Delayed Radio Flares in Tidal Disruption Events from Star-Disk Collision Outflows

This paper proposes that delayed radio flares in tidal disruption events are caused by massive, slow outflows generated when a pre-existing stellar extreme-mass-ratio-inspiral collides with an expanding accretion disk years after the initial disruption.

The Gist

The Mystery: The "Late-Blooming" Radio Fireworks

Imagine a star gets torn apart by a supermassive black hole. This event, called a Tidal Disruption Event (TDE), usually creates a bright flash of light (optical/UV) that we see immediately. Sometimes, this event also shoots out a blast of gas that creates radio waves, like a firework going off right after the explosion.

But astronomers have noticed a weird pattern in about 40% of these events: The radio fireworks don't go off until years later.

Even stranger, the gas creating these late fireworks is moving relatively slowly and is incredibly heavy (as heavy as a star or more). This is a problem for old theories. If the gas came from the black hole's immediate neighborhood (the accretion disk), there shouldn't be that much heavy gas left there years later to make such a big explosion. There simply isn't enough leftover heavy gas in the accretion disk years later to power such a large, massive radio flare.

The New Idea: A Star-Disk Collision

The authors propose a new explanation involving a collision between a star and a gas disk.

1. The Setup: Before the star was torn apart, there was already another star orbiting the black hole in a tight circle. Think of this as an orbiting star moving along its path.
2. The Accident: When the first star gets torn apart, its debris forms a new, compact disk of gas around the black hole. At first, this gas disk is small and does not touch the orbiting star.
3. The Expansion: Over time, the gas disk slowly expands outward due to friction and viscosity.
4. The Collision: Eventually, the expanding gas disk grows large enough to hit the orbiting star. This is the star-disk collision.
5. The Delay: The "delay" we see in the radio waves isn't because the explosion was slow to start; it's because it took years for the gas disk to grow big enough to reach the orbiting star.

The Explosion: Kicking Up Dust

When the orbiting star crashes through the gas disk, it acts like a plow moving through a field.

• The Plow: The orbiting star punches a hole through the gas.
• The Debris: This crash scrapes off some of the gas disk and also shaves off layers of the orbiting star itself.
• The Ejection: This mixture of gas and star debris gets kicked out at high speeds, creating a massive cloud of material.

Because the orbiting star is moving fast, the debris it kicks up also moves fast. This cloud of debris then slams into the surrounding space (the "circumnuclear medium"), creating a shockwave. This shockwave is what we detect as the delayed radio flare.

Why This Solves the Mystery

This model solves the "mass problem" mentioned earlier.

• Old Theory: The radio flare had to come from the gas disk alone. But the disk didn't have enough heavy gas left to explain the size of the explosion.
• New Theory: The explosion gets its mass from two sources: the gas disk and the orbiting star itself. The orbiting star acts as an extra fuel tank, providing the massive amount of material needed to create the huge, slow-moving radio flare we see years later.

The Connection to "Quasi-Periodic Eruptions" (QPEs)

The paper also links this to another mysterious phenomenon called QPEs. These are systems where a black hole emits regular, repeating X-ray flares every few hours or days.

• The authors suggest that the same collisions that create the delayed radio flares might also be causing these repeating X-ray flashes.
• Every time the orbiting star hits the gas disk, it creates a small shock (an X-ray flare). If the star survives the crash, it keeps orbiting and crashing again, creating a repeating pattern.
• However, the paper notes that sometimes the conditions needed for a bright radio flare might be different from the conditions needed to see the X-ray flashes. So, we might see the radio flare without seeing the X-ray pattern, or vice versa.

Summary

In short, the paper suggests that delayed radio flares in black hole events are caused by a "late arrival" collision. A star that was already orbiting the black hole waits for the debris from a torn-apart star to expand enough to hit it. When they finally crash, they kick up a massive amount of dust and gas, creating a radio explosion years after the original event. This explains why the explosion is so heavy and why it took so long to happen.

Technical Summary

Technical Summary: Delayed Radio Flares in Tidal Disruption Events from Star-Disk Collision Outflows

Problem Statement
A growing fraction of Tidal Disruption Events (TDEs) exhibit radio emission that rises significantly (hundreds to thousands of days) after the initial optical or infrared flare. These delayed outflows are often inferred to be slow ($v_w \sim 0.02 - 0.1c$) and massive ($\gtrsim 0.01 - 0.1 M_\odot$). Existing models struggle to explain these properties:

1. Mass Budget: The inferred ejecta mass in some events approaches or exceeds the total mass budget of the TDE accretion disk at the time of launch, challenging models where the disk itself is the sole mass reservoir (e.g., via delayed jets or state transitions).
2. Timing: The delay is difficult to reconcile with standard jet-launching mechanisms or off-axis viewing angles, which typically predict faster outflows or different temporal behaviors.
3. Mechanism: It remains unclear why slow, massive outflows would turn on suddenly years after the disruption.

Methodology
The authors propose a new mechanism where delayed outflows are powered by repeated collisions between a TDE accretion disk and a pre-existing stellar Extreme Mass-Ratio Inspiral (EMRI) orbiting the supermassive black hole (SMBH). The study employs a time-dependent model to simulate the coupled evolution of the spreading TDE disk and the EMRI.

Key components of the model include:

• Disk Evolution: The TDE disk is modeled as a viscously spreading thin disk. The delay in outflow launch is determined by the viscous time required for the initially compact disk to expand radially until its outer edge intercepts the EMRI's orbit ($a_0$).
• Star-Disk Collisions: Once the disk reaches the EMRI orbit, repeated impacts occur every half-orbital period. The authors utilize hydrodynamic estimates for mass ejection, calculating the mass excavated from the disk ($\delta m_d$) and the mass ablated from the stellar EMRI ($\delta m_\star$) per collision.
• Mass Loss Efficiency: The model defines an ejection efficiency parameter ($\xi_w$) relating the outflow rate to the local disk accretion rate. It considers regimes where the outflow is dominated by either shocked disk material or ablated stellar debris, depending on the orbital period, disk viscosity, and collision inclination.
• Radio Emission: The authors apply canonical synchrotron afterglow theory to estimate the radio light curves produced when these delayed outflows interact with the circumnuclear medium (CNM) or earlier TDE ejecta.

Key Contributions and Results

1. Mechanism for Delayed Outflows: The paper demonstrates that the delay is naturally set by the viscous spreading time of the disk ($t_v \sim a_0^2/\nu$), rather than delayed jet launching. This explains the multi-year lag between the optical peak and the radio flare.
2. Mass and Energy Budgets: The model predicts that collisions can launch outflows with masses $M_w \sim (10^{-3} - 1) M_\odot$ and kinetic energies up to $10^{51}$ erg. Crucially, the EMRI acts as an additional mass reservoir (via ablation), alleviating the tension where the required ejecta mass exceeds the available disk mass.
   • For long orbital periods, the outflow is dominated by disk material.
   • For shorter periods, the outflow can be dominated by ablated stellar material, potentially destroying the EMRI.
3. Radio Predictions: The interaction of these slow ($v_w \approx 0.02 - 0.1c$) outflows with the ambient medium produces radio flares peaking on timescales of years. The predicted flux densities ($\sim 0.01 - 100$ mJy at 3 GHz) and light curve shapes are consistent with observed delayed radio flares in TDEs (e.g., WTP14adeqka, AT 2019azh).
4. Connection to Quasi-Periodic Eruptions (QPEs): The authors link this mechanism to X-ray QPEs, which are also thought to arise from star-disk collisions. The model suggests that systems exhibiting delayed radio flares may also host QPEs, though the conditions for bright radio flares (requiring unbound ejecta) may not always align with those for detectable QPEs (which depend on shock thermalization and optical depth).
5. Case Studies: The model is applied to specific sources:
   • AT 2019qiz: The authors predict a radio rebrightening around 2024-2025, coinciding with the discovery of QPEs in this system, driven by the EMRI-induced outflow.
   • WTP14adeqka: The model explains the massive, slow outflow inferred from VLBA imaging as a result of star-disk collisions, noting that the dusty environment likely suppresses X-ray QPE detection in this specific source.

Significance and Claims
The paper claims to provide a unified physical framework that resolves the mass-budget and timing challenges of delayed radio flares in TDEs. By introducing the EMRI as a mass reservoir and the disk spreading time as the delay mechanism, the model offers a self-consistent explanation for slow, massive outflows appearing years after disruption.

The authors emphasize that this mechanism predicts a direct observational connection between delayed radio flares and systems hosting EMRIs, potentially including those exhibiting X-ray QPEs. They note that while the model is consistent with current data (such as the properties of WTP14adeqka and the timing of AT 2019qiz), the survival of the EMRI and the specific observability of QPEs versus radio flares depend sensitively on system parameters like orbital period, disk viscosity, and inclination. The work suggests that future multi-messenger observations (radio, X-ray, and optical) of TDEs with QPEs will be critical for testing this star-disk collision paradigm.