Constraining the location of rapid gamma-ray flares in the flat spectrum radio quasar 3C 273

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Table 3

Parameters of fitted power laws.

Bin	JD′	F ₁₀₀	Model	Γ/α/Γ₁	β/Γ₂	E _break	ΔΓ	−2Δ(ln L)	Significance^a
	[JD–2 454 000]	(10^-6 ph cm^-2 s^-1)				(GeV)	(Γ₂ − Γ₁)

high	1042−1294	1.31 ± 0.02	PL	2.57 ± 0.01		...
			logP	2.74 ± 0.03	0.08 ± 0.01	...		44.7	6.7σ
			SBPL	2.47 ± 0.02	2.94 ± 0.06	1.2 ± 0.2	0.47 ± 0.06	40.5	6.1σ
low	1300−1720	0.24 ± 0.10	PL	2.87 ± 0.05		...
			logP	2.86 ± 0.04	0.09 ± 0.04	...		9.9	3.3 σ
			SBPL	2.70 ± 0.01	3.25 ± 0.10	1.0 ± 0.2	0.55 ± 0.10	11.9	3.3σ
Flare A	1058−1078	1.62 ± 0.07	PL	2.60 ± 0.05		...
			logP	2.82 ± 0.10	0.11 ± 0.04	...		6.3	2.6σ
			SBPL	2.48 ± 0.08	3.11 ± 0.28	1.0 ± 0.2	0.63 ± 0.28	9.8	2.9σ
Flare B	1086−1114	3.15 ± 0.08	PL	2.45 ± 0.03		...
			logP	2.63 ± 0.13	0.12 ± 0.06	...		29.6	5.1σ
			SBPL	2.32 ± 0.02	2.90 ± 0.09	1.2 ± 0.2	0.58 ± 0.09	24.9	4.7σ
Flare C	1140−1150	2.25 ± 0.11	PL	2.45 ± 0.04		...
			logP	2.56 ± 0.09	0.06 ± 0.02	...		7.3	2.9σ
			SBPL	2.37 ± 0.03	2.86 ± 0.08	1.3 ± 0.2	0.49 ± 0.08	9.9	2.9σ
Flare D	1202−1204	3.83 ± 0.32	PL	2.46 ± 0.08		...
			logP	2.74 ± 0.12	0.25 ± 0.06	...		9.8	3.3σ
			SBPL	2.47 ± 0.10	2.99 ± 0.13	1.6 ± 0.2	0.52 ± 0.16	6.3	2.2σ
Flare E	1260−1275	2.38 ± 0.11	PL	2.46 ± 0.02		...
			logP	2.63 ± 0.18	0.09 ± 0.07	...		7.2	2.7σ
			SBPL	2.36 ± 0.05	3.72 ± 0.18	1.9 ± 0.2	1.36 ± 0.18	12.1	3.1σ

Notes. Δ(ln L) is the difference of the –log(likelihood) value of logP, SBPL with respect to PL.

^(a)

We follow Wilks’ theorem to estimate the significance, i.e., twice the difference between the log(likelihood) values for the two spectral models is formally distributed as χ² with Δn degrees of freedom, where Δn is the difference in the number of degrees of freedom between the two models.

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