Left: sketch of the TEMZ model.Interpreting Multifrequency Time-Variable Brightness in Blazars
The Turbulent Extreme Multi-Zone (TEMZ) Model
Alan Marscher has proposed a model that attempts to explain much of the multi-frequency variability observed in blazars. The basis of the model is that the ambient jet flow is magneticially turbulent. The ambient jet crosses oblique or cone-shaped shocks caused by an imbalance of pressure at the jet boundary (often called a "pinch" or "sausage" instability). The model is described in the papers "Turbulent Extreme Multi-Zone Model for Blazar Variability" by A.P. Marscher (2014, Astrophysical Journal,780, 87), "Modeling the Time-Dependent Polarization of Blazars" by A.P. Marscher, S.G. Jorstad, and K.W. Williamson (2017, Galaxies,5, 63), and "Frequency and Time Dependence of Linear Polarization in Turbulent Jets of Blazars" by A.P. Marscher and S.G. Jorstad (2021, Galaxies,9, 27). Further application to observations of the variability of linear polarization of blazars appears in a paper published in the proceedings of IAU Symposium 313, "Time Variable Linear Polarization as a Probe of the Physical Conditions in Compact Blazar Jets". Another paper with later results (November 2016) is in the proceedings of the 2016 High Energy Astrophysics in Southern Africa meeting, "Multi-wavelength Behavior of Blazars: Combined Order & Disorder".
As part of his PhD thesis, Nick MacDonald has adapted a ray-tracing routine to perform total and polarized (both linear and circular, with Faraday effects) radiative transfer within the TEMZ code. A paper on this, including some preliminary results, is "Faraday Conversion in Turbulent Blazar Jets".
***Fortran source code that you can download and use (or modify for
your purposes)
Note: The code uses openmp parallelization for multi-processor
computers
temzssc.f
(seed photons for Compton scattering come from a dusty molecular torus and/or from synchrotron and first-order Compton scattering from all of the cells, including time delays); sample input file temzsscinp.txt
temz.f (seed photons for Compton scattering come from a dusty molecular torus and/or synchrotron radiation from a Mach disk); sample input file temzinp.txt
The key features of the model include:
1. Turbulent ambient jet plasma, which accelerates electrons with a
power-law energy distribution through the second-order Fermi process
and possibly magnetic reconnections. The turbulence is realized in the
model by dividing the jet into many cylindrical cells, the number of
which is selected to match the degree of linear polarization. Each cell
has its own magnetic field, part of which can be ordered (e.g., if the
jet contains a large-scale helical field) and part of which is
turbulent. The cells are in nested zones of different sizes (in factors
of 2); each zone has a turbulent component to the magnetic field that
is generated randomly from a log-normal distribution about an average
value. The direction of the field is selected at random at the upstream
and downstream boundary of each zone and rotated smoothly (but in a
random sense) in between. The magnetic field of a given cell is a
superposition of the ordered component and the sum of the fields of the
zones, weighted according to a Kolmogorov spectrum.
2. A conical standing shock that further accelerates electrons, with
the amplification in energy depending on the angle between the magnetic
field of the turbulent cell and the shock normal. Currently, this is
done by adopting two maximum electron energies: a higher value when the
field is nearly parallel to the shock normal (the "subluminal" regime
in particle acceleration parlance) and a lower value for wider angles
between the field and shock normal (the "superluminal" regime). Further
work is needed to advance from the current ad hoc relationship between
field direction and maximum electron energy to one that is determined
from calculations of particle trajectories.
3. The dependence of the particle acceleration on magnetic field
direction reduces the volume filling factor of the emission at the
highest frequencies for both synchrotron and inverse Compton radiation.
This in turn causes higher amplitude, shorter time-scale variations at
the higher frequencies. Since the number of turbulent cells N(\nu) that
radiate at higher frequencies \nu are more limited, the mean
polarization also increases with frequency.
Left: sketch of the TEMZ model.
The figures below present sample simulated multi-frequency light curves (left) and an optical polarization curve (right; from a different simulation result than for the light curves). Note the long, rather smooth rotations of the optical electric-vector polarization position angle (EVPA), which are caused by random walks as turbulent cells with different magnetic field directions pass into and out of the optical emission region just downstream of the conical shock. The rotations can occur in either direction, which distinguishes them from rotations caused by an emission region spiraling down a helical magnetic field (see the papers "The Inner Jet of an Active Galactic Nucleus as Revealed by a Radio to Gamma-ray Outburst," by Marscher et al., 2008, Nature, 452, 966-969 and "Probing the Inner Jet of the Quasar PKS 1510-089 with Multi-waveband Monitoring during Strong Gamma-ray Activity," by Marscher et al., 2010, Astrophysical Journal Letters, 710, L126-L131).
A wide variety of multi-frequency light curves can be generated by the TEMZ model, only some of which are similar to actual blazar light curves. When parameter space is fully explored, this will restrict the range of physical conditions in jets that are capable of reproducing the data. In the displayed example, the gamma-ray variations have much higher amplitude than in the optical, a property that is observed in many blazars but not seen in many of the simulations. Note also the time delays between flares at optical, millimeter, and X-ray wavelengths in this particular simulation.
Previous Models: Moving Shocks
The TEMZ model is an alternative to the long-standing scenario for blazar variability in which a strong disturbance in the jet flow generates a shock wave that moves down the jet at near-light speed. This model is capable of explaining some major outbursts that occur in bright knots of emission that appear to move down the jet at apparently superluminal (faster than light) speeds. 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 multi-frequency light curves expected from such a shock wave. The key point is that electrons are accelerated at the shock front and then lose energy as they move away from the front. Since higher-energy electrons lose energy faster through the production of radation, the highest-frequency synchrotron and inverse Compton emission, which can only be generated by the high-energy electrons, is produced in a thin layer behind the shock front. In contrast, the lower-frequency emission is spread out over a larger volume behind the shock front. This leads to time lags of the peak of the light curves toward lower frequencies, although the starting time of a flare should be the same at all optically thin frequencies. At radio frequencies, the evolution of the continuum spectrum follows a pattern that is unique to the model. Turbulence was added to the moving shock model by Marscher, Gear, & Travis ("Variability of Nonthermal Continuum in Blazars", 1992, in Variability of Blazars, ed. E. Valaoja & M. Valtone, Cambridge U. Press, p. 85), but its effects were not studied intensively.
Andrei Sokolov (PhD 2005, Boston University - now a postdoctoral research associate at the University of Central Lancashire, England) and Alan Marscher developed theoretical models for short flares of 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's calculations 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 can explain 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 Andrei's thesis work are contained in two papers, "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 "External Compton Radiation from Rapid Nonthermal Flares in Blazars" by Sokolov, A.S., and Marscher, A.P, 2005, Astrophysical Journal, 629, 52-60. 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.