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In leptonic scenarios the high energy peak observed in blazars is explained with the inverse Compton process: energetic electrons scatter on low energy photons (see Sec- tion 1.4.2). In the simplest scenario, the emission is produced in a single region and low energy photons are the synchrotron photons (SSC - synchrotron self-Compton models) [55, 117, 121, 133, 140, 180] or photons external to the emission region [78, 168]. In this section, the effects of the inverse Compton process considering different

1_{In leptonic models, the blob is supposed to contain both electrons and protons, but only}

electrons are accelerated to energies sufficient to radiate high energy γ rays.

2_{As it will be explained in the section on hadronic models, we refer to radiation-dominated jets}

Figure 3.4: The spectral energy distribution in a synchrotron self-Compton sce- nario [124]. The low energy peak is synchrotron radiation of relativistic electrons (see Fig. 3.5): self-absorption, break and maximum energy of the electron popula- tion cause breaks in the emitted synchrotron spectrum. The high energy peak is due to inverse Compton process, targets being synchrotron photons.

low energy photons are summarised: spectral shape, peak and maximum energies are reported [58, 77].

The emission region is moving with Lorentz factor Γ and Doppler factor δ = 1/(Γ(1 − βΓcos ϑ) where ϑ is the angle between the direction of motion of the blob

and the line of sight. The distribution of electrons has a low energy γmin and a high

energy cut-off γmax, and a peak at γpeak, and above the peak is a power-law function

with index p.

The synchrotron photon field has a broad distribution in energy, and the SSC spectrum is a featureless continuum, extending over a wide range of energies (Fig. 3.4). The effects of Klein-Nishima suppression reduce gradually the emission at higher energies (see Section 1.4.2). Since the synchrotron spectrum is broad, extending from radio up to the UV band and in some cases soft X-rays, photons for scattering in Thomson regime are available (εγmax ≪ 1) also for ultra-relativistic

electrons (γmax & 106). The peak of the SSC spectrum (in Thomson regime) is

εpeak_SSC ∼ εpeak syn γ

2

peak (3.1)

where εpeak

syn is the synchrotron spectrum peak. The high energy end of the spectrum,

Figure 3.5: The spectrum of accelerated relativistic electrons [124].

γmax by

εmax_SSC ∼ γ2δ (3.2)

hence electrons with high energy cut-off γmax ∼ 106 radiate TeV γ rays.

Often, together with the SSC emission, scattering on low energy photons external to the emission region contribute to the high energy flux. Consider the target photons listed in the previous section. They all produce a spectrum whose shape between the peak energy εpeak and the maximum energy εmax is a power law whose

spectral index α is related to the spectral index of the electron distribution p by α = (p − 1)/2. The differences are mainly in the processes causing the end of the spectrum at high energies (either the electron maximum energy or the Klein-Nishima suppression). Depending on the geometry, different transformations are applied and low energy photons result de-boosted or blue-shifted in the rest frame of the emission region. In the following discussion photons energies are given in units of the electron rest mass. In detail:

• accretion disc: the disc emits in the UV range, so that the peak of disc emission is at εdisc ∼ 10−5. If the emission region is located at a distance

d > ΓRdisc, where Rdisc is the disc size, the radial structure of the disc and the

angular dependence of the disc emission may be neglected. In this geometry, disc photons enter the emission region from behind and are de-boosted of a

factor ∼ 1/Γ. The peak energy of the inverse Compton is εpeak_disc ∼ εdiscγpeak2

δ

Γ (3.3)

and the high energy end of the spectrum, for electrons with γmax . 106, is

determined by the end of electrons distribution εmax_disc ∼ εdiscγpeak2

δ

Γ (3.4)

which for typical values of γpeak, δ and Γ corresponds to MeV-TeV γ rays.

• broad line region: for optical lines a peak energy of εBLR ∼ 10−5 can be

assumed. The emission region is located within the broad line region, low energy photons are isotropic and are boosted by a factor ∼ Γ in the rest frame of the emission region. In this frame, the peak of Compton emission is located at

εpeak_BLR ∼ εBLRγpeak2 δΓ (3.5)

which corresponds to γ rays in the energy range detectable by Fermi-LAT (100 MeV-GeV). The end of the spectrum at high energies (multi-GeV) is due to the Klein-Nishima suppression.

• infra-red torus: it consists of low energy photons with εIR ∼ 10−7, which

are blue-shifted by a factor ∼ Γ in the rest frame of the emission region. The inverse Compton peak is given by

εpeak_IR ∼ εIRγpeak2 δΓ (3.6)

and for such low energy photons the Klein-Nishima suppression is negligible and the maximum energy is due to the electrons maximum energy

εmax_disc ∼ εdiscγpeak2 δΓ (3.7)

so that inverse Compton on low energy photons of the torus can produce γ rays up to very high energies (> 100 GeV).

• cosmic microwave background: are low energy photons with εCM B ∼ 10−9

which are blue-shifted by a factor ∼ Γ in the rest frame of the emission region due to their isotropy. Applying the same relations used for scattering on the infra-red torus it follows that the radiation from soft X-rays up to medium γ ray energies is emitted.

Simple single zone models are not always successful in reproducing the observed emission (fit of the spectral energy distribution, variability patterns) and often more complicated scenarios are used. Different populations of low energy photons can be considered where the high energy peak results from a super-position of inverse Compton on various target fields [93]. In some cases complex variability patterns indicate that the emission in different energy ranges is not generated in the same region and two or more emission zones are required. Another leptonic scenario is the slow-sheat model where the target field of photons comes from a slow outer layer of the jet [95]. In the following chapter different leptonic models are proposed to explain the multiwavelength emission, both spectral energy distribution and light curve, of the three studied blazars:

• 1ES 1727+502 (BL Lac): one zone synchrotron self-Compton model; • 3C 279 (FSRQ):

– one zone models considering two different populations of low energy pho- tons (photons from the broad line region or from the infra-red torus: both can fit the spectral energy distribution of Period-1);

– a two-zone model where the high energy emission is generated in an inner region of the blazar and the low energy peak in another one, located further down the jet (fits the spectral energy distribution and is consistent with the constraints from the multiwavelength light curve of Period-2); • PKS 1510-089 (FSRQ): two different scenarios are proposed: a one zone model

considering low energy photons from the infra-red torus (accounts only for the spectral energy distribution) and a slow-sheat model (not only fits the spectral energy distribution, but is consistent with multiwavelength constraints). In general in leptonic models a population of accelerated relativistic electrons is assumed, whose spectrum is a power law function with a break at γbreak (where

radiative cooling time scale equals escape time scale) dNe dEe =  K1Ee−p1 for γ ≤ γbreak K2Ee−p2 for γ > γbreak (3.8) and the photons radiated via synchrotron have a power law spectrum with indices αi = (pi−1)/2 for i = 1, 2 (Fig. 3.5). This approximation reproduces adequately the

temporal evolution of the electrons energy distributions obtained solving the kinetic equation [121]. Self-consistent models are also available which include electrons ac- celeration via Fermi mechanisms [194]. Synchrotron self Compton models contain a number of parameters, specifying the properties of the emission region and of the population of electrons:

• emission region: size R, Doppler factor δ, Lorentz factor Γ and magnetic field B of the emission region;

• distribution of electrons: the minimum, break and maximum energy γmin,

γbreak and γmax, the spectral indexes p1, p2 (usually p1 = 2 for non-relativistic

shocks or p1 = 2.2 − 2.3 for relativistic parallel shocks and p2 = −(p1+ 1)), and

the normalisation factors K1 and K2 related to the total number of electrons.

Estimates of such parameters are problematic, since independent measurements are not always available. For example, the magnetic field is an unknown quantity in blazars jets, and spectral energy distribution models with values of magnetic field spanning over orders of magnitude reproduce satisfactorily the observed behaviour. For some parameters, however, it is possible to derive constraints from multi- wavelength observations. For example, the variability time scale tvar, which can be

estimated from the light curves, limits the size of the emission region R according to

R ≤ ctvarδ

1 + z (3.9)

where z is the redshift of the source. Correlations and delayed emission among different energy ranges allow to establish co-spatiality and eventually determine the location of the emission region in the jet so that the relevant low energy external photon fields can be included.