Propagation of Precessing Jet in Envelope of Tidal Disruption Events

It is likely that the disk of a tidal disruption event (TDE) is misaligned with respect to the equatorial plane of the spinning supermassive black hole (SMBH), since the initial stellar orbit before disruption is most likely has an inclined orbital plane. Such misaligned disk undergoes Lense-Thirring precession around the SMBH spin axis, leading to a precessing jet if launched in the vicinity of the SMBH and aligned with the disk angular momentum. The bound debris can also build a thick envelope which powers optical emission. In this work, we study the propagation of the precessing jet in the TDE envelope. We adopt a ‘‘zero-Bernoulli accretion’’ (ZEBRA) envelope model. A episodic jet will be observed if the line of sight is just at the envelope pole direction and $θ_{\rm LT}=θ_{\rm env}$, since the jet can freely escape from this low density rotation funnel, where $θ_{\rm LT}$ and $θ_{\rm env}$ are the jet precessing angle and the angle between the envelope polar axis and the SMBH spin axis, respectively. The jet will be choked at other directions. For $θ_{\rm LT} < θ_{\rm env}$, the jets can also break out of the envelope for very small precession angle $θ_{\rm LT}$ or if the jet is aligned with SMBH spin. If the jet is choked within the envelope, the radiation produced during cocoon shock breakout will imprint characteristic signatures on the X-ray emission, such as low-amplitude fluctuation in the light curve.

💡 Research Summary

This paper investigates how a relativistic jet, launched from the inner accretion flow of a tidal disruption event (TDE), propagates through the dense, quasi‑spherical envelope described by the “Zero‑Bernoulli Accretion” (ZEBRA) model. The authors start by summarizing the ZEBRA envelope: it is a radiation‑pressure‑dominated, optically thick structure whose density, pressure, and specific angular momentum follow self‑similar power‑law profiles (Equations 2‑4). The key structural parameter q (related to the radial dependence of the accretion rate) evolves with time as the envelope gains mass from fallback material (Ṁ_fb) and loses mass to the black hole (Ṁ_acc). Using typical supermassive black‑hole masses (10⁵–10⁶ M⊙) and stellar masses (0.5–1 M⊙), the authors compute the time evolution of q, the inner density ρ₀, the outer radius r_out, the envelope temperature T_env, and the jet power L_j (Figure 1). They find that for M• ≈ 10⁵–10⁶ M⊙ a ZEBRA envelope forms and persists for months to years, while for larger black holes the envelope does not develop.

The second part introduces the Lense–Thirring precession of the tilted accretion disk. Because the original stellar orbit is generally inclined relative to the SMBH spin, the disk precesses with angle θ_LT ≤ θ_env, where θ_env is the inclination of the envelope’s symmetry axis relative to the spin axis. The jet is assumed to be launched normal to the disk, thus sharing the same precession period P_LT. Using the analytic expression from Franchini et al. (2016) and Stone & Loeb (2012), the authors calculate P_LT as a function of SMBH spin a·, inner and outer disk radii, and the surface‑density index ζ. For a· = 0.1, 0.5, 1.0 the precession periods are ≈ 40 d, 6 d, and 1 d respectively (Figure 3).

The core of the study is the jet breakout condition. An observer sees the jet only when the line‑of‑sight angle θ_obs lies within the instantaneous jet cone, i.e., θ_obs ∈ (θ_LT − θ_j, θ_LT + θ_j), where θ_j is the jet opening angle. The duty cycle of the episodic jet is defined as ξ_duty = t_on / P_LT, with t_on the time the jet points toward the observer during one precession cycle. The jet head propagates at v_h ≈ c (1 − 1/2Γ_j²) while the tail moves at nearly c. The authors derive a “catch‑up” time t_c from (v_t − v_h) t_c = Δ_j, where Δ_j ≈ T_j c is the shell thickness and T_j = ξ_duty P_LT. If the catch‑up radius r_c exceeds the photospheric radius r_ph (defined by κ ρ r_ph = 1), the jet breaks out of the envelope; otherwise it stalls inside, inflates a cocoon, and eventually releases its energy in a shock breakout.

Three regimes emerge:

1. θ_LT = θ_env – When the precession cone aligns with the envelope’s polar funnel, an observer located near the funnel axis sees a clear, episodic jet. The jet escapes unimpeded because the funnel density is low.

2. θ_LT < θ_env – Two sub‑cases allow breakout: (i) a very small precession angle (θ_LT ≈ 0) so the jet remains essentially fixed, or (ii) the jet aligns with the SMBH spin axis. In both situations the jet can travel through the low‑density polar region despite the envelope’s tilt.

3. θ_LT > θ_env – For most viewing angles the jet must traverse the dense envelope body and is typically choked. The stalled jet inflates a cocoon; when the cocoon shock reaches the photosphere it produces a brief X‑ray flash with low‑amplitude variability, a signature distinct from the bright, non‑thermal emission of successful jetted TDEs.

The authors argue that this geometric constraint—particularly the relative size of θ_LT and θ_env—provides a natural explanation for the observed rarity of jetted TDEs (∼10⁻³–10⁻² of all TDEs). Only when the precession angle is comparable to or smaller than the envelope tilt does the jet escape, producing the luminous X‑ray and radio afterglows seen in events like Swift J1644+57. In the majority of cases the jet is choked, and the resulting cocoon shock breakout yields modest X‑ray variability that may be mistaken for ordinary, non‑jetted TDE emission.

Finally, the paper compares its results with earlier works that emphasized disk‑wind confinement (e.g., Teboul & Metzger 2023; Lu et al. 2024). While those studies focused on the wind’s opening angle and jet power, the present work adds the envelope inclination as an independent, potentially dominant factor. The authors suggest that future high‑cadence X‑ray monitoring, combined with radio follow‑up and polarimetric studies, could test the predicted signatures: periodic jet visibility for θ_LT ≈ θ_env, low‑amplitude X‑ray fluctuations for choked jets, and a correlation between inferred precession periods and black‑hole spin. Moreover, three‑dimensional radiation‑hydrodynamic simulations would be valuable to verify the analytic breakout criteria and to explore the detailed morphology of the cocoon and shock breakout emission.

In summary, the paper provides a comprehensive analytic framework linking Lense–Thirring precession, envelope geometry, and jet dynamics, offering a plausible explanation for why only a tiny fraction of TDEs produce observable relativistic jets and predicting observable X‑ray signatures for the much more common choked‑jet population.