It is explained why one can observe a leading spiral pattern in close pairs of galaxies where the direction of the orbital momentum of the satellite is opposite to the direction of the spin of the spiral galaxy

Fridman, A. M.

English

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N I 
ON LEADING SPIRAL ARMS IN CLOSE PAIRS OF GALAXIES 
A. M. Fridman 
Astronomical Council of the USSR Academy of Sciences 
48, Pyatnitskaya Stree, 109017 
MOSCOW, USSR 
ABSTRACT. It is explained why one can observe a leading spiral 
pattern in close pairs of galaxies where the direction of the 
orbital momentum of the satellite is opposite to the direction of 
the spin of the spiral galaxy. 
INTRODUCTION 
One can hardly find any other problem in galaxy physics 
which has been discussed so long and experienced so frequently 
changing opinions, than the problem of the direction of winding 
of galactic spiral arms. According to the initial point of view 
followed from Lindblad theory (l), all spiral galaxies must have 
leading spiral arms. The observations however have not confirmed 
this conclusion (2). Though the interpretation was critisized in 
( 3 1 ,  following ( 4 )  scientists give preference to trailing spirals 
almost unanimously. But the currently prevailing point of view 
that all spirals are trailing seems too categorical. There are 
exceptions to this rule ( 5 1 ,  and the analysis of their reasons is 
the aim of the present note. 
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https://ntrs.nasa.gov/search.jsp?R=19910007622 2020-03-19T19:49:33+00:00Z
WHERE MAY THE LEADING GALACTIC'SPIRAL W l S  BE OBSERVED? 
Examining 190 sp i r a l  galaxies ,  Pasha h a s  found t h a t  o n l y  
t h r e e  of them show l e a d i n g  arms ( 5 ) .  A l l  t h e  t h r e e  have a close 
massive companion. One of them, NGC 5426, w a s  s t u d i e d  more 
c a r e f u l l y ;  its s p i n  is o p p o s i t e  to  t h e  o r b i t a l  momentum. 
According t o  Werner ( 6 )  8 69% of t h e  p a i r e d  galaxies show t h e  same 
p r o p e r t y .  
BASIC HYPOTHESIS 
L e t  u s  d e s i g n a t e  as l e a d i n g  t h o s e  sp i r a l s  which are r o t a t i n g  
w i t h  t he i r  " t i p "  forward .  S i n c e  t h e  q u e s t i o n  is about  t h e  
r o t a t i o n  of t h e  s p i r a l  " t ips , "  a p e r i p h e r a l  r e g i o n  of t h e  
g a l a c t i c  d i s k  i s  meant h e r e .  To i d e n t i f y  a sp i r a l  as l e a d i n g ,  i t  
is enough f o r  t h e  l a r g e s t  par t  of t h e  d i s k  ( i n c l u d i n g  p e r i p h e r y )  
t o  be r o t a t i n g  i n  t h e  same d i r e c t i o n  t o  which t h e  s p i r a l  arms' 
t i p s  are o r i e n t e d .  L e t  u s  now take a sp i ra l  t o  be t r a i l i n g  i n  
t h e  whole of t h e  galactic d i s k  except its p e r i p h e r y .  Under t h e  
i n f l u e n c e  of t h e  t i d a l  wave from t h e  g a l a x y ' s  s a t e l l i t e ,  t h e  main 
p a r t  of t h e  d i s k  ( i n c l u d i n g  p e r i p h e r y )  is r o t a t i n g  o p p o s i t e  w i t h  
r e s p e c t  t o  t h e  r o t a t i o n  of t h e  c e n t e r  p a r t  of t h e  d i s k  ( F i g u r e  
1) . Then d e t e r m i n i n g  t h e  type  of s p i r a l  w i t h  r e s p e c t  to t h e  
d i r e c t i o n  of r o t a t i o n  of t h e  main par t  of t h e  d i s k ,  w e  can make a 
c o n c l u s i o n  abou t  t h e  l e a d i n g  form of t h e  s p i r a l  p a t t e r n .  
556 
F i g u r e  1. The center p a r t  of t h e  s p i r a l  g a l a x y  seen face-on 
r o t a t i n g  coun te r - c lockwise ;  t h e  main p a r t  of t h e  d i s k  ( i n c l u d i n g  
t h e  p e r i p h e r a l  r e g i o n )  is r o t a t i n g  clockwise (as t h e  s a t e l l i t e ) .  
A r r o w s  show a v e c t o r  f i e l d  of l i n e a r  v e l o c i t i e s  f of t h e  
g a l a c t i c  d i s k  and the  s a t e l l i t e .  On t h e  r a d i u s  r - R hodograph 
of motion has a "k ink"  which is t y p i c a l  of VK-galaxies ( 9 ,  1 0 ) .  
I t  can be s e e n  i n  F i g u r e  1 t h a t  t h e  same g a l a c t i c  s p i r a l  is 
t r a i l i n g  i n  t h e  center p a r t  of the  d i s k ' s  r e g i o n ,  b u t  i n  t h e  main 
p a r t  of t h e .  d i s k  ( d o t t e d )  t h e  s p i r a l  is l e a d i n g .  
0 4  
557 
CONCLUSIONS OF THE THEORY 
Last years' 6-meter telescope observations (7, 8 )  to 
determine the profiles of rotation velocities of the gas disk in 
spiral galaxies have shown that so-called VK-galaxies (with 
velocity kinks on their rotational velocity profiles (9, 10)) "to 
be a rule rather than an exception" ( 8 ) .  So let us assume all 
the three spiral galaxies identified as leading in (5) to belong 
to VK-type. Then according to (lo), the density waves are 
generated in the gas disk in the form of spiral arms 
characterized by the perturbed surface density u as the following 
function T and 4: 
Here we have introduced the following designations: 
2 2 2rGuoi 1 2 -  dPoi 
1 d'oi 
I csi = Cgi 3 Csi - l ~ l ~ g  , R = 
I+? I K I  hg g
, Q E -  , p  3 -  , i =  1,2 . cg2 Q 2  
Ql g2 Ql 
q 3 -  
R is the radius of kink velocity of the gas disk (Figure 11, h is 
its typical thickness; parameters q, Q-I and u characterize the 
558 
relations of values of angular velocities, surface densities, and 
dispersions of gas velocities in exterior region (r>R) to their 
values in interior regions (r<R). 
The augend in curly brackets (I) describes the decrease of 
the perturbed amplitude with radius, the addend -i determines the 
form of the spiral pattern. If the latter is rewritten in the 
form of K r ~  + m4 = const, then 
will correspond to the perturbation (1). 
Let the interior region (r<R) be rotating counter clockwise, 
i.e., Ql > Q. 
which direction the external region (r>R) is rotating: Kr/m>Q, 
i.e., the spiral in the "wave meaning" (5) is trailing - it is 
rotating with its convex side forward. If the main part of the 
disk (including the periphery) is rotating in the opposite 
direction, the spiral will be rotating with its tips forward in 
this region, i.e., it will appear to be leading. 
Then as follows from (21, if q<l no matter in 
559 
CONCLUSION OF THE LABORATORY EXPERIMENT 
In (10) it is proved that with the help of a simple 
redesignation the main dynamic equations of the self-gravitating 
gas disk transform in shallow water equations. It makes possible 
'?,.to use a model "Spiral" with rotating shallow water for modeling 
the generation process of the galaxies' spiral structure (11- 
15). When the periphery was' immovable (n2 = 0, i.e., q = 0) 
density waves were trailing spirals (11-15). It is obvious from 
physics of generation process that if we rotate the periphery 
slowly (no matter in which direction), i.e., if we keep to the 
condition Iql << 1, the form of the spirals will change very 
little. 
At the same time, with respect to the counter-rotating 
periphery (i.e., when q < 0, but as before Iq] << 11, the spiral 
waves will be oriented with their tips forward. The spiral in 
the "wave meaning" (5) will already be leading. Therefore, in 
all the region of the galactic disk, except for a small central 
part, the spiral will be oriented with its concave side in the 
direction of the rotation velocity vector. Without going into 
details, one can say that such a picture is observed in the 
laboratory experiment (13-15) (in detail see (15)). Thus, the 
region of the leading spiral (Figure 1) is wholly determined by 
the "trapped" region of the galactic disk by the tidal wave, 
Let us note in conclusion that it is simple to determine 
from ( 3 )  the angle of the spiral winding (W E arc tan (m/F T I .  
- 
560 
This formula can be experimentally checked substituting the 
parameters of the gas galactic disk by the parameters of the 
rotating shallow water and using (10). In particular, one can 
determine the relation tan a for leading and trailing spirals. 
If, for example, one manages all the parameters (except q sign) 
in both cases to make constant, then the leading spiral. in its 
relation to the trailing one must look more winding, 
because (tan a )  lead/(tan aItr = (1 - Iql)/(l + lql) and if ]a1 
<< 1, this relation = 1-21ql. 
ACKNOWLEDGMENTS 
I express my gratitude to F. A. Tsytsyn, D. A. Werner, and 
A. V. Zasov for useful discussions. 
56 I 
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563 


On leading spiral arms in close pairs of galaxies

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