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UBC Theses and Dissertations

A study of the binary radio star LSI +61 303 Xu, Huangjian 1987

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A STUDY OF THE BINARY RADIO STAR L S I + 6 1 ° 3 0 3 b y HUANGJIAN XU B . S c , U n i v e r s i t y o f S c i e n c e a n d T e c h n o l o g y o f C h i n a , 1 9 8 5 A T H E S I S SUBMITTED IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF S C I E N C E i n THE F A C U L T Y OF GRADUATE S T U D I E S DEPARTMENT OF P H Y S I C S We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE U N I V E R S I T Y OF B R I T I S H COLUMBIA D e c . 1987 " © H u a n g j i a n X u , 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia 1956 Main Mall Vancouver, Canada Department V6T 1Y3 11 Abstract We present new 6 cm observations of the binary radio, X-ray and 1-ray star GT0236+610 (LSI+61°303) obtained i n August 1984 and September 1986. Ve calculate an improved period for the source's periodic radio outbursts of 26.50 ± 0.03 days. No s i g n i f i c a n t period derivative was found. Based on an analysis of 201 f l u x density measurements from 1977 August to 1986 September, we fi n d evidence for a possible 4 year modulation of the amplitude of the 26.50 day periodic radio outbursts. A precessing j e t model for t h i s long period modulation i s discussed. I i i Table of contents page Abstract i i L i s t of Tables i v L i s t of Figures v Acknowledgements v i i Chapter 1 Introduction 1 Chapter 2 Observations 4 2.1 Instrumentation 4 2.2 Method 6 2.3 Calibrations 8 2.4 Data reduction for the fl u x density of GT0236+610 16 Chapter 3 Search for p e r i o d i c i t i e s 23 3.1 Simple period folding analysis 25 3.2 Cross c o r r e l a t i o n analysis 27 3.3 Two parameters searching for period and period derivative 32 3.4 Monte carlo simulations 40 3.5 A possible 4-year period of long term modulation . 45 Chapter 4 A processing j e t model for the long term modulation 51 Chapter 5 Summary and conclusions 56 References 57 Appendix A Reduction for the phase value 59 Appendix B Telescope track s t a b i l i t y 60 Iv L i s t of Tables Table page 1. Summary of the observations 7 2. GT0236+610 radio flux densities in September 1986 22 3. GT0236+610 radio flux densities in July-August 1984 24 4. Approximate binary radio f l a r e maxima 48 V L i s t o f F i g u r e s F i g u r e page 1 . The o r i e n t a t i o n o f t h e f e e d a s s e m b l y 5 2 . R i g h t a s c e n s i o n p o i n t i n g e r r o r f o r s o u t h b o u n d s c a n s . . 11 3 . R i g h t a s c e n s i o n p o i n t i n g e r r o r f o r n o r t h b o u n d s c a n s . . 11 4 . D e c l i n a t i o n p o i n t i n g e r r o r f o r s o u t h b o u n d s c a n s 12 5 . D e c l i n a t i o n p o i n t i n g e r r o r f o r n o r t h b o u n d s c a n s 12 6 . D i s h g a i n f o r f e e d 7 13 7 . E a s t - w e s t beam m o d e l 14 8 . R e d u c t i o n o f peak due t o s m o o t h i n g 15 9 . S e q u e n c e 0 ' s r a w d a t a 17 1 0 . S e q u e n c e 4 a n d s e q u e n c e l ' s raw d a t a 18 1 1 . The s c a t t e r o f t h e d a t a a b o u t mean l i g h t ( 1 0 . 5 GHz) 26 1 2 . The s c a t t e r o f t h e d a t a a b o u t mean l i g h t c u r v e (5 GHz) 26 1 3 . The rms p h a s e s c a t t e r i n t h e peak o f t h e c r o s s c o r r e l a t i o n o f t h e mean l i g h t c u r v e w i t h i n d i v i d u a l o u t b u r s t s 29 1 4 . Mean l i g h t c u r v e a t 5 GHz 30 1 5 . Mean l i g h t c u r v e a t 1 0 . 5 GHz 30 1 6 . T e n o u t b u r s t s ' d a t a p l o t t e d i n p h a s e s p a c e f o r p e r i o d o f 2 6 . 5 0 d a y s 31 1 7 . Two d i m e n s i o n a l s e a r c h f o r p e r i o d a n d p e r i o d d e r i v a t i v e 34 v l 18. Window effects test . 35 19. Window effects test 36 20. A fi n e r two dimensional search for period and period derivative .... 37 21. Cross-section of two dimensional contours at dT/dt = 4x l0~ 5 days/day 38 22. Cross-section of two dimensional contours at T = 26.49 days 39 23. Monte carlo simulation 42 24. Contour plot for pe r f e c t l y sampled data " 43 25. Another contour plot for perfectly sampled data 43 26. Ten outbursts' data plotted l n phase space for best f i t t e d period an period derivative 44 27. Binary radio f l a r e maxima plotted i n phase space for period of 1458 days 49 28. Binary radio f l a r e maxima plotted vs J u l i a n date .... 50 29. The coordinate system i n deriving the j e t model 54 30. The j e t model f i t 55 31 Telescope Declination tracking errors 60 v i i Acknowledgements F i r s t , I would l i k e to thank my supervisor Dr. P. c. Gregory for providing the 1984 data. His assistance and guidance throughout t h i s work are greatly appreciated. I wish to thank my colleague Chris Backhouse for his great help and advice on computing. He was responsible for creating the 1986 Radio Patrol data base from the raw telescope tapes, without which, t h i s thesis would not be possible. Also I would l i k e to thank him for providing some results of c a l i b r a t i o n data and for reading of t h i s manuscript. F i n a l l y , I would l i k e to thank the s t a f f at Green Bank for t h e i r help and h o s p i t a l i t y . Thanks also to Dr. M. J. Coe for providing 10.7 GHz data. 1 Chapter 1 Introduction The binary star GT0236 +610 (LSI +61°303 ) is one of the most unusual objects in our Galaxy. Over the l a s t decade, i t has been the object of considerable observational e f f o r t because of i t s very exceptional properties. During the Gregory and Taylor (Gregory and Taylor 1978) survey of the g a l a c t i c plane for variable radio emission/GT0236+610 was discovered as a highly variable radio source. Based on an accurate radio po s i t i o n , GT0236+610 was i d e n t i f i e d with LS I+61°303 (Gregory et a l . 1979). It has also been found to be both an X-ray source (Share et a l . 1979; Bignami et a l . 1981) and a probable Tf-ray source (Gregory et a l . 1979; P e r o t t i et a l . 1980; Pollock et a l . 1981 ). The high radio v a r i a b i l i t y and high X-ray luminosity place this source in the class of such exotic objects as SS433 and Circinus X - l . O r i g n i a l l y thought to be a supergiant (Gregory et a l . 1979), the star has been c l a s s i f i e d as a main sequence BO-BO.5 (L=10 3 8 erg s e c - 1 , T e £ £ = 2.6*104 K) emission-line star with high r o t a t i o n a l v e l o c i t y , undergoing mass loss through an equatorial disk( Hutchings and Crampton,1981 ). Hutchings and Crampton (1981 ) also found evidence for a binary period of 26.4 ± 0.1 days from an analysis of three years of r a d i a l v e l o c i t y data. The radio emission from GT0236+610 i s characterized by 2 nonthermal outbursts with r i s e times of a few days and t y p i c a l duration of about 10 days. Based on an analysis of 144 flux density measurements at 5 GHz and 10.5 GHz from 1977 August to 1981 March, Taylor and Gregory ( 1982 ) derived a period of 26.52 ± 0.04 days. This period of radio outburst has been confirmed by Coe et a l . (1983). Except for the pulsars, GT0236 +610 i s one of the only two known periodic radio sources (Circinus X-1,P = 16.59 days), and the f i r s t to be discovered soley through radio measurements. It i s worthwhile to point out that so far no v a r i a b i l i t y i s seen in the X-ray data, although the r e s u l t i s not conclusive. A review of the basic features of GT0236 + 610 is given by Taylor and Gregory (1982). As a part of 1986 Galactic survey project, observations of GT0236 + 610 were carried out in September using the 91 m t r a n s i t telscope of National Radio Astronomy Observatory at Green Bank. A t o t a l of 8 flux measurements from September 11 to 29 were obtained. The observations and flux density data reduction are discussed in chapter 2. Together with the 170 flux density measurements made by Taylor and Gregory (1981,1982) from August 1977 to September 1981 and 21 unpublished flux density measurements in July and August 1984 made by Gregory, we were able to analyse a t o t a l of 201 flux densite over about 9 years. We repeated the simple period folding analysis and cross c o r r e l a t i o n analysis discussed by Taylor and Gregory (1981) confirming the period of about 26.50 days. Also a new method of searching for both the 3 period and period derivative simultaneously was developed. The analysis of searching for the p e r i o d i c i t i e s i s discussed in chapter 3. With the 9 years of observations, we find an indication that GT0236 + 610 has a long term modulation that is superimposed on i t s binary motion with a period of about 4 years. A processing j e t model for th i s long term modulation i s discussed in chapter 4. 4 Chapter 2 O b s e r v a t i o n s 2.1 I n s t r u m e n t a t i o n O b s e r v a t i o n s were c a r r i e d out i n September of 1986 u s i n g the 91 meter t r a n s i t t e l e s c o p e of N a t i o n a l Radio Astronomy O b s e r v a t o r y a t Green Bank, West V i r g i n i a . For the f i r s t time we used the new 7-feed r e c e i v e r system (see F i g . 2.1). The feed system c o n s i s t s of 7 f e e d s , one l o c a t e d a t the c e n t e r of hexagon and the o t h e r 6 feeds l o c a t e d a t each c o r n e r of the hexagon. Each f e e d was connected t o two r e c e i v e r s s e n s i t i v e t o r i g h t and l e f t hand p o l a r i z a t i o n , r e s p e c t i v e l y . At a wavelength of 6 cm, the h a l f power beam w i d t h (HPBW) of the beams was a p p r o x m a t e l y 2.8 a r c m i n u t e s . With the feeds box r o t a t e d a t 19.1° from the scan d i r e c t i o n (see F i g . 1 ) , the t r a c k s p a c i n g between the a d j a c e n t beams was about 2.7 a r c m i n u t e s . The r e c e i v e r was f i x e d t o a r o t a t a b l e mount c e n t e r e d on the t e l e s c o p e a x i s of symmetry a t the f o c u s . For the purpose of the s u r v e y p r o j e c t , a scan r a t e of 120'/min and sample time of 0.2 seconds were chosen. Each r e c e i v e r had a 3db bandwidth of 600 MHz. The t h e o r e t i c a l rms r e c e i v e r n o i s e f l u c t u a t i o n s ( T i u r i , 1 9 6 6 ) was A T r m s = K s x T s y s ' <Av' x ^ < 2.1) g i v e n the c o n s t a n t K s = 1 f o r a t o t a l power r e c e i v e r . T h i s g i v e s T r m s = 7 mk f o r a system temperature of 70 K. T h i s n o i s e can be reduced by f a c t o r of 2^ by combining the two r e c e i v e r 5 6 o u t p u t s f r o m t h e same f e e d a s s u m i n g t h e s i g n a l s a r e u n p o l a r i z e d . The o u t p u t s o f t h e 14 r e c e i v e r s t o g e t h e r w i t h p o i n t i n g i n f o r m a t i o n were w r i t t e n o n t o m a g n e t i c t a p e a t t h e t e l e s c o p e s i t e a n d l a t e r s h i p p e d t o The U n i v e r s i t y o f B r i t i s h C o l u m b i a f o r f i n a l a n a l y s i s . 2 . 2 M e t h o d The s u r v e y s e q u e n c e s a n d c a l i b r a t i o n p r o c e d u r e s were d e v e l o p e d b y C h r i s B a c k h o u s e . A d e t a i l e d d e s c r i p t i o n o f t h e 1986 o b s e r v i n g p r o c e d u r e i s d i s c u s s e d b y B a c k h o u s e ( M . S c t h e s i s , 1 9 8 7 ) . H e r e we j u s t g i v e a b r i e f d i s c u s s i o n o f t h e s u r v e y m e t h o d . The s u r v e y r e g i o n i s t h e p o r t i o n o f t h e g a l a c t i c p l a n e w i t h i n t h e o p e r a t i o n a l d e c l i n a t i o n r a n g e o f t h e t e l s c o p e . The a p p r o x i m a t e b o u n d a r i e s o f t h e s u r v e y r e g i o n a r e 2 5 ° < 1 < 2 2 0 ° a n d - 5 ° < b < 5 ° . To o b t a i n t h i s c o v e r a g e o f t h e g a l a c t i c p l a n e , a s e q u e n c e o f 10 a l t e r n a t i n g n o r t h b o u n d ( NB ) a n d s o u t h b o u n d ( SB ) s c a n s was e x e c u t e d , p r o d u c i n g a z i g - z a g p a t t e r n o f s c a n s c e n t e r e d on t h e g a l a c t i c p l a n e . A f t e r e a c h NB s c a n , t h e t e l e s c o p e was h e l d s t a t i o n a r y f o r 12 s e c o n d s f i r i n g a s t a b l e n o i s e t u b e t o p r o v i d e a t e m p e r a t u r e c a l i b r a t i o n o f t h e d a t a . The s o u r c e GT0236+610 was c o v e r e d b y f o u r o f t h e s c a n s e q u e n c e s ( s e q u e n c e 0 , 1 , 4, 5 ) . S e q u e n c e 0 was r e p e a t e d s e v e n t i m e s t o m e a s u r e t h e v a r i a b l i t y o f i t s r a d i o e m i s s i o n . U n f o r t u n a t e l y , due t o t e l e s c o p e c o n t r o l s y s t e m f a i l u r e s a n d 7 TABLE 1 UT Date Sequence Scan Peed 1986 Sep 11 0 1251 7 Sep 15 4 2158 7 Sep 20 0 3247 7 Sep 24 1 4112 7 Sep 25 0 4322 7 Sep 26 1 4534 7 Sep 27 0 4751 . 7 Sep 29 0 4957 7 8 tape recording error, 4 scans through GT0236+610 were l o s t . We have a t o t a l of 8 flux density measurements of the source during September 11 to September 28. A summary of the observations is given in table 1. 2.3 Calibrations To get the flux density of the source from the raw data on the tapes, two processes were involved; 1) measurements of the signal strength in Kelvin, 2) conversion of the measurements to flux density. A noise tube was f i r e d every 5 minutes to ca l i b r a t e the receiver output in K. To carry out process 2) we have to know a number of telescope parameters. The signature of an unresolved source in a scan is given by the North-South cross-section of the instrumental p r o f i l e . After removing a baseline, the source strength (in K) was measured. In general the source did not pass through the center of the telescope beam and thus i t was necessary to correct for thi s after f i r s t applying the telescope pointing error. For this c a l c u l a t i o n the East-west cross section of the beam p r o f i l e was measured. F i n a l l y , to convert the source strength to a absolute flux density (in mJy), the telescope gain for the par t i c u l a r feed involved was required. The following telescope c a l i b r a t i o n s were carried out: a) systematic pointing errors, b) East-West beam p r o f i l e , c) peak beam gain (dish gain) to convert antenna temperature (K) to flux density. Due to g r a v i t a t i o n a l d i s t o r t i o n , a l l these 9 t e l e s c o p e p a r a m e t e r s v a r y w i t h d e c l i n a t i o n . I t was n e c e s s a r y t o o b t a i n c a l i b r a t i o n m e a s u r e m e n t s c o v e r i n g t h e e n t i r e - 1 0 ° t o 7 0 ° d e g r e e d e c l i n a t i o n r a n g e o f t h e s u r v e y o b s e r v a t i o n s . S i n c e we u s e d t h e 7 - f e e d s y s t e m , a c o n s i d e r a b l e amount o f c a l i b r a t i o n t i m e was u s e d t o c a l i b r a t e e a c h f e e d . C a l i b r a t i o n s c a n s were o b t a i n e d b y t r a c k i n g e a c h o f t h e 7 beams a c r o s s a s e t o f a p p r o x i m a t e l y 150 u n r e s o l v e d s o u r c e s o f known f l u x d e n s i t y a t d e c l i n a t i o n b e t w e e n - 1 0 ° a n d 7 0 ° . D r i f t s c a n s ( t y p e 1) w i t h t h e f e e d box r o t a t e d a s f o r n i g h t s u r v e y s c a n s ( NB a n d SB) were f i r s t o b t a i n e d t h r o q g h t h e c e n t r a l beam t o d e t e r m i n e t h e RA p o i n t i n g c o r r e c t i o n s a n d t h e i r d e c l i n a t i o n d e p e n d e n c e ( s e e F i g . 2 a n d F i g . 3 ) . W i t h t h i s RA p o i n t i n g e r r o r a p p l i e d , NB a n d SB d r i v e n s c a n s ( t y p e 2 ) , w i t h t h e f e e d box r o t a t e d a s f o r n i g h t s u r v e y s c a n s , were e x e c u t e d t h r o u g h t h e c e n t r a l beam t o o b t a i n t h e DEC p o i n t i n g e r r o r ( s ee F i g . 4 a n d F i g . 5) a n d peak beam g a i n ( d i s h g a i n , s e e F i g . 6 , r e p r o d u c e d f r o m B a c k h o u s e ' s t h e s i s , 1987 ) a s w e l l a s t h e N o r t h - S o u t h beam p r o f i l e f o r t h e c e n t r a l beam. K n o w i n g t h e DEC p o i n t i n g c o r r e c t i o n s , a n o t h e r s e t o f d r i f t s c a n s were e x e c u t e d t h r o u g h t h e c e n t r a l beam t o m e a s u r e t h e E a s t - W e s t beam p r o f i l e (two t y p i c a l r e s u l t s a s w e l l a s t h e m o d e l f i t a r e shown i n f i g u r e 7 ) . T o c a l i b r a t e t h e o f f s e t b e a m s , NB a n d SB d r i v e n s c a n s ( t r a c k i n g a n o f f s e t beam a c r o s s a c a l i b r a t i o n s o u r c e ) were c a r r i e d o u t ( t y p e 3 ) . The DEC o f f s e t o f a p a r t i c u l a r o f f s e t beam was o b t a i n e d b y c o m p a r i n g t h e d e c l i n a t i o n s o f t h e same 10 c a l i b r a t i o n s o u r c e i n t y p e 2 a n d t y p e 3 s c a n s . T h i s DEC o f f s e t i s d i f f e r e n t f o r SB a n d NB s c a n s due t o t h e d i f f e r e n t r o t a t i o n a n g l e s , a n d i t was a n a l y s e d i n d e p e n d e n t l y . W i t h a k n o w l e d g e o f t h e DEC o f f s e t o f t h e beam, d r i f t s c a n s ( t y p e 4) were c a r r i e d o u t t o d e t e r m i n e i t s RA o f f s e t a n d d i s h g a i n a s w e l l a s t h e E a s t - W e s t beam p r o f i l e . K n o w i n g t h e RA o f f s e t , d r i v e n s c a n s t r a c k i n g t h r o u g h t h e o f f s e t beam were e x e c u t e d t o m e a s u r e t h e N o r t h - S o u t h beam p r o f i l e . To a c c o u n t f o r a n y d i r e c t i o n a l e f f e c t s , a l l t h e t e l e s c o p e p a r a m e t e r s were a n a l y s e d i n d e p e n d e n t l y f o r NB a n d SB s c a n s . No s i g n i f i c a n t d i f f e r e n c e s i n p a r a m e t e r v a l u e s was o b s e r v e d e x c e p t f o r t h e d e c l i n a t i o n p o i n t i n g e r r o r s . P r e l i m i n a r y r e d u c t i o n o f t h e t e l e s c o p e c a l i b r a t i o n s was c a r r i e d o u t a t G r e e n Bank b y m y s e l f u s i n g t h e NRAO s o f t w a r e " P O P S " . F i n a l r e d u c t i o n o f t h e c a l i b r a t i o n d a t a was done by C h r i s B a c k h o u s e a t U B C . The E a s t - w e s t beam p r o f i l e a n a l y s i s d i s c u s s e d b e l o w i s t h e work o f t h e a u t h o r . F o r t h e p u r p o s e o f d a t a r e d u c t i o n , a m a t h e m a t i c a l beam m o d e l was u s e d t o a p p r o x m a t e t h e E a s t - W e s t beam p r o f i l e ( T a y l o r , 1 9 8 2 ) . The m o d i f i e d g a u s s i a n m o d e l u s e d was p ( x , c ) = e x p { - 2 . 7 7 2 6 [ l + c x ( x - 0 . 5 ) ] x 2 } ( I I . 2 ) where t h e v a r i a b l e x i s t h e a n g u l a r o f f s e t f r o m t h e p r o f i l e peak m e a s u r e d i n h a l f - p o w e r beam w i d t h s . The beam m o d e l i s e q u a l t o a s i m p l e g a u s s i a n , w i t h same HPBW, a t x=0 a n d x = l / 2 . The m o d e l i s c o m p l e t e l y s p e c i f i e d b y two p a r a m e t e r s ; t h e HPBW o f t h e p r o f i l e a n d t h e c o e f f i c i e n t " c " . 11 4.0 2.4 _ o.e C - O . B u o H M u -2.4 -4.0 -20.0 0.0 20.0 DEC ( a r c m l n ) 40.0 60.0 BO.O F i g u r e 2 . R i g h t a s c e n s i o n p o i n t i n g e r r o r ( m e a s u r e d - t r u e p o s i t i o n ) f o r s o u t h bound s c a n s . 4.0 2.4 O . B ™ - O . B M H -2.4 -4.0 -21.0 0.0 20.0 40.0 DEC ( a r c m i n ) 60.0 60.0 F i g u r e 3. R i g h t a s c e n t i o n p o i n t i n g e r r o r ( m e a s u r e d - t r u e p o s i t i o n ) f o r n o r t h bound s c a n s . 12 90.0 54.0 „ 1B.0 u «. n u M n o M W W -18.0 --54.0 --90.0 -20.0 0.0 20.0 DEC (arcmln) 40.0 60.0 F i g u r e 4. D e c l i n a t i o n p o i n t i n g e r r o r (measured-true p o s i t i o n ) for south bound s c a n s . 60.0 u w n U u n M O w H w 90.0 54.0 S8.0 -JB.0 --54.0 --90.0 -20.0 0.0 20.0 DEC (arcmin) 40.0 60.0 80.0 F i g u r e 5. D e c l i n a t i o n p o i n t i n g e r r o r (measured-true p o s i t i o n ) for nor th bound s c a n s . 13 0.90 -: 0,80 4 0.70 ^ -I 0.60 § -j 0.50 « -j 0.40-5 -j 0.30 5 -j 0.20 -I 0.10 0.00 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 II 111111111111111111111111111111111 D e c l i n a t i o n ( d e g r e e s ) The nor th a o l l d l ln#) and south I D . dashed l l n v l bound antenna ga in eurvaa for faad 7. Figure 6. Dish gain for central beam (feed 7) (reproduced from Backhouses's t h e s i s ) . 14 Figure 7 . Comparison of the beam model to measured East-Vest beam p r o f i l e s . 15 .0 DEC ( a r c m l n ) Figure 8. Reduction of peak due to smoothing. Solid l i n e is a simple gaussian with HPBW of 3 arcmin. Dots are the sample points of the smoothed curve of the simple gaussian beam model showing a reduction of 7 % in the peak value. 16 To a c c o m m o d a t e beam a s y m m e t r y e a c h s i d e o f t h e beam p r o f i l e was m o d e l l e d i n d e p e n d e n t l y . A f t e r r e m o v i n g a l i n e a r b a s e l i n e f r o m t h e c a l i b r a t i o n s c a n s . The HPBW o f t h e p r o f i l e ( f o r e a c h s i d e ) was m e a s u r e d b y f i t t i n g a s i m p l e g a u s s i a n . K n o w i n g t h e HPBW, t h e c o e f f i c i e n t "c" was d e t e r m i n e d b y l e a s t s q u a r e f i t t i n g t h e d a t a w i t h t h e m o d e l i n ( I I . 2 ) u s i n g o n l y t h o s e d a t a v a l u e s g r e a t e r t h a n 10% o f t h e peak t e m p e r a t u r e . T y p i c a l m o d e l f i t s t o a beam p r o f i l e a r e shown i n f i g u r e 7 . 2 . 4 D a t a r e d u c t i o n f o r t h e f l u x d e n s i t y o f GT0236+610 T o t a l i n t e n s i t y m e a s u r e m e n t s made a t a w a v e l e n g t h o f 6 cm o r s h o r t e r c a n be s u b j e c t t o c o n s i d e r a b l e d e g r a d a t i o n due t o a t m o s p h e r i c w a t e r v a p o r . To c a n c e l t h e f l u c t u a t i o n s i n a t m o s p h e r i c e m i s s i o n , i n t h e same s c a n , t h e beam t h a t t r a c k e d GT0236+610 i s s u b t r a c t e d f r o m a n a d j a c e n t o f f s e t beam. The s u b t r a c t i o n o p e r a t i o n w i l l d e c r e a s e t h e s i g n a l t o n o i s e r a t i o b y a f a c t o r o f a b o u t 2Vi . T h i s c a n be c o m p e n s a t e d b y c o m b i n i n g t h e two r e c e i v e r s ' o u t p u t s b e f o r e s u b t r a c t i o n . To i n c r e a s e t h e s i g n a l t o r e c e i v e r n o i s e r a t i o , t h e d a t a was s m o o t h e d o v e r 5 s a m p l e s u s i n g t h e f o r m u l a : s m t h l i ] = { / 2 x [ i - 2 ] + ! 4 x [ i - l ] + x [ i ] + ^ix[ i + l ] + H x [ i + 2 ] } / 3 where x [ i ] i s t h e raw d a t a s e t a n d s m t h t i ] i s t h e d a t a s e t a f t e r s m o o t h i n g . The e q u i v a l e n t i n t e r g r a t i o n t i m e o f 1 s e c o n d r e d u c e d t h e r e c e i v e r n o i s e b y a f a c t o r o f a b o u t 2 . 3 . H o w e v e r , t h e s m o o t h i n g o f t h e d a t a a l s o r e s u l t s i n a n a t t e n u a t i o n o f t h e s i g n a l p e a k o f a b o u t 7% ( s e e F i g . 8 ) . T h i s f a c t o r i s l a t e r 17 6 6 . 9 r-3 3 . 4 7 5 . 4 3 7 . 7 5 B 8 - 3 x 3 3 4 . 2 fc. 9 3 . 4 4 6 . 7 7 2 . 2 r-3 6 . 1 - 3 0 . 0 0 o.oo-DEC (arcmln) 3 0 . 0 0 F i g u r e 9 . F i v e sequence O's raw data ( s o l i d l i n e s ) and b a s e l i n e s (dashed l i n e s ) . From bottom to top are scan 1251, 3247, 4322, 4751, 4957 (see t a b l e 1 ) . 18 .00 D E C ( a r c m l n ) Figure 10. One sequence 4 and two sequence l ' s raw data ( s o l i d l i n e s ) and b a s e l i n e s (dashed l i n e s ) . From bottom to top are scan 2118, 4112, 4S34 (see table 1). 19 corrected. Before any meaningful data reduction, a l o c a l baseline was removed. The baseline can be due to highly structured extended emission, or as a resu l t of the v a r i a t i o n in the pickup of ground s p i l l - o v e r radiation with declination, or, as pointed out by Backhouse, due to the gain v a r i a t i o n . Scans through the c a l i b r a t i o n sources generally have very l i t t l e extended structure to complicate the choice of suitable regions for baseline d e f i n i t i o n . However, GT0236+610 happens to be in a highly confused region, the choice of the region for the baseline posed a problem. Due to the highly structured extended emission and short time scale gain v a r i a t i o n , the baseline regions should be chosen as l o c a l l y as possible. In this reduction for the flux of GT0236+610, the slope and level of the baseline is determined by a linear least square f i t to the data in two 4' segments separated by the width of an instrumental p r o f i l e and centered on the position of the source. The smoothed raw data and linear baselines are shown in figure 9 and figure 10. After subtracting the baseline, the strength ( S ) was calculated from a simple gaussian least square f i t to the peak portion of the data. Taking into consideration both receiver noise and confusion signal in the region of the detection, an estimate of the confusion signal c s is given by the residuals of the linear f i t to the l o c a l baseline o^. The flux density of the source can be expressed by the 20 r e l a t i o n J = S / { P ( x , c ) X G } ( I I . 3 ) where S i s s o u r c e s t r e n g t h i n mK, J i s t h e f l u x d e n s i t y o f t h e s o u r c e i n m i l l i - J a n s k y , G i s t h e d i s h g a i n ( i n K / m J y ) w h i c h i s d e c l i n a t i o n d e p e n d a n t P ( x , c ) i s t h e E a s t - W e s t beam p r o f i l e g i v e n b y ( I I . 2 ) . The v a r i a b l e x i s t h e s o u r c e o f f s e t , c l o s e s t a p p r o a c h o f t h e s o u r c e t o t h e t r a c k m e a s u r e d i n h a l f - b e a m power w i d t h s . The s o u r c e o f f s e t x was c a l c u l a t e d f r o m t h e f o r m u l a x= c o s ~ ^ [ c o s E X C O S S Q x c o s (O>:-(XQ ) + s i n S x s i n S f j 3/HPBW ( I I I . 4 ) where ( ° c n ^ S n ) a r e t h e c o o r d i n a t e s o f t h e GT0236 + 610 i n 1986 e p o c h , ( <*, S ) t h e p o s i t i o n on t h e t r a c k a t c l o s e s t a p p r o a c h t o t h e s o u r c e . A c c o r d i n g t o r e l a t i o n ( I I . 3 ) , t h e f l u x d e n s i t y d e p e n d s on s o u r c e s t r e n g t h S , d i s h g a i n G , HPBW o f t h e E a s t - W e s t beam p r o f i l e a n d s o u r c e o f f s e t x . T h e r e f o r e , a n e s t i m a t e o f t h e one s i g m a e r r o r i s g i v e n by o-j = ( K 1 x c s 2 + K 2 x t f G 2 + K 3 x o - x 2 + K 4 x o - H 2 ) ^ ( I I . 4 ) where c r s , c/ G , a n d a r e t h e one s i g m a e r r o r on s o u r c e s t r e n g t h , d i s h g a i n , o f f s e t d i s t a n c e a n d HPBW o f t h e E a s t - W e s t beam p r o f i l e , a n d K 2 / K 3 a n d K 4 a r e Kx = ( a j / 9 S ) 2 K 2 = O J / 3 G ) 2 K 3 = OJ/3X ) 2 K 4 = ( 3 J / 3 H ) 2 ( I I . 5 ) As m e n t i o n e d b e f o r e , c s was e s t i m a t e d f r o m t h e r e s i d u a l s o f t h e b a s e l i n e f i t o^ , w h i c h i s due t o r e c e i v e r n o i s e a n d c o n f u s i o n s i g n a l . S i m i l a r l y , c G a n d c H were e s t i m a t e d f r o m t h e rms s c a t t e r o f t h e m e a s u r e d v a l u e s a b o u t t h e s m o o t h c u r v e f i t t o 21 t h e i r d eclination dependence. Because of the high drive rate of 120'/min, o j x i s mainly due to the errors in the RA pointing. From the same consideration, c x was estimated from the rms scatter of measured RA pointing correction about the smooth curve f i t to their declination dependence. Table 2 shows the measured flux density and their one sigma errors. 22 TABLE 2 GT0236 + 610 RADIO FLUX DENSITIES IN SEPTEMBER 1986 UT Date 1986 Sep 11 1986 Sep 15 1986 Sep 20 1986 Sep 24 1986 Sep 25 1986 Sep 26 1986 Sep 27 1986 Sep 29 Juli a n Date (2,440,000+) 6684.9 6689.9 6693.9 6696.9 6697.9 6698.9 6699.9 6701.9 Frequency (Ghz) 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 Flux density (mJy) 52 ± 20 < 33 171 ± 20 92 ± 8 43 ± 8 41 + 10 88 ± 15 38 ± 17 23 C h a p t e r 3 S e a r c h f o r p e r i o d i c i t i e s T a y l o r a n d G r e g o r y (1982) r e p o r t e d t h e d i s c o v e r y o f t h e p e r i o d i c r a d i o e m i s s i o n a t T = 2 6 . 5 d a y s GT0236+610 , b a s e d on a n a n a l y s i s o f 144 f l u x d e n s i t y m e a s u r e m e n t s f r o m 1977 A u g u s t t o 1981 M a r c h . L a t e r t h i s r e s u l t was c o n f i r m e d b y Coe e t a l . (1983) b y t h e i r 66 o b s e r v a t i o n s f r o m 1981 May t o 1982 A p r i l . I n t h i s c h a p t e r , s t a t i s t i c a l t e s t s a r e c a r r i e d o u t u s i n g a l l t h e a v a i l a b l e r a d i o f l u x d e n s i t y m e a s u r e m e n t s a t 5 GHz and 1 0 . 5 GHz i n o u r g a l a c t i c p a t r o l d a t a b a s e . T h e s e i n c l u d e 144 m e a s u r e m e n t s made b y T a y l o r a n d G r e g o r y (1982) a t 5 GHz a n d 1 0 . 5 G H z , 28 o b s e r v a t i o n s a t b o t h f r e q u e n c i e s i n 1981 A u g u s t ( T a y l o r a n d G r e g o r y , 1 9 8 4 ) , 21 m e a s u r e m e n t s a t 5 GHz i n 1984 A u g u s t ( p r o v i d e d by G r e g o r y ) a n d 8 f l u x d e n s i t y m e a s u r e m e n t s a t 5 GHz i n S e p t e m b e r 1986 i n t h i s u n d e r t a k i n g . W i t h t h e s e t o t a l 201 f l u x d e n s i t y m e a s u r e m e n t s , s p a n n i n g a b o u t 3334 d a y s , we a r e a b l e t o c h e c k t h e r e p o r t e d r a d i o p e r i o d a n d i t s s t a b i l i t y . A l s o we have e n o u g h l o n g t e r m d a t a t o s e a r c h f o r m o d u l a t i o n i n v a r i a b l e r a d i o f l a r e m a x i m a . The f l u x d e n s i t y d a t a f r o m 1977 t o 1981 were l i s t e d b y T a y l o r a n d G r e g o r y ( 1 9 8 2 , 1 9 8 4 ) . T a b l e 3 l i s t s t h e r a d i o f l u x d e n s i t y m e a s u r e m e n t s i n 1984 J u l y - A u g u s t ( G r e g o r y u n p u b l i s h e d ) . 24 TABLE 3 GT0236 + 610 RADIO FLUX DENSITIES IN JULY-AUGUST 1984 UT Date Ju l i a n Date Frequency Flux Density (2,440,000+) (Ghz) (mJy) 1984 Jul 19 5900.96 5.0 46 + 7 1984 Jul 20 5901.96 5.0 5 5 + 7 1984 Jul 21 5902.96 5.0 54 ± 7 1984 Jul 22 5903.96 5.0 63 + 8 1984 Jul 23 5904.96 5.0 71 + 8 1984 Jul 24 5905.96 5.0 74 + 8 1984 Jul 25 5906.96 5.0 84 ± 9 1984 Jul 26 5907.96 5.0 69 ± 8 1984 Jul 27 5908.96 5.0 54 ± 7 1984 Jul 28 5909.96 5.0 6 3 + 8 1984 Jul 29 5910.96 5.0 49 + 7 1984 Ju l 30 5911.96 5.0 61 ± 8 1984 Aug 4 5916.96 5.0 23 ± 6 1984 Aug 5 5917.96 5.0 < 18 1984 Aug 6 5918.96 5.0 31 + 6 1984 Aug 8 5920.96 5.0 29 + 6 1984 Aug 10 5922.96 5.0 <18 1984 Aug 11 5923.96 5.0 <18 1984 Aug 12 5924.96 5.0 19 + 6 1984 Aug 15 5927.96 5.0 <18 1984 Aug 16 5928.96 5.0 65 ± 8 25 3.1 Simple period folding analysis The search was carried out using a simple folding type time analysis discussed by Taylor and Gregory (1982). Based on an adoped t r i a l period T, each flux density is assigned a phase phs = ( t - t Q ) / T - i n t [ ( t - t 0 ) / T ] ( I I I . l ) where t i s the J u l i a n Date of the observation, t Q i s the phase zero set at J u l i a n Date of 2,4443,366.775 as used by Taylor and Gregory (1982) and phs is the assigned phase for the flux density. According to the value of the phase, the flux is binned into one of ten phase bins. At each t r i a l period T, the sum of variances in ten bins, V, is calculated. This quantity V is a measure of the scatter of the data about the mean l i g h t curve. True p e r i o d i c i t y w i l l r e s u l t in a minimum of the scatter as the t r i a l period approaches the true period. The analysis is carried out for t r i a l period of 25.0 days to 28.0 days. To accommodate any systematic difference between the l i g h t curves at 5 GHz and 10.5 GHz, the data were analysed independently for the two frequencies. This simple period folding analysis is most sensitive when outbursts have a constant amplitude, but as figure 22 shows thi s was not the case. The implication of the variable f l a r e maxima are discussed in section 3.5. For the purposes of t h i s analysis,the data is normalized ( i . e . , the fluxes were scaled according to the empirical modulation of f l a r e maxima) for each outburst before the simple period folding analysis is employed. The results are shown in figure 11 and figure 12 . A 5^ minimum occurs at a t r i a l period about 26 .0 T r i a l period (days) Figure 11. The scatter of the data about mean light curve (10.5 GHz). 0.229 j 1 1 1 1 ! 1 , 1 , 1 .0 T r i a l period (days) Figure 12. The scatter of the data about mean light curve (5 OHs). 27 26.4 days at 10.5 GHz data and a 8c minimum occurs at a t r i a l period about 26.5 days at 5GHz. From these two figures one sees a strong suggestion of a period of about 26.5 days. 3.2 Cross c o r r e l a t i o n analysis While the results of simple period folding analysis provide strong evidence for periodcity, t h i s method Is sens i t i v e to the i n t r i n s i c v a r i a b i l i t y i n the magnitude of the outburst, and the re s u l t i n g noise reduces the accuracy to which the period can be determined. To t r y to define t h i s period more preci s e l y and to quantify i t s significance a second test was employed. As discussed by Taylor and Gregory (1982), the test i s aimed at emphasizing the r e p r o d u c i b i l i t y of the shape of each outburst, rather than i t s amplitude. For each t r i a l period, a mean l i g h t curve at both frequencies was calculated by binning and averaging a l l of the data as dicussed i n the previous analysis. This mean l i g h t curve was then cross-correlated, i n phase space, with the res u l t s from the 10 observing session's. For the purpose of the t e s t , each session's data and mean l i g h t curve were normalized. The phase difference between the indi v i d u a l and mean l i g h t curve i s measured by the phase of the peak i n the cross-correlation curve. For each t r i a l period T, the quantity X = (S x t 2 )* / 1 0 (III.2) was calculated. Where i s the phase difference between one of the session's data and mean l i g h t curve. Therefore the quantity 28 X i s a s t a t i s t i c a l measure of the phase difference between the outbursts and the mean l i g h t curve. For a true period, t h i s X i s zero. The r e s u l t of the analysis i s shown in figure 13 . A 8c minimum occurs at a t r i a l period of 26.50 ± 0.03 days . It i s worthwile to point out that in carrying out t h i s test, we assumed no period derivative (this should be a good approxmation over r e l a t i v e l y short observational time base). Further analysis for searching for the period derivative is discussed in the next section. The data were binned modulo the period of 26.50 days using the phase zero of J.D. 2,4443,366.775. The binned mean l i g h t curve at 5 GHz and 10.5 GHz are shown in figure 14 and figure 15. They are in good agreement with results by Taylor and Gregory (1982). Figure 16 shows the 10 sessions data in phase space. V e r t i c a l lines indicate the phase of the peak of mean l i g h t curves. 29 T r i a l period (days) Figure 13. The rms phase scatter i n the peak of the cross c o r r e l a t i o n of the mean l i g h t curve with i n d i v i d u a l outbursts. 30 leo.o 144.0 >• 108.0 X 9 lib 72 .0 -36 .0 -"1 0 .0 0 .0 0 .4 O B Phase 1.? 1 .6 2.0 Figure 14. Binary r a d i o mean l i g h t curve a t 5 GHz f o r period of 26.50 days. J u l i a n Date of phase zero - 2,4443,366.775. X 9 1B0.0 144.0 -108.0 h. 72 .0 -3 6 . 0 -0 .0 0 .0 2 .0 Figure 15. Binary r a d i o mean l i g h t curve a t 10.5 GHz f o r period of 26.5 days. J u l i a n pate of phase zero > 2,4443,366.775. 31 240 160 BO 150 100 50 150 100 50 90 60 30 30 20 10 > 60 "2 40 E 20 x 240 D 160 - 80 240 160 80 75 50 25 150 100 50 « • * • • . • • • • • • • • • • < • • • « , • t • • • • • • • • • • • • . • . . • * • • * • « • • * * • • * t • • • • • l l 1 1 1 1 1 1 1 1 Aug 1977. 5GHz Feb 1978. 10.5GHz Aug 1978. 5GHz Aug 1979, 5GHz Jun 1980. 10.5GHz Aug 1980. 5GHz Aug 19B1. 5GHz Aug 1981. 10.5GHz Aug 1984. 5GHz Sep 1986. 5GHz 0 0.2 0.4 0.6 0.8 1.0 Phase Figure 16. Ten outbursts plotted i n phase space for the period of 26.50 days. V e r t i c a l l i n e s indicate the phase of the peak of mean l i g h t curves. 32 3.3 Two parameters searching for the period and period derivative As has been pointed out, the previous cross-correlation analysis assumed the period derivative to be 0.0. To further check the assumption and quantitavely put a constraint to the period d e r i v a t i v e , a t h i r d test was employed. This test had the same philosophy as the previous cross-correlation analysis, i.e , the phase difference between the mean l i g h t curve and individual outbursts i s at minimum when the t r a i l period T equals the true period. The same method was extended to search for both the period T and period derivative T simultaneously. For a t r i a l period T and period derivative T, each flux density i s now assigned a phase phs = l n [l+ T x(t-t 0)/T]/T - i n t { l n [1+Tx(t-t Q)/TJ/T} (III .3) (see Appendix A for reduction of the formula) Where t , t Q and phs are described in the r e l a t i o n ( I I I . l ) . By binning and averaging of a l l the data according to thi s new phase, a mean l i g h t curve at each frequency i s constructed. And by the same consideration, the s t a t i s t i c a l phase difference between mean l i g h t curve and individual outbursts X described in r e l a t i o n ( III .2) i s evaluated for each t r i a l period T and period derivative T. For true period T and period derivative T thi s quantity X i s 0.0 or at minimum. Taylor and Gregory have put an upper l i m i t on ITI <1.6"10~4 days/day (1984) for an 33 assumed period of 26.52 days. However, t h i s value might be underestimated i f we take the period T as an additional v a r i b l e . Therefore, the present two dimensional analysis was carried out for t r i a l period derivatives from - l . O x l O - 3 to l . O x l O - 3 days/day, and t r i a l periods from 25.5 to 27.5 days using the extended data base to 1984 ( the 1986 data were consided too sparse to be used in t h i s a n a l y s i s ) . The contour plot produced i s shown i n figure 17. The contour l e v e l i s the value of mean phase difference between the mean l i g h t curve and ind i v i d u a l outbursts. The contour values are equally spaced from minimum to maximum mean phase difference for a l l the contour plots presented in t h i s chapter. Figure 17 shows 2 minima. Except for the minimum at about T = 26.5 days and T=0.4xl0 - 4 days/day, another minimum is due to the observational window effects introduced by the method of the analysis. To further confirm that the window effects were introduced by the method, a set of a r t i f i c i a l periodic data with T = 26.0 days to T = 27.0 days and T = -3"10~4 to 3 » 1 0 ~ 4 days/day, sampled in the exactly the same way as our observation data were inserted into the same program that produced figure 17. Two t y p i c a l r e s u l t s are shown i n figure 18 and figure 19. Both show s i m i l a r structure to that obtained for the r e a l data. At t h i s stage, we have confidence that the true minimum i s close to T =26.5 days and T =0.0 days/days. A fi n e r search was carried out i n the area of T = 26.0 days to 27.0 days and T = - 1 . 5 x l 0 ~ 4 days/day to 2.5*10~ 4 34 5s 10 «o •o n » o 1.0 u •o •o o M tD a 0.6 tt) —( 0. JJ > 2 - 0 . 2 -- 0 . 6 -- 1 . 0 2 5 . 5 2 5 . 9 2 6 . 3 2 6 .7 2 7 . 1 T r i a l period (days) 2 7 . 5 Figure 17. Two dimensional search for period and period der i v a t i v e . The contours give the rms phase scatter i n the peak of the cross-correlation of the mean radio l i g h t curves with i n d i v i d u a l outbursts. Contour levels are equally spaced from minimum to maximum of rms phase scatter. 35 Figure 18. window e f f e c t s t e s t . The r e s u l t of a r t i f i c i a l data for T = 26.5 days and T = 0.0 days/day. 36 Figure 19. Window e f f e c t s t e s t . The r e s u l t of a r t i f i c i a l data for T • 26.80 days and T = 0.5*10" 3 days/day. 3 7 T r i a l period (days) Figure 2 0 . Two dimensional search for period and period d e r i v a t i v e . A finer search. Contour lev e l s are equally spaced from minimum to maximum of rms phase scat t e r . 38 T r i a l period (days) Figure 21 . Cross-section of two dimensional contours at T = 4 * 1 0 ~ 5 days/day. 39 Figure 22. Cross-section of two dimensional contours T = 26.49 days. 40 days/day. After cleaning the window ef f e c t s , figure 20 shows the re s u l t s of the test with the r e a l data. The minimum is found at T = 26.49 days and T = 0.4 *10~4 days/day. Figure 21 and figure 22 also shows the cross-section of the contour cut at T = 26.49 days and T = 0.4*10~4 days/day. The further test of t h i s reduction method and significance of the detection of period T and period derivative f are discussed in the next section. 3.4 Monte carlo simulations From the o r i g i n a l flux density measurements to the f i n a l detection of the period and period derivative, several processes were involved. In such a complex reduction program, i t i s not easy to determine the s i g n i f i c i a n c e of the detected T and T. In addition, the properties of t h i s complex interface between the raw data and the results should be considered when interpreting the r e s u l t s . It becomes necessary to calibrate the reduction program. This was done by treating the program as a black box and measuring the response to the controlled input. Monte carlo type simulation runs were carried out to determine (1) the systematic errors introduced by the reduction program, (2) the significance of the detection of T and T, (3) to further check the widow ef f e c t s discussed in the previous section. To determine the s i g n i f i c i a n c e of detected T and T and 41 the systematic errors introduced by the reduction program, a set of a r t i f i c i a l data with period T = 26.49 days and period derivative T = 4.0"10~5 days/days were created. The shape of the a r t i f i c i a l data in one cycle i s an asymmetrical gaussian with amplitude of 100 mJy and peak at binary phase 0.66 ( which is approximately the same shape as the observed mean l i g h t curve). From observed flux density measurements, the one sigma noise i s about 13 mJy. Therefore, the random noise with gaussian d i s t r i b u t i o n (sigma = 13 mJy,mean = 0.0) were added to the above a r t i f i c i a l data to simulate the noise. A t o t a l of twenty runs were carried out. No s i g n i f i c a n t systematic error was found. A t y p i c a l r e s u l t is shown in figure 23. Ninety percent of the results l i e within range T = 26.46-26.52 days and T = 1.0 "10" 5-7*10 -^ days/day. We conclude that £ T i s about 0.03 days and £ T about 3.0"10 - 5 days/day. Therefore the best f i t t e d period and period derivative are T = 26.49 ± 0.03 days T = (4.0 ± 3.0)*10~ 5 days/day. We have demonstrated that the window eff e c t s are due to the sparse sampling of observational data. With perfect period data which i s p e r f e c t l y sampled, th i s window eff e c t s should disappear. As a further check, two sets of a r t i f i c i a l data which were p e r f e c t l y sampled and with 10 cycles uniformly d i s t r i b u t e d in the observational time base were created. The contour plots produced are shown in figure 24 and figure 25. As one can see, the window effects do disappear. Figure 26 shows 10 sessions data in phase space for the 42 T r i a l period (days) Figure 23. A r e s u l t of monte c a r l o simulation. 43 •0 •o n « •o 1.0 O.B -2 0.2 -> m > v -0.2 •o •a o u Q i * -O.B -1.0 25.5 25.9 2G.3 26.7 T r i a l per iod (days) 27.1 27.5 F i g u r e 2 4 . A r e s u l t of per fect sampled data with T = 2 6 . 4 7 days and T •= 5«10" 5 days/day. >e •o v . n >» •o 1.0 O.B -S 0.2 « > 4 J * > £ "0.2 v o —4 M Cl Q i ~ H -0.6 -1.0 25.5 25.9 26.3 26.7 T r i a l period (days) 27.1 27.5 Figure 25. A r e s u l t of perfect sampled data with T » 26.50 days and f • 0.00 days /day. 44 240 160 BO 150 100 50 150 100 50 90 60 30 30 20 10 > 60 "2 40 £ 20 x 240 z> 160 r1 80 240 160 80 75 50 25 150 100 50 • * • » « . * ~i 1 r Aug 1977. 5GHz Feb 1978. 10.5GHz Aug 1978. 5GHz Aug 1979. 5GHz Jun 1980. 10.5GHz Aug 1980. 5GHz Aug 1981. 5GHz Aug 1981. 10.5GHz Aug 1984. 5GHz Sep 19B6. 5GHz r 1 1 1 1 r 0 0".2 0.4 0.6 0.8 1.0 Phase Figure 26. Ten outbursts plotted l n phase space for the period of 26.49 days and period d e r i v a t i v e of 0.4*10~4 days/day. V e r t i c a l l i n e s indicate the phase of the peak of mean l i g h t curves. 45 best f i t t e d period T =26 .49 days and T = 0 .4xl0~ 4 days/day. A phase s h i f t of 0.2 to right and 0.1 to the l e f t have been seen. Also the phase of the peak of 1986's data does not agree with the predicted phase. Comparaison of figure 16 and 26 suggests that a constant period of 26.50 days i s q u a l i t a t i v e l y better. Therefore, the phase scatter for the period of 26.50 days (see F i g . 16) i s un l i k e l y due to a period d e r i v a t i v e . The detection of the period derivative can not be regard as s i g n i f i c a n t . The scatter may be due to observational errors, or, due to sparse sampling of observational data ( i . e . , the observed l i g h t curves were not well defined). However, they may indicate that the underlying clock is not very t i g h t l y coupled to measured flux density v a r i a t i o n . One should note that simular feature exists in Hercules XI (Priedhorsky and Holt, 1986). 3.5 A possible 4-year period of long term modulation One of the major goals of thi s undertaking was to examine the long term modulation of the radio f l a r e s of thi s extraordinary system. As suggested by P.C. Gregory, such an exotic object might contain a precessing accretion disk or j e t s . If t h i s were the case, the effects might be refl e c t e d in the long term v a r i a t i o n of the radio emission. Taking advantage of the 9 years of the data base, tests were carried out to search for the possible long term modulation. Figure 16 shows c l e a r l y that the binary f l a r e maxima vary slowly with time. As shown in the binary mean l i g h t curve 46 (see F i g . 14 and F i g . 15), s t a t i s t i c a l y the peak portion of the binary outbursts is at o r b i t a l phase 0.4-0.8 for best f i t t e d period 26.52 days. In t h i s t e s t , the c h a r a c t e r i s t i c amplitude of each outburst i s measured as the peak flux density of the outburst. In cases where the peak flux density was not well defined due to a paucity of data (in a few instances only a single measurements in a 26.5 day cycle) only a lower l i m i t on the f l a r e maximum was a v a i l a b l e . Only those data in the binary phase 0.4-0.8 were selected a*s providing a lower l i m i t on the amplitude of the outburst. The c h a r a c t e r i s t i c amplitude of each outburst and date are l i s t e d in Table 4. An outburst with an amplitude of about 284 mJy occurred in 1977 August. After about 4 years, in 1981 August, another giant outburst at the l e v e l of about 300 mJy was observed, in addition the two lowest outbursts in 1980 August and 1984 August are also spaced by about 4 years. Coe et a l (1983) observed the source at 10.7 GHz from 1981 May to 1982 A p r i l . On A p r i l 24,1982 ( o r b i t a l phase about 0.56) the average emission l e v e l was about 220 mJy which was at the same l e v e l about 4 years p r i o r , on A p r i l 22,1978 at 10.5 GHz ( o r b i t a l phase 0.64). Again these re s u l t s suggested a possible periodic modulation (about 4 years ) of the amplitude of the binary outburst. For t h i s reason, the data in Table 4 are binned modulo the period of 1458 days using the phase 0.0 of J.D. 2,443,330.9. Figure 27 shows the binned data plotted in phase space. Since some of the observed l i g h t curves were not well defined ( i . e . , the data 46 (see F i g . 14 and F i g . 15), s t a t i s t i c a l y the peak portion of the binary outbursts is at o r b i t a l phase 0.4-0.8 for best f i t t e d period 26.52 days. In t h i s t e s t , the c h a r a c t e r i s t i c amplitude of each outburst i s measured as the peak flux density of the outburst. In cases where the peak flux density was not well defined due to a paucity of data (in a few instances only a single measurements in a 26.5 day cycle) only a lower l i m i t on the f l a r e maximum was a v a i l a b l e . Only those data in the binary phase 0.4-0.8 were selected a*s providing a lower l i m i t on the amplitude of the outburst. The c h a r a c t e r i s t i c amplitude of each outburst and date are l i s t e d in Table 4. An outburst with an amplitude of about 284 mJy occurred in 1977 August. After about 4 years, in 1981 August, another giant outburst at the l e v e l of about 300 mJy was observed, in addition the two lowest outbursts in 1980 August and 1984 August are also spaced by about 4 years. Coe et a l (1983) observed the source at 10.7 GHz from 1981 May to 1982 A p r i l . On A p r i l 24,1982 ( o r b i t a l phase about 0.56) the average emission l e v e l was about 220 mJy which was at the same l e v e l about 4 years p r i o r , on A p r i l 22,1978 at 10.5 GHz ( o r b i t a l phase 0.64). Again these re s u l t s suggested a possible periodic modulation (about 4 years ) of the amplitude of the binary outburst. For t h i s reason, the data in Table 4 are binned modulo the period of 1458 days using the phase 0.0 of J.D. 2,443,330.9. Figure 27 shows the binned data plotted in phase space. Since some of the observed l i g h t curves were not well defined ( i . e . , the data 47 were too s p a r s e ), o n l y the lower l i m i t of the f l a r e maxima c o u l d be e s t i m a t e d . T h i s i s i n d i c a t e d by arrows i n f i g u r e 27 and 28. The observed b i n a r y f l a r e maxima as w e l l as a model l i g h t c u r v e (dashed l i n e ) d i s c u s s e d i n c h a p t e r 4 a r e shown i n f i g u r e 28. Another o b s e r v a t i o n t h a t s u p p o r t s t h i s 4-year m o d u l a t i o n i s : the mean l i g h t c u r v e g i v e n i n f i g u r e 27, p r e d i c t s t h a t the r a d i o e m i s s i o n l e v e l i n 1986 September s h o u l d be about 172 mJy i n e x c e l l e n t agreement w i t h the l a t e r o bserved peak f l u x d e n s i t y of about 171 mJy. I t i s w o r t h w h i l e t o p o i n t out t h a t i f t h i s 4-year m o d u l a t i o n i s c o r r e c t , i t r e a d i l y e x p l a i n s the h i g h e r peak f l u x i n t he mean l i g h t c urve g i v e n by Coe e t a l . ( 1 9 8 3 ) . T h e i r o b s e r v a t i o n a l windows happens t o be around the phase of the peak of t h i s 4-year m o d u l a t i o n . However, we would l i k e t o p o i n t out t h a t due t o the l i m i t e d d a t a i n the l a t t e r p o r t i o n of our time base and s p a r s e o b s e r v a t i o n a l windows, any c o n c l u s i o n s drawn are v e r y t e n t a t i v e . A l t h o u g h t h i s l o n g term v a r i a t i o n i s an i n t e r e s t i n g c a n d i d a t e f o r a s u p e r o r b i t a l c y c l e , i t has been observed f o r t o o few c y c l e s t o be c o n s i d e r e d c o n f i r m e d . High q u a l i t y o b s e r v a t i o n s need t o be c o n t i n u e d on t h i s unique s o u r c e t o c o n f i r m t h i s p o s s i b l e l o n g term p e r i o d . 48 TABLE 4 APPROXIMATE BINARY RADIO FLARE MAXIMA Ut date Ju l i a n date Frequency Peak flux density (2,440,000+) (Ghz) (mJy) 1977 Aug 27 3383 5.0 284 1978 Mar 1 3569 10.5 138 1978 Mar 28 3596 5.0 > 160 1978 Apr 22 3622 10.5 220 1978 Aug 9 3723 5.0 176 1979 Mar 31 3964 10.5 149 1979 Jul 23 4078 10.5 > 84 1979 Aug 15 4101 5.0 100 1979 Nov 30 4208 10.5 > 58 1980 Jun 25 4417 10.5 38 1980 Aug 28 4480 5.0 66 1980 Sep 11 4497 10.5 112 1980 Nov 3 4547 10.5 94 1980 Dec 5 4610 10.5 131 1981 Jan 18 4623 10.5 146 1981 Aug 24 4841 5.0 309 1981 Aug 24 4841 10.5 250 1981 Dec 10 4947 10.7 239 1982 Apr 18 5078 10.7 220 1984 Ju l 26 5177 5.0 84 1986 Sep 20 6694 5.0 171 49 350.0 Figure 27. Binary radio f l a r e maxima plotted i n phase space for the period of 1458 days. J u l i a n date of phase zero = 2,443,330.9. Arrow indicates lower l i m i t of the binary peak. 50 3 5 0 . 0 2 8 0 . 0 £ 2 1 0 . 0 E ••H X ro E 1 4 0 . 0 0) M ro 7 0 . 0 0 . 0 1-I 5GHZ 1 0 . 5 G H Z A u g . , 2 0 . 1 9 8 9 i i _ 3 3 3 0 . 9 _ J 1 4 5 0 7 . 4 _ J 1-5 6 8 3 . 9 _L 6 8 6 0 . 4 J u l i a n date (2,440,000 + ) _ J u 8 0 3 6 . 8 Figure 28. Binary radio f l a r e maxima from 1977 August to 1986 September. Dashed l i n e is a model l i g h t curve discussed in chapter 4. 51 Chapter 4 A precessing jet model for the long term modulation Two binary models have been proposed to account for the radio, x-ray and possible Tf-ray emission associated with GT0236+610. Taylor and Gregory (1982) discussed a model in which the radio flux modulation is due to variable accretion onto a compact companion in an eccentric o r b i t . Alternately, Maraschi and Treves (1981) have proposed a model in which the companion is a moderately young pulsar losing energy through a r e l a t i v i s t i c wind. However, both models give no consideration of the or i g i n of the f l a r e maxima v a r i a t i o n . Although the detection of the periodic long term modulation has low si g n i f i c a n c e , the source c e r t a i n l y is an interesting candidate for a superorbital cycle. Only a few binary sources have long cycles. Longer-term v a r i a t i o n are both harder to observe and poorly understood. Ear l y attempts to explain the long period X-ray cycles in binary systems (for example,Her X-l) have involved precession (what i s precessing-and why-are s t i l l uncertain). Here we examine a precessing j e t model as a possible explanation of the 4-year modulation of GT0236+610. For the purpose of th i s analysis, we treat a jet as stream of i d e n t i c a l packets of radiating matter (plasmons). Following the analysis of Gower et a l . (1982 ), the plasmons are ejected at a fixed speed 0 = v/c with respect to the source. The source i s at rest at the or i g i n of the right-handed 52 coordinated system x,y,z as shown in figure 29. z' i s the axis about which the plasmon ejection v e l o c i t y precesses with an angular v e l o c i t y H and at an angle <f. With the geometry shown ln figure 29, we can write for the v e l o c i t y components of plasmon along the l i n e of sight where I i s the angle between the axis z 1 and l i n e of sig h t . We assume that the emission from each plasmon i s o p t i c a l l y t h i n with a spectrum in the rest frame of the plasmon of the form: sp e c t r a l power emitted, PO')oC v _ t*. Following Ryle and Longair (1967) the flux density, S{\>) (W _ 1m" 2Hz - 1) of a moving plasmon is given by where D = Doppler s h i f t factor [ t(1-0 X)] , S r ( v ) = flux density of an i d e n t i c a l plasmon at rest and instantaneously at the same distance From r e l a t i o n (IV.1) and (IV.2), we note that the periodic modulation i s assumed to be due to the Doppler s h i f t factor D. The maximum and minimum flux should be observed when the je t i s clo s e s t to the l i n e of sight and farthest from the l i n e of sig h t . Combining (IV.1) and (IV.2) we have $x = 6 ( s i n l sinvcos (S?t+eQ )+cosI cosv) (IV.1) SO') = S r ( V ) D 3+fX (IV.2) { ( l - 0 c o s ( f + < P ) )/(l-0cos(I-<e) } 3+oc (IV.3) we have B = ( x - l ) / ( xcos(l-v) -cos(5+<P) ) (IV.4) 53 Then the shape of the l i g h t curve can be expressed as S ( e ) / S m i n = { (l-0cos (I+<f) )/(l-0 (sinlsinvcose+coslcosf) } 3 + c C (IV.5) where 6 = nt+e D (IV.6) substitute (IV.4) into (IV.5) and after some manipulation we have S ( 6 ) / S m i n = { 2x/[l+cos9+ X(l-cos9) ] } 3 + o C (IV.7) Note that the shape of the l i g h t curve i s independent of and I and determined by the r a t i o S m a x / S m i n > Taking a: = 0.0, the model is f i t t e d to the binned l i g h t curve (see F i g . 30). The jet processing model (IV.7) predicts a symmetrical l i g h t curve which is in disagreement with observed data. The binned l i g h t curve shows a more rapid r a i s e . However, as has been pointed out before, the measure of the l i g h t curve can only be considered tentative. We do not yet have confidence to rule out the jet model. High q u a l i t y observations need to be continued on the source. 54 Y Figure 29. The coordinate system i n deriving the j e t model. Z' i s j e t precessing axis and v cone angle. X i s the l i n e of sight, and YZ the plane of the sky. 55 Figure 30. The f l a r e maxima and the j e t model f i t . 56 Chapter 5 Summary and conclusions New 6 cm observations of GT0236+610 in August 1984 and September 1986 using the 91 meter t r a n s i t telescope of National Radio Astronomy Observatory at Green Bank were presented. We analysed 201 flux density measurements over the period from August 1977 to September 1986. We repeated the cross c o r r e l a t i o n analysis discussed by Taylor and Gregory (1982) and obtained an improved period of 26.50 ± 0.03 days. A method of searching for both period and period derivative simultaneously was developed. A phase s h i f t of about 0.15 in both d i r e c t i o n has been seen for the best f i t t e d period and period derivative. This suggests that the phase scatter i s u n l i k e l y due to the period d e r i v a t i v e . The scatter may be due to observational errors or the fact that the underlying clock is not t i g h t l y coupled to the radio flux density v a r i a t i o n . We found evidence that GT0236+610 has a second period of about 4 years which is superimposed on the 26.50 days binary motion. A precessing j e t model was proposed to account for the long period modulation. The model predicts a symmetrical l i g h t curve which i s in disagreement with observed data. However, we do not yet have confidence to rule out the j e t model due to the limited data. High q u a l i t y observations are needed to confirm the long period and test the model. P a r t i c u l a r l y we suggest radio observations in August 1989 (predicted peak of the outburst is about 300 mJy around August 20, 1989). 57 References Backhouse, C , (1987). M.S. thesis, University of B r i t i s h Columbia. B a r t o l i n l , C , et a l . 1983, Astr. Ap., 118P 365. Bignami, G.F., et a l . 1980, IAU C i r c , No. 3518. Bignami, G.F., Carveo, P.A., Lamb, R.C, Markert, T.H., and Paul, J.A., 1981, Ap.J. (Letters), 247. L85. Bignami, G.F., et a l . 1983, M.N.R.A.S., 203r 791. Bondi, H., and Hoyle, F., 1944, M.N.R.A.S., 104. 273. Coe,M.J., et a l . 1978, Nature, 274. 343. Coe, M.J., Bowring, S.R., Court, A.J., H a l l , C.J., and Stephen, J.B., 1983, M.N.R.A.S., 202.791. Davidson, K., and Ostrlker, J.P., 1973, Ap. J., 179_,585. Gregory, P.C., and Taylor, A.R., 1978, Nature, 272. 704. Gregory, P.C., et a l . 1979, A. J., 8_i, 1030. Gower, A.C, Gregory, P.C, Hutchings, J.B. and Unruh, W.G., 1982, Ap. J . , 262. 478. Haynes, R.F., Lerche, I., and Murdin, P., 1980, Astr. Ap., 87., 299. Howarth, I.D., 1983, M.N.R.A.S., 2111/ 801. Hutchings, J.B., 1980, Pubis a s t r . Soc. Pacif., 9JL, 657. Hutchings, J.B., and Crampton, D., 1981, Pub.A.S.P., 9_3_, 486. Maraschl, L., Tanzi, E.G., and Treves, A., 1981, Ap. J., 248, 1010. 58 Maraschi, L., and Treves, A., 1981, M.N.R.A.S., 194, IP. Perotti,F., et a l . 1980, Ap... J . ( L e t t e r s ) , 239. L49. Pollock, A.M.T., et a l . 1981, as t r . Ap., 9_i, 116. Prledhorsky, W.C., and Holt,S.S., 1986, preprint. Ryle, M., and Longair, M.S., 1967, M.N.R.A.S., 136. 123. Seaton, M.J., 1979, M.N.R.A.S., 187. 73P. Share, G.H., et a l . 1979, ln X-ray Astronomy, Proc. of the 21st plenary Meeting of the Committee on Space Research, ed. W.A. Baity and L.E. Peterson (New York: Pergamon), p.535. Tanzi, E.G., et a l . 1982, NASA Conference Proc. 2338, p.615. Taylor, A.R.,(1982). Ph.D thesis, University'of B r i t i s h Columbia. Taylor, A.R., and Gregory, P.C, 1982, Ap. J., 255. 210. Taylor, A.R., and Gregory, P.C., 1984. Ap. J., 283f 273. Wil l s , R.D., et a l . 1980, Advances in Space Exploration,Vol.7. 59 Appendix A Reduction of ( I I I . 3 ) Assuming a constant period derivative T, we have dT/dt = T (1) or T(t) = T Q + T * ( t - t 0 ) (2) where T 0 i s the period at J u l i a n date t Q . Regarding the Julian date t as a function of cycle. N that goes through from t Q to t, we have t(N+AN) = t(N) +ANxT(t) ( 3 ) On the other hand t(N+AN) = t(N) + ANxdt/dN ( 4 ) comparing ( 3 ) and ( 4 ) , one has dt/dN = T(t) (5) which yie l d s N = X f c —1— dt t 0 T(t) °Z (6) Insert in T(t) in ( 6 ) , one has N = ln( l + T x ( t - t Q ) / T 0 )/T (7) The phase of the measurement at J u l i a n date t is phs = N - i n t (N) ( 8 ) This is the r e l a t i o n ( I I I . 3 ) 60 Appendix B Telescope tracking s t a b i l i t y To measure varible radio emission, i t i s important to keep the telescope pointing and beam p r o f i l e stable. As has been pointed out by J.R. Picha (1966) that beam p r o f i l e s change with telescope drive rates. Tests were carried for night d r i v i n g scans to check the drive rate of the telescope. The designed drive rate for night survey scan is 120 f/min. The telescope pointing position R a t i ] , DECtil (data set for ri g h t ascension and declination) was f i t t e d by a linear function: dec = v * ra + dec 0 where v i s the drive rate and dec Q i s the s t a r t i n g declination. Tests for 8 night scans track through GT0236+610 showing the actu r a l drive rate i s about 123'/min which is good agreement with the designed value of 120*/min. However, the residual of the actural telescope pointing and linear model showing o s c i l l a t i o n s (except for scan 4322, which shows no clear o s c i l l a t i o n ) . As shown in figure 31, telescope o s c i l l a t e s around mean track with amplitude of about 0.7 arcmin and period of about 5 seconds. The u n s t a b i l i t y of the pointing may be contribute to the beam broading ( or narrowing). The cause of t h i s i n s t a b i l i t y Is not yet known, i t might due to the declination drive mechanism of the telescope. 61 0.9 -0.5 -0.2 -0.2 --0.5 --0.9 V. n A A n n SCAN 1251 J 0.00 0.19 0.39 0.5B 0.77 0.97 SCAN 3247 0.00 0.20 0.39 Time (minute) 0.59 0.78 0.9B Figure 31. The r e s i d u a l of telescope p o i n t i n g and l i n e a r f i t ( D E C o b s e r v e d - D E C l l n e a r £ i t ) 

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