# Revealing the formation of stellar-mass black hole binaries: The need for deci-Hertz gravitational wave observatories

## TL;DR

This paper emphasizes the importance of deci-Hertz gravitational wave observatories like DECIGO or Tian Qin for understanding the formation of stellar-mass black hole binaries, especially in dense stellar environments, by complementing LIGO and LISA observations.

## Contribution

It demonstrates that deci-Hertz observatories can improve detection prospects and help distinguish formation channels of black hole binaries, especially when LISA cannot detect high-eccentricity mergers.

## Key findings

- High eccentricities may prevent LISA detection of some mergers.
- Non-detection by LISA sets a lower eccentricity limit of 0.005.
- Deci-Hertz observatories enhance joint detection capabilities.

## Abstract

The formation of compact stellar-mass binaries is a difficult, but interesting problem in astrophysics. There are two main formation channels: In the field via binary star evolution, or in dense stellar systems via dynamical interactions. The Laser Interferometer Gravitational-Wave Observatory (LIGO) has detected black hole binaries (BHBs) via their gravitational radiation. These detections provide us with information about the physical parameters of the system. It has been claimed that when the Laser Interferometer Space Antenna (LISA) is operating, the joint observation of these binaries with LIGO will allow us to derive the channels that lead to their formation. However, we show that for BHBs in dense stellar systems dynamical interactions could lead to high eccentricities such that a fraction of the relativistic mergers are not audible to LISA. A non-detection by LISA puts a lower limit of about $0.005$ on the eccentricity of a BHB entering the LIGO band. On the other hand, a deci-Hertz observatory, like DECIGO or Tian Qin, would significantly enhance the chances of a joint detection, and shed light on the formation channels of these binaries.