Effective potentials and morphological transitions for binary black hole spin precession

Area of Science:

• Astrophysics
• General Relativity
• Gravitational Wave Astronomy

Background:

• Binary black hole (BBH) mergers are key sources of gravitational waves.
• Understanding BBH spin dynamics is crucial for interpreting gravitational wave signals.
• Previous models often simplified spin precession effects.

Purpose of the Study:

• To derive an effective potential for BBH spin precession at second post-Newtonian order.
• To analytically solve the orbit-averaged spin-precession equations.
• To classify BBH spin precession morphologies and understand their evolution.

Main Methods:

• Derivation of an effective potential for BBH spin precession.
• Analytical solution of orbit-averaged spin-precession equations.
• Analysis of quasiperiodic spin solutions and their implications.

Main Results:

• BBH spins exhibit quasiperiodic evolution, returning to initial orientations and precessing jointly.
• Three distinct morphologies of BBH spin precession are identified.
• A new class of spin-orbit resonances is discovered, capable of tilting the total angular momentum.

Conclusions:

• The derived solutions enable accurate modeling of gravitational waves from generic BBH mergers.
• These findings improve predictions for final BBH spins and gravitational recoils.
• The study provides a deeper understanding of relativistic spin dynamics in compact object binaries.