2.3.3. Dissipative Jet: Hybrid Spectrum

If the jet is dissipative across the photosphere, a hybrid spectrum can emerge where the spectral peak is dominated by a quasi-thermal component but- the low and high-energy wings are dominated by non-thermal emission either from synchrotron or Comptonization. The final outcome depends on the nature of the dissipation and how that leads to particle acceleration/heating. Gill et al. [128], who carried out numerical simulations, and Beniamini and Giannios [129], who performed semi-analytic calculations, considered a steady PFD striped wind outflow, which is heated due to magnetic dissipation commencing at radii when the flow is optically thick to Thomson scattering with initial *τT*<sup>0</sup> = 100. At higher *τT*, and equivalently lower radii, the flow maintains thermal equilibrium while it is being accelerated due to gradual magnetic dissipation. Localized reconnecting layers accelerate the baryonic electrons, as well as any produced *e* ±-pairs, into a relativistic powerlaw distribution. In this instance, since the flow is strongly magnetized with *σ* > 1, the relativistic particles are predominantly cooled by synchrotron emission. The development

of the spectrum as the flow expands is shown in the left panel of Figure 2 as a function of the total *τT*. The final observed spectrum is indeed Band-like, but it is different from the optically thin synchrotron spectrum even though by the end of the radially extended dissipation the total spectrum (energetically) is synchrotron dominated.

**Figure 2.** Spectral evolution in a dissipative steady PFD striped wind flow, shown as a function of the Thomson optical depth as the jet is heated accross the photosphere. The spectra are shown for two different particle heating scenarios: (**Left**)—relativistic power-law particles produced by magnetic reconnection, and (**Right**)—mildly relativistic particles forming an almost mono-energetic distribution due to distributed heating and Compton cooling. The flow was evolved from initial *τT*<sup>0</sup> = 100 until the total optical depth of baryonic electrons plus produced *e* ±-pairs was much less than unity. The observed spectrum is effectively a sum over the optically thin spectra. See [128] for more details.

Alternatively, particle heating can occur in a distributed manner [31,124,126,130,131] throughout the whole causal region due to MHD instabilities. In this case, particles remain only mildly relativistic. Their mean energy is governed by a balance between (gradual and continuous) heating and Compton cooling, which leads to a mono-energetic distribution. The spectral evolution as the flow expands is shown in the right panel of Figure 2. In this case the high-energy spectrum is again Band-like, but unlike the previous case it is completely formed through Comptonization [124,126,131]. The mildly relativistic particles do produce some synchrotron emission but only at energies (1 + *z*)*E* . 1 keV.

Both particle energization mechanims can give rise to a Band-like spectra; however, they can produce completely different energy-dependent polarization. In both, if the jet is uniform and can be approximated as part of a spherical flow (i.e., away from the jet edge in a top-hat jet), then no polarization is expected near the spectral peak, as it is dominated by the quasi-thermal component. In such a scenario, away from the peak, where the spectrum is dominated by non-thermal emission, it is possible to measure high polarization (Π . 50%) if the emission is synchrotron and the flow has a large scale ordered magnetic field, e.g., a *<sup>B</sup>*tor field. Other field configurations, namely, *<sup>B</sup>*<sup>⊥</sup> and *<sup>B</sup>*<sup>k</sup> , will yield vanishingly small net polarization. Alternatively, if the non-thermal component is produced by Comptonization, then the expected polarization is again almost zero. On the other hand, if the LOS passes near the sharp edge of a top-hat jet or the edge of the almost uniform core in a structured jet, then the entire spectrum with non-thermal emission from Comptonization can produce Π . 20%. Similarly, the non-thermal wings coming from synchrotron emission can now yield significant polarization with 4% . Π . 28% for *B*<sup>⊥</sup> and 10% . <sup>Π</sup> . 56% for *<sup>B</sup>*<sup>k</sup> , while *B*tor again yields higher levels with 10% . Π . 60%.
