## Orbiting Scalar Charges

Date

Abstract

### 1 Introduction

This thorn provides a source term to the scalar ﬁeld evolution for two rotating binary charges.

### 2 Physical System

The 3D scalar wave equation with a source term $\rho \left(t,x,y,z\right)$ is written

$\nabla \varphi =4\pi \rho$

Each scalar source with charge $Q$ and radius $R$ contributes

$\rho =\frac{3Q}{4\pi {R}^{3}}$

### 3 Numerical Implementation

The only involved part of this thorn arise in working out where the sources are located (if at all) on each local grid for a multiprocessor run. The source terms are not numerically evolved, but are calculated exactly, based on the physical time and their orbital velocity.

A routine is scheduled to run after the homogeneous equation for the scalar ﬁeld has been evolved, and simply updates the value of the scalar ﬁeld by adding on the source contribution.

### 4 Parameters

 binary_charge Scope: private REAL Description: Charge of source Range Default: 0.1 : No restriction

 binary_omega Scope: private REAL Description: Frequency of the circular binary orbit Range Default: 2.0 0.0: Some positive value

 binary_radius Scope: private REAL Description: Radius of the circular binary orbit Range Default: 2.0 0.0: Some positive value

 binary_size Scope: private REAL Description: Radial extension of the binary source Range Default: 0.5 0.0: Some positive value

 binary_verbose Scope: private KEYWORD Description: Rotating binary source verbose Range Default: no yes Info on charge location/extension on ﬁrst iteration debug Info on charge location/extension on all iterations no no output

Implements:

binarysource

Inherits:

wavetoy

grid

### 6 Schedule

This section lists all the variables which are assigned storage by thorn CactusWave/WaveBinarySource. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

NONE

#### Scheduled Functions

CCTK_EVOL

wavebinaryc

provide binary source during evolution (c)

 After: wavetoy_evolution Language: c Storage: wavetoy::scalarevolve[1] Type: function