Observational data being the basis of contemporary cosmological models are not numerous: Hubble law of redshift for galaxies, element abundances, and observation of cosmic microwave background radiation (MBR). The significance of MBR discovery predicted in the Big-Band model is particularly stressed. Radio astronomical measurements give an information on MBR only near the Earth. Experimental confirmation of evolution of MBR, i.e., its probing in remote epochs, might obviously present a direct verification of the hypothesis of hot expanding Universe. The carriers of similar cosmological information should be particles which, firstly, effectively interact with MBR, and secondly, make it possible to identify unambiguously the epoch of interaction. A possibility to verify a number of cosmological hypotheses by searching the cutoffs in spectra of ultrahigh energy gamma-rays (UHEGR) from extragalactic sources is discussed

Aharonian, F. A.

Atoyan, A. M.

English

NASA Technical Reports Server

301 . UG 2.7-14
ULTRAHIGH ENERGY GAMMA RAYS - CARRIERS
OF COSMOLOGICAL INFORMATION
Aharonian F.A. and Atoyan A.M.
Yerevan Physics Institute, Markarian St.2,
375036, Yerevan, Armenia, U.S.S.R.
ABSTRACT
A possibility to verify a number of cosmological hypotheses
by searching the cutoffs in spectra of ultrahigh energy
gamma-rays (UHEGR) from extragalactic sources is discussed.
\.
One of the most significant problems of cosmology is the nature of
the evolution of the Universe. Observationaldata being the basis of
contemporary cosmologicalmodels are not numerous: Hubble law of red-
shift for galaxies, element abundances, observation of cosmic microwave
background radiation (MBR). The significance of MBR discovery predicted
in the Big-Bang model should particularly be stressed. Meanwhile, radio-
astronomical measurements give an information on MBR only near the
Earth, i.e. at present epoch. Experimental confirmation of evolution of
MBR, i.e. its probing in remote epochs, might obviously present a dl-
rect verification of the hypothesis of hot expanding Universe. The car-
riers of similar cosmological information should be particles which,
firstly, effectively interact with MBR, and secondly, make it possible
to identify unambiguously the epoch of interaction.These requirements
are satisfied with gamma rays of ultrahigh energies (E,_ 10_ eV)
emitted by discrete sources at cosmological distances,u
The cross section of e+- e- pair production at photon-photon colli-
sions of gamma rays with isotropicallydistributed monoenergetic photons
depends only on parameter b:_ooE_/rn2c _ , E_ and _o_ being the ener-
gies of gamma rays and field photons, respectively. Starting from the
threshold value of b=l the cross section increases rapidly to the maxi-
mum at b:3, and then decreases slowly as _nb /1/. In the case of
Planckian distribution of MBR (temperatureTo - 2.7 K) the free path A
of gamma rays is minimal at E_-vIO _ eV being equal to _,8 kpc. A weak
• -£ " 4G
increase of _ o:E_n E_ at E_- 10 eV is explained by the decrease
of the cross section at b>_l, whereas at E_<< 10_s eV the free path
. _(E_ ) increases sharply due to the threshBld nature of the reaction
I1 II
owing to which gamma rays interact only with the Wien tall photons of
MBR. In the latter case a simple dependence of A on E_ takes place
. /1,2/: 3 "_
where V = Fn2c_//K_o_ . At E_ changing in the range (0.7+1.4).
•10_ eV, A changes in a wide _ange 1_+10_ Mpc. In Eq.(1), however,
the evolution of MBR is not taken into account, whereas it becomes es-
sential for R _ 100 Mpc. The evolution of the MBR in the Big-Bang model
being considered, the optical depth t with respect to palr production
is expressed in the form /2/:
301 
ULTRAHIGH ENERGY GAMMA RAYS - CARRIERS 
OF COSMOLOGICAL INFORMATION 
Aharonian F.A. and Atoyan A.M. 
Yerevan Phys cs Institute, Markarian St.2, 
375036, Yerevan, Arm nia, U.S.S.R. 
ABSTRACT 
/ UG 2.7-14 
A possibility to verify a number of cosmological hypotheses 
by searching the cuto fs in spectra of ultrah gh energy 
gamma- ays (UHEGR) fr m extragalactic sources is discussed. 
One of the most significant problems of cosmology is the nature of 
the evolution of the U verse. Observational data being the b sis of 
contemporary c smological models ar  not numerous: Hubble law of red-
shift for galaxies, element abund nces, observation of cosmic microwave 
background radiation (MBR). The sig ificance of MBR discovery predicted 
in the Big-Bang model should particularly be stressed. Meanwhile, radio-
astronom cal measurements give an information on MBR only near the 
Earth, i.e. at present epoch. Experimental c firmation of evolution of 
MBR, i.e. its probing in remote epochs, might obviously present a di-
rect verification of the hyp hesis of hot expanding Univer e. The car-
ri rs of similar cosmological information should be particles which, 
firstly, effectively interact with MBR, a d secondly, make it possible 
to identify unambiguously the epoc  of interacti . These requirements 
are satisfied with allllla rays of ultrahigh nergies (E" ~ 1013 eV) 
emitted by discrete sources at cosmological distances. 
The cross section of e+- e- pair production at photon-photon colli-
sions of gamma rays with isotropical1y distributed m n energetic photons 
depends only on parame er b=tiwEcI'/m2clf, £4 and 1\w being the ener-
gies of gamma rays and field photons, respectively. Starting from th  
thr shold value of b=l the cross section increas s rapidly to the maxi-
mum at b=3, and then decreases slowly as bJ.t.nb /1/. In the case of 
Planckian distribution of MBR (temperature To = 2.7 K) the free p th A 
of gamma rays is minimal at E.t""lOLS eV b ing equal to ""8 kpc. A weak 
increase of A cc E.rln-!E,t at E,t ~ 10 iii eV is expl ined by the decrease 
of th  cross sectio  at b~l, whereas at EJ « lOiS eV the fr e path ~(E.r ) increases sh rply due to the threshold nature of t  reaction 
owing to whi h gamma r ys interact only with the Wien "tail" photons f 
MBR. In the latter case a simple dependence of ). on E ~ takes place 
/1,2/: _! 
A(Ect)~lJ'10-2L~+ :v}rv-'] eY Mpc) (1) 
where \>= rn2c4/KroE~ . At E,t changing in the range (0.7+1.4). 
'lOi~ e  t ).. hanges in a wide range 10'.,.10" Mp·c. In Eq. (1), however, 
the evolution of MBR is not tak n i to account, whereas it becom s es-
sential for R ~ 100 Mpc. The evolution of the MBR in the Big-Bang model 
b i g considered. the optical depth ~ with respect to pa r production 
is expressed in the form /2/: 
https://ntrs.nasa.gov/search.jsp?R=19850025674 2020-03-20T18:05:46+00:00Z
302 OG 2.7-14
where Zo 1 _
''= j0
To =2.7 K is the present value of MBR temperature,Ea is the energy of
detected gamma rays, Ho is the Hubble constant, zo is the cosmological
redshift of the gamma-ray source, and _CL=_/p_ =_-Gp/3Wo _ . The
accuracy of Eq.(2) is acceptable if v[_-C£+Zo) -2] >3 . Since ob-
servable spectrum of gamma rays N(E_ ) is related to initial gamma-ray
spectrum of the source No (E_) by equation N = No.exp (-_), in the
energy/range of E_ , when _(E_) _1, a sharp cutoff of the spectrum
N(E#) should be expected. Eqs.(1) and (2) correspond to Planckian dis-
tribution of MBR. Meanwhile, the reliable data which are in good agree-
ment with this distribution correspond only to Rayleigh-Jeanspart of
the spectrum. Moreover, for submillimeter wavelengths there are intense-
ly discussed in literature possible deviations of MBR from Planckian
distribution, particularly due to comptonization of MBR /3/. The analy-
sis performed by Field and Perrenod /4/ indicates that current observat-
ional data do not contradict the comptonizationparameter y___0.05. The
deviations of MBR from Planckian distribution (y=O) may lead to notice-
able shift of expected cutoff energy Ec , determined by equation
t_(Ec ) = 1.
Thus, cutoff energy Ec of the spectrum N/No is defined by the dis-
tance R from the source, by the spectrum of MBR in submillimeter range,
and by the character of MBR evolution in time. Therefore there is a
unique opportunity to solve a number of urgent cosmological problems /2/.
i) Probing of submillimeterrange of MBR spectrum.
The distance R to the gamma-ray source with zo <<I being known, the
optical deptll_ depends mainly on MBR spectrum at submillimeterwave-
lengths. In Fig.1 the spectra N/No expected from a source at the dis-
tance R=5 Mpc (corresponding to distance of the nearest radiogalaxy
Cen A) are plottea Comptonization parameter y changes from 0 to 0.05,
the cutoff energy E¢ shifts down from 1.4 .lO_eV to 8.10_eV. It can
be seen from the figure that to obtain the comptonization parameter with
accuracy of _y = 0.01 the energy resolution of a detector should be
_<i0%.
i i ) QSOdi s_tance ranging.
Though most of astronomers are in agreement that the redshifts of
QSOs have a cosmological origin, there is not yet a final refutation of
the arguments brought in favour of the local placement of these surpris-
ing objects (see, e.g. /5/). Above we have discussed the possibility to
probe the submillimeter range of the MBRspectrum observing the sources
at well-known distances R. Supposing now that the spectrum of MBRis es-
302 
.  2.7-14 
( 2) 
r (0 d ] 2 
g = 1 + ~Q+~cy3l J(i+X?J~+J2Xl 
o 
where 
To =2.7 K ; s the present va 1 ue of MBR tempera ture, E ~ is the energy of 
etected ga a ra s, o is t e ubble c sta t, Zo is t e c s ol ical 
redshift of the gamma-ray source, and ..n.=J/Pcr =$-rrGp/3Ho2. • The 
accuracy of Eq.(2) is acceptable if v[i-(i+~Gy2] >3 • Since ob-
servable spectrum of gamma rays N(E6 ) is related to initial gamma-ray 
spectrum of the source No (E4 ) by equation N = No·exp (-1:"'), in the 
energy range of E4 ,when 1:"(E If ) ~ 1, a sharp cutoff of the spectrum 
N(E6') should be expected. Eqs.(1) and (2) correspond to Planckian dis-
ib ion  B . ean hil , h  iable  hi    q  q
n~  it  t is istribution rrespond l  t  gh-Jean~ rt" f 
t e s ectrum. oreover, f r s rnillirneter avele ths t ere are i te se-
ly discussed in literature possible deviations of MBR from Planckian 
distribution, particularly due to co ptonization of BR 13/. he analy-
sis performed by Field and Perrenod /41 indicates that current observat-
i al ata do t c tra ict the c pt ization ara eter  ~ . . he 
e iations f BR from la c ian istribution (y=O) ay lead to tice-
able shift of expected cutoff energy Ec , determined by equation 
t"(Ec ) = 1. 
Thus, cutoff energy Ec of the spectrum NINo is defined by the dis-
tance  from the source, by the spectrum of MBR in sub illimeter range, 
and by the character of MBR evolution in time. Therefore there is a 
unique opportunity to solve a number of urgent cos ological proble s 12/. 
i) Probing of sub ill imeter range of MBR spectrum. 
he istance  to the ga a-ray so rce ith Zo «1 eing known, the 
optical depth 1:: depends mainly on MBR spectrum at submillimeter wave-
lengths. In Fig.1 the spectra NINo expected from a source at the dis-
tance R=5 Mpc (corresponding to distance of the nearest radiogalaxy 
Cen A) are plottea. o ptonization para eter y. changes fro  a to O.O~, 
the cutoff energy Ec shifts down from 1.4 . 10 '"leV to 8 • 10 i3 eV. It can 
be seen fro  the figure that to obtain the co ptonization para eter ith 
accuracy of by  0.01 the energy resolution of a detector should be 
:E: 10 . 
ii) QSO distance ranging. 
Though most of astronomers are in agreement that the redshifts of 
QSOs have a cosmological origin, there is not yet a final refutation of 
the arguments brought in favour of the local placement of these surpris-
ing objects (see, e.g. 15/). Above we have discussed the possibility to 
probe the submillimeter range of the MBR spectrum observing the sources 
at ell-known distances R. Supposing now that the spectru  of ~1BR is es-
.. 
3@3 OG 2,7-14
tablished with sufficient accuracy, it would be possible to carry out
model-independent estimations of the distances to the extraaalactic
sources: R = _(Ec ). To prove unambiguously the cosmological origin of
QSOs, it would be enough to observe even one QSO spectrum with cutoff
in the range Ec _ lOi_eV. Precise measurements of R is however a more
complicated problem. For example, to determine the value of R with ac-
curacy of_--50% the energy resolution of detectors should be _5%.
Moreover, when carrying out precise spectrometricmeasurements, it
should be taken into account that the secondary gamma rays produced at
development of relativistic electromagneticcascade in MBR field may
result in deviations of observed spectrum from the law N/No = exp (-_).
This is illustrated in Fig.2 where the spectrum of gamma rays which is
formed at R=IO0 Mpc from a source is shown. Numerical calculations have
been performed by Monte-Carlo simulation in accordance with /6/. As one
can see from the figure, the cutoff region is somewhat "smeared" around
the value of Ec expected from the condition A(Ec )=100 Mpc. It should
be noted, however, that the deflections of secondary electrons in mao-
netic field being taken into account, a detector with angular resolution
A_ _-_5 will not be sensitive to the photons of the electromagnetic
cascade, if H_3 -10-9 G.
i °Y:Q_ Y:O,_ Y=O E I#,2z
........
02 _ R=IOOMpc ,
1 a ..... HI , , ,,,,HJ ....... H
6 789 1011121_14_16 106 107 I0B Ec
(_,_1_;vl E_,m_
Fig. 1 Fig. 2
Provided the cosmological origin of redshifts of QSOs, it will be
possible to measure Hubble constant for distances R>_IO0 Mpc. In Fig.3
the spectra expected from a gamma-ray source with zo =0.025, correspond-
ing to R =100 Mpc (Ho =75 km/s Mpc) or to R=150 Mpc (Ha =50 km/s Mpc),
are given. For the choice of Ho from these two values, the energy reso-
lution of a detector should be not worse than 5%. For realization of
above mentioned problems most suitable objects seem to be nearest QSOs
3C 273 (zo =0.158) and 0241+622 (zo =0.043), for which the effects of
MBR evolution are not so significant.
.. 
0  G .  
tablished ith sufficient accuracy, it ould be possible to carry out 
odel-independent estimations f the istances to the e traoalactic 
sources:   ~(Ec)' To prove una biguously the cos ological origin of 
s, it ld e enou2h to serve en e SO spectrum ith toff 
in the ange c ~ 10! eV. ise ea em ts   is r  re 
pl ated oblem.  xa e, o termine the ue   i h -
acy  - 50% the rgy esolution  t tors ld  ~  
Ivioreover, hen carrying out precise spectrometric easure ents, it 
should be taken into account that the secondary gamma rays produced at 
development of relativistic electromagnetic cascade in MBR field may 
result in deviations of observed spectrum from the law N/No = exp (-~). 
is is illustrated in i .2 here the s ectrum f gamma rays hich is 
ormed  100  rom  ce s how . u eri l ations ve 
ee  rformed by onte- rlo si l tion in ordance ith / /. s e 
  from the figure, the t ff r ion is som t red" round 
the lue f  c ted from th  ition ~(Ec )=100 pc. It s ld 
 t , e r, t t the flections f econdary l trons in aa-
netic field being taken into account, a detector ith angular resolution 
~e ~ 5 ill not be sensitive to the photons of the electromagnetic 
,   ~3 '1 9  
1.0, --~=-------I, 
qgt-
0.8 
Q7 
iQ 
"-
z 0,4 
0.2 
o~ 
o _u.' , I I I I I 
3 4 ~ 0   9 10 11 12 13 14 15 16 
(E&/ld~v) 
i .  
..-
u 
C1J 
5} -:1 
-10 ~ 
C1J ;: 
o 
R=100Mpc 
t , , ",,", """ "I 6 7 
ES,mc2 
i g.  
I , , , ,"I ~ I 
r i ed t e c s ol ical rl l  of re s ifts f S s, it ill be 
possible to easure ubble constant for distances  ~100 pc. In Fiq.3 
the spectra expected from a gamma-ray source with Zo =0.025, correspond-
ing to  =100 Mpc (Ho =75 k /s pc) or to R=150 Mpc (Ho =50 k /s pc), 
are given. For the choice of Ho from these t o values, the energy reso-
l tio  f  et t  ld  t ors  t  5 . r r li tion  
above entioned problems ost suitable objects seem to be nearest QSOs 
3  2  (  =0.  a   (  0. ), f r hi  t  f t  f 
BR e ol tio  are t s  si ifica t. 
OG 2.7-14
304
1,o I- I i,.i1Q7
o3 ',I I
P
i ] i i i , , , ±
2 3 4 5 6 7 8 9 10 11 12 1314 (EMI(_V)
E_/IO%V Fig. 4
ill) Probing of MBRin remote epochs.
The observations of UHEGRfrom distant QSOswith Zo_ I will give
unique information on MBR in remote epochs. Since according to the model
of hot expanding Universe both temperature of MBRand energy of gamma
rays were (1+zo) times as great as the detected ones, expected cutoffs
will be (1+zo)=times shifted towards smaller energies. In the case of
Planckian distribution this follows directly from Eq.(2). In Fig.4 it is
seen that for different Zo the cutoffs should be expected in the wide
energy range 10_.lO_eV (solid curves). In the absence of MBRevolution
in time the spectra will be cut off near E,_-7 .lO_eV (dotted curve).
Since possible deviations of MBRspectrum _rom Planckian distribution
anu uncertainties of Ho cannot result in substantial changes of Ec from
the law EcOC(l+zo) "2, the observations of QSOswith zo_l may Qive unam-
biguous information on presence or absence of MBRevolution in'time. Ob-
viously, for these observations it is not necessary to have high energy _"
resolution of detectors.
In conclusion, it should be noted that correlated v_V observations
will enable one to establish unambiguously the nature of cutoffs expect-
ed in UHEGRspectra of QSOs and AGN: whether these cutoffs are related
to the absorption in MBRor they simply reflect the peculiarities in the
spectra of parent accelerated protons. Theoretically expected fluxes of
high-energy gammarays and neutrino from QSOs and AGNallow us to hope
that the considered possibilities can be realized (at least partially)
in the near future.
/i/ Gould R.J., Schreder G.P., Phys.Rev., 1967, 15___55,140.
/2/ Aharonian F.A., Atoyan A.M., Preprint, 1985.
/3/ Zeldovich Ya.B., Sunyaev R.A., Ap.Sp.Sci., 1969, 4_, 285.
/4/ Field G.B., Perrenod S.C., Ap.J., 1977, 215, 717.
/5/ Burbidge G., in: Objects of High Redshift-_--1980, D.99.
/6/ Aharonian F.A. et al. ,Ap.Sp.Sci., 1985 (in press).
1,°1----..;;;:-
Q9' 
(y3 
0.7 
-£ 0.6 
Fig. 3 :z: 
4 
100--\ 
Z=3 \ 
- Ho=7S 
---Ho=50 
-,1 
t"r 
~ 
I 
Z=1 
or; -14 
1 
Z=Q158 1 
(3C 273) : 
1 
1 
, 
0.1 1(ll_~---L.-L~-'--L.L1  -'-j-I 1---'1--'---'-1 ---L.ii 
0,1 10 
34 7 8 
E~/1d3ev 
iii) Probing of MBR in re ote epochs. 
The observations of UHEGR from distant QSOs with Zo ~ 1 will give 
unique information on r~BR in re ote epochs. Since according to the model 
of hot expandin~ niverse both te perature of MBR and energy of gamma 
rays were (l+zo) ti es as great as the detected ones, expected cutoffs 
ill be (1+zo)2times shifted to ards s aller energies. In the case of 
Planckian distribution this follows directly fro  Eq.(2). In Fig.4 it is 
seen that for different Zo the cutoffs should be expected in the ide 
r  r e ~+lOt" eV (solid rves). I  t e e f R olution 
i  ti e t e s ectra ill be c t ff ear  ~  • 10i3eV ( otted c rve). 
ince ssible viations f BR s tr  tr  la ckian istribution 
ana uncertainties of Ho cannot result in substantial changes of Ec from 
the law EeOC: (1+zot2., the observations of QSOs ith Zo ~1 may give una -
i uous information  rese ce r e f R olution in time. -
viously, for these observations it is not necessary to have high energy 
esolution  etectors. 
In conclusion, it should be noted that correlated K-v observations 
ill enable one to establish una biguously the nature of cutoffs expect-
ed i  EGR s ectra f S s and : hether t ese c toffs are related 
to the a sorption i  BR r t e  si ply reflect the eculiarities in t e 
spectra of parent accelerated protons. heoretically expected fluxes of 
high-energy gamma rays and neutri no fro  QSOs and AGN a 110\,1 us to hope 
that the considered possibilities can be realized (at least partially) 
n e r uture. 
/1/ Gould R.J., Schreder G.P. , Phys.Rev., 1967, 155, 140. 
/2/ haronian . ., toyan . ., reprint, 1985. 
/3/ Zeldovich Ya.B., Sunyaev R.A. , Ap.Sp.Sci., 1969, 4, 285. 
/4/ Field .B., Perrenod S.C., p.J., 1977, 215, 717.-
/5/ urbidge . , in: bjects of igh edshifr,-1980, 0.99. 
/6/ haronian F. . et al. , p.Sp.Sci., 1985 (in press). 
~,. 


Ultrahigh energy gamma rays: Carriers of cosmological information

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