Table 9.
Coefficients of polynomial fits to the surface-brightness parameter S in Johnson B and V and Gaia GBP and G bands for dwarfs and subgiants.
| Band | Colour | Number | Valid over | a0 | a1 | a2 | a3 | a4 | a5 | σ |
|---|---|---|---|---|---|---|---|---|---|---|
| X | of stars | colour range | % | |||||||
| Fifth-order polynomial fits | ||||||||||
| B | (B − J) | 52 | [−0.2:2.4] | 2.471 | 1.786 | −0.499 | 0.386 | −0.121 | 0.0131 | 2.1 |
| B | (B − H) | 52 | [−0.35:2.8] | 2.566 | 1.483 | −0.236 | 0.127 | −0.0313 | 0.0280 | 2.3 |
| B | (B − K) | 54 | [−0.3:2.9] | 2.516 | 1.515 | −0.358 | 0.220 | −0.0597 | 0.0056 | 1.2 |
| V | (V − J) | 52 | [−0.2:1.55] | 2.460 | 2.195 | −1.041 | 1.143 | −0.493 | 0.0720 | 2.1 |
| V | (V − H) | 52 | [−0.3:2.0] | 2.575 | 1.649 | −0.422 | 0.331 | −0.117 | 0.0148 | 2.4 |
| V | (V − K) | 54 | [−0.2:2.1] | 2.521 | 1.708 | −0.705 | 0.623 | −0.239 | 0.0313 | 1.1 |
| GBP | (GBP − J) | 50 | [−0.2:1.75] | 2.474 | 1.934 | −0.524 | 0.539 | −0.220 | 0.0305 | 2.2 |
| GBP | (GBP − H) | 52 | [−0.3:2.2] | 2.580 | 1.544 | −0.272 | 0.199 | −0.0673 | 0.0082 | 2.4 |
| GBP | (GBP − K) | 52 | [−0.3:2.3] | 2.535 | 1.566 | −0.472 | 0.404 | −0.148 | 0.0184 | 1.2 |
| G | (G − J) | 50 | [−0.15:1.3] | 2.434 | 2.339 | −0.579 | −0.036 | 0.392 | −0.146 | 2.3 |
| G | (G − H) | 52 | [−0.3:1.7] | 2.567 | 1.717 | −0.334 | 0.124 | 0.0129 | −0.0086 | 2.5 |
| G | (G − K) | 52 | [−0.2:1.9] | 2.522 | 1.724 | −0.648 | 0.597 | −0.249 | 0.0372 | 1.2 |
Notes. The S parameter is defined by Eq. (5). Infrared magnitudes are in the 2MASS photometric system. Limb-darkened stellar angular diameter θLD, expressed in milliarcseconds, follows from the equation log θLD = 0.2 × (a0 − m + a1 × X + ⋯ + a5 × X5), where m is the observed magnitude (extinction-free) of a star in a particular band and X is a colour (extinction-free). The last column gives the precision in predicting the angular diameter of stars in a valid colour range.
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