Delayed radio emission in tidal disruption events from collisions of outflows driven by disk instabilities

Technical Summary: Delayed Radio Emission in Tidal Disruption Events from Collisions of Outflows Driven by Disk Instabilities

Problem Statement
Delayed radio emission has been increasingly observed in Tidal Disruption Events (TDEs), often appearing hundreds to thousands of days after the optical peak. While prompt radio emission is typically attributed to the interaction of non-relativistic outflows with the circumnuclear medium (CNM) shortly after disruption, the mechanism driving these delayed, mildly relativistic outflows remains uncertain. Previous hypotheses include off-axis jets, stream-stream collisions, or interactions with inhomogeneous CNM clouds. However, the specific origin of outflows launched $\sim100$–$1000$ days post-disruption, particularly those exhibiting multiple flares or distinct late-time peaks, requires further theoretical investigation. This work posits that these outflows may result from instabilities or state transitions in the accretion disk formed by the TDE, leading to mass ejections ("flares") that collide with each other or with the surrounding medium.

Methodology
The authors model the hydrodynamical evolution and subsequent synchrotron radio emission resulting from the collision of mass outflows. The study considers two primary collision scenarios:

1. Flare+Flare: The collision of two successive flares ejected from the accretion disk with a time interval $\Delta t$.
2. Flare+CNM: The collision of a single flare with the surrounding circumnuclear medium (CNM).

The outflow properties are motivated by the disk instability scenario described in A. L. Piro & B. Mockler (2025), where thermal instabilities in a high-accretion state disk drive mass ejections. The flares are modeled with a density profile $\rho_{fl} \propto r^{-2s-3}$ (where $s=0.5$) and a velocity range $v_{min} < v < v_{max}$ (specifically $0.04c$ to $0.4c$). The authors explore flare masses ($M_{fl}$) of $0.01$ and $0.1 M_\odot$.

For the CNM, two density profiles are tested: a constant density ($\alpha=0$) and a power-law decline ($\rho \propto r^{-2.5}$, $\alpha=2.5$), covering observationally inferred slopes. The hydrodynamical evolution of the shock formed by these collisions is calculated using mass and momentum conservation equations for a thin shell. The resulting radio emission is computed using synchrotron radiation theory, accounting for free-free absorption (FFA) and synchrotron self-absorption (SSA). The models assume a power-law electron energy distribution with index $p=3$ and equipartition parameters $\epsilon_B = \epsilon_e = 0.1$.

Key Results
The simulations demonstrate that shock collisions can produce radio luminosities ($L_\nu$) in the range of $10^{27}$–$10^{30}$ erg s$^{-1}$ Hz$^{-1}$ at 6 GHz, with shock velocities evolving between $0.05c$ and $0.3c$ at radii of $\sim10^{17}$ cm. The light curve morphology is highly dependent on the collision type and environmental parameters:

• Flare+Flare Collisions: These produce rapidly evolving light curves with rise and decay timescales of $\sim10$–$100$ days. The peak is typically determined by the SSA optical depth dropping to unity. These models are capable of reproducing events with multiple, sharp radio peaks.
• Flare+CNM Collisions (Constant Density, $\alpha=0$): These models yield light curves that can be sustained over $\sim10^2$–$10^3$ days. The peak timescale is generally set by the Sedov time (when the swept-up mass equals the flare mass). Higher CNM densities lead to faster deceleration and shorter peak timescales.
• Flare+CNM Collisions (Power-law, $\alpha=2.5$): These models exhibit intermediate behavior. For lower densities, they peak earlier and are fainter; for higher densities, they last longer and are brighter. The peak timescale is often set by the SSA optical depth, similar to the Flare+Flare case.

The authors compared their model predictions against a selection of observed TDEs with delayed radio emission:

• PS16dtm: Well-reproduced by a Flare+$\alpha=0$ CNM model with $M_{fl}=0.1 M_\odot$ and $n_0=30$ cm$^{-3}$.
• ASASSN-15oi: The second radio peak is consistent with a Flare+$\alpha=0$ CNM model ($M_{fl}=0.1 M_\odot$, $n_0=10^3$ cm$^{-3}$), though the first peak likely requires a different mechanism (e.g., stream-stream interaction).
• AT2020vwl: The second peak matches a Flare+$\alpha=0$ CNM model ($M_{fl}=0.01 M_\odot$, $n_0=10^2$ cm$^{-3}$).
• AT2024tvd: The two sharp, rapidly evolving peaks are well-suited to Flare+Flare models, suggesting multiple ejection episodes.
• AT2019azh and AT2018zr: These events show mixed characteristics, where single models struggle to fit both rise and decay timescales simultaneously, suggesting complex underlying physics or multiple components.

Significance and Claims
The paper claims that the collision of disk-instability-driven outflows is a viable mechanism for powering the delayed radio emission observed in a significant fraction of TDEs. Specifically:

1. Mechanism Validation: The models successfully reproduce the light curves and spectral energy distributions (SEDs) of several observed TDEs, supporting the hypothesis that delayed, mildly relativistic outflows originate from accretion disk instabilities or state transitions.
2. Differentiation of Scenarios: The study provides a framework to distinguish between different physical origins based on light curve evolution. Flare+Flare collisions are uniquely capable of explaining bright, rapidly evolving (timescales $\sim100$ d) multiple peaks, whereas Flare+CNM collisions (particularly with constant density) better explain slower, long-duration decays ($\sim10^3$ d).
3. Observational Constraints: The authors note that while their models fit many events, discrepancies in SEDs (e.g., electron spectral index $p$) and light curve rise times for some events (e.g., ASASSN-14ae, AT2018hyz) suggest that not all delayed emission can be explained by this single mechanism, or that additional physics (such as inverse Compton cooling or different density profiles) may be required.

The work concludes that while disk instabilities offer a promising explanation for specific classes of delayed radio emission, particularly those with multiple peaks, further late-time radio and multi-wavelength monitoring is necessary to fully constrain the diversity of outflow origins in TDEs.