component can be detected with increased reliability. It was shown empirically that the best results are obtained for smoothing with a Gaussian filter with a ° width of S = 0.5-1.0 A(15-30 pix.). To more clearly demonstrate the method used to search for weak profile variations, we used a smoothed time-variation spectrum, smTVS, which is a collection of spectra of the normalized standard deviation (, S ) = TVS(, S ) with the differential spectra smoothed with a Gaussian filter with a variable width S . Figure 4 presents density diagrams for the timevariation spectra for the HeII4686 and H line profiles. Darker areas correspond to higher amplitudes of the smTVS spectrum. Only values corresponding to significance levels < 10-4 for the hypothesis that the profiles are not variable are presented. The density diagrams show that the variability of the H and HeII4686 lines is clearly present. The smTVS spectrum for the HeII4686 line ° profile with the filter width S > 0.3 A indicates variability of the CIII4673.95, OII4673.75, 4676.234,
ASTRONOMY REPORTS Vol. 50 No. 11 2006

NII4674.909, 4678.14, and SiIII4673.273 lines, which cannot be detected using ordinary methods. With larger filter widths, variability of a large group of OII, NIII, and ArII lines at wavelengths from ° 4871to4890 Abecomes visible. Note that, in spite of the fact that these lines are extremely weak and their residual intensities do not exceed the noise level (by one pixel along the spectrum) at the adjacent continuum, their variability is clearly detected. Unfortunately, our technique cannot be used to localize weak lines with variable profiles accurately when larger filter widths are used. Note that the efficiency of this method of using the smTVS spectra to search for weak line-profile variability is sensitive to the number of spectra obtained, and increases substantially as this number increases.

4.4. Wavelet Analysis for the Line-Profile Variations
Analysis of the differential line profiles in the spectra of a star (Fig. 3) indicates the presence of a number of discrete features. Many small-scale features are connected with the noise component of the profiles, whereas larger-scale features may be due to the regular component of the profile variations [12]. A very suitable mathematical technique for studying the development of different-scale profile features is wavelet analysis (see, for example, [5, 33]). It is advisable to use as the analyzing (or mother) wavelet the socalled MHAT wavelet, (x) = (1 - x2 )exp(-x2 /2), which displays a narrow energy spectrum and whose zero and first momenta are equal to zero. The MHAT wavelet is essentially the second derivative of a Gaussian function (taken with a minus sign) that can be used to describe features in the differential line profiles. Using this wavelet, the integral wavelet transformation can be written [33, 34]: 1 W (s, u) = s =
-

f (x)

-

x-u s

dx

(2)

f (x)su (x)dx,

where f (x) is the studied function (in our case, a differential line profile). The signal energy energy, EW (s, u) = W 2 (s, u), characterizes the energy distribution of the studied signal in (s, u) = (scale, coordinate) space. Further, we will analyze the differential line profiles in the form r (V ) = Fi (V ) - F i (V ),where the Doppler shift V from the central frequency of the line is used as the x coordinate. In this case, the scale variable s is expressed in km/s.


894

KHOLTYGIN et al.

0 ­0.5 ­1 ­1 ­2 ­2 log S (å) .0 .5 .0 .5 4660 0 ­0.5 ­1 ­1 ­2 ­2 .0 .5 .0 .5 4850 4860 4870 , å 4880 4890

4670

4680 , å

4690

4700

Fig. 4. Time variation spectrum for the HeII4686 (top) and H (bottom) line profiles. The vertical axis plots the logarithm of the filter width.

To study the evolution of features in the differential profiles, we calculated wavelet spectra, W (s, V ) = W (s, V , t), for the HeII4686, HeI4713, and H absorption lines and the CIII5696 emission line for all times t corresponding to our spectra. We will call the collection of functions W (s, V , t) the dynamical wavelet spectrum for the differential line profiles. Figure 5 presents density diagrams for the dynamical wavelet spectra of the studied lines for the scale parameter s = 50 km/s. The diagrams present the ratios d = (W - Wmin )/W rather than the function W (s, V , t) itself. Here, W = Wmax - Wmin , where Wmax and Wmin are the maximum and minimum W (s, V , t) for all possible t in the interval of V within the line profile. Darker regions correspond to larger W (s, V , t). We have marked only the values for the parameter d dcut "-- the cutting parameter of the wavelet spectrum. In Fig. 5, dcut = 0.6. For comparison, the average line profiles are placed beneath the wavelet spectra diagrams. In the average profiles, the dotted lines delineate the region -V sin i-V sin i for the primary, Aa1 (see Table). We can see in Fig. 5 that all the wavelet spectra display broad structures moving along the line profiles, with features moving from the violet to red edge of the line being most prominent. The same type of features are visible in the wavelet spectra of the absorption HeII4686, HeI4713, and H differential line profiles, moving from -110--100 km/s to 100-110 km/s over the total observation time,

2h 50m . The estimated crossing time Tcross for the entire band of -V sin i-V sin i is 4h .Note