Towards a Better Understanding of the GRB Phenomenon: a New Model for GRB Prompt Emission and its effects on the New Non-Thermal L$_\mathrm{i}^\mathrm{NT}$-E$_\mathrm{peak,i}^\mathrm{rest,NT}$ relation

We reanalyze the prompt emission of two of the brightest Fermi GRBs (080916C and 090926A) with a new model composed of 3 components: (i) a thermal-like component--approximated with a black body (BB)--interpreted as the jet photosphere emission of a magnetized relativistic outflow, (ii) a non-thermal component--approximated with a Band function--interpreted as synchrotron radiation in an optically thin region above the photosphere either from internal shocks or magnetic field dissipation, and (iii) an extra power law (PL) extending from low to high energies likely of inverse Compton origin, even though it remains challenging. Through fine-time spectroscopy down to the 100 ms time scale, we follow the smooth evolution of the various components. From this analysis the Band function is globally the most intense component, although the additional PL can overpower the others in sharp time structures. The Band function and the BB component are the most intense at early times and globally fade across the burst duration. The additional PL is the most intense component at late time and may be correlated with the extended high-energy emission observed thousands of seconds after the burst with the Fermi/Large Area Telescope (LAT). Unexpectedly, this analysis also shows that the additional PL may be present from the very beginning of the burst. We investigate the effect of the three components on the new time-resolved luminosity-hardness relation in both the observer and rest frames and show that a strong correlation exists between the flux of the non-thermal component and its E$_{peak}$ only when the three components are fitted simultaneously to the data (i.e., F$_i^{NT}$-E$_{peak,i}^{NT}$ relation). In addition, this result points toward a universal relation between those two quantities for all GRBs when transposed to the central engine rest frame (i.e., L$_i^{NT}$-E$_{peak,i}^{rest,NT}$ relation).