Erratum: “A Hadronic Synchrotron Mirror Model for the "Orphan" TeV Flare in 1ES 1959+650” (ApJ, 621, 176 [2005])

Abstract

In the estimate of the synchrotron radiation energy density from the primary synchrotron flare (eq. [3]), I had neglected to include the numerical value of νFν(sy) as quoted earlier in the paper. With this, equation (3) should readusy(Rm)~(d2L)/(R2mc)νFν(sy)~8.2×10-5Γ-41Δt-220 ergs cm-3, (3)and equation (4) will be, accordingly,u'r,sy~(τmΓ2usy(Rm))/4π~6.5×10-5Γ-21Δt-220τ-1 ergs cm-3. (4)Furthermore, equation (5) should include a factor of Δγ'p, representing the width (FWHM) of the Δ resonance, Δγ'p/γ'p~ΔE/EΔ~1/2. With these corrections, the following equations should readνFν(VHE)~(L'VHEΓ4)/(4πd2L)~1.4×10-65Np(γ'p)Δt-220τ-1E-2sy,1 ergs cm-2 s-1, (6)Np(γ'p)~2.2×1055Δt220τ-1-1E2sy,1, (7)Np~2.2×1056((300)s)/s-1Γ1-2s1Δt220τ-1-1E2-ssy,1, (8)n'p~5×1012Γ-31Δt220τ-1-1R-316 cm-3(s=2), (9)E'b,p~1.2×1057Γ-21Δt220τ-1-1 ergs, (10)Lkinp~2.7×1050R-116Δt220τ-1-1f-3 ergs s-1. (11)The estimates concerning the π+ production and decay, and the resulting (optical) secondary synchrotron flare, remain unaffected by these changes. Equations (9)-(11) indicate that unreasonably high values of the relativistic proton density and hadronic jet power would be required in the model's original form. However, it should be noted that a similar synchrotron mirror model may still be viable if one takes into account the contribution of reflected synchrotron radiation of the blob as it travels close to the reflector. Although the synchrotron luminosity drops by a factor of a few between the primary synchrotron outburst and the orphan TeV flare, the proximity of the synchrotron-emitting source (replacing Rm by a distance r