Table A.1
Detailed gradient results for different selection criteria and fit methods, respectively.
| ⟨ RU ⟩ | ⟨ RP ⟩ | All data | Slow ascent (green) | Slow descent (blue) | ||||
|
|
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| Fit (1) | Fit (2) | Fit (1) | Fit (2) | Fit (1) | Fit (2) | |||
|
|
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| 0.45 | 0.44 | |||||||
| Gr = | 3.8 ± 0.7 | 3.3 ± 0.9 | 5.4 ± 1.5 | 3.5 ± 2.2 | 3.5 ± 0.7 | 3.2 ± 0.9 | ||
| Gθ = | −0.17 ± 0.02 | −0.14 ± 0.03 | −0.17 ± 0.04 | −0.13 ± 0.07 | −0.17 ± 0.03 | −0.14 ± 0.04 | ||
| χ2/ndf = | 0.8 | 0.7 | 0.5 | 0.4 | 1. | 1. | ||
|
|
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| 0.45 | 0.46 | |||||||
| Gr = | 3.9 ± 0.6 | 3.9 ± 0.8 | 4.2 ± 1.2 | 3.6 ± 1.9 | 3.8 ± 0.6 | 3.9 ± 0.8 | ||
| Gθ = | −0.01 ± 0.02 | −0.09 ± 0.03 | −0.09 ± 0.04 | −0.08 ± 0.06 | −0.1 ± 0.03 | −0.09 ± 0.04 | ||
| χ2/ndf = | 0.6 | 0.6 | 0.3 | 0.2 | 0.9 | 0.9 | ||
|
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| 0.46 | 0.46 | |||||||
| Gr = | 4.4 ± 0.5 | 4.4 ± 0.8 | 4.4 ± 1.2 | 3.8 ± 2. | 4.3 ± 0.6 | 4.5 ± 0.8 | ||
| Gθ = | −0.09 ± 0.02 | −0.09 ± 0.03 | −0.09 ± 0.04 | −0.08 ± 0.06 | −0.1 ± 0.02 | −0.09 ± 0.04 | ||
| χ2/ndf = | 0.8 | 0.8 | 0.3 | 0.3 | 1.2 | 1.2 | ||
|
|
||||||||
| 0.49 | 0.46 | |||||||
| Gr = | 2.3 ± 0.6 | 2.8 ± 0.8 | 2.5 ± 1.3 | 2.8 ± 2.1 | 2.4 ± 0.6 | 2.8 ± 0.9 | ||
| Gθ = | −0.12 ± 0.02 | −0.13 ± 0.03 | −0.13 ± 0.04 | −0.14 ± 0.06 | −0.13 ± 0.03 | −0.13 ± 0.04 | ||
| χ2/ndf = | 0.8 | 0.8 | 0.3 | 0.3 | 1.2 | 1.1 | ||
|
|
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| 0.49 | 0.49 | |||||||
| Gr = | 1.6 ± 0.6 | 2.7 ± 0.8 | 1.8 ± 1.3 | 2.9 ± 2. | 1.6 ± 0.6 | 2.7 ± 0.9 | ||
| Gθ = | −0.09 ± 0.02 | −0.12 ± 0.03 | −0.11 ± 0.04 | −0.14 ± 0.06 | −0.10 ± 0.03 | −0.12 ± 0.04 | ||
| χ2/ndf = | 1.1 | 1. | 0.6 | 0.6 | 1.5 | 1.4 | ||
|
|
||||||||
| 1.13 | 1.11 | |||||||
| Gr = | 3.5 ± 0.3 | 3.2 ± 0.2 | 4.9 ± 0.4 | 5.3 ± 0.6 | 3.2 ± 0.2 | 2.8 ± 0.3 | ||
| Gθ = | −0.06 ± 0.01 | −0.03 ± 0.01 | −0.04 ± 0.01 | −0.05 ± 0.02 | −0.06 ± 0.01 | −0.05 ± 0.01 | ||
| χ2/ndf = | 5.3 | 5. | 1.8 | 1.8 | 5. | 4.8 | ||
|
|
||||||||
| 1.63 | 1.61 | |||||||
| Gr = | 3.3 ± 0.2 | 3.2 ± 0.2 | 2.2 ± 0.3 | 2.2 ± 0.4 | 3.6 ± 0.2 | 3.4 ± 0.2 | ||
| Gθ = | −0.04 ± 0.01 | −0.04 ± 0.01 | −0.03 ± 0.01 | −0.03 ± 0.02 | −0.04 ± 0.01 | −0.03 ± 0.01 | ||
| χ2/ndf = | 5.1 | 4.9 | 3.6 | 3.6 | 5.7 | 5.7 | ||
|
|
||||||||
| 1.90 | 1.85 | |||||||
| Gr = | 2.8 ± 0.2 | 2.7 ± 0.2 | 2.1 ± 0.3 | 2.3 ± 0.4 | 3.1 ± 0.2 | 2.7 ± 0.2 | ||
| Gθ = | −0.06 ± 0.01 | −0.06 ± 0.01 | −0.06 ± 0.01 | −0.06 ± 0.02 | −0.05 ± 0.01 | −0.04 ± 0.01 | ||
| χ2/ndf = | 4.5 | 4.4 | 3.7 | 3.7 | 4.5 | 4.2 | ||
|
|
||||||||
| 0.46† | 0.46 | |||||||
| Gr = | 3.5 ± 0.6 | 3.7 ± 0.8 | 3.7 ± 1.3 | 3.4 ± 2. | 3.5 ± 0.6 | 3.7 ± 0.9 | ||
| Gθ = | −0.1 ± 0.02 | −0.10 ± 0.03 | −0.11 ± 0.04 | −0.10 ± 0.06 | −0.11 ± 0.03 | −0.10 ± 0.04 | ||
Notes. Proton mean rigidities ⟨ RU ⟩ and ⟨ RP ⟩ (both in GV) as measured by Ulysses/KET and PAMELA, respectively, that are used to calculate the corresponding gradients. Radial and latitudinal gradients (in %/AU and %/degree, respectively), and quality of fit for different selection criteria (cf. Fig. 2) and fit methods. Indicated by (1) are the values obtained by the bootstrap Monte Carlo approach; while (2) marks the fit routine using the fitexy algorithm.
Note that each gradient in the last row is calculated by the arithmetic mean of the corresponding gradients of rows 2, 3, and 4 (see Sect. 3.2 for details).
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