AT2021lwx: Another Neutrino-Coincident Tidal Disruption Event with a Strong Dust Echo?

We discuss the possible association of an astrophysical neutrino (IC220405B) with the recently reported, extremely energetic tidal disruption event (TDE) candidate AT2021lwx (ZTF20abrbeie, aka “Scary Barbie”) at redshift z = 0 . 995. Although the TDE is about 2 . 6 ◦ off the direction of the reconstructed neutrino event ( outside the 90% C.L. localization region), the TDE candidate shares some important characteristics with so far reported neutrino-TDE associations: a strong infrared dust echo, high bolometric luminosity, a neutrino time delay with respect to the peak mass accretion rate of the order of hundred days, and a high observed X-ray luminosity. We interpret this new association using an isotropic emission model, where neutrinos are produced by the collision of accelerated protons with infrared photons. After accounting for the high redshift of AT2021lwx (by interpreting the data in the SMBH frame), we find that the expected neutrino fluences and neutrino time delays are qualitatively comparable to the other TDEs. Since data are only available up to 300 days post-peak in the SMBH frame, significant uncertainties exist in the dust echo interpretation, and therefore in the predicted number of neutrinos detected, N ν ≃ 3 . 0 × 10 − 3 − 0 . 012. We recommend further follow-up on this object for an extended period, and suggest refining the reconstruction the neutrino arrival direction in this particular case.


INTRODUCTION
Tidal disruption events (TDEs) are energetic optical transients that originate from stars that are tidally destroyed as they transit within the tidal radius of a supermassive black hole (SMBH).Approximately half of the stellar mass remains bound, and its subsequent accretion could power an electromagnetic flare that lasts from months to years (Rees 1988;Phinney 1989).Nowadays, increasingly detailed multi-wavelength observations of TDEs by the Zwicky Transient Facility (ZTF, Bellm et al. 2019), the Wide-field Infrared Survey Explorer (WISE, Wright et al. 2010), and X-ray/radio surveys, such as eROSITA (Sazonov et al. 2021) and Very Large Array Sky Survey (VLASS, Lacy et al. 2020), facilitate comprehensive modeling of the radiation processes and cosmological distributions of this source population (e.g., van Velzen et al. 2021a;Hammerstein et al. 2023;Yao et al. 2023).
Among the hundred or so observed TDEs and TDE candidates, three have been found to be coincidentin time and position -with three IceCube astrophysical neutrino events.They include an event that was classified as a TDE with high confidence, AT2019dsg (Stein et al. 2021), and two TDE candidates, AT2019fdr (Reusch et al. 2022) and AT2019aalc (van Velzen et al. 2021b) (associated neutrinos: IC191001A, IC200530A and IC19119A, respectively).These three candidate neutrino emitters share some prominent similarities.For instance, they all exhibit high optical/ultra-violet (OUV) luminosities accompanied by bright and delayed infrared (IR) emissions, which have been interpreted as dust echoes, i.e., reprocessed radiation from the OUV and X-ray bands into IR wavelengths by surrounding dust (Lu et al. 2016;Jiang et al. 2016;van Velzen et al. 2016).These three TDEs are located within the 90% C.L. localization region of the corresponding neutrino events (Abbasi et al. 2023), with an angular deviation ∆θ ∼ 1.3 • − 1.9 • (van Velzen et al. 2021b).The neutrino events were detected with significant time delays -approximately 150-300 days -after the OUV peak in the observer's frame.
Recently, two additional dust-obscured TDE candidates, exhibiting strong dust echo signatures, were reported to be spatially and temporally coincident with Gold-type (the chance of astrophysical origin is larger than 50%) astrophysical neutrinos events at IceCube (Jiang et al. 2023).
Here, we point out the potential coincidence between another energetic TDE candidate, AT2021lwx (ZTF20abrbeie, aka "Scary Barbie"), and an IceCube neutrino event, IC220405B (Necker et al. 2022).Noting that AT2021lwx is not within the 90% confidence level (C.L.) area of the neutrino event, and IC220405B is classified as one Bronze-type neutrino alert (where the chance of astrophysical origin is larger than 30%), the probability of the neutrino-correlation of AT2021lwx is lower than the candidates mentioned before.However, AT2021lwx shares some prominent signatures with other neutrino-coincident TDEs and candidates, encompassing a strong dust echo which explains the IR observations, high bolometric OUV and X-ray luminosities, and a comparable time delay of the neutrino detection.These similarities suggest that AT2021lwx may be another member of a class of neutrino-emitting TDEs, for which a common underlying mechanism exists.In this context, it is interesting to investigate the neutrino correlations and multi-messenger implications.
In this paper, we offer an interpretation of AT2021lwx in terms of a model where neutrinos and EM cascade emissions originate from accelerated protons colliding with IR target photons, similar to the one presented in Winter & Lunardini (2023) and Yuan & Winter (2023) (model "M-IR" therein).We first discuss the likelihood of the neutrno correlation in Sec.2.1.Given the crucial role of the IR radiation, in Sec.2.2, we fit the IR light curve using early-time (ET) component in addition to a delayed component produced by the spherical dust torus, and discuss the uncertainties arising from the absence of late-time IR data.In Sec. 3, we further employ an isotropic wind model, constructed based on OUV/IR/X-ray observations, as described in Winter & Lunardini (2023) and Yuan & Winter (2023), to investigate the spectral and temporal signatures of neutrino and EM cascade emissions produced within the dust radius.In addition, we compare AT2021lwx to AT2019dsg/fdr/aalc in terms of bolometric OUV and IR luminosities, as well as predicted neutrino fluences, and discuss the γ-ray constraints and the likelihood of producing one neutrino event at IceCube in Sec. 4.

Localization of AT2021lwx and IC220405B
Motivated by the similarities among the neutrinocoincident TDE candidates, here we investigate the potential spatial and temporal coincidence between AT2021lwx and IC220405B (Necker et al. 2022).AT2021lwx was initially discovered by ZTF on the 13th of April 2021 and was classified as a TDE candidate at redshift of z = 0.995 (Subrayan et al. 2023).The peak bolometric optical luminosity, after correcting for extinction, is exceptionally high, reaching, 10 46 erg s −1 .Multi-wavelength follow-ups have revealed bright X-ray and IR emissions (Wiseman et al. 2023).The latter has been preliminarily interpreted as a dust echo.We point out one Bronze-type neutrino alert, IC220405B 1 , which is close to the TDE direction with an angular offset of ∆θ ≃ 2.6 • degrees, and arrived approximately 370 days after the OUV peak, equivalent to ∼ 185 days in the SMBH rest frame.
Fig. 1 depicts the locations of AT2021lwx and IC220405B.We obtain the 2σ and 3σ containment areas of the neutrino event by performing the Gaussian extrapolation of the 90% C.L. box 2 (the dashed red rectangular, Necker et al. 2022) and applying a systematic uncertainty of arrival directions σ sys = 1.0 • motivated by the estimates in IceCube Collaboration (2013) and Plavin et al. (2020).We find that AT2021lwx locates in the 3σ containment contour in the refined localization analysis.Caution must be exercised when establishing the significance of the association since it is inferred from the initial 90% C.L. localization box, and a more precise localization constraint requires detailed point source reconstructions from the IceCube Collaboration.

Dust echo modeling
Modeling of ZTF photometry indicates that AT2021lwx was produced by the tidal disruption of a massive star of M ⋆ ∼ 14 M ⊙ by a SMBH of M BH ∼ 10 8 M ⊙ (Subrayan et al. 2023).However, it is important to note that this object is not exclusively identified as a TDE, given the low likelihood of such an event involving a massive star.At first, it was classified as a flare from an active galactic nucleus (AGN, Grayling et al. 2022); another plausible interpretation is an unusually powerful accretion of a giant molecular cloud by a SMBH of 10 8 − 10 9 M ⊙ (Wiseman et al. 2023).Nevertheless, the classification does not significantly influence our multi-messenger modeling, since our model ingredients, such as the proton injection rate and target photon fields, are build on the OUV/IR/Xray observations, including the light curves and the spectra.
For AT2021lwx, the IR light curve was measured by WISE in W1 and W2 bands before and after the OUV peak.The IR data points in the upper panel of Fig. 2 and the OUV light curve of AT2021lwx are taken from  Wiseman et al. (2023), respectively, following bolometric corrections.The OUV and IR spectra are consistent with black body distributions and the temperatures are measured to be T OUV ∼ 1.2 − 1.6 × 10 4 K (1.03−1.38 eV) and T IR ∼ 10 3 K (0.9 eV) in the SMBH rest frame (Subrayan et al. 2023;Wiseman et al. 2023).Using these temperatures, we calculate the bolometric correction factors, defined as the ratio of the energy flux from the entire black body spectrum to the energy flux in the r/g/W1/W2 bands.

Subrayan et al. (2023) and
From that, we then obtain the OUV and IR bolometric luminosities, denoted as L OUV and L IR , respectively.We stress that here L OUV is corrected for extinction; as will be clear from the derivation in the reminder of this section.The red square markers in Fig. 2 show L IR as inferred from WISE measurements, as a function of the time in SMBH rest frame, e.g., (t obs − t pk )/(1 + z), where t obs is the time in the observer's frame and t pk is the time that OUV luminosity peaks.The red solid curve in the lower panel represents L OUV for the time interval where data exist; its extrapolation to later times is shown as a red dotted curve.We find the peak val- ues of L OUV and L IR to be ≃ 1.2 × 10 46 erg s −1 and ≃ 3.1 × 10 45 erg s −1 , respectively.Our bolometric OUV luminosity, L OUV , is roughly a factor of ∼2 higher than the value in Subrayan et al. (2023), since we corrected it for absorption by ambient dust, which induces the dust echo.This correction will be introduced in the end of this section.
The first impression we obtain from Fig. 2 is that AT2021lwx exhibits a comparable neutrino time delay with the other three TDEs in the SMBH frame (see the vertical lines in Fig. 2), and its flat/steady IR luminosity after the OUV peak is consistent with a dust echo.This dust echo interpretation is supported by the measured IR temperature, T IR ∼ 10 3 K, which is below the dust sublimation temperature of T sub ∼ 1800 K (van Velzen et al. 2016).
We neglect the contribution of X-rays to the dust echo as was done in Winter & Lunardini (2023) since the X-ray emission was first observed more than 300 days after the OUV peak by Swift X-ray Telescope (XRT) and the unabsorbed luminosity was inferred to be L X ∼ 1.5 × 10 45 erg s −1 ≪ L OUV (Wiseman et al. 2023).
To fit the bolometric IR luminosity, we model L IR as the convolution of L OUV with a (normalized) time spreading function f (t), which depends on the spatial distribution of the surrounding dust (Reusch et al. 2022;Winter & Lunardini 2023): where ϵ dust < 1 represents the fraction of the incident radiation that is re-processed to IR radiation by the illuminated dust, and ϵ Ω is the solid angle coverage factor of the dust distribution.Our chosen form of f (t) is inspired from the IR lightcurve in Fig. 2. We notice that, unlike AT2019dsg/fdr/aalc, whose IR emissions are very weak before the OUV peak, for AT2021lwx the IR light curve seems to have a component that evolves like L OUV at early times.The late time evolutions of L IR and L OUV suggest that the former may eventually overtake the latter, and persist over a longer time scale.These considerations lead to a two-component model of the echo, where the early-time component is attributed to either anisotropic dust distribution or the pre-existing dust around the SMBH (with no time delay with respect to L OUV ), whereas the late-time part is attributed to a dust torus similar to those of AT2019dsg/fdr/aalc.Fig. 3 schematically illustrates the physical picture of the spherical and early-time components of the dust echo, where the SMBH, accretion disk, disk corona, isotropic wind envelope, dust torus and potentially a jet are shown.The red dashed lines indicate the optical paths that cause the the time delay of the dust torus component due to the extended dust torus.Observationally, 2∆T IR is comparable with the IR time delay defined as the time difference between the IR and OUV peaks in the SMBH frame, with which we can infer the radius of the inner edge of dust torus, i.e., R dust ≃ c∆T IR .An external dust cloud, responsible for the undelayed component of L IR , is also shown in the figure.Formally, in the function f (t), the early-time component is represented by a Dirac Delta, f ET (t) = δ(t), whereas the torus component can be represented by the commonly used box function (see, e.g., Reusch et al. 2022 Combining f ET and f S , we explicitly write down the normalized time spreading function where the weighting parameter 0 ≤ λ ≤ 1 represents the fraction of total IR power that can be attributed to LoS dust, and H(x, a, b) is the step function, e.g., We assume an overall dust echo efficiency ϵ dust ϵ Ω ≃ 0.3 − 0.4 comparable to Winter & Lunardini (2023) and use Eqs. 1 and 2 to explain the bolometric IR light curve.Combining ϵ dust ϵ Ω and ET weighting factor λ, we infer the dust echo efficiencies for the early-time component and the spherical dust torus component respectively as λϵ dust ϵ Ω and (1 − λ)ϵ dust ϵ Ω .The best fit values of λ and ∆T IR are given in Table 1, whereas the best-fit IR light curves are shown in the upper panel of Fig. 2. Since the IR data is only available up to 300 days after the OUV peak and the IR light curve maintains a flat shape until the latest data point, the IR time delay is therefore uncertain, which is illustrated by the magenta shaded area.The solid magenta line predicts immediate decrease after the latest data point, e.g., ∆T IR = 180 d, while the dashed-dotted magenta line corresponds to a more extended dust torus R dust ∼ 10 18 cm as reported in Wiseman et al. (2023).Table 1 lists the dust echo parameters from the IR interpretation.The dust radius is estimated to be R dust = c∆T IR ∼ 5.4 × 10 17 − 10 18 cm and is consistent with the dust sublimation radius (e.g., Namekata & Umemura 2016;Jiang et al. 2019) where L IR,45.5 = L IR /(10 45.5 erg s −1 ), T sub ≃ 1800 K is the sublimation temperature and a dust ∼ 10 −5 a dust,−5 cm is the dust grain radius.Fig. 2 demonstrates that our two-component model can explain the IR observations very well and could be tested by further IR follow-ups.However, we need to note that based on the current observations, our fitting suggests that a static spherical dust torus is not sufficient to explain the whole IR light curve, and we cannot exclusively determine the physical meaning of the earlytime component.For instance, it could arise from the anisotropic or irregular dust distribution, or from preexisting dust clumps around the SMBH (e.g., Jiang et al. 2019), as shown in Fig. 3. Another possibility is an expanding dust torus pushed by radiation or winds, which introduces the time evolution of the dust compared to a static distribution described by f S .A detailed study of the physical interpretation of f ET is beyond the scope of this work.In the following text, we use our twocomponent fitting to describe the evolution of IR target photons for neutrino production.Our IR light curve can be considered as an "effective" description that reproduces the data well.Different physical scenarios -if they fit the data well -should give a similar light curve.Therefore, our IR model is sufficient for the purpose of this study.
Using the dust echo efficiency ϵ dust ϵ Ω in Table 1, we can estimate the IR-corrected OUV bolometric energy is the IR bolometric energy obtained by integrating L IR over time.From this chain of equations, and assuming that the absorbed and un- absorbed OUV luminosities have the same time dependence, we finally obtain L OUV .One caveat in our IR interpretation is the assumption of ϵ dust ϵ Ω , which renders the unabsorbed L OUV model-dependent.Nevertheless, we will demonstrate later that the IR photons would dominate the neutrino and EM cascade emissions, and our conclusions do not depend sensitively on ϵ dust ϵ Ω .

NEUTRINO AND EM CASCADE EMISSIONS
The observational parameters for AT2021lwx and the potentially associated neutrino event IC220405B are summarized in Table 1.We follow the treatments in Winter & Lunardini (2023) and Yuan & Winter (2023) and assume the injected proton luminosity is a fraction of the accretion power, e.g., L p = ε p ṀBH c 2 , where an efficient proton injection efficiency ε p = 0.2 is used as the fiducial value as in Winter & Lunardini (2023) for AT2019dsg/fdr/aalc.We assume the accretion rate aligns with the OUV light curve, e.g., ṀBH ∝ L OUV as it is consistent with the t −5/3 prediction which re-  2015).Our IR-corrected OUV bolometric peak luminosity reaches ∼ 1.2 × 10 46 erg s −1 and is comparable with the Eddington luminosity L Edd = 1.3 × 10 46 erg s −1 for a SMBH of mass M BH = 10 8 M ⊙ .In this case, the peak mass accretion rate can reach a few ×10 L Edd /c 2 with ṀBH (t pk )/ ṀEdd = 1 and η rad ∼ 0.01 − 0.1.Hence, our fiducial ṀBH (t pk ) = 40L Edd /c 2 is not too optimistic.We assume a power-law injection rate for the accelerated protons in the isotropic wind region inside the dust torus, e.g., Q p ∝ E −2 p exp(−E p /E p,max ) and normalize the spectrum with E Qp dE p = L p /V , where V ≈ 4πR3 dust /3 is the volume within the dust4 .With-out explicitly specifying the accelerator, we instead parameterize the acceleration zone by the maximal proton energy E p,max .In general, the protons can be energized in the compact inner jet, accretion disk or disk corona, or an extended isotropic wind (e.g., Murase et al. 2020) with magnetic field strength comparable to AGNs, e.g., B ∼ 0.1 − 1 G.While propagating inside the radiation zone (the yellow region in Fig. 3), the protons will undergo photomeson (pγ) and hadronuclear (pp) energy losses via interactions respectively with target thermal photons and wind protons.The resulting neutral (π 0 ) and charged (π ± ) pions would decay into neutrinos, γ rays and secondary electrons.These secondary electrons together with the electron/positron pairs generated from γγ annihilation and Bethe-Heitler (BH) interactions will subsequent initiate EM cascade emissions via synchrotron and inverse Compton radiation.We denote the EM cascade components originating from pγ, γγ, and BH processes respectively as 'pg-syic', 'pair-syic', and 'bh-syic'.To obtain the neutrino and EM cascade spectra, we use AM 3 (Astrophysical Multi-Messenger Modeling, Gao et al. 2017;Klinger et al. 2023) software to numerically solve the coupled time-dependent transport equations for all relevant particle species; see Yuan & Winter (2023) for a detailed description and discussion of the transport equations, including the particle injection, energy loss and escape terms.
As demonstrated by Winter & Lunardini (2023) and Yuan & Winter (2023), the contribution to neutrino and EM cascade emissions from pp interactions is typically 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 E [GeV] subdominant compared to the pγ processes, even if a significant fraction of the accreted mass is converted to non-relativistic winds with velocities of 0.1c (Dai et al. 2018;Yuan et al. 2020Yuan et al. , 2021)).In the following text, we specifically focus on the pγ contributions.For the target photon fields, we consider the thermal IR, OUV and Xray photons isotropized within the dust radius.Since the early-time (ET) component in the IR light curve interpretation could be produced by the dust outside the radiation zone, as shown in Fig. 3, we consider only the dust torus component for the IR target photons, i.e., the magenta curves in the upper panel of Fig. 2, in a conservative case.For the X-ray component, we assume a constant luminosity of L X = 1.5 × 10 45 erg s −1 as in Winter & Lunardini (2023) and use an AT2019dsg-like temperature k B T X = 72 eV.We use the magnetic field strength B = 0.1 G as the fiducial value as in Winter & Lunardini (2023).
Fig. 4 shows the proton energy loss rates (left panel) and the neutrino/EM cascade spectral energy distribution (SEDs, right panel) produced in the isotropic wind of radius R dust at neutrino detection time t ν .We assume the maximum energy of the injected proton to be 1.5 × 10 9 GeV.In the left panel, the red green, orange, and black curves respectively depict the pγ, BH, proton synchrotron and escape rates.The horizontal gray lines show the free streaming rates (t −1 f.s.= c/R dust ) for neutral particles.The cases of shorter and longer IR time dispersion, e.g., ∆T IR =180 d and 330 d, are shown as the dashed and solid curves.In both cases, the pγ interactions are efficient and fast in the proton energy range E p ∼ 10 7 − 10 9 GeV, e.g., t −1 pγ /t −1 f.s.> 1, which implies that the neutrino radiation is mainly constrained by the proton luminosity.Given the acceleration efficiency η acc ∼ < 1, the proton acceleration rates, t −1 p,acc = η acc eBc/E p , are illustrated as blue lines.Despite E p,max is treated as a free parameter without specifying the acceleration sites, we demonstrate that E p,max = 1.5 × 10 9 GeV is achievable within the wind (one possible site for proton acceleration) for the magnetic field B = 0.1 G.The red circles in the left panel demonstrate that the chosen E p,max can be obtained for reasonable/conservative acceleration efficiencies η acc = 0.3 and 1.0 for the IR time spreads ∆T IR = 330 d and 180 d, respectively, from balancing the acceleration rate with the proton interaction rate.The right panel of Fig. 4 shows the SEDs for target photons (magenta curves), overall EM cascades (black curves) and neutrinos (red curves).The dashed and solid curves have the same meaning with the left panel.For the shorter IR time delay case (∆T IR = 180 d), the orange, green and blue curves illustrate the contributions from secondary electrons/positions originated from γγ annihilation, pγ and BH processes, respectively.The γ-rays from π 0 decays are completely depleted via γγ annihilation with in-source thermal photons and extragalactic background lights.A more detailed and quantitative description of the EM cascade SEDs can be found in Yuan & Winter (2023).The orange and cyan areas depict the Swift XRT and Fermi Large Area Telescope (LAT) energy ranges.The non-detection of γ-rays by Fermi LAT in the direction of IC220405B place an upper limits in the energy range 0.1 − 800 GeV (Garrappa et al. 2022), shown as the cyan upper limit.We find that our results are consistent with the observational constraints even for the optimistic parameter sets.
The comparison of the predicted neutrino fluence, obtained by integrating the flux, and neutrino luminosity in the SMBH frame of AT2021lwx with AT2019dsg/fdr/aalc are illustrated in the left and right panels of Fig. 5.The red areas correspond to the uncertainties from IR interpretations, e.g., ∆T IR = 180 − 330 d and R dust = 5.4 × 10 17 − 10 18 cm.The IceCube sensitivities for point source (PS, Aartsen et al. 2014) and gamma-ray follow up (GFU, Blaufuss et al. 2019) searches are ploted in the thin gray dasheddotted curves.We observe that the neutrino spectra of AT2021lwx are similar to those of the other three TDEs but at a lower fluence level due to the high redshift.Using the GFU effective area5 , we estimate the expected neutrino number from AT2021lwx to be in the range of N ν ≃ 3.0×10 −3 −0.012, which is lower than the other three TDEs.From the right panel, the peak time of the neutrino luminosity of AT2021lwx, e.g., 100-200 days in the SMBH frame, could explain the time delay of IC220405B (vertical red dashed line).

DISCUSSION
Let us first of all note that the description of the IR emission is a crucial part in our scenario, because the chosen maximal proton energies reaching E p,max ≃ 10 9 GeV allow for pγ interactions beyond the threshold with the abundant IR photons -which are dominating the neutrino and accompanying EM cascade emissions.Moreover, the radius of the dust torus, which determines the target photon density and consequently the pγ interaction efficiency, can be inferred from the time delay appeared in the IR light curves, defined as the time difference between OUV and IR peaks.We propose an interpretation of the IR light curve that consists of a spherical dust torus and an early-time components, denoted as f S and f ET , respectively.
The primary uncertainty in the multi-messenger modeling of AT2021lwx arises from the lack of IR data since 300 days after the OUV peak in the SMBH frame, which leads to the uncertainties in the evaluation of the time delay, the time dispersion ∆T IR of the dust torus component (the magenta curves in Fig. 2 and the f S term in Eq. 2), and equivalently the radius R dust = c∆T IR .Our IR interpretation demonstrates that the time dispersion (∼ half of the time delay in the SMBH frame) lies in the range ∆T IR ≃ 180 − 330 d, which corresponds to the dust radius R dust = c∆T IR ≃ (5.4 − 10) × 10 17 cm.The resulting uncertainties in neutrino and EM emissions are illustrated in Figs. 4 and 5, and the predicted neutrino number is limited to be N ν ≃ 3 × 10 −3 − 0.12.Further follow-up observations up to 2(1 + z)∆T IR ∼ 1300 days after the OUV peak are advisable to obtain more stringent constraints on the neutrino number and on our model.
On the other hand, two-component dust echo scenario is constructed to interpret the early-time IR light curve.There could be other alternative models, such as the dust clumps in the broad-line regions for TDEs in AGNs (Jiang et al. 2019) or the bounded/unbounded debris.If the early IR emissions are produced within the dust radius (i.e., our radiation zone), one should take these IR photons (inferred from the cyan curve in the upper panel of Fig. 2) into account as additional targets for the pγ interactions.We tested that potential additional contribution of early time IR photons and found that the neutrino fluence is affected by a factor less than 1.5.The reason is that the system is already pγ efficient, and the neutrino power is limited by the injected proton luminosity, which is determined by ε p ṀBH (t pk ) and is also constrained by the Fermi -LAT upper limit.
Our multi-messenger model, which gives N ν ∼ < 0.012, seems to disfavor the neutrino-TDE coincidence together with the misalignment of the TDE outside the neutrino 90% error box.However, aside from the similarities with AT2019dsg/fdr/aalc and the potential correlation with IC220405B, AT2021lwx remains an important TDE candidate, being one of the non-jetted TDEs with the highest redshifts (see, e.g., Yao et al. 2023, for a TDE sample), and could have profound implication on the redshift distribution of TDEs, including the SMBH mass and the mass of disrupted stars.For AT2021lwx, the total energy released in the OUV bands reaches given the radiation efficiency η rad ∼ 0.1 − 0.01.Indeed, the volumetric rates, i.e., ρTDE,⋆ , of TDEs with M BH ∼ 10 8 M ⊙ and M acc ∼ 3 − 30M ⊙ are low.On the other hand, given the high redshift of AT2021lwx, such detection is not impossible especially for a high cosmological volume if the event is bright enough.Considering a rapid redshift evolution, e.g., ρTDE,⋆ ∝ (1 + z) −3 , we compare the relative TDE rate, i.e., ṄTDE (z < z lim ) ∼ V co (z lim ) ρTDE,⋆ (z lim ), within redshift z lim = 0.995 to the AT20l9fdr-like redshift z lim = 0.26, ṄTDE (z < 0.995)/ ṄTDE (z < 0.26) ∼ V co (0.995)/[4V co (0.26)] ∼ 8, where V co (z) is cosmological comoving volume at z.This implies that a powerful object involving a massive star has a larger abundance across large cosmological volumes.Similar results could be obtained using the TDE rate inferred from star formation history and SMBH mass function (e.g., Kochanek 2016).
In addition to the IR photons, pγ interactions with X-ray photons could also dominate neutrino production within a relatively compact radiation zone, as proposed by Winter & Lunardini (2023) (model "M-X"); this option is attractive because it requires much lower maximal proton energies, and, thus, a much less efficient accelerator.For AT2021lwx, due to the absence of early-time X-ray observations and incomplete information about the radius of the X-ray emitters, we focus on the dust echo model and do not consider the scenario where Xrays are dominant.

SUMMARY AND CONCLUSIONS
We have investigated the potential correlation between the neutrino event IC220405B and an energetic TDE candidate, AT2021lwx, at redshift z = 0.995.In addition to luminous thermal OUV emissions, AT2021lwx exhibits bright and long-lasting IR luminosities, which can be interpreted as a strong dust echo incorporating the dust torus component originating from the dust torus and the early-time contributions.We have pointed out that AT2021lwx shares crucial similarities with the other three neutrino-coincident TDEs and TDE candidates, e.g., AT2019dsg/fdr/aalc, including strong X-ray/OUV emissions, strong dust echoes, and comparable time delays (∼ 150 − 300 days) of the neutrino detection with respect to the OUV peaks in the SMBH rest frame.We have studied the neutrino and EM cascade emissions from an isotropic radiation zone inside the dust radius in a fully time-dependent manner following the treatments in Winter & Lunardini (2023) and Yuan & Winter (2023).We have demonstrated that the outputs, such as the EM/neutrino SEDs, neutrino light curves and fluences, are qualitatively consistent with the other three TDEs.Especially, the neutrino time delay could be explained by dust echo target photons.These similarities make AT2021lwx an interesting target and imply that these objects may share similar underlying physical processes.
Our results indicate that, in consistency with the nondetection of γ-rays by Fermi -LAT, the expected neutrino numerical number is limited to the range N ν ≃ 3.0×10 −3 −0.012, which is expected for far away sources and might suggest that the association could have low significance.However, the expected event rate is not very different from the other three TDEs, and such low event rates are expected for single neutrino event detections from many far-away sources (Eddington bias, see Strotjohann et al. 2019).
We suggest conducting further multi-wavelength follow-ups, especially in the IR band, on this object for an extended period.Additionally, we recommend studying the neutrino track reconstruction in this particular case for a more definitive conclusion regarding the neutrino correlation.The extended IR observations, such as the upcoming annual data release of the WISE survey, along with the confirmation or exclusion of the neutrino coincidence, would test our dust echo model and shed more light on the physical picture of TDEs, such as the geometry of the dust torus and the origin of the early time IR component.After all, our time-dependent multi-messenger diagnosis, consisting of the neutrino and EM cascade counterparts, provides a comprehensive and generic template for interpreting the spectral and temporal signatures of future neutrinocoincident TDEs.
Note added: after the paper was submitted, the NE-OWISE 2024 data was released, extending the IR light curve to MJD 60252, equivalent to approximately 481 days after the OUV peak in the SMBH rest frame.The latest data release7 indicates that the late-time W1/W2 apparent magnitudes remained roughly unchanged from the early epochs.We infer that the unbinned data points lie within the uncertainties of our model (red shaded areas in Fig. 2).Refined analyses of the late-time IR data would be needed to obtain a robust constraint on R IR .

Figure 3 .
Figure 3. Schematic picture of the dust echo model.The central SMBH, accretion stream, accretion disk, disk corona, wind, dust torus and potentially a jet are shown.To fit the IR light curve, we model the dust torus as a spherical segment (e.g., the dashed red lines) and consider an additional early-time component (e.g., the red solid line).The physical origins of the ET component are discussed in the main text.The radius of dust torus R dust determines the IR time delay.

Figure 4 .
Figure 4. Left panel: In-source interaction rates shown at the neutrino detection time tν .The solid and dashed curves correspond to the shorter (∆TIR = 180 d) and longer (∆TIR = 330 d) IR time delays with different assumptions for R dust , respectively.The gray shaded area shows the region beyond the maximum proton energy, whereas the acceleration efficiencies, ηacc = 1.0 − 0.3 can be used to describe Ep,max, see red circles.Right panel: SED of the muon neutrino (red curves) and EM cascade (black curves) emissions at the neutrino detection time.The magenta curve shows the spectrum of target black body photons.The dashed and solid curves have the same meaning with the left panel.For the ∆T = 180 d case, the orange, green and blue dashed curves represent the components of EM cascades.The orange and cyan areas depict the XRT and Fermi LAT energy ranges, whereas the Fermi upper limit is shown as the cyan arrow.flects the accretion history.The peak accretion rate 3 ṀBH (t pk ) = 40L Edd /c 2 is estimated to avoid exceeding the hard up limit of the accreted mass ṀBH dt ∼ < M ⋆ /2, where L Edd = 1.3 × 10 46 erg s −1 (M BH /10 8 M ⊙ ) is the Eddington luminosity.On the other hand, the peak accretion rate can be interpreted as the super-Eddington accretion with ṀBH (t pk )/ ṀEdd = O(1.0),where the Eddington accretion rate ṀEdd = L Edd /(η rad c 2 ) indicates the accretion rate to power Eddington radiation with the radiation efficiency η w ∼ 0.01−0.1 (McKinney et al.2015).Our IR-corrected OUV bolometric peak luminosity reaches ∼ 1.2 × 10 46 erg s −1 and is comparable with the Eddington luminosity L Edd = 1.3 × 10 46 erg s −1 for a SMBH of mass M BH = 10 8 M ⊙ .In this case, the peak mass accretion rate can reach a few ×10 L Edd /c 2 with ṀBH (t pk )/ ṀEdd = 1 and η rad ∼ 0.01 − 0.1.Hence, our

Figure 5 .
Figure 5. Left panel: Cumulative single-flavor neutrino fluences at tν for AT2021lwx (red curves) and the other three TDEs, AT2019dsg/fdr/aalc (green/orange/blue dashed curves, taken from Winter & Lunardini 2023).The thin and thick dashed-dotted gray curves show the IceCube sensitivities for point-source and GFU searches.The uncertainties in IR lightcurve interpretation leads to the expected GFU neutrino number in the range Nν = 3 × 10 −3 − 0.012.Right panel: Neutrino luminosities for AT2021lwx and the other three TDEs measured in the SMBH frame.The vertical lines represent the corresponding neutrino detection times.The solid (dashed) curves correspond to ∆TIR = 180 d (330 d), and the red areas correspond to the uncertainties from dust echo interpretations.