Study of the variability of Blazars gamma-ray emission

The gamma-ray emission of blazar jets shows a pronounced variability and this feature provides limits to the size and to the speed of the emitting region. We study the gamma-ray variability of bright blazars using data from the first 18 months of activity of the Large Area Telescope on the Fermi Gamma-Ray Space Telescope. From the daily light-curves of the blazars characterized by a remarkable activity, we firstly determine the minimum variability time-scale, giving an upper limit for the size of the emitting region of the sources, assumed to be spheroidal blobs in relativistic motion. These regions must be smaller than ~10^-3 parsec. Another interesting time-scale is the duration of the outbursts. We conclude that they cannot correspond to radiation produced by a single blob moving relativistically along the jet, but they are either the signature of emission from a standing shock extracting energy from a modulated jet, or the superposition of a number of flares occurring on a shorter time-scale. We also derive lower limits on the bulk Lorentz factor needed to make the emitting region transparent for gamma-rays interacting through photon-photon collisions.

💡 Research Summary

This paper presents a systematic study of gamma‑ray variability in a sample of bright blazars using the first 18 months of observations from the Large Area Telescope (LAT) aboard the Fermi Gamma‑Ray Space Telescope. The authors begin by extracting daily light curves (E > 100 MeV) for all LAT‑monitored sources and apply a statistical selection: only sources with an average flux above 2 × 10⁻⁶ ph cm⁻² s⁻¹ and a reduced chi‑square greater than 8 when compared to a constant‑flux model are retained. Five objects satisfy these criteria: 0235+164, 3C 273, 3C 279, PKS 1510‑089, and 3C 454.3.

For each source the unbinned likelihood analysis (gtlike) provides daily fluxes and photon indices (Γγ). The minimum variability time‑scale (Δt_min) is defined as the shortest interval in which the flux changes by at least 4σ between adjacent daily bins. The resulting Δt_min values are typically ≤ 1 day, with the most rapid change observed in 3C 454.3 (≈ 3 h) and the others ranging from 5 to 8 h.

Using the causality relation R < c Δt_min δ/(1 + z) and the γ‑γ transparency condition of Dondi & Ghisellini (1994), the authors derive lower limits on the Doppler factor δ and upper limits on the size of the emitting region R. For the five blazars the inferred Doppler factors lie between ≈ 2 and 8, while the corresponding radii are ≤ 10⁻³ pc (∼10¹⁵–10¹⁶ cm). These dimensions are comparable to a few tens of Schwarzschild radii for a typical supermassive black hole, indicating that the gamma‑ray emission originates from a very compact zone within the jet.

The paper then addresses longer‑lasting outbursts, defined as coherent flux increases lasting several days to weeks. Detailed inspection of the light curves shows that 3C 454.3 experienced an 11‑day outburst in late 2009, while 3C 273 displayed a series of sharp spikes each lasting 3–4 days. The authors test whether a single spherical blob moving relativistically along the jet can reproduce the observed outburst duration. By relating the observed outburst time Δt_outburst to the blob’s intrinsic travel time Δt_e through Δt_outburst ≈ Δt_e Γ²/(1 + z) (assuming a viewing angle θ ≈ 1/Γ), they find that reproducing multi‑day outbursts would require bulk Lorentz factors Γ of several tens. This is inconsistent with the much lower Doppler factors derived from the minimum variability analysis (Γ ≈ δ ≈ 2–8). Consequently, a single moving blob model is ruled out.

Two alternative scenarios are proposed. First, a standing shock (a stationary disturbance in the jet) could be illuminated by a modulated flow, producing a prolonged emission episode without requiring extreme bulk speeds. Second, the apparent outburst could be the superposition of many short flares (each with Δt_min ≈ hours) that occur in rapid succession, effectively smoothing the light curve into a longer event. The authors estimate the expansion of a blob during its travel using a jet opening angle ψ ≈ 0.1 rad, showing that the increase in radius is modest compared with the initial size set by Δt_min.

Finally, the paper calculates lower limits on the bulk Lorentz factor required for the emitting region to remain transparent to internal γ‑γ pair production. The resulting Γ_min values are comparable to the Doppler factors obtained earlier, reinforcing the conclusion that the emission region must be both compact and moderately relativistic. The authors note that while very high Γ values (≫ 10) might be acceptable for BL Lac objects, they would cause severe γ‑γ absorption in flat‑spectrum radio quasars (FSRQs) because of the enhanced external photon fields involved in external‑Compton scattering.

In summary, this work leverages the continuous, all‑sky monitoring capability of Fermi‑LAT to place stringent constraints on the size, Doppler factor, and bulk Lorentz factor of gamma‑ray emitting zones in bright blazars. It demonstrates that the rapid, hour‑scale variability implies sub‑parsec emitting regions, while the multi‑day outbursts cannot be explained by a single moving blob. The findings favor either stationary shock structures or a cascade of short flares as the origin of long‑duration gamma‑ray activity, providing valuable inputs for theoretical models of jet dynamics and high‑energy emission mechanisms.