Tidal Events Across Messengers

A tidal disruption event (TDE) is not one clock but a causal sequence: stellar disruption sets a debris-energy distribution; bound debris returns; streams dissipate and circularize; an accretion flow forms; radiation is reprocessed; and a wind or jet interacts with its surroundings. Optical, X-ray, radio, and neutrino signals can therefore peak in different orders without contradiction. The scientific task is to test whether one mass-and-energy flow produces all of them, including nondetections, rather than assigning every lag to a new component. Instrument-specific gravitational-wave likelihood methods are outside this page’s scope.

Helpful background. Black-Hole Geometry and Mechanics supplies relativistic orbital and capture scales; Relativistic Matter and Compact Objects supplies stellar structure and radiation; Black-Hole Astrophysics supplies fallback, disks, winds, and jets; Gravitational-Wave Astronomy supplies localization and association statistics; Relativistic Cosmology supplies host distance, redshift, and frame conversion.

A causal chain, not a sequence of labels

For a star of mass $M_\star$ and radius $R_\star$ disrupted by a black hole of mass $M$, the characteristic tidal radius is $r_t\simeq R_\star(M/M_\star)^{1/3}$. In the Newtonian teaching model with a flat debris-mass distribution over bound specific energies $-\Delta\epsilon\leq\epsilon\lt0$, let $M_{\rm bound}$ be the mass in that interval and $t_{\min}$ the first return time. The Kepler return relation $t\propto|\epsilon|^{-3/2}$ gives

$$\dot M_{\rm fb}(t)\simeq \frac{2M_{\rm bound}}{3t_{\min}} \left(\frac{t}{t_{\min}}\right)^{-5/3}.$$

The normalization passes a useful check: integrating from $t_{\min}$ to infinity returns $M_{\rm bound}$, since $\int_1^\infty x^{-5/3}dx=3/2$. For an ideal complete parabolic disruption with half the stellar mass bound, it becomes $M_\star/(3t_{\min})$. A realistic energy distribution changes the early curve, while the late exponent follows only if $dM/d\epsilon$ tends to a nonzero constant near zero energy; see the fallback derivation. This rate is an input to emission physics, not a bolometric light curve. A band $b$ can be represented by a causal transfer,

$$L_b(t)=\int_0^t K_b(t-t';\theta_b)\, \dot M_{\rm fb}(t')c^2\,dt' ,$$

where $K_b$ has units of inverse time and its integral gives the efficiency into that band in this linear model. It includes circularization delay, accretion, reprocessing, obscuration, and outflow propagation. A narrow X-ray kernel might trace a compact disk; a broad optical kernel can represent reprocessing or stream shocks; a radio kernel includes expansion until synchrotron self-absorption falls. Evolving opacity and nonlinear heating can require a time-dependent kernel or an explicit radiation model. The source-frame chain must be transformed once, with $t_{\rm obs}=(1+z)t_{\rm src}$, not band by band; moving emitters also require the photon travel-time correction described for merger counterparts.

Mass closure requires disjoint accreted, wind, and initially unbound rest-mass components:

$$\int\dot M_{\rm acc}\,dt+\Delta M_{\rm wind} +\Delta M_{\rm unbound}\leq M_\star ,$$

while an illustrative energy bound for an accretion-powered source is

$$E_{\rm rad}+E_\nu+E_{\rm out,remaining}+E_{\rm CR,escaping} \leq \eta\int\dot M_{\rm acc}c^2\,dt .$$

The energy inequality is an accretion-powered example: $\dot M_{\rm acc}$ is the supplied rest-mass rate reaching that flow, $\eta$ is its total available conversion efficiency, and black-hole spin extraction or independent stellar-orbital reservoirs are excluded. A stream-shock model must instead compute the dissipated orbital energy, and a spin-powered jet must include its additional reservoir. Do not add stream dissipation and the full accretion binding-energy release when they describe the same energy lost at successive stages. Geometry and beaming must be declared on both sides. The output terms are disjoint: cosmic rays subsequently converted to neutrinos or radiation are not also counted as escaping cosmic rays, and outflow energy means the energy remaining after those transfers.

A frozen population product and a named association

For population context, freeze TDECat, CDS VizieR J/A+A/707/A171, inserted 2026-03-12 and retrieved 2026-08-18. Its tdecat table has 134 rows—131 optical TDEs and three established jetted events—and table1 has 24 candidates. The main sample requires photometric-survey detection and a classification spectrum near the flare, with documented exceptions. It is a comprehensive compilation through discoveries in 2024, not a survey-complete rate sample. The classification rules, optical selection, and exclusions are explicit in Langis et al. 2026, §§2–2.2 and Appendix A.

The catalog aligns identifiers, redshifts, classes, and multiwavelength flags, but it does not homogenize every instrument response or follow-up trigger. Preserve original UTC/MJD timestamps, barycentric correction where relevant, astrometric frame, photometric system, spectral response, aperture, host subtraction, Galactic extinction, and upper-limit confidence. Candidate and main tables must remain separate. A neutrino cross-match additionally needs each alert revision, localization probability map, energy and quality selection, detector background, angular and temporal windows, and the number of alerts searched.

AT2019dsg and IceCube-191001A provide a concrete formulation test. ZTF discovered the nuclear transient in 2019 April; the high-energy neutrino arrived on 2019 October 1, roughly five months after optical discovery. Stein and collaborators found spatial consistency, multiband evidence for a radio-emitting TDE, and a 0.2% chance probability for an event at least this bright under their eight-campaign follow-up selection. The exact optical, X-ray, radio, neutrino, and gamma-ray products—and gamma-ray upper limits—are documented in Stein et al. 2021, pp. 510–518, Figures 1–4, Extended Data Figures 2–7, and Supplementary Tables 1–5. That is evidence for a candidate association, not proof that a relativistic jet made the neutrino.

Association likelihood and physical closure

Let $H_c$ denote a common source and $H_b$ a background coincidence. A defensible odds ratio is

$$\mathcal O_{c/b} =\frac{\pi_c}{\pi_b} \frac{\int p(d_{\rm EM},d_\nu\mid\vartheta,H_c) \pi(\vartheta\mid H_c)\,d\vartheta} {p(d_{\rm EM}\mid H_b)\,p(d_\nu\mid H_b)} .$$

The common-source likelihood includes localization overlap, the delay distribution generated by the disruption-to-outflow model, neutrino energy and direction, survey coverage, and electromagnetic detections and limits. Priors on the TDE neutrino fraction, delay, beaming, and source luminosity must be reported. The background uses the detected rate of nuclear transients passing the same cuts, not the total TDE rate. Statistical uncertainty comes from event counts, fluxes, and localizations; classification, trials, alert selection, host contamination, and population incompleteness are systematics.

Physical closure then asks whether the candidate can make the neutrino. If hadronic efficiency is $f_\pi$ and nonthermal proton loading is $\xi_p$,

$$E_\nu L_{E_\nu}\lesssim \frac{3}{8}f_\pi\xi_p L_{\rm acc}.$$

The coefficient $3/8$ assumes about half the pion energy goes into charged pions and that pions and muons decay before cooling. Here $\xi_pL_{\rm acc}$ is the total nonthermal proton power, so the bound is generous for any one logarithmic neutrino-energy interval; a spectral calculation distributes that power over proton energies. All luminosities must use the same frame and beaming convention. The hadronic-jet discussion develops these assumptions.

The same pion production supplies an electromagnetic cascade. X-ray and gamma-ray upper limits must be propagated through opacity and reprocessing, while the radio-inferred outflow cannot be silently promoted to a relativistic jet. VLA and ALMA observations spanning 55–560 days instead infer approximately free expansion at about $0.07c$ and a kinetic-energy plateau of order $5\times10^{48}$ erg under the equipartition formulation Cendes et al. 2021, §§2–4, Tables 1–2 and Figures 1–5. That ordinary outflow is a counterweight to jet-based interpretations, though it does not exclude a hidden compact accelerator.

Results and limitations through 2026-08-18

Results after 2026-08-18 are out of scope. Durable observables are separated below from mutable causal claims.

Evidence or result	Causal link tested	Scope and limitations	Independent check
TDECat J/A+A/707/A171, 134 main rows plus 24 candidates	Population context for optical, X-ray, infrared, radio, and repeating behavior	Literature compilation is heterogeneous and not rate-complete; neutrino selection is external	Reproduce row counts and keep candidate table separate
AT2019dsg optical/X-ray/radio time series	Disruption leads to accretion, reprocessing, and an outflow	Circularization time, obscuration, and launch geometry are model-dependent	Fit one latent delay chain and require mass/energy closure
IceCube-191001A localization and time	A TDE produced a high-energy neutrino months after discovery	One event; significance depends on brightness cut, eight follow-up campaigns, delay window, and background	Recompute common-source odds with predeclared cuts and alert revisions
VLA/ALMA 55–560-day radio sequence	The radio source traces an ordinary nonrelativistic outflow	Equipartition and geometry affect energy and speed; a hidden inner zone is not measured	Test spherical and collimated fits and cascade limits

At the cutoff, AT2019dsg–IceCube-191001A and other reported TDE–neutrino pairings remained candidates. No gravitational-wave product had established a TDE association. It remains unresolved whether thermal reprocessing, prompt disk X-rays, stream shocks, ordinary winds, or relativistic jets dominate across the class, and whether TDEs contribute appreciably to the diffuse neutrino flux.

Competing positions and parameter regimes

One position assigns optical light to reprocessing and X-rays to a compact disk; another makes stream self-intersection shocks the primary optical engine. Radio emission can arise from an ordinary wind or a relativistic jet. A hidden hadronic zone can make neutrinos while gamma rays are absorbed, whereas the neutrino can simply be unrelated to the nuclear transient. Parameter regime axes include prompt versus delayed circularization, sub- versus super-Eddington accretion, optically thin versus reprocessing-dominated transfer, and on-axis jet versus wide-angle wind. Each changes the delay prior and selection function.

Reproducing the result and testing its robustness

Download the VizieR ReadMe and both tables, record the insertion and retrieval dates, and verify 134 and 24 rows. For AT2019dsg archive photometry, spectra, response files, radio flux tables, IceCube alert version and localization, gamma-ray upper limits, and all clocks. Reconstruct the chance-coincidence likelihood, inject causal delay chains through the actual follow-up cadence, include nondetections, and publish posterior predictive light curves plus complete mass and energy budgets.

What could change the conclusion. The interpretation could change when a new neutrino or gravitational-wave association survives a predeclared population analysis, a complete radio follow-up sample changes the jet fraction, alert reconstruction or TDE classification changes, or polarization, reverberation, or cascade data decisively identify the emitting zone.

Formulation-choice diagnostic

A candidate model assigns $0.04M_\odot$ to accretion with $\eta=0.1$, $E_{\rm rad}=3\times10^{51}$ erg, $E_{\rm out}=8\times10^{50}$ erg, and an isotropic-equivalent neutrino energy $E_{\nu,\rm iso}=2\times10^{52}$ erg with beaming fraction $f_b=0.02$. Does it pass energy closure?

Solution

The available accretion energy is

$$E_{\rm acc}=0.1(0.04M_\odot)c^2 \simeq7.2\times10^{51}\ {\rm erg}.$$

The true neutrino requirement is $f_bE_{\nu,\rm iso}=4\times10^{50}$ erg, so the accounted output is $3.0+0.8+0.4=4.2\times10^{51}$ erg. It passes this necessary bound with about $3\times10^{51}$ erg of margin. It is not thereby validated: the model must derive the same $f_b$ from its geometry, supply a hadronic efficiency and proton loading below the remaining power, reproduce the observed delay, and keep the pion cascade within X-ray and gamma-ray limits. Treating the neutrino as isotropic would instead require $2.38\times10^{52}$ erg total and fail immediately.

References

• Cendes, Y., Alexander, K. D., Berger, E., Eftekhari, T., Williams, P. K. G., and Chornock, R. (2021), “Radio Observations of an Ordinary Outflow from the Tidal Disruption Event AT2019dsg,” The Astrophysical Journal 919, 127, doi:10.3847/1538-4357/ac110a.
• Gezari, S. (2021), “Tidal Disruption Events,” Annual Review of Astronomy and Astrophysics 59, 21–58, doi:10.1146/annurev-astro-111720-030029.
• Langis, D. A. et al. (2026), “Repeating Flares, X-Ray Outbursts and Delayed Infrared Emission: A Comprehensive Compilation of Optical Tidal Disruption Events—TDECat,” Astronomy & Astrophysics 707, A171, doi:10.1051/0004-6361/202554882; CDS VizieR J/A+A/707/A171, catalog record.
• Stein, R. et al. (2021), “A Tidal Disruption Event Coincident with a High-Energy Neutrino,” Nature Astronomy 5, 510–518, doi:10.1038/s41550-020-01295-8.