Table 2.
Some astrophysical properties of the inner engine for GRB 190114C and AGN, in the latter adopting as a proxy M 87* (Rueda & Ruffini 2020).
| GRB 190114C | AGN (M 87*-like) | |
|---|---|---|
| M (M⊙) | 4.4 | 6.0 × 109 |
| α | 0.4 | 0.1 |
| B0 (G) | 4.0 × 1010 | 10 |
| τpole | 4.33 × 10−5 s | 0.68 d |
| ΔΦ (eV) | 3.12 × 1018 | 2.66 × 1017 |
| ℰ (erg) | 7.02 × 1037 | 6.96 × 1044 |
 (erg s−1) |
1.62 × 1042 | 1.18 × 1040 |
| χ (°) | 0.1805−18.05 | 0.0451−4.51 |
| tc (s) | 1.45 × 10−16 − 1.45 × 10−14 | 0.2939−29.39 |
| LGeV (erg s−1) | 4.83 × 1051 − 4.83 × 1053 | 2.37 × 1043–2.37 × 1045 |
Notes. The timescale of particle acceleration along the BH rotation axis τpole is given by Eq. (11); the maximum energy gained in such acceleration ΔΦ is given by Eqs. (8a) and (8b). The energy ℰ available for acceleration and radiation is given by Eqs. (7a) and (7b). The maximum power available for acceleration (i.e., to power UHECRs) is 
and is given by Eq. (13). The pitch angle χ is computed from Eq. (16) adopting the photon energy range 0.1−1 GeV photons; the corresponding synchrotron radiation timescale tc is given by Eq. (18), and an estimate of the associated GeV luminosity, LGeV ∼ ℰ/tc, is also shown. In both cases the corresponding inner engine parameters (BH mass M, spin α, and surrounding magnetic field strength B0) have been fixed to explain the observed high-energy (≳GeV) luminosity (see Sect. 7 for the case of GRB 190114C and Rueda & Ruffini 2020 for M 87*).
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