Table 5.
Fit parameters for the empirical relations.
| Y | X | a | b | c | d | e | R2 | ΔX |
|---|---|---|---|---|---|---|---|---|
| (mag) | (mag) | (mag) | (mag−1) | (mag−2) | (mag−3) | (mag−4) | (mag) | |
| Mr′ | r′−J | +8.38 ± 2.68 | –2.74 ± 2.36 | +1.47 ± 0.68 | –0.132 ± 0.063 | 0 | 0.9398 | [2.0, 5.1] |
| MG | G − J | +16.24 ± 4.57 | –13.04 ± 4.80 | +5.64 ± 1.66 | –0.622 ± 0.188 | 0 | 0.9308 | [2.0, 4.0] |
| log L/L⊙ | MJ | +2.051 ± 0.075 | –0.662 ± 0.030 | +0.0267 ± 0.0039 | –0.00102 ± 0.00016 | 0 | 0.9923 | [4.4, 11.2) |
| –3.906 ± 0.998 | +0.334 ± 0.156 | –0.0263 ± 0.0061 | 0 | 0 | 0.9477 | [11.2, 14.8] | ||
| log L/L⊙ | MG | +0.145 ± 0.201 | +0.074 ± 0.060 | –0.0382 ± 0.0060 | +0.00119 ± 0.00019 | 0 | 0.9901 | [6.4, 14.0) |
| –2.329 ± 0.687 | +0.092 ± 0.084 | –0.0103 ± 0.0025 | 0 | 0 | 0.9782 | [14.0, 20.2] | ||
| BCG | G − J | +0.404 ± 0.187 | +0.161 ± 0.239 | –0.465 ± 0.112 | +0.1159 ± 0.0225 | –0.0115 ± 0.0017 | 0.9960 | (1.5, 5.4] |
| BCr′ | r′−J | +0.557 ± 0.085 | –0.036 ± 0.091 | –0.318 ± 0.035 | +0.0552 ± 0.0056 | –0.0037 ± 0.0003 | 0.9983 | (1.5, 7.5] |
| BCJ | G − J | +0.576 ± 0.094 | +0.735 ± 0.104 | –0.132 ± 0.038 | +0.0115 ± 0.0045 | 0 | 0.9547 | (0.5, 4.0] |
| BCW2 | G − J | –2.592 ± 0.667 | +5.845 ± 1.005 | –2.611 ± 0.559 | +0.586 ± 0.136 | –0.0496 ± 0.0122 | 0.9727 | (1.5, 4.0] |
Notes. In all cases, the polynomial fits follow the form Y = a + bX + cX2 + dX3 + eX4 and are applicable in the range ΔX. In all cases, R2 is the correlation coefficient from the Pearson product-moment matrix. These relations should be applied to solar-metallicity stars only (Sect. 4). More significant figures are available at GitHub (Sect. 5).
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