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Douglas N. C. Lin

Publications and source records attributed to Douglas N. C. Lin.

At least 19 recordsLinked to original sources
arXiv2026

Formation of Merging Black Hole Binaries Inside Massive AGN Stars

Stars embedded in the disks of active galactic nuclei (AGN) can grow to hundreds of solar masses, and the same disks are expected to host a population of stellar-mass black holes. A star may therefore capture passing black holes, turning its interior into a potential factory for forming compact binary black hole systems and, ultimately, for the gravitational-wave events seen by our detectors. We test how readily this channel operates using three-dimensional hydrodynamic simulations of black hole--star encounters. As a proof of principle, we adopt a star-to-black-hole mass ratio of $34\!:\!1$, and find that the capture does not disrupt the structure of the star: it heats the star by $10$--$30\%$, and the star loses only $\lesssim1\%$ of its mass throughout. The captured black hole loses its orbital angular momentum rapidly to dynamical friction, sinking to the stellar center within a stellar dynamical time $\lesssim10^{4}\,$s. If the star already harbors a black hole at its center, the two form a bound binary whose gravitational-wave coalescence time falls below $10^{4}\,$yr. Depending on the geometry and speed of the encounter, the resulting orbit may be nearly circular or retain substantial eccentricity. Our calculations confirm that black hole--star encounters in AGN disks are indeed a viable channel for assembling stellar-mass black hole binaries and supplying sources for gravitational-wave detectors.

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arXiv2026

Chaotic migration of LISA Extreme Mass Ratio Inspirals in a turbulent accretion disk: effect on waveform de-phasing

Gravitational wave (GW) detector LISA will observe near-coalescence extreme mass ratio inspirals (EMRIs), which typically form in galactic central accretion disks. Torques from the disk can alter the GW-driven inspiral trajectory of an embedded EMRI from the vacuum expectation, leading to potentially observable GW dephasing ($Δψ_{\rm gas}$). So far, all studies compute $Δψ_{\rm gas}$ for a thin, laminar disk, with negligible flow turbulence, whereby the disk exerts the well-understood linear torque ($T_{\rm lin}$). However, these disks must be turbulent due to magneto-rotational instability in the inner regions. Hence, we present a proof-of-concept general prescription for the turbulent torque ($T_{\rm turb}$) acting on an EMRI by modeling it as a Gaussian distribution around $T_{\rm lin}$, inspired by recent global simulations that study such torques. We compute $Δψ_{\rm gas}$ for the ``golden'' circular EMRI with total source mass $M=10^6~{\rm M}_\odot$ and mass ratio $q=5\times10^{-5}$ in its final four-year evolution at redshift $z=0.276$ and signal-to-noise ratio (SNR) $=50$ by varying turbulence amplitude $C$ ($=1$ in the aforementioned study), maximum correlation timescale ($N_{\rm max}$), Eddington ratio ${\rm f}_{\rm Edd}$, disk aspect ratio $h_0$, and turbo-viscous coefficient $α$ in a reasonable parameters space. For $N_{\rm max}=100$ orbits, we find that for $C\gtrsim{10}$, ${\rm f}_{\rm Edd}\gtrsim0.3$, $h_0\gtrsim0.03$, and $α\gtrsim0.1$, dephasings due to $T_{\rm lin}$ are unobservable but could become detectable ($Δψ_{\rm gas}>8/$SNR) if EMRIs experience turbulent torques. Hence, this work motivates running MHD simulations of accretion disks with embedded early-inspiral LISA EMRIs over long timescales to understand the imprint of the turbulent environment on their orbital parameters and gravitational waveforms.

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arXiv2026

Dynamical formation of high-eccentricity compact binaries through BH--BH*/TZO collisions

The rapidly accumulating discoveries of binary stellar-mass black-hole (sBH) coalescences, detected by LIGO, have opened a new window into the formation and evolution of compact binaries. In particular, residual orbital eccentricity may provide a distinctive signature of their formation channels. Here, we investigate a scenario in which high-eccentricity compact binaries form through the sequential capture of multiple sBHs by massive main-sequence stars, using a combination of hydrodynamical and semianalytic few-body simulations. We find that sBHs with $M_\bullet\lesssim 0.2\,M_{\star}$ can be captured by massive stars and settle into a quasi-hydrostatic black-hole star (BH*) through gas dynamical friction. A subsequent encounter with a second sBH can then produce a compact binary embedded within the stellar envelope. Our hydrodynamical simulations show that through captures with small impact parameter, some binaries are born with high eccentricity ($e\gtrsim 0.5$), with its orbital frequency already entering the LISA band. Our semianalytic models further demonstrate that gas dynamical friction can pump the eccentricity to $e_{\rm 10\,Hz}>0.9$ before gravitational-wave emission eventually circularizes the binary during the final stage of coalescence. Once formed, the binary can merge quickly in $\sim 10$ hours. This channel may operate in dense stellar environments, such as star clusters and active galactic nucleus (AGN) disks. The same mechanism can also be applied to Thorne-Żytkow objects. A high-eccentricity binary in the LIGO band could therefore provide a distinctive signature of this formation scenario.

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arXiv2026

Formation of black hole stars via star--black hole collisions

In dense stellar environments such as globular clusters and active galactic nucleus (AGN) disks, stellar-mass black holes (sBHs) may frequently collide with massive stars. We investigate this process using semi-analytic models, three-dimensional hydrodynamical simulations, and one-dimensional stellar evolution calculations, focusing on collisions between sBHs and a $100\,M_\odot$ main-sequence star. We find that gas drag retains the BH within the stellar envelope unless the impact velocity exceeds $\sim2\sqrt{G(M_\star+M_\bullet)/R_\star}$. The post-collision outcome depends primarily on the BH-to-star mass ratio. For $M_\bullet\gtrsim30\,M_\odot$, the retained envelope is either quasi-spherical or disc-like, but remains dynamically unstable because of shock heating. In contrast, for $M_\bullet\lesssim10\,M_\odot$, the collision forms a ``black hole star'' (BH*): a quasi-hydrostatic, extended stellar envelope surrounding the embedded BH. These results agree with our analytic prediction that BH* formation necessarily requires $M_\bullet\lesssim0.2\,M_\star$. Follow-up \texttt{MESA} calculations further show that, for these low-mass BHs, the shock-heated remnant thermally relaxes without triggering runaway expansion. We discuss several astrophysical implications of BH*s, including their evolution, the possibility of gravitational-wave events from BH binaries assembled within a stellar envelope, and repeated star--sBH collisions as a pathway for rapid BH growth in dense stellar systems. This mechanism may contribute to the formation of massive BHs in high-redshift nuclear star clusters and may be relevant to the origin of the ``little red dots'' discovered by JWST.

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arXiv2026

Stellar mergers and chemical element mixing: implications for the metamorphic stellar evolution in AGN disks

Chemical mixing during stellar mergers can significantly influence the subsequent evolution of the merger remnant. We perform a suite of three-dimensional hydrodynamical simulations of stellar mergers, each evolved for $\sim100$ stellar dynamical times until the remnant reaches a quasi-hydrostatic equilibrium. The simulations incorporate subgrid-scale diffusion models to capture the turbulent mixing of chemical elements. Starting with an idealized polytropic equation of state (EOS), we first identify the dominant mixing mechanisms and investigate how the merger outcome depends on the mass ratio, relative velocity, impact parameter, and stellar structure. We then extend our simulations to the context of stars embedded in active galactic nucleus (AGN) disks, using a realistic, composition-dependent EOS and AGN stellar models generated with the stellar evolution code MESA. We find that mergers with both younger metamorphic stars and H-rich accreting AGN stars can substantially rejuvenate old metamorphic stars through efficient core mixing after thermal relaxation. The merger remnants are nitrogen-enriched, with ${\rm N/O}\sim1$--3 and ${\rm N/C}\gtrsim5$, comparable to the abundances observed in the nebula surrounding SN 1987A. During subsequent stellar evolution, the remnants may converge onto the main sequence of isolated metamorphic AGN stars once they reach accretion--wind equilibrium. They may also deposit a significant amount of chemically enriched material into the AGN disk. This work provides a physical framework for connecting hydrodynamical stellar mergers with the long-term evolution of AGN stars and their observational and chemical signatures.

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arXiv2026

The complex kinematics of the young stars orbiting the supermassive black hole in the Galactic center can be explained by the presence of an intermediate mass companion of Sgr A$^\star$

The sub-parsec proximity around the Sgr A$^\star$ supermassive black hole (SMBH) in the center of the Milky Way contains an inner cluster of eccentric S-stars with randomly oriented orbits, a midway-disk of clockwise-rotating stars (CWSs), and a surrounding population of off-the-disk stars (ODSs). Despite their diverse kinematic properties, all three-populations appear to be massive (WR/O/B types) and have similarly limited life span $τ_\star \sim 6-15$ Myr. Several scenarios, including star formation induced by SMBH's close encounters with one or more gas clouds as well as impulsive close scattering by a putative intermediate-mass companion (IMC) of Sgr A$^\star$ possible an intermediate-mass black hole (IMBH), have been proposed to explain piecemeal for the origin and dynamical evolution of S-stars, CWSs, ODSs, as well as hyper-velocity stars in the Galaxy. But, their coexistence and the origin of a recently discovered zone of avoidance in S-stars' eccentricity-peri-centric-distance distribution remain enigmatic. Here, we construct a unified model to comprehensively take into account these stars' interaction with each other, their single natal disk, and an independent IMC. We show their disparate present-day orbits would only be concurrently attainable, within their multi-Myr age, under the combined influence of IMC's secular perturbation and these stars' resonant relaxation in a depleting gaseous-disk environment.

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arXiv2026

JWST unveils a high mean molecular weight atmosphere for mini-Neptune TOI-1130b: Evidence for formation beyond the water ice line

We present the combined JWST/NIRSpec G395H and NIRISS SOSS transmission spectrum of a warm mini-Neptune, TOI-1130b (3.66 R$_{\oplus}$, 19.8 M$_{\oplus}$, $T_{eq}\sim825$ K). It is part of a rare and unique multi-planet system TOI-1130, which hosts an inner mini-Neptune and an outer hot Jupiter locked in a 2:1 mean motion resonance. From the transmission spectrum of TOI-1130b we detect multiple molecules -- H$_2$O (7.5$σ$), CO$_2$ (3.3$σ$), and SO$_2$ (3.6$σ$), as well as a tentative detection of CH$_4$ ($\sim$2$σ$). We find a strong optical slope in the NIRISS/SOSS spectrum, which is consistent with TESS and CHEOPS transit depth measurements. From equilibrium chemistry retrievals we measure the atmospheric metallicity ($\log{Z/Z_{\odot}}=1.8^{+0.4}_{-0.3}$) and C/O ratio ($<$0.75 at 3$σ$ level confidence) and constrain the atmospheric mean molecular weight, $μ$ = 5.5$^{+1.3}_{-0.8}$ amu. These constraints are consistent with self-consistent forward model grids. We detect no significant He I 1.083$μ$m absorption signal and put a mass-loss rate upper limit of $10^{11}$g\s$^{-1}$. The volatile-rich high mean molecular weight atmosphere of TOI-1130b along with the `pebble-filtering' effect of the outer hot Jupiter supports the ex-situ formation scenario beyond the water ice line and subsequent migration, coherent with its present orbital architecture. A volatile-rich formation scenario could also potentially explain the location of TOI-1130b at the edge of the `radius cliff'. This result hints that the mini-Neptune population may not a homogeneous formation history; rather, volatile-rich ex-situ formation also contributes to its population.

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arXiv2026

Turbulent infall onto class 0 disks as cause of CAI brief condensation episode in the solar system

Calcium-aluminum-rich inclusions (CAIs) in carbonaceous chondritic meteorites are the oldest relics in the solar system. Notably, their radiogenic age feature a brief (100 kyr) condensation episode. In contrast, the reservoirs of the short-lived isotopes in CAIs, presumably supernovae or asymptotic giant stars, pollutes star-forming regions in giant molecular cloud complexes (GMC) over much longer (Myr) duration. Through a series of numerical simulations, we show here the possibility that, within an extended region (2$\sim$3 AU), nearly all ``pre-solar'' CAI-loaded grains in the infall clouds were sublimated and re-condensed during the early ($ \lesssim 10^5$ yr) infall and formation of class-0 disks. We adopt a set of initial conditions from a previous hydrodynamic simulation of the collapse of GMC and the formation of young stellar clusters. We analyze the evolution of the disk's thermal distribution and dynamical structure resulting from the interaction between circumstellar disks and infalling gas. Our follow-up simulations, with much higher resolution, show significant and rapid changes in the disk orientation and morphology due to the dynamic infall of external streamers. Warps and global spiral density waves commonly appear. They lead to intense dissipation which heats the gas to sufficiently high temperature to sublimate prior-generation CAIs. This solid-to-gas phase transition is followed by subsequent cooling and re-condensation. The CAI contained in the meteorites today could be the relics of the last episode of major infall onto class 0 disks.

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arXiv2026

A Robust Launching Mechanism for Freely-Floating Planets from Host Stars with Close-in Planets

Secular perturbations from binary stars and distant massive planets can drive cold planets onto nearly parabolic orbits with pericenter passages extremely close to their host stars. Meanwhile, short-period super-Earths are frequently observed around nearby stars. Gravitational scattering between these two distinct populations can lead to substantial orbital energy exchange, liberating some intruders from the gravitational confinement of their host systems. This process offers a robust formation channel for a subset of the abundant freely floating planet population. It may also significantly perturb the original orbits of close-in planets, induce collisional trajectories between close-in planets and their host stars, and disrupt the dynamical evolution of cold planets toward close stellar encounters.

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arXiv2026

Enhancement of the Rate of Tidal Disruption Events in Active Galactic Nuclei due to the Sweeping Secular Resonance Mechanism

Tidal disruption event (TDE) rates in active galactic nuclei (AGN) consistently exceed predictions from two-body relaxation, particularly in post-starburst and green valley galaxies. We explain this excess with a new mechanism: a sweeping secular resonance (SSR) driven by an intermediate-mass companion (IMC) and a depleting gaseous disk. As the disk mass declines, a resonance between stellar and IMC orbital precession sweeps through the nuclear cluster, exciting stellar eccentricities to near unity on orbital timescales far faster than gravitational relaxation. Our analytical framework, validated by N-body simulations (REBOUND), shows this mechanism requires IMC-to-SMBH mass ratios of $q \geq 10^{-3}$, disk mass ratio $p \geq 10^{-3}$, and few Myr-scale disk depletion. It is highly effective for co-orbiting IMCs but negligible for counter-orbiting ones. The TDE rate peaks at $10^{-3}-10^{-2}$ per galaxy per year for a depletion timescale $τ_{\rm dep} \sim 10$ Myr. Even lower-mass IMCs can produce significant enhancements with compact, long-lived disks. Our model naturally explains elevated AGN TDE rates and implies that a high TDE incidence is a potential tracer of hidden parsec-scale IMCs, offering testable predictions for future AGN monitoring.

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arXiv2026

Planet Migration in Protoplanetary Disks with Rims

Complex structures, including sharp edges, rings and gaps, have been commonly observed in protoplanetary disks with or without planetary candidates. Here we consider the possibility that they are the intrinsic consequences of angular momentum transfer mechanisms, and investigate how they may influence the dynamical evolution of embedded planets. With the aid of numerical hydrodynamic simulations, we show that gas giants have a tendency to migrate away from sharp edges, whereas super-Earths embedded in the annuli tend to be retained. This implies that, observationally, Jupiters are preferentially detected in dark rings (gaps), whereas super-Earths tend to be found in bright rings (density bumps). Moreover, planets' tidal torque provide, not necessarily predominant, feedback on the surface density profile. This tendency implies that Jupiter's gap-opening process deepens and widens the density gap associated with the dark ring, while super-Earths can be halted by steep surface density gradient near the disk or ring boundaries. 13Hence, we expect there would be a desert for super-Earths in the surface density gap.

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arXiv2025

Tidal disruption and evaporation of rubble-pile and monolithic bodies as a source of flaring activity in Sgr A^\star$

Sgr A*, the supermassive black hole at the center of the Milky Way, exhibits frequent short-duration flares with luminosity greater than 1e34 erg/s across multiple wavelengths. The origin of the flares is still unknown. We revisited the role of small planetary bodies, originally from the stellar disk, and their tidally disrupted fragments as a source of flaring activity in Sgr A*. We refined previous models by incorporating material strength constraints on the tidal disruption limit and by evaluating the evaporation dynamics of the resulting fragments. We analyzed the tidal fragmentation and gas-induced fragmentation of small planetary bodies with rubble-pile and monolithic structures. Using constraints from recent space missions (e.g., NASA OSIRIS-REx and JAXA Hayabusa2), we estimated the survivability of fragments under aerodynamic heating and computed their expected luminosity from ablation, modeled as fireball flares analogous to meteor events. We find that planetary fragments can approach as close as 8 gravitational radii, consistent with observed flare locations. The fireball model yields luminosities from 1e34 to 1e36 erg/s for fragments whose parent bodies are a few kilometers in size. The derived flare frequency vs. luminosity distribution follows a power law with index 1.83, in agreement with observed values (1.65 - 1.9), while the flare duration scales as L^(-1/3), consistent with observations. We consider the young stars around Sgr A* as the planetary reservoir. Given a small-body population analogous in mass to the primordial Kuiper belt and the common existence of close-in super-Earths and long-period Neptunes, we show that this planetary reservoir can supply the observed flares.

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arXiv2025

Outward Migration of a Gas Accreting Planet: A Semi-Analytical Formula

Type II orbital migration is a key process to regulate the mass and semimajor axis distribution of exoplanetary giant planets. The conventional formula of type II migration generally predicts too rapid inward migration to reconcile with the observed pile-up of gas giant beyond 1 au. Analyzing the recent high-resolution hydrodynamical simulations by Li et al. (2024) and Pan et al. (2025) that show robust outward migration of a gas accreting planet, we here clarify the condition for the outward migration to occur and derive a general semi-analytical formula that can be applied for broad range of planet mass and disk conditions. The striking outward migration is caused by azimuthal asymmetry in corotation torque exerted from cicumplanetary disk regions (connecting to horseshoe flow) that is produced by the planetary gas accretion, while the conventional inward migration model is based on radial asymmetry in the torques from the circumstellar protoplanetry disk. We found that the azimuthal asymmetry dominates and the migration is outward, when the gap depth defined by the surface density reduction factor of $1/(1+K')$ is in the range of $0.03 \lesssim K' \lesssim 50$. Using simple models with the new formula, we demonstrate that the outward migration plays an important role in shaping the mass and semimajor axis distribution of gas giants. The concurrent dependence of planets' accretion rate and migration direction on their masses and disk properties potentially reproduces the observed pile-up of exoplanetary gas giants beyond 1 au, although more detailed planet population synthesis calculations are needed in the future.

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arXiv2025

Concurrent Accretion and Migration of Giant Planets in their Natal Disks with Consistent Accretion Torque (II): Parameter Survey and Condition for Outward Migration

Migration typically occurs during the formation of planets and is closely linked to the planetary formation process. In classical theories of non-accreting planetary migration, both type I and type II migration typically result in inward migration, which is hard to align with the architecture of the planetary systems.In this work, we conduct systematic, high-resolution 3D/2D numerical hydrodynamic simulations to investigate the migration of an accreting planet. Under different disk conditions, we compared the dynamical evolution of planets with different planet-to-star mass ratios. We find that accretion of planets can significantly diminish the inward migration tendency of planets, or even change the migration direction. The migration of low-/high-mass planets is classified as Type I/II inward migration, respectively, while intermediate-mass planets, which have the strongest accretion, show an outward migration trend. We confirm that the outward migration is mainly attributed to the positive torque from the azimuthal asymmetric structures around the accreting planet, similar to Li et al. (2024). The termination of planetary mass growth is thus synonymous with the transition from outward to inward migration. For the high viscosity $α=0.04$ and disk aspect ratio height $h_0=0.05$ cases, the mass ratio range for planetary outward migration is $1\times10^{-4}\lesssim q\lesssim4\times10^{-3}$. For the low viscosity case with $α=0.001$, and/or the low disk aspect ratio cases $h_0=0.03$, the mass ratio range for the outward migration will shift toward the lower end. Our parameter survey reveals that a simple gap opening parameter determines the outward migration condition; details of the analytical interpretation are presented in Ida et al. (2025).

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arXiv2025

Stellar Evolution with Radiative Feedback in AGN Disks

Stars embedded in the inner pc region of an active galactic nucleus (AGN) experience extreme accretion conditions that significantly alter their evolution. We present one-dimensional MESA simulations of stars growing and decaying within AGN disks, implementing radiative-feedback-regulated accretion which limits stellar growth near the Eddington luminosity, as well as wind-driven mass loss. Unlike stand-alone stars in the field, these embedded stars follow unique evolutionary tracks with well-determined mass evolution and chemical yields. We distinguish two regimes: ``immortal" stars that indefinitely remain on the main sequence due to efficient hydrogen mixing; and ``metamorphic" stars that evolves off the main sequence, ultimately enriching the disk with heavy elements upon hydrogen and helium exhaustion in their cores. Results indicate that embedded stars in AGN disks can attain large masses, but gas retention and limited mixing likely render the ``immortal" track unsustainable. We show radiative feedback plays a critical role in preventing runaway growth, since it regulates the inflow to at most of order-unity the Eddington-limited mass-loss rate. Embedded metamorphic stars significantly enrich AGN disks with helium and $α$-elements, potentially explaining the observed high metallicity in broad-line regions (BLR) without excessive helium enrichment. This study underscores the critical interplay between stellar feedback and accretion physics in shaping the stellar populations and chemical evolution within AGN disks.

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arXiv2025

A dust condensation instability in AGN atmospheres: failed winds and the broad line region

Active galactic nuclei (AGN) are important drivers of galactic evolution; however, the underlying physical processes governing their properties remain uncertain. In particular, the specific cause for the generation of the broad-line region is unclear. There is a region where the underlying accretion disc atmosphere becomes cool enough for dust condensation. Using models of the disc's vertical structure, accounting for dust condensation and irradiation from the central source, we show that their upper atmospheres become extended, dusty, and radiation-pressure-supported. Due to the density--temperature dependence of dust condensation, this extended atmosphere forms as the dust abundance slowly increases with height, resulting in density and temperature scale heights considerably larger than the gas pressure scale height. We show that such an atmospheric structure is linearly unstable. An increase in the gas density raises the dust sublimation temperature, leading to an increased dust abundance, a higher opacity, and hence a net vertical acceleration. Using localised 2D hydrodynamic simulations, we demonstrate the existence of our linear instability. In the non-linear state, the disc atmosphere evolves into ``fountains'' of dusty material that are vertically launched by radiation pressure before being exposed to radiation from the central source, which sublimates the dust and shuts off the radiative acceleration. These dust-free clumps then evolve ballistically, continuing upward before falling back towards the disc under gravity. This clumpy ionized region has velocity dispersions $\gtrsim 1000$ km/s. This instability and our simulations are representative of the Failed Radiatively Accelerated Dusty Outflow (FRADO) model proposed for the AGN broad-line region.

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arXiv2025

A high mutual inclination system around KOI-134 revealed by transit timing variations

Few planetary systems have measured mutual inclinations, and even less are found to be non-coplanar. Observing the gravitational interactions between exoplanets is an effective tool to detect non-transiting companions to transiting planets. Evidence of these interactions can manifest in the light curve through transit timing variations (TTVs) and transit duration variations (TDVs). Through analysis of Kepler photometry and joint TTV-TDV modeling, we confirm the detection of KOI-134 b, a transiting planet with mass and size similar to Jupiter on a period of ~67 days, and find that it exhibits high TTVs (~20-hr amplitude) and significant TDVs. We explain these signals with the presence of an innermost non-transiting planet in 2:1 resonance with KOI-134 b. KOI-134 c has a mass $M = 0.220^{+0.010}_{-0.011} M_\text{Jup}$ and a moderately-high mutual inclination with KOI-134 b of $i_\text{mut} = 15.4_{-2.5}^{+2.8}{^\circ}$. Moreover, the inclination variations of KOI-134 b are so large that the planet is predicted to stop transiting in about 100 years. This system architecture cannot be easily explained by any one formation mechanism, with other dynamical effects needed to excite the planets' mutual inclination while still preserving their resonance.

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arXiv2025

Capture and Escape of Planetary Mean-motion Resonances in Turbulent Discs

Mean-motion resonances (MMRs) form through convergent disc migration of planet pairs, which may be disrupted by dynamical instabilities after protoplanetary disc (PPD) dispersal. This scenario is supported by recent analysis of TESS data showing that neighboring planet pairs in younger planetary systems are closer to resonance. To study stability of MMRs during migration, we perform hydrodynamical simulations of migrating planet pairs in PPDs, comparing the effect of laminar viscosity and realistic turbulence. We find stable 3:2 resonance capture for terrestrial planet pairs migrating in a moderately massive PPD, insensitive to a range of laminar viscosity (alpha = 0.001 to 0.1). However, realistic turbulence enhances overstability by sustaining higher equilibrium eccentricities and a positive growth rate in libration amplitude, ultimately leading to resonance escape. The equilibrium eccentricity growth rates decrease as planets migrate into tighter and more stable 4:3 and 5:4 MMRs. Our results suggest that active disc turbulence broadens the parameter space for overstability, causing planet pairs to end up in closer-in orbital separations. Libration within MMR typically lead to deviation from exact period ratio |Delta| \sim 0.5%, which alone is insufficient to produce the typical dispersion of |Delta| \sim 1 to 3% in TESS data, suggesting that post migration dynamical processes are needed to further amplify the offset.

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