Electron-positron Pair Production in Global GRMHD Simulations of Black Hole Accretion Flows

Abstract

We present global, three-dimensional general relativistic magnetohydrodynamic simulations of accreting black holes that incorporate pair physics. Pairs are modeled as a passive scalar that maintains a constant temperature. For high accretion rate models, we observe a maximum pair fraction of $\sim \mathcal{O}(0.01)$, consistent with those inferred from some X-ray binaries, and identify a `pair void' extending to a few gravitational radii from the black hole. Pair fractions peak in the midplane just outside the plunging region and within a thin strip at the base of the corona. For moderate to high accretion rate models, pairs are near equilibrium close to the disk midplane, where the scattering optical depth is high and pair equilibrium timescales are short, and could be comparable to the Coulomb collision timescale. This suggests the possibility of a pair-regulated coronal temperature. In contrast, the upper corona and jets, where the scattering optical depth is relatively low and pair equilibrium timescales are long, are populated with pairs that may exceed their equilibrium value by orders of magnitude. These pairs are transported by advection from the disk, which dominates over local pair processes. This result highlights advection as a significant source of pair injection, which may be relevant for certain X-ray binaries exhibiting $γ$-ray signatures. The pair density along the magnetically dominated poles exceeds the Goldreich-Julian density in some models.

Figures (12)

• Figure 1: (a) The time evolution (in $GM/c^{3}$) of $z$ obtained by solving Equation \ref{['eqn:onezone']}. Here, $T_{e} = 10^{9}$ K and $H = GM_{\rm BH}/c^{2}$ with $M_{\rm BH} = 10^{8}$$M_{\odot}$. We show cases of different $\tau_{p} = H\sigma_{t}n_{p}$. Blue (orange) lines indicate initial condition of $z$ being below (above) the equilibrium value $z_{\rm eq}$. We also mark horizontal dashed lines of $2z_{\rm eq}$ (black) and $z_{\rm eq}/2$ (red). The time-coordinate of the intersection between the orange and black (blue and red) is defined as the equilibrium timescale with initial $z$ being above (below) $z_{\rm eq}$; (b) Pair equilibrium timescale against proton scattering optical depth, determined via solving Equation \ref{['eqn:onezone']} and using the strategy outlined in Figure (a). Here, $\tau_{p}$ ranges from $10^{-5}$ to the point where pair equilibrium is unattainable (i.e., we find $z$ diverges in solving Equation \ref{['eqn:onezone']}), and $T_{e} = 10^{9}$, $10^{9.5}$, $10^{10}$, and $10^{10.5}$ K. Note that the dashed (solid) line displays the timescale for cases where the initial $z$ is above (below) the equilibrium value.
• Figure 2: (a) Spatial distribution of the time- and $\phi$-averaged pair fraction, $z$ (right), and the ratio $z/z_{\rm eq}$ (left), for model hr01, characterized by $\eta = 0.05$ and $T_{e} = 10^{9}$$\mathrm{K}$. The equilibrium value $z_{\rm eq}$ is computed using the one-zone equilibrium model, based on the local $\tau_{p}$ derived from time- and $\phi$-averaged fluid variables. Time averaging is performed over the final $2000$$GM/c^{3}$ of the pair injection phase, with a cadence of $10$$GM/c^{3}$. Contour lines indicate $z/z_{\rm eq} = 1$, $\tau_{p} = 1$, and $\tau_{p} = 0.1$. The hatched region marks zones where $\tau_{p} \geq \tau_{\rm crit}$, and no pair equilibrium solution is available under the constant-temperature assumption. (b) Same as (a), but for model hr02_hot, with $\eta = 0.005$ and $T_{e} = 10^{10}$$\mathrm{K}$. Contour lines for $\tau_{p} = 1$ are omitted.
• Figure 3: Positron number density (log$_{10}$ scale) at the onset of the pair injection phase for models (a) hr01_high ($\eta = 0.4$ and $T_{e} = 10^{9}$$\mathrm{K}$) and (b) hr02_hot $\eta = 0.005$ and $T_{e} = 10^{10}$$\mathrm{K}$). Velocity field lines are overlaid in both plots, and all panels within each subplot share a consistent color scale. In (a), pairs rapidly reach their peak and settle into equilibrium within a thin strip at the coronal base, sustained by a short equilibrium timescale. The bulk fluid flow subsequently advects these pairs into the jet and upper corona, where the pair equilibrium timescale exceeds the dynamical timescale. In (b), the midplane pair density rises more gradually due to a longer equilibrium timescale relative to (a), though advection similarly transports pairs into the jet and upper corona.
• Figure 4: Ratios of the pair equilibrium timescale (computed for an initial $z$ that is above $z_{\rm eq}$) to the inflow timescale, $t^{r}$, for the high accretion rate model hr01_high. Hatched region has no pair equilibrium solution.
• Figure 5: The radial profiles of $z$ (top left), $z/z_{\rm eq}$ (top right), $\tau_{p}$ (bottom left), and the positron mass flux $-\sqrt{-g}\rho_{+}u^{r}$ (bottom right) shown at different altitudes $\theta$ for the high accretion rate model hr01_high. In the bottom left panel, we shade the region where $\tau_{p} \geq \tau_{\rm crit}$, for which no pair equilibrium solution exists. Note also that the positron mass flux is calculated in code units. Vertical dotted grey lines represent the position of the ISCO.