A one-parameter two-zone leptonic model for the blazar sequence

TL;DR

Blazar spectra and the blazar sequence pose a challenge for unifying jet emission with accretion physics. The authors develop a self-consistent two-zone leptonic framework in which electrons are accelerated in a compact region and escape into a larger cooling zone illuminated by disk-photon scattering in a magnetohydrodynamic wind, with the mass accretion rate $\dot{m}$ as the sole driver. They derive scaling relations for the acceleration timescale $t_{\rm acc}$ and energy densities $U_B$ and $U_{\rm ext}$ as functions of $\dot{m}$ and black-hole mass ${\cal M}$, finding that $t_{\rm acc}$ must scale nearly linearly with $\dot{m}$ (for $\dot{m} \lesssim 0.1$) to reproduce the observed blazar sequence. The two-zone treatment naturally explains why BL Lacs are SSC/synchrotron-dominated while FSRQs are EC-dominated, and it matches key statistical trends from Fermi-LAT, including Compton dominance and the positions of synchrotron and inverse Compton peaks; it also provides testable predictions, such as possible time delays between X-ray and $\gamma$-ray emission during flares. This framework links accretion-powered physics to the diversity of blazar spectra in a unified, predictive picture.

Abstract

Blazars, a subclass of radio-loud active galactic nuclei with relativistic jets aligned close to our line of sight, emit highly variable non-thermal radiation across the electromagnetic spectrum. The physical origin of their emission and the blazar sequence remain open questions. We present a self-consistent two-zone leptonic model in which relativistic electrons accelerate in a compact region, losing energy via synchrotron and inverse Compton processes, and escape into a larger zone permeated by an external photon field associated with magnetohydrodynamic winds from the accretion disk. By varying only the mass accretion rate onto the central black hole, the model naturally reproduces the blazar sequence, including Compton Dominance, $γ$-ray spectral indices, and the positions of synchrotron and inverse Compton peaks, while variations in secondary parameters account for the observed spread in the data. Flat Spectrum Radio Quasars exhibit strong external Compton emission from the extended zone, whereas BL Lac objects are dominated by synchrotron and synchrotron self-Compton emission from the compact acceleration region. This framework highlights the key role of accretion rate and spatially structured emission zones in shaping blazar spectra and provides a unified interpretation of their diverse phenomenology.

Figures (5)

• Figure 1: Bottom: Calculated Spectral Energy Distributions of BL Lac objects for various values of the normalized accretion rate $\dot{m}$. Inset (top center): Dependence of the acceleration timescale $t_{\rm acc}$ on $\dot{m}$, showing the nearly linear scaling required to explain BL Lac sources. Colored points correspond to the SED curves, indicating that higher $\dot{m}$ produces more luminous sources.
• Figure 2: Sketch of the two-zone model. Particles accelerate and radiate in the acceleration zone (dark blue). A fraction escapes into the cooling zone (light blue), where it continues to radiate.
• Figure 3: Results for FSRQ and BL Lac objects according to the two-zone model. Straight lines represent the emission from the acceleration zone, and dotted lines represent the emission from the cooling zone. The shaded region depicts the Fermi $\gamma$-ray energy band.
• Figure 4: Theoretical Blazar Sequence according to the superposition of the two-zone emission by varying only the mass accretion rate, see Table \ref{['tab:blazar_seq_input']} for the values of the input parameters.
• Figure 5: Application of the two-zone model to the FSRQ 3C273, focusing on the high-energy spectral range. The acceleration zone is located at $z=0.01$ pc, with a magnetic field strength of $B=1~\mathrm{G}$ and radius $R_I=5 \times 10^{15}$ cm, the cooling zone is one order of magnitude more distant and larger than the acceleration zone. The external photon field arises from isotropic scattering of disk photons on wind particles between radii $R_1 = 9 \times 10^{14}$ cm and $R_2 = 3 \times 10^{18}$ cm, with energy density $U_{\rm ext} = 2.5 \times 10^{-3}~\mathrm{erg\,cm^{-3}}$. The bulk Lorentz factor is $\Gamma=30$, the Doppler factor is $\delta=15$, and the characteristic disk temperature is $T_{\rm disk} = 3 \times 10^4$ K. Observational data are taken from GIommi12P.