The construction and use of LISA sensitivity curves

Abstract: The Laser Interferometer Space Antenna (LISA) will open the mHz band of the gravitational wave spectrum for exploration. Sensitivity curves are a useful tool for surveying the types of sources that can be detected by the LISA mission. Here we describe how the sensitivity curve is constructed, and how it can be used to compute the signal-to-noise ratio for a wide range of binary systems. We adopt the 2018 LISA Phase-0 reference design parameters. We consider both sky-averaged sensitivities, and the sensitivity to sources at particular sky locations. The calculations are included in a publicly available {\em Python} notebook.

• The paper details a systematic approach to construct LISA sensitivity curves by integrating noise parameters and averaging techniques.
• It computes signal-to-noise ratios for various binary systems, including extreme mass ratio inspirals and galactic binaries.
• Researchers can utilize publicly available Python tools to simulate LISA’s response and enhance astrophysical model accuracy.

Constructing and Utilizing LISA Sensitivity Curves

The paper "The construction and use of LISA sensitivity curves" by Travis Robson, Neil J. Cornish, and Chang Liu presents a detailed methodology for defining and applying sensitivity curves associated with the Laser Interferometer Space Antenna (LISA), an ambitious project set to explore gravitational wave signals within the millihertz frequency band. This range of the gravitational wave spectrum is relatively unexplored and could offer insights into various astrophysical phenomena.

The paper provides an in-depth discussion of the design parameters for the LISA mission as of 2018, focusing on how these parameters influence the construction of sensitivity curves. These curves are pivotal for modeling what sources LISA will be capable of detecting and how signal strength is plotted against these sensitivity parameters. Particularly, sensitivity curves facilitate the calculation of the signal-to-noise ratio (SNR) for various binary systems, which is a crucial factor in determining the detectability of gravitational wave signals.

Key Contributions

The paper is divided into multiple sections, each tackling a specific aspect of LISA's sensitivity:

1. Baseline Sensitivity Curve: The sensitivity curve for LISA, expressed by the power spectral density of noise $S_n(f)$, is derived, including the influence of various noise sources on the LISA arms and the transfer function related to the signal response. The authors stress the importance of sky and inclination averaging in obtaining a representative sensitivity curve across various parts of the sky.
2. Signal-to-Noise Calculations: Understanding and computing SNR for binary systems with the aid of the defined sensitivity curves is emphasized. They describe handling four types of binary sources within this framework: equal mass inspirals, extreme mass ratio inspirals (EMRIs), stellar-mass binaries, and galactic binaries. These are presented with appropriate frequency ranges and strain descriptions.
3. Sky-Dependence Considerations: The paper tackles variability in sensitivity as a function of sky location, a critical consideration given the non-uniform sensitivity of LISA across different sky regions. For known sky-dependent sources, like verification binaries within our galaxy, they recommend specific computational techniques to assess SNR accurately.
4. Practical Computations and Tool Availability: The authors have provided a publicly accessible set of tools, written in Python, which enables researchers to compute LISA sensitivity curves and perform necessary simulations for SNR analysis for various anticipated gravitational wave sources.

Implications for LISA and Gravitational Wave Astronomy

The methodology and results presented in the paper have significant implications. The accurate sensitivity curves and SNR computations allow for refined and accurate pre-mission planning, including prioritizing potential sources for observation. This preparatory work enhances the scientific yield of the LISA mission by guiding detector designs and data analysis approaches.

The theoretical implications extend beyond astrophysical exploration. By employing these sensitivity curves, theorists can model gravitational wave sources with better fidelity, refining our understanding of phenomena such as black hole mergers, neutron star interactions, and other exotic events. Given LISA's capacity to detect waves from binaries far from coalescence, the research potentially opens up new avenues for understanding cosmic evolution and dynamics.

Future Directions

While the paper provides a thorough approach to sensitivity curves, future research could focus on further refining these models with updated LISA design specifications or more comprehensive noise models. Moreover, extending the analysis to incorporate dynamical changes in the detector's configuration or environmental factors further enhances the applicability of these sensitivity curves.

In summary, the provision of clear computational guidelines and openly accessible tools ensures that the LISA mission is well-prepared to tackle the challenges of mHz gravitational wave astronomy, promising exciting advancements in our understanding of the universe.