The observed relationship between mass-luminosity ratios for groups and clusters of galaxies and their population is interpreted on basis of a model developed by the author (1968) in which unstable groups of galaxies are thought to be the result of the fragmentation of a parent galaxy.Asociación Argentina de Astronomí

Sérsic, J.L.

English

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42
A S?ECTROSCO?TC ANALYSIS OF PECULIAR STARS 
IV. THE STRONTIUM GROUP 
M. Jaschek and Estela Brandi 
(Observatorio Astronomico, La Plata)
About 1500 lines of the Ap strontium star HR 710 were identi­
fied on a Coudé plate having a dispersion of 4,5 A/mr ”he^behavior 
of the different elements is analysed, specially of those at the 
iron peak. It is concluded that this star is very similar to the 
Am stars.
The paper in full will be published elsewhere.
OBSERVATIONS OF LUNAR OCCULTATIONS OF THE GALACTIC CENTER REGION 
IN THE OK AND HYDROGEN LINES 
F. Kerr
(University of .Maryland, Dpt. of Physics pTnd Astronomy])
A series of lunar occultations oÿ' the galactic center region 
is being observed with the 140 foot telescope at Green Bank, West 
Virginia. In line observations, main interest lies in the/ fine
structure of the absorbing clouds of OH or HI in front of the con­
tinuum sources near thô center.
The +40 km/sec component of the OH absorption spectrum Is 
found _to originate in a cloud of dimensions 3' x 5', which appears 
to rotate as a uniform body. Internal structure has been detected 
in the -130 km/sec component of the order of 30”. The results for 
the 1665 and 1567 MHz lines are significantly different.
This paper has now been published in Astrophysical Letters,
2, 195 - 200 C1968T.
( + )UNSTABLE OF GALAXIES
mêr sic
(Observatorid JHMpanémico de Cérdoba)
Abstract: The observed reletdiemihip between mass-luminbpity ratios 
for groups and clusters of galaxies and their population is inter­
♦3
preted on basis of a model developed by the author (1968) in which 
unstable groups of galaxies are thought to be the result of the 
fragmentation of a parent galaxv.
1- In a former paper (S^rsic, 1968=paper I, henceforth) we have de 
veloped a model for galaxv formati^on through fragmentation of giant 
ellipticals. We shall give here a restricted formulation of the 
model which seems to fit the observed properties of groups and 
clusters of galaxies.
Let us recall the (relationship of paper T,
T.^ = + T^+ uc'^ - (d^J/dt^)
where and the T^’s are respectivelv the kinetic energies of
the parent galaxv prior to the explosive event, the fragments after
2the explosive event, and the svstem of fragments, uc is the ener­
gy radiated when the nucleus of the parent galaxv collapses and J 
the moment of inertia of the svstem of fragments. We shall assume 
that the svstem of fragments is unstable, so that (see the Appen­
dix) d^J/dt^ = c^ w.
With the above hypothesis we readily have for the specific 
energies,
T /M = T/M + T,/M o o 1 o
after introducing the average values of the Tj^s and M^s through 
nT = r and nM =XM^, n being the number of fragments.
For we have the relationship
T^/M^ = l/2(p - 1/2(W^/M^)
where W^ is the potential energy of the svstem of fragments. The 
assumed relation J" = yc implies the expansion of the system or 
fragments. After a tim.e considerably lonper than the dynamical
time-scale of the parent system, -W. «vriD become much smaller than
2 2 . ^ . 
p c and = 1/2 p c will be a good approximation.
Eq, (4) of paper I is written now
^ 2 . , ^.2 21 - s = 1/nr + h r
O O
where s ~ 1/2 pc R /M , and 1/m = n = M^/M is the number of frag- o o o
ments resulting from the violent event, s means the expansion rate 
(+) With the support of the Consejo Nacional de Investigaciones, 
Argentina,
'f the unst.^ble Proup frapr^erts lonp tir^c' a*"ter the explosion,
i-ven in units of the velocity’ e’isoersion 6 of the uarento o
palaxv- Exanession (1) relates to fhp proua aopu.la'^ion n and
the averape affective radfus r o^' their oa] axn es. v?e assur.e a
ra X irrur jossihie rate of exaans'r; ■•■hat ds'^/dt ' o, v;e find
= 1 - 3(h/2n) 2/3
ecause the effective radius at the ^ax'oun is related to the prouD
3 2hopujation throuph r^ = l/2h'n. '’’e see now that in this model the 
expansion rate onlv deaervjs on n.
Tt is customarv to estimate the masses of proups of palaxies 
throuPh the virial theorem, assuminp their steadv state. The masses 
calculated in that wav are exapperated, and it is a matter of dis­
cussion whether this is so because extra matter is not considered 
or because the assurjption fora steadv state fails.
Let us write M'’ for the total mass of a eroup of palaxies 
computed throuph the vir'al theorem and he the radius of the 
svstem, A a numerical factor and o the pravitational constant. We 
then have
= (A/G) = (A/G) aj t
where is the velocity dispersion of the proup of palaxies and t 
'he time elapsed since the explosive event. Now, as in paper I,
X. = s a and takinp k = 1/2 for the sake of claritv, we pet
MO = (ao^/G) (1 - 3/4 n
the biased mass derived from the virial theorem.
Let f = N /L be now the true averape mass-luminositv ratio o
"he proup, and f° the same ratio, but derived with the biased
. We have then
f° = f.< o /P )(1 - 3/4 o o
o
‘■ecallinp that ^ = (A/G) o P is the mass of the parent palaxv.o o o .
Tntroducinp now the dvnamical time-scale t = P^/ of the parent 
palaxv, finally results
fo = f(l - 3/4 n"^''^)^^^.(t/T ) 
an expression that evidences tn.e dependence of f” on the popula­
tion n and the ape t of the proup of i^rapments.
45
Figure 1 has been borrowed from a paper of I,D. Karachtensev
(1966) wliere the mass-luminos)j.tv ratios for several groups and
clusters are discussed. We have adapted to the figure a pair of
curves computed with the above :relationshipi which gives a reasona
ble good fit of the points in the diagram. If we assume an age of 
1010 years for the Metagalaxy, we find that small groups with 3-30
9members should be; only 2,5 x 10 years old. A similar diagram due
to T.L. Page (1965) is given in figure 2.
The discussion of equation (1) in paper I showed galaxies with
small r should be ellipticals because the angular momentum per 
. ■ 2 .unit of mass hr is a fortiori very small. This conclusion allow 
us to arrive at another, regarding the dominant type of galaxy 
in a group or cluster. In fact, the larger n is, the smaller will 
be rj^ = 1/2 h n in case of efficient expansion, and the average 
galaxy must be of early type. So we would expect large clusters to 
be populated'mainly by E-SO galaxies and be of a regular spherical 
structure because the high value of s (— 1) would not allow for
i . *
large statistical fluctuations in the velocitv d: sion. A less 
efficient expansion will probably broaden the spectrum of galaxian 
types, but then s will be smaller, statistical fluctuations will 
become important and the cluster will loose its regular structure. 
We think this is'the case for large clusters and clouds containing 
many spirals and irregular galaxies.
To end, we may include in this picture the field galaxies, 
also discussed in paper I. If we assume again th^t fragmentation 
proceeds with maximum efficiency and recall that s =0.75 (q^ in 
paper I) for field galaxies, we get 
n = -21 h = 5 to 10
for the average number of galaxies per fragmentation event. Here 
we took k = 1/4 or 1/2. This estimate of n agrees well with the 
average population of these loose groups of galaxies which are 
believed to constitute the 'field’ (de Vaucouleurs, 1968),.
FEFEPENCES
1- Karachtensev; 1966, Astrofizika.
2- “age T.L., 1965, Smithsonian Special Report N° 95,
3- Sersic J,L., 1968, BAG, 19, 3, p.l05.
46
4- de Vaucouleurs G. , 1968, Stars and Stellar Systems, IX, eh.17, 
Chicago, Univ, Press.
Appendix ;
Assume a mechanical system in ste^idy state, so that the kine­
tic (T) and potential (W) energies afe linked bv 
2T + W = 0
-E'T + W (1)
where E® >0 is the binding energy. Let us imagine now that the
librium mass distribution has a dense core which collapses in a
2short scale of time radiating an energv pulse l/'2 yc , The poten-' 
tial energy W will be. before the event,
w = (1 - 1/2 u o’
where V/^ is the potential of the mass distribution without the core,
the interaction energv between the core and the rest of the 
2
svstem and - l/2ji.c the potential energy of the core itself.
After the collapse of the core, the new configuration is con­
trolled by the relations
2T + W = 1/2 uc - u W
AM
T + W = 1/2 yc^ - y W - E® 
” AM
(2)
In case of unstability we have
1/2 J" = 2T + W = 1/2 yc^ - y W > E® = T 
° AM °
the last relation coming from (1). If we introduce the velocity
2dispersion (T associated with T = 1/2 M a (M is the total mass
of the system) we easily get
2. 2C to (3a)
for the unstable condition. On the other hand, if 
(IL) ^
(3b)2^ 2 c +0
the svstem is stable and
1/2 J" = l/2"yc^ - JL - T
AM °
which means that stable vibrational modes are excited. The condi-
47
tion (3a) .with o<< c is assu'jned in the text.
Introducing now the absolute value i of the average potential
2corresponding, to W, the first equation of (1) gives a =4» and (3, 
may be written
i > C^(y/M)/(l_y/M)
for respectively unstable and stable configurations after the co­
llapsing of the core.
(1)A.G. Wilson has discussed the observational evidence for
_4 3 2the existence of a potential bound 4> £^10 ‘ c for astronoTnical
systems (galaxies, groups and clusters of galaxies): later on, D. 
Edelen and A.G. Wilson accept the upper bound for «¡> as "an
observed fact whose significance is uncertair’". The foregoing re­
sults suggests a simple interpretation. In fact, if cosmic systems 
are the result of a hierarch of fragmentation processes through 
succesive explosions and the resulting syst<»ms of fragments are 
unstable, an upper bound for <i> is found, namely
i ^ c^(y/M)(1 - u/M)
which together with the figure given by Wilson, requires than a 
given fraction of the mass of the parent svstem must be radiated 
awav in order to fly it to pieces. Such a result is not surprisinc' 
when we think that all parent systems (cD .galaxies for example) 
follow the same structural pattern. This means approximate homolo­
gous conditions in the growth and developement of the core, and
the existence of a critical fractional mass (y/b) for uiistabili tv.
- 5 ^
From V/ilson’s figures = 5.10 which gives a mass of the order 
12of 10“ suns for a giant D galaxv with M = 2.10 suns. These figu­
res together with the foregoing interpretation of the upper bound 
for , mean that the svstem of fragments is alwavs unstable (See
paper I). , .
(Ter figuras en paginas 111 y 112)
^EFEPEMCES
(1) - A.G. Wilson; A.J. 71., 402 , 1966.
(2) - D. Edelen and A.G, Wilson Ap.J., 1171 , 1968 .
SOLUCION NUMERICA DEL ?R0BLE^^A DE KEPLER EN VARIABLES UNIVERSALES 
P.E. Zadunaiskv y R.C. Blanchard 
(Instituto Torcuato Di Teila , Buenos Aires v National
48
Academy of Sciences, U.S.A.)
(NASA Goddard Space Flight Center, Greenbelt, MD.)
Cuando se trata de resolver en la forma clásica el problema de 
encontrar la posición sobre una orbita, correspondiente a un siste 
ma dado, se hace necesario resolver una de las tres ecuaciones de 
Kepler. Acuì reducimos esas ecuaciones a una forma ' ^ndard expre­
sada mediante las variables v funciones universales introducidas 
por Herrick, Stumpf v otros. La solución se obtiene resolviendo 
primero una ecuación cubica aue representa aproximadamente la for­
ma standard mencionada. Esta primera aproximación, oue constituye 
una modificación de la ecuación de Kepler para el caso parabólico, 
es bastante buena para todas las excentricidades comprendidas en el 
intervalo (0,1,5); los casos más favorables se presentan cuando las 
posiciones son cercanas al pericentro, Luepo se calculan sucesi­
vas correcciones de la primera aproxim.ación oara lo cual se debe 
resolver en forma reiterada una ecuación ciiadrática o bien cubica. 
En el primer caso, oue es enuivalente a una corrección del tipo 
'lewton-Raphson cuadrática, se da un criterio para elepir la raiz 
cue corresponde al problema v se encu^-ntra nue dos correcciones su 
cesivas dan en todos los casos por lo rnenos 8 ci‘‘ras sipnificativas 
correctas. En el caso de la corrección cubica se da un esouem.a' sen 
cilio para el cálculo numerico.
En varios gráficos se hace una descrioción detallada del prado 
de precisión obtenido en todos los casos v con diversas aproxima­
ciones .
Se estudian alpunas propiedades anal iti cas de las variables v 
funciones universales introducidas en el pT’oblema.
LA ABSORCION EN EL ESPECTRO CO’^'ttmho RAnionrrMTE 18SIA
ASOCIADA A LA NEBULOSA OASEOSA M.o.C. 6618 
P. Ouircpa
(Instituto Argentino de ’íadioastronomia, Buenos Aires)
Con el radiotelescopio de “erevra de 1”. de ant'.'na


Unstable groups of galaxies

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Unstable groups of galaxies

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