Blazar Anti-Sequence of Spectral Variability for Individual TeV Blazars

We compile from literature the broadband SEDs of twelve TeV blazars observed simultaneously or quasi-simultaneously with Fermi/LAT and other instruments. Two SEDs are available for each of the objects and the state is identified as a low or high state according to its flux density at GeV/TeV band. The observed SEDs of BL Lac objects (BL Lacs) are fitted well with the synchrotron + synchrotron-self-Compton (syn+SSC) model, whereas the SEDs of the two flat spectrum radio quasars (FSRQs) need to include the contributions of external Compton scattering. In this scenario, it is found that the Doppler factor delta of FSRQs is smaller than that of BL Lacs, but the magnetic field strength B of FSRQs is larger than that of BL Lacs. The increase of the peak frequency of the SEDs is accompanied with the increase of the flux for the individual sources, which seems opposite to the observational phenomena of the blazar sequence. We refer this phenomenon to blazar anti-sequence of spectral variability for individual TeV blazars. However, both the blazar sequence from FSRQs to BL Lacs and blazar anti-sequence of the spectral variability from low state to high state are accompanied by an increase of the break Lorentz factor of the electron’s spectrum gamma_b and a decrease of B. We propose a model in which the mass accretion rate is the driving force behind both the blazar sequence for ensembles of blazars and the blazar anti-sequence for individual blazars. Specifically we suggest that the differences in mass accretion rate of different blazars produce the observed blazar sequence, but \Delta M in each blazar results in the observed blazar anti-sequence.

💡 Research Summary

This paper presents a systematic study of the broadband spectral energy distributions (SEDs) of twelve TeV‑detected blazars—ten BL Lac objects and two flat‑spectrum radio quasars (FSRQs)—using simultaneous or quasi‑simultaneous observations from Fermi/LAT together with a suite of ground‑based and space‑based instruments. For each source, two SEDs are compiled, representing a low‑state and a high‑state, the latter being defined by a higher flux density at 1 TeV (or at 10 GeV for PKS 1510‑089 where the TeV data are incomplete).

The authors model the SEDs with a one‑zone leptonic framework. For BL Lac objects, external photon fields are assumed negligible, so a synchrotron plus synchrotron‑self‑Compton (syn+SSC) model is applied. For the two FSRQs (3C 279 and PKS 1510‑089), the contribution of external photons from the broad‑line region (BLR) is included, leading to a synchrotron + SSC + external‑Compton (EC/BLR) model. Model parameters—Doppler factor (δ), magnetic field strength (B), break Lorentz factor of the electron distribution (γ_b), electron density normalization, and jet power (P_jet)—are constrained by fitting the observed SEDs. The BL Lac sample yields δ values ranging from 8 to 50 (clustered around 11–30) and B ≈ 0.1–0.6 G, while the FSRQs have lower δ (≈10–20) but higher B (≈0.3–1 G).

A key observational result is that, for virtually all sources, the high‑state SED is shifted to higher frequencies (both synchrotron peak ν_s and inverse‑Compton peak ν_c) and exhibits a larger flux than the low‑state SED. This “anti‑sequence” behavior—peak frequency increasing together with luminosity—is opposite to the classic blazar sequence, where ν_s rises as the bolometric luminosity L_bol and the Compton‑to‑synchrotron luminosity ratio L_IC/L_syn decrease.

Quantitatively, the authors find that the break Lorentz factor γ_b and the jet power P_jet are systematically larger in the high state. A tentative correlation between the ratio of γ_b (high/low) and the ratio of 1 TeV flux (high/low) is reported (Spearman r ≈ 0.55, p ≈ 0.08), suggesting that the spectral shift is driven primarily by changes in the electron energy distribution. Magnetic energy density U_B tends to be lower in the high state, whereas the available photon energy density (U′_ph) and the synchrotron and IC luminosities (L_syn, L_IC) are higher, indicating more efficient inverse‑Compton scattering despite reduced magnetic fields.

The paper then juxtaposes the anti‑sequence (individual source variability) with the traditional blazar sequence (population‑wide trend from FSRQs to BL Lacs). Both phenomena share two common trends: (i) an increase of γ_b and (ii) a decrease of B when moving from low to high states (anti‑sequence) or from FSRQs to BL Lacs (sequence). The authors argue that these parallel trends point to a single underlying driver: the mass accretion rate (ṁ).

A conceptual flow chart is proposed: a decrease in ṁ leads to (a) reduced magnetic field strength in the jet (assuming equipartition between magnetic and other forms of energy in the accretion disk), (b) higher γ_b because radiative cooling becomes less efficient, and (c) lower bolometric luminosity L_bol (since L_bol ∝ ṁ). For the population‑wide sequence, objects with intrinsically lower ṁ (often associated with smaller black‑hole masses) appear as BL Lacs, while higher ṁ objects retain a luminous BLR and are classified as FSRQs. Within a single source, temporary fluctuations in ṁ can produce the observed high‑state anti‑sequence: a modest drop in ṁ reduces B, raises γ_b, and shifts the SED to higher frequencies while simultaneously increasing the observed flux due to enhanced particle acceleration.

The authors also examine correlations between γ_b and the total comoving energy density U′ (sum of synchrotron, magnetic, and external photon fields). Although scatter is large, a general anti‑correlation is consistent with earlier works, supporting the idea that γ_b is limited by radiative cooling in environments with higher U′. Moreover, γ_b shows a positive correlation with magnetic energy density across the combined sample, reinforcing the notion that magnetic fields influence the maximum electron energies attainable in the jet.

In summary, this study provides robust observational evidence that individual TeV blazars exhibit a spectral “anti‑sequence”—higher peak frequencies accompany higher fluxes—contrasting with the classic blazar sequence observed across different source classes. By demonstrating that both trends are linked to simultaneous increases in γ_b and decreases in B, the authors propose that variations in the mass accretion rate, whether intrinsic between different objects or transient within a single object, constitute the fundamental physical mechanism governing both the blazar sequence and the anti‑sequence. This unified picture offers a compelling framework for interpreting blazar jet physics, the role of external photon fields, and the connection between accretion processes and high‑energy emission in active galactic nuclei.