Astronomy Object of the Month: 2025, August
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Synthetic spectra from particle-in-cell simulations of relativistic jets with initial toroidal magnetic field
Relativistic jets are observed across the entire electromagnetic spectrum in a variety of astrophysical systems, such as active galactic nuclei (AGNs), gamma-ray bursts (GRBs), and some black hole X-ray binaries, being launched from compact objects (black holes or neutron stars) typically surrounded by accretion discs. They are well-collimated outflows of plasma and fields, propagating with velocities close to the speed of light. Relativistic jets are supersonic, producing shocks that lead to a turbulent magnetic field, which can play an important role in acceleration of jet particles. They are also sources of kinetic instabilities driven by currents and shears as well as magnetic reconnection.
Illustration 1: Artistic image of the relativistic jets from a black hole. Credit NASA.
Illustration 2: Jet from Virgo A (M87 or NGC 4486). The combined image in visual and X-ray bands. Credit: NASA & The Hubble Heritage Team (STScI/AURA).
Relativistic jets are typically studied with 3D particle-in-cell (PIC) simulations, as well as magnetohydrodynamic modeling. Although MHD simulations can complement PIC simulations, they cannot explore particle interactions with self-generated electromagnetic fields, nor include kinetic instabilities. PIC simulations self-consistently solve plasma dynamics, but they are inherently limited by the size and resolution of the plasma system. The PIC simulations performed in the framework of the current study are complementary to the MHD simulations. Besides, they allow to calculate the particle energy spectra "in situ", directly during the simulation.
Figure 3 represents the distribution of magnetic field in axial section of the modeled jet, with the use of the sign-preserving logarithmic color scaling for By. Different regimes of turbulence can be specified based on the structures of the observed wave modes: region (a) represents the nonlinear stage, region (b) represents the turbulent plasma stage, and region (c) is behind the jet head containing wave vectors that are perpendicular to the jet direction. To the left of the region (a), the linear growth of instabilities takes place. The striping structures in region (c) are formed by a double layer plasma, and they are associated with an ambipolar electrostatic field.
Fast Fourier Transform (FFT) has been used convert the amplitude of the By wave components of the magnetic field shown in Figure 3 from the spatial domain to the wave vector domain, in order to estimate the characteristic length-scale of the turbulence in the selected regions. These regions are marked with white rectangles: (a) for x ∈ [400 − 600] ∆, (b) for x ∈ [600 − 750] ∆ and (c) for x ∈ [780 − 820] ∆. The selection has been made in a way to avoid the mixture of different waves in the same region, to make the FFT plots cleaner and easier for interpretation. Figure 4 shows the power spectra of the waves excited by kinetic plasma instabilities, computed for the regions (a), (b) and (c). These spectra are plotted in logarithmic color scale, in the (kx, kz) wave vector space, where the wave vector is defined as |⃗k| ≡ 2π/λ.
Besides, the impact of the initial helical magnetic field on the emission of radiation from the jet electrons has been analyzed. Figure 5 represents the spectra of the radiated power P(ω) = d2W/dΩdω as a function of the emitted frequencies, ω/ωpe, for a moderate, B0 = 0.5, initial toroidal magnetic field (red lines) and for a weaker field of B0 = 0.1 (orange lines), for two viewing angles: head-on emission of jet electrons (solid lines) and for 5 degree-off emission (dashed lines).
Illustration 3: Distribution of the magnetic field in the axial section (x-z plane of the simulation box) of e- – i+ jet with a bulk Lorentz factor of γ = 15, given for the case with B0 = 0.5. The out-of-plain By component is shown with with use of the sign-preserving logarithmic color scaling. The regions (a), (b) and (c) marked with white rectangles were used for FFT plots presented in Fig.4. Credit: The Authors.
Illustration 4: FFT-images of the magnetic field distribution (by component) shown in Fig. 3. The panels represent three regions: (a) x ∈ [400 − 600] ∆, (b) x ∈ [600 − 750] ∆ and (c) x ∈ [780 − 820] ∆, which are also marked with white rectangles in Fig. 3. The color scale is logarithmic and normalized to the maximum wave power, so that numbers at the color bar mean log(Pw/Pw max). Corresponding values of Pw max are given in right upper corners. P∗w max = 0.007 in panel (a) corresponds to the local maximum at ∆ ≈ (0.095, 0.1). These FFT-images are used for estimating the characteristic length-scale of the turbulence in the jet plasma. Credit: The Authors.
Illustration 5: Synthetic spectra for e± jet with a bulk Lorentz factor of Γ = 100. The continuous line corresponds to the spectra for a head-on emission of jet electrons, whereas the dashed lines represent for 5◦-off emission of radiation. The red lines show the cases with a stronger amplitude of the initial toroidal magnetic field, B0 = 0.5, whereas the orange lines represent the spectra for B0 = 0.1. The slopes of the power-law segments at lower (∼0.94) and higher (∼−2.2) frequency are indicated. Credit: The Authors.
To conclude, using self-consistent, 3D PIC calculations, we have obtained the first synthetic spectra of jitter-like radiation emitted by electrons in relativistic jets containing an initial toroidal magnetic field. The jitter radiation covers the regime where the magnetic field is inhomogeneous on scales smaller than the Larmor radius and the transverse deflections of the electrons in these fields are much smaller than the relativistic beaming angle.
Original publication: Ioana Duţan, Kenichi Nishikawa, Athina Meli, Oleh Kobzar, Christoph Köhn, Yosuke Mizuno, Nicholas MacDonald, José L. Gómez, Kouichi Hirotani, Synthetic spectra from particle-in-cell simulations of relativistic jets containing an initial toroidal magnetic field, MNRAS, 540: 1 (2025).
The research described is part of the research topics conducted at the Department of High Energy Astrophysics of Astronomical Observatory of the Jagiellonian University in Kraków. This work was supported by the Polish NSC (grant 2016/22/E/ST9/00061) and the Poland's high-performance Infrastructure PLGrid (ACK Cyfronet AGH) within computational grant PLG/2024/017211.
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Oleh Kobzar Astronomical Observatory Jagiellonian University Oleh.Kobzar [at] uj.edu.pl |
