Optical Emission and Particle Acceleration in a Quasi-stationary Component in the Jet of OJ 287

OJ 287 is one of 37 blazars monitored roughly monthly at a wavelength of 7 mm with the VLBA under the VLBA-BU-BLAZAR project⁸ (Jorstad & Marscher 2016). Calibration of the data, as well as total and polarized intensity imaging procedures, are essentially identical to those described by Jorstad et al. (2007, 2017). In order to calibrate the absolute value of the EVPA of the VLBA data, we use (1) Very Large Array observations at 7 mm of a number of VLBA-BU-BLAZAR blazars, including OJ 287, within 1–3 days of the VLBA observations; and (2) the "D-terms" method (Gómez et al. 2001). We analyze Stokes-parameter I, Q, and U images at 95 epochs from 2007 June 14 to 2016 March 18. Time intervals of VLBA observations are roughly one month, and most of them are within two months. All images are convolved with an elliptical Gaussian restoring beam of an FWHM of 0.33 × 0.16 mas oriented along position angle (PA) = −10°, approximating the angular resolution with a uniform weighting of the visibilities. To check for signs of Faraday rotation and optical depth effects, we compared the EVPA in the 43 GHz images when the EVPA was uniform across the main emission regions with a measurement of the integrated 86 GHz polarization at the 30 m antenna of the Institut de Radioastronomie Millimétrique (Agudo et al. 2018a, 2018b) within 2 days of the VLBA observation. Six epochs from 2008.50 to 2014.57 met these criteria. The mean 43–86 GHz EVPA difference was 2° ± 3°, leading us to conclude that the 43 GHz polarization was unaffected by either Faraday rotation or synchrotron self-absorption.

We use data from optical polarization observations of OJ 287 performed at: (1) the 1.83 m Perkins Telescope of Lowell Observatory (Flagstaff, AZ) in the R band with the Perkins Re-Imaging SysteM (PRISM) camera⁹ ; (2) the 0.7 m AZT-8 telescope of the Crimean Astrophysical Observatory (Nauchnij, Crimea) in the R band; (3) the 0.4 m LX-200 telescope of St. Petersburg University (St. Petersburg, Russia) without a filter (central wavelength ${\lambda }_{\mathrm{eff}}\approx 670$ nm); (4) the 1.54 m Kuiper and 2.3 m Bok telescopes of Steward Observatory (Tucson, AZ) in spectral-polarimetric mode covering a wavelength¹⁰ range of 4000–7550 Å; (5) the 2.2 m Telescope of Calar Alto Observatory (Almería, Spain) in the R band with the Calar Alto Faint Object Spectrograph (CAFOS) multi-purpose focal reducer (acquired as part of the Monitoring AGN with Polarimetry at the Calar Alto Telescopes (MAPCAT) project¹¹ ); and (6) the 1.5 m Kanata telescope of Higashi-Hiroshima Observatory (Hiroshima, Japan) in the V band. Details of the polarimetric data reduction can be found in Larionov et al. (2008), Smith et al. (2009), Jorstad et al. (2010), and Ikejiri et al. (2011). The differences in the EVPA among the different optical bands are negligible compared with the temporal variations during the time spans between the observations. Finally, most of the time intervals are within one day in the time series of the measured polarization.

We have examined the data sets to identify 43 pairs of VLBA and optical polarization observations simultaneous within ±1 day. The optical polarization measurements were collected nearly every night during periods when OJ 287 was visible. At epochs when multiple optical measurements matched the simultaneity criterion, we average the I, Q, and U values to obtain the degree ${P}_{\mathrm{opt}}=\sqrt{{Q}^{2}+{U}^{2}}/I$ and the position angle ${\chi }_{\mathrm{opt}}=\tfrac{1}{2}\ {\tan }^{-1}\left(\tfrac{U}{Q}\right)$.

We employ the Gnu R programming language (v3.2.1; R Core Team 2015) for an analysis of the VLBA images at these 43 epochs. At each epoch, we determine I_i, Q_i, and U_i as the mean values over circular area i, i = 1 to N; the circular areas have radii of 0.05 mas and centers spaced every 0.05 mas along the jet trajectory. The averaged N of 43 epochs is approximately 25. The degree of polarization, _Pi, and the EVPA, χ_i, of each area are calculated from the corresponding Stokes parameters. The uncertainties δI, δQ, and δU are derived as the mean values of the noise in eight off-source regions in each I, Q, and U image. The uncertainties of _Pi and χ_i are calculated via the standard propagation of errors (e.g., Kawabata et al. 1999). The results are corrected for the Rice bias, as described by Wardle & Kronberg (1974), with data for which ${P}_{{\text{}}i}/\delta {P}_{{\text{}}i}\lt 0.5$ were excluded from consideration.

Optically thin synchrotron radiation has only a weak wavelength dependence of polarization, even as the spectral slope changes. The optically emitting region can, therefore, potentially be identified in VLBA images by comparing optical polarization with radio polarization along the jet, provided that the optical depth and Faraday effects are weak, as in OJ 287. In order to do this, we determine the jet trajectory in each VLBA image and calculate Stokes parameters (I, Q, and U) to determine the polarization vector at each step along the trajectory.

We perform the following procedures to determine the jet trajectory. (1) A line is drawn that roughly follows the jet axis on the VLBA image. (2) Line segments extending to ±0.8 mas from the axis are placed perpendicular to the local jet direction. The dashed and solid lines in panel (a) of Figure 1 illustrate this procedure. (3) The maximum-intensity position is located on the solid line shown in panel (a) of Figure 1, which displays the intensity profile along the solid line. (4) The maximum-intensity positions are determined every 0.01 or 0.02 mas, depending on the pixel size of the image. (5) A polynomial function corresponding to the jet trajectory is fit to these maximum-intensity positions, as illustrated in panel (b) of Figure 1. We define the upstream boundary of the "core" of the jet as the position of the maximum gradient in the intensity profile along this trajectory.

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The variation timescale of this object at optical wavelengths, δt, is ∼0.8 day, as determined by the Kepler spacecraft (Goyal et al. 2017). Setting this to the light-crossing time allows us to estimate the size of the high-energy emitting zone as $\delta {\rm{t}}{cD}/(1+z)\sim 0.0046$ pc, where c is the speed of light, and D ∼ 9 is the Doppler factor (Jorstad et al. 2017). The spatial distance corresponding to the angular resolution of the VLBA image of 0.1 mas is ∼1.4 pc (=θ_VLBA/sinΘ, where the angle between the jet axis and our line of sight, Θ, is assumed to be 3°). The spatial distance is much larger than the size of the emitting zone estimated from the timescale of optical variations. Several optical emitting zones could, therefore, be contained within the spatial resolution of the VLBA.

We calculate the average I, P, and χ values within each circular region of a radius of 0.05 mas, which is a half of the spatial resolution along the jet trajectory. Panels (d)–(f) of Figure 1 show an example of the distributions of the calculated intensity and polarization parameters. In this example, χ at 7 mm agrees well with that at optical wavelengths (solid line). The image and the double-peaked polarization profile in Figure 1 reveal the presence of a component, "S," northwest of the core, as also found by Agudo et al. (2011) and Hodgson et al. (2017).

If the optical and radio emissions are co-spatial, then the EVPA of the radio emission should be similar to the optical EVPA. However, there is also the possibility of a chance coincidence between the varying radio EVPA in a more extended radio-emitting region and the observed optical EVPA. To assess the extent to which such spurious coincidences affect our results, we evaluate the systematic uncertainty of a chance coincidence between a random radio EVPA and the optical value. We generate 1000 uniform random numbers representing the radio EVPA ranging from 0° to 180°. These numbers are subtracted from 1000 other random numbers selected from a normal distribution that have the same mean as the observed optical EVPAs and a standard deviation equal to its uncertainty. The distribution of these differences should be related to the probability of a chance coincidence between the optical and random radio EVPAs. We also estimate the distribution of differences between the random numbers selected from normal distributions that have the same means as the observed optical and radio EVPAs. We define EVPA-coinciding positions as those where the differences between the radio and optical EVPAs are less than 10°, which is the standard deviation of random fluctuations in the optical EVPA over 100–200 days intervals when there are no systematic EVPA variations. If the number of differences within 10° between the observed optical and radio EVPAs is at least three times larger than those between simulated EVPAs selected from the normal (optical) and uniform (radio) distributions, corresponding to 99.7 percent confidence interval, then we classify the coincidence between the observed optical and radio EVPAs as significant. We evaluate the coincidence between the radio EVPAs at each position along the jet trajectory and optical EVPAs in this manner.

Positions of low (<100) polarized intensity signal-to-noise ratios are excluded from the analysis. Applying this procedure to all 43 epochs, we find at least 1 EVPA-coinciding position along the jet trajectory in 36 of the epochs.

In the Appendix, we show all of the estimated profiles of the intensity, the degree of polarization, and the EVPA along the jet trajectory. We determine approximate values of these quantities for the core and stationary feature, S, from the profiles. The profiles varied in time, as shown in Figures 6–9. In addition, the degree of polarization at most epochs varied with its distance from the core, sometimes exceeding 10%. At some epochs, the EVPAs were constant, and at other epochs they varied, with their distance from the core.

Figure 2 shows a time series of the observed optical flux and polarization, as well as radio fluxes and polarization at both the core (at 0.05 mas) and S (at 0.25 mas), as estimated from individual profiles of the intensity, the degree of polarization, and the EVPA.

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Figure 3 plots the optical degree of polarization versus 7 mm degree of polarization at the position of the peak total intensity in the VLBA image, measured at the same epoch. The degree of optical polarization is mildly correlated with that at 7 mm, although the optical values tend to be higher. At only 18 epochs (out of 43) is the 7 mm EVPA at the location of the total intensity peak within ±10° of the optical value. There are, however, 18 other epochs at which the optical and 7 mm EVPAs coincide within 10° at positions other than the total intensity peak (see below); these are denoted by filled circles outside the dotted lines in the right panel of Figure 3. This implies that the primary site of optical emission can lie outside the brightest feature (usually the core) in the 7 mm image.

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Most of the epochs have multiple positions along the jet at which the radio and optical EVPAs have similar orientations. One can consider two possibilities: (1) the optical emission originates from multiple locations along the jet, or (2) the magnetic field is systematically ordered along the jet. On the other hand, at seven epochs, there are no coinciding positions. At some of these epochs the object was in an active state and at others it was in a quiescent phase. If the optically emitting region is optically thick at the radio frequency, then the optical emission should not have a relationship with the (more extended) radio jet. The other possibility is that the radio polarization coming from the optically emitting region is diluted, with its mean changed by the superposition of various polarization vectors associated with other regions.

The top panel of Figure 4 shows the 7 mm intensity profile along the jet trajectory, averaged over all 43 epochs. We model the profile with two point components to estimate the separate intensity profiles of the core and S. The model with a minimum χ² value corresponds to average flux densities of the core and S of 1.71 and 2.14 Jy, respectively, with a separation of 0.20 mas along PA −28°. The solid curve in Figure 4 shows the fit of the model to the data (solid circles). The small deviations suggest that both the core and S are slightly resolved rather than point-like sources.

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As seen in Figure 4, the core dominates the intensity up to a distance of 0.13 mas, while S dominates from 0.13 to 0.5 mas. The bottom panel of the figure demonstrates that the position along the jet where the optical and 7 mm EVPAs most closely correspond is sometimes associated with the core and other times with S. Some of the coinciding positions are in regions outside of the core and S. If there is no relationship between the optical and radio EVPAs, then the possibility of a chance coincidence can be estimated from the fraction of EVPA differences that exceed the threshold of 10°. This criterion indicates that the optical and radio EVPAs at 6 out of 43 epochs can be expected to be similar by chance coincidence. Fewer than 5 coincidences are expected to occur in the regions outside the core and S, but this is too many to determine whether any optical emission comes from those regions. Therefore, the optical emission originates from either the core or stationary component S (or both) at the majority of the epochs at which the optical and radio EVPAs are aligned.

Figure 5 displays the distributions of differences between the PA of the jet trajectory and the EVPAs in cases where the optical and 7 mm EVPAs most closely correspond to each other (a) in feature S and (b) in the core. Most of the EVPA–PA differences within S are <30° (with a skewness score of 2.15), while those within the core region are more broadly distributed (with a skewness score of 1.34), although most are <30°.

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D'Arcangelo et al. (2009) measured EVPA values in the 7 mm core in 2006 that were perpendicular to the previously observed parsec-scale jet direction. This caused those authors to propose a spine-plus-sheath structure with different magnetic field geometries. However, as cited above, the jet changed direction abruptly by ∼90° shortly before those observations. As a consequence, the core EVPA in 2006 was, in fact, nearly parallel to the new jet direction, which is a condition that continued with the observations reported here.