Modeling Multifrequency Time-Variable Brightness in Blazars
Andrei Sokolov (PhD 2005, Boston University - now a postdoctoral research associate at the University of Central Lancashire, England) and Alan Marscher of the BU blazar group developed theoretical models for the variable nonthermal (synchrotron and inverse Compton) emission from relativistic jets in blazars. The study included special-relativistic effects, various sources of seed photons (synchrotron emission from the jet, light from emission-line clouds, and infrared blackbody emission from a dusty torus), light-travel time delays (especially important when calculating the inverse Compton scattering of the synchrotron photons during a flare), particle acceleration, and both synchrotron and inverse Compton radiative energy losses (with "seed" photons that originate from outside the jet, often called "external Compton" or "EC" radiation, or "external radiation Compton" or "ERC" radiation).
Andrei has confirmed the result of McHardy et al. (1999, Monthly Notices of the Royal Astronomical Society, 310, 571-576) that the contribution to the SSC X-ray flux of seed photons from mm-wave to optical wavelengths is roughly equal. For example, just as many X-rays come from electrons in the jet scattering 0.1-1 THz seed photons as from scattering 10-100 THz photons. This explains the common observation of weak correlations between low-frequency flares and X-ray or even gamma-ray flares: Since the synchrotron photons at one waveband (for example optical wavelengths) can come from different locations in the jet than those at another waveband, there might be little correlation between variations at the two bands on short timescales. The X-ray variations would then vary on all timescales but can be rather weakly correlated or even anticorrelated with variations in the synchrotron flux at any particular lower frequency. This applies to variations in flux (brightness) on short timescales - longer timescale variations should show good correlations across all wavebands.
The results of this work are contained in two papers, one already published ("Synchrotron Self-Compton Model for Rapid Nonthermal Flares in Blazars with Frequency-Dependent Time Lags" by Sokolov, A.S., Marscher, A.P., & McHardy, I.M. 2004, Astrophysical Journal, 613, 725-746) and one ("External Compton Radiation from Rapid Nonthermal Flares in Blazars" by Sokolov, A.S., and Marscher, A.P.) submitted to the Astrophysical Journal and currently under review. The papers consider rapid flares such that the emission region does not expand over the timescale of the flare. This simplifies matters by allowing one to ignore cooling of the electrons and decrease of the magnetic field from expansion. Instead, the only energy losses considered are from synchrotron and external Compton radiation. A previous paper by Marscher & Gear ("Models for High-Frequency Radio Outbursts in Extragalactic Sources with Application to the Early 1983 Millimeter to Infrared Flare of 3C 273," 1985, Astrophysical Journal, 298, 114-127) considered the case of longer-term outbursts from single shock waves propagating and expanding down a relativistic jet, although in an approximate, analytic manner that did not take into account light-travel delays.
In order to deal with light-travel delays, one needs to specify the geometry of the model. In the case of the Sokolov et al. papers, the choice was the collision of two shock waves, which results in two shock fronts, one "forward" (moving faster than the jet ahead of it) and one "reverse" (which slows down higher-velocity flow entering from the direction of the source of the jet). Energization of the relativistic electrons occurs only at the shock fronts in the model; they cool by emitting synchrotron and inverse Compton scattering of "seed" photons coming from regions outside the jet. The cooling is faster for higher-energy electrons, since the rate of energy loss is proportional to the square of the energy. Because higher-energy electrons emit synchrotron radiation at higher frequencies, the emission at these frequencies is confined to a thin volume immediately behind the shock front. At lower frequencies, the emission is more spread out, although it also starts at the shock front. This frequency stratification causes time lags between the maximum flux at different frequencies of synchrotron radiation so that the flare is shorter at higher frequencies.
The light from different parts of the source takes different amounts of time to travel to the electrons to be scattered and then for the scattered photons to travel to us. Because of this, it is possible for "reverse" time delays (radio, IR, or optical flares that peak before the X-ray or gamma-ray maximum) to occur in the case of synchrotron self-Compton (SSC) emission (i.e., when the seed photons are synchrotron radiation from the same population of relativistic electrons that do the scattering). In fact, we such such reverse lags in some objects that the Blazar Group is monitoring at X-ray and other frequencies; see the X-ray page on this website.
Light-travel reverse time delays are not expected if the X-rays or gamma-rays are from the external Compton (EC) process, since the externally generated photon field is already present when the electrons are excited. However, at X-ray and lower gamma-ray energies the electrons that do the scattering have lower energies than those that emit synchrotron radiation at optical and near-infrared frequencies. In this case, the frequency stratification discussed two paragraphs above can cause a reverse lag between the peak of the high-frequency synchrotron flare and the peak of the EC flare. See the Sokolov et al. papers for details.
What hasn't been done yet - by us or anybody else, as far as we know - is to deal properly with synchrotron self-Compton (SSC) energy losses. This requires the incorporation of retarded-time radiative transfer as viewed by each electron when calculating the inverse Compton energy losses. This will require faster computers and heavy code development. Other future work should include the effects of acceleration of the jet flow, which may occur on parsec scales (see the theoretical paper by N. Vlahakis & A. Konigl, 2004, Astrophysical Journal, 605, 656).