Impact of spin in compact binary foreground subtraction for estimating the residual stochastic gravitational-wave background in ground-based detectors (2024)

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  Figure 1

  Results from treatment (i) for 9-$d$ PE for BBHs (upper left) and BNSs (lower left), and 11-$d$ PE for BBHs (upper right) and BNSs (lower right). Each subfigure shows the total GW energy spectrum ${\mathrm{\Omega }}_{\mathrm{tot}}$ in black solid line and two components (${\mathrm{\Omega }}_{\mathrm{ns}}$ and ${\mathrm{\Omega }}_{\mathrm{err}}$) of the residual GW energy spectrum for different ${\rho }_{\mathrm{thr}}$. ${\mathrm{\Omega }}_{\mathrm{ns}}$ (dashed line) comes from the events that are not subtracted while ${\mathrm{\Omega }}_{\mathrm{err}}$ (dash-dotted line) comes from the imperfect subtraction of the CBC foreground. For a direct check, the two panels on the left reproduce the results of Fig.2 in Zhou etal. [44] for the IMRPhenomD waveform.

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  Figure 2

  Same as Fig.1, but for treatment (ii).

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  Figure 3

  Subfigure (a)shows number density distribution of the relative ratio $R_{\mathrm{rel}}$ and subfigure (b)shows absolute ratio $R_{\mathrm{abs}}$. Both subfigures show results for the BNS 9-$d$ PE case with ${\rho }_{\mathrm{thr}}=12$. Plots for events with high/low $c_{\mathrm{\Gamma }}$ values (denoted with red/blue color) are shown separately. Three frequency bins are chosen for illustration. The distributions at 10, 100, 200, 400, 800, and 2000Hz have similar features, which are not shown here.

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  Figure 4

  Parameter distributions of events with high and low $c_{\mathrm{\Gamma }}$ values in four PE cases. In this figure, we set ${\rho }_{\mathrm{thr}}=8$ for BBH cases and ${\rho }_{\mathrm{thr}}=12$ for BNS cases. We show three parameters here: chirp mass in the observer frame ${\mathcal{M}}_z$, symmetric mass ratio $\eta$, and orbital inclination angle $\iota$. Red color denotes events with $c_{\mathrm{\Gamma }}>{10}^{15}$, while gray color denotes events with $c_{\mathrm{\Gamma }}<{10}^{15}$.

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  Figure 5

  Contribution from each parameter to ${\mathrm{\Omega }}_{\mathrm{err}}$ for BBHs (left panel) and BNSs (right panel). Each subfigure shows ${\mathrm{\Omega }}_{\mathrm{err}}$ from 11-$d$ PE results (black solid line) and contribution from each parameter (dashed line). We choose ${\rho }_{\mathrm{thr}}$ equal to 8 and 12 for BBHs and BNSs respectively.

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  Figure 6

  Subfigure (a)shows the relative ratio $R_{\mathrm{rel}}$ and subfigure (b)shows absolute ratio $R_{\mathrm{rel}}$. Both subfigures show results for 9-$d$ PE (blue line) and 11-$d$ PE (red line) of BBHs. We set ${\rho }_{\mathrm{thr}}=8$ and choose three frequency bins to illustrate. The BNS case has a similar feature in our simulation, which is not shown here.

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  Figure 7

  The foreground subtraction results are presented for the main method (from main text) with red color and the supplementary method (from this Appendix) with blue color. The left panels show the results for 9-$d$ PE, while the right panels show the results for 11-$d$ PE. In the top panels, each subfigure shows the ${\mathrm{\Omega }}_{\mathrm{tot}}$ with solid line and ${\mathrm{\Omega }}_{\mathrm{err}}$ with ${\rho }_{\mathrm{thr}}=8$ with a dash-dotted line. In the bottom panels, each subfigure shows the results of ${\mathrm{\Omega }}_{\mathrm{err}}$ against ${\mathrm{\Omega }}_{\mathrm{tot}}$.

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