High-resolution radio observations of astrophysical jets show moving structures or blobs thought to be shock waves propagating down the jet. Such disturbed outflows can be modelled by hydrodynamical simulations, but we present here a different approach, which is intermediate between observations and simulations.
The method consists in a decomposition of the observed total flux variations into a series of self-similar outbursts evolving with time according to a physical shock model. The decomposition uses as many observational constraints as possible from flux measurements at different epochs and wavelengths. The outburst's properties are derived by fitting the model parameters simultaneously to all observations.
This original approach aims at testing the validity of the model and at constraining the physical properties of the jet. It has been applied to both galactic jets from black-hole binaries (micro-quasars) and extra-galactic jets from distant powerful quasars and blazars. The results have been the subject of several publications listed below. We present here a brief description of the model, the method and some results illustrated by a selection of interesting complementary material - mainly animations - which cannot be included in scientific publications.
Figure: Animation of simulated high-resolution jet observations of the blazar 3C 279 for the 1990's decade. The simulation is based on the results of the decomposition of the optical-to-radio light-curves of the source. It shows the evolution of blobs at an observing frequency of 22 GHz and with a resolution (FWHM) of 0.15 milli-arcsecond (mas). We assume that all blobs are moving with a constant (for simplicity) apparent superluminal velocity of 5 times the speed of light. The color-coding and contours represent the observed flux on a square-root scale, chosen to give more emphasis to low-flux features. Lindfors et al. (2006)
The physical model is a generalization of the
shock-in-jet model of Marscher & Gear (1985). The basic principle of this model
is as follows. A shock wave is propagating along the jet. Electrons crossing the
shock front are accelerated. They emit synchrotron radiation in the shocked
medium behind the shock front. The emitted synchrotron spectrum (blue curve)
evolves following 3 stages depending on the dominant emission-loss mechanism of
the electrons: 1. Compton losses, 2. synchrotron losses and 3. adiabatic
(non-radiative) losses. The self-absorption turnover of the spectrum follows a
characteristic 3-stage pattern (red curve). While the turnover frequency is
steadily evolving from high to low freqencies, the turnover flux is first rising
during the Compton-loss stage, stays more or less constant during the
synchrotron-loss stage and decays during final adiabatic-loss stage. According
to the model, the optically thin spectral slope is expected to be steeper
(-s/2) during the first two radiative-loss stages than during the final
decay (-(s-1)/2), where s is the index of the electron energy
distribution N(E) ~ E-s.
The model presented above defines fully the evolution of a synchrotron outburst resulting from a shock wave at any frequency (wavelength) and at any time. The evolution of the spectrum with time shown above defines therefore also the shape of the light-curve (flux evolution with time) at any given frequency. For observational reasons (many observations at some fixed wavelengths), it is easier to identify and characterize the outbursts in the time-domain (light-curves) than in the frequency-domain (spectra). This is done by a simultaneous fit of the light-curves available at as many different frequencies as possible to have the best constraints on the model. In practice, many iterative fits on subsets of all parameters are needed to achieve a good match to the observations. The result is a best fit decomposition of the light-curves into a series of self-similar outbursts as shown in the figure. The fit parameters define both the average properties of a typical outburst and the specific characteristics of each individual outburst. They give valuable clues on the physical properties of the jet.
Figure: Long-term (20 years) radio-to-sub-millimetre light-curves of the quasar 3C 273 with the best fit decomposition into self-similar outbursts. The total model light-curve (grey line) is the sum of the flux of the individual outbursts (colored areas), the global decay of the outbursts peaking before 1979 (light grey), a possible constant emission from the underlying jet (medium grey) and the steady (fixed) emission from the outer jet extending on kiloparsec-scales (dark grey). Türler et al. (2000); Türler & Lindfors (2006)
The decomposition of the lightcurves into separate
model outbursts allows to produce simulated jet images at any frequency and
angular resolution. The model flux of each component is known at any frequency
and time and therefore we just have to assume a Gaussian beam and a constant
apparent speed of each knot in the jet to construct the simulated jet images at
any time. The link between the outbursts in the lightcurve and the
conrresponding structures moving in the jet is shown by the use of different
colors in the animated figure. A nicer view of the simulated jet animation of 3C
279 is shown at the top of this page.
Figure: Animation showing the link between moving jet structures and outbursts in the lightcurve of 3C 273 at 22 GHz. The simulated jet image (contours) at the top is derived from the outbursts identified in the lightcurve. Colors are used to relate the outbursts to the moving jet structures. The steady core emission is shown in grey. The apparent speed of the knots in the jet is assumed to be the same for all outbursts and to be constant in time.
The method first used for quasars like 3C 273 with a single observable jet was developped further to include as well the emission of the counter-jet. This was needed to model the outbursts of the galactic black hole binary GRS 1915+105. For this microquasar, we assumed twin outbursts propagating in two opposite jets. The decomposition of the very well sampled lightcurves enabled to derive a mildly relativistic jet speed of 0.6c during the observations of 15 May 1997 corresponding to a "baby-jet" phase (Türler et al. 2004).
Figure: Light-curves of the micro-quasar GRS 1915+105 taken on 15 May 1997 with the best fit decomposition into self-similar outbursts. The total model light-curve (red curve) with its distinct outbursts (red dotted lines) is the sum of the light-curves from the approaching jet (blue) and the receiding jet (green) plus a constant flux in the infrared at 2.2 microns. The grey line in the upper panel is the X-ray light-curve in the 2-60 keV observed by RXTE. Arrows show the onset time of the individal outbursts. Türler et al. (2004)
An interesting area of development of the modelling presented here is the inclusion of the associated synchrotron self-Compton (SSC) emission in the X-ray and gamma-ray range. This is motivated by growing evidence that X-ray and gamma-ray flaring is related to synchrotron outbursts observed at lower frequencies (e.g. Lindfors et al. 2006, Léon-Tavares et al. 2011). A preliminary analysis for the blazar 3C 279 with a simplified first-order SSC modeling was presented in Lindfors et al. (2005). Recently, an analytical description of a self-consistent SSC mechanism with multiple-order inverse-Compton scatterings was derived by Björnsson (2011). A first attempt to test and constrain this model with the wide dataset of 3C 279 is presented in Türler & Björnsson (2011). A more thorough work with the inclusion of Fermi data and the modeling of the underlying jet flow is in preparation.
Figure: Animation of the modeled evolution of the spectral energy distribution of 3C 279 (grey line). The variability is assumed to be due to the emission of a succession of self-similar shock waves (colored lines) in the relativistic jet of the blazar. Synchrotron emission and associated multiple inverse-Compton scattering account for the low- and high-frequency bumps, respectively. Observed data points from Hartman et al. (2001) and from MAGIC (Aleksíc et al. 2011 A&A 530, A4) are shown for comparison.Türler & Björnsson (2011)
The main goal of the ISSI International Team 2008-2010 on "Decrypting and Modeling the High-Energy Emission of Blazars" was to develop the modeling of the inverse-Compton emission peaking in the gamma-ray range.
A theoretical description of multiple inverse-Compton scattering in a shock-in-jet scenario has been derived by Björnsson (2010). This provides an analytical description of the expected high-energy emission. In parallel, I reworked the modeling of the synchrotron emission to make it completely physical in order to directly fit the actual jet properties (magnetic field, electron energy density, etc.) instead of the observables (Türler 2011).
The on-going step is to incorporate in the modeling the associated synchrotron self-Compton (SSC) emission based on the analytic description derived by Björnsson (2010). this will allow us to fit together the variability of some well observed blazars from the radio to the gamma-ray range, to test various emission scenarii, and to constrain the physical properties of the emission region.