# A Model of Polarisation Rotations in Blazars from Kink Instabilities in Relativistic Jets

## Abstract

**:**

## 1. Introduction

- What could be the mechanism connecting optical polarisation rotations with high-energy flares in blazars? (Section 2.1)
- Is the distinction between rotator and non-rotator blazars due to different viewing angles? (Section 2.2)
- The presentation of a novel toy model of polarisation rotations from the development of kink instability in a relativistic conical jet. (Section 2.3)
- The importance of intrinsic depolarisation in limiting the amplitude of polarisation rotations.

## 2. Results

#### 2.1. On the Connection between Polarisation Rotations and High-Energy Flares in Blazars

#### 2.2. Whether Relativistic Aberration Can Explain the Occurrence of Rotators and Non-Rotators

#### 2.3. A Model of Polarisation Rotations from Kink Instability

**${\mathsf{\Pi}}_{\mathrm{max}}\sim 70\%$**. The observed radiation may combine contributions arriving at different polarisation angles, leading to time-dependent depolarisation. Such depolarisation may result in the departure of the observed polarisation angle from intrinsic values, and this limits the observed amplitude of polarisation rotation. It turns out that such depolarisation is present already for ${\theta}_{\mathrm{obs}}=0$, due to the finite width of the jet boundary, but it does not yet limit the amplitude of polarisation rotation. However, at larger viewing angles, already at ${\theta}_{\mathrm{obs}}=0.4/{\Gamma}_{\mathrm{j}}$, the amplitude of polarisation rotation is limited to $\Delta {\chi}_{\mathrm{E}}\lesssim \pi $. The amplitude of polarisation rotation is thus sensitive to the viewing angle, but not to the intrinsic orientation of the magnetic field, whether toroidal or poloidal. The duration of the observed polarization rotation depends on the distance scale ${z}_{\mathrm{max}}^{\prime}$ occupied by the helical perturbation within the jet. In the example shown in Figure 2 and Figure 3, if the spatial units are in pc, polarization rotation would last for $\Delta {t}_{\mathrm{obs}}\sim 0.2\phantom{\rule{0.277778em}{0ex}}\mathrm{pc}\sim 240\phantom{\rule{0.277778em}{0ex}}\mathrm{d}$.

## 3. Materials and Methods: Definition of the Kink Model

## 4. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**

**Left panel**: Intrinsic viewing angle ${\theta}_{\mathrm{src}}$ vs. jet Lorentz factor $\Gamma $ for a sample of bright blazars compiled by [17]. Blazars showing rotations of optical polarisation in the RoboPol survey are indicated with red circles, the size of which indicates the number of rotation episodes;

**Right panel**: ${\theta}_{\mathrm{src}}$ vs. observed polarisation rotation amplitude for individual polarisation rotation episodes.

**Figure 2.**Polarisation signal calculated from my model of helical perturbation propagating within a relativistic conical jet for the case of a toroidal magnetic field. The first column shows the emission pattern in co-moving coordinates ${t}^{\prime}$ vs. ${z}^{\prime}$ with colour indicating the observed time ${t}_{\mathrm{obs}}$. The second column shows the emission pattern in apparent image coordinates ${x}_{\mathrm{obs}}$ vs. ${y}_{\mathrm{obs}}$. The third column shows the observed polarization angle ${\chi}_{\mathrm{E}}$ vs. ${t}_{\mathrm{obs}}$. The black line shows the effective observed signal integrated over ${t}_{\mathrm{obs}}$ bins, and the gray area shows the intrinsic polarization angle (PA) ${\chi}_{\mathrm{E}}^{\prime}$ vs. ${t}_{\mathrm{obs}}$. The fourth column shows the effective observed polarisation degree (PD) $\mathsf{\Pi}$. The rows correspond to different values of the viewing angle ${\theta}_{\mathrm{obs}}=(0,0.2,0.4)/{\Gamma}_{\mathrm{j}}$. Key parameter values are ${\Gamma}_{\mathrm{j}}=5$, ${\mathsf{\Theta}}_{\mathrm{j}}=0.1$, ${\beta}_{\mathrm{p}}=0.7$.

**Figure 3.**Same as Figure 2, but for the case of a poloidal magnetic field.

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**MDPI and ACS Style**

Nalewajko, K. A Model of Polarisation Rotations in Blazars from Kink Instabilities in Relativistic Jets. *Galaxies* **2017**, *5*, 64.
https://doi.org/10.3390/galaxies5040064

**AMA Style**

Nalewajko K. A Model of Polarisation Rotations in Blazars from Kink Instabilities in Relativistic Jets. *Galaxies*. 2017; 5(4):64.
https://doi.org/10.3390/galaxies5040064

**Chicago/Turabian Style**

Nalewajko, Krzysztof. 2017. "A Model of Polarisation Rotations in Blazars from Kink Instabilities in Relativistic Jets" *Galaxies* 5, no. 4: 64.
https://doi.org/10.3390/galaxies5040064