Statistical search for angular non-stationarities of long gamma-ray burst jets using Swift data

In Budai et al. (2020) we argued that angular non-stationarities of gamma-ray burst (GRB) jets can result in a statistical connection between the angle values deduced from jet break times and the variabilities of prompt light curves. The connection should be an anti-correlation if luminosity densities of jets follow a power-law or a uniform profile, and a correlation if they have a Gaussian profile. In this follow-up paper, we search for the connection by measuring Spearman's rank correlation coefficient in a sample of 19 long GRBs observed by the Swift satellite. Using 16 of the GRBs with well-defined angle measurements, we find $\rho = -0.20_{-0.09}^{+0.09}$ and $p = 0.46_{-0.19}^{+0.23}$. Adding three more GRBs to the sample, each with a pair of equally possible angle values, can strengthen the anti-correlation to $\rho=-0.31_{-0.08}^{+0.07}$ and $p=0.19_{-0.09}^{+0.14}$. We show that these results are incompatible with non-stationary jets having Gaussian profiles, and that $\gtrsim\!100$ GRBs with observed afterglows would be needed to confirm the potential existence of the angle-variability anti-correlation with $3\sigma$ significance. If the connection is real, GRB jet angles would be constrainable from prompt gamma light curves, without the need of afterglow observations.