1. Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT Observations Jack Singal AAS HEAD Meeting 4/10/13 With: Vahe Petrosian Allan Ko J. Singal, A. Ko, & V. Petrosian, in prep

2. Context The Fermi-LAT catalogs report gamma-ray flux (F 100 ) and photon spectral index (Γ) Spectroscopic redshifts for almost all of the Fermi-LAT 1LAC FSRQ blazars have been provided by Shaw et al. (2012, ApJ, 748, 49), providing a sample that is essentially complete only limited by the Fermi-LAT observations. Approximately half the blazars observed by the Fermi-LAT in it’s first and second catalogs are Flat Spectrum Radio Quasar (FSRQ) type With this - plus redshifts - one can determine the luminosities and would have the relevant information to find the redshift evolutions in Lγ and Γ, as well as the density evolution and the integrated output Another analysis has been done by Ajello et al. (2012, ApJ, 751, 108) Here we discuss the results of non-parametric methods to get the luminosity and spectral distributions directly from the Fermi-LAT and redshift data

3. Why is it not straightforward? The data is truncated! We are missing (many) objects. Because of the energy dependence of the Fermi-LAT PSF hard spectrum objects can be seen to a lower flux Also missing low flux high redshift objects Goal here: Compute directly the luminosity and photon index evolutions, density evolution, local distributions, and integrated output of FSRQs, properly accounting for the truncations, using techniques we’ve developed. (to get the evolutions and distributions) Missing these Fermi-LAT 1LAC blazars FSRQ BL Lac Unknown type

4. Data and Methods We have been using a custom variant of the Kendall Tau test with “associated sets” to access the true intrinsic distributions of populations from flux-limited surveys Fermi-LAT 1 LAC FSRQs with spectro-zs Techniques explored and extended in : - Singal et al., 2011, ApJ, 743, 104 - Singal et al., 2012, ApJ, 753, 45 - Singal et al., 2013, ApJ, 764, 43

5. Notation: Evolving Luminosity Functions Parameterize luminosity function in a band : density evolution ‘local’ luminosity function Luminosity evolution with redshift, can parameterize luminosity evolution with redshift Or, for samples with more high redshift objects Ψ a (L a,z) gives # of objects per luminosity per comoving volume Integrate dL dz to get total number Here we have relatively low redshift objects

6. Results: Luminosity and Index Evolutions k γ =6.5±0.3, k Γ =0±0.1 FSRQ blazars have undergone significant gamma-ray luminosity evolution with redshift, but not photon index evolution Requires simultaneous determination of best-fit evolutions τ comb = 1 and 2 contours

7. Results: Density Evolution Cumulative density evolution σ(z) determined with Lynden- Bell method (1971, MNRAS, 155, 95) modified with associated sets (e.g. Singal et al., 2012, ApJ, 764, 43) # of objects with redshift less than object j which are in object j’s associated set Raw data True density ev.

8. Results: ‘Local’ Luminosity Function (With best-fit redshift evolution taken out) Cumulative lum. fn. Determined by modified Lynden-Bell (1971, MNRAS, 155, 95) modified with associated sets (e.g. Singal et al., 2012, ApJ, 764, 43) Local cumulative gamma-ray Lum. function

9. Results: Photon Index Distribution Since there is no redshift evolution in the photon index, we can use the photon index distribution h(Γ) that we determined for all 1 LAC FSRQs in Singal et al. (2012, ApJ, 753, 45). Cumulative lum. fn. Determined by modified Lynden-Bell (integral removes correlation with flux) Observed Intrinsic For FSRQs h( Γ ) Gaussian: μ=2.52±0.08 σ=0.17±0.02 Shows for all 1LAC blazars but we have FSRQs separately as well

10. Results: Contribution to the EGB With the distributions and evolutions we can calculate the total energy output from FSRQs Integrating ψ(L γ ) by parts gives the dependence on the cumulative lum fn. Φ (L γ ). Then we express in terms of the local luminosity function Φ (L γ ’ ). Integrating over all luminosities the surface term is zero and This allows us to calculate the total directly from the determined distributions (no fitting) We find that 1.0 ( +0.4 / -0.1 ) MeV cm -2 sec -1 sr -1 This can be compared with the total EGB (resolved and unresolved) measured by the Fermi-LAT of 4.72 ( +0.63 / -0.29 ) MeV cm -2 sec -1 sr -1 We find that FSRQs in toto account for 22( +10 / -4 )% of the EGB Ajello et al. (2012, ApJ, 751, 108) report 21.7( +2.5 / -1.7 )% In Singal et al. (2012, ApJ, 753, 45) we calculated that all blazars account for 39-66% of the EGB

11. Conclusions We use well established non-parametric methods to determine the evolutions and distributions of gamma-ray luminosity and photon index directly from Fermi-LAT data for FSRQs. FSRQ blazars exhibit strong luminosity evolution with redshift in the gamma-ray band. FSRQ blazars do not exhibit redshift evolution of the photon index. FSRQ blazars have rapid density evolution, peaking at around redshift 1. FSRQ blazars in toto account for 22( +10 / -4 )% of the EGB. Further discussion / info: J. Singal, A. Ko, & V. Petrosian, in prep

12. In a nutshell: Kendall Tau Test with “Associated Sets” We determine the correlations in truncated data by the Kendall Tau test modified with the method of ‘associated sets’ (B. Efron, & V. Petrosian, 1992, ApJ, 399, 345 & 1999, JASA, 94, 447) Example of associated set: Say I wanted to determine the luminosity rank of the red point among all points of a lower redshift excluded – would not be seen if at redshift of point in question The associated set is an unbiased set for comparison Will be more complicated to form associated sets if multiple variables, etc… (Because of the truncation, the raw rank would be seriously biased) Techniques explored and extended in : - Singal et al., 2011, ApJ, 743, 104 - Singal et al., 2012, ApJ, 764, 43