kozai 0.1

Evolve hierarchical triples

# Kozai

Kozai is a Python package to evolve hierarchical triples in the secular approximation. Hierarchical triples may be evolved either using the Delaunay formalism (Naoz et al. 2013b) or the vectorial formalism (Katz et al. 2011). The quadrupole, octupole, and hexadecapole terms of the Hamiltonian may be toggled to be included (or not) in the equations of motion. Post-Newtonian terms may also be toggled to include both relativistic precession (PN 1) and gravitational radiation (PN 2.5) using terms from Blaes et al. (2002).

The package provides a TripleDelaunay object which may be integrated using the Delaunay orbital elements and a TripleVectorial which may be integrated using the eccentricity and angular momentum vectors. This allows the integration to occur within the context of an external Python program.

The underlying integrator is from the SciPy ODE package. By default this package uses VODE as its integration algorithm, but the algorithm may be changed to any of the other integration algorithms supported by the SciPy ODE package.

## Dependencies

• NumPy

• SciPy

## References

• Blaes, O., Lee, M.H., & Socrates, A., 2002, ApJ, 578, 775

• Katz, B., Dong, S., & Malhotra, R., 2011, PhRvL, 107, 181101

• Naoz, S., Farr, W.M., Lithwick, Y., Rasio, F.A., & Teyssandier, J., 2013b, MNRAS, 431, 2155