Effect of noise characterization on the detection of mHz stochastic gravitational waves

Abstract

Pulsar timing arrays' hint for a stochastic gravitational-wave background (SGWB) leverages the expectations of a future detection in the millihertz band, particularly with the LISA space mission. However, finding an SGWB with a single orbiting detector is challenging: It calls for cautious modelling of instrumental noise, which is also mainly stochastic. It was shown that agnostic noise reconstruction methods provide robustness in the detection process. We build on previous work to include more realistic instrumental simulations and additional degrees of freedom in the noise inference model and analyze the impact of LISA's sensitivity to SGWBs. Particularly, we model the two main types of noise sources with separate transfer functions and power spectral density spline fitting. We assess the detectability bounds and their dependence on the flexibility of the noise model and on the prior probability, allowing us to refine previously reported results.

Figures (6)

• Figure 1: The different priors adopted in our analyses, compared to the histogram of the whitened averaged periodogram of the time-series data (gray). Data taken from lisa-sim-data.
• Figure 2: Bayes Factors $B_{10}$ between the noise+signal $H_{1}$ and the noise-only $H_{0}$ hypotheses, for different injections of , under the assumptions of various priors on the noise model, and also different model types (parametric versus non-parametric). The first row contains the results of the runs where non-parametric models were used for all the noise and signal models, while the second row shows the results where a parametric model was used only for the signal. The last row shows the results obtained when using parametric models for all contributions to the covariance matrix. The first (respectively the second) column shows the results of the runs where the informative $\mathcal{SN}$ (respectively non-informative $\mathcal{U}$) prior was used on the instrumental noise component.
• Figure 3: (a) The detectability limits depending on the adopted type of models for the noise signal and the prior used on the noise components. The color denotes the type of prior used for the noise , while the line style denotes the type of model. This panel is basically a summary of figure \ref{['fig:bfs']}. (b) Comparison of the detectability limits for different types of models with respect to the assumed prior on the spectral shape of the noise. This figure essentially presents the ratio between the curves of the two column panels of figure \ref{['fig:bfs']}, or the ones from the left panel of this figure. The choice of informative prior is more impactful at the lower-part of the frequency spectrum, where the noise and signal transfer functions are comparable. We note similar behavior for both types of model for the . This does not hold true for the case where analytic models where adopted for all components of the data covariance matrix (orange line).
• Figure 4: Examples of signal reconstruction for an injection of a that follows the shape of a power-law with with $\Omega_0=5\times10^{-15},\, n=2$. The analysis has been performed under different assumptions about the noise priors and spectral models.
• Figure A1: Comparison of the parameter estimates of the signal ($\Omega_0=5\times10^{-15},\, n=2$) with a power-law model, under different prior assumptions, and with different models for the noise (parametric and non-parametric, based on spline interpolation). (a) Using the informative prior based on the $\mathcal{SN}$ distribution, and (b) using the flat uninformative prior. See text for details.