Population studies of
γ-ray
blazars were undertaken soon after the recognition of the
γ-ray
blazar class with EGRET
[16].
[10]
performed a < V / Vmax > analysis assuming
no density evolution and showed that luminosity evolution of EGRET
blazars was implied by the data. With a larger data set, and using
radio data to ensure the sample was unbiased in regard to redshift
determination,
[11]
again found that luminosity evolution was
required. They obtained best-fit values through the maximum likelihood
method that gave an AGN contribution to the EGRET
γ-ray
background at the level of
25%.
[40]
postulated a radio /
γ-ray
correlation in blazars, and tried to correct for the duty cycle and
γ-ray
spectral hardening of flaring states. They found that essentially 100%
of the EGRET
γ-ray
background arises from unresolved blazars and AGNs. In later work
[41],
they predict that GLAST will detect
5000 blazars to a
flux level of
2 × 10-9
ph(> 100 MeV)/(cm2-s), which will be reached with GLAST after
4 years. They did
not, however, fit the blazar redshift
distribution to provide a check on their model, nor distinguish
between flat spectrum radio quasar (FSRQ) and BL Lac objects.
The crucial underlying assumption of this approach, which has been developed in recent work [18, 33], is that there is a simple relation between the radio and γ-ray fluxes of blazars. Because a large number of EGRET γ-ray blazars (primarily FSRQs) are found in the 5 GHz, > 1 Jy [23] catalog, a radio / γ-ray correlation is expected. This correlation is not, however, evident in 2.7 and 5 GHz monitoring of EGRET γ-ray blazars [30]. X-ray selected BL objects are also not well-sampled in GHz radio surveys. Studies based on correlations between the radio and γ-ray emissions from blazars must therefore consider the very different properties and histories of FSRQs and BLs and their separate contributions to the γ-ray background.
Treatments of blazar statistics that avoid any radio /
γ-ray
correlation and separately consider FSRQs and BL Lac objects have been
developed by
[29]
and
[12].
In the
[29]
study, blazar spectra were calculated assuming an injection electron
number index of -2. Distributions in injected particle energy in BL
Lac and FSRQ jets were separately considered, with a simple
description of density evolution given in the form of a cutoff at some
maximum redshift zmax. Depending on the value of
zmax,
[29]
concluded that as much as
40
- 80% of the EGRB is produced by unresolved AGNs, with
70 - 90% of the
emission from FR 1 galaxies and BL Lac objects.
In my recent study
[12],
I also use a physical model to fit
the EGRET data on the redshift and size distribution of EGRET
blazars. The EGRET blazar sample consists of 46 FSRQs and 14 BL Lac
objects that were detected in the Phase 1 EGRET all-sky survey
[16],
with fluxes as reported in the Third EGRET catalog
[19].
A blazar is approximated by a relativistic spherical
ball entraining a tangled magnetic field and containing an isotropic,
power-law distribution of nonthermal electrons. Single electron
power-law distributions were used in the study, with indices p = 3.4
for FSRQs and p = 3.0 for BL Lac objects, giving spectral indices
= -0.2 and
= 0.0,
respectively, as shown by observations
[31,
50].
Beaming patterns appropriate to
external Compton and synchrotron self-Compton processes, and bulk
Lorentz factor
= 10
and
= 4, were used
in FSRQs and
BL Lac objects, respectively. The comoving directional luminosities
l'e and blazar comoving rate densities (blazar formation
rate; BFRs) for the two classes were adjusted to give agreement with
the data. The threshold detector sensitivity
-8,
in units of 10-8 ph(> 100 MeV)/(cm2-s), was
nominally taken to be
-8 =
15 for the two-week on-axis EGRET sensitivity, and
-8 =
0.4 for the one-year all-sky sensitivity of GLAST. Due
to incompleteness of the sample near threshold, the EGRET threshold
was adjusted to
-8 =
25. Because a mono-luminosity function
was used, the range in apparent powers is entirely kinematic in this
model, arising from the different, randomly oriented jet directions.
By using a minimalist blazar model, the model parameters were severely
constrained. The FSRQ data were fit with l'e =
1040 ergs/(s-sr) and a BFR that was
15 &215; greater at
z
2 - 3 than at
present. The BL Lac data, by contrast, could
not be fit using a fixed luminosity. A model that could jointly fit
the redshift and size distribution of BL Lac objects required that BL
Lac objects be brighter and less numerous that in the past, consistent
with a picture where FSRQs evolve into BL Lac objects
[8,
27].
Fig. 1b shows the fitted EGRET
redshift distributions and predicted redshift distributions of
γ
galaxies and blazars at different GLAST sensitivities
[12].
The fits to the EGRET size
distributions of FSRQs and BL Lac objects, and extrapolations of the
model size distributions to lower flux thresholds, are shown in
Fig. 1c. After one year of
observations with GLAST
(-8
0.4),
800 FSRQs/FR2
and
200 BL Lac/FR1
γ
galaxies and
γ-ray
blazars are predicted. This is a lower
prediction, and additional hard-spectrum blazars to which EGRET was
not sensitive could increase this number, but not by more than a
factor
2. The
contribution of unresolved blazars below a flux level of
-8
12.5 - 25 to the EGRB is
shown in Fig. 1a. As can be seen,
the total blazar /
γ galaxy
contribution is less than
20 - 30% of the EGRET
EGRB intensity, meaning that other classes of sources must make a
significant contribution.