1202.5336 (Christopher Wegg)

Pseudo-Newtonian Potentials for Nearly Parabolic Orbits    [PDF]

Christopher Wegg

We describe a pseudo-Newtonian potential which, to within 1% error at all
angular momenta, reproduces the precession due to general relativity of
particles whose specific orbital energy is small compared to c^2 in the
Schwarzschild metric. For bound orbits the constraint of low energy is
equivalent to requiring the apoapsis of a particle to be large compared to the
Schwarzschild radius. Such low energy orbits are ubiquitous close to
supermassive black holes in galactic nuclei, but the potential is relevant in
any context containing particles on low energy orbits. Like the more complex
post-Newtonian expressions, the potential correctly reproduces the precession
in the far-field, but also correctly reproduces the position and magnitude of
the logarithmic divergence in precession for low angular momentum orbits. An
additional advantage lies in its simplicity, both in computation and
implementation. We also provide two simpler, but less accurate potentials, for
cases where orbits always remain at large angular momenta, or when the extra
accuracy is not needed. In all of the presented cases the accuracy in
precession in low energy orbits exceeds that of the well known potential of
Paczynski & Wiita (1980), which has ~30% error in the precession at all angular
momenta.

View original: http://arxiv.org/abs/1202.5336