Relativistic astrospheres of gamma-ray binaries: modeling of non-thermal processes

Abstract

A long standing problem in high energy astrophysics is the nature of galactic accelerators of particles with energies above PeV. Such objects are sources of galactic cosmic rays and can produce PeV-regime photons observed by ground-based observatories. Among very likely accelerators are astrospheres of pulsars in gamma-ray binaries. These binaries have long been observed as bright sources of TeV gamma-rays. Recently, 2D relativistic magnetohydrodynamic (rMHD) simulations have shown that the astrospheres can accelerate particles to energies well above PeV, provided that they harbor a Gauss-range magnetic field. Such a strong field is necessary in the region of two colliding winds: the relativistic outflow of the pulsar or accreting black hole and the wind of its stellar companion, a massive early-type star. Here, the wind collision region is explored as the site of PeV protons acceleration. The local structure of colliding flows is illustrated using rMHD simulations of a powerful pulsar wind in 2D and 3D models. The relativistic outflow of a pulsar or black hole, evolving inside the strongly magnetized stellar wind, have an elongated shape and surrounded by a kind of magnetic cocoon providing favorable conditions for acceleration of ultra high energy ions. The simulated spectra of particles, accelerated by intermittent relativistic turbulence in these systems, have piece-wise power-law shape and extend well above PeV energies for powerful outflows. The model indicated that gamma-ray binaries harboring a powerful relativistic outflow, produced either by a pulsar or accreting black hole, can be bright sources of synchrotron MeV-regime photons and multi-PeV regime gamma-rays, as recently detected from galactic microquasars like Cyg X-3. The Gauss-range magnetic field of a massive star wind strongly influences the non-thermal emission of gamma-ray binaries with relativistic companions.

Figures (7)

• Figure 1: Wind collision region in 2D and 3D runs. Colors on the maps indicate the local magnetic field $B$ [G]. Left column: 2D model (meridional cut). Middle and right columns: 3D model (meridional and equatorial cuts). The rows illustrate the effect of increasing the strength of the stellar wind field $B_{sw}$. From top to bottom: $B_{sw} =$ 0.5, 1, 2 and 3 Gauss. $\vec{B}_{sw}$ is shown by white arrows and makes $75^{\circ}$ with the pulsar's rotation axis (pointing upward in the 1st and 2nd columns and out-of-plane in the 3rd one). The color palette (the same in all panels) highlights the flow structures, not the maximum and minimum values of $B$. 2D and 3D setups corresponds to models A1--A4 and X1--X4 in Table \ref{['Table_2D_3D']}; we show their snapshots taken 15 and 2 hours after initiation, respectively.
• Figure 2: Time evolution of the pulsar wind nebula in gamma-ray binaries (3D case). The 3D nebula is shown in section by the plane defined by the pulsar's rotation axis and the magnetic field vector of the stellar wind. The rows from top to bottom show maps of the magnetic field (in Gauss), velocity (in $c$ units), and pressure (in cgs units). The maps describe the MHD flows (as they appear in the X3 model from Table \ref{['Table_2D_3D']} in which $B_{sw}=2\:$G). In each row, three consecutive maps are obtained at 0.8, 2, and 3 (model) hours after the onset of nebula inflation. The brightness scale of the color bar (universal for all maps in a particular row) is adjusted to highlight the flow patterns and does not reflect the maximum and minimum values of $B$, $v$ and $p$.
• Figure 3: Left: Particle acceleration in the wind collision region of gamma-ray binaries (results of Monte-Carlo simulations). Several spectral energy distributions are shown in color: in red (1) -- for the particles just injected in the system, in orange (2) -- for those that were accelerated in the colliding flows alone, and in green, blue and magenta (3, 4, 5) -- for those that were accelerated in the colliding flows with the relativistic clump. The last three spectra coinciding with the orange curve below $1 \:\hbox{PeV} = 10^{6} \:\hbox{GeV}$ differ in the clump’s Lorentz factor, which is $\varGamma = 3$, 4.5 and 6, respectively. Right: simulated synchrotron spectra of the Vela-like pulsar wind nebula. Different colors refer to the synchrotron emissivity integrated over different lines of sight. Namely, over lines of sight coming close: to the termination shock (TS, in red), to the bow shock (BS, in blue), and to the contact discontinuity (CD, in green).
• Figure 4: Relativistic clumps in pulsar wind nebulae (enlarged views of the equatorial region). Shown are 2D models A5 and A6 in Table \ref{['Table_2D_3D']}: $\alpha = 45^{\circ}$, $\sigma_0 = 0.3$ (left column) and $\alpha = 80^{\circ}$, $\sigma_0 = 3$ (right column). Contour plots of the Lorentz factor are superimposed onto gray-color maps of the magnetic field $B$ [in G] provided to guide the eye. Each row corresponds to a certain point in time since the start of simulation: $t = 11.1$, $11.8$, $12.5$ and $13.2$ hours, from top to bottom. The gray-color bar is adjusted to highlight the structure of rMHD outflows and does not reflect the maximum and minimum values of $B$. Note that the contour $\varGamma_{pw}=4.5$, that outlines the region of the unshocked pulsar wind, almost coincides with the position of the wind termination shock, due to the abrupt deceleration of the wind. The axes units are AU.
• Figure 5: Relativistic clumps in pulsar wind nebulae (enlarged views of the equatorial region). Results of 2D/3D rMHD simulations of the colliding winds region in gamma-ray binaries. Top row (2D case): Colored pressure maps with superimposed contour plots of Lorentz factors of MHD-structures with $\varGamma>2$. The maps shows the nebula $7.6$ and $9.7\:$ (model) hours after the onset of its inflation. The calculation is based on the model A5 from Table \ref{['Table_2D_3D']} ($\alpha = 45^{\circ}$ and $\sigma_0 = 0.3$). The axes units are AU. Middleand bottom rows (3D case): Correlation of depressions and clumps with a high Lorentz factor. Shown are colored maps of pressure (middle row) and flow velocity (in units of $c$; bottom row). Successive maps in the rows are obtained at time points spaced $\sim 100$ seconds apart, starting at 1.3 (model) hours after the onset of nebula inflation. The calculation is based on the model X6 in Table \ref{['Table_2D_3D']} ($\alpha = 60^{\circ}$, $\sigma_0 = 0.1$). Pressure colorbars are in units of $p_0 = 9\cdot 10^{-6}\:$ dyn$\cdot$cm$^{-2}$. The brightness scales of the colorbars are adjusted to highlight the structure of flows and do not reflect the maximum and minimum values of the quantities.