## 3. A pilot test with the current dataThe only available data for the gamma ray fluxes of blazars are those given in the Second Catalog of High Energy Gamma Ray Sources compiled by the EGRET team (Thompson et al. 1995). The relevant quantities include the gamma ray number flux above 100 MeV and the power law spectral index. Since many sources are time variable and observations at different viewing periods give different fluxes and spectral indices, we average the fluxes and indices for each source with a weighting factor being proportional to the photon number recorded in each period. Then we convert the photon number flux integrated above 100 MeV into the differential energy flux at 100 MeV, assuming a single power spectrum in the energy range 100 MeV - 10 GeV. For those sources whose spectral indices are not given in the Catalog, we assume that the differential number indices are 2.0 or the differential energy indices are 1.0 in our analysis. We have compiled two sets of radio data for the gamma ray blazars.
One is from the all-sky low resolution surveys at 5 GHz (Kühr et
al. 1981; Becker, White & Edwards 1991; Gregory & Condon
1991). The relevant quantities include the radio flux density at 5 GHz
and power law spectral index between 2.7 GHz and 5 GHz. The other is
from the all-sky VLBI survey at 2.3 GHz (Preston et al. 1985). The
relevant quantity is the "correlated" flux density defined by the
authors. Cosmological redshifts are needed for the K-correction in our
analysis, and the data are taken from the Quasar Catalog of Hewitt and
Burbidge (1993). For those blazars without Table 1 lists our sample of data. Column 1 gives the name of the sources in terms of celestial coordinates (1950); column 2 gives the redshifts; column 3 gives the integrated gamma ray number fluxes above 100 MeV in units of ; column 4 gives the indices of differential gamma ray energy spectra; column 5 gives the radio flux densities at 5 GHz; column 6 gives the radio spectral indices between 2.7 GHz and 5 GHz; and column 7 gives the radio flux densities from the VLBI survey at 2.3 GHz. The radio flux densities are in units of Jy.
We start our analysis with a correlation study of the sample of
data. Fig. 1 shows the scatter plot of radio spectral index
versus gamma ray spectral index
. Here is defined in such
a way that where is the
radio frequency. There are totally 31 datum points. The Pearson's
Next, we study the correlation between radio fluxes and gamma ray
fluxes. The integrated gamma ray number fluxes are converted into
differential energy fluxes at 100 MeV. The K-correction
is made for both the gamma ray and radio flux
densities. For those gamma ray sources without
In Fig. 3, we plot the gamma ray flux density versus the radio one of high resolution (VLBI survey). These flux densities are also K-corrected with the above procedure. There are totally 45 datum points. The correlation is found to become stronger, with and the probability of confidence . This more significant correlation strengthens our view that the gamma ray and radio emission are kinematically linked. The radio core flux is normally a small fraction of the total and it may emerge only from a specific part of the jet. Further, it is likely that the gamma ray emission in blazars emerges from the radio core where the Lorentz factors for both emissions are equal or very close in value. The deviations from the correlation are due to the random spreads in the intrinsic luminosity ratio, spectral index and Lorentz factor. These effects will be studied with Monte-Carlo simulations in Sect. 4. We may conclude that the VLBI data are more suitable for the test of beaming statistics.
Now let us perform the test with our sample of data. The observed
distribution of
© European Southern Observatory (ESO) 1997 Online publication: May 5, 1998 |