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Table A.1

Theoretical limb darkening coefficients for a range of standard broadband filters and instruments.

HD 209458 HD 189733
Band λ eff c 1 c 2 c 3 c 4 c 1 c 2 c 3 c 4
Johnson U 3614 Å 0.2714 0.6757 −0.0135 −0.0423 0.6187 −0.9692 1.7593 −0.4501
Johnson B 4414 Å 0.4089 0.4379 0.0826 −0.0591 0.5269 −0.4716 1.4046 −0.5285
Johnson V 5514 Å 0.5907 0.1358 0.1310 −0.0603 0.6198 −0.3657 1.0856 −0.4616
Johnson I 8867 Å 0.7463 −0.3785 0.4081 −0.1494 0.7857 −0.6139 0.9500 −0.4035
Strömgren u 3467 Å 0.2489 0.7509 −0.0881 −0.0130 0.5627 −0.9727 1.8312 −0.4517
Strömgren v 4110 Å 0.3302 0.5697 0.0501 −0.0583 0.5298 −0.7119 1.7180 −0.5853
Strömgren b 4673 Å 0.4577 0.4220 0.0033 −0.0220 0.4970 −0.3015 1.2544 −0.5223
Strömgren y 5479 Å 0.5958 0.1268 0.1376 −0.0624 0.6171 −0.3405 1.0592 −0.4560
SDSS u′ 3572 Å 0.2616 0.7449 −0.1043 −0.0105 0.6085 −0.9915 1.8023 −0.4572
SDSS g′ 4751 Å 0.4692 0.3707 0.0510 −0.0408 0.5316 −0.3781 1.2733 −0.5102
SDSS r′ 6204 Å 0.6716 −0.0532 0.2233 −0.0901 0.6967 −0.4221 1.0160 −0.4450
SDSS i′ 7519 Å 0.7341 −0.2850 0.3645 −0.1369 0.7725 −0.5732 1.0026 −0.4293
SDSS z′ 8992 Å 0.7505 −0.4067 0.4254 −0.1552 0.7930 −0.6326 0.9467 −0.4002
Bessell J 1.241 μm 0.7277 −0.3488 0.2343 −0.0643 0.7422 −0.4298 0.5875 −0.2645
Bessell H 1.651 μm 1.0576 −1.1056 0.8110 −0.2321 0.9618 −0.6133 0.4033 −0.1357
Bessell K 2.218 μm 0.8614 −0.8792 0.6492 −0.1899 0.9065 −0.7574 0.5863 −0.2043
MK J 1.250 μm 0.7263 −0.3442 0.2243 −0.0600 0.7355 −0.4058 0.5573 −0.2537
MK H 1.634 μm 1.0481 −1.0749 0.7813 −0.2218 0.9488 −0.5850 0.3856 −0.1318
MK K′ 2.118 μm 0.8959 −0.9385 0.7010 −0.2062 0.9193 −0.7365 0.5446 −0.1860
MK Ks 2.149 μm 0.8805 −0.9149 0.6833 −0.2014 0.9133 −0.7368 0.5485 −0.1878
MK K 2.205 μm 0.8617 −0.8822 0.6530 −0.1914 0.9061 −0.7508 0.5752 −0.1995
MK L′ 3.785 μm 0.5370 −0.5436 0.4407 −0.1423 0.6874 −0.7468 0.6881 −0.2531
MK M′ 4.687 μm 0.4241 −0.3318 0.2333 −0.0696 0.6878 −0.9198 0.8999 −0.3344
STIS G430L1 4757 Å 0.4762 0.3436 0.0730 −0.0492 0.5601 −0.4054 1.2492 −0.4943
ACS HRC G800L1 7945 Å 0.7112 −0.2198 0.2926 −0.1070 0.7601 −0.5527 0.9838 −0.4226
Kepler 6641 Å 0.6434 −0.0242 0.2217 −0.0909 0.6890 −0.4600 1.0493 −0.4488
Corot 6958 Å 0.6435 −0.0410 0.2360 −0.0961 0.6987 −0.4833 1.0479 −0.4451
Spitzer IRAC 1 3.576 μm 0.5564 −0.5462 0.4315 −0.1368 0.7062 −0.7408 0.6723 −0.2464
Spitzer IRAC 2 4.529 μm 0.4614 −0.4277 0.3362 −0.1074 0.6830 −0.8708 0.8418 −0.3121
Spitzer IRAC 3 5.788 μm 0.4531 −0.5119 0.4335 −0.1431 0.6290 −0.8773 0.8715 −0.3256
Spitzer IRAC 4 8.045 μm 0.4354 −0.6067 0.5421 −0.1816 0.6189 −0.9742 0.9804 −0.3664

Notes. All computations are based on the 3D models of HD 209458 and HD 189733.

(1)

Theoretical intensity spectra were integrated over the entire accessible wavelength range of the grating, leading to small deviations from the coefficients in Tables 4 and 5.

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