High energy power-law tail in X-ray binaries spectrum and bulk Comptonization due to a conical outflow from a disk

TL;DR

This work tests bulk Comptonization in outflows as the origin of the high-energy power-law tails seen in X-ray binaries, focusing on conical versus collimated geometries. Using a Monte Carlo treatment of a torus-shaped corona with seed photons from the disk, the study shows that HEP-tails with $\Gamma>2$ and $E_c>200$ keV arise mainly for conical outflows with $\theta_b\gtrsim30^\circ$ and relativistic bulk speeds, while collimated flows fail to produce tails except under extreme conditions at high $kT_e$. When applied to GRS 1915+105, the model implies inner-disk launching at $R\sim25R_g$ and wind powers exceeding the tail luminosity, consistent with concurrent radio emission and an electron population shared between HEP-tail and radio output. The results highlight geometric and kinematic degeneracies among $kT_e$, $u_b$, $\tau$, and $\theta_b$, and suggest polarization studies as a way to lift this degeneracy and constrain the emission region.

Abstract

X-ray binaries (XRBs) often exhibit a high energy power-law tail (HEP-tail) and these tails can be generated by the bulk Comptonization (BMC) process with a free-fall bulk region onto the compact object. The radio emission (which is generated by a synchrotron-emitting outflowing electrons) is observed in all spectral state of XRBs. Interestingly, the variations of HEP-tail flux among different spectral states is similar to the variation of radio flux. We motivate to study the HEP-tail in BMC process with an outflowing medium. For this we consider a collimated and conical (of opening angle $θ_b$ with axis perpendicular to the accretion disk) outflow geometry. We simulate the BMC spectrum by using a Monte Carlo scheme. We find that the emergent spectrum has power-law tail (of photon index $Γ$ $>$ 2 and with high energy cut-off $E_{c}$ $>$ 200 keV) only for $θ_b$ greater than $\sim$30 degrees in conical outflow, while for a collimated or a conical outflow ($θ_b$ $<$ 30 degrees) these HEP-tail can be only generated when it is also found in thermal Comptonized spectra (i.e., at sufficiently high Comptonizing medium temperature). These results are approximately consistent with analytically derived expressions. We describe the observed GRS 1915+105 spectrum for two classes $χ$ and $γ$ in conical outflow, for this the outflow speed is highly relativistic and the kinetic power of wind suggest that the HEP-tail can be generated at inner region of the accretion disk, like inner disk radio emission.

Figures (5)

• Figure 1: Meridional cut of a rectangular torus shaped Comptonizing medium (or corona) of width W and height L surrounding the BH to study the outflow motion. In the left side, a schematic diagram for the collimated flow of angle $\theta_b$ is presented. In the right side we show a schematic diagram for the conical flow of opening angle $\theta_b$. Here, the conic shaded region represents a possible conical outflow direction at the scattering point P, and the PQ arrow indicates an arbitrary outflow direction ($\theta_b$, $\phi_b$) in local coordinates.
• Figure 2: The simulated emerged spectra for different outflows geometry for a low medium temperature. The left is for collimated outflow, while the middle and right panels are for the case I and case II of conical outflow, respectively (see text). In the left panel the curves 1 and 2 are for $\theta_b$ = 0 (outflow) and 180 (inflow) degrees, respectively, and for the curves 3 and 4, the $\theta_b$ is 90 degrees. The curve 2s is for the single scattering at $\theta_b$ = 180 degrees. In the middle and right panels the curves 1,2,3,4,5 and 6 are for $\theta_b$ = 20, 160, 30, 60, 110 and 90 degrees, respectively. In the middle panel the curve 7 (dashed) is for 95 degrees. The spectral parameters for all curves are $kT_e$=3.0 keV, $kT_b$=0.5 keV, $\tau$ = 3 and $u_b$ = 0.45$c$ except for the curve 4 of left panel where $\tau$ = 15 and $u_b$ = 0.65$c$.
• Figure 3: The emergent BMC spectra (left panel) and the distribution of scattering angle (right panel). The left panel is for an emergent spectra for a high medium temperature ($kT_e$ = 30 keV). The curve 3 is for a spectrum of TC dominated case ($(u_b/c)^2$$\ll$$3kT_e/(m_ec^2)$), while others are for bulk dominated case, $u_b$ = 0.75c. The curve 1 is for collimated outflow of $\theta_b$ = 15 degrees, and the curves 2 and 4 are for conical outflow of $\theta_b$ = 15 and 45 degrees, respectively. The right panel is for scattering angle distribution. Curves 1, 2, 3 and 4 are for conical outflow of $\theta_b$ = 15, 45, 60 and 90 degrees, respectively and $u_b$ = 0.75c, and the curve 6 is for $\theta_b$ = 15 degrees and $u_b$ = 0.85c. The curve 5 is for TC dominated case. The rest parameters are $kT_b$ = 0.5 keV and $\tau$ = 1.
• Figure 4: Comparison of the $\chi$ (left panel) and $\gamma$ (right panel) classes of GRS 1915+105 with the bulk Comptonization model, here the data points are taken from Zdziarski-etal2001. The two-dotted-dashed, solid, dashed, and dotted curves are for black body (BB), bulk Comptonization (BMC), BB + BMC, and residual (data-(BB+ BMC) components, respectively. Here, $\theta_b$ = 30 degrees, $u_b$ = 0.95c, $kT_e$= 3 keV, $kT_b$ = 1.2 keV and $\tau$ = 2.0 ($\chi$-class) = 2.8 ($\gamma$-class). Dotted-dashed curve is for BMC component when $u_b$ = 0.998c and $kT_e$ = 100keV, here the other components are not shown for clarity.
• Figure 5: Comparison of the BMC and TC spectra for Monte Carlo results verification. The solid curves are for bulk Comptonization ($kT_e$ = 2 keV, $u_b$=0.0766c) and dashed curves are for thermal Comptonization ($kT_e$ = 3 keV, $u_b$=0.0). The curves 1, 2, and 3 are for single scattering, multiple scattering ($\langle N_{sc} \rangle$$\sim$ 46), and Wien peak ($\langle N_{sc} \rangle$$>$ 500), respectively. Here, the dashed curve 3 is $\propto E^2 \exp ( \frac{-E}{kT_e} )$, which also determines, in general, the exponential high energy cut-off ($E_c$) for photons density in non-relativistic TC process.