Ejecta, Disks, and Kilonova Inputs

Merger calculations do not output one universal “kilonova ejecta mass”. They produce dynamically unbound matter, a bound disk and fallback tail, and later neutrino-, viscous-, or magnetically driven outflows with different velocity, geometry, entropy, and electron fraction. Turning those components into radiative-transfer inputs requires consistent extraction and no double counting. Which channel dominates remains model-dependent. Evidence summarized here is current through 2026-08-18.

Helpful background. Stress–Energy and Conservation supplies baryon and energy budgets; the Einstein equations supply merger geometry; Relativistic Two-Body Dynamics supplies binary inputs; Relativistic Matter and Compact Objects supplies EOS and neutrino physics; Gravitational Radiation and Waveforms supplies radiated losses; and Computational Relativity supplies extraction and convergence tests.

Dynamical ejecta are at least two components

Tidal torques can strip relatively cold matter into an approximately equatorial tail, especially for asymmetric binaries and compact-object disruption. Shock-heated matter is launched near collision interfaces with a broader angular distribution. Neutrino absorption can raise its electron fraction

$$Y_e=\frac{n_{p,\rm total}}{n_b},$$

while expansion, weak freeze-out, and pair processes determine the value carried into nucleosynthesis. The labels “tidal” and “shock” describe mechanisms, not perfectly separable tracer populations.

Here total proton number includes protons bound in nuclei; using only free protons after recombination would not give the net electron fraction of electrically neutral matter.

A finite-radius simulation needs an unbound criterion. Define the dimensionless specific enthalpy $h=(e+p)/\rho$, with $\rho=m_b n_b$, and let $h_\infty$ be its cold asymptotic value for the adopted nuclear composition and reference baryon mass. Two stationary estimates are

$$u_t\lt-1 \quad\hbox{(geodesic)},\qquad -h u_t\gt h_\infty \quad\hbox{(Bernoulli)}.$$

The first ignores conversion of thermal enthalpy into kinetic energy; the second uses conservation of $-hu_t$ in a sufficiently steady, adiabatic outflow: at infinity $-u_t=\gamma_\infty$, so escape requires $\gamma_\infty=-hu_t/h_\infty\gt1$. The often-used threshold $-hu_t\gt1$ additionally chooses $h_\infty=1$. Nuclear binding can change $h_\infty$, and neutrino or radioactive losses can change the available Bernoulli energy; see Foucart et al. 2021, §II.B, Eqs. (3)–(5) for this normalization and §§II.C–II.F for nuclear heating and neutrino losses. Neither test is exact in a time-dependent neutrino-heated spacetime. Extraction radius, time, atmosphere, and nuclear binding convention must therefore accompany an ejecta mass. Radice and collaborators analyze merger ejecta, composition, nucleosynthesis, and counterparts in Radice et al. 2018, §§2–5, Tables 2–3, and Appendix A.

Disk, winds, and fallback

Matter outside the central remnant but still bound forms a disk or torus. Its later mass loss can be driven by neutrino absorption, turbulent angular- momentum transport, nuclear recombination, and magnetic stress. A longer-lived neutron-star remnant generally supplies stronger irradiation than prompt black- hole formation, but the outcome also depends on disk mass, opacity set, magnetic topology, viscosity prescription, and evolution time.

Neutrino-driven winds tend to emerge earlier and more strongly in irradiated directions. Viscous or MHD outflows can continue on longer disk-evolution timescales and include material with a wide $Y_e$ distribution. Fallback is matter on eccentric bound trajectories; counting it as both early “ejecta” and later disk supply violates baryon conservation. Foucart reviews transport methods, outflow composition, and their sensitivity to leakage, moment, and Monte Carlo treatments in Foucart 2023, §§5.1–5.2, Figs. 7–9.

The continuum-to-kilonova interface should preserve distributions rather than only averages:

$$\frac{dM_{\rm ej}} {dv\,d\Omega\,dY_e\,ds\,d\tau_{\rm exp}}.$$

Here $v$ is asymptotic velocity, $\Omega$ direction, $s$ entropy per baryon, and $\tau_{\rm exp}$ expansion timescale. A nuclear network maps trajectories to abundance and radioactive-heating histories; radiative transfer then needs density geometry and wavelength- and state-dependent opacity. A single gray opacity cannot be treated as a composition-independent material constant.

Dated comparison of outflow claims

This matrix records model classes and their principal limitations as of 2026-08-18.

Component	Model and evidence type	Typical inference	Limitation and comparison controls
Tidal dynamical ejecta	General-relativistic merger hydrodynamics with finite-temperature EOS	Equatorial, relatively neutron rich; sensitive to mass ratio and stellar compactness	Unbound criterion, extraction radius, atmosphere, EOS, grid, and binary spin alter mass and velocity.
Shock dynamical ejecta	Relativistic merger simulations with weak interactions or neutrino closure	Hotter, broader-angle material can reach higher $Y_e$	Resolution of collision interface and shock, opacity set, neutrino energy treatment, and remnant lifetime are coupled.
Neutrino-irradiated wind	Remnant-plus-disk transport calculations	Irradiation can raise $Y_e$, especially toward polar directions	Leakage, gray or spectral moments, closure, flavor assumptions, and inner remnant boundary can give different conclusions.
Viscous or magnetic disk outflow	Long-duration alpha-viscosity, GRMHD, or axisymmetric disk evolution	A substantial part of the bound disk can become unbound after angular-momentum transport and recombination	Prescribed viscosity and self-consistent MHD are different model classes; runtime, magnetic topology, resolution, and neutrino treatment matter.
Kilonova interpretation	Nuclear-network plus multidimensional radiative transfer conditioned on outflow trajectories	Color and timescale constrain a mixture of mass, velocity, geometry, heating, and opacity	Atomic data, thermalization, viewing angle, density geometry, and component overlap prevent a one-to-one color–$Y_e$ map.

Burns places these source components in the multimessenger merger context in Burns 2020, §§2.1.5, 2.9, 3.4, and 5. Evidence for a blue component can favor some higher-$Y_e$ material, while contrary combinations of geometry, heating, thermalization, and opacity can produce different colors from the same mass-averaged composition. Numerical- relativity ejecta, long-term disk outflows, network yields, and radiative- transfer components must not be added if their mass reservoirs overlap.

Budgets, convergence, and unresolved physics

At matched times, a baryon budget should close schematically as

$$M_{b,0}=M_{b,\rm core}+M_{b,\rm disk} +M_{b,\rm unbound}+M_{b,\rm fallback} +M_{b,\rm boundary}+\delta M_b .$$

Energy and angular momentum require analogous budgets including gravitational radiation and neutrinos. An independent check reruns representative thermodynamic trajectories through a second nuclear network or heating fit and compares abundance groups and deposited power.

Convergence must cover grid, atmosphere, extraction surface and time, neutrino energy groups and closure, magnetic resolution or viscosity, disk runtime, and trajectory sampling. Report uncertainty on total mass and on distributions; a converged bulk disk mass does not guarantee converged fast polar ejecta.

The unresolved question is how much matter each channel supplies, with what composition and geometry, across binary parameter space. Competing GRMHD and effective-viscosity results can differ because they impose different initial magnetic fields, symmetry, transport, and runtime. A concrete re-review trigger is a converged long-duration GRMHD calculation with spectral neutrino transport, revised nuclear masses or heating, wavelength-complete opacity data, or a well-observed merger whose geometry and composition exclude a leading model family.

Check two unbound criteria

At an extraction sphere a fluid element has $u_t=-0.98$ and dimensionless specific enthalpy $h=1.08$. Assume $h_\infty=1$ and no subsequent heating or loss. How do the geodesic and Bernoulli criteria classify it, and which answer should be reported?

Solution

The geodesic test gives $-u_t=0.98<1$, so it classifies the element as bound. The Bernoulli test gives

$$-hu_t=-(1.08)(-0.98)=1.0584>1,$$

so it classifies the element as unbound if thermal enthalpy converts to asymptotic kinetic energy. The disagreement should be reported as a model dependence, followed by farther-radius or tracer evolution; these estimates are not guaranteed upper and lower bounds in a time-dependent flow. Choosing Bernoulli is justified only if the flow is sufficiently steady and adiabatic; choosing geodesic discards possible thermal acceleration.

References

• Burns, Eric. “Neutron Star Mergers and How to Study Them.” Living Reviews in Relativity 23 (2020): 4. DOI.
• Foucart, François, Philipp Mösta, Teresita Ramirez, Alex James Wright, Siva Darbha, and Daniel Kasen. “Estimating Outflow Masses and Velocities in Merger Simulations: Impact of r-process Heating and Neutrino Cooling.” Physical Review D 104 (2021): 123010. DOI; Open PDF.
• Foucart, François. “Neutrino Transport in General Relativistic Neutron Star Merger Simulations.” Living Reviews in Computational Astrophysics 9 (2023): 1. DOI.
• Radice, David, Albino Perego, Kenta Hotokezaka, Steven A. Fromm, Sebastiano Bernuzzi, and Luke F. Roberts. “Binary Neutron Star Mergers: Mass Ejection, Electromagnetic Counterparts, and Nucleosynthesis.” Astrophysical Journal 869 (2018): 130. DOI.