Diagnosing Interstellar Magnetic Turbulence with TeV Pulsar Halos

Abstract

Interstellar magnetic field is essential in various astrophysical phenomena and processes. Pulsar halos are a recently discovered class of TeV gamma-ray sources formed by escaping electrons/positrons from pulsars. The morphology of the halo is regulated by the diffusion of those escaping particles, and hence carries information of the interstellar magnetic field. We suggest that the morphology of TeV pulsar halos can be used as a novel probe of the properties of interstellar magnetic field around the pulsar, such as the Alfvénic Mach number and the mean direction. We establish a theoretical relation between these quantities and the observational features of the halo's morphology based on the anisotropic diffusion model, and show how X-ray observations of the pulsar halos can further improve the diagnosis of the magnetic field.

Figures (4)

• Figure 1: The 3D sketch of the pulsar halo and the corresponding TeV map on the plane of sky(grey shade). The dashed blue line is the direction of line-of-sight (LoS), while the solid black arrows are right ascension (RA) and declination (DEC). The coherent magnetic field lines are shown by the green arrows. The black ellipsoid denotes the distribution of electrons residing in such magnetic field. $\phi$ is the inclination angle between LoS and mean magnetic field. $\chi$ is the angle between RA and the projection of magnetic field lines on the plane of sky.
• Figure 2: Normalized radial profile in 0.1 - 100 TeV of the longer and shorter axes for three sets of $M_A$ and $\phi$ values, as texted in the plots. We use solid lines for longer axis and dashed lines for shorter axis. We also show the $1/e$ flux radius with dotted lines and $68\%$ containment radius ($R_{68}$) with dash-dotted lines. The spindown luminosity of the test pulsar is assumed to be $10^{35}$ erg/s. The injection spectrum is assumed to be a power-law distribution with a slope $-2$, followed by an exponential cutoff at energy 300 TeV. Note that the predicted profile is insensitive to these parameters. In the calculation, typical interstellar magnetic field strength $B=3\,\mu$G and parallel diffusion coefficient $D_0=10^{28} (E/\rm GeV)^{1/3} \, cm^2 s^{-1}$ are employed for calculation.
• Figure 3: The ratio of longer axis and shorter axis $(a/b)$ for different Alfvénic Mach number and inclination angles. Crosses and squares represent the outcomes of numerical calculations for two different definitions of the axes as marked in the legend, whereas the solid curves correspond to the analytical results formulated in Eq. (\ref{['eq:relation']}). The parameters of the pulsar is the same as Fig. \ref{['fig:profile']}.
• Figure 4: Predicted SED with different Alfvénic Mach number and inclination angles. Red, blue and green colors represent $M_A$ = 0.2, 0.5 and 0.8 respectively. The IC peak flux is normalized at unity. Dashed, dash-dotted and dotted linestyles represent inclination angle $\phi=10^\circ, 30^\circ$ and $60^\circ$ respectively. The solid lines are inverse Compton emission, which remain the same despite varying inclination angles and Alfvénic Mach numbers. The parameters of the pulsar are the same as Fig. \ref{['fig:profile']}.