Residual count map in a 6° × 6° (pixel size of 0.05°) region around the Cygnus Loop (smoothed with a Gaussian kernel of 0.2°) obtained from 0.1 to 100 GeV. The Cygnus Loop was not included in the model (null hypothesis). Different templates are overlaid. Top left: best-fit disk and Gaussian models represented in red and white, respectively. The 4FGL point sources are shown as green stars. The ring model (4FGL J2051.0+3049e) introduced by Katagiri et al. (2011) is shown in green. Top right: best-fit ring model (green). The blue lines define the four sections used in Tables 1 and 2. Bottom left: contours of the ROSAT X-ray template (cyan, see Sect. 2.2). The templates were smoothed with a Gaussian kernel of σ = 0.2° to make the contours more regular. Contours for the X-ray template are at 30%, 20%, 10%, and 1% of the maximum. Bottom right: contours for the GALEX UV template (cyan, see Sect. 2.3) are at 40%, 25%, 15%, and 2% of the maximum.