Simultaneously search for multi-target Galactic binary gravitational waves

Abstract

The search for Galactic binary gravitational waves is a critical challenge for future space-based gravitational wave detectors, such as LISA. We propose an innovative approach to simultaneously explore gravitational waves originating from Galactic binaries by developing a new Local Maxima Particle Swarm Optimization (LMPSO) algorithm. This new approach effectively addresses the inaccuracies often associated with signal subtraction contamination, a challenge for traditional iterative subtraction methods, particularly when dealing with low signal-to-noise ratio (SNR) signals (e.g., SNR $<$ 15). We also account for the effects of overlapping signals and degeneracy noise. To demonstrate the effectiveness of our approach, we use residuals from the LISA mock data challenge (LDC1-4), where 10,982 injected sources with SNR $\ge$ 15 have been removed. For the remaining sources with SNR $<$ 15, our method successfully identifies 6,508 signals, yielding a false alarm rate of $\text{FAS}_{0.8} = 36.8\%$. By focusing on a subset of sources-specifically, those with $f > 3$ mHz and those with $f \le 3$ mHz but SNR $\ge 13$-we identify 3,406 signals, with a reduced false alarm rate of $\text{FAS}_{0.8} = 22.5\%$. We further demonstrate that, within the same detection SNR range, our method achieves a comparable or lower $\text{FAS}$ than other existing methods.

Figures (25)

• Figure 1: Galactic binaries distribution in the galactic coordinate system of LDC1-4 (SNR $>$ 7). The color bar represents the number of binaries within one square degree on the celestial sphere. The two red lines mark the area where the Galactic Latitude is between -0.5 rad and 0.5 rad ($-28.65 \degree \sim 28.65 \degree$), and there are 27,436 binaries in this area out of 27,680 binaries in total. This prior information will be used in the data analysis (See Sec. \ref{['sec:Restrict_the_Galactic_latitude']} for details).
• Figure 2: Distribution of Galactic binaries in different frequency bins of the LDC1-4 data. Each bin has a width of 0.01 mHz. We categorize the signals into two groups based on SNR: those with SNR $>$ 15 and those with 7 $<$ SNR $<$ 15. In the figure, we observe that binaries are more concentrated at low frequencies ($f < 1 \times 10^{-3}$ Hz) and medium frequencies ($1 \times 10^{-3}$ Hz $<$$f$$<$$4 \times 10^{-3}$ Hz) when considering signals with 7 $<$ SNR $<$ 15.
• Figure 3: The $x-y$ coordinate plane represents the ecliptic plane, with the $x$-axis directed toward the vernal equinox. LISA orbits the SSB within the ecliptic plane at a speed denoted by $\vec{\nu}$, and the origin $o$ corresponds to the SSB's position. Within the LISA data, there exists a GW signal originating from binary $A$ with parameters $f_{A}$, $\beta_A$ and $\lambda_A$. Employing a match filtering method, for detection involves assuming that the match waveform corresponds to binary $A^{\prime}$ ($f_{A^{\prime}},~\beta_{A^{\prime}},~\lambda_{A^{\prime}}$).
• Figure 4: The parameter degeneracy from binary $A$ is derived according to Eq. \ref{['con:3']}. The parameters of binary $A$—$f_{A},~\beta_A,~\lambda_A$—are known, and the position of binary $A$ is denoted by red cross marks. In Fig. \ref{['fig:degeneracy_noise1']}, $\beta_A^{\prime}=\beta_A$, and in Fig. \ref{['fig:degeneracy_noise2']}, $\lambda_A^{\prime}=\lambda_A$. The horizontal axis represents the frequency ($f_{A^{\prime}}$) of the matched waveform, binary $A^{\prime}$, while the vertical axis represents its Ecliptic Longitude or Ecliptic Latitude ($\lambda_A^{\prime}$ or $\beta_A^{\prime}$). $\theta$ denotes the angle between LISA and binary $A$, with different $\theta$ values representing various positions of LISA relative to binary $A$.
• Figure 5: Slices of the $\mathcal{F}$-statistic in three-dimensional parameter space for binary $A$. The parameter position of binary $A$ is marked in the subfigure (2, 5) with a red cross. The frequency intervals between two adjacent subfigures correspond to the minimum frequency resolution $\mathrm{d}f=1.59\times10^{-8}$ Hz. In each subfigure, the horizontal coordinate represents Ecliptic Longitude $\lambda$, and the vertical coordinate is Ecliptic Latitude $\beta$. The figure does not encompass the entire frequency range of the degeneracy noise distribution.