Observations of optical polarization can be a powerful tool to study temporal variations observed in blazars. The position angle of polarization (PA) is perpendicular to the direction of the magnetic field of the emitting region in the optically-thin regime. Hence, we can obtain a clue to the magnetic field structure in the jet from the observed features of PA.
For example, the observed PAs of BL Lac are concentrated in a narrow range centered at ∼
, which is close to the direction of the radio jet [1
]. This suggests that the magnetic field is perpendicular to the jet direction. Systematic changes in PA—in other words, polarization swings/rotations—also receive attention, because they may be a diagnostic feature of more complicated structures, such as bending structures of the jet and helical structures of the magnetic field (e.g., [2
It is easy for us to find noteworthy patterns in the time-series data of the degree of polarization (PD) and PA. The situation, however, changes if multiple polarization components are possibly present. In such cases, we need to carefully see the trajectory of the object in the Stokes
plane. In general, our goal is to extract universal patterns in the trajectory which correlate with the flux and color variations. This can be achieved if we have only tens of data points for a few objects. However, it is hard to find such patterns when the data size is large. The amount of polarimetric data of blazars has been increasing recently [5
]. A possible way to handle such large amount of data is component separation to see the features of each component (e.g., [8
]). Such an approach is generally based on some assumptions for the observed variation. Proper descriptions of the data are first needed to construct proper assumptions for models. Hence, we need a tool to properly visualize the data in order to obtain more knowledge from more data.
In this article, we propose a visualization tool, called “TimeTubes”, for blazar polarization [9
]. We can see the temporal variations of the flux, color, and Stokes
in one view using this tool, which helps us to find interesting features in the polarization data. In the next section, we describe TimeTubes. In Section 3
, we introduce applications to the real data observed with the Kanata telescope. In the last section, we discuss the astrophysical implications of the results shown in Section 3
, and future plans for our project.
We consider the time-series data of the total flux, color, and fractional Stokes parameters
. In this article, we use not
, but the fractional values, because the variations in polarization are emphasized. Of course, TimeTubes can also be used for
. Figure 1
shows the light curve, color–magnitude diagram, and polarization data plots on the Stokes
plane for 3C 66A observed with the Kanata telescope [5
]. The red points in each panel indicate the data taken on the same night. Such views are ineffective when searching for noteworthy patterns of the trajectory in the
plane which correlate with the flux and color.
A visualization tool, “TimeTubes” has been developed for the polarization variations in blazars [9
]. In TimeTubes, the trajectory is visualized in 3D space with the time axis as the third axis, in addition to the 2D
plane. We express the trajectory as “tubes” in this 3D space. Figure 2
shows an example of the TimeTubes view for the data of 3C 66A, around MJD 52000 when a rapid flare was observed. The center of the tube corresponds to the observed
. The widths of the tube represent the measurement errors. Figure 3
shows the color map for the tube. Using this 2D color map, the observed color and flux are visualized as the tube’s color. As a result, we can see six variables (
, their errors, flux, and color) in one TimeTubes view. In Figure 2
, we can see a brightening and bluing period; that is, a flare with a variation in polarization.
TimeTubes is still under development. Some useful functions which are currently available are described as follows: (i) The temporal progress can be controlled with the mouse wheel, while we can jump to any given times using the “Time Search” function; (ii) The scales of the color map can be adjusted for any given ranges; (iii) The data with large errors can be located by different colors using the “Outlier filtering” function; (iv) The appearance of the tube can be adjusted from solid-like to blurring structures by using the “Opacity transfer function editor”; (v) The data can also be shown in the classical scatter plots. More details are available in [9
4. Discussion and Summary
In the last section, we introduced the TimeTubes view of two blazars and compared them with more standard plots, like light curves, time-series of PA, and the Stokes planes. Both features of PKS 1749+096 and 3C 454.3 were first noticed in the TimeTubes views, and then confirmed in more standard plots. These results demonstrate that TimeTubes helps us to find interesting patterns in the polarization data of blazars. In this section, we first discuss astrophysical implications of the two examples, and then comment on the future plans of TimeTubes.
PKS 1749+096 is a BL Lac object classified as LBL [10
]. As mentioned in the last section, the optical PA is distributed over a wide range, while the peaks of flares tend to have a common direction of PA
. The polarization rotation also follows this trend. This favored PA is close to the position angle of the radio jet in its downstream region (
]. A scenario with the spiral path of the shocked region through a toroidal magnetic field is proposed to explain the polarization rotations [3
]. Those observations suggest that a geometrical effect makes the flare peaks. We propose that the flares reached their peak at the time when the beaming factor becomes maximum, while the flares themselves are probably due to the moving shocks in the spiral path.
3C 454.3 is a famous flat spectrum radio quasar (FSRQ). In the last section, we reported a polarization rotation episode of the consecutive flares. A similar event was reported in the same object in 2007, in which the average polarization vectors of at least five flares exhibited a rotation-like feature within 80 d in that event [12
]. The situation is also similar to the long-term polarization rotation of PKS 1510-089 observed in 2009, when the object was active, and a number of short flares were observed during the rotation episode [4
]. The rotation that we detected is centered not on the origin of
, but on
. The polarization component of
is probably a component of the active state. It is hard to find such an off-axis rotation in the standard plots, such as a time-series plot of PA, making it a good example to demonstrate the advantage of TimeTubes.
More detailed reports about the above two observations will be published in forthcoming papers.
In this article, we demonstrated how we obtained new insights through a visualization tool for the blazar polarization, TimeTubes. This approach to handle the data is crucial for the study of blazar variations with polarization when the data size is large. Even in the case of small data sets, to use TimeTubes is an effective way to find interesting features in the data. TimeTubes is still an ongoing project. We have a plan to add more functions for better usage. In particular, a dynamic connection between the TimeTubes view and scatter plots will be quite useful for our analysis. One can download the current version of TimeTubes at our project page: http://fj.ics.keio.ac.jp/index.php/projects/spm/
. The functions of TimeTubes are described in [9