Probing the axial symmetry of gamma-ray burst jets using afterglow polarimetry

TL;DR

This paper investigates how departures from axial symmetry in GRB jets imprint on afterglow polarisation near jet breaks. Using an elliptical-head toy model, the authors show that axisymmetric (top-hat) jets typically produce two peaks in the polarisation degree with a PA rotation of $\Delta\phi=\pi/2$, while non-axisymmetric heads reduce or remove the dip between peaks and yield variable PA evolution; structured jets further modify the results, often producing a single peak with smoother PA changes. By exploring distributions of viewing angles and jet eccentricities, the work provides quantitative expectations for $|\Delta\phi-\pi/2|$ and $R_{pd}$ and demonstrates how observations of GRBs 020813, 091018, 121024A, and 210610B can constrain jet eccentricity and luminosity structure. The findings have practical significance for interpreting afterglow polarimetry and for inferring jet-launching physics and angular energy distributions in GRBs, with implications for multi-wavelength polarimetric campaigns and future X-ray polarimetry.

Abstract

Polarisation measurements of gamma-ray burst afterglows provide a powerful tool for probing the structure of relativistic jets. In this study, we revisit polarisation signals observed in gamma-ray burst afterglows, focusing on the effects of non-axisymmetric jet structures. To characterize these non-axisymmetric jets, we adopt a simple elliptical jet head model and investigate how deviations from axisymmetry influence the temporal evolution of polarisation properties, particularly around the jet break. Our results show that the polarisation degree curve typically exhibits two peaks for top-hat jets or a single peak for structured jets, even in the presence of an elliptical jet head. In non-axisymmetric jets, a complete drop in polarisation between peaks is generally absent, and the position angle rotation between the peaks can deviate significantly from 90 degrees. In single-peak cases, the polarisation position angle evolves gradually, contrasting with the constant position angle expected in axisymmetric jets. We also explore the implications of these findings for recent GRB events, including GRB 121024A, GRB 091018, GRB 020813, and GRB 210610B.

Figures (11)

• Figure 1: The shaded area represents the physical extent of the jet head, with the line of sight intersecting it at Point A. The location of Point A is specified by two angles: viewing angle $\theta_{view}$, measured from the jet axis (or equivalently expressed as $\xi = (\theta_{view}/\theta_j)$, and the azimuthal angle $\chi$, measured from the semi-major axis of the jet head. The ring surrounding Point A marks the visible region. Red double-headed arrows indicate the polarisation directions of fluid element emission. The point symmetric to Point A with respect to the jet axis (the origin) is Point B, while the point symmetric to Point A with respect to the x-axis is labelled Point C.
• Figure 2: Top panel: Polarisation as a function of time, with both quantities normalised to the the local polarisation degree $P_0$ and the characteristic jet-break time $t_{ j }$
• Figure 3: Distribution functions of deviations from $\pi/2$ in the PPA rotation between polarisation peaks for uniformly sampled jets with eccentricities of $e=0.3$ (blue lines), $e=0.45$ (orange lines), and $e=0.6$ (green lines). Solid lines represent probability density distributions, while dashed lines show their corresponding cumulative distributions.
• Figure 4: The PPA deviations from $\pi/2$ are shown in 16 bins of equal angular width $\chi$ for jets with eccentricities $e=0.3$ (blue), $e=0.45$ (orange), $e=0.6$ (green). The dot represent the averaged values, and the bars indicate the 1 $\sigma$ spreads for each bin.
• Figure 5: The deviation of the PPA rotation from $\pi/2$ and the peak-to-trough ratio $R_{pd}$ are shown for the same random sample ($e=0.45$) that generates the orange lines in Figure \ref{['fig:CDF_PDF_PArot']}. The colour map indicates the offset $\xi$ value of each sample.