FERMIGAMMA-RAY SPACE TELESCOPE OBSERVATIONS OF THE GAMMA-RAY OUTBURST FROM 3C454.3 IN NOVEMBER 2010

The radio source 3C454.3, a well-known flat-spectrum radio quasar (FSRQ) at redshift z = 0.859, has shown remarkably high activity since 2000. It has been particularly bright in the γ-ray band covered by AGILE and the Fermi-Large Area Telescope (LAT), reaching a daily record flux level F[E > 100 MeV] (F₁₀₀ in units of 10⁻⁶ photons cm⁻² s⁻¹) of 22 ± 1 in 2009 December (Striani et al. 2010; Ackermann et al. 2010). This high flux allowed detailed analysis to be performed, making it the best-studied blazar in the GeV band. Gamma-ray variability on timescales as short as a few hours (Tavecchio et al. 2010) and a flux-doubling timescale of less than 3 hr for a short subflare on 2009 December 5 (MJD55170; Ackermann et al. 2010) have been reported. In the LAT energy band, 3C454.3 exhibits a spectrum with a clear departure from a power-law (PL) distribution, characterized by a break around 2 GeV (Abdo et al. 2009). This is found to be a common feature of bright γ-ray FSRQs (Abdo et al. 2010d). Little variation of the break energy and spectra for large differences in flux states was observed for 3C454.3 (Ackermann et al. 2010). From γγ-opacity constraints, a minimum Doppler factor δ_min ≈ 13 was derived from the flux variability time (Ackermann et al. 2010), and highest-energy photon measurements, in accord with independent measurements of δ from superluminal motion observations (Jorstad et al. 2005).

In 2010 November, the source displayed sustained activity at a flux of F₁₀₀ ≈ 10 for several days before showing a fast rise to record levels of F₁₀₀ = 55, then rising to F₁₀₀ ≈ 80 (as measured over 6 hr long periods). In this Letter, the intraday variability and the associated spectral changes in the γ-ray band of 3C454.3 are studied and comparisons are made with the findings obtained from earlier major flares. In Section 2, observations and analysis of Fermi-LAT data from 2010 September 1 to December 13 are presented. Results are presented in Section 3 and discussion is given in Section 4. A flat ΛCDM cosmology with H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_m = 0.27, and $\Omega _\Lambda$ = 0.73 is used in this Letter.

The analysis performed for this Letter is very similar to that reported in Ackermann et al. (2010), to which we refer for details. The data presented in this Letter are restricted to the 100 MeV–200 GeV range and were collected from MJD55440 (2010 September 1) to MJD55543 (2010 December 13) in survey mode.

Spectral analyses were performed by fitting the spectra with multiple different models over the whole energy range covered by the LAT at E > 100 MeV. The spectral forms considered are a broken power law (BPL, $N(E) = N_0 (E/E_{\rm break})^{-\Gamma _{i}}$, with i = 1 if E < E_break and i = 2 if E > E_break), a log-parabola function ($N(E) = N_0\:(E/E_{p})^{-\alpha -\beta \:\log (E/E_p)}$, where E_p is fixed at 1 GeV), a PL with exponential cutoff function (PLEC, N(E) = N₀ (E/E_p)^−Γexp (− E/E_cutoff)), and a PL model over equally spaced logarithmic energy bins with Γ kept constant and equal to the value fitted over the whole range.

Source variability was investigated by producing light curves with various time binnings (3 hr, 6 hr, 1 day, 1 week) and over different energy ranges (E > 100 MeV, E > 1 GeV, E = 0.1–1 GeV). Although the actual spectral shape exhibits definite curvature, light curves were produced by modeling the spectra in each time bin as a simple PL over the considered energy range, since the statistical uncertainties on the PL indices are smaller than those obtained from BPL fits. In order to minimize spurious correlations between integrated flux and Γ, the fluxes $F_{E>E_0}$ were also computed above the "decorrelation energy" E₀ where this correlation is minimal. For the 2009 December and 2010 April flares, E₀ was found to be 163 MeV (Ackermann et al. 2010). The same value has been used here for consistency. The estimated systematic uncertainty on the flux is 10% at 100 MeV, 5% at 500 MeV, and 20% at 10 GeV. The energy resolution is better than 10% over the range of measured E_break.

Figure 1 (top panel) showing the historical F₁₀₀ light curve illustrates the spectacular rise in activity of 3C454.3 over the years. It is evident that the 2010 December outburst dwarfs any previously recorded flares. The second panel displays the light curves with time binnings of 1 day (open circles) and 1 week (filled circles) during the outburst period. A 13 day long plateau precedes the 5 day long flare, confirming the trend previously observed in the 2008 July and 2009 December flares, but it is longer in duration and higher in flux than those in previous flares (Ackermann et al. 2010). The onset of this plateau is clearly accompanied by a weak but significant hardening of the spectrum (Γ changes from 2.50 ± 0.02 to 2.32 ± 0.03), as observed on a weekly timescale in the bottom panel of Figure 1. The daily flux decreases by a factor of about three in 4 days at the end of the flare. The flare is followed by a slowly decaying activity around F₁₀₀ = 20. Different time periods labeled pre-flare, plateau, flare, and post-flare in Figure 1 are considered in the following.

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The light curves for F₁₀₀ with 6 hr and 3 hr time binnings (focusing on the flare period) are shown in the upper panel of Figure 2. The F[E > 1 GeV] light curves with 6 hr and 3 hr time binnings are given in the second panel of Figure 2. The corresponding evolution of Γ is plotted in the third and bottom panels. As can be seen, the major flare lasts for about 5 days. In the F₁₀₀ light curves, it seems to comprise three to four subflares, with the flux peaking during the last one. The rise time of the MJD55516.5 flare is 12 hr for a factor of four increase in flux (i.e., a doubling time of 6 hr). This is shorter than the previous fastest relative flux variation claimed in the GeV band for a major flare, which was from PKS 1502+106, when an increase by a factor of three in 12 hr (i.e., a doubling time of 7.5 hr) was found (Abdo et al. 2010c). In the upper panel of Figure 2, a fit consisting of a slowly varying background and four faster temporally evolving components was performed between MJD55516.5 and MJD55522 for both the 6 hr and 3 hr light curves. Each component is assumed to be fit by a function of the form

$$\begin{equation} F = 2F_0(e^{(t_0-t)/T_r}+e^{(t-t_0)/T_f})^{-1} \; \end{equation} \tag{ 1 }$$

(Abdo et al. 2010b), where T_r and T_f are the rising and falling times, respectively, and F₀ is the flux at t₀ representing approximately the flare amplitude. With the rise time T_r set equal for all subflares, and likewise for the fall time T_f, we find that T_r = 4.5 ± 1 hr and T_f = 15 ± 2 hr gives a good fit to both the 3 hr and 6 hr light curves. The highest-energy photon collected during the MJD55516–55522 period within the energy and inclination-angle-dependent 95% containment angle around the source position has E_max = 31 ± 3 GeV and was detected at MJD55521.46. Its detection time is depicted with an arrow in the upper panel of Figure 2.

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Significant differences between light curves for fluxes in the E = 0.1–1 GeV (F_{0.1–1 GeV}) and E >1 GeV (F_1 GeV) ranges are observed (see the second panel of Figure 2). The peak of the first subflare occurs approximately 15 hr after F_{0.1–1 GeV} has leveled off, demonstrating clear spectral variability. This behavior is confirmed by a progressive decrease of Γ (spectral hardening) from Γ ≈ 2.35 to Γ ≈ 2.1 as the subflare develops beyond the 100 MeV peak (black points in the third panel of Figure 2). Overall, the F_1 GeV light curve shows sharper structures than the F_{0.1–1 GeV} light curve. A clear difference is also observed in the decaying stage, with the high-energy component starting to fade away later than the lower-energy component. In the lower two panels of Figure 2, the spectral indices obtained over the two restricted energy ranges are shown as well. As F_{0.1–1 GeV} levels off in the first subflare while F_1 GeV keeps rising, the 0.1–1 GeV index is fairly constant, indicating that the hardening is limited to the range above 1 GeV. This hardening is confirmed by the evolution of Γ measured in the >1 GeV range (blue points in the bottom panel of Figure 2).

The pronounced spectral evolution observed during the flare can be further investigated by plotting Γ versus the flux above E₀ = 163 MeV. This is done, with a 6 hr binning in Figure 3 for two consecutive time periods covering approximately the first-half and the second-half of the major flare and two different photon energy ranges: E > 0.1 GeV and E = 0.1–1 GeV. For orientation, the points associated with the earlier times have labels corresponding to those given in the third panel of Figure 2. In addition, 4 day averages obtained during the plateau period are displayed as blue squares. In contrast to the 2009 December–2010 April flares for which no clear pattern was found in the data, a clockwise pattern is observed for the second period. The reduced χ²_r for a fit with a constant Γ are 37.6/8 (P = 8.9 × 10⁻⁶, ∼ 4.4 σ) and 35.4/8 (P = 2.3 × 10⁻⁵, ∼ 4.2 σ) for the first and second periods, respectively (for the E > 0.1 GeV case). For the first period, a flux increase by a factor of four is accompanied by an essentially constant Γ (or one becoming weakly harder). This is followed by a clear hardening of the spectrum at constant flux, with Γ changing from 2.24 ± 0.06 to 2.11 ± 0.04 in 12 hr.

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Such a hard lag can also be observed in the top right-hand panel of Figure 3, where a hardening by Δ Γ = 0.42 ± 0.13, associated with the decaying stage of the flare, occurs over 2.25 days. The spectrum softens fairly quickly afterward, with Γ changing from 2.0 ± 0.1 to 2.31 ± 0.07 in 6 hr. This behavior may be driven by cooling. During the flare, the electron energy distributions may reflect the alternative dominance of acceleration and cooling processes.

Restricting the analysis to the E = 0.1–1 GeV range (bottom panels of Figure 3) produces a pattern similar to the E > 0.1 GeV case for the second period, but somewhat different for the first period, although the patterns are less clear due to larger statistical uncertainties. The rise in flux is accompanied by a pronounced hardening in this energy range followed by a state of essentially constant spectral hardness evolving into a slow softening. This behavior confirms the conclusions obtained in the context of Figure 2. Due to insufficient statistics, no clear pattern of the photon spectral index above 1 GeV versus flux can be observed with 6 hr time binning.

Figure 4 shows the ν F_ν distributions of the Fermi-LAT data for the four different time periods delineated in Figure 1. These distributions have been fitted with BPL (solid), log-parabola function (dashed), and PLEC (dashed-dotted) functions. The parameters of the different fits can be found in the Table 1. As the likelihood method does not provide an absolute goodness-of-fit measure, the χ² of the ν F_ν data points for the different functions have been calculated. For the pre-flare and plateau periods, both BPL and PLEC give fits of similar quality, while the log-parabola fit is notably worse. The PLEC function is preferred for the post-flare period. None of the tested functions provides a very good fit to the energy distribution in that period, which may be a result of the significant spectral evolution during the flare. The ν F_ν spectra obtained over time intervals where the four subflares alternatively dominate are consistent for the first three subflares in terms of curvature, while a significantly harder spectrum is observed between MJD55520.0–55521.5. In that interval, the PLEC fit gives E_cutoff = 8.3 ± 1.7 GeV. A total of 10 photons with E > 10 GeV (out of 12 detected during the entire 5 day flare) were collected in that 1.5 day time lapse (second panel of Figure 2). The variation of E_break and E_cutoff with flux is displayed in the inset of Figure 4. As already found during the 2009 December and 2010 April flares, no strong evolution of either E_break or E_cutoff is found. E_break remains constant within a factor of ≈2 while the flux varies by a factor of ≈40.

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During its 5 day outburst from 2010 November 17 to 21 (flare interval in Figure 1), 3C454.3 was the brightest GeV γ-ray source in the sky, with a flux F₁₀₀ = 66 ± 2 on 2010 November 18–19. Prior to the flaring phase, the Fermi-LAT light curve displays a 13 day long flux plateau preceding the major outburst. The onset of the plateau is marked by a rapid (<1) day flux increase by a factor of ≈2. This feature appears to be a characteristic behavior indicating that 3C454.3 is about to flare, as noted in Ackermann et al. (2010). In the 2009 December flare, the plateau lasted for 6 days at a level of F₁₀₀ ≈ 10 before flaring to a daily flux of ≈22, while for the 2010 April outburst, it lasted for 7 days at a level of F₁₀₀ ≈ 7 before reaching a peak flux of ≈16. The spectrum hardens slightly from the pre-flare to the plateau preceding the giant flare. Spectral hardening and clustering of photons with E > 10 GeV is also seen in the decaying stage of the gamma-ray outburst at MJD55520.0–55521.5, which could point to the presence of radiating hadrons or γγ-absorption effects. In the former case, protons require additional time to accelerate and cool while the <1 GeV flux, if due to rapidly cooling electrons, would decline more rapidly. In the latter case, the emergence of the hard component could occur if the radiating plasma becomes optically thin to γγ-absorption, either due to a larger bulk Lorentz factor or increased size of the radiating plasma.

The features of the giant flare can be compared to those of the two earlier, fainter flares (2009 December and 2010 April) that have been carefully investigated in the LAT energy band (the different observation mode used during most of the 2008 July flare provided poorer-quality data). The overall light curves show similarities (presence of a pre-flare plateau, main flare lasting a few days, several week-long fading period). The rise time T_r of the 2010 November flare is about half that of the 2009 December flare (4.5 hr versus 8.9 hr). Whereas the latter showed indication of "flickering" activity on timescales as short as 3 hr above 100 MeV, this effect is not clearly present here, as demonstrated by similar 3 hr and 6 hr light curves in Figure 1. For the first time, a significant temporary hardening of the spectrum leading to Γ ≃ 2.1 has been observed for 3C454.3. Note that in the first LAT active galactic nucleus (AGN) catalog (Abdo et al. 2010a), less than 2% of FSRQs are found with 11 month averaged Γ < 2.1. The moderately hard spectrum during the large luminosity flare deviates from the trend seen in the blazar divide (Ghisellini et al. 2009), where the most γ-ray luminous blazars generally have Γ ≳ 2.5. Despite the overall spectral variation, the energy cutoff remains essentially unchanged as observed in earlier flares (Figure 4). Interestingly, several-day long spectral variations are also observed during the post-flare period (beyond MJD55524 in Figure 1). No such effect was found in previous flares despite sufficient measurement statistical accuracy. Significant spectral hardening at the end of the main flare was not seen either.

The minimum Doppler factor δ_min can be numerically evaluated from γγ-opacity constraints. From Swift X-ray Telescope public data, the total energy flux in the 2–10 keV range is $0.8\times 10^{-10}\:\rm {erg}\:\rm {cm}^{-2}\:\rm {s}^{-1}$ and the photon-number index is 1.70. Correlated X-ray and GeV variability supports the assumption that the γ-rays are made cospatially with the X-rays. At the time that the 31 GeV photon was observed, t_var = 0.4 days (taken as ln (2) × T_f in the fading phase of the flare), giving δ_min = 16, which is somewhat larger than the value of δ_min = 13 found by Ackermann et al. (2010). The estimated comoving size of the emission region is R' = c t_var δ_min/(1 + z) ≈ 3 × 10¹⁵ cm. For the 31 GeV photon, the optical depth to pair production by the extragalactic background light (EBL) is ≈1 for the high-EBL model of Stecker et al. (2006), so no absorption constraints are provided by these data.

An upper limit on the optical depth τ_γγ(E_max) ≈ 2 arising from the interaction of γ rays with broad-line-region (BLR) photons can be obtained by comparing the flux measured at E_max = 31 GeV, with the flux extrapolated from lower energy. Assuming a BLR luminosity of 3×10⁴⁵ erg s⁻¹(Pian et al. 2005) and adopting a BLR size r_BLR ≈ 6 × 10¹⁷ cm ≈0.2 pc from reverberation mapping (Kaspi et al. 2007; Bonnoli et al. 2011), we calculate τ_γγ(z_em), where z_em is the distance of the emitting blob from the black hole (following Reimer 2007). Assuming that the BLR clouds are distributed between 0.01 pc and r_BLR, the condition τ_γγ(E_max) = 2 is satisfied for z_em ≃ 0.14 pc. Therefore, the emission region must have been located either close to the outer boundary of the BLR or beyond at the time of emission of the 31 GeV photon.

The asymmetry of the time profiles derived for the subflares can be produced by acceleration/radiative losses or light-travel effects in quasi-spherical emission regions (Sikora et al. 2001; Dermer 2004). Assuming a spherical geometry of the emission region, then r < 2c Γ² t_var/(1 + z) ≈ 0.1 pc for a bulk Lorentz factor Γ = δ_min = 16 and a variability timescale t_var ≃ 0.4 days. If the jet opening angle θ_j ≪ 1/δ_min ≃ 3°, then this estimate can be compatible with the location estimated above.

The 3 hr peak F₁₀₀ is 85 ± 5, corresponding to an apparent isotropic γ-ray luminosity L_γ = 10⁵⁰L₅₀ erg s⁻¹ with L₅₀ = 2.1 ± 0.2, assuming a spectral shape for the flare as given in Table 1. This is ≈4 times the luminosity of PKS 1622−297 (L₅₀ ≃ 0.5 with the current cosmological model) during its 1995 flare (Mattox et al. 1997), making this the largest γ-ray luminosity ever observed for a blazar. Foschini et al. (2011) derived a luminosity of L₅₀ ≈ 3.0 during this flare by assuming a PL shape and considering a short 4.7 ks time interval where F₁₀₀ ≳ 100.) During the 5 day flare, F₁₀₀ = 43 ± 1 implies L₅₀ ≃ 1.0. The black hole mass for 3C454.3 is estimated to be in the range of (0.5–4) × 10⁹ M_☉ (Bonnoli et al. 2011; Gu et al. 2001), so L_Edd ≈(0.6–5)× 10⁴⁷ erg s⁻¹. In order for the time-averaged flare luminosity to be lower than L_Edd, θ_j ≲ 2°–6°, and a beaming factor (1 − cos  θ_j)⁻¹ ≳ 200–1700 is implied. For highly efficient γ-ray production, the absolute jet power is comparable to the disk luminosity of L_d = $6.75\,{\times}\, 10^{46}\:\rm {erg}\:\rm {s}^{-1}$ estimated in Bonnoli et al. (2011).

This flaring episode marks a record among AGNs and, indeed, all non-gamma-ray burst sources for its rate of change in apparent luminosity, L_γ/Δt. Using a 6 hr variability timescale, then L_γ/Δt ≃ 10⁵⁰L₅₀ erg s⁻¹/(10⁴ t₄ s) $\simeq 10^{46}L_{50}/t_4\:\rm {erg}\:\rm {s}^{-2}$, noting that 6 hr/(1 + z) ≃ 10⁴ s. By comparison, the giant flares of PKS 2155−304 (Aharonian et al. 2007) reached only ≲ 10⁴⁷ erg s⁻¹/300 s ≈3 × 10⁴⁴ erg s⁻² (in the TeV regime). This value now greatly exceeds L_Edd/(R_S/c) ≈ 1.3 × 10⁴³ erg s⁻² given by the ratio of the Eddington luminosity and the light crossing time across the Schwarzschild radius of a black hole, and strongly violates optically thin, Eddington-limited accretion scenarios (Elliot & Shapiro 1974), showing that such a condition is unlikely to apply to the highly asymmetric disk/jet system of a blazar.

We thank the AGILE team for providing their published data points.

The Fermi-LAT Collaboration acknowledges support from a number of agencies and institutes for both development and the operation of the LAT as well as scientific data analysis. These include NASA and DOE in the United States, CEA/Irfu and IN2P3/CNRS in France, ASI and INFN in Italy, MEXT, KEK, and JAXA in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the National Space Board in Sweden. Additional support from INAF in Italy and CNES in France for science analysis during the operations phase is also gratefully acknowledged.