Particularly meaningful modeling of blazar broadband spectra can be done if one has not only an individual snapshot spectrum, but a collection of simultaneous broadband spectra in different gamma-ray intensity states. Since it is likely that only a few parameters of the model will change between different states of the same source, such a comparative modeling of broadband spectra allows to put rather tight constraints on those model parameters that are likely to change, if all other parameters are held fixed for different model fits. This has been done in three recent papers presenting broadband spectra and spectral modeling results in various intensity states of PKS 0528+134 (see Fig. 2.2 and Mukherjee et al. 1999), 3C 279 (see Fig. 1.3 and Hartman et al. 2001), and Mrk~501 (see Fig. 2.3 and Petry et al. 2000).

Model results along the blazar sequence: General results from this model fitting of various objects confirm that in FSRQs (like PKS 0528+134 or 3C 279) a strong contribution of radiation external to the jet is necessary as seed photon field for Compton scattering to produce the gamma-ray emission, while HBLs (like Mrk 501) can be modelled successfully with a pure SSC model. The LBL BL Lacertae itself requires a moderate, but non-negligible contribution of external photons as the seed for Compton scattering, while the X-ray and soft gamma-ray spectrum up to ~ 1 MeV seems to be dominated by synchrotron self-Compton emission (see Fig. 1.4 and Böttcher & Bloom 2000).

The spectral variability between different gamma-ray intensity states seems to be related to very different intrinsic mechanisms in different subclasses of blazars. In the case of quasars, we find that gamma-ray high states can be modelled successfully by an increasing bulk Lorentz factor of the material moving along the jet, while the low-energy cutoff of the co-moving electron distribution seems to decrease at the same time. This correlation between the high-energy gamma-ray (EGRET) flux and the two fit parameters is illustrated in Fig. 2.4, which contains the results of our model fitting to broadband spectra of PKS 0528+134 and 3C 279. Interestingly, in both objects we do not find a significant correlation between the spectral index of the nonthermal electrons injected into the jet, with the gamma-ray intensity.

An interesting prediction from this driving mechanism of broadband spectral variability in quasars concerns the location of the peak energy of the synchrotron spectrum. If the reduction of the low-energy cutoff of the electron spectrum in the jet is indeed caused by increased radiative cooling of the electrons in the high state, and if this radiative cooling is dominated by Compton cooling on external radiation, then one would expect that in the gamma-ray high state, the synchrotron spectrum actually peaks at lower frequencies than in gamma-ray low states (see Böttcher 1999). Unfortunately, the synchrotron peak in quasars is generally located in the infrared, where it is notoriously hard to observe. In particular, it has so far been very difficult to perform sufficiently sensitive infrared observations of quasars simultaneous with observations at gamma-ray energies. With more sensitive infrared observations in the future, to be coordinated with observations of the upcomming gamma-ray satellite missions like GLAST or AGILE, it should become possible to test this prediction.

In contrast, for the HBL Mrk 501, we find that gamma-ray high state is strongly correlated with the spectral index of the nonthermal electrons at the time of injection into the radiating volume of the jet. However, the broadband spectral variability patterns on the intermediate time scales investigated in Petry et al. (2000) can not be reproduced by simply varying one single parameter between intensity states. The effects of such variations can be calculated analytically in the framework of a pure SSC model, and the predicted spectral variability patterns for such variations are plotted in Fig. 2.5. The actually measured intermediate-term variability seen in Mrk 501 shows significantly larger scatter than allowed by such simple one-parameter variations.

W Comae in 1998: We have carried out a detailed theoretical modeling study of the broadband spectrum and variability of the LBL W Comae, which is currently of great interest to the STACEE and CELESTE experiments. In Böttcher, Mukherjee, & Reimer (2002), we have modelled the emission from W Comae with both leptonic and hadronic jet models and found that it is a very interesting object for future observations with STACEE, CELESTE, and VERITAS, because the two types of models make very different predictions with respect to the high-energy emission of W Comae. A possible detection at energies beyond ~ 100 GeV would be hard to reconcile with leptonic jet models. Figs. 2.6 and 2.7 illustrate representative model fits with leptonic and hadronic models, respectively.

BL Lacertae in 2000: In Böttcher & Reimer (2004), we have modeled the broadband spectral energy distributions (SEDs) and spectral variability of BL Lacertae as observed in our multiwavelength campaign in 2000. During the campaign, BL Lacertae was observed in two different activity states: A quiescent state with relatively low levels of optical and X-ray fluxes and a synchrotron cutoff at energies below the X-ray regime, and a flaring state with high levels of optical and X-ray emission and a synchrotron cutoff around or even beyond ~ 10 keV. We used both leptonic and hadronic jet models to fit the broadband spectra and spectral variability patterns observed in both activity states in 2000.

Fig. 2.8 shows our resulting leptonic model fits. For this model, we find that the short-term variability, in particular the optical and X-ray spectral variability, can be best represented with a flaring scenario dominated by a spectral-index change of the spectrum of ultrarelativistic electrons injected into the jet. Figs. 2.9 and 2.10 show the comparison of our leptonic model simulations with the observed optical and X-ray spectral variability patterns.

The hadronic synchrotron-proton blazar (SPB) model can reproduce the observed SEDs of BL Lacertae (see Fig. 2.11) in a scenario with muon-synchrotron dominated high-energy emission. It requires a significantly higher magnetic field than the leptonic model (~ 40 G vs. ~ 2 G in the leptonic model) and a lower Doppler factor associated with the bulk motion of the emission region (D ~ 8 vs. D ~ 18 in the leptonic model). The hadronic model predicted a significantly larger > 100 GeV flux than the leptonic models, well within the capabilities of VERITAS and MAGIC. In fact, in 2005, MAGIC did detect very-high-energy gamma-ray flux from BL Lacertae at a level just in-between our leptonic and hadronic model predictions (see Fig. 2.11). However, there were no simultaneous measurements at X-ray energies with the VHE gamma-ray detection, so that detailed modeling of the SED including the VHE flux is not possible at this time.

Various blazars detected by VERITAS. I have applied my leptonic blazar jet model to several blazars recently detected by the VERITAS Very-High-Energy gamma-ray Cherenkov telescope array.

Fig. 2.12 shows two leptonic model fits to the broadband SED of the intermediate BL Lac object W Comae during its VHE gamma-ray detection by VERITAS in 2008 (Acciari et al. 2008a). Most high-frequency-peaked BL Lac objects (HBLs) detected at VHE gamma-ray energies can usually be fit very well with pure SSC models. The most important result from our modeling of W Comae was that a pure SSC model in this case would require an unusually low magnetic feld and large Doppler factor of the jet material. Much more reasonable parameters could be used under the assumption of an additional external radiation field as source for Compton upscattering to produce the observed VHE gamma-ray emission.

Fig. 2.13 shows our model fit to the recently detected HBL 1ES 0806+524 (Acciari et al. 2008b). In this case, a pure SSC fit with parameters in the usual range as used for other HBLs was appropriate to reproduce the observed simultaneous spectral energy distribution during the VERITAS discovery observations in 2008.

VHE Gamma-Ray Emission and Variability of 3C279. The recent detection of the quasar 3C279 at a redshift of z = 0.536 by the MAGIC VHE gamma-ray telescope came as a big surprise to the high-energy astronomy community. This is because (a) VHE gamma-rays from an object at that distance are expected to be heavily absorbed by the extragalactic background light, and (b) most quasars seemed to have a peak of their gamma-ray emission component at MeV - GeV energies, and it was generally considered unlikely that their gamma-ray emission extends beyond 100 GeV.

We have combined simultaneous optical data (from our WEBT campaign in 2006, see below) and RXTE X-ray data from Alan Marscher with the MAGIC detection, to estimate the shape of the broadband SED of 3C279 during the time of the VHE gamma-ray detection (Febraury 23, 2006). In Fig. 2.14, this SED is compared to other simultaneous SEDs measured in the 1990s, coincident with MeV - GeV gamma-ray flux measuements by EGRET on the Compton Gamma-Ray Observatory, as well as a spectrum from June 2003, coincident with an INTEGRAL observation of 3C279.

General considerations on the basis of rough estimates of the locations of the synchrotron and gamma-ray peaks in the SED of 3C279 on Feb. 23, 2006, allowed us to conclude that one-zone leptonic models have great problems reproducing this SED. A pure SSC model can almost certainly be ruled out. However, even including an external Compton component does not improve the situation very much: This would either require an unusually low magnetic field of B ~ 0.03 G, or (in order to achieve approximate equipartition between magnetic field at B ~ 0.25 G and relativistic electrons) an unrealistically high Doppler factor of Gamma ~ 140. In addition, such a model fails to reproduce the observed X-ray flux (see Fig. 2.15). We therefore concluded that a simple one-zone, homogeneous leptonic jet model is not able to plausibly reproduce the SED of 3C279.

However, comparing the results of our WEBT campaign in 2006 with RXTE monitoring by Alan Marscher, we (Böttcher, Reimer, & Marscher 2008) found that the variability in the optical did not reflect the apparently dramatic gamma-ray variability evidenced by the VHE gamma-ray detection by MAGIC. This, in combination with the substantial gamma-gamma opacity of the BLR radiation field to VHE gamma-rays suggests a multi-zone model in which the optical emission is produced in a different region than the VHE gamma-ray emission. In particular, an SSC model with an emission region far outside the BLR reproduces the simultaneous X-ray - VHE gamma-ray spectrum of 3C279 (Fig. 2.15).

Alternatively, a hadronic model is capable of reproducing the observed SED of 3C279 reasonably well, both in scenarios in which only the internal synchrotron field serves as targets for photo-pion production (dot-dashed pink curve in Fig. 2.15), and with a substantial contribution from external photons, e.g., from the BLR (long-dashed pink curve in Fig. 2.15). However, either version of the hadronic model requires a rather extreme jet power of up to L_j ~ 10⁴⁹ erg/s, compared to a requirement of L_j ~ 2 X 10⁴⁷ erg/s for a multi-zone leptonic model.

Another interesting aspect of 3C279 showed up during our WEBT campaign of 2006: At least one period of a remarkably clean exponential decay of monochromatic (BVRI) fluxes with time, with a time constant of 12.8 d, over about 14 days (see Fig. 2.16). This is clearly too long to be associated with radiative cooling. In Böttcher & Principe (2008), we have suggested that this may be the signature of deceleration of the synchrotron emitting jet component. We developed a model analogous to the relativistic blast wave model for gamma-ray bursts, including radiative energy losses and radiation drag, to simulate the deceleration of a relativistically moving plasmoid in the moderately dense AGN environment. Fig. 2.16 shows that the observed optical light curve decay can be successfully reproduced with this model. Fig. 2.17 links to an animation of the time evolution of the entire SED during the time corresponding to this quasi-exponential light curve decay.

The decelerating plasmoid model predicts a delayed X-ray flare, about 2 -- 3 weeks after the onset of the quasi-exponential light curve decay in the optical. A robust prediction of this model, which can be tested with GLAST and simultaneous optical monitoring, is that the peak in the gamma-ray light curve at ~ 100 MeV is expected to be delayed by a few days with respect to the onset of optical decay, while the VHE gamma-rays are expected to track the optical light curve closely with a delay of at most a few hours.