# Analysis of the Conformally Flat Approximation for Binary Neutron Star Initial Conditions

## Abstract

The spatially conformally flat approximation (CFA) is a viable method to deduce initial conditions for the subsequent evolution of binary neutron stars employing the full Einstein equations. Here in this paper, we analyze the viability of the CFA for the general relativistic hydrodynamic initial conditions of binary neutron stars. We illustrate the stability of the conformally flat condition on the hydrodynamics by numerically evolving ~100 quasicircular orbits. We illustrate the use of this approximation for orbiting neutron stars in the quasicircular orbit approximation to demonstrate the equation of state dependence of these initial conditions and how they might affect the emergent gravitational wave frequency as the stars approach the innermost stable circular orbit.

- Authors:

- Univ. of Notre Dame, IN (United States). Center for Astrophysics, Dept. of Physics and Center for Research Computing
- Univ. of Notre Dame, IN (United States). Center for Astrophysics, Dept. of Physics
- Univ. of Notre Dame, IN (United States). Center for Astrophysics, Dept. of Physics ; Hanoi National Univ. of Education (Vietnam); Univ. of Notre Dame, IN (United States). Joint Inst. for Nuclear Astrophysics (JINA)

- Publication Date:

- Research Org.:
- Univ. of Notre Dame, IN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1366506

- Grant/Contract Number:
- FG02-95ER40934

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Advances in Astronomy

- Additional Journal Information:
- Journal Volume: 2017; Journal ID: ISSN 1687-7969

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS

### Citation Formats

```
Suh, In-Saeng, Mathews, Grant J., Haywood, J. Reese, and Lan, N. Q.
```*Analysis of the Conformally Flat Approximation for Binary Neutron Star Initial Conditions*. United States: N. p., 2017.
Web. doi:10.1155/2017/6127031.

```
Suh, In-Saeng, Mathews, Grant J., Haywood, J. Reese, & Lan, N. Q.
```*Analysis of the Conformally Flat Approximation for Binary Neutron Star Initial Conditions*. United States. doi:10.1155/2017/6127031.

```
Suh, In-Saeng, Mathews, Grant J., Haywood, J. Reese, and Lan, N. Q. Mon .
"Analysis of the Conformally Flat Approximation for Binary Neutron Star Initial Conditions". United States.
doi:10.1155/2017/6127031. https://www.osti.gov/servlets/purl/1366506.
```

```
@article{osti_1366506,
```

title = {Analysis of the Conformally Flat Approximation for Binary Neutron Star Initial Conditions},

author = {Suh, In-Saeng and Mathews, Grant J. and Haywood, J. Reese and Lan, N. Q.},

abstractNote = {The spatially conformally flat approximation (CFA) is a viable method to deduce initial conditions for the subsequent evolution of binary neutron stars employing the full Einstein equations. Here in this paper, we analyze the viability of the CFA for the general relativistic hydrodynamic initial conditions of binary neutron stars. We illustrate the stability of the conformally flat condition on the hydrodynamics by numerically evolving ~100 quasicircular orbits. We illustrate the use of this approximation for orbiting neutron stars in the quasicircular orbit approximation to demonstrate the equation of state dependence of these initial conditions and how they might affect the emergent gravitational wave frequency as the stars approach the innermost stable circular orbit.},

doi = {10.1155/2017/6127031},

journal = {Advances in Astronomy},

number = ,

volume = 2017,

place = {United States},

year = {Mon Jan 09 00:00:00 EST 2017},

month = {Mon Jan 09 00:00:00 EST 2017}

}