A statistical analysis is presented of the orientations of ionic comet tails in the solar wind. The analysis indicates that the radial solar wind speed is not necessarily higher near the solar poles than near the equator. The results refer to a long-term, global flow pattern and do not refer to short-term variations of solar wind speed

Brandt, J. C.

English

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LATITUDINAL PROPERTIES OF T H E  SOLAR WIND 
FROM STUDIES OF IONIC CCFET TAILS 
John C. Brandt 
Laboratory fo r  Solar  Physics and Astrophysics 
NASA-Goddard Space F l igh t  Center 
Greenbelt, Maryland 20771 
Abstract - Analysis of the o r i en t a t i ons  of ion ic  comet t a i l s  
gives  no support fo r  the suggestion tha t  the r a d i a l  s o l a r  wind speed 
i s  higher  near the so l a r  poles than near the  equator. These r e s u l t s  
r e f e r  t o  a long- term, global flow pa t te rn  and do not r e f c r  t o  short.. 
term var ia t ions .  
https://ntrs.nasa.gov/search.jsp?R=19760017038 2020-03-22T15:45:18+00:00Z
Evidence from comets concerning the l a t i t u d i n a l  va r i a t i on  of 
so l a r  wind parameters has been discussed previously by Pflug (1966), 
Brandt (1967), and by Bertaux, Blamont and Festou (1973). In t h i s  
short  report,  I summarize the evidence based on ion ic  comet-tail  
o r ien ta t ions  as  recent ly analyzed by Brandt, Harrington, and Roosen 
(1975), and show the d i s t r i b u t i o n  of the sample i n  l a t i t ude ,  time, 
and phase of the so la r  cycle. 
The basic  observation i s  the posi t ion angle of the t a i l  ax i s  on 
the plane of the sky (Belton and Brandt 1966). The posi t ion angle P 
i s  in te rpre ted  i n  terms of a t a i l  vector T-whose d i r ec t ion  i n  space i s  
determined by dynamical aberra:ion, viz. ,  
where w_is the so l a r  wind ve loc i ty  vector and V i s  the vector  ve loc i ty  
of the comet. Thc astrometric technique developed by Brandt, Rooscn, 
and Harrington (1972) does not assume that  the comct t a i l  l i e s  i n  the 
plane of the comet's o rb i t .  Each observation de tennincs e s s e n t i a l l y  
a ha l f  plane i n  ve loc i ty  space. A preferred so lar  wind ve loc i ty  vector  
w ) i s  determined as the one which minimizes the sum of the (wr, we, @, 
squares of the residuals  be tween the computed and obscrved posi t ion angles. 
At present,  a sample of 678 observations a re  ava i lab le  and these 
a r e  spread over approximately 75 years i n  time and between roughly 0.5 
t o  1.5 a,u. i n  hcl ioccntr ic  dis tance.  llle basic r c s u l t s  a re  a r ad i a l  
veloci ty ,  c: w > -- 400 kmlsec, an azimuthal ve loc i ty  < w > = 6-7 kmlsec 
r d 
(varying with so l a r  l a t i t u d e  b and dis tance r a s  cos 2*315 l b  l / r ) ,  and a 
RMS dispersion of 3?7. An addi t iona l  r e s u l t  from comet t a i l  
o r ien ta t ions ,  but not from the astrometr ic  techniquc, i s  t ha t  
Wr b 225 kmlsec (Brandt and Heise 1970). These values a r e  i n  good 
agreement with r e s u l t s  from spacecraf t  and provide confirmation of 
the basic approach. 
This technique has been previously used t o  search f o r  a 
meridional flow pa t te rn  i n  the so l a r  wind. A value w 2.5 kmlsec 
m 
( a t  0 = 45O, varying a s  s i n  20) has  been found i n  the sense of a flow 
diverging from the plane of the s o l a r  equator by Brandt, Harrington, 
and Roosen (1973). This r e s u l t  implies a rad ia l  va r i a t i on  i n  the 
equatorial  densi ty  of the s o l a r  wind of N a r -2*013. 1f t h i s  law 
held from the sun t o  ear th ,  the densi ty  would be 7% smaller than on 
spherical ly  symmetric models. 
The basic  technique can be used t o  search f o r  a l a t i t u d i n a l  
va r i a t i on  of the rad ia l  so l a r  wind speed by assuming tha t  i t  va r i e s  as  
where w and dvrldlb 1 a r e  constants  t o  be determined. The r e s u l t s  
0 
a re  given in  Table 1. 
Table 1. 
Solar-Wind Speeds With and Without a  
L a t i t u d i n a l  Var ia t ion  i n  Radia l  Speed 
w o r  w dw / d l b  1 w w 
r o  m 
RMS Dispers ion 
0 -1 
(kn s e c - l )  (h sef" deg-l)  (lo. see-') (kn sec  i n  (a - eC)  
The l a t i t u d i n a l  v a r i a t i o n  found i.n our  sample, i f  any, i s  i n  the  
sense of decreas ing r a d i a l  speed wi th  inc reas ing  l a t i t u d e .  However, 
the  e r r o r  i n  rdwrld(bl ]  i s  almost  a s  l a r g e  a s  the va lue  of-0.9 km sec-' deg-' 
found, and t h e r e  i s  c l e a r l y  no trend.  In  a d d i t i o n ,  the  b e s t  s o l u t i o n  a s  
judged by RMS d i s p e r s i o n  i s  s t i l l  t he  s o l u t i o n  wi th  [dwr/d lbl! 1 0. 
When an a d d i t i t n a l  s i g n i f i c a n t  parameter i s  included i n  the  model, the  
d i s p e r s i o n  must decrease  even i f  on ly  marginally.  The l a c k  of a  decrcase  
i s  .a d e f i n i t e  f l a g  t h a t  the  a d d i t i o n a l  parameter h a s  no s ign i f i cance .  
The s l i g h t  inc rease  i n  RFlS d i s p e r s i o n  i s  simply due t o  round-off e r r o r .  
The e r r o r s  i n  the  components o f  t h e  s o l a r  wind spccd inc rease  with a  
l a t i t u d i n a l  v a r i a t i o n  included because then a l l  cornponcnts a r e  f u n c t i o n s  
of  he l iograph ic  l a t i t u d e  and can be c o r r e l a t e d .  Poss iblc  c o r r e l a t i o n s  
between cornponcnts a r e  c a l c v l a t e d  and a r c  used t o  a s s i g n  the  probqblc 
e r r o r s .  This  i s  thc  exp lana t ion  f o r  the i~crcrrsra i n  e r r o r s  w l l i l c  the 
RMS r e s i d u a l s  remained e s s e n t i a l l y  cons tan t .  
'l'he negative r e s u l t  fo r  s ign i f  i c m t  l a t i t u d i n a l  va r i a t i on  i n  wr 
r e f e r s  only t o  a long-term, global s i tua t ion .  I t  does not ru le  out  shor te r  
term r e s u l t s  such a s  the one presented by Ricket t  (1975; preceeding paper). 
It does appear t o  imply t h a t  such short-  term v?.riations average out  
over the long term. 
The sample i s  concentrated i n  the range 0 S lb 5 50' a s  shown 
i n  Figure l a  where the so l id  l i n e  represents  the present sample of 
678 observations and the dasked l i n e  represents  the same number 
d i s t r i bu t ed  a t  randon; only 60 observations l i e  i n  the range 
50' S Ib(  S 90'. I f  we p lo t  the d i s t r i bu t ion  aga-nst l a t i t u d e  
instead of the absolute  value of l a t i t u d e  a s  shown i n  Figure l b ,  wc 
f ind  n strong concentration of  observations i n  the northern hemisphere. 
There i s  no obvious reason t o  expect an adverse e f f e c t  from t h i s  
observational bins. The sample by year of observation i s  shown i n  
Figure l c  which r e f l e c t s  the i r regular  nature of cometaLy appar i t ions  
and the reduction of observations.  ~ . i g u r r  Id shows the d i s t r i b u t i o n  
of t h e  sample with phase i n  the so la r  cycle; the observations are  
concent rhied toward so la r  maximum. 
Because the astrometr ic  technique can be applied only t o  f a i r l y  
la rge  groups of observations,  r e s u l t s  oc short-term va r i a t i ons  i n  the 
so l a r  wind s p e ~ d  cannot bc obtaiaed d i rec t ly .  Work on an i nd i r ec t  
technique i s  cur ren t ly  i n  progress. 
Nevertheless, there  i s  ample d i r e c t  evidence for  l a rge ,  short-  
term va r i a t i ons  i n  s o l a r  wind propert ies .  The time required t o  
e s t ab l i sh  a meaningful measuremel~t of an average property a t  a 
particular Ictltude i s  prubablp at  least one solar rotation. This 
was Xouad tu ba the case for spacecraft observations of w as reported 6 
by Lazzrus and Gol~stetn (1971). Hence, direct out-of-the-ecliptic 
observations of the solar wind s'lruld uti l ize  an orbit wZth a slowly 
changing latitude. Several passes throu&~ a l l  solar latitudes and 
possibly several spacecraft will be required to map out the basic 
structcre of the solar wind tn three dimensions. 
' 
Belton, H. J. S., and J. C. B r d t ,  Interplanetary Gas. X I I .  A ca ta log  
of c a m e - t a i l  odeatatFoane, &. J. Suppl., & 125 (No. 117), 1966. 
Bertar~c, J. L., J. E. Blamont ,  and IY. Festou, In t e rp re t a t ton  of hydrogen 
Lyman-alpha observations o f  Comets Bennett an6 Encke, A s t r .  and Ap., 
2& 415, 1973. 
Brandt, J.  C., In te rp lane tary  Gas, XIII. Gross plabma v e l o c i t i e s  from 
the or ien ta t ions  of ion ic  cornet tails,  &, J,, _147, 201, 1367. 
Brandt, 3. C,, R. S. Harrington, and R. G. Roosen, In te rp lane tary  Gas, 
XU. Observati.orm1 evidence f o r  a t leridional solar-wind flow 
diverging from the plane of the so l a r  equator, &. J., l8s 27, 1973, 
Brandt, J. C., R. S. Harrington, and R. G. Roosen, lntcrplaneeary Gas. XX. 
Does the r a d i a l  so l a r  wind speed increase with l a t i t ude? ,  &. J . ,  
l9& 877, 1975. 
~ r a n d t ,  3. C,, and J. Heise, Interplanetary Gas, XV. No- radial plasma 
motions from the or ien ta t ions  of ion ic  comet t a i l s ,  &. J., I& 
1057, 1970. 
~ r a n d t ,  J, C., R. G. Roosen, and R. S. Harrington, Interplanetary Gas. 
X V I I .  An astrometr is  d t  termination of ~olar -wind  v e l o c i t i e s  from 
orientations of ionic  comet t a i l s ,  &. L., lj7L 277, 1972. 
Lazarus, A. J., and B. E. Goldstein, Observation of the angular-momentum 
f l ax  car r ied  by the so l a r  wind, 4. J . ,  1% 571, 1971. 
Pf lug, K., Die bestimmung der ausbreitut~gsgescl~windigkeit und anderer 
cigcnscllaftc~l des intcrylailctarcn plasnws nus dcr riclitung dcr 
gasschweife dcr kometen, Pub. &. e. Potsdnm, Bo. l o b ,  1966. 
Rickett, B. J. The solar wind velocity in 1972-1974 as 
measured qP radio scintillations, preceding paper, 1975. 
FIGURE CAPTION 
Figure 1. The distribution of the sample of comet observations: 
(a) in absolute value of solar latitude; (b) in solar latitude; 
(c) in date of observation; and (d) in solar cycle phase. See t e x t  
for discussion. 

-go0-80"-70 0 - ~ ~ 0 - ~ 0 ~ 0 - 3 ~ 0 - 2 ~ ~ ~ ~ 0  0  O +loot 20°+3  '140 O + 5 0 ~ + 6 0 ~  + 70~+80~+90 
SOLAR LATITUDE, b 
YEAR OF OBSERVATION 
200 
180 
160 
140 
120 
100 
80 
60 
40 
I I I I I I I I I I I 
- 
- 
- 
- 
- 
- 
- 
- 
I 
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 
SOLAR CYCLE PHASE, P 
MINIMUM, P=Od - 
MAXIMUM, P=OA 
- 
- 
1 
20 - 
- 
- 
! 
i 
- 
- 
- 
- 
- 
- 
0 I 1 1 I I 


Latitudinal properties of the solar wind from studies of ionic comet tails

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