Probing Formation of Double Neutron Star Binaries around 1mHz with LISA

TL;DR

This paper introduces a statistical method to determine if Galactic double neutron star binaries form within the LISA frequency band by analyzing their orbital parameters and effective time fractions.

Contribution

It proposes a novel approach using the effective time fraction and statistical tests to detect in-band binary formation with LISA data.

Findings

Method can identify in-band formation signatures

Applicability depends on the number of detected binaries

Provides a new tool for understanding binary evolution

Abstract

We propose a novel method to examine whether Galactic double neutron star binaries are formed in the LISA band. In our method, we assign an effective time fraction $\tau$ to each double neutron star binary detected by LISA. This fraction is given as a function of the observed orbital period and eccentricity and should be uniformly distributed in the absence of in-band binary formation. Applying statistical techniques such as the Kolmogorov-Smirnov test to the actual list of $\tau$, we can inspect the signature of the in-band binary formation. We discuss the prospects of this method, paying close attention to the available sample number of Galactic double neutron star binaries around 1mHz.