[Paper Review] Relativistic Flows in TeV Blazars

Amir Levinson|ArXiv.org|Aug 3, 2008

Astrophysics and Cosmic Phenomena1 references3 citations

TL;DR

The paper proposes that rapid TeV flares in blazars require relativistic outflows powered by the Blandford-Znajek mechanism, with black hole masses below 10⁸ M⊙ and magnetic fields ~2×10⁴ G, enabling efficient energy dissipation via internal shocks or recollimation shocks. The model explains short-timescale variability and high luminosities via focused jet energy dissipation at small radii, reconciling observed TeV emission with central engine energetics and kinematics.

ABSTRACT

Rapid variability of the TeV emission in several blazars implies a central black hole mass $M_{BH}<10^8M_\odot$, appreciably smaller than the values estimated from the $M_{BH}-L_{bulg}$ relation, and Doppler factors for the $γ$-ray emitting fluid much larger than those associated with radio patterns. We discuss the conditions in the central engine required to account for the short timescales and large luminosities observed, and propose some explanations for the inferred kinematics of the source on various scales.

Motivation & Objective

• To resolve the discrepancy between observed rapid TeV variability timescales and inferred black hole masses from the M_BH-L_bulge relation.
• To explain the large Doppler factors inferred from TeV emission versus those from radio structures, suggesting different emission zones or kinematic mechanisms.
• To account for the high isotropic equivalent luminosities (L_TeV ≥ 10⁴⁶ erg s⁻¹) in TeV flares through efficient energy dissipation in relativistic outflows.
• To investigate whether the TeV emission zone lies close to the black hole or at larger radii (e.g., HST-1 in M87), and what physical conditions enable such short variability.
• To assess the viability of the Blandford-Znajek mechanism and magnetic field configurations in powering the observed flares under extreme accretion conditions.

Proposed method

• Uses variability timescale t_var ≈ 300 s (for PKS 2155-304) to infer black hole mass via r_g/c, yielding M_BH ≲ 5×10⁷ M⊙ t_300.
• Applies the Blandford-Znajek power formula L_BZ = 10⁴⁵ ε B₄² M₈² erg s⁻¹ to estimate required magnetic field strength B₄ ≳ 2(ε/0.1)^{-1/2} t_300^{-1} θ_{-1} L_TeV,46^{1/2}.
• Considers energy dissipation via internal shocks or collisions with obstacles, where only (d/r_g)² of bulk power is radiated, leading to modified L_j ∝ (r_g/d)² f_b L_TeV.
• Evaluates jet focusing via recollimation shocks at large radii (e.g., HST-1 in M87), where modest cooling can reduce cross-sectional radius a to a/r_HST1 ≲ 10⁻³.
• Models γγ pair production optical depth τ_γγ(Γ₀ε_max) ≳ few to assess deceleration of relativistic fronts and TeV photon escape.
• Compares minimum jet power from VLBI radio data with TeV luminosity, showing consistency when background radiation (L_s ~ 10⁴¹–10⁴² erg s⁻¹) is included.

Experimental results

Research questions

• RQ1 What black hole mass is implied by the observed 300 s variability timescale in PKS 2155-304, and how does it conflict with the M_BH-L_bulge relation?
• RQ2 What magnetic field strength and Blandford-Znajek power are required to power the observed TeV luminosities (L_TeV ≥ 10⁴⁶ erg s⁻¹) in short flares?
• RQ3 Can the observed TeV emission originate at large distances (e.g., HST-1 in M87), and what physical mechanisms could enable such short variability at that scale?
• RQ4 How does the presence of a soft photon background (e.g., from LLAGN-like emission) affect the propagation and escape of TeV γ-rays in relativistic jets?
• RQ5 Can recollimation shocks at parsec-scale distances focus the jet sufficiently to explain the observed variability timescales without requiring a very compact emission region?

Key findings

• A black hole mass of M_BH ≲ 5×10⁷ M⊙ t_300 is inferred from the 300 s variability timescale in PKS 2155-304, significantly below the M_BH-L_bulge estimate of ~2×10⁸ M⊙.
• A magnetic field strength of B₄ ≳ 2(ε/0.1)^{-1/2} t_300^{-1} θ_{-1} L_TeV,46^{1/2} is required to power the TeV flares via the Blandford-Znajek mechanism, implying B₄ ≳ 2 for typical parameters.
• The required field strength can be achieved with accretion rates near the Eddington limit (ṁ ~ 1) and η ~ 0.1 if the field is in equipartition with disk energy density.
• The HST-1 knot in M87, located at ~60 pc from the black hole, exhibits X-ray variability with t_var ≲ 0.14 yr, implying a source size Δr ≲ 0.022ΓD pc, much smaller than the distance to the hole.
• Jet focusing via recollimation shocks at HST-1 can reduce the cross-sectional radius to a/r_HST1 ≲ 10⁻³, enabling short variability timescales even at large radii.
• The model explains the observed propagation of γ-ray flares from low to high energies via increasing γ-spheric radius with energy, consistent with recent Mrk 501 observations.