Improved limits on a stochastic gravitational-wave background and its anisotropies from Advanced LIGO O1 and O2 runs

We integrate the entire, publicly available, Advanced LIGO (ALIGO) data set to obtain maximum-likelihood constraint maps of the Stochastic Gravitational-Wave Background (SGWB). From these we derive limits on the energy density of the stochastic background ${\mathrm{\Omega }}_{\mathrm{G}\mathrm{W}}$, and its anisotropy. We find 95% confident limits ${\mathrm{\Omega }}_{\mathrm{G}\mathrm{W}}<5.2\times {10}^{-8}$ at $50$ Hz for a spectral index $\alpha =2\mathrm{/}3$ consistent with a stochastic background due to inspiral events and ${\mathrm{\Omega }}_{\mathrm{G}\mathrm{W}}<3.2\times {10}^{-7}$ for a scale (frequency) invariant spectrum. We also report upper limits on the angular power spectra $C_{\mathrm{\ell }}$ for three broadband integrations of the data. Finally we present an estimate where we integrate the data into ten separate spectral bins as a first attempt to carry out a model-independent estimate the SGWB and its anisotropies.