Red and blue shift frequency distribution of quasi-stellar objects from nearby galaxie

Jokipii, J. R.

Noerdlinger, P. D.

Woltjer, L.

English

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SPECTRAL SHIFTS IN QUASISTELLAR OBJECTS* 
Peter D. NoerdIinger+ and J. R. Jokipii 
Enrico Fermi Institute for Nuclear Studies 
The University of Chicago, Chicago, Illinois 
and 
L. Woltjer 
Department of Astronomy 
Columbia University, New York 
Laboratory for Astrophysics and Space Research 
Preprint Number EF INS 66-56 
I 
* This work was supported in part by the National Aeronautics and Space 
Administration under Grant Nos. NASA NsG 96-60 and NsG179-6 1 
and by the Air Force Office of  Scientific Research under Contract 
AF (638) 1358 
+ 
and Department of Physics 
I . 
SPECTRAL SHIFTS IN QUASISTELLAR OBJECTS 
Peter D. Noerdlinger+ and J. R. Jokipii 
Enrico Fermi Institute for Nuclear Studies 
The University of Chicago, Chicago, I l l i n o i s  
and 
L. Woitier 
Department of Astronomy 
Columbia University, New York 
e' ABSTRACT 
The hypothesis that Quasistellar Objects have been ejected 
with relativistic velocities from many comparatively nearby galaxies i s  con- 
sidered. The expected frequency distribution of blueshifts a d  redshifts i s  cal- 
culated. If a l l  members of a given group of objects with similar velocities 
could be observed, redshifts would be more numerous thun blueshifts, but be- 
cause the blueshifted objects are much brighter, they can be seen at much 
larger distances. If the groups are created at random through a Euclidean wr- 
tion of space and a sample brighter than some limiting magnitude is  examined, 
blueshifts should be far more numemus than redshifts. This appears contrary to 
abservat ion. 
+ 
and Department of Physics 
i 
-2 - 
Terrell (1964), Burbidge and Hoyle (1966) and Arp (1966) 
have considered that the Quasistellar Objects (QSO) may not be at cosmo- 
logical distances. In the first two papers this possibility i s  taken to imply that 
the redshifts are Doppler shifts associated with large velocities. Also in Arp's 
picture this interpretation seems difficult to avoid, since gravitational red- 
shifts can be definitely ruled out because the forbidden line emission in these 
objects requires large volumes. NO strong enough gravitational field can pre- 
vail in such large volumes (Greenstein and Schmidt, 1964). Terrell considemd 
that a l l  QSO had been ejected from our galaxy and thus no blueshifts would 
occur. This leads to difficulties with the total mass and energx involved 
(Setti and Woltjer, 1966). Thus it might be more likely with a local theory 
that many galaxies would have ejected QSO; this i s  of course explicitly sug- 
gested by Arp. In this paper we discuss the relative frequencies of redshifts 
and blueshifts to be expected within this kind of theory. 
I 
Let us suppose that we observe an isotropic explosion in 
which a large number of objects are ejected, a l l  with the same speed 
If  the angle between the line of sight and V for an object i s  e 
reference frame) the relation between the frequencies Y 
(in our 
.L 
of radiation ob- 
served by US and 1/, of radiation emitted in the reference frame of the 
object i s  (Jackson, 1962) 
- 3 -  
where 
has been taken to correspond to approach. Since the explosion is isotropic 
N( 6 ), the number of obiects ejected per unit interval in 
=v/c, z = A 1 /” , r  i s  as defined, and 6 =O 
i s  
N sin f!? d 6 , with No the total number of objects. For the distri- a 0  
and N(C ) = 0 outside the stated interval for p 
observed, more red-shifted than blue-shifted objects are found. If the QSO 
observed with = 3.1 correspond to the maximum -r ,aboutfoyr 
times more red-shifted than blue-shifted objects would be found. If not a l l  ’ob- 
jects have the same velocity V, but if isotropy i s  maintained, we s t i l l  have 
N(f ) = N( 5 -I)  and the redshifts predominate since they extend over a 
larger interval in  . 
. Thus - if a l l  objects are 
Modifications are needed, however, when the lifetimes of the 
objects are taken into account. If the intrinsic lifetime of the objects is TW 
then the observed lifetime wi l l  be Tor (Noerdlinger, 1966). Thus the blue- 
shifted objects have the shortest lives and i f  we consider the result of one ex- 
plosive event, equation (2) would overestimate the abundance of blue-shifted 
objects after enough time had elapsed for some of these to become unobservable. 
- 4 -  
If, however, we consider the more interesting case, where objects are observed 
from a large number of explosive events (distributed randomly in time) we 
clearly k v e  
<NIP)) = i 4 
where the brackets indicate the time avemge and where No i s  now the number 
of objects produced per interval of time To (in our reference frame). The 
-1 are the same as in equation (2). Intebrating over the 
we have for the mean numbers R of red-shifted and B 
limits P and P 
relevant range of 1 
of blue-shifed objects 
the sum of which exceeds No because the average observed lifetime exceeds 
To. The mean values of for the two classes of emitters (R and B) are ob- 
tained byiputtiplying equation (3) by 
number of objects. We have 
, integrating and dividing by the 
- 5 -  
It i s  interesting to note that in the highly relativistic l im i t  
( p 1, f9) the mean blue shift tends to the value , while the 3 
mean red shift i s  asymptotic to 
The reason for the 
objects have 8 
imit to the mean blue shift i s  that most of the blue-shifted 
values in a s m a l l  range near the point of zero redshift, on 
account of the larger solid angle available there. If a l l  the objects are as- 
sumed to have the same velocity and we take p -' =3.1 as'before, we now 
expect about ten times as many red shifts as blue shifts. - 
These results are valid only i f  a l l  objects are observable 
during their lifetime. However, i f  we consider that the objects w i l l  be found 
a t  different distances and that in practice we can only observe spectral shifts 
down to some limiting magnitude, further discussion of the expected brightness 
of the objects i s  needed. If we assume that the emission of the objects i s  
isotropic in the object's rest frame, the radiative flux emitted at  angles between 
8, and 8, + d 8, with respect to the velocity vector of the object and 
per unit frequency interval a t  frequency .,bo i s  given by 
. 
- 6 -  
The observer sees the radiation a t  frequency y= 4/r andat an 
angle 6 given by (Jackson, 1962) 
Since the energy density per unit frequency interval in an 
electromagnetic wave tmnsforms as the frequency and since the solid angle. ih 
which the radiation is emitted tmnsforms as 1/ 2, from equations (1) and p) wd 
have for the flux in the observer's fmme (also see Robertson, 1b38 and Hoyle, 
1962) 
Thus taking a typical spectrum for a quasistellar object of 
so that the observed flux at some frequency for a set of objects at the same 
distance with the same intrinsic spectrum varies as . For 
typical QSO 4 appean to be near zero or slightly positive and thus the 
. -7- 
blue-shifted objects should be quite bright. If many explosion centers are now 
distributed randomly through a locally Euclidean portion of the universe, the 
brighter objects w i l l  be observed from a larger volume if the intrinsic brightness 
of a l l  objects i s  the same. Thus i f  N(m, p ) is the number of objects per unit 
which are brighter than a limiting magnitude 
the same for a l l  objects) 
m we wi l l  have 
P (again with 
between the appropriate limits ( p and p-') of p . For the ratio of the 
numbers of blue and red-shifted objects we now have 
<a) . 
p r f +  s 3  
- *  e- 
= 3.1, corresponding to the largest red shi f ts  observed in QSO we have 
= 0, which corresponds to the optical continuum 
with P < B > /< R) = 16.9 for Q( 
in 3 C 273 and O( = 0.5. This is to be contmsted 
with the case where a l l  objects are observable when we would have from equation 
(4) < B  > /(p)= p = 0.10. The brightening of the blue-shifted objects 
and the relevance of blue-shifted objects to a local theory have been pointed out 
also by B. Hoffman (1964). 
(B) / (R > = 39.6 for 
-2 
Expression (1 1) has been derived under the assumption that al I objects 
have the same velocity. If this is  not the cesc, the results would have to be 
. 
c 
-8- 
somewhat modified, but the ratio N (m, p ) / N ( m , l  -') would remain un- 
changed from that found from equation (10). Thus if we take the observed distri- 
bution of redshifts for the QSO as observed by Schmidt and others and reported 
in the litemture before the middle of April, 1966, we can calculate the expected . 
- distribution of blue shifts. The results are given in Table 1. 
Insert Table I here 
It would appear that the last case considered should represent the s i t -  
uation if the QSO are not associated w i th  our galaxy, but s t i l l  qre located at 
distances where the cosmological red shift is not yet large. The disagreement with 
observation i s  striking already, but can be further enhanced by consideration of 
the mean red and blue shifts to be expected in this model. The mean values of 
5 for the two classes of observable emitters, based on Eq. (10) are now , 
3 3  -t - 4 3 - 6 L  - '2 (12) 
5 + 3 4  
where A = + 3 
Provided o( > -1, < r > g o a s  p+ 00 (unbounded mean blueshift) but 
+ A as p+ 80 . Since (p)R never exceeds A (unless p)R . -  < < -1) one cannot possibly f it the mean value <q% = 1.93 found from 
the observed values in Table I unless o( < -.28. Unless o( i s  rather less 
. 
. 
f 
-9- 
must also be taken very large. Negative values of d( do not P than -.28, 
correspond to observation at a l l  except in the very low frequency radio region 
( <  100 Mc/s). The relevance of this region wi l l  be discussed presently, but for 
now we may note that if optical observability i s  the criterion for detection, no 
#it to the data is  possible without the unreasonable assumption that a( < -.3. 
This conclusion would hold even if none of the blue-shifted objects were observable! 
Before accepting the conclusion that an excessively large number of 
blue-shifted objects should have been observed among the QSO some possible 
selection effects must be noted. First of all, most QSO have been found by 
identification of X radio sources. The 3C catalog should be a pasonably complete 
catalog of the brighter radio sources at 159 Mc/s. Since at low frequencies 
many QSO show a decrease of flux with decreasing frequency, corresponding to 
negative 
abiects. It i s  difficult to estimate the importance of this effect, but we do not 
6 , there would be a tendency to miss some of the blue-shifted 
think it could be large, since for at  least several sources the maximum of the spec- 
trum occurs well below 100 Mc/s. If the effect were large, sources with large blue 
shifts should be found in great numbers in surveys at higher frequencies. The 
available data do not seem to indicate this. For example, in a survey at  1b21 Mc/s, 
Kellermann and Read (1965) found 28 sources brighter than 2 flux units, of which 
22 had already been included in the X catalog. Thus no strong discrimination 
abainst finding blueshifted objects arises from the radio frequency spectrum. It 
i s  conceivable, of course, that some mechanism ascertainable only on the basis 
of a detailed model could inhibit radio emission in the direction of motion; this 
. 
-10- 
8 .  
~ 
I 
I 
I .  
would suppress the detection of blueshifted objects, since for large p 
emitters are redshifted unless seen nearly head on. 
the 
A more intriguing possibility i s  related to the strong infrared emission 
in X273. If the source had a blue shift corresponding to 
no longer be a blue object. Since QSO have frequently been discovered by 
searches for blue objects, this might mean that many blue-shifted objects could 
= 0.5 it would 
have been missed. In this cose the assumption & = 0 i s  rather conservative 
and the number of blueshifted QSO with red appearance should be quite large. 
It appears unlikely, however, that there are enough unidentified small-diameter 
radio sources in the X catalog for this interpretation to be possible. Thus unless 
a significant fraction of the red shifts is  incorrect -- which appears unlikely*, 
though not impossible, since many red shifts are based on only two lines -- a 
generalized local theory appears to encounter difficulties. 
Of course, if the blue-shifted objects were so distant that the cosmo- 
logical red shift were important, the fraction of blue-shifted objects would again 
I 
be less than indicated in Table 1. However, cosmological redshifts should be 
relatively minor out to 500 Mpc distance or more. Even i f  only the five OS0 
identified by Arp as nearby ( < 100 Mpc) are taken as our red-shifted sample, the 
accessible volume for the blue-shifted objects within 500 Mpc would be 100 times 
* We have actually attempted to interpret the spectra of 3C9, X245, X287, and 
CTA 102 by blueshifting the stronger lines that are observed in the red and 
infrared in planetaries; although some reasonable fits (with lines of COlU , 
C 0111 1, and C S l l  1 could be obtained, except in X9, the absence of some 
expected lines like H makes this interpretation implausible. 
- 1  1- . 
as large, and we should expect to see about 50 such objects. In fact, i f  Arp's 
proposal i s  correct, one would expect many of the 23 observed objects in Table I 
to be within 100 Mpc, bringing the count of blue-shifted objects within 500 Mpc 
close to the values in the last column. The f i t  of the theory to the data seems 
. so poor that cosmological effects do not merit further discussion at this time. 
As an aside, we remark that the dimming of approaching objects 
receding at relativistic speeds might conceivably lead to an apparent asymmetry 
in the ejection of jets in radio sources. For example, in X273, i f  the iet 
i s  approaching us an identical jet located symmetrically but receding might be 
too faint for observation. 
This research has been supported in part by the National Aeronautics 
and Space Administration under Grants NASA NsG 96-60 (P.D.N.) and NASA 
NsG 179-61 (J.R.J.) and by the Air Force Office of Scientific Research under 
contract AF 49 (638) 1358 (L.W.) 
I 
* -12- 
Arp, H. 1966, Science 151, 1214. 
Burbidge, G. R. and Hoyle, F. 1966, Ap. J., 144, 534. 
Greenstein, J. L. and Schmidt, M. 1964, Ap. J. 140, 1. 
Hoffman, 6. 1964, Science 145, 1336. 
w 
- e  
w -
w 
~ 
Hoyle, F. 1962, in Evidence for Gmvi(ltibna1 Theories, Academic Press, New York. 
Jackson, J. D. 1962, Classical Electrodynamics, John Wiley, New York. 
Kcllennann, K. E. and Read, R. D. 1965. Publications of the Owens Valley Radio 
Observatory Vol. 1, No. 2, "A Continuum Survey for Discrete Radio 
c 
Sources at 1M1 Mc/s. 
w 
Noerdlinger, P. D. 1966, Ap. J. 143, 1004. 
m 
Robertson, H. P. 1938, Z. Astrophys. 15, 69. * 
Setti, G. and Woltjer, L. 1966, Ap. J., 14, 838. 
-Ire 
Terrell, J. 1964, Science 14, 918. 
bvb- 
I 
. 
Table 1 
I .  
I .  
Observed redshift frequency distribution for QSO and the predicted frequency 
distribution for blueshifts, first for the unrealistic cpse where a l l  objects are 
observed and then for a fully local theory where sources are observed down to 
some limiting magnitude in a homogeneous Euclidean portion of the universe. 
n A l l  Objects Objects to Limiting 
Observed Magnitude (4 =0) 
3.33 - 2.50 7 0.30 - 0.40 ' 0.1 1400 
2.50 - 2.00 8 0.40 - 0.50 0.3 450 
2.00 - 1.67 5 0.50 - 0.60 0.5 100 
1.67 - 1.33 8 0.60 - 0.75 1.6 59 
1.33 - 1.00 3 0.75 - 1.00 1.7 '6 
I 


Spectral shifts in quasi-stellar objects

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