Table 1
Fitted values of the gravity darkening exponent β in the correlation between Teff and geff as a function of the mass ratio q = M2/M1 and the filling factor ρ.
| Mass ratio (q) | Filling factor (ρ) | ||||||
| ρ = 0.3 | ρ = 0.5 | ρ = 0.7 | ρ = 0.8 | ρ = 0.9 | ρ = 0.95 | ρ = 0.99 | |
| q = 0.0 | 0.2456 (0.00004%) | 0.2308 (0.0038%) | 0.2034 (0.078%) | 0.1854 (0.27%) | 0.1641 (0.96%) | 0.1509 (2.08%) | 0.1365 (6.08%) |
| q = 0.001 | 0.2464 (0.00002%) | 0.2342 (0.0021%) | 0.2110 (0.043%) | 0.1958 (0.15%) | 0.1789 (0.48%) | 0.1708 (0.92%) | 0.1666 (1.55%) |
| q = 0.01 | 0.2472 (0.00002%) | 0.2374 (0.0013%) | 0.2188 (0.025%) | 0.2068 (0.090%) | 0.1948 (0.31%) | 0.1901 (0.56%) | 0.1880 (1.31%) |
| q = 0.1 | 0.2482 (0.00004%) | 0.2420 (0.0012%) | 0.2303 (0.014%) | 0.2232 (0.049%) | 0.2168 (0.18%) | 0.2143 (0.36%) | 0.2131 (0.66%) |
| q = 1.0 | 0.2489 (0.00004%) | 0.2452 (0.0013%) | 0.2385 (0.011%) | 0.2346 (0.050%) | 0.2308 (0.23%) | 0.2291 (0.52%) | 0.2280 (1.44%) |
| q = 3.0 | 0.2490 (0.00004%) | 0.2455 (0.0015%) | 0.2394 (0.020%) | 0.2359 (0.092%) | 0.2324 (0.37%) | 0.2308 (0.80%) | 0.2297 (2.18%) |
| q = 10.0 | 0.2489 (0.00005%) | 0.2453 (0.0019%) | 0.2391 (0.036%) | 0.2355 (0.15%) | 0.2320 (0.55%) | 0.2304 (1.16%) | 0.2292 (3.09%) |
| q = 100.0 | 0.2487 (0.00005%) | 0.2447 (0.0029%) | 0.2377 (0.061%) | 0.2337 (0.23%) | 0.2298 (0.82%) | 0.2279 (1.75%) | 0.2267 (4.57%) |
Notes. As the relation does not follow exactly a power law, the maximum relative error in Teff calculated using the fit compared with the exact value is included in parentheses.
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