L~TTV,~ AL NUOVO CItY,TO

VOL. 44, ~. 8

16 Dicembre 1985

Possible Evidence for Gravitational Bohr Orbits in Double Galaxies. ~.

DI~RSARKISSIA:N

Department o/ Physics, Temple University - Philadelphia, PA 19122, U.S.A. (ricevuto il 27 Settembre 1985) PACS. 98.80. - Cosmology.

Summary. - I t is suggested t h a t a double galaxy may be the cosmic analog of a hydrogen atom, in the sense that q u a n t u m mechanics applies to both. An empirica approach is suggested to explore a possible Bohr model for double galaxies and some preliminary calculations are presented. The calculations provide cautious support for gravitational Bohr orbits in double galaxies. I n a previous paper (i), it was suggested that a cosmic version of ordinary q u a n t u m mechanics m a y be responsible for the observed physical properties of galaxies. This intriguing possibility has emerged, because recession velocities for single and double galaxies appear to be quantized (2). If this apparent example of cosmic quantization stands the test-of-time and if it receives independent verification b y several different investigators and with much larger and more representative samples, it m a y be one of the most significant experimental observations in the 20-th century. The idea clearly has the potential for revolutionizing the way astronomers and physicists view the largescale properties of the universe. At the present time, few scientists are aware of the idea and even fewer beheve that cosmic q u a n t u m mechanics really exists, primarily because there is skepticism about a variable Planck's constant. A recent informal worldwide survey (by mail) of 33 physicists and astronomers (including several Nobel Laureates) produced very little enthusiasm for the idea and some skepticism concerning the interpretation of the data reporte~[ in ref. (3). Of course, the survey is not grounds for rejecting the idea, but there is no strong reason (at this time) for the isolated supporters to become over-confident. The purpose of this paper is to apply cosmic q u a n t u m mechanics to an isolated double galaxy, defined as two point masses (m1 and m2) bound together by the Newtonian gravitational force. Let the point masses be separated b y a distance, r, that is small compared to the distance, x, from a galactic observer to the center of mass (COM) of the pair. Let x 1= the distance from the galactic observer to ml; x 2 to m2. By using

(:L) M. DERSARKISSIAN: Left. Nuovo Ctmento, 40, 390 (1984)4 (2) W. TIFFT and W. GOOKE: .dstrophys. J., 287, 492 (1984) and references cited therein.

629

6~0

M. DERSARKISSIAN

t h e i d e a s d e v e l o p e d in ref. (1) a s a g u i d e , t h e e i g e n v a l u e p r o b l e m for t h e H a m i l t o n i a n o p e r a t o r , /~, of t h e d o u b l e g a l a x y h a s t h e f o r m (3) (1)

B ~ ( x l , x~) = s ~ ( x l , x 2 ) ,

w h e r e e : t h e t o t a l n o n r e l a t i v i s t i c e n e r g y of t h e p a i r . I n t h e v a r i a b l e s (x, r ) , it is t h e n a straightforward matter to show that the form of/~, which contains the results derived i n ref. (1) for a n e q u i v a l e n t p o i n t m a s s M = m 1 - t m2 ' is g i v e n b y

M H2 ~2]

w h e r e f~ = t h e r e d u c e d m a s s = m l m 2 / ( m ~ ~- m2), V o = - - Gmlm2/r = t h e g r a v i t a t i o n a l potential energy (with G = the Newtonian gravitational constant), H o = the Hubble p a r a m e t e r e v a l u a t e d a t t h e p r e s e n t c o s m i c t i m e ( = to) a n d g i v e n t h e s a m e v a l u e (4) as in ref. (1): H o = 50 k m / s / M p c , i~ = t h e l i n e a r m o m e n t u m o p e r a t o r f o r # a n d P = t h e s a m e f o r 3i. B y s e p a r a t i o n of v a r i a b l e s , eq. (1) r e d u c e s t o t w o e q u a t i o n s : 1) ]or the C 0 M

motion:

M 2^2~

( ~ M @ ~ H o x ~ ~p(x) = ecoM~P(x) .

(3)

T h e o n e - d i m e n s i o n a l v e r s i o n of cq. (3) w a s s o l v e d i n ref. (1). I t y i e l d s a q u a n t i z e d k i n e t i c e n e r g y of r e c e s s i o n for t h e p a i r , as w e l l as q u a n t i z e d v e l o c i t y , m o m e n t u m a n d r e d - s h i f t (since t h e y a r e c l o s e l y r e l a t e d ) . 2) /or the internal motion:

(p2/2u + l?o)q~(r ) = e i ~ ( r ) .

(4)

T h e s o l u t i o n of eq. (4) is f o r m a l l y i d e n t i c a l t o t h e e i g e n v a l u e p r o b l e m f o r t h e h y d r o g e n a t o m in o r d i n a r y q u a n t u m m e c h a n i c s . I t l e a d s to q n a n t i z e d e n e r g y l e v e l s (e~~)) a n d o r b i t a l r a d f i ( r . ) :

]or the energy levels: (5)

~>=

- ~ (/~e ~) ~2,(~/n ~) ,

w h e r e e = t h e s p e e d of l i g h t , n = a p o s i t i v e i n t e g e r , % = Gm~mJ(hge) = t h e g r a v i t a t i o n a t f i n e - s t r u c t u r e c o n s t a n t a n d ~---- t h e c o s m i c P l a n e k ' s c o n s t a n t / 2 z ~ 7.1074 e r g (s) ( t h e

(3) The large-scale properties of the Universe are very nearly * static ,), thereby providing justification for the quantum description of a double galaxy as approximately in a ~ stationary state *. It is, therefore, plausible to construct and to solve the time-independent eigenvalues problem for the operator, _/~r, as an approximate description of the quantum state of an equivalent point mass trapped in the Hubble expansion. The same idea was used in ref. (1). (4) Los ttouches Leclures (1979: Sessionc X X X I I ) : Physical Cosmology, edited by 1%. BAI,IAN, J. AxSDOXTZ~.and D. Scm~A~IM (Amsterdam, 1980), p. 117 (in the review article by G. TAMMANN, •. SAND2~GE and A. YAmL: The determination o] cosmological parameters).

POSSIBLE E V I D E N C E FOR G R A V I T A T I O N A L BOHR ORBITS I N D O U B L E GALAXIES

631

cosmic analog of the ordinary h). A numerical benchmark for the ground-state energy of a ((typical)~pair c a n b e calculated by taking m l = m 2 ~ 1044g ( ~ the mass of the Milky Way). Then e~1) ~ -- 1056 erg. The lifetime for excited states can be estimated b y generalizing the u n c e r t a i n t y principle developed in ref. (1) to include energy (AE) and time (At): i.e. (AE)(At)~hJ2. If (AE) is approximated as the energy difference between the ground state and the first excited state ( ~ le~)[), then (At) ~ 2.1011 y. The excited state has a lifetime ~ 10 x (the age of the Universe), as estimated using the standard cosmological model (5). Therefore, if a double galaxy is formed in an excited state (or if it somehow reaches one after birth), it remains in that state for its entire existence. The (~( = h~v) is monochromatic gravitational radiation initially. It must somehow be converted to a spectrum of electromagnetic radiation, which is then emitted during the lifetime of the double galaxy. The conversion mechanism may possibly be related to gravitational collapse in the galactic nuclei of the pair. Since hg is so large, it is plausible to expect radio wave emission to dominate, just as visible light dominates the emission spectrum of excited atoms (because h is so small). This consideration leads to two interesting possibilities which have not been considered (to m y knowledge). a) Double galaxies m a y be strong radio sources, compared to singles. Preliminary evidence (e) supports this idea. I t was shown for a sample of isolated galaxies (37) and isolated doubles (47), virtually all of them being spirals, that compact radio sources occurred four times more frequently in doubles t h a n in singles. There was also a higher occurrence of strong radio emission from doubles compared to singles, with (on the average) a greater power output in doubles associated with the more frequent occurrence of active galactic nuclei in their components, iklthough these results are encouraging, they are not definitive, because of the small sample size and of other possible selection biases. b) Some radio-active quasars m a y be cleverly disguised double galaxies in highly excited q u a n t u m states and at an early stage of evolution. Preliminary evidence suggests there may be localized radio sources inside some quasars, b u t better telescope resolution may be required to test the idea. However, there is some cause for cautious optimism. A rough estimate of the quasar's average power output in this model is of an acceptable order of magnitude, providing the mass of a (~typical ~ component is taken as m l = m 2 ~ 104Sgr and the average time of existence is ~ 109y: i.e. ~ e ~ (~(Z~) - - e(~l))/V ~ 104e erg/s ~ 1013j50, where L 0 = the Sun's luminosity. ~or

the orbital r a d i i ( a s s u m e d circular):

(6) A numerical benchmark for the ground-state radius of a ~ typical ,~ double galaxy follows from m l = m 2 ~ 1044gr. Then r 1 ~ 1.4.1025 cm ~ 1.4. l0 TLy ~ (140) • (the diameter of the Milky W a y disk). Equation (6) is explored in more detail later. The solution of eq. (4) also leads to quantization of the orbital angular moment u m of a double galaxy and its z-component (in units of h~). There does not appear to be any evidence to support or to reject this prediction at this time. When ordinary q u a n t u m mechanics is applied to problems in particle physics, all angular momenta

S. WEINBERG: (gravitation and Gosmology (John Wiley and Sons, New York, N.Y., 1972). (6) G, TOVMASYAN:Astrophys., 18, 14 (1982) and references cite4 therein (translated from Astro/izika).

(5)

632

M. D]~I~SAI~KISSIAN

are q u a n t i z e d : orbital, intrinsic (<~spin ~>) and total. This fact suggests an i n t e r e s t i n g possibility for galaxies t h a t has not been considered (to m y knowledge): t h a t galactic spin m a y also be quantized. E x p e r i m e n t M d a t a is f r a g m e n t a r y and subject to subs t a n t i a l errors. Nevertheless, one positive n o t e emerges (7): the spin of t h e Milky W a y and of A n d r o m e d a (M31) are consistent w i t h the assignment: s , = ~ / 2 . The available e x p e r i m e n t a l evidence also appears to support the idea t h a t ( S 0 ) - t y p e galaxies and spirals possess similar a m o u n t s of spin (s), suggesting t h a t alla spiral galaxies / t r e a t e d as e q u i v a l e n t p o i n t particles) m a y be spin-~- fermions, in t h e same sense as e l e m e n t a r y particles. This issue m a y h a v e bearing on galactic clustering, because of the connection b e t w e e n spin and statistics. I n this c o n t e x t , n o t e t h a t clusteriDg is a well-known p r o p e r t y of o r d i n a r y q u a n t u m mechanics: i.e., quarks <~cluster >> into h a d r o n s ; n e u t r o n s and protons <,cluster ,> into nuclei; electrons <~cluster ,> into atoms. M a n y (if not all) observed properties of galaxies m a y simply be c l e v e r l y disguised reflections of cosmic q u a n t u m mechanics. Only t i m e will tell. F o r now, it seems approp r i a t e to briefly raise some of t h e n e w ideas in this paper, w i t h m o r e details to be r e p o r t e d elsewhere. There are two issues which require emphasis before exploring eq. (6). 1) Ref. (~), and the ideas p r e s e n t e d in this paper, b o t h adhere to the <,Principle of E c o n o m y ~>, so e v i d e n t in v i r t u a l l y e v e r y successful theory. N a t u r e appears to cons i s t e n t l y exploit economical forms for p h y s i c a l theories, always interlocking t h e m as l i m i t i n g cases. Therefore, if q u a n t u m mechanics is really a variable-h theory, t h e <~Principle of E c o n o m y ~>suggests t h a t t h e cosmic and o r d i n a r y forms should b o t h flow f r o m t h e same formal s t r u c t u r e and from the same basic equations. One nonrelativistic, variable-h q u a n t u m t h e o r y which satisfies the principle was r e c e n t l y p r o p o s e d b y KAPVgcIx (9). I n his theory, h~ and h m u s t be n u m e r i c a l l y related. One possible relationship was r e c e n t l y derived in the form (10): hg/h ~ (mJmr~) ~-, where ~ = the pion mass and ms = the mass of a typical spiral galaxy. The d e r i v a t i o n exploits the idea (suggested earlier) t h a t galaxies m a y be the <~elementary particles >> of cosmology. 2) An a l t e r n a t i v e form of cosmic q u a n t u m mechanics was suggested i n d e p e n d e n t l y b y Coc~>~ (~). This m o d e l deviates f r o m the <~Principle of E c o n o m y ~>, b y r e q u i r i n g a t w o - c o m p o n e n t spinor formalism. O r d i n a r y q u a n t u m mechanics has no need for such c o m p l e x i t y at the nonrelativistic level. The need for spinors p r e s u m a b l y arises as an a p p r o p r i a t e relativistic generalization (as is the case in o r d i n a r y q u a n t u m mechanics). The m o d e l quantizes the red-shift b y i n v e n t i n g a (, red-shift o p e r a t o r >>( = 2,), assumed to be p r o p o r t i o n a l to the linear m o m e n t u m o p e r a t o r for an e q u i v a l e n t p o i n t galaxy. B y contrast, ref. (~) quantizes the kinetic e n e r g y b y using a plausible f o r m for the wellestablished k i n e t i c - e n e r g y operator. B o t h physical q u a n t i t i e s are closely r e l a t e d and b o t h m a y be considered observables for an e q u i v a l e n t p o i n t galaxy. The red-shift j u s t h a p p e n s to be easier to m e a s u r e d i r e c t l y at this time. The kinetic energy is measu r e d i n d i r e c t l y at this time, b u t the possibility of direct m e a s u r e m e n t does n o t appear to be r u l e d out (in principle).

Carg~se Lectures in Physics, edited by E. SCnATZ~IA.N ~ (Gordon and Breach, New York, N.Y., 1973), p. 581 (in the review article by E. HARRISON: Galaxy formation and the early Universe). (s) F. BERTOLA and 5I. CAPACCIOLI:AMrophys. J., 219, 404 (1978). (9) E. KAPU~CIK: The .\'ewtonian form of wave mechanics, Institute of Nuclear Physics (Krak6w, Poland), prcprint No. NR-1260/PL (October, 1984). (lo) ~J[. DERSARKISSIAN:Left. Nuovo Cimenlo, 43, 274 (1985). (11) W. COCKE: Ast~ophys. tell., 23, 739 (1983). I thank Dr. COGKE for bringing his work to my attention. The qnantnm properties of double galaxies were not considered in his paper. (7)

POSSIBLE EVIDEIVCE FOR G R A V I T A T I O N A L BOI-LR ORBITS I N D O U B L E GALAXIES

6~

The above comments represent i m p o r t a n t , b u t essentially cosmetic, differences between the two models. A substantive difference emerges b y considering the predictions of both models for the velocity spacing between adjacent quantum states of recession (Av) = (vm+1 - vm). Reference (1) predicts a (Av) proportional to 1/(m)89for large (m). I n ref. (n), the eigenvalue problem for the kinetic-energy operator is essentially equivalent to the eigenvalue problem for the operator (2) 2. The resulting eigenvalues are (zm)2, proportional to (m). The large (m) behaviour of (Av) is, therefore, also proportional to 1/(m)t. However, the model then invokes the ~(red-shift combination principle ~), which does not flow from the spinor formalism for equivalent point galaxies, but is a subsidiary assumption designed to exclude certain red-shift states and to achieve the results: (Av)---- constant. (This principle m a y also be invoked in conjunction with ref. (1) to achieve the same results.) The v a l i d i t y of the result, (Av) = constant, depends on the basic assumptions built into the red-shift combination principle. F r o m p. 241 in ref. (n), the following s t a t e m e n t m a y be found: (~If red-shift are observed to be quantized, it is easy to demonstrate a simple relation t h a t the quantization rule must satisfy, provided we require all galaxy observers use the same quantization rule ~). The simple relation is the red-shift combination principle. I t appears to follow only with the above-underlined constraint. F o r all g a l a x y observers to use the same quantization rule, t h e y m a s t agree on the general form of the fundamental equations for cosmic quantum mechanics: i.e., the fundamental equations must be covariant under the group of co-ordinate transformations which links galaxy observers. F o r nonrelativistic cosmic quantum mechanics in flat space, it is reasonable to require eovariance under Galilean transformations. The spinor formulation of cosmic quantum mechanics does not appear to satisfy this requirement, The fundamental equation in ref. (1) is the Sehrhdinger wave equation, which is well-known to be covariant under Galilean transformations. Therefore, (Av) = constant does not appear to be valid in conjunction with ref. (n), but it m a y be valid in conjunction with ref. (1)--providing conclusive experimental evidence justified its use. I t was emphasizes in ref. (~), based on general considerations, t h a t (Av) appears to decrease for sufficiently large (m): i.e., for the relativistic domain, where essentially no d a t a for single or double galaxies is available at this time. The relativistic form of cosmic quantum mechanics for point galaxies must also be constructed with other constraints: it must be eovariant under Lorentz transformations and it must lead to quantization of recession velocities for single and double galaxies. The problem of galactic spin (and its possible quantization) then becomes an i m p o r t a n t issue. F o r a spin (89 0) point galaxy, a (Dirac; Klein-Gordon) equation appears to be inevitable. One startling possible consequence is t h a t the early universe m a y have been symmetric in galaxies and anti-galaxies. Equation (6) m a y be considered an empirical equation, potentially relevant to doubleg a l a x y dynamics and one w a y to evaluate h, using experimental data. Both h~ and h are assumed to be universal constants, with numerical values determined b y the distance scale on which quantum effects are observed. The credibility o] ordinary quantum mechanics rests largely in the observation that all experimental methods used to calculate h give consistent and extremely accurate numerical values. In this connection, ordinary quantum mechanics has the distinct edge, since the experimental d a t a is extensive, accurate and available in a wide variety of experiments. The situation for cosmic quantum mechanics is awkward. Not only is the experimental d a t a sparse and fragmentary, it also contains large experimental uncertainties and is subject to ambiguous statistical interpretation inherent in relatively small and unrepresentative samples. The double galaxy is probably the most common galactic cluster; there arc probably

634

M. DERSARKISSIAN

hundreds of millions of them in the universe. The samples cataloged and studied by various investigators represent an infinitesimal fraction, with all pairs relatively close to thc ]~'Iilky Way. Under these conditions, it is only possible to calculate h~ approximately. This program wa~ initiated in ref. (~) with the result : hz = 7.10 7~ erg(s). Approximately the same value was found to be compatible with the requirements of the cosmic uncertainty principle (ref. (~)) and also produced a decent estimate for the mass of a typical spiral galaxy (ref. (10)). 0 n e purpose of this paper is to outline a procedure which may provide a preliminary, independent estimate of h~ using eq. (6) and the data available for m~, m~ and r~. The form of eq. (6) appears to be compatible with some of the alleged properties of double galaxies reported in the published astronomical literature (~o). However, it must be considered a first-order approximation at this time, since the possible effects of some parameters on the Bohr model are not included in this preliminary study: e.g,, galactic structure for the componc~lts ((~ morphology ,>); location in clusters (isolated or not?); ... etc. A more useful form of eq. (6) is obtained by using Hubble's law (with routine geometry) and by introducing statistical complications (due to the assumed random orientation of the plane of the pair). Equation (6) then becomes (7)

(n~g) 2 :

((~)~*~1~2//)(~(~r) V r e c / ( 2 S 0) ,

where ~ = the angular separation between m~ and m2, Vr~r the recession velocity for the COb{ of the pair and ~r(= 2.2) is the average radial projection factor suggested by P~:T~.:eSO> (1~). A search of the published astronomical literature revealed only two sets of data (~a~,b) which may be used in conjunction with equation (7). Although the data may contain a selection bias (favouring spiral pairs and a total number of pairs = 17), it gives calculated values for h~ with the proper order-of-magnitude (see tables I and II). With h~ = 7.1074 erg(s), the data suggests that pairs may exist primarily in low states of excitation. For ]i~ = 2.107a erg(s), as suggested in ref. (1,), pairs may exist primarily in somewhat higher excited states. I n both cases, there appears to be a systematic increase in the degree of excitation with total pair mass. These preliminary results give cause for cautious optimism: that the trends for (n, h~) may continue as the sample is enlarged and as the possible selection bias slowly disappears. I n this connection, one pair was omitted from table I and two from table II, because a m i n i m u m mass limit (estimated below) probably exists for m 1 and m 2 iu order to form a stable double galaxy. The minimum mass would probably be determined by the condition that the gravitationl binding energy cannot get too small for fixed radius. Otherwise, the components may be separated in competition between neighboring superclusters and the double galaxy would be destroyed. If the components get too close for fixed mass, the pair may coalesce into a single galaxy. A crude static model for estimating the m i n i m u m mass for a pair

(12) a) S. PETERSON: _4slrophys. J . , 232, 20 (1979); A s t r o p h y s . J . S u p P l . S e t . , 40, 527 (1979); b) i. I(ARACttENTSEV: ~dslrophysies, 17 (1981): P a r t . I, p. 135; P a r t I I , p. 238; P a r t I I I , p. 363; P a r t IV, p. 375 ( t r a n s l a t e d f r o m Astrofizikr c) XV. TIFFT: J s l r o p h y s . J . S u p p l . S e t . , 50, 319 (1982); el) S. \VHITE, J. HUCHRA, D. LATlt-X)~ a n d M. DAVIS: Moil. Not. R. Aslron. Soc., 203, 701 (1983). e) F o r a c o m p r e h e n s i v e r e v i e w of tile m a s s e s a n d m a s s / l i g h t r a t i o s for d o u b l e g a l a x i e s s t u d i e d p r i o r to 1979, see S. FABER a n d J. GALLAGHER: A~I~U. t-:eL'. Astron. A s l r o p h y s . , 17, 135 (1979). (~) (t) J. DICKEL a n 4 H . ROOD: Aslror~. J . , 85, 1003 (1980); b) G. VAN MOORSEL: Astrore..Astrophys. S u p p l . Ser.: P a r t I, 53, 271 (1983); P a r t I I , 53, 287 (1983); P a r t I I I , 54, 1 (1983); P a r t I V , 54, 19 (1983); c) this c o n s t r a i n t w a s n o t u s e d to e l i m i n a t e a n y p a i r s in t a b l e s I a n d I I . One o b v i o u s m a s s l i m i t is t h e m a s s of t h e c l u s t e r in w h i c h t h e d o u b l e g a l a x y is e m b e d d e d , a s s u m i n g all p a i r s a r e a s s o c i a t e d w i t h clusters.

POSSIBLE

EVIDENCE

FOR

GRAVITATIONAL

BOliR:t O R B I T S

IN DOUBLE

~35

GALAXIES

in its g r o u n d s t a t e i n v o l v e s l o c a t i n g it m i d w a y b e t w e e n t w o s p h e r i c a l s u p e r c l u s t e r s w i t h i d e n t i c a l m a s s e s (Ms) a n d r a d i i (R). E q u a l i t y of t h e c o m p e t i n g g r a v i t a t i o n a l p o t e n t i a l s t h e n leads t o t h e m a s s c o n s t r a i n t (with b = m J m l > l ) : m~= rlMdbR = ~-h2~(1 q - b ) M J G b 3 R . W i t h 21/8= 1015Mo a n d /~ = 1 0 0 M p c ( t a k e n for t h e local s u p e r e l u s t e r ) a n d b = 3 ( t a k e n f r o m t h e a v e r a g e in t a b l e s I a n d II), a simple calculat i o n gives: ml--~ 1011MG. To d e s t r o y t h e d o u b l e g a l a x y w o u l d p r o b a b l y r e q u i r e a s o m e w h a t s m a l l e r m a s s , w i t h a p l a u s i b l e e s t i m a t e b e i n g ml/lO = 10~~ o . A m a x i m u m m a s s (18r p r o b a b l y also exists for a s t a b l e pair. Otherwise, t h e p a i r m a y d e s t r o y TABLE I.

-

-

The Rood/Dickel data ]or double Galaxies.

Double Galaxy

a (rad)

Vr~o (km/s)

m I a n d m2 ( M o )

r . (Mpc)

n?~ (erg(s))

NGC-3454 NGC-3455 NGC-4294 NGC-4299 NGC-3991 NGC-3992 NGC-5774 NG0-5775 NGC-7537 NGC-7541 NGC-770 NGC-772

1,08" 10 -3

1110

0.026

0.44" 1074

1.65" 10-3

301

0.011

0.16' 107~

1.1 9 10 -3

3225

1,25" 10-3

1619

0.90" 10 -3

2683

1.05" 10 -3

2434

3.9" 101~ 5.2" 101~ 1.4" 101~ 8.8" 10 l~ 25.9" 101~ 34.2" 101~ 22.3" 10 l~ 42.3" 10 l~ 34.3" 101~ 100.2" 101~ 55.2" 101~ 132 910 l~

0.078

13

91074

0.044

10

91074

0.053

28

9 1074

0.053

51

9 1074

TABLE II. - The Van Moorsel data ]or double Galaxies. (!Y~pe)

nh~ (erg(s))

Double Galaxy

~ (rad)

Vr~c (km/s)

m I a n d m2 ( M o )

r n

UGC-6542 UGC-6528 NGC-3504 NGC-3512 NGC-4085 NGC-4088 UGC- 625 UGC- 622 UGC-9347 UGC-9361 NGC-4016 NGC-4017 NGC-5289 NGC-5290 UGC- 725 UGC- 728 NGC-3958 NGC-3963 UGC-3809 UGC-3834 NGC- 797 NGC- 801

2.21' 10-3

3293

0.160

0.36" 1074

3.49" 10 -3

1459

0.112

0.28" 1074

3.35" 10 -3

756

0.058

0.28" 1074

5.67- 10 -3

2662

0.332

1.7 9 1074

2.82" 10 -3

2231

0.138

1.4 9 7474

1.69- 10 -3

3442

0.128

0.94" 1074

3.69' 10 -3

2548

0.207

3.2 9 10 ~4

3.28' 10 -3

4974

0.359

4.7 9 10:4

2.42' 10 -3

3270

0.174

4

5.87" 10 -3

2119

0.274

5.6 9 1074

2.65" l 0 -3

5714

2.7" 10 l~ 1.7' l01~ 1 9 10 l~ 5 9 10 l~ 1.3" 101~ 6.0" 10 l~ 9.8" 101~ 2.6" 101~ 3.2" 10 l~ 10.6" 101~ 1.7- 101~ 16 910 l~ 6.4- 10 l~ 11.5- 101~ 8.3' 101~ 10 "101~ 12 9101~ 9 9101~ 31 .101~ 5.1" 101~ 40 - 10 TM 28 "101~

0.333

32

9 1074

9 10 ~a

636

~r

DERSARKISSIAN

itself b y t i d a l d i s t r u p t i o n a n d m a s s a c c r e t i o n or b y coalescence. I f t h e g a l a x i e s are too far a p a r t ( w i t h l a r g e masses), t h e y m a y couple to o t h e r g a l a x i e s to f o r m s m a l l clusters, a g a i n effectively d e s t r o y i n g t h e pair. 5iass l i m i t s for p a i r s were n o t c o n s i d e r e d in selccting s a m p l e s in ref. (12). T h i s f a c t m a y r e p r e s e n t a serious bias w h i c h m a y d i s t o r t t h e conclusions d r a w n f r o m e a c h analysis. O t h e r selection biases a p p e a r to b e m o r e e v i d e n t , i n c l u d i n g : t h e likely p r e s e n c e of a n u n k n o w n n u m b e r of s p u r i o u s p a i r s ; t h e m o r p h o l o g i c a l m a k e - u p of p a i r s ( w h i c h a p p e a r s t o f a v o r spiral g a l a x i e s ) ; t h e selection of p a i r s p r i m a r i l y w i t h n o n r e l a t i v i s t i c recession v e l o c i t i e s ; ... etc. One e x p e c t s d o u b l e g a l a x i e s to r a p i d l y i n c r c a s e i n n u m b e r d e n s i t y in t h e r e l a t i v i s t i c d o m a i n : i.e., for large ( ~ ) , w h e r e e s s e n t i a l l y no d a t a is c u r r e n t l y a v a i l a b l e . T h e correct w a y to s i m u l a t e q u a n t u m r e l a t i v i s t i c effects i n a n e s s e n t i a l l y n o n r e l a t i v i s t i e s a m p l e is n o t k n o w n . T h e s e c o n s i d e r a t i o n s s u g g e s t i t is p r e m a t u r e t o d r a w r e l i a b l e g l o b a l conclusions (") a b o u t t h e v e l o c i t y s p ~ c i n g (Av) for single a n d d o u b l e g a l a x i e s or to h a v e reliable confidence i n all t h e alleged p r o p e r t i e s of singles a n d d o u b l e s s u g g e s t e d i n ref. (%~2). T h e s e p a p e r s , a l t h o u g h h i s t o r i c a l l y significant, s h o u l d b e i n t e r p r e t e d n o w as t e n t a t i v e first s t e p s in u n d e r s t a n d i n g t h e c o m p l e x p r o p e r t i e s of galaxies. T h e s a m e s t a t e m e n t applies to ref. (~) a n d to t h i s p a p e r . T h e r e are s e v e r a l a n a l y s e s for s a m p l e s (~4) of d o u b l e g a l a x i e s w h i c h are alleged to be free f r o m selection bias. U n f o r t u n a t e l y , t h e e x p e r i m e n t a l d a t a o n l y p e r m i t s a calc u l a t i o n of t h e t o t a l p a i r m a s s ( = ~]/), w i t h s e v e r a l u n d e s i r a b l e c o n s t r a i u t s , i n c l u d i n g : t h e c o m p o n e n t m a s s e s m u s t be e q u a l (m l = m2); t h e c a l c u l a t i o n of M c o n t a i n s t h e u s u a l a m b i g u i t i e s a s s o c i a t e d w i t h v e l o c i t y a n d r a d i a l p r o j e c t i o n f a c t o r s ; ... etc. T h e s e c o n s t r a i n t s a d d t h o r n y p r o b l e m s for t h i s k i n d of d a t a u s e d in c o n j u n c t i o n w i t h eq. (7). N e v e r t h e l e s s , c a l c u l a t i o n s of ]i: m a y still b e of v a l u e , since t h e s a m p l e s p r o b a b l y c o n t M n less selection b i a s t h a n t h e s a m p l e s in t a b l e s I a n d I I a n d t h e e q u a l - m a s s cons t r a i n t m a y b e b a r e l y t o l e r a b l e . F o r t h e s e l a r g e r s a m p l e s , t h e r e is also t h e i n t e r e s t i n g p o s s i b i l i t y for a n e w c a t a l o g of d o u b l e g a l a x i e s in f a m i l i e s w i t h fixed (n), t h e d e g r e e of e x c i t a t i o n . T h e s e a r c h for c o r r e l a t i o n s in t h e s e families, a l o n g w i t h {t~ c a l c u l a t i o n s for p a i r s in e a c h s a m p l e , ~,-ill b e r e p o r t e d s e p a r a t e l y .

I a m i n d e b t e d to Dr. J. C h o w , w h o (as C h a i r m a n of t h e P h y s i c s D e p a r t m e n t ) m a d e i t possible for m e to t e a c h q u a n t u m m e c h a n i c s a t t h e s~me t i m e I was e x p l o r i n g prob l e m s in cosmology. T h e ideas p r e s e n t e d h e r e b e g a n to c r y s t a l l i z e d u r i n g t h a t period. T h i s w o r k r e c e i v e d p a r t i a l s u p p o r t f r o m a F a c u l t y R e s e a r c h F e l l o w s h i p , a w a r d c d to m e b y T e m p l e U n i v e r s i t y for S u m m e r , 1983.

(14) See ref. (12). For circular orbits, M = 32 (AV)~(X)/(3,nG), where X = the projected separation of the pair and ( A v ) = the differcncc in the recession velocities. A reliable value for ~I requires an accm.ate value for (AV), since it is squared. Since (Av) is independent of the choice of co-ordinates, there is no chance for confusion when comparing data compiled by different authors. Unfortunately, different authors (15) frcqucntly give radically different experimental values for (Av) for the same pair. The result is wild differences in the calculated value for ~1I. This problem is just one of several associated with this method for calculating ~: using data taken from ref. (1,) in conjunction ~'ith eq. (7). (1~) For example: compare the pairs in ref. (1~r with the corresponding pairs used by K:AEACttl~NT" SEV et al. in Astron. Astrophys., 41. 375 (1975) or by ]~ARACHENTSEV in ref. (**~).