3.5 Emissivity

As with the velocity, we use a separable function for the rest-frame emissivity: $\epsilon(\rho,s) = \epsilon_\rho(\rho)\epsilon_s(s)$. We found that very different gradients of the on-axis emissivity $\epsilon_\rho(\rho)$ were required in the three regions, and therefore adopted a power-law form, with different exponents allowed for the regions, and for the spine and shear layer (Table 4). One additional parameter is needed to set the relative emissivity of spine and shear layer at a fiducial point. We enforce continuity at the outer boundary, but could not fit the data without introducing a discontinuity at the inner boundary (see Section 4.3.3). The transverse variation has the same form as that assumed for the velocity: constant in the spine, with a linear (SSL) or truncated Gaussian decrease in the shear layer to a fraction $\bar{e}(\rho)$ at the jet edge. The absolute value of the emissivity is determined by normalizing to the observed flux density.