The most promising model proposed for the origin of the GeV range
extragalactic -ray
background (EGRB), first detected by SAS-2
and later confirmed by EGRET
[1],
is that it is the collective emission of an isotropic distribution of faint,
unresolved blazars (See Ref.
[7]
and references therein.).
Such unresolved blazars are a natural candidate for explaining the EGRB
since, they are the only significant non-burst sources of high energy
extragalactic
-rays
detected by EGRET.
2.1. The Unresolved Blazar Model:
To determine the collective output of all
-ray blazars, one can use the
observed EGRET distribution of
-ray luminosities and
extrapolate to obtain a "direct"
-ray luminosity function
(LF) per comoving volume,
f
(l
, z)
[8].
Alternatively, one can make use of much larger catalogs at other wavelengths
and assume a relationship between the source luminosities at the catalog
wavelength and the GeV region
[9],
[10].
Both methods have uncertainties.
With regard to the former method, only the "tip of the iceberg" of the
-ray LF has been observed
by EGRET. Lower luminosity
-ray sources
whose fluxes at Earth would fall below EGRET's minimum detectable
flux, i.e. EGRET's point source sensitivity (PSS), are not
detected.
Extrapolating the
-ray LF
to fainter source luminosities must then involve
some extra assumption or assumptions.
We have chosen to use the latter method and have assumed a
linear relation between the luminosities of a source at radio
and -ray wavelengths in an
attempt to estimate a LF which would hold
at fainter luminosities. The extent of such a correlation
is by no means well established
[10] -
[12].
However, since most theoretical models invoke the same high energy
electrons as the source of both the radio and
-ray emission,
a quasi-linear relation between radio and
-ray luminosities is a logical
assumption. In fact, recent observations support this supposition
[13].
We used this latter method to estimate the contribution of unresolved
blazars to the EGRB, and found that up to 100% of the EGRB measured by
can be accounted for
[7]. Our
model assumes a linear relationship between the differential
-ray luminosity
l
at
Ef = 0.1 GeV and the differential radio
luminosity lr at 2.7 GHz for all sources,
l
lr
with
determined by the
observational data.
One can then used the measured radio LF
fr(lr, z) for blazars
(flat spectrum radio sources)
[14]
to calculate the collective
-ray output of all
blazars. This LF is shown in Figure 2.
![]() |
Figure 2. Radio luminosity (power) function at 2.7 GHz after Dunlop and Peacock [14]. |
The simplified elements of our calculations are as follows:
We assume that blazars spend 97% of their time in a quiescent state
and the remaining 3% of their time in a flaring state
We assume that the -ray and
radio LFs in their quiescent state are related by
f
(l
, z) =
-1
fr(
-l
, z).
This relation changes by an average
-ray "amplification factor",
< A > = 5, when the blazars are flaring.
We assume that
-ray spectra
for all sources are of the power-law form l(E) =
l
(E /
Ef)-
, where
is assumed to be
independent of redshift. We have taken the distribution of such spectral
indeces,
, from
appropriately related EGRET data.
We also assume a slight hardening of the
blazar spectra when they are in the flaring state which is supported by
the EGRET data. For further details, see Ref.
[7].
The number of sources N detected is a function of the
detector's PSS at the fiducial energy Ef,
[F(Ef)]min,
where the integral -ray
photon flux F is related to
l
by
![]() | (2) |
where R0 r(1 + z) is the luminosity distance to the source. The number of sources at redshift z seen at Earth with an integral flux F(Ef) is given by
![]() | (3) |
where l
in the integrand depends on z(r) and
F(Ef) from eq. 2. The LF,
f
, includes
both quiescent and flaring terms.
Figure 3 shows the results of our calculation
of the number of sources versus flux above 0.1 GeV, i.e., our
predicted source count curve, compared to the EGRET detections
[7]. The
cutoff at ~ 10-7 cm-2 s-1 for
Ef = 0.1 GeV, their quoted PSS,
is evident by the dropoff in the detected source count below this flux
level.
To calculate the EGRB, we integrate over all sources not detectable by the telescope to obtain the differential number flux of EGRB photons at an observed energy E0:
![]() | (4) |
This expression includes an integration over the probability
distribution of spectral indices
based on the second
EGRET Catalog
[15].
There is also an important attenuation factor in this expression; the
attenuation occurring as the
-rays produced by blazars
propagate through intergalactic space and interact with
cosmic UV, optical, and IR background photons to produce
e± pairs.
If a substantial fraction of the EGRB is from high-z sources, a
steepening
in the spectrum should be seen at energies above ~ 20 GeV caused by the
attenuation effect
[16].
Figure 4, from Ref.
[16],
shows the calculated EGRB spectrum (based on the EGRET PSS)
compared to EGRET data. The slight curvature in the spectrum
below 10 GeV is caused by the distribution of unresolved blazar spectral
indeces; the harder
sources dominate the higher energy EGRB and the softer sources dominate the
lower energy EGRB. The steepened spectra above ~ 20 GeV in
Figure 4 show
the attenuation effect and its uncertainty.
![]() |
Figure 4. The predicted EGRET EGRB from unresolved blazars compared with the EGRET data. GLAST should see an EGRB about a factor of 2 lower at energies above 1 GeV (see text). |
2.2. Critique of the Assumption of Independence of Blazar Gamma-Ray and Radio Luminosities
Chiang and Mukherjee
[17]
have attempted to calculate the EGRB from
unresolved blazars assuming complete independence between blazar
-ray
and radio luminosities. They then used the intersection between the sets
of flat spectrum radio sources (FSRSs) of fluxes above 1 Jy found in the
Kühr catalogue and the blazars observed by EGRET as their
sample,
optimizing to the redshift distribution of that intersection set to obtain
a LF and source redshift evolution. Using this procedure,
they derived a LF which had a low-end cutoff at 1046 erg
s-1.
Then, with no fainter sources included in their analysis, they
concluded that only ~ 1/4 of the 0.1 to 10 GeV EGRB could be accounted
for as unresolved blazars and that another origin must be found for the EGRB
in this energy range.
We have argued above that it is reasonable to expect that the radio and
-ray
luminosities of blazars are correlated. Any such correlation will
destroy the
assumption of statisitical independence made by Chiang and Mukherjee and
introduce a bias in their analysis. In fact, their analysis leads to many
inconsistencies. Among them are the following:
A. The LF derived by Chiang and Mukherjee [17] allows for no sources with luminosities below 1046 erg s-1. In fact, all of the six sources found by EGRET at redshifts below ~ 0.2 have luminosites between ~ 1045 erg s-1 and ~ 1046 erg s-1 [18]. Elimination of fainter sources from the analysis can only lead to a lower limit on the EGRB from unresolved blazars. The fainter sources contribute significantly in acounting for unresolved blazars being the dominant component of the EGRB. (In this regard, see also, Ref. [19])
B. Chiang and Mukherjee limit the EGRET sources in their analysis
only to the FSRSs in the Kühr catalogue. However, if there is truly no
correlation between blazar radio and
-ray luminosities, then any
of the millions
of FSRSs given by the Dunlop and Peacock radio LF
[14] are equally
likely to be EGRET sources. In that case, of the 50 odd sources
in the
2nd EGRET catalogue, virtually none, i.e. ~
10-6, should be Kühr sources.
The above discussion indicates that the assumption of non-correlation
between
the radio and -ray fluxes
of blazars made by Chiang and Mukherjee in their
analysis is not a good one and that this assumption invalidates their
conclusions.
With an estimated point source sensitivity (PSS) nearly two orders of magnitude lower than EGRET's, GLAST will be able to detect O(102) times more blazars than EGRET, and measure the EGRB spectrum to > 1 TeV (assuming the EGRET power law spectrum). These two capabilities will enable GLAST to either strongly support or reject the unresolved-blazar hypothesis for the origin of the EGRB.
Figure 3 shows that O(103) blazars should be detectable by GLAST, assuming it achieves a PSS of ~ 2 × 10-9 cm-2 s-1. Using this PSS and our derived source count curve as shown in Figure 3, we have estimated that the remaining "diffuse" EGRB seen by GLAST should be a factor of ~ 2 lower for E > 1 GeV. Below 1 GeV, this factor of 2 will not apply because source confusion owing to the poorer angular resolution of GLAST at these lower energies will reduce the number of blazars resolved out of the background.
We conclude that GLAST can test the unresolved blazar background model in three ways:
A. GLAST should see roughly 2 orders of magnitude more blazars than
EGRET because of its ability to detect the fainter blazars which
contribute to the EGRB in our model. It can thus make a much deeper
determination of the source count curve. GLAST can also
determine the redshift distribution of many more identified
-ray
blazars, using its better point source angular resolution to make
identifications with optical sources having measured redshifts.
With its larger dynamic range, GLAST can then test the assumption
of an average linear relation between
the
-ray and radio fluxes
of identified blazars.
All of these determinations will test the basic assumptions and results
of our model.
B. With its better PSS, GLAST will resolve out more blazars from the background. Thus, fewer unresolved blazars will be left to contribute to the EGRB. reducing the level of the measured EGRB compared to EGRET's by a factor of ~ 2 if our predictions are correct.
C. The much greater aperture of GLAST at 100 GeV will allow a
determination of whether or not a steepening exists in the EGRB, since
the number of EGRB -rays
recorded by GLAST above 100 GeV
will be of order 103 to 104, assuming a
continuation of the EGRET power-law spectrum. Such a steepening
can be caused by both absorption and intrinsic turnovers in blazar spectra.
Given enough sub-TeV spectra of individual blazars with known redshifts,
these two effects can be separated.