An outflow from the X-ray corona as the origin of millimeter emission from radio-quiet AGN

Abstract

Recent observations of radio-quiet active galactic nuclei (RQAGN) have shown the presence of millimeter emission, whose origin remains unknown, from within parsec scales of the central black hole. We argue that the mm emission comes from a spatially extended region that is magnetically connected to the compact X-ray corona, in analogy to the solar wind and corona. We present an analytic model scaled to corona values in which non-equipartition electrons from multiple heights along an extended conical outflow shape the mm emission. In this model, the 100 GHz emission originates from within $\lesssim10^4$ gravitational radii ($r_g$) of the central black hole, though the projected distance from the black hole can be as low as $50r_g$ depending on the line-of-sight. Our model predicts a flat emission spectrum $F_ν\sim{\rm const}$ and a mm-to-X-ray luminosity ratio $L_{\rm mm}/L_X\sim10^{-4}$, consistent with observations. These quantities depend weakly on the underlying electron power-law distribution function and black hole mass. We demonstrate this model's plausibility using a general relativistic magneto-hydrodynamic (GRMHD) simulation of a thin accretion disc as a case study. Our model highlights the need to study continual dissipation along the outflow to connect the X-ray- and mm-emitting regions.

Figures (10)

• Figure 1: Lower bounds on the magnetic field at $10r_g$ for a strongly magnetized corona with size $R_c$. The constraint $B_X$ comes from converting magnetic energy into X-ray luminosity (equation \ref{['eq:LX']}), while $B_{\rm eq}^e$ comes from the requirement that electrons are colder than equipartition magnetic fields because they radiate (equation \ref{['eq:Beq']}). For comparison, recent observational fits to magnetic field are shown in black markers. Here, we abbreviate inoue2018 as ID18 and shablovinskaya2024 as S24. Arrows indicate that these lines yield lower bounds. This figure assumes $L_X=10^{43}~{\rm erg/s}$shablovinskaya2024, $\tau_0=1$, and $T_e=10^9~{\rm K}$.
• Figure 2: Diagram of the outflow set-up. The coordinate $z$ runs along the length of the outflow, while $r$ runs perpendicular to the outflow axis. The X-ray corona, shown in orange, is located somewhere within $10r_g$ of the black hole. The extended mm-emitting region, shown in green, connects to the corona via magnetic field lines (red).
• Figure 3: As a result of the inhomogeneity in the outflow, a flat spectrum develops between the turnover frequency at the outflow base and the turnover frequency at the outflow top. The specific intensity at select heights is shown by the colored lines. The outflow base has a turnover frequency of around $10^{14}$ Hz (purple peak). Above this peak, the total spectrum (dashed line) drops off as $\nu^{-(p-1)/2}=\nu^{-1/2}$. Below this peak lies the flatter, intermediate regime wherein the peaks from each outflow height sum together. Below the turnover frequency of the outflow top (yellow peak, $\approx 10$ GHz), the spectrum demonstrates the familiar $\nu^{5/2}$ dependence. The flux has been normalized to its maximum value. The dotted red vertical line shows $\nu=100$ GHz. Above $\approx300$ GHz, the flat power-law is likely obscured by dust.
• Figure 4: Dependence of the outflow turnover frequency as a function of height in the outflow. The left and right panels show dependence of $\nu_t(z)$in Hz on the black hole mass and electron power-law index, respectively. In both panels, colors show different values of the electron magnetization at the outflow base $\sigma_{e0}$. See equation \ref{['eq:nut_sigmaM_scaling']} and \ref{['eq:nut_z_scaling']}. Horizontal dotted red lines show where the outflow emits $100~{\rm GHz}$ radiation.
• Figure 5: Vertical slice of the radiative GRMHD simulation of a thin disc showing the poloidal 3-velocity (equation \ref{['eq:vpol']}). The "outflow" refers to the region inside the dashed black contours marking $\sigma_h\in[10^{-2},2]$. The right panel shows a zoom-in of the same slice colored according to mass density, with magnetic field lines in black. The white line shows where the Bernouilli constant is zero, such that material above this line is unbound. The red dashed line shows the value of the equatorial innermost stable circular orbit. These slices have been azimuthally-averaged and time-averaged over $17.5\times10^4 <tc/r_g<17.9\times10^4$.