COMMISSION 27 OF THE I. A. U. INFORMATION BULLETIN ON VARIABLE STARS Number 1948 Konkoly Observatory Budapest 1981 April 3 HU ISSN 0374-0676 RADIAL AND NON-RADIAL OSCILLATIONS IN HD 116994 (V743 Cen) HD 116994 (V743 Cen) is a large amplitude (deltaV ~0.25 mag) delta Scuti variable which McAlary and Wehlau (1979-MW) have pointed out may be oscillating in non-radial modes. In a frequency analysis of four consecutive nights of Johnson B observations MW derived a principal frequency of 9.79 d^-1 for HD 116994 with two subsidiary frequencies at 9.66 d^-1 and 9.85 d^-1. In analogy with Shobbrook and Stobie's (1974) work on 1 Mon, they suggested that the three closely spaced frequencies in HD 116994 may be due to pulsation in rotationally perturbed non-radial m-modes. Since McAlary and Wehlau's work, however, Balona and Stobie (1980a) have reanalysed 1 Mon and by applying their theory of phase shifts between the V light curve and B-V colour curve (Balona and Stobie 1980b) have shown that the frequency of highest amplitude in 1 Mon is due to radial pulsation. Similarly, the frequencies of highest amplitude in delta Scuti itself (Balona, Stobie, and Dean 1980), HD 188136 (Kurtz 1980a), and HR 1170 (Kurtz 1980b) have all been shown to be due to radial pulsation using this same technique. The suspicion therefore arises that the frequency of highest amplitude in HD 116994 may also be due to radial oscillation. We decided to test this hypothesis by applying Balona and Stobie's theory to the B and V phases of the frequency of highest amplitude in HD 116994. Observations in both B and V colours are available in the literature for this star in the original discovery paper by Chen (1968) as well as in a subsequent analysis by Chambliss (1968). However, before actually fitting the principal frequency of HD 116994 to Chen's and Chambliss' data to find the V and B-V phases, we felt a new frequency analysis of all of the available data on HD 116994 was warranted. Frequency Analysis A considerable number of observations of HD 116994 are scattered throughout the literature. Table I. summarizes them. Table I Data for HD 116994 JD Source Colours Comments 2440000+ 39243,4,8 Chen (1968) UBV observations given 39594,39603 Jones (1969) unspecified maxima only 39634,5,6,7,8 Chambliss UBV observations available - (1968) IAU(27). RAS-5 41445 Kilambi (1976) uvby observations given, magnitude scale inverted 42886,7,8 Geyer and Vogt UBV maxima only (1976) 42887,88,89,90 McAlary and B observations given Wehlau (1979) 43291 Balona and BV observations given Stobie (private communication) Using the technique of Fourier analysis of unequally spaced data (Deeming 1975) we have reanalysed some of the above B data with the results given in Table II. The column labelled 6 is the rms scatter of the residuals after prewhitening by each frequency. Table II. Frequencies derived for Various Subsets of the B data Data Set f A sigma d^-1 m mag m mag Chen (+-0.19) 82.9 9.78 109.4 29.0 19.56 28.9 20.9 9.90 15.7 17.5 (+-0.20) 111.4 Chambliss 9.78 153.1 31.1 19.57 31.4 20.1 (+-0.30) 86.5 McAlary and 9.79 119.1 20.9 Wehlau 19.60 22.3 13.9 10.57 12.8 or 9.60 12.4 The frequency of highest amplitude derived from all three of these data sets is the same. This is also true of the frequency of second highest amplitude which is clearly just the first harmonic of the frequency of highest amplitude. The third derived frequency presents some problems, however. For Chen's data we found a peak in the amplitude spectrum at f = 9.90 d^-1, for Chambliss' data we could find no outstanding third peak, and for MW's data we found the peak at f = 10.57 d^-1 to be slightly higher than its 1 d^-1 alias at f = 9.60 d^-1 which they selected. The discrepancy between our analysis of MW's data and their analysis may have to do with our slightly different analysis techniques, but, in any case, resolution problems inhibit a thorough analysis of any of the data sets in Table II. Loumos and Deeming (1978) have shown by analysing artificial data that two frequencies of equal amplitude can only be completely resolved using Fourier techniques if they are separated in frequency space by at least 1.5/DeltaT where DeltaT is the time span of the data set. For each of the data sets in Table II. 1.5/DeltaT is given in parentheses as the error in frequency. It can immediately be seen that the two frequencies at f = 9.66 d^-1 and at f = 9.85 d^-1 derived by MW are too close to the principal frequency at f = 9.79 d^-1 to be completely resolved. In order to circumvent this problem we attempted to derive the frequency of highest amplitude from all of the B data in the literature which have a time span of 4048 d (11 yr). Because each of the individual data sets span only a few days, cycle count across the yearly gaps is difficult to keep. Fortunately, the timing of Jones' observations some 40 d prior to Chambliss' observations in the same year suppress most of the yearly aliases in the amplitude spectrum. We artificially recreated Jones' data by shifting MW's light curve for JD 2442888 to match Jones' times of maximum and then produced an amplitude spectrum of all the B data listed in Table I. The frequency derived is not absolutely secure because of large 1 yr^-1 and ~1/10 yr^-1 aliases, but a highest peak does occur at f_1 = 9.77708 d^-1. For purposes of further analysis we adopt this frequency. Using a multivariate least squares program we fit the principal frequency f_1 = 9.77708 d^-1 and its first (2f_1) and and second 3(f_1) harmonics to all of Chen's, Chambliss', MW's, and Balona and Stobie's B data. The amplitude of the second harmonic is a negligible 4 m mag. Our final fit of f_1 and 2f_1 to the B data is given in Table III. Table III. Fit of f_1 and 2f_1 to all of Chen's, Chambliss', MV's, and Balona and Stobie's B data. f A phi sigma d^-1 m mag m mag f_1 9.77708 111+-2 1.952+-0.016 2f_1 19.55416 26+-2 1.679+-0.067 39 These parameters fit the relation DeltaB = Summa_i A_i * cos[2pi*f_i * (t-t_0)+phi_i] where t_0 = JD 2439000. We have determined a value of f1 of sufficient accuracy to resolve it from secondary frequencies more than +- 0.00025 d^-1 away. Thus the resolution problem discussed for the results in Table II. can be greatly reduced by prewhitening all of the B data by the parameters given for f_1 and 2f_1 in Table III.and then analysing the residuals. That gives the results as found in Table IV. For all three of these data subsets we find a frequency near f_2 = 9.9 d^-1 and hence consider the identification of that frequency to be secure. The close spacing of f_2 to f_1 indicates that at least one of those two frequencies must be due to pulsation in a non-radial mode. From both Chambliss' and MW's data we find another frequency which, within the resolution limits of those subsets, is coincident with 2f_1. It is Table IV. Frequencies derived from the residuals of the various data sets after prewhitening by f_1 and 2f_1 given in Table 3 Data Set f A sigma d^-1 m mag m mag Chen f_2 9.94 21.0 17.9 11.33 9.3 16.6 Chambliss f_2 9.80 38.8 19.5 19.61 12.9 17.1 MW f_2 9.90 17.6 13.4 10.53 8.7 11.9 19.54 8.3 10.5 impossible to say with only these data whether this coincidence is due to problems with the fit of f_1 and 2f_1 to the data or whether a real pulsation with a frequency very near 2f_1 is being resonantly driven. Finally we fit f_l and 2f_1 by least squares to Chen's and Chambliss' B and V data. Table V. Fit of f1 and 2f1 to Chen's and Chambliss' B and V data f A_B phi_B A_v phi_v A_B-V phi_B-V Delta phi(V,B-V) d^-1 m mag m mag m mag +-1.6 +-1.6 9.77708 126.4 2.011+-0.013 95.1 1.975+0.016 31.5 2.120+-0.052 -8+-3d 19.55416 32.0 1.788+-0.050 24.0 1.966+0.064 9.4 1.319+-0.170 C_B 25.2 sigmaV = 22.4 The amplitudes and phases for B-V have been analytically derived from their B and V components and the error in phase for B-V has been estimated by scaling the phase error in B proportionally to amplitude. The last column in Table V. gives the phase shift between the V light curve and the B-V colour curve, Delta phi(V,B-V) = phi(V) - phi(B-V), for f_1. Assuming linearity, a direct relationship between B-V and surface brightness, and a phase lag between the flux and radius variations of roughly 90d, Balona and Stobie (1980b) have shown that Delta phi(V,B-V) in an oscillating star is dependent on the pulsation mode. We expect that Delta phi(V,B-V) should be about -11d for radial pulsation, 0d for odd-l non-radial pulsation, +16d for l = 2 non-radial pulsation, and greater than +120d for l >= 4 and even non-radial pulsation. From the phase shift given for f_1 in Table V. of Delta phi(V,B-V) = -8+-3d we can conclude with good confidence that f1 is due to radial pulsation although odd-R non-radial pulsation is not absolutely ruled out. The phase shift for 2f_1 depends on the shapes of the light curves and not on the pulsation mode of f_1. Our conclusion then is that the principal frequency in HD 116994 is very probably due to pulsation in a radial mode and that a secondary frequency is present at about f = 9.9 d^-1 which is due to pulsation in a non-radial mode. This is a pattern similar to that seen in 1 Mon, delta Scuti, HD 188136, and HR 1170. D.W. KURTZ Department of Astronomy, University of Cape Town. References: Balona, L.A., and Stobie, R.S., 1980a, Mon. Not. R. astr. Soc., 190, 931. 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