7.4.5. Yonetoku or *L* <sup>p</sup>–*E*<sup>p</sup> Correlation

The Yonetoku or *L*p–*E*p, [65] correlation functional form here adopted reads

$$\log\left(\frac{L\_{\rm P}}{\text{erg/s}}\right) - 52 = m\_0 + m\_1 \log\left(\frac{E\_{\rm P}}{\text{keV}}\right). \tag{41}$$

Here, the free terms are *m*<sup>0</sup> and *m*<sup>1</sup> and require to be calibrated. Again, *σ*<sup>m</sup> is the extra scatter term.

Detailed hydrodynamical simulations suggest that Yonetoku correlation may be due to the emission of photons from the photosphere of a relativistic jet, where the outflow becomes optically thin, whereas most of it is still optically thick (see Section 3.1.5). Quasithermal radiation is thus expected and the expected spectral shapes are obtained [162].

Like previous correlations, for the Yonetoku correlation there are also ongoing discussions whether it is a by-product of some selection effect or not [149,154–157]. For this correlation, however, a weak redshift dependence has been confirmed, which may contribute to the dispersion of the correlation [158].
