Upper limit map of a background of gravitational waves

We searched for an anisotropic background of gravitational waves using data from the LIGO S4 science run and a method that is optimized for point sources. This is appropriate if, for example, the gravitational wave background is dominated by a small number of distinct astrophysical sources. No signal was seen. Upper limit maps were produced assuming two different power laws for the source strain power spectrum. For an $f^{-3}$ power law and using the 50 Hz to 1.8 kHz band the upper limits on the source strain power spectrum vary between $1.2\times {10}^{-48}{\mathrm{Hz}}^{-1}$ $(100\mathrm{Hz}/f{)}^3$ and $1.2\times {10}^{-47}{\mathrm{Hz}}^{-1}$ $(100\mathrm{Hz}/f{)}^3$, depending on the position in the sky. Similarly, in the case of constant strain power spectrum, the upper limits vary between $8.5\times {10}^{-49}{\mathrm{Hz}}^{-1}$ and $6.1\times {10}^{-48}{\mathrm{Hz}}^{-1}$. As a side product a limit on an isotropic background of gravitational waves was also obtained. All limits are at the 90% confidence level. Finally, as an application, we focused on the direction of Sco-X1, the brightest low-mass x-ray binary. We compare the upper limit on strain amplitude obtained by this method to expectations based on the x-ray flux from Sco-X1.

Figure 1

Injected pulsar No. 3: The analysis was run using the108.625 Hz–109.125 Hz frequency band. Theartificial signal of pulsar No. 3 at 108.86 Hz standsout with a signal-to-noise ratio of 9.2. The circle marks the position ofthe simulated pulsar.

Figure 2

Periodic timing transient in the gravitational wave channel (DARM_ERR),calibrated in $\mu \mathrm{V}$ at the ADC (Pentek card) for H1 (left two graphs) andL1 (right two graphs) shown with a span of 200 and 14 msec inblack. The $x$ axisis the offset from a full GPS second. About $1.4\times {10}^6\sec$ of DARM_ERR data was averaged to get this trace. Alsoshown in gray is the GPS_RAMP signal that was used as a timing monitor. Itwas identified as a cause of the periodic timing transient in DARM_ERR. TheH1 trace shows an additional feature at 6 msec.

Figure 3

Point spread function $A(\widehat{\Omega },{\widehat{\Omega }}^{\prime })$ ofthe radiometer for $\beta =-3$ (top two figures) and for $\beta =0$ (bottom two figures). Plotted is the relative expectedsignal strength assuming a source at right ascension 12 h anddeclinations 20° and 60°. Uniform day coverage was assumed, so theresulting shapes are independent of right ascension. An Aitoff projectionwas used to plot the whole sky.

Figure 4

S4 Result: Histogram of the signal-to-noise ratio (SNR) for $\beta =-3$. The gray curve is a maximum likelihoodGaussian fit to the data. The black solid line is an ideal Gaussian, the twodash-dotted black lines indicate the expected one sigma variations aroundthis ideal Gaussian for 100 independent points ($N_{\mathrm{eff}}=100$).

Figure 5

S4 Result: Map of the 90% confidence level Bayesian upper limit on $H_{\beta }$ for $\beta =-3$. The upper limit varies between $1.2\times {10}^{-48}{\mathrm{Hz}}^{-1}$ $(100\mathrm{Hz}/f{)}^3$ and $1.2\times {10}^{-47}{\mathrm{Hz}}^{-1}$ $(100\mathrm{Hz}/f{)}^3$, depending on the position in the sky. All fluctuationsare consistent with the expected noise.

Figure 6

S4 Result: Histogram of the SNR for $\beta =0$. The gray curve is a maximum likelihood Gaussian fit tothe data. The black solid line is an ideal Gaussian, the two dash-dotted blacklines indicate the expected one sigma variations around this ideal Gaussianfor 400 independent points ($N_{\mathrm{eff}}=400$).

Figure 7

S4 Result: Map of the 90% confidence level Bayesian upper limit on $H_{\beta }$ for $\beta =0$. The upper limit varies between $8.5\times {10}^{-49}{\mathrm{Hz}}^{-1}$ and $6.1\times {10}^{-48}{\mathrm{Hz}}^{-1}$ depending on the positionin the sky.

Figure 8

S4 Result for Sco-X1: Histogram of the signal-to-noise ratio calculatedfor each 0.25 Hz wide frequency bin. There are no outliers.

Figure 9

S4 Result for Sco-X1: The 90% confidence Bayesian upper limit asa function of frequency—marginalized over the calibration uncertainty.The standard deviation (one sigma error bar) is shown in gray.