Table 3.
Fit summary results for the metrics and Bayesian criteria with GRAVITY uncertainties.
| Data’s metric | ⟨χred2⟩ | ⟨BIC⟩ | ⟨log10 K⟩ | detectability | ⟨log10 K|Kerr⟩ |
|---|---|---|---|---|---|
| Schwarzschild | 0.94 ± 0.14 | 65 ± 7 | −0.04 ± 0.52 | ✗✗ | 0.59 ± 0.68 ✗ |
| Boson star 2 | 0.92 ± 0.22 | 63 ± 11 | 0.73 ± 0.48 | ✗✗ | 3.9 ± 1.6 ✓ |
| Boson star 3 | 0.99 ± 0.22 | 66 ± 11 | 0.16 ± 0.13 | ✗✗ | 1.4 ± 0.9 ✗ |
| Fluid sphere 2 | 1.01 ± 0.13 | 68 ± 7 | 0.01 ± 0.32 | ✗✗ | 0.81 ± 0.45 ✗ |
| Fluid sphere 3 | 0.91 ± 0.23 | 63 ± 11 | 0.20 ± 0.47 | ✗✗ | 1.7 ± 1.2 ✗ |
| Gravastar 1 | 1.00 ± 0.13 | 67 ± 7 | 0.18 ± 0.16 | ✗✗ | 1.7 ± 0.5 ∼ |
| Gravastar 2 | 0.97 ± 0.25 | 65 ± 12 | 0.13 ± 0.09 | ✗✗ | 2.2 ± 1.1 ∼ |
| Gravastar 3 | 1.01 ± 0.21 | 68 ± 11 | 0.02 ± 0.20 | ✗✗ | 1.0 ± 0.7 ✗ |
Notes. The first column lists the metric we used for simulated data. The second column reports the average best ⟨χred2⟩ with its standard deviation. The third column shows the average associated BIC with its standard deviation. The fourth column shows the average BIC-based Bayes factor and its standard deviation. The fifth column indicates the background metric detectability according to the criteria defined in Sect. 4.2.2. The final column reports the BIC-based Bayes factor between the best-fitting metric and Kerr, and assesses the exclusion of the latter.
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