Propagation of Precessing Jet in Envelope of Tidal Disruption Events

TL;DR

This paper analyzes how a Lense-Thirring precessing jet propagates inside an inclined ZEBRA envelope formed during tidal disruption events. It develops a twofold model: (i) a zero-Bernoulli, self-similar ZEBRA envelope with an inclined geometry and (ii) a precessing jet with opening angle $\theta_{j}$ that sweeps through the envelope with a period $P_{LT}$ and angle $\theta_{LT}$. The study derives jet breakout conditions as functions of envelope inclination $\theta_{env}$, jet precession $\theta_{LT}$, jet power $\epsilon$, and SMBH/donor properties, revealing regimes where jets freely escape via polar funnels or become choked, imprinting cocoons or delayed signatures; alignment processes can yield late-time jet emergence, consistent with diverse observations such as J1644+57 and AT2022cmc. The framework connects the optical/UV prominence of TDEs to jet-envelope interactions and provides a basis to interpret multiwavelength variability, polarization, and radio/X-ray delays in jetted TDEs, with applicability to observed events like J1644, J12580, ASASSN-14li, and AT2020ocn.

Abstract

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.

Figures (5)

• Figure 1: The solution of q with time (Panel a) and the characteristics of the ZEBRA envelope evolve as a function of time, i.e., the effective temperature ($T_{\rm env}$, panel b), the density at the inner radius ($\rho_0$, panel c), the jet luminosity ($L_{\rm j}$, panel d) and the outer radius ($r_{\rm out}$, panel e). In the calculation, we adopt the initial value of $q$ as $q_0=1$, for the mass disrupted star $M_*= M_\odot$ (solid line) and $M_*= 0.5 M_\odot$ (dashed line) with $M_{\bullet}=10^5M_\odot$ (black line) and $10^6M_\odot$ (red line). And we use the accretion efficiency $\epsilon=0.01$, $\chi =5$, $y=0.5$ and $\delta=0.05$.
• Figure 2: A schematic picture of the precession jet in an inclined ZEBRA envelope, the central orange ring represents the inner accretion disk within the ZEBRA envelope. The jet precess with angle $\theta_{\rm LT}$. The angle between the SMBH spin axis ($\Omega_{\bullet}$) and the envelope's rotation axis ($\Omega_{\rm env}$), i.e., the envelope inclination, is $\theta_{\rm env}$. Left panel: $\theta_{\rm LT}=\theta_{\rm env}$. In the low density polar regions, i.e, "free zone", the relativistic jet can escape freely when it precess to this direction. The jet is choked at other regions. Middle and right panels: $\theta_{\rm LT}<\theta_{\rm env}$. The jet will be choked in all directions if $\theta_{\rm LT}$ is large (middle panel), or break out of envelope if $\theta_{\rm LT}$ is small (right panel).
• Figure 3: The precessing period $P_{\rm LT}$ as a function of SMBH spin $a_\bullet$ for $M_{\bullet}\sim 10^6M_\odot$ and $M_*\sim M_\odot$.
• Figure 4: The logarithm of the ratio between the reverse-shock crossing radius and the photosphere of the envelope for the jet, $\log (r_{\rm c}/r_{\rm ph}$). Successful breakout jet requires $\log (r_{\rm c}/r_{\rm ph})>0$, as shown by the red area. panel (a) is the fiducial case for $M_{\bullet}=10^6M_\odot$, $t=100~\rm day$, $\theta_{\rm j}=0.1$, $\epsilon=0.01$, $P_{\rm LT}=5~\rm day$, $M_*=M_\odot$ and $\theta_{\rm LT}=\theta_{\rm env}\in (0,\pi/2)$. In other panels, we only change one parameter for comparing with fiducial case; Panel (b), $\epsilon=0.05$, panel (c), $M_{\bullet}=10^5M_\odot$, panel (d), $t=500~\rm day$; panel (e), $\theta_{\rm j}=0.4$; panel (f), $P_{\rm LT}=10~ \rm day$; panel (g), $M_*=0.5M_\odot$; panel (h), $\theta_{\rm LT}<\theta_{\rm env}=0.5$; panel (i), $\theta_{\rm LT}<\theta_{\rm env}=1.5$. Besides, since larger $M_{\bullet}$ leads to a later onset of envelope evolution, we adopt the time of the peak $q$ to weaken the influence of the time. The red and purple dashed lines are the results of Teboul-Metzger(2023) and Lu-et-al.(2024) for $\epsilon=0.01$ and $0.05$, respectively.
• Figure 5: The estimation of $\theta_{\rm obs}$ and $\theta_{\rm LT}$ for Swift j1644+57 (panel a), AT 2022cmc (panel b), IGR J12580 (panel c) and AT 2020ocn (panel d) with the special $\xi_{\rm duty}$ or $\lambda$. The pink point in each panel represents the values of ($\theta_{\rm obs}$, $\theta_{\rm LT}$) that we adopt.