Table 1
Best-fit spatial properties and test statistics of the Cygnus Loop for different morphological models compared with the null hypothesis of no γ-ray emission associated with the Cygnus Loop (0.1–100 GeV).
| Model | RA |
Dec |
 |
Test statistic(a) | Additional DoF |
|---|---|---|---|---|---|
| Null hypothesis(b) | 0 | 0 | |||
| Uniform disk | 312.905 ± 0.016 | 31.130 ± 0.018 |  |
6120 | 6 |
| Gaussian 2D | 312.959 ± 0.022 | 31.269 ± 0.021 |  |
5874 | 6 |
| Ring | 312.905 | 31.130 |  ,  |
6172 | 7 |
| Non-uniform ring(c) | 312.905 | 31.130 | rmax = 1.50, rmin = 0.50 | 6442 | 16 |
| X-ray (0.1–2 keV)(d) | 6446 | 3 | |||
| Optical (1.7–2 eV)(e) | 6584 | 3 | |||
| UV (4–9 eV)(f) | 6650 | 3 | |||
| Radio 21 cm (1427 MHz)(g) | 4986 | 3 | |||
| Radio 11 cm (2725 MHz)(g) | 4878 | 3 | |||
| Radio 6 cm (4996 MHz) (h) | 4750 | 3 | |||
| X-ray + UV | 6870 | 6 |
Notes. Spectral model: LogParabola. (a) 
, where 
and 
are the maximum likelihoods for the model with or without the source component, respectively. (b) Background only (no model for the Cygnus Loop). (c)A ring (same radius as the ring model) divided into four regions as shown in Fig. 3 and allowing an independent normalization and spectral index for the four portions of the ring. (d) The X-ray template is based on data from ROSAT (see Sect. 2.2). (e) The optical template is based on data from DSS2 (see Sect. 2.4). (f) The UV template is based on data from GALEX (see Sect. 2.3). (g) Template based on data from the Effelsberg 100 m Radio Telescope (see Sect. 2.5). (h) Template based on data from the Urumqi 25 m Telescope (see Sect. 2.5).
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