Optimally setting up directed searches for continuous gravitational waves in Advanced LIGO O1 data

In this paper we design a search for continuous gravitational waves from three supernova remnants: Vela Jr., Cassiopeia A (Cas A) and G347.3. These systems might harbor rapidly rotating neutron stars emitting quasiperiodic gravitational radiation detectable by the advanced LIGO detectors. Our search is designed to use the volunteer computing project Einstein@Home for a few months and assumes the sensitivity and duty cycles of the advanced LIGO detectors during their first science run. For all three supernova remnants, the sky positions of their central compact objects are well known but the frequency and spin-down rates of the neutron stars are unknown which makes the searches computationally limited. In a previous paper we have proposed a general framework for deciding on what target we should spend computational resources and in what proportion, what frequency and spin-down ranges we should search for every target, and with what search setup. Here we further expand this framework and apply it to design a search directed at detecting continuous gravitational wave signals from the most promising three supernova remnants identified as such in the previous work. Our optimization procedure yields broad frequency and spin-down searches for all three objects, at an unprecedented level of sensitivity: The smallest detectable gravitational wave strain $h_0$ for Cas A is expected to be 2 times smaller than the most sensitive upper limits published to date, and our proposed search, which was set up and ran on the volunteer computing project Einstein@Home, covers a much larger frequency range.

Figure 1

This histogram shows the mismatch distribution for the grid spacing: $m_f=0.15$, $m_{\dot{f}}=0.3$, $m_{\ddot{f}}=0.003$, ${\gamma }^{(1)}=8$, ${\gamma }^{(2)}=20$ and $T_{\mathrm{coh}}=15$ days for Vela Jr. and it is the setup that was eventually chosen for the search. The average measured mismatch is $⟨\mu ⟩=15.8\%$.

Figure 2

Distribution of the runtimes of the Einstein@Home O1 low frequency all-sky search work units. The data in this figure is taken from a sample of 3076 hosts out of total 28764 hosts of Einstein@Home.

Figure 3

432 setups with $T_{\mathrm{coh}}=15$ days. The 19 blue stars in red circles are selected for further consideration as explained in the text.

Figure 4

Parameter space coverage assuming uniform $f,\dot{f}$ priors, Vela Jr. at 200 pc (C) and 3 EM computing budget. In panel (a) we assume Vela Jr.’s age is 700 years (Y) and in panel (b) we assume that Vela Jr. is 4300 years old (O). The plane is indicated in aqua. Cells in blue are searched with 10-day $T_{\mathrm{coh}}$ setups, magenta indicates 15-day $T_{\mathrm{coh}}$, yellow the 20-day $T_{\mathrm{coh}}$, red the 30-day $T_{\mathrm{coh}}$, and green the 60-day $T_{\mathrm{coh}}$ (although not used in either cases). The computing power used on Cas A, Vela Jr. and G347.3 is 1.36 EM, 1.14 EM and 0.50 EM, respectively, for the setups of panel (a), and 1.97 EM, 0.21 EM and 0.82 EM for the setups of panel (b). The contribution to the total detection probability from Cas A, Vela Jr. and G347.3 is 1.3%, 14.4% and 3.1% for panel (a), and 1.4%, 11.5% and 3.1% for panel (b). Note that each color represents setups which have the same coherent duration, but might differ in the grid spacings. Part (c) shows the setup details on Vela Jr. plane in part (a). For example, the blue circles represent the cells that need to be searched by using the setup: $m_f=0.15$, $m_{\dot{f}}=0.15$, $m_{\ddot{f}}=0.001$, ${\gamma }^{(1)}=8$, ${\gamma }^{(2)}=10$, and $T_{\mathrm{coh}}=10$ day.

Figure 5

Optimal setup details. The left-hand-side parts show the setups assuming Vela Jr. is close and young. The right hand-side parts show the setups assuming Vela Jr. is close and old. As explained in Sec. 5d, the arrows indicate the setups that will finally be adopted in the search.

Figure 6

$\mathcal{R}$ versus computing budget $C$.

Figure 7

$\mathcal{R}$ versus computing budget $C$ from 357911 combinations of setups with different priors. Each dot on this plot is a combination of setups, one per target. The green curve shows the optimal $\mathcal{R}$ as a function of $C$. The golden stars highlight the best setup combinations around 3 EM.

Figure 8

Expected 90% confidence upper limit on the GW amplitude $h_0^{90\%}$ from the directed searches proposed here, based on the noise level of the LIGO O1 data and on the estimated sensitivity of the proposed searches. We stress that this is not an observational result but a prediction of it.