3.1. Single-Epoch Modeling: Study of Jet Properties during the Fermi Era
A motivation for the modeling is to identify flow conditions in the jets of γ
-ray flaring blazars. In the initial phase of this work we analyzed individual time segments of the UMRAO data in 4 sources exhibiting moderate to strong γ
-ray flares. The sources were selected based on the appearance of well-separated outbursts in the UMRAO data, and simultaneous or near-simultaneous flaring in the centimeter and GeV bands. In the case of one source, 1156+295, two adjacent time windows were modeled which included nearly-identical radio-band outbursts in terms of amplitude and spectral evolution in total flux density and maximum linear polarization amplitude. However, the second radio-band outburst was paired with a γ
-ray flare, while the first outburst was an orphan radio outburst (no temporally-associated γ
-ray flare). The difference in the γ
-ray to radio-band activity was attributed to the presence of a larger number of shocks in the paired event [5
] and more complex structure at VLBI scales found from 43 GHz imaging data [9
The data for the most recently modeled source in this group, 0716+714, are shown in Figure 2
left. MOJAVE source-integrated data taken from the MOJAVE webpage at http://www.physics.purdue.edu/astro/MOJAVE/sourcepages/0716+714.shtml
are included for comparison. The fact that this blazar is extreme is apparent from the unusual shape of the outbursts in total flux density (lower panel in Figure 2
left). These exhibit an unusual triangular shape with nearly equal rise and fall times, and several of these events are captured within the time window modeled. Also, the maximum fractional linear polarization is unusually high, near 14% at 14.5 GHz, compared with the values for the other sources modeled (typically 5% to 8% at maximum). The adopted shock onsets used in the simulation shown in the right figure are denoted by upward purple arrows along the abscissa; these onsets correspond to the times at which the leading edge of the shock enters the flow.
In the simulation shown to the right the three model frequencies are color and symbol coded to match those used for the data. The scaling of time in the simulation is set by the duration of the activity modeled, while the total flux density amplitude is scaled to match the peak value at the highest UMRAO frequency, 14.5 GHz. This simulation reproduces the general character of the variability including the spectral behavior as a function of time, the amplitude range of the total flux density flares, and the global shape of the outbursts and the position of features. Note that in this source a multi-year time window has been modeled with a single set of jet parameters. However, while many of the global features are simulated with the adopted model, refinements are required to reproduce the spectral character of the 8 GHz polarization, especially during shocks 2 through 5. In the early part of the simulation the values of P% are too high at all three frequencies; this is an artifact of the modeling which starts from quiescence and neglects the effect of earlier activity.
The derived jet flow and shock attributes for the 4 blazars modeled in this phase of the work are summarized in Table 2
. As expected, several parameters found for 0716+714 are extreme compared with the other 3 blazars modeled. These include the high bulk Lorentz factor which was determined from the unusually high value of P% and which is consistent with the high values of
determined from VLBI observations for the fastest components by MOJAVE [10
] and other programs, e.g., [11
Another notable property is the unusually-high viewing angle when compared with the other modeled blazars and with results based on alternative analysis procedures for 0716+714 [11
]. While a viewing angle of 12
provides the best match between the simulation and the data, we could not rule out values as low as 5.8
] since the model linear polarization is less sensitive to changes in viewing angle at values of
3.2. Multi-Epoch Modeling: Internal Changes in the Jet on Timescales of Years to Decades
In order to look for temporal changes in jet flows on time scales of decades to years we have modeled three epochs of the UMRAO data for the highly-compact source OT 081: 1985.0 to 1986.0 (T1985), 2008.4 to 2010.7 (T2008) and 2010.8 to 2011.9 (T2010). As shown in Figure 1
this source exhibited strong and persistent variability throughout the UMRAO program making it an ideal target for a long-term study. Further, the data used in the analysis presented here were consistently obtained with the 26-m paraboloid under automatic computer control using the same observing and reduction procedures throughout; hence the work is based on a homogeneous data set. The UMRAO data for the 1985 outburst had previously been modeled using an earlier simulation code [13
]. This work identified reverse shocks in order to obtain the slow flows (of order c) expected based on the limited VLBI data available at the time.
In Figure 3
we compare the data (left) and and the new simulation (right) for T1985. The simulation is able to reproduce the spectral character and maximum amplitude of the total flux density (bottom panel), the detailed behavior of the fractional polarization light curve including the small flare near the start of the time window and the maximum value of P% attained at all 3 frequencies, and the nearly constant value of the EVPA during most of the time window modeled. However, the details of the EVPA variability are not reproduced, and the variability apparent in the observed EVPA light curve is again very complex.
In Figure 4
we show the data and the simulated light curves for T2008. Here we have again been able to reproduce the major features of the light curves including the spectral character and maximum amplitude of the total flux density, the low levels of the fractional polarization (under 5% in general) and the fractional polarization spectral character during the activity, and the frequency-dependent EVPA separation. While we do not show the results for T2010, we have simulated the major features apparent in the UMRAO light curves using a model incorporating the parameters given in Table 3
. The variability across each of these time windows is not self-similar, and scaling from a fiducial epoch in the simulations cannot reproduce the data at other epochs.
Results for OT 081 spanning 1985 to 2012 are presented in Table 3
. In addition to the parameters listed in Table 1
we include the shock Lorentz factor which comes from the bulk Lorentz factor of the quiescent flow and the shock strength (the compression factor). The shocks in this source are all moderately strong but not as strong as those in the 0716+714 time period modeled. The modeling identifies forward shocks, a viewing angle nearly in the line of sight, and component speeds in agreement with VLBA measurements at 15 and 22 GHz which are in the range 5–21 c based on VLBA data obtained over 11 years from 1995 to 2005 [14
]. While the flow speeds are consistent with VLBA estimates of the flow based on the maximum component speed, our low value of the viewing angle is not consistent with the value of 4.2
obtained from a combination of VLBA component speeds and a Doppler variability factor [15
]. Unlike 0716+714, the low viewing angles obtained are very well constrained by the linear polarization data.
Comparison of the derived parameters as a function of time shows that systematic changes with time have occurred within the flow. These are most extreme between T1985 and T2008, and the trends continue into T2010. As noted, these changes cannot be reproduced simply by scaling, and they are changes in the flow intrinsic to the source. However, from our analysis we cannot distinguish whether these are changes in the properties of the flow at a single location or whether the observer is looking at a different segment of the flow in each time window, possibly associated with changes in the orientation of the jet. The latter interpretation is plausible since changes in the orientation of the inner jet position angle have been identified from an analysis of MOJAVE data for this source [16
3.3. Inclusion of a Helical Magnetic Field Component
Because of the mounting observational evidence for the presence of helical magnetic fields in the parsec scale jets of blazars, including a 5-σ
determination of a helical/toroidal magnetic field in OT 081 [17
], we have investigated the effect of including a helical magnetic field on the simulated light curves for epoch T1985. This additional ordered component is included in the form of a magnetic flux rope which permeates the emitting plasma, and it is compressed along with the turbulent magnetic field component by the passage of a shock. While the presence of a dominant helical magnetic field was ruled out in earlier work [4
], the new result presented here reflects the interplay of three magnetic field components.
The light curve allowing for a turbulent magnetic field, an axial component, and the additional helical field component, is shown in Figure 5
right for the case of a strong helical component (following the notation of [4
], an order multiple ≥3). This can be compared with the simulation based on the adopted parameters shown to the left. The effect of the inclusion of the helical field into the simulation is to suppress the structure in the fractional linear polarization light curve and to produce a frequency-dependent separation of the EVPAs with a spread by as much as ΔEVPA = 35
. In contrast, the data exhibit a flat EVPA spectrum which persists throughout most of the modeled time window. This simulation, thus, does not reproduce the major features of the observed fractional linear polarization and EVPA light curves.
We conclude from a comparison of the simulation with the UMRAO data for OT 081 that a dominant helical magnetic field is excluded. However, the inclusion of a modest ordered helical magnetic field component, in addition to the turbulent and axial components already described, improves the fit showing that the model can accommodate a modest helical B field. This result supports a scenario where a modest helical magnetic field is present in the parsec scale jet downstream of the centimeter-band VLBI core region [18