SYNCHRONOUS OPTICAL AND RADIO POLARIZATION VARIABILITY IN THE BLAZAR OJ287

Since the dramatic increase in the degree of polarization of OJ287 during the 2006 campaign occurs both at optical/near-IR wavelengths and in the emission from the 43 GHz core, it indicates that the regions of emission are at least partially cospatial. Further evidence for this is provided by the close correspondence of χ(optical/IR) and χ(radio core) during both the 2005 and 2006 campaigns. We conclude that the variable optical/near-IR emission originates from the core region of the parsec-scale jet.

The polarization vector in the core of OJ287 is oriented roughly perpendicular to the flow of the jet. Under the standard relativistic synchrotron model for production of optically thin polarized emission—wherein χ is transverse to the magnetic field lines—the orientation of χ in OJ287 reveals that the mean magnetic field in the core is aligned parallel to the flow of the jet. To more precisely map the orientation of the magnetic field in the jet, we determine the closest observed epoch to the ejection of each component, and note χ(core) at each of these epochs. We find a consistent difference of 99° ± 13° between χ(core) at the time of ejection and the subsequent path of the emerging components. Therefore, the observed magnetic field in the core is approximately aligned with the axis of the jet at any given epoch, parallel to the direction of flow. A region of velocity shear in the core is the simplest explanation for this observed field geometry. The shear could be produced when fast plasma near the jet axis flows past slower material closer to the boundary, resulting in a gradient of velocities that stretches and aligns the magnetic field, which may have originally been randomly oriented in turbulent cells, along the direction of flow.

We also investigate the possibility that multiple radio components contribute to the change in polarization, and conclude that this is not a feasible solution. We observe a distinct stability of the orthogonality between χ(core) and the jet axis, even for significant changes in the projected P.A. of the jet. Combined with the constant agreement between χ(core) and χ(R), we conclude that the changes in χ and P are consistent with intrinsic changes in the viewing angle of the jet, which causes changes in the observed angle of aligned magnetic field. In addition, throughout the period of increasing polarization, we observe no variation in optical spectral index with time or frequency, nor do we observe any evidence for wavelength-dependent χ. These are two tendencies that are commonly observed in the case of multiple-component flares in OJ287 (Holmes et al. 1984) and other blazars (Brindle et al. 1986).

During the 2006 observations of OJ287, we see the optical flux density increase, then decrease, while the percentage polarization continues to grow (Figure 5). To explain this behavior, we create a structural model for the inner jet as a combination of three elements. The first element is a large, relatively slow turbulent sheath, which surrounds a thinner, faster, turbulent spine along the axis of the inner jet. The transition region between the two zones produces the final element, with the magnetic field there aligned longitudinally by shear. We use Γ = 16.5 as the average Lorentz factor of the spine, derived from observations of the fast jet components of OJ287 in the detailed VLBA study of Jorstad et al. (2005). The Lorentz factor of the bulk jet flow is calculated from the observed pattern speeds of components—which cannot exceed Γ—and the concurrent jet viewing angle, and is therefore greater than or equal to the fastest observed component speed. In addition, we set the half-opening angle of the spine to be within the range 0.8° ± 04, also derived for OJ287 in Jorstad et al. (2005). The average Lorentz factor of the sheath is stepped through a series of values to find the best fit, and the boundary region is assigned a Lorentz factor that is the arithmetic mean between Γ_spine and Γ_sheath. As the sheath is a large structure, we hold its viewing angle steady, using the value of 32 derived in Jorstad et al. (2005). We then allow the viewing angle of the small spine and boundary region to vary with time. As the viewing angle of a spine-boundary structure changes when the jet direction swings slightly, the effects on the Doppler beaming of the radiation from this region are dramatic, while balanced by the radiation of the larger, slower sheath. This yields a combination of a strongly varying component superposed on one having a relatively steady flux density.

We initially reproduce the R-band flux density and polarization variations with this model, as it is the waveband with the highest sampling during the campaign. We assign to all emission elements the average observed optical spectral index of −1.29. To model the degree of polarization and flux density of the optical emission, we utilize the equations for total flux density from optically thin sources derived by Cawthorne (2006), based on previous work by Hughes et al. (1985). The models of Cawthorne (2006), created to describe synchrotron emission from conically shocked plasma, provide equations for the total flux density from regions of both aligned and turbulent magnetic field. The proportionalities, adapted to a variable α, are as follows:

$$\begin{equation} F_{||} \propto (B_{||} \sin \theta _{||}^{*})^{1-\alpha } \nu ^{\alpha } \delta _{||}^{2-\alpha } \end{equation} \tag{ 1 }$$

and

$$\begin{equation} F_{\rm turbulent} \propto B_{\rm turb}^{1-\alpha } \frac{1}{\kappa ^{2}} (2-(\sin \theta _{\rm turb}^{*})^{1-\alpha }(1-\kappa ^{2})) \nu ^{\alpha } \delta _{\rm turb}^{2-\alpha }. \end{equation} \tag{ 2 }$$

In the above equations, δ is the Doppler factor, which is a function of viewing angle θ, jet speed β, and Lorentz factor Γ: δ = [Γ(1 − βsin θ)]⁻¹. The compression factor due to shocking in the region is described by factor κ and B_|| and B_turb are, respectively, the parallel and turbulent components of the magnetic field. The influence of the magnetic field on flux density is described with the angle θ*, the angle between the aligned magnetic field and the line of sight, corrected for relativistic aberration. We adapt these formulae for our usage by instituting a lack of compression (i.e., no shock, κ = 1) and by removing the ν factor, as we are modeling a single waveband. Applying our observed optical spectral index to these formulae, we find the following proportionalities for flux density in the R waveband:

$$\begin{equation} F_{\rm R, spine} \propto \delta _{\rm spine}^{3.29} B_{\rm turb, spine}^{2.29}, \end{equation} \tag{ 3 }$$

$$\begin{equation} F_{\rm R, transition} \propto \delta _{\rm transition}^{3.29} B_{||}^{2.29} (\sin \theta ^{*})^{2.29}, \end{equation} \tag{ 4 }$$

and

$$\begin{equation} F_{\rm R, sheath} \propto \delta _{\rm sheath}^{3.29} B_{\rm turb, sheath}^{2.29}, \end{equation} \tag{ 5 }$$

in which we approximate the parallel and turbulent components of the magnetic field to be roughly equal for the purpose of simplicity in the model. This approximation is valid under the assumption that the magnetic field in the turbulent cells is aligned by shear, but not enhanced. The equations for total flux density from the turbulent sheath and spine regions contain factors to account for the strength of the magnetic field and for the relativistic beaming effect. The equation for total flux density from the transition region of aligned magnetic field contains an additional factor (sin θ*)^1−α, reflecting the directionality of synchrotron emission, which peaks at a rest frame viewing angle perpendicular to the magnetic field.

Utilizing these equations, we consider a circular cross section of the jet (See Figure 8 for an illustration of the model structure). For each potential value of the viewing angle (calculated for 1000 steps between 0° and 8°), we integrate the flux density across the spine and sheath, where the jet cross section is separated into concentric rings with width 01. We consider a range of values of the width of the sheath, the width of the spine (within the errors stated above from Jorstad et al. 2005), and the average Lorentz factor of the sheath, to find the best model fit. We calculate the degree of polarization by approximating that the turbulent sheath and chaotic magnetic field component in the spine have negligible polarization, and that the boundary region has the maximum polarization possible for synchrotron radiation, 77.5% for a spectral index α = −1.29. We use this simplifying assumption to minimize the number of parameters, given our limited sample size. Further monitoring of this blazar would allow the introduction of additional modeling factors, such as the level of magnetic field alignment. We then manipulate the viewing angle of the spine and boundary region to simulate variations in flux density and polarization. Figure 9 displays the modeled quantities, with values discussed below.

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Two factors contribute to the changes in observed flux density with viewing angle. The first is the Doppler factor, the decline of which decreases the flux density with increasing viewing angle. In addition, the effect on the emission of the ordered component of the magnetic field, parallel to the jet axis, varies with the sine factor of Equation (4). As the deaberrated viewing angle increases up to 90°—up to an observer's viewing angle in radians of ∼1/Γ—the observed flux density from the ordered component increases. These two multiplicative factors affect the observed emission of the boundary layer such that the flux density first grows, then declines, as the viewing angle increases while the spine changes direction. The flux density of the turbulent spine is, however, only affected by the Doppler factor. The resultant combined flux density for all components peaks at a lower viewing angle than does the peak of total polarization. This leaves an observable signature, in which the flux density of the combined system can grow to a maximum while the degree of polarization rises less steeply and peaks later in time (see Figure 5).

To model the observed flux density, we find the viewing angle required for an observed value of P(R band), then determine the modeled flux density corresponding to that viewing angle. We compare the modeled flux density to the observed quantity to find the closest fit using our three variables. The best fit is found for a spine of half-width 12, a sheath of width 46 (between the outer and inner boundaries), and a Lorentz factor in the sheath of 5.0. Figure 9 shows the modeled flux density and polarization graphs for this simulation. We find that a decrease in viewing angle from 75 to 32 can create a simultaneous increase in flux and polarization, as observed during the 2006 campaign.

Figure 10 compares the observed and modeled flux density as well as the observed and modeled polarized flux density, and plots the required viewing angle. We demonstrate in Figure 10, panels A and B, the excellent fit of the spine and sheath model to the observed flux density and polarized flux density. Following the peak, we observe a decline in flux density combined with a delayed decline in percentage polarization. We interpret this as a reversal of viewing angle over a period of 7 days from 318 ± 006 to 70 ± 04, as shown in Figure 10, panel C. The optical EVPA (Figure 5) swings from 67 to −37° throughout the rise and fall of the flux density. Based on the previously stated relationship between χ(core) and jet direction, this corresponds to the spine tracing an arc from projected P.A. −83° to −127° over a two-week period, with the swing in χ_opt providing further evidence for rapid, erratic behavior in jet direction. This projected arc swung toward, then away from, the line of sight, resulting in the decrease, then increase, of the viewing angle, and thus the increase and decrease observed in polarization and flux density.

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We can check the feasibility of such a spine and sheath structure by examining the distance downstream necessary for such a boundary layer to form in the presence of a velocity mismatch. For this purpose, we use a formulation from Jorstad et al. (2007) for shearing from transverse velocity gradients. This equation describes the amount of alignment of magnetic field expected by such a gradient, assuming that the field is initially turbulent. Given the speeds of flow in the spine and sheath, β_spine and β_sheath, we can calculate the fractional alignment f_align at a given distance from the initial area of turbulence:

$$\begin{equation} f_{\rm align} \approx \frac{x \beta _{\rm rel}}{\Gamma R} \frac{\Delta z}{R} \, \end{equation} \tag{ 6 }$$

where Γ is the Lorentz factor of the sheath, β_rel = (β_spine − β_sheath)(1 − β_spineβ_sheath)⁻¹, R is the half-width of the jet, x is the size of the turbulent cells, and Δz is the distance between the point where the field is completely turbulent and the location of the feature. We set an upper limit to R based on component widths close to the 43 GHz core, as determined by model fitting of the VLBA data. We estimate x by first calculating the number of cells required to reduce the maximum polarization of incoherent synchrotron radiation P_max to the observed value of P within a single resolution element, N = (P_max/P)², where N is the number of turbulent cells within the beam (Burn 1966). Then x is of order the beam width divided by N^1/3, ∼0.049 pc. As a check on our value for x, we calculate the scale size of turbulent cells from the two-day quasi periodicity in P(optical) shown in Figure 6, transformed to the plasma frame, which gives a value with the same order of magnitude, x∼0.024 pc. We find that for the modeled ratio of boundary layer area to turbulent spine area, such alignment can occur within 2.5 pc of the core.

Although the model presented above well describes the observed behavior, we must address the issue of a rapidly changing viewing angle, as indicated in Figure 10. Previous studies of OJ287 have suggested that the viewing angle of the jet is relatively steady over short time intervals, with major excursions only on timescales of years. According to the binary black hole model of Valtonen et al. (2006), the viewing angle of the jet has a mean value of 27 and varies on the order of 05 over 30 years. This angular variation is too small to describe the variation of viewing angle in our model. Additionally, Tateyama & Kingham (2004) suggest that the 8 GHz inner jet demonstrates ballistic precession with a period of 11.6 years. However, this precession is on a timescale that is orders of magnitude larger than the 10 day variation we model. To describe variations in polarized flux and χ such as we observe, Hughes et al. (1998) consider helical modulation of the velocity vector in OJ287 by a disturbance in the jet. A helical velocity field would produce the modeled change of viewing angle, which swings first toward, then away from, the line of sight. However, due to physical constraints, this mechanism requires that rotation of the flow occur on a timescale of greater than a year. The variations we report here are too rapid to be explained by either a slowly precessing jet or velocity vector rotation.

Instead, we propose that the change in viewing angle that we infer is most likely the combination of wiggles caused by an instability and minor fluctuations in the optical depth along the jet. If the position of the core is defined by the surface at which the optical depth becomes unity (Blandford & Königl 1979; Königl 1981), a small change in the optical depth of the jet will move the position of the core upstream or downstream. As the core, the brightest feature, moves along the jet, it will highlight different parts of the helical velocity field. Figure 11 illustrates the jet structure that we propose. If the quasi-steady jet is subject to transverse oscillations, perhaps produced by the helical velocity modulation, then the change in core position will cause apparent swings in the direction of the section of the spine that contains the core. Such movement of the core could be induced by a change in magnetic field and electron density in the wake of the disturbance that creates a new knot, namely component 2 shown in Figures 1–3. This conclusion is supported by Jorstad et al. (2002), in which phase-referencing observations of OJ287 at 43 GHz indicate possible motion of the core during a period of prominent flaring. We therefore ascribe the swing in the viewing angle needed in our model to a temporary change in the position of the core. This affects the direction of motion of the emitting plasma in the spine without changing the previously established long-term integrity of the overall jet.

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While we are able to use this model to describe the variable emission in 2006 March, we must also address the emergence of knots from the core. The polarization vectors of the observed knots tend to align well with the direction of their motion. For each component, we calculate the difference between its P.A. and χ. We find a difference of 3° ± 9° for the combined values of component 2, component 3, and the western component observed only in 2005 October. This alignment can be explained by the propagation of transverse shock waves (Hughes et al. 1985), which enhance the magnetic field component in the plane of the shock, within the turbulent spine of the inner jet. The presence of relativistic shocks within the spine of an otherwise longitudinally aligned spine-sheath system has been previously theorized (Gopal-Krishna et al. 2004) and observed to exist at radio wavelengths (e.g., Attridge et al. 1999; Gabuzda 2003b) as well as at optical wavelengths on kiloparsec scales (e.g., Dulwich et al. 2007). The observed extent of these jets, as well as the consistently high flow speed at large distances, provides evidence for the spine and sheath model. In addition, optical observations demonstrate the longevity of magnetic structure in the jet, characterized by perpendicular magnetic field in the spine and parallel, aligned magnetic field along the boundary layer.

At times, when the viewing angle and flux density of the shocked emission are such that the polarized flux density from the shock exceeds that of the sheared boundary layer, the observed χ(core) can switch such that it becomes parallel to the jet. This parallel χ(core) appeared throughout the 1970s and 1980s with some rapid switching to and from a perpendicular χ (Hagen-Thorn 1980). Sillanpää (1991) proposed that changes in χ could be due to temporary intervals of dominance of transversely shocked magnetic field over an underlying, structurally stable longitudinal field in the inner jet. Roberts et al. (1987) reported a change of χ(core) from 160° to 99° in late 1982, coincident with the extrapolated birth of knot K3 (Gabuzda et al. 1989) along P.A. = −100°. Our conclusions are supported by those of Hagen-Thorn & Gataullina (1991), in which decomposition of the polarized optical flux of OJ287 revealed two distinct components, one with χ = 163° (corresponding to our sheared component) and the other with χ = 84° (corresponding to a transverse shock). In our model, the slow and stationary knots observed intermittently in OJ287, such as component 1 in Figures 1–3 with Γ = (5.3 ± 0.6)c, could be associated with shocks propagating along the slower sheath, as suggested in Komissarov (1990), Laing et al. (1999), Chiaberge et al. (2000), and Ghisellini et al. (2004). In addition, component 1 exhibits a difference between P.A. and χ of 53° ± 15°, suggestive of a more oblique shock than those seen in faster components. Thus, the spine and sheath dichotomy can produce distinctly separate classes of fast and slow knots as well as the behavior of χ observed in OJ287 during our campaigns and in previous studies. These include the fast (Γ = 11.6 to 18.0) and slow (Γ = 0.4 to 1.3) groups of knots noted in OJ287 by Jorstad et al. (2005).

We find a clear discrepancy between the optical and radio core polarization in both the 2005 and 2006 campaigns. In the 2005 observations, P(R band) is consistently 2.5 times larger—and P(H band) 2.1 times larger—than P(43 GHz core), while the flux density and degrees of polarization are at high levels. In 2006, we observe similar low optical, IR, and radio core percent polarization at a fainter flux density, followed by an increasing ratio between the wavelengths as the flux density and P increase (Figure 7).

We explain this behavior by appealing to a steepening of the spectrum with frequency. We apply a range of spectral indices to the multiwavelength polarization measurements, and find a good fit for the following wavelengths: α_B = −1.41, α_V = −1.35, α_R = −1.29, α_I = −1.21, and α_H = −0.81. These spectral indices reproduce the observed polarization ratio changes. The spectral index has little impact on percentage polarization at a high viewing angle, which agrees with the similarity in observed values at low flux density. We then see a greater impact on polarization at smaller viewing angles, as found in the data, with flatter spectra producing a lower percent polarization. To check whether the observed steepening in optical index is consistent with synchrotron theory, we examine the indices produced by a uniform synchrotron source for a given index of the electron power-law energy distribution (Pacholczyk 1970). We find that the steepening can be reproduced with a synchrotron critical frequency of ∼1.2 × 10¹⁵ Hz, or λ ∼ 2500 Å, for an electron energy distribution N(E) ∝E^−s with index s = 2.5.

We examine the optical spectra to determine whether this steepening in index was in fact observed. We are not able to detect such steepening within the optical region given the error in spectral index for individual wavebands, σ(α)∼±0.25. In Figure 12, we display the average optical-to-IR spectrum overlaid with the model steepened spectrum. For each epoch at which both IR and optical measurements are available, we normalize the observed spectrum to log[Flux Density(H)]=1, then average the spectra to produce the displayed data. As is shown in Figure 12, we observe a clear steepening between the IR to far-red index (α_H−I = −0.9 ± 0.1) and the optical index (α_opt = −1.3 ± 0.1), which is fit well by the model steepened spectrum. In addition, all five modeled indices agree with the observed values within one standard deviation. Historically, such steepening between IR and optical wavelengths has been observed in OJ287 by Rieke & Kinman (1974), Worrall et al. (1982), Holmes et al. (1984), Sitko & Junkkarinen (1985), Ballard et al. (1990), Ghosh & Soundararajaperumal (1995), and Hagen-Thorn et al. (1998).

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When we extend the spectrum to fit the 43 GHz data, we find that the percentage polarization in the radio requires an optically thin spectral index near zero. From this, we conclude that the 43 GHz polarization is diluted by emission from an optically thick region. As described in Gabuzda (2003a), the agreement between χ(optical) and χ(43 GHz core) suggests that the polarized radio emission is dominated by the optically thin region. We calculate the necessary dilution by the weakly polarized optically thick zone using the formula derived in Pacholczyk (1970), under the assumption that the optically thin spectral index ∼−0.8, roughly that inferred for the IR H-band (compared to the spectral energy distribution derived by Impey & Neugebauer 1988). From the observed percentage, we determine that ∼30% of the 43 GHz core emission is optically thick.

Examination of the 2005 campaign results reveals behavior that, while less dynamic, agrees with the above model. As Figure 4 indicates, we observe an upward trend in both optical and 43 GHz core flux, as well as an increase in P(optical), accompanied by a swing in χ(optical). A change in the viewing angle of the spine can explain all three observed effects.

We consider two alternative explanations for the observed behavior of χ in the 43 GHz core of OJ287. In one recent proposal, Gabuzda et al. (2004) used complex rotation measures and close examination of χ values to describe the parsec-scale jets of BL Lac objects as containing a helical field in which the toroidal component of magnetic field dominates. While this description is consistent with the steadiness of χ in components 2 and 3 as they proceed down the jet, it fails to explain either the dynamical nature of the core or the fast increase in flux and polarization. In addition, although many BL Lac objects display a χ(core) parallel to the jet direction (Gabuzda et al. 2000; Marscher et al. 2002), our study of OJ287 shows a highly polarized χ(core) perpendicular to the jet, a condition that would necessitate extreme, nearly longitudinal pitch angles of the helix. Historically, the core of OJ287 has high polarization in instances when it maintains a transverse χ—shown in our data—as well as when it possesses a longitudinal χ (Hagen-Thorn 1980; Hagen-Thorn & Gataullina 1991), which is not expected in the helix model.

Another study of OJ287, by Vicente et al. (1996) using the models of Hardee (1987), suggests that the progression of components along the jet is in fact the motion of shocks following a helical path. If this path were to change by 90° within the resolution of the VLBA, it could very well describe the dichotomy we see between χ in the core and that of its ejected components, as well as the change in the viewing angle as plasma proceeds down the parsec-scale jet. Nonetheless, we observe no helical behavior in the path of motion of the components within positional errors (see Figure 3), contradicting the model. Furthermore, Tateyama & Kingham (2004) had examined this model for OJ287 and concluded that it is insufficient to fully describe the data, proposing instead that ballistic precession produces a changing inner jet direction on longer timescales than seen in our observations. We note, however, that the conclusions of Vicente et al. (1996) described components on scales of several milliarcseconds and on timescales of several years, and are therefore not entirely applicable to the data that we display.