A statistical criterion has been proposed to reveal the random and physical clusterings among stars, galaxies and other objects. This criterion has been applied to the galaxy triples of the list by Karachentseva, Karaschentsev and Scherbanovsky, and the double galaxies of the list by Dahari where the primary components are the Seyfert galaxies. The confident physical, probable physical, probable optical and confident optical groups have been identified. The limit difference of radial velocities of components for the confident physical multiple galaxies has also been estimated

Anosova, Joanna P.

English

NASA Technical Reports Server

A CLASSIFICATION OF THE GALAXY GROUPS 
Joanna P. Anosova 
Astronomical Observatory 
Leningrad State University 
Bibliotechnaya pl.1 
198904 Leningrad Petrodvorets USSR 
ABSTRACT. A statistical criterion has been proposed to reveal 
the random and physical clusterings amQng stars, galaxies and 
other objects. This criterion has been applied to the galaxy 
triples of the list by Karachentseva, Karaschentsev and 
Scherbanovsky, and the double galaxies of the list by Dahari 
where the primary components are the Seyfert galaxies. The 
confident physical, probable physical, probable optical and 
confident optical groups have been identified. The limit 
difference of radial velocities of components for the confident 
physical multiple galaxies has also been estimated. 
CLASSIFICATION OF GROUPS 
The study of the structure of some class of gravitating 
bodies - the field of the stars or galaxies, as well as the 
simulated field of the N-body systems at some time of their 
evolution - is a search for the subsystems of different nature - 
the groups and the clusters with different numbers of members and 
the various forms, the chains, the voids, etc. It is possible to 
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propose  (Anosova 1986, 1988)  t h e  f o l l o w i n g  c l a s s i f i c a t i o n  of 
g roups  of g r a v i t a t i n g  o b j e c t s  ( s ta rs ,  g a l a x i e s  or t h e i r  g r o u p s l  
c l u s t e r s ,  e tc . )  i n  o r d e r  t o  d e t e c t  t h e s e  g r o u p s  o b j e c t i v e l y :  
( I )  The g roups  i n  which a l l  or a few compoents are by chance  
i n  t h e  g roup  r e g i o n  of t h e  phase  space ;  f o r  t h e s e  g roups  t h e  
c r i t e r i o n  of i so l a t ion  from t h e  background o b j e c t  i n  t h e  phase  
s p a c e  is n o t  f u l f i l l e d ;  one may q u a l i f y  such  g roups  as chance 
g roups  of o b j e c t s  or o p t i c a l  sys t ems ;  
(11) The g roups  which are not  such  chance groups ;  t h e i r  
components have some common f e a t u r e s ;  however, t h e  g r a v i t a t i o n a l  
f o r c e s  between components are small or approx ima te ly  e q u a l  t o  t h e  
r e g u l a r  f o r c e s  of t he  environment;  f o r  t h e s e  g roups  t h e  c r i t e r i o n  
of i so l a t ion  from t h e  background o b j e c t s  i n  t h e  c o o r d i n a t e  s p a c e  
is n o t  f u l f i l l e d ;  one may q u a l i f y  such  g roups  as non-chance 
g r o u p s  of o b j e c t s .  One might  d i v i d e  t h e s e  g roups  i n t o  t w o  
clsses: 
( I I a )  g roups  which are comple t e ly  i s o l a t e d  i n  v e l o c i t y  s p a c e  
( e . g . ,  moving s t a r  c lus te rs ) ;  
( I I b )  g roups  which are p a r t i a l l y  i s o l a t e d  i n  v e l o c i t y  s p a c e  
( e . g . ,  i n  one or t w o  of t h e  v e l o c i t y  components, l i k e  some of t h e  
well-known Eggen 's  k i n e m a t i c a l  g r o u p s ) ;  
(111) the  g roups  f o r  which t h e  cr i ter ia  of i s o l a t i o n  from 
t h e  background o b j e c t s  are f u l f u l l e d  i n  t h e  c o o r d i n a t e  s p a c e ;  i n  
these g roups  t h e  i r r e g u l a r  g r a v i t a t i o n a l  forces between 
components (which are n i n  t o t a l  number) e s s e n t i a l l y  exceed  t h e  
r e g u l a r  forces of t h e  environment;  one may q u a l i f y  such  groups  as 
m u l t i p l e s  w i t h  a p h y s i c a l  c o n n e c t i o n  between components. 
660 
(111-1) the multiple systems in which there is not a 
dynamical connection among all the components or a part of them; 
their total energy is non-negative E > 0. One might also divide 
such systems into two subclasses: 
(111-la) multiple systems in which there is no genetic 
connection among all the components or a part of them: all those 
n objects in a system, which are single, rapidly pass by each 
other or a number s ( s  < n) of single components and subsystems 
inside this system rapidly pass by each other: 
(111-lb) multiple systems in which there is a genetic 
community of components but also there is a 'recession' of 
components (E > 0); e.g., according to the well-known concept of 
Ambartsumian; 
(111-2) the multiples in which there is a dynamical 
connection between components, their total energy is negative E < 
0; one might also divide such systems into two subclasses: 
(III-2a) multiple systems in which there is no genetic 
community inside any part of components: s ( s  < n) of single 
components and subsystems with a smaller multiplicity inside a 
system slowly (E < 0) pass by each other; 
(III-2b) multiples in which there is a genetic community 
amongst all components (a co-formation), such systems may belong 
to one of the two dynamical types: 
(III-I)* dynamically stable multiples; 
(111-II)* dynamically unstable ones. 
' 661 
CRITERIA OF CLASSIFICATION 
In order to recognize the systems of type I - the optical 
systems, or chance groups of objects, among the observed multiple 
stars or galaxies one can use a statistical criterion (see 
Anosova 1987) which consists in obtaining a probability P of this 
system being such one, and in estimating an expectation EX of the 
number of such chance groups in some phase volume e .  One assumes 
for a calculation of P and EX that the objects under study are 
randomly distributed inside the e .  Generally speaking, this 
criteriori may be generalized for every distribution of the phase 
density of objects. If the values P and EX obtained are too 
big ( P  - 1, EX - N/n, where N/n is the maximum number of groups 
with multiplicity n in the volume e ) ,  then this group is a 
probable chance group. Otherwise (P-0 ,  EX $ I), such a group is 
a probable non-chance group of objects and it belongs to the 
multiples of types I1 or 111. 
In order to recognize the groups of types I1 and I11 
impartially one might use an analogous statistical criterion of 
isolation of the groups in the coordinate space. If such a 
criterion is not fulfilled, a group belongs to type 11; 
otherwise, this multiple system is one with components connected 
physically. 
The values Pn and EXn can be expressed as follows: 
'n - 'N-I 
n n-I (I-B)N'n; , EXn = CN B - n-I Bn-I N-n (I - B) 
B= V(u)/V(c), where V ( O )  and V(C) are the volumes of 0 and c ,  u 
662 
is t h e  p h a s e  space, of  t h e  g roup  of m u l t i p l i c i t y  n ,  E is t h e  
phase  s p a c e ,  of t h e  whole sample of  N objects,  N = 
3 (4n/3)R u, r- t h e  r a d i u s  of t h e  s p h e r i c a l  volume E, u-the mean 
number d e n s i t y  of  N objects i n  C .  
When a p p l i e d  t o  g a l a x i e s ,  B h a s  t h e  f o l l o w i n g  form 
where p n  is t h e  a n g u l a r  s e p a r a t i o n  between t h e  g a l a x i e s  n and I; 
rn and rI are t h e i r  l i n e - o f - s i g h t  d i s t a n c e s  ( t h r o u g h o u t  t h i s  
p a p e r  t h e  Hubble c o n s t a n t  H=75 km/s/Mpc is assumed) .  For  
o b t a i n i n g  t h e  maximum estimate f o r  Pn, w e  have t a k e n  R = rI. 
rn > rI, t h e  i n d e x e s  I and n change t h e i r  p o s i t i o n s  by r i n  t h e  
fo rmula  f o r  B. 
I f  
W e  s h a l l  u s e  t h e  above s t a t i s t i c a l  c r i t e r i o n  f o r  a n a l y z i n g  
membership i n  t h e  list of t r iples  by K a r a c h e n t s e v a ,  K a r a c h e n t s e v  
and Scherbanovsky (1979)  and i n  t h e  d o u b l e  g a l a x i e s  of t h e  l ist  
by Dahar i  (1985). T a b l e  I p r e s e n t s  t h e  d i s t r i b u t i o n s  o f  
m u l t i p l e s  N ( E X ) .  T a b l e  I shows t h e  numbers of  t h e  c o n f i d e n t  
p h y s i c a l  ( E X  < 1) and p r o b a b l y  p h y s i c a l  ( E X  < 300) sys t ems  as  
w e l l  as t h e  numbers of t h e  p r o b a b l y  chance  (300 < EX < 1000)  and 
c o n f i d e n t  chance  ( E X  > 1000)  g r o u p s  of  g a l a x i e s .  An i n c r e a s e  of 
t h e  c u t o f f  v a l u e  EXcr = 300 may be caused  by t h e  i n t e r n a l  
d i s p e r s i o n  of v e l o c i t i e s  o f  g a l a x i e s  as w e l l  as by t h e  
u n c e r t a i n t i e s  of  t h e  v a l u e s .  
I 
-, 
One might  a l so  c a l c u l a t e  by u s i n g  t h e  above s t a t i s t i c a l  
c r i t e r i o n  t h e  c u t o f f  d i f f e r e n c e s  Aver of  t h e  r a d i a l  v e l o c i t i e s  o f  
g a l a x i e s  i n s i d e  t h e  c o n f i d e n t  p h y s i c a l  m u l t i p l e s  of  EX < 1, t h e  
663 
T a b l e  1. The d i s t r i b u t i o n s  of t h e  v a l u e s  EX f o r  t h e  triples ( I )  
and t h e  d o u b l e  g a l a x i e s  (11). 
I 10 5 16 1 3  3 3 33 
I1 17 11 7 6 7  3 2 
T a b l e  2. The t o l e r a n t  d i f f e r e n c e s  of t h e  r a d i a l  veloci t ies  of 
g a l a x i e s  i n  t h e  c o n f i d e n t  p h y s i c a l  s y s t e m s  by EX < 1. 
ZD kpc I O  30 50 I 70 
Io-2 1000* 150 60 
2 Io-2 200 20 10 
3 10-2  50 5 2 
4 Io-2 25 2 1 
30 
5 
1 
0.5 
d i f f e r e n t  s e p a r a t i o n s  D between t h e  components and t h e  Hubble 
d i s t a n c e s  cz/Ho. 
d o u b l e  g a l a x i e s :  by t h e  smaller D and Z t h e  v a l u e  Aver = 1000 is 
p o s s i b l e ,  by an i n c r e a s i n g  D and Z t h e  v a l u e s  Aver are s t r o n g  
d e c r e a s i n g .  
T a b l e  2 shows such  r e s u l t s  f o r  t h e  D a h a r i ' s  
CONCLUSION 
A f t e r  c o n s t r u c t i n g  t h e  h i e r a r c h i c a l  s t r u c t u r e  of some f i e l d  
( e . g . ,  Materne 19781, one might  u s e  t h e  above s t a t i s t i c a l  
c r i t e r i o n  i n  order t o  r e c o g n i z e  o b j e c t i v e l y  t h e  subsys t ems  of 
v a r i o u s  n a t u r e  w i t h  d i f f e r e n t  numbers of members and t h e  v a r i o u s  
forms  . 
664 
REFERENCES 
Anosova, J . P .  1986, Astrofizika, 25, 2,297. 
Anosova, J. P. 1987, Astrofizika, 27, 3,535. 
Anosova, J. P. 1988, , 142 , 1-2 , 103 . 
Dahari, 0. 1985, 
Karachentseva, V. E., Karachentsev, I. D., Sherbanovsky, A. L. 
/ 
1979, Izv. Spec. Astrofiz. Obs. , 11, 3. 
Meterne, J. 1978, Astron. Astrophys., 63, 401. 
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A classification of the galaxy groups

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