Table 2
Numerical tests of abundance DI inversions.
| Abundance map | Magnetic field | Line list | σ/σ0 | ⟨ δε ⟩ (dex) | ⟨ | δε | ⟩ (dex) | | δε | 75 (dex) |
|
|
||||||
| Reference inversions | ||||||
| 4 spots | included | 7 Fe i | 0.97 | 0.01 | 0.09, 0.07 | 0.12, 0.11 |
| ring | included | 7 Fe i | 0.97 | 0.00 | 0.06, 0.06 | 0.08, 0.08 |
| Reduced line list and blended lines | ||||||
| 4 spots | included | 2 Fe ii | 0.99 | 0.02 | 0.11, 0.10 | 0.15, 0.13 |
| 4 spots (Fe) | included | 2 Fe ii + 1 Cr ii | 1.07 | 0.01 | 0.13, 0.11 | 0.16, 0.15 |
| ring (Cr) | included | 2 Fe ii + 1 Cr ii | 1.07 | 0.00 | 0.08, 0.08 | 0.11, 0.11 |
| Ignoring magnetic field | ||||||
| 4 spots | ignored | 7 Fe i | 1.11 | 0.32 | 0.22, 0.19 | 0.33, 0.28 |
| ring | ignored | 7 Fe i | 1.22 | 0.31 | 0.22, 0.19 | 0.32, 0.28 |
| uniform | ignored | 7 Fe i | 1.09 | 0.34 | 0.13, 0.13 | 0.18, 0.19 |
| Effect of local atmospheric structure | ||||||
| 4 spots | included | 7 Fe i | 1.25 | 0.05 | 0.21, 0.19 | 0.29, 0.27 |
| ring | included | 7 Fe i | 2.16 | 0.01 | 0.21, 0.21 | 0.29, 0.29 |
Notes. Columns 1–3 describe the surface abundance distribution adopted for the test, indicate the treatment of magnetic field in chemical abundance DI, and provide information on the spectral line list used for the inversion. Column 4 lists the ratio of the final standard deviation of the model fit to the amplitude of the random noise in simulated data. Column 5 gives the mean offset between the true and reconstructed abundance map for latitudes ≥−30°; Column 6 lists the mean absolute error of the reconstructed horizontal abundance structure for latitudes ≥−30° and ≥ 0°; Column 7 gives the 75th percentile of the abundance difference map for latitudes ≥−30° and ≥0°.
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