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The search for unmodeled, persistent GWs focuses on three directions: Scorpius X- 1 (ScoX1), the galactic center (GC), and supernova 1987a (SN1987a). We searched in frequency bins of varying size (described below) between 20 and 1726 Hz. As described in section 2.5, we combine detector-frame frequency bins in order to set limits on the strain amplitude, h0, for a neutron star rotating at a given frequency in the source’s

frame of reference. In the case of Scorpius X-1, a low-mass X-ray binary system, we combine frequency bins in order to account for both the binary motion of the potential source, as well as the motion of the Earth over the 116 days of O1. This results in an

All-sky (broadband) Results

Max SNR (% p-value) Upper limit range

α θ (deg) lmax BBR SHD BBR (×10−8) SHD (×10−8)

0 55 3 3.32 (7) 2.69 (18) 10 – 56 2.5 – 7.6

2/3 44 4 3.31 (12) 3.06 (11) 5.1 – 33 2.0 – 5.9

3 11 16 3.43 (47) 3.86 (11) 0.1 – 0.9 0.4 – 2.8

Table 3.2: Values of the power-law index α investigated in this analysis are shown in the first column. The angular resolution θ, and corresponding harmonic order lmax

(equation (2.55)) for each α are also shown. The right hand section of the table shows the maximum SNR, associated significance (p-value), and best upper limit values from the broadband radiometer (BBR) and the spherical harmonic decomposition (SHD). The BBR sets upper limits on energy flux [erg cm−2 s−1 Hz−1(f /25 Hz)α−1], while the SHD sets limits on the energy density parameter per steradian [ΩGW sr]. This table is

a subset of table 1 in [24].

Figure 3.9: All-sky radiometer maps for point-like sources. In the top we show SNR and in the bottom we show upper limits at 90% confidence on energy flux Fα,Θ0

[erg cm−2s−1 Hz−1]. Each column represents a different power law spectral index from the analysis with α = 0, 2/3 and 3, from left to right. The search parameters, maximum SNR, and associated p-values are summarized in table 3.2). These plots are reproduced from [24]

optimal combined-bin size that is frequency-dependent.

In the case of the other two directions, we expect isolated sources of GWs but wish to remain as agnostic about the signal model as possible when making a detection. Therefore, we combine frequency bins to account for the spread of a monochromatic signal in the detectors due to the motion of the Earth according to equation (2.70).

Figure 3.10: All-sky spherical harmonic decomposition maps for extended sources. In the top row we show SNR and in the bottom row we show upper limits at 90 % confidence on the GW energy density parameter in each direction, Ωα[ sr−1]. Each column displays

a different choice of the power law spectral index. From left, these correspond to α = 0, 2/3 and 3. The search parameters, maximum SNR, and associated p-values are summarized in table 3.2). These plots are reproduced from [24]

Figure 3.11: Upper limits on C_l1/2 at 90% confidence vs l for the SHD analyses for α = 0 (top, blue squares), α = 2/3 (middle, red circles) and α = 3 (bottom, green triangles). This plot and caption are reproduced from [24].

Instead of implementing a frequency-dependent bin size, as we did for ScoX1, we chose the maximum across the frequency band of that spread and all bins were combined to the same width. For SN1987a, we choose a combined bin size of 0.09 Hz. This leaves us sensitive to spin-modulations of a neutron star of up to_{| ˙}fspin| < 9×10−9Hz s−1. For GC,

which is at a lower declination, and therefore likely to experience larger modulation due to the Earth’s motion, we choose a bin size of 0.53 Hz across the frequency band. In this

Narrowband Radiometer Results

Direction Max SNR p-value (%) Freq (Hz) Best UL (_×10−25) Freq (Hz)

Sco X-1 4.58 10 616_{− 617} 6.7 134_{− 135}

SN1987A 4.07 63 195− 196 5.5 172− 173

GC 3.92 87 1347− 1348 7.0 172− 173

Table 3.3: Results for the narrowband radiometer search for three sky directions. From left we show maximum SNR and the corresponding p-value and 1 Hz frequency band in which the max SNR fell. We also show the 90% gravitational wave strain upper limits, and corresponding frequency band. The best upper limits are taken as the median of the most sensitive 1 Hz band. This table is reproduced from [24]

case, we are sensitive to frequency modulation in the range of_{| ˙}fspin| < 5.3×10−8Hz s−1.

In all three cases, we use the method defined in section 2.5 to estimate the back- ground distribution for the SNR of our frequency bins. We find that the resulting measurements are consistent with fluctuations of Gaussian noise. A summary of the maximum SNR and its p-value for each direction is shown in table 3.3. Therefore, we set upper limits on h0 in each frequency bin using the method described in section 2.5.

Plots of the 1σ sensitivity and 90% upper limits on h0 in each frequency bin are shown

in figure 3.12. In table 3.3 we show the best upper limit set in each direction in each frequency bin. Due to the large variation in our measurements from one frequency bin to the next, we take a running median of the upper limits in the 1 Hz region around each frequency bin and report the best of those values.

Figure 3.12: Upper limits on h0 from the narrowband radiometer search in three di-

rections. From left: Scorpius X-1, Supernova 1987a and the Galactic Center. In gray are 90% upper limits in each frequency bin, while in black is the 1–σ sensitivity of the search. The best upper limit in h0 for each direction is quoted in table 3.3.

At the time of publication, these were the best limits set on h0 for possible sources

from these three directions. Since that time, the limits on a source in the direction of Sco-X1 have been exceeded by two modeled searches that use known parameters of Scorpius X-1 to guide their search [133, 147].