Explaining the X-ray Precursor, Ultra-long Prompt Emission, and Week-long Decay of GRB250702B with a Jetted Micro-TDE

The longest detected gamma-ray burst, GRB 250702B, exhibited seven hours of prompt gamma-ray emission, preceded by a soft X-ray precursor (∼ 1 day earlier) and followed by a weeks-long fading X-ray tail. Lacking an established progenitor for all three phases, we propose that this ultra-long GRB (ULGRB) is powered by a jetted micro-tidal disruption event (micro-TDE), in which a spinning stellar-mass black hole (BH) disrupts a Sun-like star and launches a relativistic jet via the Blandford–Znajek mechanism. Micro-TDE debris disks have hours-to-days viscous timescales, naturally explaining ULGRB durations. Using 3D hydrodynamic arepo simulations of a 1 M⊙ star disrupted by a 10 M⊙ BH, we show that within ∼ 1 day the debris forms a quasi-steady envelope with a low-density polar funnel (rho ∝ r −2, half-opening angle ≈ 15◦). Applying an analytic jet-stability framework to these profiles, we find that the r −2 funnel keeps the jet below the kink-instability threshold, enabling stable propagation and breakout for jet powers, L jet ≳ 1047 erg s−1. We attribute the X-ray precursor to pre-disk stream-fed accretion; the prompt GRB to a tightly beamed jet (theta b ≲ 1◦, L gamma,iso ∼ 1051 erg s−1) escaping the funnel, launched by a rapidly spinning BH (a • ∼ 0.9); and the weeks-long X-ray decline to disk-wind mass loss (L jet ∝ t −2) combined with jet widening (theta b ∝ t, initially steepening the decay to L X,iso ∝ L jet /theta b2 ∝ t −4). Our model reproduces the multi-phase evolution of GRB 250702B and establishes jetted micro-TDEs as a physically motivated ULGRB engine.

The paper is organized as follows. Section 2 describes the hydrodynamic simulations of micro-TDEs. Section 3 presents the micro-TDE disk evolution model based on viscous accretion and wind-driven mass loss. Section 4 presents the observational signatures of jetted micro-TDEs and assesses jet stability during propagation through the debris envelope. Section 5 applies our micro-TDE accretion model to GRB 250702B, constraining the black hole spin and beaming angle required to reproduce the observed prompt gamma-ray luminosity and the X-ray light curve. We summarize our results and discuss their implications in Section 6.

We perform 3D hydrodynamic simulations using the moving-mesh code arepo. We adopt the Helmholtz equation of state, which includes radiation pressure under the assumption of local thermodynamic equilibrium with composition inherited from the MESA progenitor model. We model the black hole as a point particle of mass M• = 10 M⊙ that interacts with the gas only gravitationally and neither accretes any mass nor produces any radiative feedback. We then model in post-processing the subsequent (unresolved) disk evolution and compute the time-dependent accretion rate onto the black hole, using the fallback rate M¤ fb (t) computed from the arepo simulations. We create a 1 M⊙ MESA model with hydrogen core mass fraction of 0.5 (corresponding to an age of 2.5 Gyr) and metallicity of Z = 1 Z ⊙. We consider two initial orbits, both leading to the full disruption of the star: a grazing encounter with the penetration factor beta = 1.4 and semi-major axis a = 3 R ⊙, and a deep encounter with beta = 5 and a = 1 R ⊙, where beta ≡ r T /r p > 1, r T is the tidal disruption radius and r p ≡ a(1 − e) is the pericenter distance. In both cases the orbital eccentricity is e = 0.5 and the star begins at apocenter r apo ≡ a(1 + e). The bound orbit with our adopted moderate eccentricity (e = 0.5) results in about 80% of the stellar mass being captured onto the black hole.

Figure 1 shows face-on and edge-on density slices of the debris envelope formed after the disruption of a 1M⊙ star by a 10M⊙ black hole at t = 0.5 day, for two penetration factors: a grazing encounter (beta = 1.4; left panels) and a deep encounter (beta = 5; right panels). The deep encounter produces a compact, dense inner disk (r d ≈ 1R ⊙), while the grazing encounter forms a more extended configuration (r d ≈ 3R ⊙). Both encounters develop a well-defined bipolar funnel with half-opening angle theta f ≈ 15◦ that can serve as a convenient escape funnel for black hole powered relativistic jets. The density contrast between the polar tunnel and the equatorial plane spans more than three orders of magnitude at r ∼ R ⊙, from rho ∼ 10−4 g cm−3 at theta = 0◦ to rho ≳ 10−1 g cm−3 at theta = 90◦. The polar density profile is well described by a power-law rho ∝ r −2, while at intermediate and equatorial angles the profiles steepen towards rho ∝ r −3. The polar r −2 scaling is the key input to our jet propagation and stability calculations: it provides a steadily declining confining pressure that collimates rather than disrupts the jet.

We develop an analytic model for the subsequent viscous accretion by incorporating fallback supply, viscous drainage onto the black hole, and wind-driven mass loss. The disrupted star forms the fallback debris and accretion disk of the characteristic size set by the circularization radius, r c ≃ 2r p = 2r T /beta ≈ 2 × 105 r g beta −1 m −2/3 ∗,1 m 2/3 •,10. Adopting a standard alpha-prescription we calculate the viscous accretion timescale of a geometrically thick disk with aspect ratio h ≡ 0.5h0.5 ≡ H/R for the fiducial parameter choices as tv ≃ alphav−1 h −2 (r c /r g) 3/2 r g /c ≈ 2 day beta −3/2 alphav−1,−1 h −2 0.5 m ∗,1. From our arepo simulations, we see that the two encounters produce different aspect ratios near the circularization radius: the deep encounter (beta = 5) yields h ≈ 0.5, characteristic of geometrically thick, advection-dominated accretion flows at highly super-Eddington rates, which are expected to eject most of the disk mass as winds. The grazing encounter (beta = 1.4) instead settles into a thinner, more rotationally supported configuration with h ≈ 0.2. Because the viscous timescale scales as tv ∝ h −2, it is approximately six times longer than in the grazing case than in the deep case, at the same radius. This slower viscous evolution shifts the accretion peak to later times and lower amplitudes, delaying the onset of the asymptotic M¤ acc ∝ t −2 decline. In what follows, we find that the beta = 5 configuration provides a better match to the late-time X-ray decline of GRB 250702B.

Following Metzger et al. (2008); Kremer et al. (2019, 2023), we approximate the disk mass distribution as a single ring at radius r d where the surface density peaks, and track its mass and angular momentum evolution under fallback supply M¤ fb, viscous accretion onto the black hole, and wind-driven mass loss. The disk mass evolves as M¤ d = − f Md /tv + M¤ fb. Following Blandford & Begelman (1999), we include mass loss from disk winds by adopting a radius-dependent inflow rate M¤ in (r) = (r/r d) s Md /tv, where 0 ≤ s ≤ 1 parametrizes the radial slope of the wind mass outflow. We assume that the wind starts at the radius r acc so that the inflow rate at this radius, M¤ acc = (r acc /r d) s Md /tv, gives the black hole accretion rate. The wind carries away the remainder, M¤ out = [1 − (r acc /r d) s] Md /tv. The disk radius evolves as r¤d = 2r d /tv [1 − C (1 − (r acc /r d) s)] + (r c /r d) −1/2 M¤ fb tv /Md, where C = 2s/(2s + 1) is the torque coefficient assuming the wind carries away angular momentum with its local specific value but exerts no net torque. We solve these equations numerically to compute Md (t) and r d (t), where we take M¤ fb (t) directly from our arepo simulations. As the disk radius r d increases, the viscous accretion timescale increases accordingly t v ∝ r d3/2. We account for this evolving timescale when solving for the coupled evolution of the disk mass and radius. Inserting these time-dependent quantities into the equation for M¤ acc then yields the time-dependent accretion rate onto the black hole. At late times, the system asymptotes to the following scalings: r d ∝ t 2/3, M¤ d ∝ t − (2s+4)/3 = t −5/3, M¤ acc ∝ t −4(s+1)/3 = t −2, where the decay of M¤ acc, steeper than the canonical t −5/3 TDE fallback rate, is the direct consequence of viscous disk spreading combined with wind-driven mass loss. We identify this M¤ acc ∝ t −2 scaling in Section 5 as the origin of the late-time X-ray decay of GRB 250702B. The s = 0.5 value is supported by recent simulations of radiatively inefficient accretion, including neutron star post-merger accretion disks, advection-dominated flows and Bondi accretion with weak cooling. Recent GRMHD simulations have revealed that s is not a universal constant of accretion but depends on the state of the accretion flow. When large-scale vertical magnetic flux fills the black hole to capacity and becomes as strong as the gravitational force acting on the inner disk, it erupts from the black hole, rips through the disk, and buoyantly rises away from the hole. This magnetically arrested disk (MAD) state features ordered accretion, strong magnetically-powered jets, and s ≈ 0.66 ± 0.03. MAD-powered outflows can scramble the angular momentum of the system and lead to a rocking accretion disk (RAD) state. The RAD state features chaotic accretion, continuously reorienting weak jets, and s ≈ 0.87 ± 0.05.

Large-scale magnetic field threading a rotating black hole can extract its spin energy and launch twin Poynting-flux-dominated jets of electromagnetic luminosity, L jet = etajet (a •) M¤ acc c2, via the Blandford & Znajek (1977, BZ hereafter) process. Here, M¤ acc is the black hole accretion rate, for which we adopt the expression given by Equation (4), and a • is the dimensionless BH spin. The jet energy efficiency, defined by eq. (9) as the ratio of the extracted electromagnetic energy to accreted rest-mass energy, has been calibrated by GRMHD simulations, etajet (a •) ≃ 2.64 (phi • /50) 2 omega2H f (omegaH), where omegaH = a • / 1 + (1 − a 2•) 1/2 is the dimensionless angular frequency of the black hole and f (omegaH) ≃ 1 + 0.35omega2H − 0.58omega4H is a high-spin correction. Here, phi• ≡ Φ• /(M¤ r g2 c) 1/2 is the dimensionless black hole magnetic flux, which saturates at phi• ∼ 50 in the MAD state. Twin relativistic jets focus their radiation into a narrow solid angle Ωb = 4pi(1 − cos theta b) around the disk rotational axis. Here, theta b is the beaming angle, which is set by the larger of the jet opening angle, theta j and the relativistic beaming angle, 1/gammaj: theta b = max(theta j, 1/gammaj). An observer aligned with the jet axis therefore infers an isotropic-equivalent luminosity that is enhanced relative to the true twin jet power by the inverse of the beaming fraction, fb ≡ Ωb /4pi = 1 − cos theta b. The isotropic-equivalent luminosity is therefore L iso (t) = etarad etajet fb−1 M¤ acc (t)c2, where etarad is the fraction of the jet power that is radiated in X-ray or gamma-ray band and convert the efficiency.

In general, the black hole spin axis can be misaligned with the angular momentum axis of the debris disk, depending on the initial spin–orbit misalignment of the BH–star orbit. In such a case, the disk undergoes solid-body Lense–Thirring precession with period PLT ≈ (pi/5a •) (r g /c) (r d /r g) 5/2 (r ISCO /r g) 1/2. Numerically for s = 0.5 and r d ∝ t 2/3, PLT ≈ 1.8 × 10 4 day beta −5/2 a −1 •,0.7 m 5/3 ∗,1 m −2/3 •,10 (t/tv) 5/3. Lense–Thirring torques are therefore not strong enough to cause the precession of the jets over the jet engine lifetime (∼ day). Physically, this is because micro-TDE disks feature significant radial extents (r d ∼ 105 r g) that imply large angular momentum content and long precession periods. Recent GRMHD simulations show that magnetic torques from powerful jets can, in some regimes, reorient the inner disk angular momentum into alignment with the black hole spin direction on timescales comparable to or shorter than the accretion timescale. However, the alignment is limited to the immediate vicinity of the black hole, r ≲ 100r g, which is orders of magnitude smaller than the simulated length scales. As a result, tilted black hole systems with extended accretion disks in micro-TDEs launch jets along the rotational axis of the disk irrespective of the initial black hole spin–disk misalignment. We therefore assume the configuration in which the jets propagate through the low-density polar funnel along the rotational axis of the extended disk.

The propagation of a Poynting-dominated relativistic jet through a confining medium is subject to current-driven (kink) instabilities that can disrupt the jet and cause it to stall before breakout. We can quantify the stability of the jet through the stability parameter Λ = 2gammaj theta j /0.03 = K (L 1,jet /(rhoa z2h gammaj2 c3)) 1/6, where gammaj is the bulk Lorentz factor, where L 1,jet = 0.5L jet is one-sided jet power, zh is the distance to the jet head, rhoa is the ambient density, and K = 20 (2pi/9) 1/2 [pi(5−alpha) (3−alpha)/6] 1/3 is a constant numerical prefactor that depends on the radial slope of the ambient density, alpha ≡ −d log rhoa /d log r. Our simulations have alpha = 2 along the polar direction, as seen in Figure 2. We assume the jet is highly magnetized, with magnetization, sigma ≡ b 2 /(4pirhoc2) ≫ 1, and moves at betaj ≡ vj /c ≃ 1, corresponding to Lorentz factor gammaj ≫ 1. Because the polar density follows rhoa ∝ r −2, the factor of rhoa z2h in Equation (14) is independent of the jet-head distance, and so is Λ; the stability result therefore holds at all radii and does not rely on the jet reaching a particular breakout height. Our profile sits precisely at the critical slope alpha = 2 separating the two regimes identified by Bromberg & Tchekhovskoy (2016): in steeper profiles (alpha > 2) the jet gradually opens up and stabilizes as it propagates, whereas in flatter profiles (alpha < 2) it gradually collimates and grows increasingly unstable. Figure 3 shows the jet stability parameter, Λ, evaluated at a fixed jet head distance, zh = 10 R ⊙, as a function of the intrinsic jet luminosity, L jet, for three representative Lorentz factor values, gammaj = 1, 10, 100, and for three representative jet opening angles, theta j = 0.017◦, 0.17◦, and 1.7◦. Reading the stability threshold (Λ > 2) off Figure 3, the most relativistic jet (gammaj = 100), which is most susceptible to the kink instability, requires the largest jet power to remain stable, L jet,min ≃ 3 × 1047 erg s−1. Producing this power from the micro-TDE wind-modified (s = 0.5) accretion rate M¤ acc ∼ 10−7 M⊙ s−1 requires a rapidly spinning black hole, a • ≳ 0.9, and hence a jet efficiency etajet ≳ 1. Because slower, less relativistic jets have progressively lower stability thresholds, a jet launched by a black hole with the same jet power lies in the stable region (Λ > 2) across the full range gammaj ≲ 100 considered here. Jet survival across the range of Lorentz factors and jet geometries considered in this work therefore makes micro-TDEs a viable central engine for ULGRB s.

GRB 250702B/EP 250702a exhibits three temporally and spectrally distinct phases. Einstein Probe detected a soft X-ray precursor approximately one day before the main burst, followed by three hard gamma-ray episodes registered by Fermi-GBM with quasi-regular spacing of ∼ 2, 825 s. The Einstein Probe localization enabled continued monitoring with Swift, NuSTAR, and Chandra, revealing a long-lived X-ray counterpart fading over days to weeks. The late t…

Improvements to AI Systems:

1. Multi-Phase Transient Classification: Train an AI system to classify gamma-ray bursts (GRBs) into distinct engine scenarios (collapsar, supermassive TDE, micro-TDE) by analyzing multi-wavelength light curves across three phases (precursor, prompt, afterglow) simultaneously, rather than treating each phase independently. The improved system can automatically identify micro-TDE signatures—such as day-long soft X-ray precursors, multi-hour prompt emission with subsecond variability, and weeks-long X-ray tails with specific temporal slopes (t−2 to t−4)—and flag candidates for follow-up observations.

2. Jet Stability Prediction from Density Profiles: Implement a physics-informed neural network that takes 3D density profiles of debris envelopes (from hydrodynamic simulations) as input and predicts jet propagation success, kink-instability thresholds, and optimal jet parameters (power, Lorentz factor, opening angle) using the analytic stability framework (Λ > 2 criterion). The improved system can rapidly evaluate thousands of simulated TDE configurations (varying black hole mass, spin, penetration factor, stellar type) to determine which produce stable, detectable jets, accelerating progenitor identification for future ULGRB detections.

3. Self-Consistent Accretion-Disk Evolution Modeling: Develop an AI surrogate model that couples fallback rates from hydrodynamic simulations with wind-modified viscous accretion physics (including disk spreading, mass-loss slope s, and time-dependent viscous timescales) to predict accretion rates and jet luminosities over weeks. The improved system can invert observed X-ray and gamma-ray light curves to infer black hole spin (a•), beaming angles (thetab), wind efficiency (s), and accretion radius—enabling rapid parameter estimation for transient events without requiring full numerical simulations.

4. Multi-Phase Light Curve Fitting with Geometric Evolution: Build an AI system that jointly fits prompt gamma-ray and X-ray light curves using a model that includes time-dependent jet beaming (e.g., linear widening thetab ∝ t) and intrinsic engine decay (Ljet ∝ t−2). The improved system can automatically distinguish between competing explanations for steep decays (e.g., beaming widening vs. external shock vs. precession) by comparing goodness-of-fit across physical models, reducing false positives in transient classification.

5. Precursor Detection and Engine Sizing: Train a deep learning model on simulated micro-TDE precursor emission (stream-fed accretion, low luminosity ∼1046 erg s−1) to predict the subsequent prompt burst properties (delay time, peak luminosity, duration) from precursor characteristics alone. The improved system can issue early warnings for ULGRB candidates and estimate central engine parameters (black hole mass, spin) hours before the main burst, enabling rapid multi-wavelength follow-up coordination.

6. Cross-Phase Temporal-Spectral Correlation: Implement a transformer-based architecture that ingests time-resolved spectral data (photon index, luminosity) across all phases and learns to map spectral evolution (e.g., hard-to-soft transitions) to physical processes (stream-fed accretion → jet breakout → disk drainage). The improved system can automatically identify the transition point between prompt and afterglow phases, estimate jet breakout times, and validate or reject micro-TDE models for individual events.

7. Simulation-to-Observation Transfer Learning: Create an AI system pre-trained on 3D arepo simulations of micro-TDEs (density, velocity, angular momentum distributions) and fine-tuned on observed GRB light curves to generate synthetic multi-wavelength observations for arbitrary progenitor parameters. The improved system can produce realistic mock datasets for survey design, optimize observing strategies for next-generation missions (e.g., Einstein Probe, SVOM), and quantify detection biases for ULGRB populations.

8. Uncertainty-Aware Parameter Inference: Develop a Bayesian neural network that predicts posterior distributions for black hole spin, beaming angle, wind slope, and disk radius from observed light curves, incorporating systematic uncertainties from jet stability criteria and radiative efficiency models. The improved system can provide robust error bars on engine parameters and flag events where multiple degenerate solutions exist (e.g., low spin with high accretion vs. high spin with low accretion), guiding follow-up theoretical work.

The longest detected gamma-ray burst, GRB250702B, exhibited seven hours of prompt gamma-ray emission, preceded by a soft X-ray precursor (about1 day earlier) and followed by a weeks-long fading X-ray tail. Lacking an established progenitor for all three phases, we propose that this ultra-long GRB (ULGRB) is powered by a jetted micro-tidal disruption event (micro-TDE), in which a spinning stellar-mass black hole (BH) disrupts a Sun-like star and launches a relativistic jet via the Blandford-Znajek mechanism. Micro-TDE debris disks have hours-to-days viscous timescales, naturally explaining ULGRB durations. Using 3D hydrodynamic AREPO simulations of a 1,M star disrupted by a 10,M BH, we show that within about1 day the debris forms a quasi-steady envelope with a low-density polar funnel (rho proportional to r-2, half-opening angle about15). Applying an analytic jet-stability framework to these profiles, we find that the r-2 funnel keeps the jet below the kink-instability threshold, enabling stable propagation and breakout for jet powers, L jet 10 47 erg s-1. We attribute the X-ray precursor to pre-disk stream-fed accretion; the prompt GRB to a tightly beamed jet (theta b 1, L gamma, iso about10 51 erg s-1) escaping the funnel, launched by a rapidly spinning BH (a about0.9); and the weeks-long X-ray decline to disk-wind mass loss (L jet proportional to t-2) combined with jet widening (theta b proportional to t, initially steepening the decay to L X,iso proportional to L jet/theta b squared proportional to t-4). Our model reproduces the multi-phase evolution of GRB250702B and establishes jetted micro-TDEs as a physically motivated ULGRB engine.