The Gamma-ray Luminosity Function of Flat-Spectrum Radio Quasars

TL;DR

Problem: determine the gamma-ray luminosity function of flat-spectrum radio quasars (FSRQs) and their cosmic evolution using the largest gamma-ray selected sample to date. Approach: a parametric unbinned maximum-likelihood analysis that couples a double power-law local LF with luminosity-dependent density evolution (LDDE), incorporating a Gaussian photon-index distribution and robust sky-coverage; compare PDE, PLE, and LDDE using the Akaike Information Criterion. Findings: LDDE provides the best description, with a double power-law local LF and a luminosity-dependent turnover in evolution; higher-luminosity FSRQs peak earlier in cosmic time, while the luminosity density peaks around $z\sim1-2$ and the space density around $z\sim0.2-0.4$; an unexpected similarity arises between FSRQ and BL Lac evolutions at intermediate luminosities, raising the possibility of contamination or a shared evolutionary path. Significance: tightens constraints on blazar evolution, informs SMBH growth scenarios, and clarifies the contribution of FSRQs to the extragalactic gamma-ray background.

Abstract

We have utilized the largest sample of $γ$-ray selected Fermi flat-spectrum radio quasars (FSRQs) ever used (519 sources) to construct the luminosity function and its evolution through the cosmic history. In addition to spanning large redshift ($0<z\lesssim 4$) and luminosity ranges ($2.9\times10^{43}$ erg s$^{-1}$ - $7.3\times10^{48}$ erg s$^{-1}$), this sample also has a robust calculation of the detection efficiency associated with its observation, making its selection effects and biases well understood. We confirm that the local luminosity function is best explained by a double power law. The evolution of the luminosity function of FSRQs follows a luminosity-dependent density evolution. FSRQs experience positive evolution with their space density growing with increasing redshift up to a maximum redshift, after which the numbers decrease. This peak in redshift occurs at larger redshifts for higher luminosity sources and at lower redshifts for lower luminosity sources. We find an unexpected similarity between the luminosity function of FSRQs and that of BL Lacertae objects at intermediate luminosity. This could be a sign of a strong genetic link between the two blazar sub-classes or that BL Lac samples are contaminated by large amounts of FSRQs with their jets nearly perfectly aligned with our line of sight.

Figures (12)

• Figure 1: Observed redshift (upper left), luminosity (upper right), photon index (lower left), and intrinsic cumulative source count (lower right) distributions of LAT FSRQs. The solid line is the best-fit line of the PLE model, including the effects of selection bias to compare with the observed data. The error bars represent the statistical uncertainties based on Poisson statistics. In the case of zero sources in a given bin, the $1\sigma$ upper limits are shown Gehrels1986_errorbars. The red data points (lower right), showing the intrinsic source count distribution, are calculated using the sky coverage. The corresponding error bars show the propagated errors including the statistical uncertainty and the uncertainty in the sky coverage.
• Figure 2: Observed redshift (upper left), luminosity (upper right), photon index (lower left), and intrinsic cumulative source count (lower right) distributions of LAT FSRQs. The solid line is the best-fit line of the PDE model, including the effects of selection bias to compare with the observed data. The error bars represent the statistical uncertainties based on Poisson statistics. In the case of zero sources in a given bin, the $1\sigma$ upper limits are shown Gehrels1986_errorbars. The red data points (lower right), showing the intrinsic source count distribution, are calculated using the sky coverage. The corresponding error bars show the propagated errors including the statistical uncertainty and the uncertainty in the sky coverage.
• Figure 3: Observed redshift (upper left), luminosity (upper right), photon index (lower left), and intrinsic cumulative source count (lower right) distributions of LAT FSRQs. The solid line is the best-fit line of the LDDE model, including the effects of selection bias to compare with the observed data. The error bars represent the statistical uncertainties based on Poisson statistics. In the case of zero sources in a given bin, the $1\sigma$ upper limits are shown Gehrels1986_errorbars. The red data points (lower right), showing the intrinsic source count distribution, are calculated using the sky coverage. The corresponding error bars show the propagated errors including the statistical uncertainty and the uncertainty in the sky coverage.
• Figure 4: The intrinsic differential source count distribution (logN-logS) of FSRQs plotted against the energy flux. The solid blue line represents the intrinsic logN-logS as derived using the LDDE model. The data points are calculated using Equation \ref{['eqn:dNdS']}. The error bars show the propagated errors including the statistical uncertainty and the uncertainty in the sky coverage.
• Figure 5: The LF of Fermi FSRQs subdivided into four bins in redshift, constructed using the $N_{obs}/N_{mdl}$ method. The solid lines depict the best-fit model (LDDE) in each redshift bin, along with the space density in the previous bin given in dashed line for comparison. The systematic uncertainty shown in the blue shaded region was derived using the detection efficiency (see Section \ref{['sec:SkyCoverage']}).