Tavecchio & Ghisellini (2008) argue that the inner subparsec-scale jet of M87 is the most likely site of very high energy γ-ray emission and they note the problems a single-zone SSC model has reproducing the observed spectrum as discussed in Section 5.4. To overcome the problems inherent in a single-zone SSC model, Tavecchio & Ghisellini (2008) propose a multizone model in which the jet is made up of two components, an inner, fast-moving “spine” and an outer, slower “layer”, as shown in Figure 5.2. In the model, the layer is approximated as a hollow cylinder with internal radius R, outer radius R2, height Hl(as measured in the frame of the sheath), moving with a bulk
Lorentz factor Γl. The central spine is modelled as a cylinder with height Hs (as measured in the
frame of the spine) and radius R, moving with a bulk Lorentz factor Γs. The spine and layer are
characterised by tangled magnetic fields of intensity Bsand Bl respectively. Each region contains
relativistic electrons assumed to follow a smoothed broken power-law distribution extending from γmin to γcut, with indices n1 and n2 below and above the break at γb, respectively.
N (γ) = Kγ−n1 1 +γγ b n1−n2 eγcut−γ γ > γmin N (γ) = 0 γ ≤ γmin (5.25) The normalisation constant, K, in Equation 5.25, is found by requiring that N (γ) produce a given intrinsic synchrotron luminosity Lsyn and is one of the input parameters required for the
model. Both the spine and the layer emit through synchrotron and inverse-Compton processes; the radiation emitted by the spine is seen boosted by the layer, and vice versa, by a factor of ∼ (Γ0)2, with Γ0 given by:
Figure 5.2: Schematic of the spine-layer model: the central cylinder represents the spine, of height Hsand radius R, moving with a Lorentz factor of Γs, and the volume between the spine and outer
cylinder represents the layer, of height Hl and outer radius Rs, moving with a Lorentz factor Γl.
Photons emitted by the spine are Doppler boosted as seen by the sheath, and vice versa. After Ghisellini, Tavecchio & Chiaberge (2005).
where cβs and cβl are the velocities of the spine and layer, respectively. It is assumed that
Hl > Hs. The seed photons for inverse-Compton scattering originate not only locally in the
region being considered (spine or layer) but are also produced in the other component (referred to henceforth as external-Compton), leading to strong feedback between the two. A consequence of the structure proposed is that the emission observed from the jet will depend strongly on the angle of the jet to the line of sight. At small angles, as in blazars, the emission is dominated by boosted spine emission, while at large viewing angles (θ > 45◦), as in many radio galaxies, emission from the spine is suppressed. In the case of large viewing angles, it becomes probable that the layer, characterised by a broader beaming cone, will contribute significantly to the overall emission, possibly dominating in some cases. At intermediate angles, both components can contribute significantly to the output, as illustrated in Figure 5.3.
In the comoving frame of one component, the photons produced in the other are not isotropic and are observed to be aberrated, requiring the different beaming patterns associated with the two regions to be taken into account. Most of the external-Compton photons come from a single direction (opposite to the relative velocity vector). It is important to note that this anisotropy only applies to the external-Compton radiation, while the synchrotron and SSC emission within the region are isotropic in the comoving frame. For the spine, the external-Compton radiation is more concentrated along the jet axis with respect to its synchrotron and SSC emission, while for the layer it is more concentrated in the direction of the black hole. To simplify the transformations, the authors assumed, as in Dermer (1995), that, due to the strong aberration in the rest frame of one component, all the photons from the other component come from a single direction opposite
Figure 5.3: Amplification factors for the emission from the spine (solid lines) and layer (dashed lines) as a function of viewing angle, for Γs= 12, Γl= 4 and a spectral index, α = 1, the values
used when modelling M87 in Ghisellini & Tavecchio (2008). The black lines show the synchrotron to SSC factors and the red lines the external-Compton factors. Taken from Ghisellini & Tavecchio (2008).
to the jet axis. The net result of the transformations is that in the observer frame the external- Compton emission from the layer is less boosted than that from the spine (Ghisellini & Tavecchio, 2008).
By applying this model to M87, Ghisellini & Tavecchio (2008), were able to reproduce the spectrum of the object, and, using the parameters obtained, a theoretical spectrum for the case of a hypothetical M87-like object at a small angle to the line of sight was constructed. This blazar- like spectrum of M87 closely resembles that of LBLs, and the spine is characterised by physical parameters close to those usually inferred for such sources. In this model, the optical and X-ray emission are produced mainly in the spine, while TeV γ-rays would primarily originate in the layer, so a strict correlation between these bands is not directly required. Additionally, MeV-GeV emission from M87 would be produced primarily in the spine and so would not exactly follow the TeV component.
A major problem with this model is that it requires a large number of parameters to be determined, almost double the number for a single-zone model because two sets are required, one for the spine and another for the layer. This leads to a total of 18 free parameters that must be defined. Furthermore, the model has difficulty in reproducing the hard spectrum observed during the flaring of M87 in 2005, because the slope of the TeV spectrum found by the model is mainly dictated by the absorption of TeV photons in the dense optical radiation field rather than by the
intrinsic TeV spectrum, resulting in a predicted spectrum softer than that observed (Tavecchio & Ghisellini, 2008).