Sensitivity curves for searches for gravitational-wave backgrounds

Abstract: We propose a graphical representation of detector sensitivity curves for stochastic gravitational-wave backgrounds that takes into account the increase in sensitivity that comes from integrating over frequency in addition to integrating over time. This method is valid for backgrounds that have a power-law spectrum in the analysis band. We call these graphs "power-law integrated curves." For simplicity, we consider cross-correlation searches for unpolarized and isotropic stochastic backgrounds using two or more detectors. We apply our method to construct power-law integrated sensitivity curves for second-generation ground-based detectors such as Advanced LIGO, space-based detectors such as LISA and the Big Bang Observer, and timing residuals from a pulsar timing array. The code used to produce these plots is available at https://dcc.ligo.org/LIGO-P1300115/public for researchers interested in constructing similar sensitivity curves.

• The paper’s main contribution is developing power-law integrated sensitivity curves that combine broadband frequency and time integration for enhanced stochastic gravitational-wave background detection.
• It applies this methodology to various detectors including Advanced LIGO, space-based missions, and pulsar timing arrays to illustrate distinct sensitivity profiles.
• The findings offer a comprehensive framework that bridges theoretical predictions and experimental limits, guiding improvements in GW detector design.

Sensitivity Curves for Searches for Gravitational-Wave Backgrounds

Eric Thrane and Joseph D. Romano address an essential aspect of gravitational-wave (GW) detection: the assessment of detector sensitivity to stochastic gravitational-wave backgrounds. The study's main contribution lies in developing a graphical representation known as 'power-law integrated curves' which integrate sensitivity over frequency and time to provide a more accurate depiction of stochastic background detection capabilities. This methodology is particularly relevant for backgrounds that exhibit a power-law spectrum.

Methodological Foundation

At the heart of this research is the construction of sensitivity curves applicable to current and planned GW detectors. Instead of evaluating the characteristic strain or the power spectral density at a single frequency, power-law integrated curves consider the broadband nature of the GW signal. These curves are plotted by calculating effective strain noise power spectral densities across frequency bands for various detectors, including second-generation ground-based detectors (Advanced LIGO), future space-based detectors (LISA, Big Bang Observer), and pulsar timing arrays.

The power-law integrated curves are derived by:

1. Calculating effective strain power spectral density using detectors' noise power spectral densities and overlap reduction functions, converting them to energy density units to get $\Omega_{\text{eff}}(f)$.
2. Assuming observation durations, typically between 1 to 10 years.
3. Integrating the signal-to-noise ratio over various frequency ranges by assuming power-law indices to derive sensitivities.
4. Plotting these spectra across frequencies and identifying the envelopes formed by these plots as the power-law integrated sensitivity curve.

Analytical Outcomes

The paper provides detailed sensitivity curves for several GW detectors:

• Advanced LIGO Networks: The sensitivity curves for different configurations (e.g., H1L1, H1H2, and H1L1V1K1) depict varying enhancements in sensitivity due to multiple detectors augmenting the network's capacity to detect stochastic backgrounds.
• BBO and LISA Sensitivities: The work projects the potential sensitivity of space-based networks like BBO, emphasizing the prominent detection capabilities they offer across a spectrum of frequencies. It also demonstrates constructions for LISA under the assumption of perfect noise and unwanted signal subtraction.
• Pulsar Timing Arrays: Contrastingly, the sensitivity curve for pulsar arrays is 'pointier', reflecting its reliance on narrow, low-frequency bands; it provides a practical cap on obtainable signal-to-noise ratios due to these constraints.

Implications and Future Directions

The development of power-law integrated sensitivity curves marks an improvement over traditional GW sensitivity modeling, as it encompasses the enhancements achieved through frequency integration, previously somewhat overlooked in sensitivity assessments. This advancement is particularly insightful for evaluating GW backgrounds that span many octaves in frequency, providing a valuable tool for comparing theoretical predictions with experimental limits.

Advancements in this method can be quite influential in the broader scope of astrophysical GW searches by portraying a comprehensive picture of realistic detection abilities over traditional sensitivity graphs. Future research could focus on refining these graphical methods, for instance, by incorporating additional factors such as noise spectral fluctuations or dynamic analyses that consider transient astrophysical phenomena.

Overall, Thrane and Romano's work offers an important analytical framework that sets the stage for evaluating the true potential of future gravitational-wave detection campaigns. This paper stands as an essential resource for researchers engaged in the development and analysis of GW detection methodologies.