Cosmology, Relativity, and Gravity Commons^™

Gravitational Wave Astrophysics With Compact Binary Systems, Eric Addison

Eric Addison

Derivation Of The Binary Mass Function, Eric Addison

Eric Addison

The observational quantity f(m), the binary mass function, is derived.

Astrophysical Mechanisms For Pulsar Spindown, Eric Addison

Eric Addison

Pulsars are astrophysical sources of pulsed electromagnetic radiation. The pulses have a variety of shapes in the time-domain, and the pulse energy generally peaks in the radio spectrum. The accepted models theorize that pulsars are rapidly rotating neutron stars with strong dipolar magnetic fields. Current models predict that rotational kinetic energy is extracted from the pulsar in the form of electromagnetic and gravitational radiation, causing it to slowly lose rotational speed, or “spin down”. This spindown can be characterized by a single value n, known as the braking index. This report will review basic characteristics of pulsars, including short treatments …

Relations Relevant To The One Body Reduction Of The Gravitational Two Body Problem, Eric Addison

Eric Addison

The one body reduction of the two body problem is outlined along with several important relations. It is verified that both masses in a binary system orbit around the common center of mass.

Instantaneous Velocities Of A Two Body Orbit, Eric Addison

Eric Addison

This short note will derive expressions for the instantaneous velocity of the components in a two-body elliptical Keplerian orbit.

Derivation Of Initial Velocities For A Two-Body Orbit In The Barycenter Frame, Eric Addison

Eric Addison

The readily available information for two body orbits generally refers to the one dimensional, reduced mass case. Information about initial conditions in the barycenter frame is not easily found. In order to derive the initial velocities required for a two-body orbit in the barycenter frame, the momentum of the reduced mass can be used.

Binary Tidal Disruption Radius, Eric Addison

Eric Addison

An expression for the tidal disruption radius of a binary system is calculated.

Elliptical Orbit Node Passage Time, Eric Addison

Eric Addison

The node passage time is calculated in order to gain an understanding of the kind of velocities and time scales will be involved in BEMRI simulations during close encounters with the SMBH. The result is generalized to produce a function of time with respect to theta, t(θ).