J/A+A/674/A63 Power-2 limb-darkening coefficients (Claret+, 2023)
Power-2 limb-darkening coefficients for the uvby, UBVRIJHK, SDSS ugriz,
Gaia, Kepler, TESS, and CHEOPS photometric systems.
II. PHOENIX spherically symmetric stellar atmosphere models.
Claret A., Southworth J.
<Astron. Astrophys. 674, A63 (2023)>
=2023A&A...674A..63C 2023A&A...674A..63C (SIMBAD/NED BibCode)
ADC_Keywords: Models, atmosphere ; Photometry, SDSS ; Photometry, UBVRI
Keywords: stars: binaries: close - binaries eclipsing - planetary systems
Abstract:
The phenomenon of limb-darkening is relevant to many topics in
astrophysics, including the analysis of light curves of eclipsing
binaries, optical interferometry, measurement of stellar diameters,
line profiles of rotating stars, gravitational microlensing, and
transits of extrasolar planets. Multiple parametric limb-darkening
laws have been presented, and there are many available sources of
theoretical limb-darkening coefficients (LDCs) calculated using
stellar model atmospheres. The power-2 limb-darkening law allows a
very good representation of theoretically predicted intensity
profiles, but few LDCs are available for this law from spherically
symmetric model atmospheres. We therefore present such coefficients in
this work.
We computed LDCs for the space missions Gaia, Kepler, TESS, and CHEOPS
and for the passbands uvby, UBVRIJHK, and SDSS ugriz, using the
PHOENIX-COND spherical models. We adopted two methods to characterise
the truncation point, which sets the limb of the star: the first (M1)
uses the point where the derivative dI(r)/dr is at its maximum ---
where I(r) is the specific intensity as a function of the normalised
radius r --- corresponding to µcri, and the second (M2) uses the
midpoint between the point µcri and the point located at
µcri-1. The LDCs were computed adopting the Levenberg-Marquardt
least-squares minimisation method, with a resolution of 900 equally
spaced µ points, and covering 823 model atmospheres for a solar
metallicity, effective temperatures of 2300 to 12000K, logg values
from 0.0 to 6.0, and microturbulent velocities of 2km/s. As our
previous calculations of LDCs using spherical models included only
100µ points, we also updated the calculations for the
four-parameter law for the passbands listed above, and compared them
with those from the power-2 law. Comparisons between the quality of
the fits provided by the power-2 and four-parameter laws show that the
latter presents a lower merit function, chi2, than the former for
both cases (M1 and M2). This is important when choosing the best
approach for a particular science goal.
Description:
We computed LDCs for the power-2 law using specific intensities
from spherical model atmospheres, as such results were only previously
available for a small range of stellar parameters. To this end, we
used the phoenix-cond models for Te values from 2300K to 12000K, log g
values from 0.0 to 6.0, solar metallicity, Vξ=2.0km/s, and with
900 µ points. We also computed LDCs for the four-parameter law,
which supersede our previous calculations based on only 100 µ
points. For both laws, we computed coefficients for the uvby, UBVRIJHK;
and SDSS ugriz passbands, and for the Gaia, Kepler, TESS, and CHEOPS
photometric systems.
File Summary:
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FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
table1.dat 334 823 Eq.2 PHOENIX, Gaia, Kepler,TESS,CHEOPS/M1
table2.dat 334 823 Eq.2 PHOENIX, Gaia, Kepler,TESS,CHEOPS/M2
table3.dat 490 823 Eq.3 PHOENIX, Gaia, Kepler,TESS,CHEOPS/M1
table4.dat 490 823 Eq.3 PHOENIX, Gaia, Kepler,TESS,CHEOPS/M2
table5.dat 282 823 Eq.2 PHOENIX, ugriz/M1
table6.dat 282 823 Eq.2 PHOENIX, ugriz/M2
table7.dat 412 823 Eq.3 PHOENIX, ugriz/M1
table8.dat 412 823 Eq.3 PHOENIX, ugriz/M2
table9.dat 646 823 Eq.2 PHOENIX, uvbyUBVRIJHK/M1
table10.dat 646 823 Eq.2 PHOENIX, uvbyUBVRIJHK/M2
table11.dat 958 823 Eq.3 PHOENIX, uvbyUBVRIJHK/M1
table12.dat 958 823 Eq.3 PHOENIX, uvbyUBVRIJHK/M2
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See also:
J/A+AS/114/247 : Limb-darkening coefficients for R I J H K (Claret+, 1995)
J/A+A/335/647 : Limb-darkening coefficients for ubvyUBVRIJHK (Claret 1998)
J/A+A/401/657 : Non-linear limb-darkening law for LTE models. II.
(Claret, 2003)
J/A+A/428/1001 : Non-linear limb-darkening law for LTE models. III.
(Claret, 2004)
J/A+A/529/A75 : Limb-darkening coefficients (Claret+, 2011)
J/A+A/546/A14 : Limb-darkening for CoRoT, Kepler, Spitzer (Claret+, 2012)
J/A+A/552/A16 : Limb-darkening for CoRoT, Kepler, Spitzer. II. (Claret+, 2013)
J/A+A/600/A30 : Limb-darkening for TESS satellite (Claret, 2017)
J/A+A/618/A20 : Limb-darkening for TESS, Kepler, Corot, MOST (Claret, 2018)
J/A+A/634/A93 : Limb-darkening coefficients for compact stars (Claret+, 2020)
J/A+A/641/A157 : Limb-darkening coefficients for white dwarfs (Claret+, 2020)
Byte-by-byte Description of file: table1.dat table2.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 5 F5.2 [cm/s2] logg Log10 Surface gravity
7- 12 F6.0 K Teff Effective temperature
14- 17 F4.1 --- Z [0] log10 [M/H]
19- 22 F4.1 km/s Vel [2] Microturbulent velocity
24- 35 F12.8 --- gGbp power-2 limb darkening coefficient g (Gbp)
37- 48 F12.8 --- gG power-2 limb darkening coefficient g (G)
50- 61 F12.8 --- gGrp power-2 limb darkening coefficient g (Grp)
63- 74 F12.8 --- gKep power-2 limb darkening coefficient g (KEP)
76- 87 F12.8 --- gTESS power-2 limb darkening coefficient g (TESS)
89-100 F12.8 --- gCHEOPS power-2 limb darkening coefficient g
(CHEOPS)
102-113 F12.8 --- hGbp power-2 limb darkening coefficient h (Gbp)
115-126 F12.8 --- hG power-2 limb darkening coefficient h (G)
128-139 F12.8 --- hGrp power-2 limb darkening coefficient h (Grp)
141-152 F12.8 --- hKEP power-2 limb darkening coefficient h (KEP)
154-165 F12.8 --- hTESS power-2 limb darkening coefficient h (TESS)
167-178 F12.8 --- hCHEOPS power-2 limb darkening coefficient h
(CHEOPS)
180-191 F12.8 --- mucriGbp power-2 µcri point (Gbp)
193-204 F12.8 --- mucriG power-2 µcri point (G)
206-217 F12.8 --- mucriGrp power-2 µcri point (Grp)
219-230 F12.8 --- mucriKEP power-2 µcri point (KEP)
232-243 F12.8 --- mucriTESS power-2 µcri point (TESS)
245-256 F12.8 --- mucriCHEOPS power-2 µcri point (CHEOPS)
258-269 F12.8 --- CHI2Gbp power-2 chi2 (Gbp)
271-282 F12.8 --- CHI2G power-2 chi2 (G)
284-295 F12.8 --- CHI2Grp power-2 chi2 (Grp)
297-308 F12.8 --- CHI2KEP power-2 chi2 (KEP)
310-321 F12.8 --- CHI2TESS power-2 chi2 (TESS)
323-334 F12.8 --- CHI2CHEOPS power-2 chi2 (CHEOPS)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table3.dat table4.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 5 F5.2 [cm/s2] logg Log10 Surface gravity
7- 12 F6.0 K Teff Effective temperature
14- 17 F4.1 --- Z [0] log10 [M/H]
19- 22 F4.1 km/s Vel [2] Microturbulent velocity
24- 35 F12.8 --- a1Gbp 4-terms limb darkening coefficient a1 (Gbp)
37- 48 F12.8 --- a1G 4-terms limb darkening coefficient a1 (G)
50- 61 F12.8 --- a1Grp 4-terms limb darkening coefficient a1 (Grp)
63- 74 F12.8 --- a1KEP 4-terms limb darkening coefficient a1 (KEP)
76- 87 F12.8 --- a1TESS 4-terms limb darkening coefficient a1 (TESS)
89-100 F12.8 --- a1CHEOPS 4-terms limb darkening coefficient a1
(CHEOPS)
102-113 F12.8 --- a2Gbp 4-terms limb darkening coefficient a2 (Gbp)
115-126 F12.8 --- a2G 4-terms limb darkening coefficient a2 (G)
128-139 F12.8 --- a2Grp 4-terms limb darkening coefficient a2 (Grp)
141-152 F12.8 --- a2KEP 4-terms limb darkening coefficient a2 (KEP)
154-165 F12.8 --- a2TESS 4-terms limb darkening coefficient a2 (TESS)
167-178 F12.8 --- a2CHEOPS 4-terms limb darkening coefficient a2
(CHEOPS)
180-191 F12.8 --- a3Gbp 4-terms limb darkening coefficient a3 (Gbp)
193-204 F12.8 --- a3G 4-terms limb darkening coefficient a3 (G)
206-217 F12.8 --- a3Grp 4-terms limb darkening coefficient a3 (Grp)
219-230 F12.8 --- a3KEP 4-terms limb darkening coefficient a3 (KEP)
232-243 F12.8 --- a3TESS 4-terms limb darkening coefficient a3 (TESS)
245-256 F12.8 --- a3CHEOPS 4-terms limb darkening coefficient a3
(CHEOPS)
258-269 F12.8 --- a4Gbp 4-terms limb darkening coefficient a4 (Gbp)
271-282 F12.8 --- a4G 4-terms limb darkening coefficient a4 (G)
284-295 F12.8 --- a4Grp 4-terms limb darkening coefficient a4 (Grp)
297-308 F12.8 --- a4KEP 4-terms limb darkening coefficient a4 (KEP)
310-321 F12.8 --- a4TESS 4-terms limb darkening coefficient a4 (TESS)
323-334 F12.8 --- a4CHEOPS 4-terms limb darkening coefficient a4
(CHEOPS)
336-347 F12.8 --- mucriGbp 4-terms µcri point (Gbp)
349-360 F12.8 --- mucriG 4-terms µcri point (G)
362-373 F12.8 --- mucriGrp 4-terms µcri point (Grp)
375-386 F12.8 --- mucriKEP 4-terms µcri point (KEP)
388-399 F12.8 --- mucriTESS 4-terms µcri point (TESS)
401-412 F12.8 --- mucriCHEOPS 4-terms µcri point (CHEOPS)
414-425 F12.8 --- CHI2Gbp 4-terms µcri point (Gbp)
427-438 F12.8 --- CHI2G 4-terms chi2 (G)
440-451 F12.8 --- CHI2Grp 4-terms chi2 (Grp)
453-464 F12.8 --- CHI2KEP 4-terms chi2 (KEP)
466-477 F12.8 --- CHI2TESS 4-terms chi2 (TESS)
479-490 F12.8 --- CHI2CHEOPS 4-terms chi2 (CHEOPS)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table5.dat table6.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 5 F5.2 [cm/s2] logg Log10 Surface gravity
7- 12 F6.0 K Teff Effective temperature
14- 17 F4.1 --- Z [0] log10 [M/H]
19- 22 F4.1 km/s Vel [2] Microturbulent velocity
24- 35 F12.8 --- gu power-2 limb darkening coefficient g (u)
37- 48 F12.8 --- gg power-2 limb darkening coefficient g (g)
50- 61 F12.8 --- gr power-2 limb darkening coefficient g (r)
63- 74 F12.8 --- gi power-2 limb darkening coefficient g (i)
76- 87 F12.8 --- gz power-2 limb darkening coefficient g (z)
89-100 F12.8 --- hu power-2 limb darkening coefficient h (u)
102-113 F12.8 --- hg power-2 limb darkening coefficient h (g)
115-126 F12.8 --- hr power-2 limb darkening coefficient h (r)
128-139 F12.8 --- hi power-2 limb darkening coefficient h (i)
141-152 F12.8 --- hz power-2 limb darkening coefficient h (z)
154-165 F12.8 --- mucriu power-2 µcri point (u)
167-178 F12.8 --- mucrig power-2 µcri point (g)
180-191 F12.8 --- mucrir power-2 µcri point (r)
193-204 F12.8 --- mucrii power-2 µcri point (i)
206-217 F12.8 --- mucriz power-2 µcri point (z)
219-230 F12.8 --- CHI2u power-2 chi2 (u)
232-243 F12.8 --- CHI2g power-2 chi2 (g)
245-256 F12.8 --- CHI2r power-2 chi2 (r)
258-269 F12.8 --- CHI2i power-2 chi2 (i)
271-282 F12.8 --- CHI2z power-2 chi2 (z)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table7.dat table8.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 5 F5.2 [cm/s2] logg Log10 Surface gravity
7- 12 F6.0 K Teff Effective temperature
14- 17 F4.1 --- Z [0] log10 [M/H]
19- 22 F4.1 km/s Vel [2] Microturbulent velocity
24- 35 F12.8 --- a1u 4-terms limb darkening coefficient a1 (u)
37- 48 F12.8 --- a1g 4-terms limb darkening coefficient a1 (g)
50- 61 F12.8 --- a1r 4-terms limb darkening coefficient a1 (r)
63- 74 F12.8 --- a1i 4-terms limb darkening coefficient a1 (i)
76- 87 F12.8 --- a1z 4-terms limb darkening coefficient a1 (z)
89-100 F12.8 --- a2u 4-terms limb darkening coefficient a2 (u)
102-113 F12.8 --- a2g 4-terms limb darkening coefficient a2 (g)
115-126 F12.8 --- a2r 4-terms limb darkening coefficient a2 (r)
128-139 F12.8 --- a2i 4-terms limb darkening coefficient a2 (i)
141-152 F12.8 --- a2z 4-terms limb darkening coefficient a2 (z)
154-165 F12.8 --- a3u 4-terms limb darkening coefficient a3 (u)
167-178 F12.8 --- a3g 4-terms limb darkening coefficient a3 (g)
180-191 F12.8 --- a3r 4-terms limb darkening coefficient a3 (r)
193-204 F12.8 --- a3i 4-terms limb darkening coefficient a3 (i)
206-217 F12.8 --- a3z 4-terms limb darkening coefficient a3 (z)
219-230 F12.8 --- a4u 4-terms limb darkening coefficient a4 (u)
232-243 F12.8 --- a4g 4-terms limb darkening coefficient a4 (g)
245-256 F12.8 --- a4r 4-terms limb darkening coefficient a4 (r)
258-269 F12.8 --- a4i 4-terms limb darkening coefficient a4 (i)
271-282 F12.8 --- a4z 4-terms limb darkening coefficient a4 (z)
284-295 F12.8 --- mucriu 4-terms µcri point (u)
297-308 F12.8 --- mucrig 4-terms µcri point (g)
310-321 F12.8 --- mucrir 4-terms µcri point (r)
323-334 F12.8 --- mucrii 4-terms µcri point (i)
336-347 F12.8 --- mucriz 4-terms µcri point (z)
349-360 F12.8 --- CHI2u 4-terms chi2 (u)
362-373 F12.8 --- CHI2g 4-terms chi2 (g)
375-386 F12.8 --- CHI2r 4-terms chi2 (r)
388-399 F12.8 --- CHI2i 4-terms chi2 (i)
401-412 F12.8 --- CHI2z 4-terms chi2 (z)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table9.dat table10.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 5 F5.2 [cm/s2] logg Log10 Surface gravity
7- 12 F6.0 K Teff Effective temperature
14- 17 F4.1 --- Z [0] log10 [M/H]
19- 22 F4.1 km/s Vel [2] Microturbulent velocity
24- 35 F12.8 --- gu power-2 limb darkening coefficient g (u)
37- 48 F12.8 --- gv power-2 limb darkening coefficient g (v)
50- 61 F12.8 --- gb power-2 limb darkening coefficient g (b)
63- 74 F12.8 --- gy power-2 limb darkening coefficient g (y)
76- 87 F12.8 --- gU power-2 limb darkening coefficient g (U)
89-100 F12.8 --- gB power-2 limb darkening coefficient g (B)
102-113 F12.8 --- gV power-2 limb darkening coefficient g (V)
115-126 F12.8 --- gR power-2 limb darkening coefficient g (R)
128-139 F12.8 --- gI power-2 limb darkening coefficient g (I)
141-152 F12.8 --- gJ power-2 limb darkening coefficient g (J)
154-165 F12.8 --- gH power-2 limb darkening coefficient g (H)
167-178 F12.8 --- gK power-2 limb darkening coefficient g (K)
180-191 F12.8 --- hu power-2 limb darkening coefficient h (u)
193-204 F12.8 --- hb power-2 limb darkening coefficient h (v)
206-217 F12.8 --- hv power-2 limb darkening coefficient h (b)
219-230 F12.8 --- hy power-2 limb darkening coefficient h (y)
232-243 F12.8 --- hU power-2 limb darkening coefficient h (U)
245-256 F12.8 --- hB power-2 limb darkening coefficient h (B)
258-269 F12.8 --- hV power-2 limb darkening coefficient h (V)
271-282 F12.8 --- hR power-2 limb darkening coefficient h (R)
284-295 F12.8 --- hI power-2 limb darkening coefficient h (I)
297-308 F12.8 --- hJ power-2 limb darkening coefficient h (J)
310-321 F12.8 --- hH power-2 limb darkening coefficient h (H)
323-334 F12.8 --- hK power-2 limb darkening coefficient h (K)
336-347 F12.8 --- mucriu power-2 µcri point (u)
349-360 F12.8 --- mucriv power-2 µcri point (v)
362-373 F12.8 --- mucrib power-2 µcri point (b)
375-386 F12.8 --- mucriy power-2 µcri point (y)
388-399 F12.8 --- mucriU power-2 µcri point (U)
401-412 F12.8 --- mucriB power-2 µcri point (B)
414-425 F12.8 --- mucriV power-2 µcri point (V)
427-438 F12.8 --- mucriR power-2 µcri point (R)
440-451 F12.8 --- mucriI power-2 µcri point (I)
453-464 F12.8 --- mucriJ power-2 µcri point (J)
466-477 F12.8 --- mucriH power-2 µcri point (H)
479-490 F12.8 --- mucriK power-2 µcri point (K)
492-503 F12.8 --- CHI2u power-2 chi2 (u)
505-516 F12.8 --- CHI2v power-2 chi2 (v)
518-529 F12.8 --- CHI2b power-2 chi2 (b)
531-542 F12.8 --- CHI2y power-2 chi2 (y)
544-555 F12.8 --- CHI2U power-2 chi2 (U)
557-568 F12.8 --- CHI2B power-2 chi2 (B)
570-581 F12.8 --- CHI2V power-2 chi2 (V)
583-594 F12.8 --- CHI2R power-2 chi2 (R)
596-607 F12.8 --- CHI2I power-2 chi2 (I)
609-620 F12.8 --- CHI2J power-2 chi2 (J)
622-633 F12.8 --- CHI2H power-2 chi2 (H)
635-646 F12.8 --- CHI2K power-2 chi2 (K)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table11.dat table12.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 5 F5.2 [cm/s2] logg Log10 Surface gravity
7- 12 F6.0 K Teff Effective temperature
14- 17 F4.1 --- Z [0] log10 [M/H]
19- 22 F4.1 km/s Vel [2] Microturbulent velocity
24- 35 F12.8 --- a1u 4-terms limb darkening coefficient a1 (u)
37- 48 F12.8 --- a1v 4-terms limb darkening coefficient a1 (v)
50- 61 F12.8 --- a1b 4-terms limb darkening coefficient a1 (b)
63- 74 F12.8 --- a1y 4-terms limb darkening coefficient a1 (y)
76- 87 F12.8 --- a1U 4-terms limb darkening coefficient a1 (U)
89-100 F12.8 --- a1B 4-terms limb darkening coefficient a1 (B)
102-113 F12.8 --- a1V 4-terms limb darkening coefficient a1 (V)
115-126 F12.8 --- a1R 4-terms limb darkening coefficient a1 (R)
128-139 F12.8 --- a1I 4-terms limb darkening coefficient a1 (I)
141-152 F12.8 --- a1J 4-terms limb darkening coefficient a1 (J)
154-165 F12.8 --- a1H 4-terms limb darkening coefficient a1 (H)
167-178 F12.8 --- a1K 4-terms limb darkening coefficient a1 (K)
180-191 F12.8 --- a2u 4-terms limb darkening coefficient a2 (u)
193-204 F12.8 --- a2v 4-terms limb darkening coefficient a2 (v)
206-217 F12.8 --- a2b 4-terms limb darkening coefficient a2 (b)
219-230 F12.8 --- a2y 4-terms limb darkening coefficient a2 (y)
232-243 F12.8 --- a2U 4-terms limb darkening coefficient a2 (U)
245-256 F12.8 --- a2B 4-terms limb darkening coefficient a2 (B)
258-269 F12.8 --- a2V 4-terms limb darkening coefficient a2 (V)
271-282 F12.8 --- a2R 4-terms limb darkening coefficient a2 (R)
284-295 F12.8 --- a2I 4-terms limb darkening coefficient a2 (I)
297-308 F12.8 --- a2J 4-terms limb darkening coefficient a2 (J)
310-321 F12.8 --- a2H 4-terms limb darkening coefficient a2 (H)
323-334 F12.8 --- a2K 4-terms limb darkening coefficient a2 (K)
336-347 F12.8 --- a3u 4-terms limb darkening coefficient a3 (u)
349-360 F12.8 --- a3v 4-terms limb darkening coefficient a3 (v)
362-373 F12.8 --- a3b 4-terms limb darkening coefficient a3 (b)
375-386 F12.8 --- a3y 4-terms limb darkening coefficient a3 (y)
388-399 F12.8 --- a3U 4-terms limb darkening coefficient a3 (U)
401-412 F12.8 --- a3B 4-terms limb darkening coefficient a3 (B)
414-425 F12.8 --- a3V 4-terms limb darkening coefficient a3 (V)
427-438 F12.8 --- a3R 4-terms limb darkening coefficient a3 (R)
440-451 F12.8 --- a3I 4-terms limb darkening coefficient a3 (I)
453-464 F12.8 --- a3J 4-terms limb darkening coefficient a3 (J)
466-477 F12.8 --- a3H 4-terms limb darkening coefficient a3 (H)
479-490 F12.8 --- a3K 4-terms limb darkening coefficient a3 (K)
492-503 F12.8 --- a4u 4-terms limb darkening coefficient a4 (u)
505-516 F12.8 --- a4v 4-terms limb darkening coefficient a4 (v)
518-529 F12.8 --- a4b 4-terms limb darkening coefficient a4 (b)
531-542 F12.8 --- a4y 4-terms limb darkening coefficient a4 (y)
544-555 F12.8 --- a4U 4-terms limb darkening coefficient a4 (U)
557-568 F12.8 --- a4B 4-terms limb darkening coefficient a4 (B)
570-581 F12.8 --- a4V 4-terms limb darkening coefficient a4 (V)
583-594 F12.8 --- a4R 4-terms limb darkening coefficient a4 (R)
596-607 F12.8 --- a4I 4-terms limb darkening coefficient a4 (I)
609-620 F12.8 --- a4J 4-terms limb darkening coefficient a4 (J)
622-633 F12.8 --- a4H 4-terms limb darkening coefficient a4 (H)
635-646 F12.8 --- a4K 4-terms limb darkening coefficient a4 (K)
648-659 F12.8 --- mucriu 4-terms µcri point (u)
661-672 F12.8 --- mucriv 4-terms µcri point (v)
674-685 F12.8 --- mucrib 4-terms µcri point (b)
687-698 F12.8 --- mucriy 4-terms µcri point (y)
700-711 F12.8 --- mucriU 4-terms µcri point (U)
713-724 F12.8 --- mucriB 4-terms µcri point (B)
726-737 F12.8 --- mucriV 4-terms µcri point (V)
739-750 F12.8 --- mucriR 4-terms µcri point (R)
752-763 F12.8 --- mucriI 4-terms µcri point (I)
765-776 F12.8 --- mucriJ 4-terms µcri point (J)
778-789 F12.8 --- mucriH 4-terms µcri point (H)
791-802 F12.8 --- mucriK 4-terms µcri point (K)
804-815 F12.8 --- CHI2u 4-terms chi2 (u)
817-828 F12.8 --- CHI2v 4-terms chi2 (v)
830-841 F12.8 --- CHI2b 4-terms chi2 (b)
843-854 F12.8 --- CHI2y 4-terms chi2 (y)
856-867 F12.8 --- CHI2U 4-terms chi2 (U)
869-880 F12.8 --- CHI2B 4-terms chi2 (B)
882-893 F12.8 --- CHI2V 4-terms chi2 (V)
895-906 F12.8 --- CHI2R 4-terms chi2 (R)
908-919 F12.8 --- CHI2I 4-terms chi2 (I)
921-932 F12.8 --- CHI2J 4-terms chi2 (J)
934-945 F12.8 --- CHI2H 4-terms chi2 (H)
947-958 F12.8 --- CHI2K 4-terms chi2 (K)
--------------------------------------------------------------------------------
Acknowledgements:
Antonio Claret, claret(at)iaa.es
(End) Patricia Vannier [CDS] 13-Apr-2023