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Rapid spectral variations of Be stars Thompson, Harold Ian Bruce 1974

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J C ; RAPID SPECTRAL VARIATIONS OF Be STARS by H. Ian B. Thompson B.Sc. , University of B r i t i s h Columbia, 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of GEOPHYSICS and ASTRONOMY We accept t h i s thesis as conforming to the required standard The University of B r i t i s h Columbia A p r i l , 1974 ' In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requ i rement s f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Co lumb ia , I ag ree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s tudy. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i thout my w r i t t e n p e r m i s s i o n . Department o f The U n i v e r s i t y o f B r i t i s h Co lumbia Vancouver 8, Canada i i A b s t r a c t H i g h t i m e r e s o l u t i o n o b s e r v a t i o n s o f two Be s t a r s ( K, D ra a n d XCas) h a v e b e e n made w i t h a n I m a g e I s o c o n t e l e v i s i o n c a m e r a i n an a t t e m p t t o d e t e c t r a p i d r a d i a l v e l o c i t y a n d / o r i n t e n s i t y v a r i a t i o n s o f t h e H y d r o g e n e m i s s i o n l i n e s . A n a l y s i s o f v a r i a n c e t e s t s h a v e b e e n u s e d t o d e t e r m i n e t h e s i g n i f i c a n c e o f p o s s i b l e v a r i a t i o n s . F l u c t u a t i o n s o f t h e i n t e n s i t y o f t h e H a l p h a l i n e o f V C a s w e r e s e e n on a t i m e s c a l e o f a f e w m i n u t e s . U p p e r l i m i t s t o t h e r a d i a l v e l o c i t y v a r i a t i o n s w e r e i m p o s e d by a n a p p a r e n t n o n - l i n e a r e x p a n s i o n o f t h e c a m e r a r e a d i n g beam s c a n n i n g r a s t e r . T h e v a r i a t i o n s o f H a l p h a f o r \C D r a were m a r g i n a l l y s i g n i f i c a n t , s h o w i n g a s l o w c h a n g e i n t h e p o s i t i o n o f t h e l i n e w i t h no s i g n i f i c a n t c h a n g e i n i n t e n s i t y o v e r t h e 30 m i n u t e s o f o b s e r v a t i o n . No s i g n i f i c a n t v a r i a t i o n s w e r e p r e s e n t i n o b s e r v a t i o n s o f H b e t a and H gamma o f } f C a s . i i i Table of Contents page Introduction 1 The Observations 4 Preprocessing of the Data 7 Significance Test 33 Application to the Data 36 Summary and Conclusions 53 Bibliography 57 IV L i s t of Tables page I. The Observations 6 II. Values of the Dark Noise 19 I I I . Values of F f o r the Data 37 L i s t of Figures page 1. F i r s t blocks f o r each set of data 8 2. Variance vs. s i g n a l plots 14 3. S h i f t s vs. l i n e position for 27 Tau and 19 Psc 21 4. The difference plots 23 5. Difference plots for $ Cas H beta and H gamma, f i l t e r e d 0 to 4 per cent 30 6. H alpha area vs. spectrum area, )fcas 43 7. H alpha area vs. normalizing area, Kcas 44 8. H alpha s h i f t s vs. spectrum number 46 9. H alpha s h i f t s vs. applied correction, ^Cas 48 10. H alpha s h i f t s vs. f i d u c i a l separation, V Cas 49 11. H alpha s h i f t s vs. applied correction, \C Dra 51 12. H alpha s h i f t s vs. f i d u c i a l separation, \C Dra 52 Acknowledgments I would l i k e to acknowledge my supervisor. Dr. Gordon Walker, for his continued patience and support while this work was i n progress. Dr. Greg Fahlman and Dr. John Glaspey contributed to many helpful discussions. Dr. Fahlman wrote many of the computer programs that were used and I thank him fo r making them available. I thank the Department of Geophysics and Astronomy and the national Research Council for f i n a n c i a l support, as well as the Dominion Astrophysical Observatory for making observing time available to the n. B . C. astronomers. F i n a l l y , i t i s a pleasure to thank the rest of my friends i n the department who have made i t such a j o y f u l place to work and play. 1 Introduction The stars of spe c t r a l c l a s s Be show hydrogen l i n e s i n emission. The strongest emission i s at H alpha and there i s a large range i n Balmer decrements over the cl a s s . Usually l i t t l e emission i s observed from lines past H delta although emission i s seen to H 22 in 11 Cam (Underhill 1960). The l i n e s are often double with the i n t e n s i t i e s of the R/V (long wavelength / short wavelength) components unequal. The hydrogen emission spectrum i s a low-excitation spectrum with some s e l f absorption in the higher order Balmer l i n e s . Some of the stronger Fe II l i n e s are occasionally observed in emission but forbidden l i n e s are only rarely seen. A subgroup of the Be stars are the s h e l l stars which show sharp absorption l i n e s (mainly from singly-ionized metals : Cr II, Fe II , T i II, etc., as well as deep, narrow hydrogen absorption cores on top of the Be spectrum. The sharp absorption spectrum usually mimics that of an early A-type supergiant (Underhill). The t y p i c a l q u a l i t a t i v e model i s that of a rapidly rotating B star (producing broad, shallow absorption lines) and an equatorial envelope, revolving around the star and producing the emission. The unequal i n t e n s i t i e s of the R/V components are interpreted as the effects of r a d i a l motion i n the envelope. The absorption core i s believed to come frcm material projected against the star and the wavelength of the core w i l l r e f l e c t the r a d i a l velocity of that material. As the R/V r a t i o changes the position of the core i s observed to move while the emission 2 p r o f i l e (determined from the wings of the line) remains stationary with respect to the star. Quoted envelope sizes range from 3 to 100 s t e l l a r r a d i i . The Be stars have been observed for long periods of time (Lockyer (1888) reports that Secchi observed V c a s i n emission i n 1863) and show remarkable changes i n the i r spectra. Some variat i o n s , such as the changes in the B/V components of the hydrogen l i n e s , and appearance and disappearance of s h e l l spectra, occur on a time scale of years and are interpreted as changes i n the envelope as a whole. Typical examples are 48 Lib and ^ Tau (Underhill 1966) and Pleione (Merril 1952). Observations have also been made of variations on a much shorter time scale. Hutchings (1970) found an intermittent p e r i o d i c i t y of 0.7 days i n the B/V separation and int e n s i t y r a t i o cf H beta and H gamma in ^"Cas and s i m i l i a r e f f e c t s were observed i n K-Bra and 4 Her with no evident periodic behavior (Hutchings 1971). In the case of Xcas, the variations were only observed during a time when the envelope was expanding and perhaps can be explained by density inhomogeneities forming from material entering the envelope at i t s base from the rapidly rotating star and subsequently revolving around the star. In addition, Hutchings et a l . (1971) reported rapid (on the order of a few minutes) fluctuations of H alpha i n K Dra and 4 Her. In the case of VC Dra, the position of the l i n e appeared to change by up to 2 A (92 km s e c - 1 ) . Again no p e r i o d i c i t i e s were observed. Other examples are variations of the H beta p r o f i l e of Vt Dra (Adam et a l . 1969) and the periodic s h e l l behavior of BB 2142 3 (Peters 1971). (See also Delplace et a l . 1969). Variations of the H alpha and H beta emission strengths of } Tau have been reported by Bahng (1971) on the time scale of 10 minutes. Models of the envelopes of Be stars have been able to reproduce observed l i n e p r o f i l e s and give explanations for the long time scale variations using a s t e l l a r wind approach to the envelope (Limber 1964, 1967, 1969, Marlborough 1969, 1971). An alternate view i s to treat the material as an eguatorial ring. Huang (1972, 1973) explains the periodic B/V variations geometrically by the apsidal rotation of an e l l i p t i c a l ring of emitting gas. Fluctuations can be produced by a non-uniform d i s t r i b u t i o n of material i n the r i n g . It i s clear that some of the observations indicate changes on time scales that are too short to be explained by such models. Some authors (Hutchings 1970, Bohlin 1971) have suggested that the rapid fluctuations are caused by unstable condensations in the envelope, s i m i l i a r to those producing the 0.7 day periodic variations. In order to investigate these more rapid variations, high dispersion, high time resolution observations of the two Ee stars Y Cas (mv = 2.65, spectral type BO IVe) and K, Dra (mv = 3.84, sp. type B7p) were made and significance tests applied to obtain confidence l e v e l s f ror the existence of the variations. 4 The Observations The observations were made with a refrigerated English E l e c t r i c P850 image isocon t e l e v i s i o n camera. The spectrum i s integrated for a s p e c i f i e d time and the target then i s scanned by the reading beam. The scan i s normal to the spectrum, and the video output from the camera i s sampled and d i g i t i z e d to 12 b i t s at the spectrum, each t o t a l scan giving 840 data points over 70 mm of the cathode. The integration time includes f i v e scans of the tube which wipe off the previous charge d i s t r i b u t i o n . Observations of the dark current t y p i c a l l y l a s t one or two minutes and are taken immediately after the star data has been obtained. The integration time i s l e f t unchanged. The system i s monitored by an Interdata Model 4 computer and the data i s stored on magnetic tape. For a more detailed description of the system see Walker et a l . (1972). A l l of the observations were taken with the coude spectrograph of the Dominion Astrophysical Observatory 122-cm (48-inch) r e f l e c t o r . A 244-cm (96-inch) camera with a mosaic of four 800 l i n e mm-1 gratings was used giving a r e c i p r o c a l dispersion of 4.8 & mm-*. Table I gives a l i s t of the stars observed, date cf observation, wavelength region, dispersion, integration time, t o t a l number of spectra, and t o t a l length of observation. The observations with a dispersion of 0.5 A mm-1 were obtained with a transfer lens at the second order which magnifies a small 5 section of the spectrum and matches the curvature of the f o c a l plane to the curvature of the photocathode (Richardson 1973). Because the point to point separation on the target i s f a i r l y high (250 microns) t h i s magnification provides more e f f i c i e n t use of the high spectrograph resolution. 6 I Star | Wavelength | Integ. | Number j Total | | Date | Dispersion | time | of I time | I I (A mm-1) | (sec) | spectra | (min) | I K. Dra | H alpha | 2.16 | 832 | 30 | I 10 Apr. 1973 | 4.8 | | I I I Yeas | H alpha | 3.40 | 1167 | 66 | | 27 Sept. 1973 | 2.4 | | | | I Yeas | H beta I 4.63 | 480 | 37 | | 9 Aug. 1972 | 0.5 | | | | I XCas | H beta I 1.54 | 1168 | 30 | | 13 Oct. 1972 | 0.5 | | | | | tfCas | H gamma | 3.09 | 663 | 34 | | 19 July 1972 | 0.5 | I I I TABLE I . THE OBSEBVATIONS 7 E£§E„£§ssin_ of the Data For each star the numerical average of the dark signal was found and smoothed by a 31 point running mean (an a r b i t r a r i l y chosen f i g u r e ) . The spectra of the star were subgrouped into blocks of about two minutes, each spectrum contributing to the subgroup having the dark subtracted from i t . The spectra were added, and the f i n a l sum was normalized such that the area in a spe c i f i e d point range was set to 1000 units. The normalizing range was chosen away from the emission l i n e to prevent possible variations from influencing the normalization process. Figure 1 shows the f i r s t block in each set of data. The two features at each end of the spectrum are f i d u c i a l markers on the face of the photocathode. They consist of thin s t r i p s of black tape and are used to determine any variations in the scanning raster and also to follow any changes in the l e v e l of the dark current. The numbers on the wavelength axis correspond to the i n d i v i d u a l data points i n the spectrum, high wavelengths being to the l e f t . To determine-the accuracy of the set of mean spectra, the variance i s calculated for each point in each subgroup. Each spectrum contributing to the variance c a l c u l a t i o n i s normalized as described above and i s assigned a weight proportional to i t s unnormalized area. Thus: Var(i) = Slw(l)[B(i;I)/w{I) p {JL [ B (i;I)/w (I) ]w (I) _ j _ , — — — — i « d ) [ i w ( i ) i 2 Figure 1 (b) . F i r s t block of X Cas H alpha data. Figure 1 (d) . F i r s t block of Vcas H beta (1168) data. 12 Figure 1(e). F i r s t block of X Cas H gamma data. 13 l B ( i ; I ) 2/w(D [ | l B ( i ; I ) ] 2 v. = c r.= i i - i where: w(I) area i n defined point range divided by 1000 f o r spectrum I point number i n spectrum B (i;I) (observed i n t e n s i t y - dark) for spectrum I and data point i N number of i n d i v i d u a l spectra i n a subgroup The signal to noise c h a r a c t e r i s t i c s of the image isocon tube are discussed t h e o r e t i c a l l y by Lowrance and Zucchino (1971) and f o r the case of the D.B.C. tube i n p a r t i c u l a r by Buchholz et a l . (1973). Buchholz found a l i n e a r signal to noise relationship from spectra with strong absorption l i n e s . Figure 2 shows variance vs. si g n a l plots for the data described above. Except for the Vcas H gamma data, the plots appear to be l i n e a r , indicating that the tube c h a r a c t e r i s t i c s i n th i s respect are independent of the type of spectrum observed. This demonstrates one of the valuable assets of the isocon system -addition of N spectra gives a xHT1 improvement i n the signal to noise r a t i o . The basic system noise (dark noise) i s the sguare root of the variance at zero s i g n a l . This value from the plots can be changed into units of photo-electrons since the peg l e v e l of the A-D converter i s approximately one t h i r d of the saturation l e v e l of the tube. From data given by Nelson (1969) Figure 2 (a). Variance vs. s i g n a l f o r & Dra H alpha data. 03 o to a' LU CJ •—»«-,*• CC a' > 0.0 2.0 4.0 SIGNRL 6.0 8.0 l 10 15 Figure 2(b). Variance vs. s i g n a l f o r Kcas H alpha data. in o CM" in C E a — ' J -o: C E in a a ' - 4 . 0 1.0 6.0 SIGNAL n . o 16.0 21.0 4 Figure 2(c). Variance vs. sign a l f o r V c a s H beta (1168) data. in a L U C _ C M 1 1 1 1 1 0.0 2.0 4.0 6.0 8.0 10.0 SIGNRL Figure 2(d). Variance vs. si g n a l for Cas H beta (480) data tn O C C O J CL > 0.0 • 2.0 4.0 SIGNAL 6.0 8.0 10.0 Figure 2(e). Variance vs. si g n a l f o r X Cas H gamma dat< in LU C_> ZZ. CE-4 — t C d a CC > in a 0.0 2.0 I 4.0 SIGNAL 6.0 8.0 10.0 18 the saturation charge i s 3100 electrons for a picture element of s i z e 250 by 100 microns. The calculated noise values are given i n Table II. These values are in reasonable agreement with those given by Buchholz. The scanning pattern of the camera reading beam i s known to vary with time (Fahlman and Glaspey 1973). This w i l l produce inaccuracies in the observed i n t e n s i t y in regions cf the spectrum where there i s a large modulation i n i n t e n s i t y (e.g. the "edges" of the H alpha p r o f i l e s shown in figure 1). By finding the s h i f t of the pattern at features i n the spectrum assumed to be fix e d , the e f f e c t can be corrected f o r . Unfortunately, i n the data obtained, the only well defined, fixed features are the f i d u c i a l markers and so one must assume that the s h i f t i s l i n e a r across the tube. The corrections are calculated using a program described by Fahlman and Glaspey. The technique uses the s h i f t property of the Fourier transform, s l i d i n g the spectrum with respect to a defined standard u n t i l minimum error i s achieved in a least squares sense. A straight l i n e i s f i t t e d through the s h i f t s of the f i d u c i a l s and the correction to be applied to the emission l i n e i s found. This was not done for the H beta and H gamma data because the p r o f i l e s were not strong (large s h i f t s give a f a i r l y small change in intensity) and because the s h i f t s that were to be applied were small. The corrections were applied to the H alpha data, again using Fourier techniques, the variation i n s h i f t across the p r o f i l e being ignored. For a l l of the Star Wavelength I K. Dra H alpha Photo-electrons at a sign a l l e v e l of 5 * Noise (electrons) — + -183 X Cas H alpha 164 13 V Cas H beta 208 X Cas H beta 207 X Cas H gamma 439 15 * Refer to Figure 1. TABLE I I . VALUES OF DARK NOISE 20 cal c u l a t i o n s , the f i r s t spectrum in each series was used as the standard. The assumption of l i n e a r i t y for the raster expansion appears to be a good one. Fahlman and Glaspey show that the s h i f t s are lin e a r for a r t i f i c i a l l y produced data consisting of the f i d u c i a l s , two broad emission l i n e s and one bread absorption l i n e on a background continuum. Figure 3 shows plots of s h i f t s vs. l i n e position for observations of 19 Psc taken on the same night as the V Cas data and 27 Tau, observed on the same night that the vt Dra data was obtained. Ninety-six spectra of 27 Tau and 120 spectra of 19 Psc were subgrouped into 4 blocks and the s h i f t s of the l i n e s for the l a s t three blocks were calculated using the f i r s t block as the standard. The l i n e s used were H alpha and the two f i d u c i a l s for 27 Tau and various l i n e s i n the 4960 k range and the two f i d u c i a l s for 19 Psc. The li n e s on the plots were f o r c e - f i t t e d through the values for the f i d u c i a l s . The error bars are 70 percent confidence l e v e l s for the c h i -sguared d i s t r i b u t i o n of the sum of squares. Each set of data was then f i l t e r e d to improve the signal to noise quality of the data. h bandpass f i l t e r was used, truncated with a Lanczos window (Jenkins and Watts 1968). The high frequency cutoff point of the f i l t e r was chosen as the frequency where the power spectrum of a single block of data f e l l below the value -50 dB. This ranged from 20 per cent of the Nyquist frequency for & Cas H beta to 30 per cent for Vt Era H alpha. The low frequency cutoff was set at zero. This 21 Figure 3 (a). Line s h i f t vs. l i n e position f o r 27 Tau. 0.5 t o.o o.o 1 •0.5 -•1.0 0.5 -i 0.0 -•0.5 — i i 7 0 0 1 0 0 3 0 0 5 0 0 Po in t Number Figure 3(b). Line s h i f t vs. l i n e position for 19 Psc. o.o • 0,5 0.0 - 0.5 0.0 -0.5 --1.0 I-i — i r 1 0 0 3 0 0 5 0 0 Point N u m b e r 7 0 0 22 f i l t e r i n g does not s i g n i f i c a n t l y reduce the resolution. The 20 per cent f i l t e r i s almost equivalent to a 5 point running mean whereas the instrument p r o f i l e i s 5 to 6 points. Following Hutchings et a l . (1971) variations in the spectra were looked for by subtracting the i n d i v i d u a l spectra in a set of observations from the numerical average of a l l the spectra in that set. The advantages of t h i s method are that i t gives a v i s u a l display of i n t e n s i t y as well as r a d i a l velocity variations and that i t retains the wavelength i d e n t i f i c a t i o n of the data (that i s , any va r i a t i o n can immediately be i d e n t i f i e d with a feature in the l i n e , p a r t i c u l a r l y f o r the higher dispersion spectra). Figure 4 shews the resulting difference spectra. The units of change i n i n t e n s i t y and the wavelength scale are the same as for the corresponding spectra i n Figure 1. The data i s plotted between points 105 and 730. For two sets of data (those of H alpha) there appear to be changes i n i n t e n s i t y and position (from the S-shaped curves) at the position of the l i n e . For the other sets of data any possible variations are hidden by an apparent low frequency d r i f t in the response of the isocon camera. This d r i f t i s not i n the dark current since the values of the difference spectra at the locations of the f i d u c i a l s are zero. The d r i f t s are also not interpreted as changes i n the star. They are present to the edges of the vobservable section of the spectra which are up to 20 A away from the centres of the l i n e s . This i s f a r into the wings of even the underlying s t e l l a r absorption l i n e s (Hutchings 1970) and the spectra are thus e s s e n t i a l l y at continuum l e v e l s . These three 23 26 Figure 4(d). Difference spectra f o r JT Cas H beta (480). r- 1 . 0 27 Figure 4(e). Difference spectra f o r ^Cas H beta (1168). r- 1.0 28 Figure 4 (£). Difference spectra f o r & Cas H gamma. 1.0 29 sets of data were obtained when two spectra were read from the camera, the second being used to monitor dark current l e v e l s . The H beta observations, which show the largest amount of tube response changes, also show some "cross-talk" between the spectra. The cross-talk i s caused by overshoot of the video amplifier between the spectra which allows the sampling of one spectrum to include some signal from the other. The two e f f e c t s might be related, although t h i s seems unl i k e l y . A more plausible explanation i s that the variations are caused by incorrect alignment of the optics, producing a t i l t of the spectrum with respect to the isocon tube. The variations might then be produced by poor guiding, seeing, etc. This ef f e c t would be magnified when the transfer lens i s i n use. These variations were removed by again f i l t e r i n g the data. The f i l t e r used was s i m i l i a r to those described above except that the lower and upper frequency cutoffs were set to 4 and 100 per cent of the Nyquist frequency respectively. The "corrected" difference spectra are shown i n Figure 5. For the X Cas H beta (1168 spectra) and H gamma data there do not appear to be any changes. There do appear to be variations i n the H beta (480 spectra) difference plots, although they are of very small amplitude. We are l e f t with the problem of determining whether any of the features in the difference spectra are s t a t i s t i c a l l y s i g n i f i c a n t . 16 32 33 S _ _ f _ _ _ _ _ a _ _ e t e s t We w i s h t o t e s t t h e h y p o t h e s i s t h a t t h e i n d i v i d u a l p o i n t s o f a d i f f e r e n c e s p e c t r u m a r e t h e s a m e . T h e t e s t u s e d i s t h e a n a l y s i s o f v a r i a n c e t e s t f o r t h e e q u a l i t y o f m e a n s . E a c h p o i n t i n t h e d i f f e r e n c e s p e c t r u m c a n be t h o u g h t o f a s t h e mean o f t h e n u m b e r o f s p e c t r a c o n t r i b u t i n g t o e a c h s u b g r o u p w i t h t h e o v e r a l l mean r e m o v e d . I f t h e r e a r e no v a r i a t i o n s i n t h e e m i s s i o n l i n e t h e n a l l o f t h e s e m e a n s ( i n o n e d i f f e r e n c e s p e c t r u m ) s h o u l d be e q u a l t o z e r o . G i v e n t h e v a l u e s o f a s e t o f means a n d t h e v a r i a n c e s a s s o c i a t e d w i t h e a c h o f t h e s e v a l u e s , t h e a n a l y s i s o f v a r i a n c e m e t h o d g i v e s c o n f i d e n c e l e v e l s f o r s t a t i n g w h e t h e r t h e r e a r e any means i n t h e s e t w h i c h a r e d i f f e r e n t f r o m t h e o t h e r s . F o r a g o o d summary s e e W o n n a c o t t a n d W o n n a c o t t ( 1 9 6 9 ) . L e t t h e d i f f e r e n c e s p e c t r u m v a l u e s be I ( i ; N ) f o r d a t a p o i n t i a n d N c o n t r i b u t i n g s p e c t r a . L e t s ( i ) 2 b e t h e v a r i a n c e o f d a t a p o i n t i o f t h e d i f f e r e n c e s p e c t r u m . The t e s t i n v o l v e s f i n d i n g t h e r a t i o F = N (S*2/Sp2) w h e r e : S x 2 = [ 1 / ( r - 1 ) ] Z [ I ( i ; N) - I mea n ] 2 = t h e v a r i a n c e o f t h e v a l u e s o f t h e d i f f e r e n c e s p e c t r u m ; r = n u m b e r o f p o i n t s f r o m t h e d i f f e r e n c e s p e c t r u m u s e d i n t h e c a l c u l a t i o n ; I m e a n = ( 1 / r ) 1_ I ( i ; N ) , t h e n u m e r i c a l mean L — * o f t h e v a l u e s o f t h e d i f f e r e n c e s p e c t r u m . 3H Sp 2 = (1/r) Z s ( i ) 2 = the numerical mean of the variances of the difference spectrum values used i n the c a l c u l a t i o n . The s t a t i s t i c F has the F d i s t r i b u t i o n with (r-1) degrees of freedom i n the numerator and r(N-1) degrees of freedom i n the denominator; that i s , i t i s the r a t i o of the two values Sx 2 and Sp 2 which have)6<-_\ and£>^A » -D d i s t r i b u t i o n s respectively. If the experimental value of F i s greater than the tabulated value at some confidence l e v e l for a given r and N then the conclusion i s that the hypothesis i s to be rejected to that confidence l e v e l ; i . e . there are features i n the difference spectrum that are s i g n i f i c a n t . One advantage of thi s method i s that the rest of the spectrum i s used and not discarded as would be the case i f only some measure of eguivalent width were calculated. The analysis of variance test makes some assumptions about the data that may not be s a t i s f i e d . They are: 1. Normality of the data; 2. Equality of the variances; and 3. S t a t i s t i c a l independence of the data. The fac t that the variances are unequal i s immediately obvious from Figure 2. In addition, tests indicate that f i l t e r i n g the data reduces the variance by a factor of about two (the linear s i g n a l - variance r e l a t i o n remains). This simply means that the variances are overestimated. F i l t e r i n g the data introduces c o r r e l a t i o n and th i s must be taken into account by reducing the number of degrees of freedom in the wavelength d i r e c t i o n (e.g,. the value 35 of r used to f i n d F in the table w i l l be reduced by a factor of f i v e i n the case of Vcas H alpha). However, the test i s described as "robust" in that departures from assumptions do not seriously a f f e c t the r e s u l t s . For a discussion see Scheffe (1959). The effect of departures can be minimized by ensuring that the number of contributions to each mean i s the same, as i s the case for t h i s data. We can also demand that the hypothesis be rejected to the 99 per cent l e v e l . 36 „£lic§tion to the Data For the data tested, only the points between the f i d u c i a l s were used. This i s because the data that has been shifted w i l l show the eff e c t s of the s h i f t i n g at the f i d u c i a l s where the decrease i n in t e n s i t y i s very abrupt. In addition, the response of the tube drops to low lev e l s beyond the f i d u c i a l s and the value of the intensity measurements in th i s region i s doubtful. Table III gives the derived values of F for the difference spectra in Figure 3 (a,b) and Figure 4 as well as the point l i m i t s used in the cal c u l a t i o n , the value of N and the tabulated value of F for the 99 per cent l e v e l . These l a t t e r values were taken from Scheffe. There are no s i g n i f i c a n t variations i n the Yeas H beta or H gamma data i n spite of the apparent changes in Figure (5a). This i s due in part to the f i l t e r i n g that was done to remove the low freguency tube response errors. The f i l t e r i n g " flattened" the difference plots but the values of the variance f o r the in d i v i d u a l points r e f l e c t the block to block changes i n the tube response and are abnormally high. There are, however, s i g n i f i c a n t variations of If Cas H alpha and \C Dra H alpha. - These results indicate that r e a l changes in i n t e n s i t y and/or position of the H alpha p r o f i l e of these stars are occuring on the time scales of a few minutes. A rough measure of the int e n s i t y of the H alpha line can be made by finding the area under the l i n e from the normalized spectra. The point l i m i t s used to define the line were 385 to I Star : tC Dra (B alpha) N = 50 J Point l i m i t s : 200 to 600 F (99%) = 1.34 | Spectrum F | Spectrum F I Number I Number I 1 1.42 | 9 0.51 I 2 1.09 | 10 0.60 | 3 1.07 | 11 0.48 I 4 1 . 1 4 | 12 1.71 | 5 0.86 \ 13 0.83 I 6 0.72 | 14 0.83 I 7 1.05 j 15 0.42 | 8 0.43 | 16 1.11 L 1 I Star : <fcas ( H alpha) N = 35 | Point l i m i t s : 250 to 600 f (99%) = 1.45 r ~ ~ — — "' I Spectrum F — r Spectrum F | Number I Number L r + i 1 0.64 i 18 1.35 I 2 1.47 i 19 0.53 I 3 4.41 1 20 0.52 I 4 1. 19 i 21 0.79 I 5 9.05 1 22 0.59 I 6 6. 11 i 23 2.32 I 7 3. 26 i 24 1.25 I 8 1. 10 1 25 2.29 I 9 1. 32 1 26 4.51 I 10 1.73 ! 27 3.37 I 11 2.87 1 28 4.85 I 12 3.90 i 29 2.57 I 13 4. 59 i 30 3.66 I 14 1.69 i 31 3.35 I 15 2.68 i 32 0.63 I 16 2.51 i 3 3 0.59 I 17 0.79 i L L . i 39 r 1 | Star : Y e a s (fl beta 480) N = 26 | | Point l i m i t s : 250 to 650 F (995?) = 1.44 | r r 1 | Spectrum F | Spectrum F | | Number I Number | ., A | 1 0.49 I 10 0.28 | | 2 0.31 | 11 0.31 | | 3 0.38 | 12 0.57 | I 4 1.05 | 13 0.30 | | 5 0.25 | 14 0.27 | | 6 0.28 | 15 0.39 | | 7 0.62 | 16 0.21 | | 8 0.34 | 17 0.16 | | 9 0.41 | 18 0.40 | L J . I „ B L E IIIJC__ I Star : y Cas (H beta 1168) N = 73 | | Point l i m i t s : 200 to 600 F {99%) = 1.44 | j Spectrum F | Spectrum F j j Number | Number I | 1 0.31 | 9 0.31 | | 2 0.35 | 10 0.23 | | 3 0.42 | 11 0.27 | | 4 0.23 | 12 0.32 | | 5 0.18 | 13 0.26 | J 6 0.31 | 14 0.34 | | 7 0.30 | 15 0.26 | | 8 0.37 | 16 0.23 I I Star : )fcas (H gamma) N = 39 I I Point l i m i t s : 250 to 650 F(99%) = 1.37 | Spectrum F j Spectrum F | | Number | Number | h + ^ I 1 0.45 | 10 0.35 | I 2 0.27 | 11 0.33 | I 3 0.36 j 12 0.34 | I 4 0.28 | 13 0.44 | I 5 0.37 | 14 0.37 ( I 6 0.40 | 15 0.44 | I 7 0.42 | 16 0.35 J I 8 0.48 I 17 0.33 | I 9 0.42 | | _____ I I I J E l i 42 425 f o r K. Dra and 360 to 430 for Vcas. The ^ D r a values were constant to less than one per cent (with an error cf less than one per cent) in d i c a t i n g that the most prominent cause of the variations i s a s h i f t i n the position of the l i n e . However the values for ^Cas vary up to 6 per cent from the mean. The areas are plotted i n arb i t r a r y units against spectrum number in Figure 6, each spectrum representing 119 seconds. The error in each point i s less than one per cent. No evident pattern of v a r i a t i o n i s present over the 66 minutes of observation. While a measure of equivalent width i s extremely d i f f i c u l t to determine for t h i s data (because instrument p r o f i l e , tube response, dark current l e v e l s , etc., a l l have to be considered), an approximate c a l i b r a t i o n of the amount of flux involved in the Xcas variations can be made. A suitable standard was not obtained on the same night as the data presented here and so observations of ^Cas at H alpha ( f i r s t order) and the standard star ^ Lyr obtained on 5 Oct., 1972 along with the flux c a l i b r a t i o n of <*.Lyr given by Oke and Schild (1970) were used, giving a flux l e v e l of 1 0 - 1 1 erg cm-z s e c - 1 A - 1 for each i n t e n s i t y unit of Figure 4 (b). This value i s only correct to an order of magnitude. As a check that the normalization process did not "create" the variations, the area of the H alpha l i n e was plotted against the normalizing area (Figure 7). This i s a scatter p l c t except for two points, i d e n t i f i e d as spectra 23 and 24. Investigation of the raw data showed that over this time the star was l o s t igure 6. Area of Vcas H alpha vs. spectrum number. e a J v • B 4 d|B H 44 Figure 7. Area cf Y e a s H alpha v s . normalizing area. (0 « CM C E I O * 45 from the spectrograph s l i t . It should be noted that the point i n Figure 6 which deviates strongly from the general trend i s spectrum 23. Removing these spectra from the ca l c u l a t i o n of the o v e r a l l mean does not a l t e r the difference spectra. The difference plots in Figures 4 (a) and 4(b) also indicate changes i n the position of the l i n e as well as i n t e n s i t y changes. This i s p a r t i c u l a r l y noticeable i n the \C Dra plots. As a r e s u l t , the positions of the H alpha l i n e s were calculated with respect to the o v e r a l l means using the same program that was used to fi n d the s h i f t s of the f i d u c i a l markers. The s h i f t s r e l a t i v e to the means are plotted i n Figure 8. They appear to be increasing l i n e a r l y in the K- Dra data but show a marked sinusoidal behavior i n the Teas data. In both cases the root mean square error (from the c a l c u l a t i o n of the f i d u c i a l and l i n e positions) i s approximately ±0.2 points. It i s obviously important to show that the s h i f t s are not correlated with any process i n the data reduction that has anything to do with the d r i f t of the scanning raster. For the Yeas data no cor r e l a t i o n i s shown between the H alpha s h i f t s and the applied correction (Figure 9) but a rough co r r e l a t i o n does e x i s t between the H alpha s h i f t and the difference between the two f i d u c i a l positions (Figure 10). This indicates that the expansion of the scanning raster i s not li n e a r as was assumed. Without more features in the spectrum i t i s only possible to place an upper l i m i t to the s h i f t of the l i n e of one point (9 km s e c ~ l ) . It i s tempting to note that the apparent sinusoidal Figure 8 ( a ) . S h i f t s of H alpha (\oDra) vs. spectrum number i i i r" O (D Si E 3 E CO 3 O Q. (•sid) u !MS ' e q d | e H 47 Figure 8(b). S h i f t s cf H alpha ( V Cas) vs. spectrum number. CM «0 CO CM CM O 0) N _> E 3 z 9 I u 01 a. cn — i — ( S j d ) U ! 4 S e q d | B H 48 Figure 9. S h i f t s cf H alpha (YCas) vs. applied correction. - i 1 r T 1 1 1 r ( s » d ) U!MS eqd|B H Figure 10. S h i f t s cf H alpha ( If Cas) vs. f i d u c i a l separation C\l O I te o I ID O I ( S » d ) U!MS e q d | e H 50 pattern i s a closer r e l a t i o n than the H alpha s h i f t - f i d u c i a l separation c o r r e l a t i o n . This non-linear expansion i s not r e s t r i c t e d to strong emission l i n e data. Glaspey (private communication) has found s i m i l i a r results for observations of ftp sta r s . In the case of the \(> Dra data, there appears to be a very rough cor r e l a t i o n between the applied corrections and the H alpha s h i f t s (Figure 11), however no co r r e l a t i o n i s seen between the B alpha s h i f t s and the f i d u c i a l separations (Figure 12). In view of the fact that only two of the difference plots gave s i g n i f i c a n t deviations and taking into account the size of the errors i n the H alpha s h i f t s , t h i s l i n e a r trend must be viewed with some reserve. If true, the r e s u l t s indicate a d r i f t of the H alpha l i n e of 0.8 point (15 km s e c - 1 ) over the t h i r t y minutes of observation. Figure 1 1 . S h i f t s of H alpha (K/Dra) vs. applied correction o • at a c o o « o o cv a a. < C O o I CO © -r- - I — ("s»d) DIMS BMd|e H Figure 12. S h i f t s of H alpha (\CDra) _ s . f i d u c i a l separation. 1 <0 a CO <=. a CO a o (•s»d) H ! M S egd|B H 53 Summary and conclusions The H alpha i n t e n s i t y of \ Cas i s observed to vary on a time scale of a few minutes. The t o t a l change in?flux i s approximately 3 x I O - 1 1 erg cm-2 s e c - 1 A - 1 and the variations appear to be ir r e g u l a r over the 66 minutes of observation. These changes cannot be explained by the geometrical e f f e c t s of a non-uniform envelope (Huang 1973), and must be caused by some physical process within the envelope. An upper l i m i t of 9 km sec-* was placed on the variation of the r a d i a l velocity of the l i n e by the non-linear expansion of the camera scanning r a s t e r . Observations of H beta and H gamma of t h i s star were affected by low s p a t i a l frequency respose changes of the tube and no s i g n i f i c a n t variations were seen. The observations of K Dra indicate no change in the emission strength of the H alpha l i n e (to less than one per cent) and only a marginally s i g n i f i c a n t variation of 15 km s e c - 1 f o r the r a d i a l velocity of the l i n e . There did seem to be a s l i g h t c o r r e l a t i o n between the applied s h i f t and the calculated s h i f t of the l i n e . It i s obviously d i f f i c u l t to make any conclusions from these r e s u l t s . The rapid fluctuations of the H alpha l i n e of t h i s star reported by Hutchings et a l . are most l i k e l y spurious since no corrections were made f o r the i n s t a b i l i t y of the scanning raster (when that data was obtained no f i d u c i a l markers were on the tube and so the data cannot be re-analyzed). 54 In spite of the i n s t a b i l i t i e s of the tube, the isocon camera remains an excellent instrument for the types of observations reported here, and the observations of Be stars should continue. I f the response variations of the tube were caused by poor alignment of the system then more care must be taken in t h i s respect i f the transfer lens i s used. However, the problem of the d r i f t i n the scanning raster i s l i k e l y to remain. It i s suggested that the observations of V c a s and k. Dra at H alpha be re-done, using the transfer lens to obtain higher dispersion. At the higher dispersion the observed s h i f t s w i l l be much larger than the raster e f f e c t s and t h i s w i l l enable the variations to be confirmed or at l e a s t greatly improve the upper l i m i t s that can be placed on them. In addition, the c a l c u l a t i o n of the s h i f t s w i l l be more accurate since there w i l l be more points i n the l i n e s . The higher dispersion might make i t possible to resolve these l i n e s (there i s some suggestion of an asymmetry in the X Cas p r o f i l e and the k. Dra p r o f i l e i s known to have a central absorption core). Both stars are bright enough that the loss of time resolution would not be substantial. To attempt to calculate the e f f e c t s of the raster s h i f t more accurately, i t might be possible to introduce a wavelength standard onto the s t e l l a r spectrum. This could be done by imaging a reference arc onto the tube face as well as the observed spectrum. This would give more standard l i n e s across the spectrum and enable non-linear e f f e c t s to be corrected f o r . However, i t i s l i k e l y that the o p t i c a l arrangement would be very 55 d i f f i c u l t to set up. This reference spectrum would have to be included constantly or at least observed often since the changes i n the raster pattern are known to occur on the time scale of a few minutes. I t would obviously not be a good idea to put more f i d u c i a l s on the tube face. another p o s s i b i l i t y that should be investigated i s the observation of of the H alpha l i n e with the Reticon array of s i l i c o n diodes. This array has comparable e f f i c i e n c y to the isocon system at H alpha and has the obvious advantage of a fixed pattern of detectors. Beticons with 1024 diodes are available and t h i s would give even better resolution than the isocon. There are p r a c t i c a l considerations to be taken into account i f and/or when these observations are made. The f i r s t i s that the isocon tube response to input l i g h t l e v e l s becomes non-li n e a r before the peg l e v e l of the a-D converter i s reached (some observations of ^CDra at H alpha had to be discarded because of a c o r r e l a t i o n between the normalizing area and the area of the l i n e ) . The peak i n t e n s i t i e s of the spectrum should be kept at about one half of the peg l e v e l . also, to use the f i d u c i a l s as indicators of the raster s h i f t , one must ensure that they are well defined; that i s , the response of the tube must be tuned such that the i n t e n s i t y l e v e l of the star in the region of the f i d u c i a l s i s f a i r l y high. This i s tc ensure that the error i n the c a l c u l a t i o n of the f i d u c i a l positions i s kept to acceptable l e v e l s . L i t t l e i s known about the long term 56 s t a b i l i t y of the tube (over a few hours), p a r t i c u l a r l y with respect to the dark current. I t i s recommended that some investig a t i o n of this be made. For observations l a s t i n g a long time, the dark should be observed several times during the run. 57 Bibliography. Adam, G., Bigay, J-H., Delplace, A.M., Duval, M,, Gamier, B,, Herman, R. and Peton, A. 1969, CR. Ser B, 269, 1332. ^ Bahng, J.D.R. 1971, Ap.J. (Letters), 167, L75. Bohlin, B.C. 1970, Ap.J., 162, 571. Buchholz, V.L., Walker, G.A.H., Auman, J.R. and Isherwood, B.C. 1973, i n Astronomical Observations with Television-type Sensors, ed. J.W. Glaspey and G.A.H. Walker (Univ. of B r i t i s h Columbia, Inst, of Astronomy and Space Science), p. 199. Delplace, A.M., Herman, R. and Peton, A. 1969, i n Nonperiodic Phenomena in Variable Stars, ed. L. Detre (Eudapest : Academic Press), p. 223. Fahlman, G.G. and Glaspey, J.W. 1973, i n Astronomical Observations with Television-type Sensors, ed. J.W. Glaspey and G.A.H. Walker (Univ. of B r i t i s h Columbia, Inst, of Astronomy and Space Science), p. 347. Hutchings, J.B. 1970, M.N.R.A.S., J50, 55. . 1971, ibid.,1.52, 109. Hutchings, J.B., Auman, J.R., Gower, A.C and Walker, G.A.H. 1971, Ap.J. (Letters), V70, L73. Jenkins, G.M. and Watts, D.G. 1968, Spectral Analysis and i t s Applications (San Francisco : Holden Day). Limber, D.N. 1964, Ap.J., .140, 1391. — . 1967, i b i d . , 148, 141. . 1969, i b i d . , 157, 785. Lockyer, J.N. 1888, Proc. Roy. S o c , 44, 1. Lowrance, J.L. and Zucchino, P.M. 1969, Report on Evaluation of Television Tubes for Space Astronomy (Princeton University, Dept. of Astrophysical Sciences). Marlborough, J.M. 1969, Ap.J., 156, 135. . 1971, i b i d . , 163, 525. M e r r i l , P.W. 1952, Ap.J., JM5, 145. 58 Nelson, P.D. 1969, Advances i n Electronics and Electron Physics, 28A, 209. Oke, J.B. and Sch i l d , R.E. 1970, Ap.J., 161, 1015. Peters, G.J. 1971, Ap.J. (Letters), 163, L107. Richardson, E.H. 1973, i n Astronomical Observations with Television-type Sensors, ed. J.W. Glaspey and G.A.H. Walker (Univ. of B r i t i s h Columbia, Inst, of Astronomy and Space Science), p. 4 33. Scheffe, H. 1959, The Analysis of Variance (New York : Wiley). Struve, 0. 1942, Ap.J., 95, 134. Underhill, A.B. 1960, in Stars and S t e l l a r Systems Vol VI, ed. J. Greenstein (Chicago : Univ. of Chicago Press), p. 411. Underhill, A.B. 1966, The Early-type Stars (Dordrecht : D. Reidel) Walker, G.A.H., Auman, J.R., Buchholz, V.L., Goldberg, E.A., Gower, A.C., Isherwood, B.C., Knight, R. and Wright^ D. 1972, Advances in Electronics and Electron Physics, 33B, 819. Wonnacott, T.H. and Wonnacott, R.J. 1969, Introductory S t a t i s t i c s (Toronto : Wiley). 

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