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

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A STUDY  OF T H E B I N A R Y  RADIO  STAR  LSI  +61°303  by  B.Sc,  University  A THESIS  HUANGJIAN  XU  of  and  Science  SUBMITTED  THE REQUIREMENTS MASTER  Technology  FOR T H E D E G R E E OF  OF S C I E N C E  OF GRADUATE  DEPARTMENT OF  We a c c e p t to  this  the  thesis  required  THE UNIVERSITY  "©  STUDIES  PHYSICS  as  conforming  standard  OF B R I T I S H Dec.  China,1985  IN P A R T I A L F U L F I L M E N T OF  in THE FACULTY  of  COLUMBIA  1987  Huangjian Xu,  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.  Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  11 Abstract We present new 6 cm observations of the binary r a d i o , X-ray and 1-ray s t a r GT0236+610 (LSI+61°303) obtained i n August 1984 and September 1986.  Ve c a l c u l a t e an improved period f o r  the source's p e r i o d i c r a d i o outbursts of 26.50 ± 0.03 days. No s i g n i f i c a n t period d e r i v a t i v e was found. Based on an a n a l y s i s of 201 f l u x d e n s i t y measurements from 1977 August to 1986 September, we f i n d evidence f o r a p o s s i b l e 4 year modulation of the amplitude of the 26.50 day p e r i o d i c r a d i o outbursts. A precessing j e t model f o r 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  iv  L i s t of Figures Acknowledgements  v 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 r e d u c t i o n f o r the f l u x d e n s i t y of GT0236+610  Chapter 3  Search f o r p e r i o d i c i t i e s  16 23  3.1  Simple period f o l d i n g a n a l y s i s  25  3.2  Cross c o r r e l a t i o n a n a l y s i s  27  3.3  Two parameters searching f o r period and period derivative  32  3.4  Monte c a r l o s i m u l a t i o n s  40  3.5  A p o s s i b l e 4-year period of long term modulation .  45  Chapter 4  A processing j e t model f o r the long term modulation  Chapter 5  Summary and conclusions  References  51 56 57  Appendix A  Reduction f o r the phase value  59  Appendix B  Telescope track s t a b i l i t y  60  Iv  List  of Tables  Table  page  1.  Summary of the observations  2.  GT0236+610 r a d i o f l u x d e n s i t i e s i n September 1986  3.  GT0236+610 r a d i o f l u x d e n s i t i e s i n July-August 1984  4.  Approximate b i n a r y r a d i o f l a r e maxima  7 22  24 48  V  List  of  Figures  Figure  page  1.  The  orientation  2.  Right  ascension  pointing  error  for  south  bound  scans  ..  11  3.  Right  ascension  pointing  error  for  north  bound  scans  ..  11  4.  Declination  pointing  error  for  south  bound s c a n s  12  5.  Declination  pointing  error  for  north  bound  12  6.  Dish  7.  gain  for  of  the  assembly  5  scans  7  13  East-west  beam m o d e l  14  8.  Reduction  of  9.  Sequence Sequence  11.  The s c a t t e r (10.5  peak  0's  10.  feed  feed  due  to  smoothing  15  raw d a t a  4 and of  17  sequence  l's  the  about  data  raw d a t a mean  18  light  GHz)  12.  The s c a t t e r  13.  T h e rms  26 of  phase  data  scatter  correlation individual  the  of  the  about  in  the  mean  mean peak  light  light of  curve  the  curve  (5  GHz)  26  cross  with  outbursts  29  14.  Mean  light  curve  at  5 GHz  30  15.  Mean  light  curve  at  10.5  30  16.  Ten o u t b u r s t s ' period  17.  of  26.50  Two d i m e n s i o n a l derivative  data  GHz  plotted  in  phase  space  for  days  search  31 for  period  and  period 34  vl  18. Window e f f e c t s t e s t  .  19. Window e f f e c t s t e s t  35 36  20. A f i n e r two dimensional search f o r period and period d e r i v a t i v e 21. Cross-section  37  of two dimensional contours a t  dT/dt = 4 x l 0 ~ 22. Cross-section  ....  5  days/day  38  of two dimensional contours a t  T = 26.49 days  39  23. Monte c a r l o simulation  42  24. Contour p l o t f o r p e r f e c t l y sampled data "  43  25. Another contour p l o t f o r p e r f e c t l y sampled data  43  26. Ten outbursts'  data p l o t t e d l n phase space f o r  best f i t t e d period an period d e r i v a t i v e  44  27. Binary r a d i o f l a r e maxima p l o t t e d i n phase space for period of 1458 days  49  28. Binary r a d i o f l a r e maxima p l o t t e d vs J u l i a n date ....  50  29. The coordinate system i n d e r i v i n g the j e t model  54  30. The j e t model f i t  55  31  60  Telescope D e c l i n a t i o n t r a c k i n g errors  vii  Acknowledgements  First,  I would l i k e t o thank my s u p e r v i s o r Dr. P.  c.  Gregory f o r p r o v i d i n g the 1984 d a t a . His a s s i s t a n c e and guidance throughout t h i s work are g r e a t l y a p p r e c i a t e d . I wish to thank my c o l l e a g u e C h r i s Backhouse f o r h i s great help and advice on computing. He was r e s p o n s i b l e f o r c r e a t i n g the 1986 Radio P a t r o l data base from the raw t e l e s c o p e tapes,  without  which, t h i s t h e s i s would not be p o s s i b l e . A l s o I would l i k e t o thank him f o r p r o v i d i n g some r e s u l t s of c a l i b r a t i o n data and f o r r e a d i n g of t h i s Finally,  manuscript.  I would l i k e t o thank the s t a f f a t Green Bank  f o r t h e i r help and h o s p i t a l i t y . Thanks a l s o t o Dr. M. J . Coe f o r p r o v i d i n g 10.7 GHz d a t a .  1  Chapter 1  Introduction  The  b i n a r y s t a r GT0236 +610  most unusual o b j e c t s has  i n our Galaxy. Over the  been the o b j e c t of c o n s i d e r a b l e  because of i t s very e x c e p t i o n a l and  (LSI +61°303 ) i s one  Taylor  (Gregory and  the  l a s t decade, i t  observational  effort  p r o p e r t i e s . During the  T a y l o r 1978)  of  Gregory  survey of the g a l a c t i c  plane f o r v a r i a b l e r a d i o emission GT0236+610 was /  discovered  as  a h i g h l y v a r i a b l e r a d i o source. Based on an a c c u r a t e  radio  p o s i t i o n , GT0236+610 was  (Gregory  et a l . 1979). I t has (Share et a l . 1979; source al.  i d e n t i f i e d with LS  a l s o been found to be both an X-ray source Bignami et a l . 1981)  (Gregory e t a l . 1979;  1981  ).  The  l u m i n o s i t y place  and  1979), the s t a r has erg s e c  - 1  high  Pollock  ,  et  X-ray  t h i s source i n the c l a s s of such  exotic  Circinus X - l .  O r i g n i a l l y thought to be a supergiant  38  a probable Tf-ray  P e r o t t i e t a l . 1980;  high r a d i o v a r i a b i l i t y and  o b j e c t s as SS433 and  (L=10  I+61°303  (Gregory et a l .  been c l a s s i f i e d as a main sequence BO-BO.5 T  e £  £ = 2.6*10  4  K) e m i s s i o n - l i n e s t a r with  high r o t a t i o n a l v e l o c i t y , undergoing mass l o s s through an e q u a t o r i a l d i s k ( Hutchings and Crampton (1981 26.4  ± 0.1  velocity  Crampton,1981 ). Hutchings  ) a l s o found evidence f o r a b i n a r y p e r i o d  days from an a n a l y s i s of three years of  and of  radial  data.  The  r a d i o emission  from GT0236+610 i s c h a r a c t e r i z e d  by  2  nonthermal outbursts  with r i s e times of a few days and t y p i c a l  d u r a t i o n of about 10 days. Based on an a n a l y s i s of d e n s i t y measurements a t 5 GHz and 10.5 GHz  144 f l u x  from 1977 August t o  1981 March, T a y l o r and Gregory ( 1982 ) d e r i v e d a p e r i o d of 26.52 ± 0.04 days. T h i s p e r i o d of r a d i o outburst  has been  confirmed by Coe e t a l . (1983). Except f o r the p u l s a r s , GT0236 +610 i s one of the o n l y two known p e r i o d i c r a d i o sources ( C i r c i n u s X-1,P = 16.59 days), and the f i r s t t o be d i s c o v e r e d s o l e y through r a d i o measurements. I t i s worthwhile t o p o i n t out t h a t so f a r no v a r i a b i l i t y i s seen i n the X-ray data, the r e s u l t i s not c o n c l u s i v e . A review of  the b a s i c  although features  of GT0236 + 610 i s given by T a y l o r and Gregory (1982). As a p a r t of 1986 G a l a c t i c survey p r o j e c t ,  observations  of GT0236 + 610 were c a r r i e d out i n September u s i n g the 91 m t r a n s i t t e l s c o p e of N a t i o n a l Radio Astronomy Observatory a t Green Bank. A t o t a l of 8 f l u x measurements from September 11 to 29 were obtained.  The observations  r e d u c t i o n are d i s c u s s e d  i n chapter  and f l u x d e n s i t y  data  2.  Together with the 170 f l u x d e n s i t y measurements made by T a y l o r and Gregory (1981,1982) 1981 and 21 unpublished  from  August 1977 to September  f l u x d e n s i t y measurements i n J u l y and  August 1984 made by Gregory, we were able t o analyse 201 f l u x d e n s i t e over about 9 y e a r s . We repeated  a t o t a l of  the simple  p e r i o d f o l d i n g a n a l y s i s and c r o s s c o r r e l a t i o n a n a l y s i s discussed  by T a y l o r and Gregory (1981) c o n f i r m i n g  about 26.50 days. A l s o a new method of s e a r c h i n g  the p e r i o d of f o r both the  3  p e r i o d and p e r i o d d e r i v a t i v e s i m u l t a n e o u s l y was developed. The a n a l y s i s of s e a r c h i n g f o r the p e r i o d i c i t i e s i s d i s c u s s e d i n chapter  3. With the 9 years of  o b s e r v a t i o n s , we  f i n d an  indication  t h a t GT0236 + 610 has a long term modulation t h a t i s superimposed on i t s b i n a r y motion with a p e r i o d of about 4 y e a r s . A p r o c e s s i n g j e t model f o r t h i s long term modulation i s d i s c u s s e d i n chapter  4.  4  Chapter  2.1  2  Observations  Instrumentation O b s e r v a t i o n s were c a r r i e d o u t i n S e p t e m b e r o f 1986  the  91 m e t e r t r a n s i t t e l e s c o p e o f N a t i o n a l  O b s e r v a t o r y a t Green used  t h e new  Bank, West V i r g i n i a .  7-feed r e c e i v e r  system  s y s t e m c o n s i s t s o f 7 f e e d s , one h e x a g o n and  r i g h t and of  6 cm,  left  time  ( s e e F i g . 2 . 1 ) . The  feed  located  was  a t each c o r n e r of the  c o n n e c t e d t o two r e c e i v e r s  sensitive to  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 . A t a  2.8  we  a t the c e n t e r of  wavelength  t h e h a l f power beam w i d t h (HPBW) o f t h e beams  approxmately 19.1°  feed  Astronomy  For the f i r s t  the other 6 feeds located  hexagon. Each  Radio  using  a r c m i n u t e s . W i t h t h e f e e d s box  was  rotated  at  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  b e t w e e n t h e a d j a c e n t beams was r e c e i v e r was  about  2.7  arc minutes.  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  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  1 2 0 ' / m i n and  of the s u r v e y p r o j e c t , a scan r a t e  s a m p l e t i m e o f 0.2  seconds  receiver  had a 3db b a n d w i d t h  receiver  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  rms = s K  x  given the constant K gives  T  r m s  = 7 mk  s  T  of  were c h o s e n .  sys ' < ' Av  600 MHz.  x  The  ^  of  Each  t h e o r e t i c a l rms  <  2.1)  = 1 f o r a t o t a l power r e c e i v e r . T h i s  f o r a system temperature  o f 70 K. T h i s n o i s e  c a n be r e d u c e d by f a c t o r o f 2^ by c o m b i n i n g t h e two  receiver  5  6  outputs  from the  unpolarized. pointing  Columbia  site for  developed  and  were  the  14  written shipped  the  signals  receivers onto  to  are  together  magnetic  tape  The U n i v e r s i t y  with at  of  the  British  analysis.  by  sequences  Chris  ).  and  Backhouse.  procedure Here  we  is  calibration  A detailed  discussed  just  give  a  procedures  description  by  Backhouse  brief  were  of  the  ( M.Sc  discussion  of  the  method.  within  The  survey  the  operational  approximate -5°  plane,  < b  a  region  < 5°.  sequence (  pattern  scans  of  the  stable  SB  of  10  scans  was  tube  portion  the  to  survey this  was  held  the  a  galactic  plane  of  the  telscope.  region  are  25° < 1  of  the  northbound  (  galactic  NB )  plane.  for  temperature  12  The <220°  galactic  producing a  stationary  provide  the  coverage  executed,  on  of  range  alternating  centered  telescope noise  the  To o b t a i n of  )  is  declination  boundaries  southbound  a  assuming  of  later  final  observing  survey  scan,  outputs  survey  thesis,1987  and  feed  Method The  1986  The  information  telescope  2.2  same  and  zig-zag After  e a c h NB  seconds  calibration  firing of  data. The sequences seven  source (  times  GT0236+610  sequence to  Unfortunately,  0,  measure due  to  1, the  4,  was 5  covered ).  Sequence  v a r i a b l i t y of  telescope  by  control  its  four  of  0 was radio  system  the  scan  repeated emission.  failures  and  the  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 r e c o r d i n g e r r o r , 4 scans through GT0236+610 were l o s t . We have a t o t a l of 8 f l u x d e n s i t y measurements d u r i n g September 11 t o September observations  2.3  i s given  of the source  28. A summary of the  i n t a b l e 1.  Calibrations To get the f l u x d e n s i t y of the source  on the tapes,  two processes  were i n v o l v e d ; 1) measurements of  the s i g n a l s t r e n g t h i n K e l v i n , 2) conversion measurements  i n K. To c a r r y out  2) we have to know a number of t e l e s c o p e  The s i g n a t u r e of an unresolved  source  i n a scan  North-South c r o s s - s e c t i o n of the instrumental removing a b a s e l i n e , the source In g e n e r a l the source  strength  parameters. i s given by the  p r o f i l e . After  ( i n K) was measured.  d i d not pass through the center of the  t e l e s c o p e beam and thus i t was necessary after  of the  to f l u x d e n s i t y . A noise tube was f i r e d every 5  minutes t o c a l i b r a t e the r e c e i v e r output process  from the raw data  to correct f o r t h i s  f i r s t a p p l y i n g the t e l e s c o p e p o i n t i n g e r r o r . For t h i s  c a l c u l a t i o n the East-west c r o s s s e c t i o n of the beam p r o f i l e was measured. F i n a l l y , t o convert  the source  s t r e n g t h to a a b s o l u t e  f l u x d e n s i t y ( i n mJy), the t e l e s c o p e gain f o r the p a r t i c u l a r feed i n v o l v e d was r e q u i r e d . The f o l l o w i n g t e l e s c o p e c a l i b r a t i o n s were c a r r i e d out: a) s y s t e m a t i c peak beam g a i n  p o i n t i n g e r r o r s , b) East-West beam p r o f i l e , c) ( d i s h gain)  to f l u x d e n s i t y . Due to  t o convert  antenna temperature (K)  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  telescope  parameters  vary with  declination.  obtain  c a l i b r a t i o n measurements  covering  degree  declination  survey  used  the  7-feed  time  was  used  range  system,  to  beams  across  known  flux  scans  (type  scans  ( NB a n d  to  determine  dependence applied,  a  the  SB  Fig.  5)  and  from  Backhouse's for  corrections, central  typical  obtained  3).  were  beam.  set  of  measure well  as  gain,  Knowing  drift the the  we  see as  the  with  the  fit  survey  central  beam  declination error  feed  Fig.  box the  4 and  reproduced  North-South  beam  DEC p o i n t i n g executed  through  beam p r o f i l e are  shown  (two  in  figure  ) . To (tracking carried b e a m was  calibrate  the  an  beam a c r o s s  out  offset (type  obtained  3).  offset  The  beams, a  by c o m p a r i n g  the  NB a n d  calibration  DEC o f f s e t  of  a  of  Drift  through  6,  the  sources  70°.  the  (see  Fig.  were  East-West  of  RA p o i n t i n g  error  scans  model  the  executed  well  each  night  their  this 2),  DEC p o i n t i n g  ) as  for  and  With  scans,  (dish  - 1 0 ° and as  corrections  1987  70°  Since  unresolved  throqgh  survey  central  as  rotated  (type  thesis,  - 1 0 ° to  calibration  tracking  150  scans  beam g a i n  beam t o  by  between  box  Fig.  the  of  to  feed.  obtained  first  necessary  entire  amount  driven  obtain  another  results  feed  2 and  night  peak  the  were  RA p o i n t i n g  NB a n d  beam t o  each  the  was  observations.  considerable  declination  were  Fig.  central  the  approximately  the  (see  for  of  at  SB)  as  the  set  with  rotated  profile  scans  density 1)  a  calibrate  Calibration 7  of  It  SB d r i v e n source)  particular  declinations  of  the  scans were  offset same  7  10  calibration is  source  different  angles,and  for  it  DEC o f f s e t  out  to  through  North-South effects,  all  pointing  for  "POPS".  Final  at  was  the used  (Taylor,1982). p(x,c)  The of  the  the  scans and  parameters scans.  observed  a  gain  were  knowledge  as  to  well  as  the  scans  measure  the  directional  analysed  No s i g n i f i c a n t  except  of  carried  driven  executed any  rotation  4) w e r e  (type  for  DEC o f f s e t  different  RA o f f s e t ,  To a c c o u n t  SB  This  With  dish  to  model  for  the  differences  declination  of  the  calibrations  using  NRAO  purpose to  work of  data  approxmate  The m o d i f i e d {  the  x  is  the  gaussian,  completely the  angular  model  coefficient  software done  by  analysis  same by  "c".  beam  profile  used  was (  from the  The  HPBW, two  mathematical  }  2  offset  beam w i d t h s .  specified  a  East-West  gaussian  with  was  author.  reduction,  the  was  beam p r o f i l e  -2.7726[l+cx(x-0.5)]x  half-power  and  of  the  c a l i b r a t i o n data  the  in  profile  by m y s e l f  telescope  is  simple is  the  U B C . The E a s t - w e s t  variable  a  of  at  = exp  measured  the  to  beam were  reduction  reduction  below  For  equal  drift  offset  was  due  Knowing the  G r e e n Bank  Backhouse  discussed  peak  RA o f f s e t  NB a n d  3 scans.  errors.  out  where  its  values  carried  model  beam,  telescope  Preliminary  Chris  the  the  the  parameter  type  independently.  beam p r o f i l e .  independently in  of  beam p r o f i l e .  tracking  2 and  analysed  determine  East-West  type  SB a n d NB s c a n s  was  the  in  II.2)  profile  beam m o d e l at  x=0  parameters;  beam  and the  is x=l/2. HPBW  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  Figure  2.  Right ascension  40.0  60.0  BO.O  (arcmln)  pointing  position)  f o r south  0.0  20.0  error  bound  (measured-true  scans.  4.0  2.4  O.B  ™  M H  -O.B  -2.4  -4.0  -21.0  DEC  Figure  3.  40.0  60.0  (arcmin)  Right ascention pointing position)  60.0  f o r n o r t h bound  error  (measured-true  scans.  12 90.0  54.0  „  1B.0  u «. n u M  n  o  -18.0  -  -54.0  -  M W W  -90.0  -20.0  0.0  20.0 DEC  Figure  4.  Declination position)  40.0  60.0  (arcmln)  pointing error  for  60.0  s o u t h bound  (measured-true scans.  90.0  54.0  S8.0 u w n U  u n M O  -JB.0  -  -54.0  -  w H w  -90.0  -20.0  0.0  20.0 DEC  Figure  5.  40.0  (arcmin)  Declination pointing error position)  for  60.0  n o r t h bound  (measured-true scans.  80.0  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 D e c l i n a t i o n (degrees)  111111111111111111111111111111111  The n o r t h a o l l d lln#) and south I D . dashed bound antenna g a i n eurvaa f o r faad 7 .  Figure  llnvl  6. Dish gain f o r c e n t r a l beam (feed 7) (reproduced  from Backhouses's t h e s i s ) .  14  F i g u r e 7 . Comparison of the beam model to measured E a s t - V e s t beam p r o f i l e s .  15  .0 DEC  F i g u r e 8.  (arcmln)  Reduction of peak due  to smoothing. S o l i d  line is a  simple gaussian with HPBW of 3 arcmin. Dots are the sample p o i n t s of the smoothed curve of the  simple  gaussian beam model showing a r e d u c t i o n of 7 % peak v a l u e .  i n the  16  To profile  accommodate was  from  the  for  side  ) was  Knowing square those  the  Typical  2.4  model  Data  or  the  data  to  atmospheric  water  atmospheric  emission, is  with  a  model  10% o f  flux  subject  vapor. in  subtracted  to  same  from an  the scan,  decrease  the  by  of  2  This  be  the  two  signal  receivers' to  samples  about  receiver  using  smthli]  =  the  after  smoothing.  reduced the  the  is  peak  the  of  of  can  before  ratio,  only  figure  7.  wavelength degradation  offset  compensated  was  6  due  to  tracked  beam.  to  of  in  beam t h a t  signal  data  least  GT0236+610  subtraction.  the  by  using  in  a  the  (  The  noise by  To  ratio  combining  increase  smoothed  over  the 5  formula: !4x[i-l] + x[i]+  raw d a t a The  receiver  smoothing  signal  noise  2  x[i]  .  outputs  {/ x[i-2]+  where  Vi  profile  temperature.  of  at  adjacent  will  linear  gaussian.  fluctuations  operation  factor  peak shown  made  a  the  (II.2)  the are  beam  determined  in  subtraction a  the  simple  considerable  To c a n c e l the  a  density  measurements  of  removing  " c " was  beam p r o f i l e  the  side  T h e HPBW o f  fitting  the  than  for  intensity be  by  coefficient  reduction  can  scans.  measured  greater  fits  shorter  GT0236+610  After  the  values  Total cm  independently.  calibration  HPBW,  fitting data  each  modelled  baseline each  beam a s y m m e t r y  the  about  set  and  ^ix[i + l ] +  smthti]  is  Hx[i+2]}/3 the  equivalent  intergration  noise  factor  of  about  results  in  an  data  by a also  7% ( s e e  Fig.  8).  This  time  data  set  of  second  2.3.  1  However,  attenuation  factor  is  of  later  the  17  66.9  r-  33.4  75.4  37.7  5 x  3  B8  -  3  34.2  fc. 93.4  46.7  72.2  r-  36. 1  30.00  o.oo-  -30.00  DEC  Figure  9.  Five  sequence  baselines  1).  O's  raw d a t a  (dashed l i n e s ) .  a r e s c a n 1251, table  (arcmln)  3247,  4322,  (solid  lines)  and  From b o t t o m t o  top  4751,  4957  (see  18  .00 DEC  Figure  10.  One  sequence  (solid  4 and  (arcmln)  two sequence  l i n e s ) and b a s e l i n e s  bottom t o t o p a r e s c a n 2118, table 1).  l ' s raw  data  (dashed l i n e s ) . 4112,  4S34 (see  From  19  corrected. Before  any meaningful data r e d u c t i o n , a l o c a l  baseline  was removed. The b a s e l i n e can be due to h i g h l y s t r u c t u r e d extended emission, pickup  or  as a r e s u l t of the v a r i a t i o n i n the  of ground s p i l l - o v e r r a d i a t i o n with d e c l i n a t i o n , or, as  pointed  out by Backhouse, due to the gain v a r i a t i o n .  through the c a l i b r a t i o n sources g e n e r a l l y have very extended s t r u c t u r e t o complicate  Scans little  the choice of s u i t a b l e regions  f o r b a s e l i n e d e f i n i t i o n . However, GT0236+610 happens to be i n a h i g h l y confused r e g i o n , the choice of the r e g i o n f o r the b a s e l i n e posed a problem. Due to the h i g h l y s t r u c t u r e d extended emission regions  and s h o r t time s c a l e gain v a r i a t i o n , the b a s e l i n e should  reduction  f o r the f l u x of GT0236+610, the slope and l e v e l of  the b a s e l i n e data  be chosen as l o c a l l y as p o s s i b l e . In t h i s  i s determined by a l i n e a r l e a s t square f i t to the  i n two 4' segments separated  instrumental source.  p r o f i l e and centered  by the width of an on the p o s i t i o n of the  The smoothed raw data and l i n e a r b a s e l i n e s are shown i n  f i g u r e 9 and f i g u r e 10. A f t e r s u b t r a c t i n g the b a s e l i n e , the s t r e n g t h calculated  from a simple  gaussian  p o r t i o n of the data. Taking noise and c o n f u s i o n estimate  ( S ) was  l e a s t square f i t to the peak  i n t o c o n s i d e r a t i o n both r e c e i v e r  s i g n a l i n the r e g i o n of the d e t e c t i o n , an  of the c o n f u s i o n  signal c  s  i s given by the r e s i d u a l s  of the l i n e a r f i t t o the l o c a l b a s e l i n e o ^ . The  f l u x d e n s i t y of the source can be expressed by the  20  relation J where  S is  source  = S /  source  in  by  of  widths. x=  dependant  the  The s o u r c e  cos~^[  cosE  ( °c ^S  where  n  ( <*, S  )  X C O S S Q  to  source.  the  According on  source  profile sigma  and s o u r c e  error  o-j = where  is  (K xc 1  dish  beam p r o f i l e ,  K K  mentioned  baseline  fit  gain,  K  scatter  of  the  c  density K/mJy)  in  of  track  the  ( I I I . 4 )  closest  flux the  in  1986  approach  density  depends  East-West  x.  Therefore,  an e s t i m a t e  +  K xo-  K xo-  power  formula  G T 0 2 3 6 + 610  the  is  closest  3/HPBW  at  the  profile  half-beam  from  the  of  which  offset,  measured  G , HPBW o f  the  2  /  distance  K  and K  3  G  was is  measured  4  H  to were  values  H  of  error  )^ on  a n d HPBW o f  beam  the  one  (II.4) source the  East-West  are  4  = OJ/3G  )  =  (3J/3H  )  from  the  estimated  due  and c  2  2  4  sigma  K s  x  one  2  c  +  2  3  K  which  Similarly,  source  I I . 3 ),  2  before,  signal.  (in  + sinSxsinSfj  gain  offset  and  o^,  2 G  are  OJ/3X )  =  3  the  the  (  gain  calculated  )  on  flux  .3)  by 2  )  is  the  E a s t - W e s t beam  coordinates  offset  = (aj/9S  x  (O>:-(XQ  dish  G  strength,  As  S,  dish  track  relation  c r , c/ , and s  x  the  is  the  x was  cos  K xtf  +  2  the is  position  given s  x  the  to  strength  to  offset  ) are  n  epoch, the  i n mK, J  P(x,c)  source  ( I I  }  The v a r i a b l e  ( I I . 2 ) .  approach  strength  m i l l i - J a n s k y , G is  declination given  { P(x,c)XG  receiver  the  (I I . 5 )  2  residuals  noise  estimated  about  2  from  smooth  and  of  the  confusion  the curve  rms fit  to  21  t h e i r d e c l i n a t i o n dependence. Because of the high d r i v e r a t e of 120'/min, o  j x  i s mainly due t o the e r r o r s  From the same c o n s i d e r a t i o n ,  c  x  i n the RA  pointing.  was estimated from the rms  s c a t t e r of measured RA p o i n t i n g c o r r e c t i o n about the smooth curve f i t to t h e i r d e c l i n a t i o n dependence. Table 2 shows the measured f l u x d e n s i t y and t h e i r one sigma e r r o r s .  22  TABLE 2 GT0236 + 610 RADIO FLUX DENSITIES IN SEPTEMBER 1986 UT Date  J u l i a n Date (2,440,000+)  Frequency (Ghz)  Flux density (mJy) 52 ± 20  1986 Sep 11  6684.9  5.0  1986 Sep 15  6689.9  5.0  < 33  1986 Sep 20  6693.9  5.0  171 ± 20  1986 Sep 24  6696.9  5.0  92 ±  8  1986 Sep 25  6697.9  5.0  43 ±  8  1986 Sep 26  6698.9  5.0  41 + 10  1986 Sep 27  6699.9  5.0  88 ± 15  1986 Sep 29  6701.9  5.0  38 ± 17  23  Chapter  3  Search  Taylor periodic  analysis  to  1981  (1983) this  chapter,  our  (1982)  emission  at  144  density  flux  Later  their  available in  of  March. by  periodicities  and G r e g o r y  radio  an  for  66  this  galactic  observations  flux  patrol  data  made  10.5  observations  (Taylor August at  (  201  are  flux  able  to  check  Also  modulation  in  from  1984). 1984  we  3  to  have  1981  lists  July-August (  was  are  both 21  in  enough radio  the  out  at  8  1977  flux  1982  (1982)  at  radio  1981  listed flux  about  term data  by T a y l o r density  unpublished).  to  The  In  the  1 0 . 5 GHz  August 1984  measurements  p e r i o d and  maxima.  all  5 GHz i n  density  spanning  al.  5 GHz a n d  u n d e r t a k i n g . With  long  August  144  in  at  on  April.  using  include  the  based  5 GHz a n d  frequencies  flare  radio  Gregory  May t o  carried  These  this  reported  were  1981  measurements and  from  of  c o n f i r m e d b y Coe e t  from  measurements,  the  variable  1977  Table  1986  density  stability.  data  at  discovery  GT0236+610,  measurements  p r o v i d e d by G r e g o r y ) September  days  and G r e g o r y  1984),  the  measurements  base.  by T a y l o r  Gregory,  5 GHz i n  total we  and  tests  density  measurements G H z , 28  T = 26.5  result  statistical  radio  reported  these 3334 its  search  flux  days,  for  density  and Gregory measurements  (1982, in  24  TABLE 3 GT0236 + 610 RADIO FLUX DENSITIES IN JULY-AUGUST 1984 UT Date  J u l i a n Date (2,440,000+)  Frequency (Ghz)  Flux  Density  (mJy)  1984 J u l 19  5900.96  5.0  46 + 7  1984 J u l 20  5901.96  5.0  55+7  1984 J u l 21  5902.96  5.0  54 ± 7  1984 J u l 22  5903.96  5.0  63 + 8  1984 J u l 23  5904.96  5.0  71 + 8  1984 J u l 24  5905.96  5.0  74 + 8  1984 J u l 25  5906.96  5.0  84 ± 9  1984 J u l 26  5907.96  5.0  69 ± 8  1984 J u l 27  5908.96  5.0  54 ± 7  1984 J u l 28  5909.96  5.0  63+8  1984 J u l  29  5910.96  5.0  49 + 7  1984 J u 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 p e r i o d The  search  folding analysis  was  c a r r i e d out using a simple  time a n a l y s i s d i s c u s s e d an adoped t r i a l phs  by T a y l o r and  f o l d i n g type  Gregory (1982). Based  p e r i o d T, each f l u x d e n s i t y  i s assigned  = (t-t )/T -int[(t-t )/T] Q  on  a phase  (III.l)  0  where t i s the J u l i a n Date of the o b s e r v a t i o n ,  t  i s the phase  Q  zero s e t at J u l i a n Date of 2,4443,366.775 as used by Taylor Gregory (1982) and  phs  d e n s i t y . According  to the value  binned i n t o one sum  i s the assigned  phase f o r the  of the phase, the  of ten phase b i n s . At each t r i a l  of v a r i a n c e s  i n ten b i n s , V,  and  flux  flux is p e r i o d T,  the  i s c a l c u l a t e d . This quantity  V  i s a measure of the s c a t t e r 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 as the t r i a l c a r r i e d out  p e r i o d approaches the true p e r i o d . The for t r i a l  accommodate any at  5 GHz  the two  and  r e s u l t i n a minimum of the s c a t t e r  p e r i o d of 25.0  systematic  10.5  GHz,  frequencies.  most s e n s i t i v e when  days to 28.0  T h i s simple p e r i o d outbursts  as f i g u r e 22 shows t h i s was  not the case. The  amplitude,  11 and  f i g u r e 12  .  but  i m p l i c a t i o n of  i n s e c t i o n 3.5. (i.e.,  For  the  the  to the e m p i r i c a l modulation of  f l a r e maxima) f o r each outburst f o l d i n g a n a l y s i s i s employed.  curves  independently f o r  purposes of t h i s a n a l y s i s , t h e data i s normalized according  light  folding analysis is  have a constant  the v a r i a b l e f l a r e maxima are d i s c u s s e d  f l u x e s were s c a l e d  days. To  d i f f e r e n c e between the  the data were analysed  analysis is  before The  the simple  period  r e s u l t s are shown i n f i g u r e  A 5^ minimum occurs at a t r i a l  p e r i o d about  26  .0 Trial  period  (days)  Figure 11. The s c a t t e r of the data about mean l i g h t curve (10.5 GHz). 0.229  j  1  1  1  1  !  1  ,  1  ,  1  .0 T r i a l period Figure 12.  (days)  The s c a t t e r of the data about mean l i g h t curve  (5 OHs).  27  26.4 days a t 10.5 GHz data and a 8c minimum occurs a t a t r i a l period about 26.5 days a t 5GHz. From these two f i g u r e s 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 a n a l y s i s While the r e s u l t s of simple period f o l d i n g a n a l y s i s  provide strong evidence f o r p e r i o d c i t y , t h i s method Is s e n s i t i v e t o 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 r e s u l t i n g noise reduces the accuracy to which the period can be determined. To t r y t o define t h i s period more p r e c i s e l y and to q u a n t i f y i t s s i g n i f i c a n c e a second t e s t was employed. As discussed by Taylor and Gregory (1982), the t e s t i s aimed a t 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 p e r i o d , a mean l i g h t curve a t both frequencies was c a l c u l a t e d by b i n n i n g and averaging a l l of the data as dicussed i n the previous a n a l y s i s . This mean l i g h t curve was then c r o s s - c o r r e l a t e d , i n phase space, with the r e s 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 d i f f e r e n c e between the i n d i 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 c r o s s - c o r r e l a t i o n curve. For each t r i a l period T, the q u a n t i t y X = (S x  2 t  was c a l c u l a t e d . Where  )* / 1 0  (III.2)  i s the phase d i f f e r e n c e 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 d i f f e r e n c e between the outbursts  and the mean l i g h t curve. For a true p e r i o d , t h i s X  i s z e r o . The r e s u l t of the a n a l y s i s i s shown i n f i g u r e 13 . A 8c minimum occurs a t a t r i a l p e r i o d of 26.50 ± 0.03 days . I t i s worthwile to p o i n t out t h a t i n c a r r y i n g out t h i s t e s t , assumed no p e r i o d d e r i v a t i v e ( t h i s should  be a good  approxmation over r e l a t i v e l y s h o r t o b s e r v a t i o n a l time Further  a n a l y s i s for searching  discussed  we  base).  f o r the p e r i o d d e r i v a t i v e i s  i n the next s e c t i o n .  The data were binned modulo the p e r i o d of 26.50 days u s i n g the phase zero of J.D. 2,4443,366.775. The binned mean l i g h t curve a t 5 GHz and 10.5 GHz are shown i n f i g u r e 14 and f i g u r e 15. They are i n good agreement with r e s u l t s by Taylor and  Gregory (1982). F i g u r e 16 shows the 10 s e s s i o n s data i n  phase space. V e r t i c a l mean l i g h t  curves.  l i n e s i n d i c a t e the phase of the peak of  29  Trial  Figure  13.  period  (days)  The rms phase s c a t t e r 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  0.0  -  "1 -  0.4  0.0  OB  1.?  1 .6  2.0  Phase Figure  14.  Binary  r a d i o mean l i g h t c u r v e a t 5 GHz f o r  p e r i o d o f 26.50 d a y s . J u l i a n Date o f phase z e r o - 2,4443,366.775.  1B0.0  144.0  -  108.0  X  9 h.  72.0  -  36.0  -  0.0  2.0  0.0  Figure  15.  Binary  r a d i o mean l i g h t  period  o f 26.5 d a y s . J u l i a n p a t e o f phase  zero  > 2,4443,366.775.  c u r v e a t 10.5 GHz f o r  31  240 160 BO  «  •  •  *  •  •  .  •  •  •  •  D  -  •  •  •  • <  •  •  •  30 20 10  x  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  t  90 60 30  E  1977. 5GHz  •  150 100 50  >  Aug  •  150 100 50  "2  •  «  ,  •  •  •  •  •  60 40 20  •  240 160 80  •  •  •  •  •  . •  240 160 80  .  .  • * •  • *  75 50 25  •  • •  *  • «  •  *  *  150 100 50  •  t  •  •  l  0  F i g u r e 16.  1  l  0.2  1  1  1  0.4 0.6 Phase  •  1  •  1  0.8  Ten o u t b u r s t s p l o t t e d  1  1  1.0  i n phase space f o r the  p e r i o d of 26.50 days. V e r t i c a l  lines  indicate  the phase of the peak of mean l i g h t c u r v e s .  32  3.3  Two parameters s e a r c h i n g  f o r the p e r i o d and p e r i o d  derivative  As  has been pointed  out, the previous c r o s s - c o r r e l a t i o n  a n a l y s i s assumed the p e r i o d d e r i v a t i v e  t o be 0.0. To f u r t h e r  check the assumption and q u a n t i t a v e l y put a c o n s t r a i n t t o the p e r i o d d e r i v a t i v e , a t h i r d t e s t was employed. T h i s t e s t had the same p h i l o s o p h y i.e,  as the previous  the phase d i f f e r e n c e between the mean l i g h t curve and  i n d i v i d u a l outbursts equals for  cross-correlation analysis,  i s a t minimum when the t r a i l  the true p e r i o d . The same method was extended t o search  both the p e r i o d T and p e r i o d d e r i v a t i v e T For a t r i a l  simultaneously.  p e r i o d T and p e r i o d d e r i v a t i v e T, each f l u x  d e n s i t y i s now assigned phs  period T  a phase  = l n [l+Tx(t-t )/T]/T -int{ln 0  [1+Tx(t-t )/TJ/T} Q  (III.3)  (see Appendix A f o r r e d u c t i o n of the formula) Where t , t  Q  and phs are d e s c r i b e d  b i n n i n g and averaging  i n the r e l a t i o n  of a l l the data a c c o r d i n g  ( I I I . l ) . By t o t h i s new  phase, a mean l i g h t curve a t each frequency i s c o n s t r u c t e d . And  by the same c o n s i d e r a t i o n , the s t a t i s t i c a l phase d i f f e r e n c e  between mean l i g h t curve and i n d i v i d u a l outbursts in r e l a t i o n  (III.2)  i s evaluated  f o r each t r i a l  X described  p e r i o d T and  p e r i o d d e r i v a t i v e T. For true p e r i o d T and p e r i o d d e r i v a t i v e T t h i s q u a n t i t y X i s 0.0 or a t minimum. T a y l o r and Gregory have put an upper l i m i t on ITI <1.6"10~  4  days/day (1984) f o r 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 a d d i t i o n a l v a r i b l e . Therefore, the present two dimensional a n a l y s i s was c a r r i e d out f o r t r i a l period d e r i v a t i v e s from - l . O x l O t o - 3  l.OxlO  - 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 i n t h i s a n a l y s i s ) . The contour plot  i s shown i n f i g u r e 17. The contour l e v e l i s the  produced  value of mean phase d i f f e r e n c e between the mean l i g h t curve and i n d i v i d u a l outbursts. The contour values are e q u a l l y spaced from minimum to maximum mean phase d i f f e r e n c e f o r a l l the contour p l o t s presented i n t h i s chapter. Figure 17 shows 2 minima. Except for the minimum at about T = 26.5 days and T = 0 . 4 x l 0  -4  days/day, another  minimum  i s due to the o b s e r v a t i o n a l window e f f e c t s introduced by the method of the a n a l y s i s . To further confirm that the window e f f e c t s were introduced by the method, a set of  artificial  p e r i o d i c data with T = 26.0 days to T = 27.0 days and T = 3"10~  4  to 3 » 1 0 ~  4  days/day, sampled i n the e x a c t l y the same way  as our observation data were inserted i n t o the same program that produced  f i g u r e 17. Two t y p i c a l r e s u l t s are shown i n  f i g u r e 18 and f i g u r e 19.  Both show s i m i l a r s t r u c t u r e to that  obtained f o r the r e a l data. At t h i s stage, we have confidence that the true minimum i s c l o s e to T =26.5 days and T =0.0 days/days. A f i n e r search was c a r r i e d 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  1.0  10  «o  •o n » o  0.6  tt) —( JJ  0. 2  >  u  •o •o  -0.2  -  -0.6  -  o  M  tD  a  -1.0  25.5  25.9  26.3  2 6 .7  27.1  27.5  T r i a l period (days)  Figure 17. Two dimensional  search f o r period and period  d e r i v a t i v e . The contours give the rms phase s c a t t e r i n the peak of the c r o s s - c o r r e l a t i o n of the mean r a d i o l i g h t curves with i n d i v i d u a l outbursts. Contour l e v e l s are e q u a l l y spaced from minimum t o maximum of rms phase s c a t t e r .  35  F i g u r e 18.  window e f f e c t s  t e s t . The r e s u l t  f o r T = 26.5 days and T = 0.0  of a r t i f i c i a l  days/day.  data  36  F i g u r e 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  f o r T • 26.80 days and T = 0.5*10"  3  days/day.  data  37  Trial  Figure  20.  Two  period  dimensional search  (days)  f o r p e r i o d and  period  d e r i v a t i v e . A f i n e r s e a r c h . Contour l e v e l s are e q u a l l y spaced from minimum t o maximum of phase s c a t t e r .  rms  38  Trial  Figure  21.  period  (days)  C r o s s - s e c t i o n of two d i m e n s i o n a l contours a t T = 4*10~  5  days/day.  39  Figure  22.  C r o s s - s e c t i o n of two d i m e n s i o n a l T = 26.49 days.  contours  40  days/day. A f t e r c l e a n i n g the window e f f e c t s , f i g u r e 20 shows the r e s u l t s of the t e s t with the r e a l data. The T = 26.49 days and  T = 0.4  *10~  4  minimum i s found a t  days/day. F i g u r e 21 and  figure  22 a l s o shows the c r o s s - s e c t i o n of the contour cut a t T = 26.49 days and  T = 0.4*10~  4  r e d u c t i o n method and and  period d e r i v a t i v e  3.4  days/day. The  s i g n i f i c a n c e of the d e t e c t i o n of period T f are d i s c u s s e d  next s e c t i o n .  f l u x d e n s i t y measurements to the  d e t e c t i o n of the p e r i o d and processes  and  i n the  Monte c a r l o s i m u l a t i o n s From the o r i g i n a l  it  f u r t h e r t e s t of t h i s  final  period d e r i v a t i v e , several  were i n v o l v e d . In such a complex r e d u c t i o n program,  i s not easy to determine the s i g n i f i c i a n c e of the detected T.  T  In a d d i t i o n , the p r o p e r t i e s of t h i s complex i n t e r f a c e  between the raw  data and  the r e s u l t s should  be considered  when  i n t e r p r e t i n g the r e s u l t s . I t becomes necessary to c a l i b r a t e the r e d u c t i o n program. T h i s was black box  and  done by t r e a t i n g the program as a  measuring the response  t o the c o n t r o l l e d i n p u t .  Monte c a r l o type s i m u l a t i o n runs were c a r r i e d out determine (1) the systematic  e r r o r s introduced  by the  reduction  program, (2) the s i g n i f i c a n c e of the d e t e c t i o n of T and t o f u r t h e r check the widow e f f e c t s d i s c u s s e d  i n the  to  T,  (3)  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 s y s t e m a t i c e r r o r s i n t r o d u c e d by the r e d u c t i o n program, a set  of a r t i f i c i a l  data with p e r i o d T = 26.49 days and period  d e r i v a t i v e T = 4.0"10~ days/days were c r e a t e d . The shape of 5  the a r t i f i c i a l  data i n one c y c l e i s an asymmetrical  with amplitude  of 100 mJy  which i s  gaussian  and peak a t b i n a r y phase 0.66  (  approximately the same shape as the observed mean  l i g h t c u r v e ) . From observed sigma noise i s about 13 mJy. gaussian d i s t r i b u t i o n the above a r t i f i c i a l  f l u x d e n s i t y measurements, the  one  T h e r e f o r e , the random noise with  (sigma = 13 mJy,mean = 0.0)  were added to  data to simulate the n o i s e . A t o t a l of  twenty runs were c a r r i e d out. No s i g n i f i c a n t s y s t e m a t i c e r r o r was  found. A t y p i c a l r e s u l t  percent of the and  is  shown i n f i g u r e 23.  r e s u l t s l i e w i t h i n range T = 26.46-26.52 days  T = 1.0 "10" -7*10 ^ days/day. We 5  about 0.03  Ninety  -  days and  £  T  about 3.0"10  -5  conclude  that £  is  T  days/day. Therefore the  best f i t t e d p e r i o d and p e r i o d d e r i v a t i v e are T = 26.49 ± 0.03 We  days  T = (4.0 ± 3.0)*10~  5  days/day.  have demonstrated t h a t the window e f f e c t s are due  the sparse sampling  to  of o b s e r v a t i o n a l d a t a . With p e r f e c t p e r i o d  data which i s p e r f e c t l y sampled, t h i s window e f f e c t s should d i s a p p e a r . As a f u r t h e r check, two  s e t s 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 c y c l e s u n i f o r m l y distributed  i n the o b s e r v a t i o n a l time base were c r e a t e d . The  contour p l o t s produced  are shown i n f i g u r e 24 and  figure  25.  As one can see, the window e f f e c t s do d i s a p p e a r . F i g u r e 26 shows 10 s e s s i o n s data i n phase space  f o r the  42  Trial  F i g u r e 23.  period  (days)  A r e s u l t of monte c a r l o  simulation.  43 1.0  •0 •o n  O.B  -  0.2  -  « •o  2 >  m  > v •o  -0.2  •a o u Qi  *  -O.B  -1.0  25.5  Figure  25.9  2 4 .  A  2G.3 26.7 T r i a l p e r i o d (days) result  27.1  of p e r f e c t sampled d a t a w i t h T  days and T •= 5 « 1 0 "  5  27.5  = 2 6 . 4 7  days/day.  1.0  >e •o v.  O.B  -  n >»  •o  S  0.2  « > 4 J * >  £  "0.2  v  o  —4  M  Cl Qi ~H  -0.6  -1.0 25.5 Figure  25.9 25.  26.3 Trial  period  26.7 (days)  27.1  27.5  A r e s u l t o f p e r f e c t sampled d a t a w i t h T » 26.50 days and f • 0.00  days /day.  44  240 160 BO  Aug  1977. 5GHz  150 100 50  Feb  1978. 10.5GHz  150 100 50  Aug  1978. 5GHz  Aug  1979. 5GHz  30 20 10  Jun  1980. 10.5GHz  > "2 £  60 40 20  Aug  1980. 5GHz  x  240 160 80 240 160 80  Aug  1981. 5GHz  Aug  1981. 10.5GHz  75 50 25  Aug  1984. 5GHz  150 100 50  Sep  19B6. 5GHz  •  *  •  90 60 30  z>  r  1  » «  .*  r  0  F i g u r e 26.  1  0".2  1  1  1  r  0.4 0.6 Phase  ~i  1  0.8  Ten o u t b u r s t s p l o t t e d period  r  1.0  l n phase space f o r the  of 26.49 days and p e r i o d d e r i v a t i v e o f  0.4*10~  4  days/day. V e r t i c a l l i n e s i n d i c a t e 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 . 4 x l 0 ~  4  days/day. A  phase s h i f t of 0.2 t o r i g h t and 0.1 t o the l e f t have been seen. A l s o the phase of the peak of 1986's data does not agree with the p r e d i c t e d phase. Comparaison of f i g u r e 16 and 26 suggests t h a t a constant Therefore,  p e r i o d of 26.50 days i s q u a l i t a t i v e l y b e t t e r .  the phase s c a t t e r f o r the p e r i o d of 26.50 days (see  F i g . 16) i s u n l i k e l y due t o a p e r i o d d e r i v a t i v e . The d e t e c t i o n of the p e r i o d d e r i v a t i v e can not be regard s c a t t e r may be due to o b s e r v a t i o n a l sampling of o b s e r v a t i o n a l  as s i g n i f i c a n t . The  e r r o r s , o r , due t o sparse  data ( i . e . , the observed l i g h t curves  were not w e l l d e f i n e d ) . However, they may i n d i c a t e t h a t the underlying  clock  i s not very t i g h t l y coupled t o measured f l u x  d e n s i t y v a r i a t i o n . One should i n Hercules XI (Priedhorsky  3.5  note that simular  feature e x i s t s  and H o l t , 1986).  A p o s s i b l e 4-year p e r i o d of long term modulation One  of the major goals  of t h i s undertaking was t o  examine the long term modulation of the r a d i o f l a r e s of t h i s extraordinary  system. As suggested by P.C. Gregory, such an  e x o t i c o b j e c t might c o n t a i n a p r e c e s s i n g  a c c r e t i o n d i s k or  j e t s . I f t h i s were the case, the e f f e c t s might be r e f l e c t e d i n the  long term v a r i a t i o n of the r a d i o emission.  Taking  advantage of the 9 years of the data base, t e s t s were c a r r i e d out t o search Figure  f o r the p o s s i b l e long term modulation. 16 shows c l e a r l y t h a t the b i n a r y f l a r e maxima  v a r y s l o w l y with time. As shown i n the b i n a r y 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 p o r t i o n of the b i n a r y o u t b u r s t s i s a t o r b i t a l phase 0.4-0.8 f o r best p e r i o d 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  fitted amplitude  of each o u t b u r s t i s measured as the peak f l u x d e n s i t y of the o u t b u r s t . In cases where the peak f l u x d e n s i t y was d e f i n e d due  not w e l l  to a p a u c i t y of data ( i n a few i n s t a n c e s o n l y a  s i n g l e measurements i n a 26.5 the f l a r e maximum was  day c y c l e ) o n l y a lower l i m i t  on  a v a i l a b l e . Only those data i n the b i n a r y  phase 0.4-0.8 were s e l e c t e d a*s p r o v i d i n g a lower l i m i t on the amplitude  of the o u t b u r s t . The c h a r a c t e r i s t i c amplitude  outburst and date are l i s t e d  i n Table  An o u t b u r s t with an amplitude i n 1977  August. A f t e r about  a d d i t i o n the two  4. of about  4 y e a r s , i n 1981  g i a n t o u t b u r s t a t the l e v e l of about  of each  300 mJy  lowest o u t b u r s t s i n 1980  284 mJy  occurred  August, another was  observed, i n  August and  1984  August are a l s o spaced by about  4 y e a r s . Coe et a l (1983)  observed the source a t 10.7  from 1981  GHz  A p r i l 24,1982 ( o r b i t a l phase about l e v e l was  about  220 mJy  years p r i o r , on A p r i l  which was  0.56)  t o 1982  the average  April.  GHz  Again these r e s u l t s suggested a p o s s i b l e  On  emission  a t the same l e v e l about  22,1978 a t 10.5  (about 4 years ) of the amplitude  May  4  ( o r b i t a l phase 0.64). periodic  modulation  of the b i n a r y o u t b u r s t . For  t h i s reason, the data i n Table 4 are binned modulo the p e r i o d of 1458  days u s i n g the phase 0.0  shows the binned data p l o t t e d observed  of J.D.  2,443,330.9. F i g u r e 27  i n phase space. Since some of the  l i g h t curves were not w e l l d e f i n e d ( 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 p o r t i o n of the b i n a r y o u t b u r s t s i s a t o r b i t a l phase 0.4-0.8 f o r best p e r i o d 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  fitted amplitude  of each o u t b u r s t i s measured as the peak f l u x d e n s i t y of the o u t b u r s t . In cases where the peak f l u x d e n s i t y was d e f i n e d due  t o a p a u c i t y of data ( i n a few i n s t a n c e s o n l y a  s i n g l e measurements i n a 26.5 the f l a r e maximum was  day c y c l e ) o n l y a lower l i m i t  l i m i t on the  of the o u t b u r s t . The c h a r a c t e r i s t i c amplitude  o u t b u r s t and date are l i s t e d  i n Table  An o u t b u r s t with an amplitude i n 1977  August. A f t e r about  of each  4. of about  4 y e a r s , i n 1981  g i a n t o u t b u r s t a t the l e v e l of about a d d i t i o n the two  300 mJy  lowest o u t b u r s t s i n 1980  284 mJy  occurred  August, another was  observed, i n  August and  1984  August are a l s o spaced by about  4 y e a r s . Coe et a l (1983)  observed the source a t 10.7  from 1981  GHz  A p r i l 24,1982 ( o r b i t a l phase about l e v e l was  about  220 mJy  years p r i o r , on A p r i l  on  a v a i l a b l e . Only those data i n the b i n a r y  phase 0.4-0.8 were s e l e c t e d a*s p r o v i d i n g a lower amplitude  not w e l l  which was  0.56)  to 1982  the average  April.  On  emission  a t the same l e v e l about 4  22,1978 a t 10.5  GHz  Again these r e s u l t s suggested a p o s s i b l e (about 4 years ) of the amplitude  May  ( o r b i t a l phase 0.64). periodic  modulation  of the b i n a r y o u t b u r s t . For  t h i s reason, the data i n Table 4 are binned modulo the p e r i o d of 1458  days u s i n g the phase 0.0  of J.D.  2,443,330.9. F i g u r e 27  shows the binned data p l o t t e d i n phase space. Since some of the observed  l i g h t curves were not w e l l d e f i n e d ( i . e . , the data  47  were t o o s p a r s e  ), o n l y t h e lower  limit  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 and  2 8 . The o b s e r v e d  l i g h t curve  (dashed  of the f l a r e  by a r r o w s  maxima  i n f i g u r e 27  b i n a r y f l a r e maxima a s w e l l a s a model line  ) 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 modulation  is:  t h e mean l i g h t c u r v e g i v e n i n f i g u r e 2 7 ,  predicts that the radio emission l e v e l be a b o u t  172 mJy  observed  peak f l u x d e n s i t y o f a b o u t  It modulation  i n 1986 S e p t e m b e r s h o u l d  i n e x c e l l e n t agreement w i t h t h e l a t e r 171 mJy.  i s worthwhile t o p o i n t out that i f t h i s i s correct,  i n t h e mean l i g h t  peak o f t h i s  flux  c u r v e g i v e n b y Coe e t a l . ( 1 9 8 3 ) . T h e i r  4-year  t h e phase o f t h e  modulation.  However, we w o u l d data  4-year  i t r e a d i l y e x p l a i n s t h e h i g h e r peak  o b s e r v a t i o n a l windows h a p p e n s t o be a r o u n d  limited  4-year  observation that supports t h i s  like  i n the l a t t e r  t o p o i n t o u t t h a t due t o t h e  p o r t i o n o f our t i m e base and s p a r s e  o b s e r v a t i o n a l w i n d o w s , a n y c o n c l u s i o n s drawn a r e v e r y t e n t a t i v e . Although t h i s candidate  long term v a r i a t i o n  fora superorbital cycle,  i s an i n t e r e s t i n g  i t has been observed f o r  t o o f e w 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 . H i g h o b s e r v a t i o n s n e e d t o be c o n t i n u e d on confirm this  possible  long term  quality  t h i s unique  period.  source t o  48  TABLE 4 APPROXIMATE BINARY RADIO FLARE MAXIMA Ut date  J u l i a n date (2,440,000+)  Frequency (Ghz)  Peak f l u x d e n s i t y (mJy)  1977 Aug  27  3383  5.0  284  1978 Mar  1  3569  10.5  138  1978 Mar 28  3596  5.0  1978 Apr 22  3622  10.5  220  1978 Aug  9  3723  5.0  176  1979 Mar 31  3964  10.5  149  1979 J u l 23  4078  10.5  1979 Aug 15  4101  5.0  1979 Nov 30  4208  10.5  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 J u l 26  5177  5.0  84  1986 Sep 20  6694  5.0  171  > 160  >  84 100  >  58  49  350.0  F i g u r e 27.  B i n a r y r a d i o f l a r e maxima p l o t t e d i n phase for  the p e r i o d of 1458  days. J u l i a n date of  z e r o = 2,443,330.9. Arrow i n d i c a t e s lower of the b i n a r y peak.  space phase  limit  50  350.0  5GHZ 10.5GHZ Aug.,  20.  1989  280.0  £  210.0  E  1-  ••H  X ro E  I  140.0  0) M  ro 70.0  0.0  i 3330.9  i_  1  _ J 4507.4  _J  J u l i a n date  F i g u r e 28.  1-  5683.9  _L  6860.4  _J  8036.8  u  (2,440,000 + )  B i n a r y r a d i o f l a r e maxima from 1977 August t o 1986 September. Dashed l i n e discussed  i n chapter  i s a model l i g h t 4.  curve  51  Chapter 4  A precessing  j e t model f o r the long term modulation  Two b i n a r y models have been proposed t o account f o r the r a d i o , x-ray and p o s s i b l e Tf-ray emission a s s o c i a t e d GT0236+610. T a y l o r and Gregory  (1982) d i s c u s s e d  with  a model i n  which the r a d i o f l u x modulation i s due t o v a r i a b l e a c c r e t i o n onto a compact companion i n an e c c e n t r i c o r b i t . A l t e r n a t e l y , Maraschi and Treves (1981) have proposed a model i n which the companion i s a moderately young p u l s a r  l o s i n g energy through a  r e l a t i v i s t i c wind. However, both models give no c o n s i d e r a t i o n  of the o r i g i n  of the f l a r e maxima v a r i a t i o n . Although the d e t e c t i o n of the p e r i o d i c long term modulation has low s i g n i f i c a n c e , the source certainly  i s an i n t e r e s t i n g candidate f o r a s u p e r o r b i t a l c y c l e .  Only a few b i n a r y sources have long c y c l e s . Longer-term v a r i a t i o n are both harder to observe and p o o r l y  understood.  E a r l y attempts t o e x p l a i n the long p e r i o d X-ray c y c l e s i n b i n a r y systems ( f o r example,Her X - l ) have i n v o l v e d (what i s precessing-and why-are s t i l l examine a p r e c e s s i n g  precession  u n c e r t a i n ) . Here we  j e t model as a p o s s i b l e e x p l a n a t i o n  of the  4-year modulation of GT0236+610. For the purpose of t h i s a n a l y s i s , we t r e a t a j e t as stream of i d e n t i c a l packets of r a d i a t i n g matter Following  (plasmons).  the a n a l y s i s of Gower e t a l . (1982 ), the plasmons  are e j e c t e d a t a f i x e d speed 0 = v/c with r e s p e c t  to the  source. The source i s a t r e s t a t the o r i g i n of the right-handed  52  c o o r d i n a t e d system x,y,z as shown i n f i g u r e 29. z' i s the a x i s about which the plasmon  e j e c t i o n v e l o c i t y p r e c e s s e s with an  a n g u l a r v e l o c i t y H and a t an angle <f. With the geometry  shown  l n f i g u r e 29, we can w r i t e f o r the v e l o c i t y components of plasmon  a l o n g the l i n e of s i g h t $  x  = 6 ( s i n l s i n v c o s (S?t+e )+cosI cosv)  (IV.1)  Q  where I i s the angle between the a x i s z  and l i n e of s i g h t . We  1  assume t h a t the e m i s s i o n from each plasmon with a spectrum i n the r e s t  isoptically  frame of the plasmon  thin  of the form:  s p e c t r a l power e m i t t e d , PO')oC v *. F o l l o w i n g Ryle and L o n g a i r _t  (1967) the f l u x d e n s i t y , S{\>) ( W m " H z ) of a moving _1  2  -1  plasmon  i s g i v e n by SO')  = S ( V ) D 3+fX  (IV.2)  r  where D = Doppler s h i f t S (v) r  factor  [t(1-0 )] X  ,  = f l u x d e n s i t y of an i d e n t i c a l plasmon a t  r e s t and i n s t a n t a n e o u s l y a t the same d i s t a n c e From r e l a t i o n  (IV.1) and (IV.2), we note t h a t the p e r i o d i c  modulation i s assumed t o be due t o the Doppler s h i f t  f a c t o r D.  The maximum and minimum f l u x s h o u l d be observed when the j e t i s c l o s e s t t o the l i n e of s i g h t . Combining  s i g h t and f a r t h e s t  from the l i n e of  (IV.1) and (IV.2) we have { (l-0cos(f+<P)  )/(l-0cos(I-<e)  }3+oc  (IV.3)  we have B = ( x - l ) / ( x c o s ( 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  = { (l-0cos (I+<f) ) / ( l - 0 ( s i n l s i n v c o s e + c o s l c o s f ) }  m i n  3+cC  (IV.5) where 6 = nt+e substitute  (IV.6)  D  (IV.4) i n t o  (IV.5) and a f t e r some manipulation we  have S(6)/S  = { 2x/[l+cos9+X(l-cos9) ] }  m i n  Note t h a t the shape of the l i g h t and  I and determined  by the r a t i o  the model i s f i t t e d t o the binned The light binned  (IV.7)  3 + o C  curve i s independent of S  m a x  /S  m i n >  l i g h t curve  Taking a: = 0.0, (see F i g . 30).  j e t p r o c e s s i n g model (IV.7) p r e d i c t s a symmetrical  curve which i s i n disagreement light  with observed data. The  curve shows a more r a p i d r a i s e . However, as has  been p o i n t e d out b e f o r e , the measure of the l i g h t curve can o n l y be c o n s i d e r e d t e n t a t i v e . We do not yet have confidence t o r u l e out the j e t model. High q u a l i t y o b s e r v a t i o n s need t o be continued on the source.  54  Y  Figure  29.  The c o o r d i n a t e  system i n d e r i v i n g the j e t  model. Z' i s j e t p r e c e s s i n g a x i s and v cone a n g l e . X i s the l i n e of s i g h t , and YZ the plane of the sky.  55  F i g u r e 30.  The f l a r e maxima and the j e t model  fit.  56  Chapter 5  Summary and  New  6 cm  September 1986  conclusions  observations  201  August 1977  and  using 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 Observatory analysed  of GT0236+610 i n August 1984  at Green Bank were presented.  We  f l u x d e n s i t y measurements over the p e r i o d from to September 1986.  We  repeated  the  cross  c o r r e l a t i o n a n a l y s i s d i s c u s s e d by T a y l o r and  Gregory (1982) and  obtained  days. A method of  an  searching  improved p e r i o d of 26.50 ±  f o r both p e r i o d and  0.03  period d e r i v a t i v e  was  developed. A phase s h i f t of about 0.15  has  been seen f o r the best f i t t e d p e r i o d and  simultaneously  i n both d i r e c t i o n period d e r i v a t i v e .  T h i s suggests that the phase s c a t t e r i s u n l i k e l y due p e r i o d d e r i v a t i v e . The e r r o r s or the coupled  s c a t t e r may  be due  to the  to o b s e r v a t i o n a l  f a c t t h a t the u n d e r l y i n g c l o c k i s not  tightly  to the r a d i o f l u x d e n s i t y v a r i a t i o n . We  found evidence  t h a t GT0236+610 has a second p e r i o d of  about 4 years which i s superimposed on the 26.50 days b i n a r y motion. A p r e c e s s i n g j e t model was long p e r i o d modulation. The  proposed to account f o r the  model p r e d i c t s a symmetrical  light  curve which i s i n disagreement with observed d a t a . However, we do not yet have confidence  to r u l e out the j e t model due  l i m i t e d d a t a . High q u a l i t y o b s e r v a t i o n s the long p e r i o d and radio observations outburst  are needed to  t e s t the model. P a r t i c u l a r l y we i n August 1989  i s about 300  mJy  confirm  suggest  ( p r e d i c t e d peak of the  around August 20,  1989).  to the  57  References  Backhouse, C ,  (1987). M.S. t h e s i s , U n i v e r s i t y of B r i t i s h  Columbia. B a r t o l i n l , C , e t a l . 1983, A s t r . Ap., 118 365. P  Bignami, G.F., e t a l . 1980, IAU C i r c , No. 3518. Bignami, G.F., Carveo, P.A., Lamb, R . C , Markert, T.H., and P a u l , J.A., 1981, Ap.J.  ( L e t t e r s ) , 247. L85.  Bignami, G.F., e t a l . 1983, M.N.R.A.S., 203 791. r  Bondi, H., and Hoyle, F., 1944, M.N.R.A.S., 104. 273. Coe,M.J., e t 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 O s t r l k e r , J.P., 1973, Ap. J . , 179_,585. Gregory, P.C., and T a y l o r , A.R., 1978, Nature, 272. 704. Gregory, P.C., e t 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, A s t r . Ap., 87., 299. Howarth, I.D., 1983, M.N.R.A.S., 2111/ 801. Hutchings, J.B., 1980, Pubis a s t r . Soc. P a c i f . , 9JL, 657. Hutchings, J.B., and Crampton, D., 1981, Pub.A.S.P., 9_3_, 486. Maraschl, L., T a n z i , E.G., and Treves, A., 1981, Ap. J . , 248, 1010.  58  Maraschi, L., and Treves, A., 1981, M.N.R.A.S., 194, IP. P e r o t t i , F . , e t a l . 1980, Ap... J . ( L e t t e r s ) , 239. L49. P o l l o c k , A.M.T., e t a l . 1981, a s t r . Ap., 9_i, 116. P r l e d h o r s k y , W.C., and Holt,S.S., 1986, p r e p r i n t . Ryle, M., and L o n g a i r , M.S., 1967, M.N.R.A.S., 136. 123. Seaton, M.J., 1979, M.N.R.A.S., 187. 73P. Share, G.H., e t a l . 1979, l n X-ray Astronomy, Proc. of the 21st p l e n a r y Meeting of the Committee on Space Research, ed. W.A. B a i t y and L.E. Peterson (New York: Pergamon), p.535. T a n z i , E.G., e t a l . 1982, NASA Conference Proc. 2338, p.615. T a y l o r , A.R.,(1982).  Ph.D t h e s i s , U n i v e r s i t y ' o f  British  Columbia. T a y l o r , A.R., and Gregory, P . C , 1982, Ap. J . , 255. 210. T a y l o r , A.R., and Gregory, P.C., 1984. Ap. J . , 283 273. f  W i l l s , R.D., e t a l . 1980, Advances  i n Space  Exploration,Vol.7.  59  Appendix A  (III.3)  Reduction of  Assuming a constant p e r i o d d e r i v a t i v e T, we have dT/dt = T  (1)  or T(t) = T where T  0  + T*(t-t )  Q  (2)  0  i s the p e r i o d a t J u l i a n date t . Regarding the J u l i a n Q  date t as a f u n c t i o n of cycle. N that goes through from t we  have +ANxT(t)  t(N+AN) = t(N)  (3)  On the other hand t(N+AN) = t(N) + ANxdt/dN comparing  ( 3 ) and  ( 4 ) , one  (4)  has (5)  dt/dN = T ( t ) which y i e l d s N = X  t Insert  —1—  fc  in T(t) in (6),  0  dt  °  Z  T(t) one  (6)  has  N = ln( l + T x ( t - t ) / T Q  0  )/T  (7)  The phase of the measurement a t J u l i a n date t i s phs = N - i n t (N) This  i s the r e l a t i o n  (III.3)  (8)  Q  to t ,  60  Appendix B  Telescope t r a c k i n g  stability  To measure v a r i b l e r a d i o emission, i t i s important t o keep the t e l e s c o p e been pointed  p o i n t i n g and beam p r o f i l e s t a b l e . As has  out by J.R. Picha  with t e l e s c o p e  (1966) that beam p r o f i l e s change  d r i v e r a t e s . Tests were c a r r i e d f o r n i g h t  d r i v i n g scans t o check the d r i v e r a t e of the t e l e s c o p e . The  designed d r i v e r a t e f o r n i g h t survey scan i s  120 /min. The telescope f  pointing position R a t i ] , DECtil  (data  s e t f o r r i g h t a s c e n s i o n and d e c l i n a t i o n ) was f i t t e d by a l i n e a r function: dec  = v * ra + dec  0  where v i s the d r i v e r a t e and d e c Tests  Q  i s the s t a r t i n g d e c l i n a t i o n .  f o r 8 n i g h t scans track through GT0236+610 showing the  a c t u r a l d r i v e r a t e i s about 123'/min which i s good agreement with the designed value of 120*/min. However, the r e s i d u a l of the a c t u r a l telescope and  l i n e a r model showing o s c i l l a t i o n s  pointing  (except f o r scan 4322,  which shows no c l e a r o s c i l l a t i o n ) . As shown i n f i g u r e 31, telescope 0.7  o s c i l l a t e s around mean t r a c k with amplitude of about  arcmin and p e r i o d  of about 5 seconds. The u n s t a b i l i t y of  the p o i n t i n g may be c o n t r i b u t e  t o the beam broading ( or  n a r r o w i n g ) . The cause of t h i s i n s t a b i l i t y Is not y e t known, i t might due t o the d e c l i n a t i o n d r i v e mechanism of the t e l e s c o p e .  61  0.9 0.5  -  n  -  SCAN 1251  A An  n  0.2 -0.2  -  -0.5  -  -0.9  V. 0.00  0.00  J 0.97  0.77  0.5B  0.39  0.19  SCAN 3247  0.39  0.20  0.59  0.78  0.9B  Time (minute) Figure  31. The r e s i d u a l o f t e l e s c o p e linear  fit (DEC  o  b  s  e  r  v  e  d  p o i n t i n g and  - DEC  l  l  n  e  a  r  £  i  t  )  

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