Binary neutron star merger

Orbit. Point-particle post-Newtonian inspiral, Ω = √(GM/a³) with 1PN and spin–orbit corrections, driven inward by Peters' radiation reaction, da/dt = −(64/5)G³m₁m₂M/(c⁵a³). The time-to-merger shown is the exact Peters value for the current separation.

Stars. Each equation of state gives R(M), the TOV maximum mass and Λ(M) ∝ compactness⁻⁵, combined into Λ̃ with the standard mass weighting. Tidal elongation scales as (m_comp/m)(R/a)³ (amplified ×3 to be visible). Mass shedding begins near Roche contact, earlier for unequal masses, a stiff EOS or prograde spin.

Merger and fate. Prompt collapse follows the Bauswein threshold M_thresh = (2.38 − 3.606·C_TOV)·M_TOV. Below it, a bar-mode hypermassive remnant forms and collapses on a mass-dependent delay if it exceeds ≈1.2·M_TOV. Ejecta mass uses a fitting-formula scaling in mass ratio and compactness; particles then move ballistically. The disk follows T ∝ r^−3/4 with relativistic Doppler asymmetry; the hole's shadow is ≈2.6·r_s across.

Magnetosphere. Tilted dipole lines (r = L·sin²θ) precess with each star's spin; χ is converted to a true period via I ≈ 0.35MR². A black hole with a disk — or a ≥10¹⁴ G remnant — launches a helical jet.

Time. The last orbits take ~0.1 s physically, so the binary integrates in physical seconds but renders in adaptive slow motion (factor in the telemetry). No hydrodynamics, neutrinos or full general relativity — but every number shown comes from the same integrated model that moves the stars.