Optimizing the StackSlide setup and data selection for continuous-gravitational-wave searches in realistic detector data

The search for continuous gravitational waves in a wide parameter space at a fixed computing cost is most efficiently done with semicoherent methods, e.g., StackSlide, due to the prohibitive computing cost of the fully coherent search strategies. Prix and Shaltev [Phys. Rev. D 85, 084010 (2012)] have developed a semianalytic method for finding optimal StackSlide parameters at a fixed computing cost under ideal data conditions, i.e., gapless data and a constant noise floor. In this work, we consider more realistic conditions by allowing for gaps in the data and changes in the noise level. We show how the sensitivity optimization can be decoupled from the data selection problem. To find optimal semicoherent search parameters, we apply a numerical optimization using as an example the semicoherent StackSlide search. We also describe three different data selection algorithms. Thus, the outcome of the numerical optimization consists of the optimal search parameters and the selected data set. We first test the numerical optimization procedure under ideal conditions and show that we can reproduce the results of the analytical method. Then we gradually relax the conditions on the data and find that a compact data selection algorithm yields higher sensitivity compared to a greedy data selection procedure.

Figure 1

Schematic representation of (a) greedy and (b) compact data selection. The middle line of squares in gray are the available SFTs of unit time, where the number inside the square denotes the PSD. The white squares without a number are gaps in the data. The selected segments are the white rectangles, where the number inside is the number of the segment.

Figure 2

Semicoherent search optimization for data from two detectors, without gaps and of constant noise floor $\sqrt{S_{\mathrm{n}}}=1{\mathrm{Hz}}^{-1/2}$. The cost constraint is $C_0=472.0\mathrm{d}$. The best numerical solution is denoted with $\times$ and the optimal analytical solution with $+$. The panels on the left side show optimal segment duration $\mathrm{\Delta }T$ and number of segments $N$, and the panels on the right side show optimal coherent $\tilde{m}$ and semicoherent $\widehat{m}$ mismatch. Panels (a) and (b) are obtained using greedy data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.08$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.29$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 1.1\mathrm{d}$, $N_{\mathrm{opt}}\approx 210.0$, $T_{\mathrm{opt}}\approx 245.0\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 80.2{\mathrm{Hz}}^{-1/2}$. Panels (c) and (d) are obtained using compact data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.09$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.37$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 1.2\mathrm{d}$, $N_{\mathrm{opt}}\approx 203.0$, $T_{\mathrm{opt}}\approx 253.8\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 80.1{\mathrm{Hz}}^{-1/2}$. Panels (e) and (f) are obtained using greedy-compact data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.10$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.32$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 1.3\mathrm{d}$, $N_{\mathrm{opt}}\approx 184.1$, $T_{\mathrm{opt}}\approx 239.3\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 80.1{\mathrm{Hz}}^{-1/2}$.

Figure 3

Semicoherent search optimization using data from two detectors with a duty cycle of 70% and of constant noise floor $\sqrt{S_{\mathrm{n}}}=1{\mathrm{Hz}}^{-1/2}$. The cost constraint is $C_0=472.0\mathrm{d}$. The best numerical solution is denoted with $\times$. The panels on the left side show optimal segment duration $\mathrm{\Delta }T$ and number of segments $N$, and the panels on the right side show optimal coherent $\tilde{m}$ and semicoherent $\widehat{m}$ mismatch. Panels (a) and (b) are obtained using greedy data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.07$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.46$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 0.9\mathrm{d}$, $N_{\mathrm{opt}}\approx 326.0$, $T_{\mathrm{opt}}\approx 364.3\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 64.8{\mathrm{Hz}}^{-1/2}$. Panels (c) and (d) are obtained using compact data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.08$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.27$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 1.3\mathrm{d}$, $N_{\mathrm{opt}}\approx 165.8$, $T_{\mathrm{opt}}\approx 220.5\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 68.0{\mathrm{Hz}}^{-1/2}$. Panels (e) and (f) are obtained using greedy-compact data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.04$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.35$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 0.7\mathrm{d}$, $N_{\mathrm{opt}}\approx 434.1$, $T_{\mathrm{opt}}\approx 364.7\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 65.0{\mathrm{Hz}}^{-1/2}$.

Figure 4

Semicoherent search optimization for data from two detectors with duty cycle 70% and a noise floor with fluctuations. The cost constraint is $C_0=472.0\mathrm{d}$. The best numerical solution is denoted with $\times$. The panels on the left side show optimal segment duration $\mathrm{\Delta }T$ and number of segments $N$, and the panels on the right side show optimal coherent $\tilde{m}$ and semicoherent $\widehat{m}$ mismatch. Panels (a) and (b) are obtained using greedy data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.03$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.32$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 0.7\mathrm{d}$, $N_{\mathrm{opt}}\approx 454.1$, $T_{\mathrm{opt}}\approx 364.9\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 64.6{\mathrm{Hz}}^{-1/2}$. Panels (c) and (d) are obtained using compact data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.08$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.27$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 1.4\mathrm{d}$, $N_{\mathrm{opt}}\approx 154.6$, $T_{\mathrm{opt}}\approx 215.3\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 68.0{\mathrm{Hz}}^{-1/2}$. Panels (e) and (f) are obtained using greedy-compact data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.04$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.35$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 0.7\mathrm{d}$, $N_{\mathrm{opt}}\approx 423.0$, $T_{\mathrm{opt}}\approx 364.8\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 64.8{\mathrm{Hz}}^{-1/2}$.

Figure 5

Semicoherent search optimization for data from the H1 and L1 LIGO detectors during the S5 run at 169.875 Hz. The cost constraint is $C_0=472.0\mathrm{d}$. The best numerical solution is denoted with $\times$. The panels on the left side show optimal segment duration $\mathrm{\Delta }T$ and number of segments $N$, and the panels on the right side show optimal coherent $\tilde{m}$ and semicoherent $\widehat{m}$ mismatch. Panels (a) and (b) are obtained using greedy data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.06$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.61$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 0.9\mathrm{d}$, $N_{\mathrm{opt}}\approx 182.2$, $T_{\mathrm{opt}}\approx 554.4\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 56.9{\mathrm{Hz}}^{-1/2}$. Panels (c) and (d) are obtained using compact data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.05$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.27$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 1.0\mathrm{d}$, $N_{\mathrm{opt}}\approx 134.3$, $T_{\mathrm{opt}}\approx 329.0\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 63.4{\mathrm{Hz}}^{-1/2}$. Panels (e) and (f) are obtained using greedy-compact data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.04$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.55$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 0.8\mathrm{d}$, $N_{\mathrm{opt}}\approx 183.1$, $T_{\mathrm{opt}}\approx 653.0\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 56.5{\mathrm{Hz}}^{-1/2}$.

Figure 6

Semicoherent search optimization with data from the H1 and L1 LIGO detectors during the S5 run at $169.875\mathrm{Hz}$. The cost constraint is $C_0=360\times {10}^3\mathrm{d}$. The best numerical solution is denoted with $\times$. The panels on the left side show optimal segment duration $\mathrm{\Delta }T$ and number of segments $N$, and the panels on the right side show optimal coherent $\tilde{m}$ and semicoherent $\widehat{m}$ mismatch. Panels (a) and (b) are obtained using greedy data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.10$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.28$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 15.4\mathrm{d}$, $N_{\mathrm{opt}}\approx 20.0$, $T_{\mathrm{opt}}\approx 464.8\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 98.6{\mathrm{Hz}}^{-1/2}$. Panels (c) and (d) are obtained using compact data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.11$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.29$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 17.9\mathrm{d}$, $N_{\mathrm{opt}}\approx 20.0$, $T_{\mathrm{opt}}\approx 387.7\mathrm{d}$, $\tilde{n}=3$, $\widehat{n}=3$, and $\mathcal{D}\approx 97.9{\mathrm{Hz}}^{-1/2}$. Panels (e) and (f) are obtained using greedy-compact data selection; the most sensitive optimal solution is ${\tilde{m}}_{\mathrm{opt}}\approx 0.04$, ${\widehat{m}}_{\mathrm{opt}}\approx 0.26$, ${\mathrm{\Delta }T}_{\mathrm{opt}}\approx 9.8\mathrm{d}$, $N_{\mathrm{opt}}\approx 35.2$, $T_{\mathrm{opt}}\approx 653.2\mathrm{d}$, $\tilde{n}=2$, $\widehat{n}=3$, and $\mathcal{D}\approx 95.6{\mathrm{Hz}}^{-1/2}$.