Upper limit map of a background of gravitational waves

Abstract

We searched for an anisotropic background of gravitational waves usingdata from the LIGO S4 science run and a method that is optimizedfor point sources. This is appropriate if, for example, the gravitationalwave background is dominated by a small number of distinct astrophysical sources.No signal was seen. Upper limit maps were produced assuming two differentpower laws for the source strain power spectrum. For an ${f}^{\ensuremath{-}3}$ power law and using the50 Hz to 1.8 kHz band the upper limits on the sourcestrain power spectrum vary between $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}48}\text{ }\text{ }{\mathrm{Hz}}^{\ensuremath{-}1}$ $(100\text{ }\text{ }\mathrm{Hz}/f{)}^{3}$ and $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}47}\text{ }\text{ }{\mathrm{Hz}}^{\ensuremath{-}1}$ $(100\text{ }\text{ }\mathrm{Hz}/f{)}^{3}$, depending on the position in the sky. Similarly,in the case of constant strain power spectrum, the upper limits vary between $8.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}49}\text{ }\text{ }{\mathrm{Hz}}^{\ensuremath{-}1}$ and $6.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}48}\text{ }\text{ }{\mathrm{Hz}}^{\ensuremath{-}1}$. As a side product a limiton an isotropic background of gravitational waves was also obtained. All limitsare at the 90% confidence level. Finally, as an application, we focused onthe direction of Sco-X1, the brightest low-mass x-ray binary. We compare theupper limit on strain amplitude obtained by this method to expectations basedon the x-ray flux from Sco-X1.