Nature of the ultrarelativistic prompt emission phase of GRB 190114C

We address the physical origin of the ultrarelativistic prompt emission (UPE) phase of GRB 190114C observed in the interval $t_{\mathrm{rf}}=1.9–3.99\mathrm{s}$, by the Fermi-GBM in 10 keV–10 MeV energy band. Thanks to the high signal-to-noise ratio of Fermi-GBM data, a time-resolved spectral analysis has evidenced a sequence of similar blackbody plus cutoff power-law spectra ($\mathrm{BB}+\mathrm{CPL}$), on ever decreasing time intervals during the entire UPE phase. We assume that during the UPE phase, the “inner engine” of the GRB, composed of a Kerr black hole (BH) and a uniform test magnetic field $B_0$, aligned with the BH rotation axis, operates in an overcritical field $|\mathbf{E}|\ge E_c$, where $E_c=m_e^2{c}^3/(e\hslash )$, being $m_e$ and $-e$ the mass and charge of the electron. We infer an $e^{+}{e}^{-}$ pair electromagnetic plasma in presence of a baryon load, a PEMB pulse, originating from a vacuum polarization quantum process in the inner engine. This initially optically thick plasma self-accelerates, giving rise at the transparency radius to the MeV radiation observed by Fermi-GBM. At times $t_{\mathrm{rf}}>3.99\mathrm{s}$, the electric field becomes undercritical, $|\mathbf{E}|<E_c$, and the inner engine, as previously demonstrated, operates in the classical electrodynamics regime and generate the GeV emission. During both the “quantum” and the “classical” electrodynamics processes, we determine the time varying mass and spin of the Kerr BH in the inner engine, fulfilling the Christodoulou-Hawking-Ruffini mass-energy formula of a Kerr BH. For the first time, we quantitatively show how the inner engine, by extracting the rotational energy of the Kerr BH, produces a series of PEMB pulses. We follow the quantum vacuum polarization process in sequences with decreasing time bins. We compute the Lorentz factors, the baryon loads and the radii at transparency, as well as the value of the magnetic field, $B_0$, assumed to be constant in each sequence. The fundamental hierarchical structure, linking the quantum electrodynamics regime to the classical electrodynamics regime, is characterized by the emission of “blackholic quanta” with a timescale $\tau \sim {10}^{-9}\mathrm{s}$, and energy $\mathcal{E}\sim {10}^{45}\mathrm{erg}$.

Figure 1

Luminosity of the Fermi-GBM in the 10 keV–10 MeV energy band together with the luminosity of Fermi-LAT during and after UPE phase expressed in the rest-frame of the source. The light grey part shows the $\nu \mathrm{NS}$–rise from $t_{\mathrm{rf}}=0.79\mathrm{s}$ to $t_{\mathrm{rf}}=1.18\mathrm{s}$. The light blue part shows the UPE phase which is in the time interval $t_{\mathrm{rf}}=1.9–3.99\mathrm{s}$, whose lower and upper edges correspond, respectively, to the moment of BH formation and to the moment which blackbody component disappears from the GBM data. The corresponding analysis for GRB 130427A, GRB 160509A and GRB 160625B is presented in [28]. The red part shows the Fermi-GBM the cavity introduced in Ruffni et al. [29]. The rest-frame 0.1–100 GeV luminosity light-curve of GRB 190114C after UPE phase is best fitted by a power-law with slope of $1.2\pm 0.04$ and amplitude of $7.75\times {10}^{52}\mathrm{erg}{\mathrm{s}}^{-1}$

Figure 2

Time-resolved spectral analysis of UPE phase GRB 190114C: from $t=2.7\mathrm{s}$ ($t_{\mathrm{rf}}=1.9\mathrm{s}$) to $t=5.5\mathrm{s}$ ($t_{\mathrm{rf}}=3.9\mathrm{s}$). For the second iteration: (a) the time interval is divided into two parts, four parts for the third iteration; b, eight parts for the fourth iteration; (c) and sixteen parts for the fifth iteration; (d) respectively. The spectral fitting parameters for each iteration are reported in Table 1. Plots are taken from Ruffni et al. [27] with permission of authors.

Figure 3

Luminosity [a] and rest-frame temperature [b] during the UPE observed by Fermi-GBM, obtained from analyses with $\mathrm{\Delta }t=0.125\mathrm{s}$ (blue circles), $\mathrm{\Delta }t=0.25\mathrm{s}$ (black circles) and $\mathrm{\Delta }t=0.5\mathrm{s}$ (red circles) time resolutions reported in Table 1. The luminosity is best fitted by a power-law of amplitude $(3.5\pm 1.1)\times {10}^{53}\mathrm{erg}{\mathrm{s}}^{-1}$ and power-law index $-1.50\pm 0.30$. The best fit of luminosity, obtained from $\mathrm{\Delta }{t}_{\mathrm{rf}}=0.125\mathrm{s}$ time-resolved analysis, is in principle independent of the resolution of data analysis and is fulfilled in all iterative sequences.

Figure 4

The decrease of the BH spin and mass, as a function of rest-frame time for GRB 190114C during the UPE phase, namely in the rest-frame time interval $t_{\mathrm{rf}}=1.9–3.99\mathrm{s}$. The values of spin and mass at the moment when BH formed are, respectively, $M=4.53M_{\odot }$ and $\alpha =0.54$. At the moment when the UPE is over, i.e., at $t_{\mathrm{rf}}=3.99\mathrm{s}$, are: $\alpha =0.41$ and $M=4.45M_{\odot }$.

Figure 5

The parameters of inner engine and transparency condition as a function of rest-frame time for GRB 190114C during the UPE phase, namely in the rest-frame time interval $t_{\mathrm{rf}}=1.9–3.99\mathrm{s}$, obtained from a time-resolved analysis down to a $\mathrm{\Delta }t=0.125\mathrm{s}$ time resolution reported in Table 1. (a): The electric field during UPE phase which is clearly overcritical. (b): The energy of dyadoregion during the UPE phase obtained from Eq. (20). (c): The width of dyadoregion obtained from Eq. (23). (d): Timescale of radiation during the UPE phase. (e): The decrease of the Lorentz gamma factor, $\mathrm{\Gamma }$, as a function of rest-frame time. (f): The evolution of transparency radius in the UPE phase of GRB 190114C. All values are obtained for magnetic field of, $B_0=1.8\times {10}^{17}\mathrm{G}$, calculated in Sec. 9.

Figure 6

The parameters of inner engine and transparency point, obtained for $B_0=2.3\times {10}^{14}\mathrm{G}$, as a function of rest-frame time for GRB 190114C during the UPE phase, namely in the rest-frame time interval $t_{\mathrm{rf}}=1.9–3.99\mathrm{s}$. (a): The electric field during the UPE phase which is clearly overcritical and reaches its critical value at the end of the UPE phase (${\mathrm{t}}_{\mathrm{rf}}=3.99\mathrm{s}$). (b): The energy of dyadoregion during the UPE phase obtained from Eq. (20). (c): The width of dyadoregion obtained from Eq. (23) which tends to zero at the end of UPE phase, indicating that the number of $e^{+}{e}^{-}$ pairs are suppressed and the UPE phase is over. (d): Repetition timescale of the inner engine during the UPE phase obtained from Eq. (44). (e): The decrease of the Lorentz factor, $\mathrm{\Gamma }$, as a function of rest-frame time. This indicates the fact that $\mathrm{\Gamma }$ tends to unity for the last layers which confirms the end of UPE is reached. (f): The evolution of transparency radius; see Sec. 10.