Changing-look Active Galactic Nuclei Behavior Induced by Disk-captured Tidal Disruption Events

Recent observations of changing-look active galactic nuclei (AGNs) hint at a frequency of accretion activity not fully explained by tidal disruption events (TDEs) stemming from relaxation processes in nuclear star clusters (NSCs), traditionally estimated to occur at rates of 10−4–10−5 yr−1 per galaxy. In this Letter, we propose an enhanced TDE rate through the AGN disk capture process, presenting a viable explanation for the frequent transitions observed in changing-look AGNs. Specifically, we investigate the interaction between the accretion disk and retrograde stars within NSCs, resulting in the rapid occurrence of TDEs within a condensed time frame. Through detailed calculations, we derive the time-dependent TDE rates for both relaxation-induced TDE and disk-captured TDE. Our analysis reveals that TDEs triggered by the disk capture process can notably amplify the TDE rate by several orders of magnitude during the AGN phase. This mechanism offers a potential explanation for the enhanced high-energy variability characteristic of changing-look AGNs.


Introduction
Active galactic nuclei (AGNs) are distinctly categorized into Type 1 and Type 2 classes based on their different emission-line characteristics (Seyfert 1943;Khachikian & Weedman 1971).The distinguishing feature of Type 1 AGNs is the presence of both broad and narrow emission lines, whereas Type 2 AGNs exhibit only narrow emission lines (Netzer 2015).
Numerous AGNs have been documented to experience transitions across various spectral types, a phenomenon classified as changing-look (CL) AGNs (Maciejewski 2004;Stern et al. 2018;Sheng et al. 2020).This phenomenon poses significant challenges to the generally accepted orientationcentric AGN unified model (Antonucci 1993;Urry & Padovani 1995), where the central engine in Type 2 AGNs is obscured by a dusty torus situated along the observer's line of sight.Moreover, this phenomenon questions the conventional disk model, particularly casting doubts on its explanations concerning the disk viscosity (Lawrence 2018).
The physical origin of CL-AGNs is still under debate.The prominent theories that have been proposed include: (1) fluctuating obscuration influenced by the movements of obscuring materials, possibly due to the dusty toroidal structure with a patchy distribution obscuring the BLR (Nenkova et al. 2008;Elitzur 2012) or accelerating outflows (Shapovalova et al. 2010); (2) changes in accretion rates, according to which an AGN undergoes a series of evolutionary phases (Penston & Perez 1984;Elitzur et al. 2014;Wang et al. 2018;Yang et al. 2018); (3) TDEs where a star is disrupted by the supermassive black hole (SMBH) (Eracleous et al. 1995;Merloni et al. 2015;Blanchard et al. 2017).
In the study of CL-AGNs, polarization measurements provide critical insight into the mechanisms driving the type transitions.Hutsemékers et al. (2017) and Marin (2017) argued that high linear polarization would be observed if the transitions were triggered by obscuration.However, polarization studies on CL-AGNs (Hutsemékers et al. 2017) revealed no significant polarization, indicating that variable obscuration was not the cause behind the type transition.This aligns with recent observations of a swift "turn-on" of the quasar J1554+3629 documented by the intermediate Palomar Transient Factory (iPTF), which noted a tenfold increase in UV and X-ray continuum flux over a period of less than a year (Gezari et al. 2017).This rapid alteration suggests an intrinsic shift in the accretion rate rather than external obscuration factors.
Further supporting this theory, systematic reviews of data from the Sloan Digital Sky Survey (SDSS) uncovered additional CL quasars exhibiting similar traits (MacLeod et al. 2016;Ruan et al. 2016).The changes in the accretion rate appeared to more adequately explain the observed variations in transition timescales and emission-line properties compared to fluctuating dust obscuration.
Recent evolutionary CL-AGN studies have shown that TDEs predominantly occur in E+A galaxies (French et al. 2016;Dodd et al. 2021).The presence of significant Balmer absorption in these galaxies indicates a considerable starburst population aged approximately 0.1-1 Gyr.Despite constituting about 2% of the local galaxy population, these E+A galaxies are host to over half of the detected TDE candidates identified up to date (French et al. 2020;Hammerstein et al. 2021).This pattern indicates that a dynamic mechanism is at play, potentially amplifying the TDE rate efficiently within 0.1-1 Gyr (Law-Smith et al. 2017).Notably, a small but significant fraction of E+A TDE hosts exhibit preflare AGN activity, as claimed in recent research (French et al. 2020), hinting that the occurrence of TDEs might be boosted by the existence of an earlier accretion disk.As a result, the potential of TDEs in driving CL phenomena, as proposed by various researchers, holds considerable promise.
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In this Letter, we propose a new mechanism that occurs during the AGN phase, where the preexisting AGN disk interacts with stars in the nuclear star cluster (NSC), leading to rapidly captured TDEs.This mechanism can potentially explain the enhanced TDE rate required during the AGN phase in CL-AGNs.The Letter is structured as follows: In Section 2, we discuss the TDE rate arising from NSC relaxations from dormant SMBHs.Following that, in Section 3 we investigate the time-dependent TDE rate from disk TDE and captured TDE during the AGN phase.Utilizing the calculated TDE rate, we estimate the fraction of CL-AGNs in the overall AGN population in Section 4. Finally, we discuss and summarize our findings in Section 5.

TDE Rate in Quiescent Galaxies
TDEs are crucial for the growth of massive black holes in stellar systems, especially in nuclei clusters.These events occur when stars come within a distance smaller than the tidal radius, r t , which is given by where, M • is the black hole mass, and M * and R * represent the mass and radius of the disrupted stars, respectively (Hills 1975;Lacy et al. 1982;Rees 1988).The maximum specific angular momentum allowed for tidal disruption is In galaxies with dormant SMBHs, two-body relaxation processes in NSCs primarily fuel TDEs.The NSC surrounding an SMBH follows a power-law density profile (Merritt 2013): where r is the distance from the SMBH, γ NSC is the radial density power-law index, m is the average mass of the stars in NSC chosen to be 1M e , and σ NSC is the velocity dispersion of the NSC based on the empirical M • -σ NSC relation (Kormendy & Ho 2013).In the NSC, the two-body relaxation process causes energy and angular momentum fluctuations in stars, characterized by the relaxation time t rel , defined as (Jeans 1913(Jeans , 1916;;Chandrasekhar 1942;Binney & Tremaine 1987) where is the specific binding energy with orbit semimajor axis a.
is the maximum specific angular momentum for a given E, N = 2M • /m is the number of stars within the NSC, Λ is the Coulomb logarithm, and T is the orbital period.For circular orbits, a is equivalent to r in Equation (2).Additional effects, such as resonant relaxation (Rauch & Tremaine 1996;Rauch & Ingalls 1998;Hopman & Alexander 2006;Kocsis & Tremaine 2011), can serve as an additional source of TDEs early in the empty loss cone regime.However, the steady rate of TDEs mainly supplied by the full cone does not change significantly due to resonant relaxation.Therefore, we neglect the contribution of the resonant relaxation in our background TDE rate calculations.
The TDE rate can be obtained by using the dimensionless parameter λ(E), which represents the fraction of stars with that particular energy E that undergo disruption each orbital period (Frank & Rees 1976;Lightman & Shapiro 1977;Rees 1988): The TDE rate depends on whether the loss cone is "full" or "empty."The full loss cone regime occurs when ΔL is significantly larger than L TDE , leading to a faster relaxation refilling rate than TDE consumption.In contrast, the empty loss cone regime happens when ΔL is much smaller than L TDE , resulting in a faster SMBH star consumption rate compared to the relaxation refilling rate.
The inner region of the NSC is in the empty loss cone regime due to a smaller semimajor axis and ΔL, whereas the outer region is in the full loss cone regime, where ΔL typically exceeds L TDE .In the empty and full loss cone regimes (Frank & Rees 1976;Lightman & Shapiro 1977;Rees 1988;Magorrian & Tremaine 1999;Stone & Metzger 2016), In the early stage when the inner loss cones have not been completely depleted, the overall TDE rate of the NSC is dominated by the empty loss cone region as λ empt (E) ?λ full (E).As the inner loss cones are completely depleted, the overall TDE rate enters into a steady state, where the TDEs are supplied relaxations in the full loss cone regime.The steady-state TDE rate from two-body relaxation can be approximated by substituting λ(E) = λ full (E) in Equation (7).The contributed region of the NSC is r ä [r c , r m ], Ω = 4π, where r c is the critical radius that ΔL = L TDE and r m (Equation ( 3)) is the size of the NSC.
Figure 1 shows the TDE rate from relaxations as a function of time for different SMBH masses and NSC profiles.As indicated in this figure, the TDE rate can be higher than the steady-state TDE rate in the early stage (with λ(E) = λ empty (E)) before the inner loss cone depletion.

Enhanced TDE Rate in AGN Phase
Once the AGN activates, an accretion disk forms around the SMBH, significantly altering the orbital evolution of stars in the NSC and affecting the TDE rates during the AGN phase.

Disk Models
The accretion disk can be simply characterized by three parameters: the accretion rate efficiency η d , the Toomre parameter Q d , and the viscosity parameter α d , which represents the efficiency of angular momentum transport from disk turbulence.The accretion rate can be approximated as follows: where  M represents the accretion rate,  M Edd denotes the Eddington accretion rate, M SMHB represents the mass of the SMBH, L Edd is the Eddington luminosity, and ò d is a constant assumed to be 0.1.
The disk surface density Σ can be described by where r represents the distance from the SMBH, H is the scale height, and Ω d denotes the orbital frequency given by GM r Beyond the simple α disk model, we also adopted the SG (Sirko & Goodman 2003) and TQM (Thompson et al. 2005) disk models.Figure 2 illustrates the surface density and specific scale height of these three disk models for a 10 8 M e SMBH.Given that the disk-captured TDE rate is highly sensitive to the surface density in the inner region of the disk, these three different disk models are expected to yield significantly different disk-captured TDE rates.

Disk TDE from In Situ Orbits
During the AGN phase, a portion of stars in the NSC with orbit inclination below the AGN disk specific scale height h intersect with the AGN disk (Artymowicz et al. 1993).Those initially fully embedded stars undergo continuous interactions with the disk.
For prograde stars, they evolve into circular orbits due to aerodynamic drag and dynamical friction, eventually corotating with the disk.Once the star becomes corotating with the disk, both aerodynamic drag and dynamical friction become very weak.However, the Lindblad resonance from the density wave inspired by the star comes into play, slowly damps the orbital  semimajor axis on the timescale of (Tanaka et al. 2002) In a turbulent disk, the orbital decay timescale may be lengthened by stochastic migration (Nelson 2005;Baruteau & Lin 2010;Zhu et al. 2013;Wu et al. 2024).Due to the orbit circularization and the long timescale of semimajor axis damping from the Lindblad resonance, solar-type stars (m ; 1M e ) with prograde orbits have a negligible contribution to the TDE rate.However, self-regulated star formation (Goodman 2003;Chen et al. 2023) can significantly increase the mass budget of the embedded prograde stars.Moreover, stars formed or captured by the disk also gain mass through disk-gas accretion (Cantiello et al. 2021;Li et al. 2021), which would reduce τ pro .But these stars evolve off the main sequence within τ å ∼ 3-5 Myr and return most of its envelope to the disk (Ali-Dib & Lin 2023) before they migrate over significant radial range from their birth place.Indeed, the observed broadline ratios indicate super solar metallicity, independent of redshifts and the observed differential metallicity between the broad-line and narrow-line regions suggests in situ pollution in AGN disks (Huang et al. 2023).These data provide support for the assumption that the stars formed in AGN disks generally demise before they venture to and undergo tidal disruption in the proximity of SMBHs so that λ pro is negligible.
Retrograde stars, moving against the disk rotation, experience significant aerodynamic drag, rapidly decreasing their semimajor axis.With a geometric cross section  pR 2 where R å is the stellar radius, this fast-damping timescale is estimated as where S = p * * m R 2 is the surface density of the star, Σ is the surface density of the AGN disk, T is the Keplerian period, and 1 3 is the Roche radius.With large relative speed between them, the accretion of disk gas onto stars with retrograde orbits is negligible.Also note that drag heating increases R å , r t and decreases Σ å and τ ret .Since τ ret = τ pro , retrograde stars primarily contribute to the in-disk TDE rate due to their shorter damping timescale (McKernan et al. 2022).
Stars with initial inclination above the specific height h of the AGN disk have their orbital inclinations damped by disk-star interactions, eventually being captured in prograde orbits (Artymowicz et al. 1993).Due to their large velocity relative to the disk gas, this effect prevents retrograde orbit stars from being refueled by disk capture (Wang et al. 2023b;Generozov & Perets 2023).Thus, the total mass budget for retrograde indisk TDEs is determined by the geometric intersection of the AGN disk and NSC: for a cluster with radial density powerlaw index γ NSC = 2.
The dotted lines in Figure 3 show the total mass budget of disk TDE for different masses of SMBH and NSC power-law index γ NSC .Despite their contributions, the total mass budget remains below 0.001% of the NSC mass.The shaded region in this figure depicts the TDE desert, which corresponds to the scenario where the tidal disruption radius of a 1 M e star by a nonspinning SMBH falls within the SMBH's event horizon.However, it should be noted that factors such as the actual physical tidal disruption radius (in contrast to the zero-order Hills argument), the type of the star, and the spin of the SMBH can significantly influence this limit (Coughlin & Nixon 2022).Massive stars can still undergo tidal disruption when encountering high-spin SMBHs with masses exceeding the limit presented here.
Similar to relaxation TDE, we can define λ disk (E) to calculate the rate of in-disk TDE In the limit of small h, Σ/2hr reduces to the midplane density, and λ disk remains finite and small.One can prove that 1 and that it is independent of α d .Thus, a larger η d and a smaller Q d will result in a larger disk-captured TDE rate.

Captured TDE from Disk-Star Interactions
In addition to stars initially situated in the AGN disk, stars from the NSC interact with the AGN disk due to aerodynamic drag.This interaction alters the stars' orbital properties, eventually resulting in their capture by the disk (Artymowicz et al. 1993;Wang et al. 2023b;Generozov & Perets 2023).This process preserves the quantity ( ) (where L is specific angular momentum and I is orbital inclination), as proven in Wang et al. (2023b).The resulting captured semimajor axis can be given by when the final orbit is circularized and coplanar.The captured objects will shrink their semimajor axis by a factor of , where a 0 , e 0 , and i 0 are the initial semimajor axis, eccentricity, and inclination, respectively.Stars with will be tidally disrupted by the SMBH during the disk capture process.
Figure 4 illustrates this type of captured TDE, highlighting an additional population of NSC stars with high orbital inclinations prone to disruption during the AGN phase.The associated timescale for this disk-captured TDE is given by (Wang et al. 2023b) and the total mass budget can be estimated as where r cap is the truncation radius beyond which I TDE is below the disk specific scale height.Utilizing we can compute the rate of these captured TDE similar to relaxation TDE by substituting λ(E) = λ cap (E) in Equation ( 7), but with the total mass budget limited by Equation ( 22).Figures 3 and 5 reveal the mass budget (Equations ( 17), ( 22)) and TDE rates (Equation ( 7) with appropriate λ and S TDE ), respectively, for different SMBH and NSC models.Captured TDEs (with ), owing to a much higher total mass budget, potentially constituting up to 1% of the total NSC mass for steep NSCs.During the AGN phase, disk-star interactions predominantly enhance TDE rates through the disk capture mechanism, especially for AGNs hosting massive SMBHs (∼10 8 M e ).

CL-AGN Activities from Captured TDE
The weak broad H α emissions and Swift/XRT observations of X-ray emissions (Parker et al. 2016;Mathur et al. 2018;Wang et al. 2023a) indicate that the "turn-on" timescale of about 1 yr for some repeating CL-AGNs coincides with the typical TDE timescale (Rees 1988), described by the equation: This similarity in timescales positions TDEs as potential mechanisms underlying CL-AGN behavior.Recently, Bandopadhyay et al. (2023) identified a more precise timescale for TDEs through numerical simulations.They found that the timescale is approximately This value is smaller than the estimate provided in Equation (24) (the difference is less than a factor of ∼2).This refinement slightly affects our upcoming discussion on the fraction of CL-AGNs relative to all AGNs.The fraction of CL-AGNs relative to all AGNs can be approximated by . Schematics of captured tidal disruption events (TDEs) resulting from disk-star interactions (not to scale).For a given semimajor axis, the green region indicates orbits with an orbital inclination greater than the critical inclination I TDE .Stars in these orbits with a capture timescale (given by Equation ( 21)) shorter than the AGN disk lifetime will be captured by the disk within the tidal disruption radius.Conversely, stars with orbital inclinations smaller than I TDE will be captured by the disk without undergoing direct TDEs.
(the above approximation is valid provided  N TIDE fall off less rapidly than t −1 ), which results in a range of 10 −5 -10 −4 for relaxation TDEs, aligning with the findings reported in Yang et al. (2018) and Yu et al. (2020).Recent spectroscopy analysis of mid-infrared variability-selected SDSS partially obscured AGNs suggests a CL-AGN ratio as high as a few percent (Wang et al. 2023a), significantly exceeding earlier estimates.This elevated ratio challenges the viability of TDEs as an explanation, especially considering the relaxation TDE rate of a mere 10 −4 -10 −5 yr −1 per galaxy.The occurrence of repeated CL activities on the timescale of decades in some AGNs further complicates the viability of the TDE explanation.
The light curves of TDEs taking place in the plane of an AGN disk, with sufficiently high density to break up the debris, could be quite different from simply adding together the light curves of regular TDEs and those of AGN disks.The initial increase in brightness might come from the close passage of a star, which shakes up and heats the inner part of the disk (Chan et al. 2019;Ryu et al. 2024).This perturbation might lead to a temporary increase in the rate at which material falls into the black hole, until the disk settles down again, based on its local thermal timescale.Therefore, we expect to see a noticeable change in the AGN's state from such a close pass, similar to what we see in AGNs that change appearance, with significant X-ray flaring (Padmanabhan & Loeb 2021).
Nevertheless, our findings illustrate a significant increase in the TDE rate during the initial AGN phase due to disk-captured TDEs.This effect could be very significant in massive AGNs with a cuspy NSC.This enhanced rate 10 −2 -10 0 yr −1 can plausibly account for the high incidence of repeating CL phenomena and the elevated CL-AGN ratio.
Figure 6 shows CL-AGN fractions among all AGNs, as anticipated by relaxation TDE and AGN-enhanced TDE for  various SMBH masses and NSC models.Notably, the AGNenhanced TDE rate predicts a CL-AGN fraction several orders of magnitude higher than that of the relaxation TDE rate, particularly for massive SMBHs accompanied by cuspy NSCs.Observationally, in searches for TDEs, AGNs are often excluded due to the potential for anomalous flares that do not signify tidal disruption and subsequent accretion, as noted by Gezari (2021).If the TDE rate in AGNs is equivalent to that in quiescent galaxies, this approach would result in excluding only a small fraction of the total TDEs, given that AGNs comprise approximately 1% of all galaxies.However, we demonstrate that the TDE rate in AGNs can be several orders of magnitude higher than in quiescent galaxies, primarily due to the disk-captured process.Consequently, a significant proportion of TDEs may have been overlooked in previous surveys.Future TDE surveys should, therefore, give greater consideration to the occurrences of TDEs in AGNs.

Relaxations with the Presence of AGN Disk
The presence of the AGN disk gives rise to disk-star interactions.Over time, the disk will gradually capture stars from the NSC, which results in a depletion of stars during the relaxation process.Once the stars are captured by the disk, they tend to maintain a near-circular orbit due to the strong circularization induced by the disk-star corotation resonance for prograde stars and eccentricity damping from aerodynamic drag for retrograde stars.This makes it difficult for them to relax back into the loss cone region, characterized by small angular momentum.Consequently, the capture process may alter the relaxation process, rendering the relaxation TDE less efficient compared to scenarios with a dormant SMBH.
MacLeod & Lin (2020) calculated the relaxation TDE rate in the presence of AGN disks.They discovered that the loss cone flux is only diminished in the inner region of the NSC, without significantly affecting the overall relaxation TDE rate.This is because the rate is predominantly determined by the full loss cone flux in the outer region.

Captured TDE Properties and Connection to QPE
For disk-captured TDEs, before the stars enter the tidal radius of the SMBH, the disk-star interaction continually damps the eccentricity of the stellar orbits.Consequently, as the star enters the tidal radius, its orbital eccentricity might have been significantly reduced by the disk capture process.Unlike in relaxation TDEs where stars approach the SMBH in a nearly parabolic orbit, stars in disk-captured TDEs will approach the SMBH with a much smaller eccentricity due to disk circularization.This means that disk-captured TDEs might be more gentle than the typical TDEs from relaxations.Scenarios such as partial disruption or tidal peeling (Guillochon & Ramirez-Ruiz 2013;Ryu et al. 2020;Xin et al. 2023) might occur.Cufari et al. (2022) demonstrated that the accretion rate exhibits two peaks and a sharp cutoff if the eccentricity is smaller (less than approximately 0.98 for typical parameters) compared to a normal TDE with e ∼ 1.Consequently, the properties of disk-captured TDEs, as well as TDEs originating from AGNs, could exhibit distinct characteristics from those of normal TDEs.This distinction might lead to confusion when differentiating them from other AGN-related activities.
Other than this, the internal tidal dissipation could become sufficiently strong to cause runaway inflation for inspiraling stars on nearly circular orbits.As the star inflates, it is easier for the star to lose mass through the inner Lagrangian point, which could slow down the inspiral rate (Gu et al. 2003), extending the timescale for TDEs.This might explain why some CL-AGNs with luminosity variations last longer than the timescale of normal TDEs.Note that Faber et al. (2005), Manukian et al. (2013), andCufari et al. (2023) suggested that the higher-order moments of a black hole's gravitational field can result in ejection of a star.According to their findings, the maximum amount of energy that can be imparted to a star by tidal forces is approximately 2% of the star's binding energy.This limitation implies that the tidal forces are inefficient, potentially leading to a reduction in the star's size rather than inflation.However, these studies assume parabolic stellar orbits, where tidal forces are predominantly efficient at the pericenter.In contrast, for disk-captured TDEs, the stars orbit the SMBH in nearly circular orbits.In such scenarios, tidal dissipation is more effective at transferring binding energy into the star.
More importantly, the light-curve power-law index of −5/3 is predicted based on the frozen-in approximation with a fully disrupted star, wherein all disrupted materials fall into the SMBH on Keplerian orbits (Rees 1988;Lodato et al. 2009).However, for partial TDEs and tidal peeling events, the existence of the remnant stellar core might alter the light-curve power-law index from −5/3 to −9/44 (Coughlin & Nixon 2019;Wang et al. 2021).Therefore, the abnormal light-curve power-law index in CL-AGNs cannot negate the potential TDE mechanism.
Since the disk-captured star could approach the SMBH in a nearly circular orbit, particularly if the circularization completes before the star enters the tidal radius, the interaction between the AGN disk and a closely circled stellar orbit may lead to quasiperiodic eruptions (QPEs; Miniutti et al. 2019;Giustini et al. 2020;Arcodia et al. 2021;Chakraborty et al. 2021;Linial & Metzger 2023).These QPEs might also originate from the disk capture process, although more detailed hydrosimulations are necessary to confirm whether such a state can be achieved through disk-star interactions.If the majority of disk-captured TDEs enter this QPE phase, and disk-captured events are the underlying mechanism for CL-AGNs, QPEs could potentially serve as a precursor to CL-AGN "turn-on."

Conclusions
In the analysis of TDEs during the AGN phase of galaxies, we confirmed that beyond background relaxation TDEs, there exist two prominent mechanisms responsible for TDE occurrences: disk TDEs and captured TDEs.Disk TDEs emerge from the rapid semimajor axis damping experienced by fully disk-embedded retrograde stars, setting them apart from captured TDEs, which occur when the disk apprehends stars from the NSC, provided the captured semimajor axis is lesser than the tidal radius of the SMBH.
In a comparative study of these mechanisms, it has been found that the rate of disk TDEs is considerably less than that of captured TDEs, especially noticeable around SMBHs with smaller masses.In the vicinity of low-mass SMBHs, the rate of disk TDEs can even be lower than the background relaxation TDE rate.Contrarily, captured TDEs boost the overall TDE rate significantly during the AGN phase, by several orders of magnitude than the background relaxation TDE rate, therefore indicating a potential mechanism for CL-AGNs.
Moreover, the disk-captured TDE mechanisms show unique signatures, distinguishing captured TDEs clearly from relaxation TDEs.The uniqueness of captured TDEs lies in the lower eccentricity of the stellar approaches to the SMBH, a consequence of the eccentricity damping experienced during the capture process.Unlike relaxation TDEs, which see stars nearing the SMBH in nearly parabolic orbits, captured TDEs exhibit a more gentle approach, potentially resulting in phenomena such as partial TDEs, tidal peelings, or QPE precursors.

• 3 .
The parameters η d and Q d are assumed to be constant values set to 1(Lin & Pringle 1987); α d is set to be 0.1(Lin et al. 1988), although the α d value is quite uncertain.The α d value from magnetorotational instability depends on the net field strength (Zhu & Stone 2018), while the α d value from gravitational instability depends on the disk cooling rate (Gammie 2001; Deng et al. 2020).

Figure 1 .
Figure 1.TDE rate from relaxations around dormant SMBHs as a function of time.The radial power-law index of the NSC γ NSC = 2.

Figure 2 .
Figure 2. Surface density Σ and specific scale height h of three different disk models adopted in this Letter.

Figure 3 .
Figure 3.Total mass budget for disk/captured TDE and total disrupted mass for relaxation TDE during the lifetime (assumed to be 10 8 yr) of the AGN for various SMBHs and NSCs.The dashed red line indicates the total mass of the NSC.

Figure 5 .
Figure 5. TDE rates of different mechanisms (indicated by different line styles) and disk models (indicated by different colors) during the AGN phase for different SMBHs and NSC models.

Figure 6 .
Figure 6.Fraction of CL-AGN among all AGNs as a function of SMBH masses for different TDE mechanisms.