J/A+A/363/1081 Non-linear limb-darkening law for LTE models (Claret, 2000)
A new non-linear limb-darkening law for LTE stellar atmosphere models:
Calculations for -5.0<log[M/H]<+1, 2000K<Teff<50000K
at several surface gravities
Claret A.
<Astron. Astrophys. 363, 1081 (2000)>
=2000A&A...363.1081C 2000A&A...363.1081C
ADC_Keywords: Models, atmosphere ; Photometry, UBVRIJKLMNH ; Photometry, uvby
Keywords: stars - atmospheres - stars: binaries: eclipsing
Abstract:
A new non-linear limb-darkening law, based on the Least-Squares Method
(LSM), is presented. This law is able to describe the intensity
distribution much more accurately than any of the old ones given that
the differences I(model)-I(fitting) are of some order of magnitude
smaller than those derived from other approximations. This new law
shows several advantages: it represents well the intensity
distribution, the flux is conserved with high accuracy and it permits
the use of a single law for the whole HR Diagram since that the
bi-parametric laws are only marginally valid in certain range of
effective temperatures. The limb-darkening coefficients are computed
for the 12 commonly used photometric bands u v b y U B V R I J H K.
Bolometric and monochromatic calculations are also available. The
computations are presented for 19 metallicities ranging from 10-5
up to 10+1 solar abundances, with log(g) varying between 0 and 5.0
and effective temperatures between 2000K-50000K. Results for
microturbulent velocities of 0, 1, 2, 4, 8 km/s are also available.
With this set of data it was possible to investigate, for the first
time, the influence of such parameters in the limb-darkening.
Limb-brightening, instead of limb-darkening, was detected for some
models. It is shown that the limb-darkening coefficients derived using
the Flux Conservation Method (FCM) do not describe very well the
intensity distribution, mainly near the border of the disk. On the
contrary, the present coefficients, based on the LSM, represent very
well the function I(µ) at any part of the disk for any filter or
wavelength, log(g), effective temperature, metallicity and
microturbulent velocity.
The results are presented here as synthetic tables containing the
limb-darkening coefficients. The 46 tables announced in the paper
are also accessible as the "original.tar" file.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
atlas.dat 135 38200 (a1,a2,a3,a4) limb-darkening coefficients
for ATLAS models
atlasco.dat 132 66857 Limb-darkening coefficients, ATLAS models,
all metallicities, v.tu=2,0,1,4,8km/s
sun.dat 135 4 (a1,a2,a3,a4) limb-darkening coefficients
for SUN (ATLAS)
vega.dat 135 4 (a1,a2,a3,a4) limb-darkening coefficients
for VEGA (ATLAS)
sunmon.dat 69 1097 (a1,a2,a3,a4) limb-darkening coefficients
SUN (ATLAS), log [M/H] = 0.0, monochromatic
vegamon.dat 69 1097 (a1,a2,a3,a4) limb-darkening coefficients
VEGA (ATLAS), log [M/H] =-0.5, monochromatic
atlasb.dat 57 9550 (a1,a2,a3,a4) limb-darkening coefficients
ATLAS models - bolometric
atlasbco.dat 30 66850 Limb-darkening coefficients, ATLAS models,
all metallicities, v.tu=2,0,1,4,8 km/s,
bolometric
phoenix.dat 135 560 (a1,a2,a3,a4) limb-darkening coefficients
for PHOENIX models (= table38.dat)
phoenixc.dat 132 979 Limb-darkening coefficients, PHOENIX models-
bolometric, log[M/H]=0.0, v.tu=2km/s
phoenixb.dat 57 139 (a1,a2,a3,a4) limb-darkening coefficients
PHOENIX models- bolometric
phoenibc.dat 30 976 Limb-darkening coefficients, PHOENIX models-
bolometric, log [M/H] = 0.0, v.tu= 2 km/s
original.tar 1079 158347 Original 46 tables
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See also:
J/A+A/401/657 : New non-linear limb-darkening law. II. (Claret, 2003)
J/A+AS/109/441 : Stellar models until He burning - I. (Claret, 1995)
J/A+AS/114/549 : Stellar models until He burning - II. (Claret+, 1995)
J/A+AS/125/439 : Stellar models until He burning - III. (Claret+, 1997)
J/A+AS/131/395 : Comprehensive tables for the interpretation (Claret, 1998)
J/A+AS/133/123 : Stellar models until He burning - IV. (Claret+, 1998)
J/A+AS/110/329 : LTE model atmospheres coeff. (Diaz-cordoves+, 1995)
J/A+AS/114/247 : Limb-darkening coefficients for RIJHK (Claret+, 1995)
J/A+A/335/647 : Very low mass stars: non-linearity of the limb (Claret 1998)
Table 1: Limb-Darkening coefficients for u v b y U B V R I J H K bands
(Least-Squares Method) (G1)
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Name Source range Teff log g log [M/H] VT Kind of fitting
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atlas.dat ATLAS 3500-50000 0.0-5.0 -5.0/+1.0 0-4 Eq. 6, 12 filters
sun.dat (Sun) ATLAS 5777 4.377 0.0 1.5 Eq. 6, 12 filters
vega.dat (Vega)ATLAS 9400 3.90 -0.5 0 Eq. 6, 12 filters
sunmon.dat (Sun) ATLAS 5777 4.377 0.0 1.5 Eq. 6, monocrom.
vegamon.dat (Vega)ATLAS 9400 3.90 -0.5 0 Eq. 6, monocrom.
astrob.dat ATLAS 3500-50000 0.0-5.0 19 metal. 0-8 Eq. 6, bolometric
atlosco.dat ATLAS 3500-50000 0.0-5.0 19 metal. 0-8 Eq. 1-4, 12 filters
atlasbco.dat ATLAS 3500-50000 0.0-5.0 19 metal. 0-8 Eq. 1-4, bolometric
phoenix.dat PHOENIX 2000-9800 3.5-5.0 0.0 2 Eq. 6, 12 filters
phenixb.dat PHOENIX 2000-9800 3.5-5.0 0.0 2 Eq. 6, bolometric
phoenixc.dat PHOENIX 2000-9800 3.5-5.0 0.0 2 Eq. 1-4, 12 filters
phoenibc.dat PHOENIX 2000-9800 3.5-5.0 0.0 2 Eq. 1-4, bolometric
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Byte-by-byte Description of file: atlas.dat phoenix.dat sun.dat vega.dat
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Bytes Format Units Label Explanations
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1- 3 F3.1 km/s VT Initial turbulent velocity
5- 7 A3 --- Coeff Limb-darkening coefficients (ai,i=1,4) (G1)
8- 12 F5.2 [cm/s+2] logg Surface gravity
14- 19 F6.0 K Teff Effective temperature
21- 24 F4.1 [Sun] log[M/H] log [metal/H]
27- 33 F7.4 --- u Limb-darkening coefficient (Filter u)
36- 42 F7.4 --- v Limb-darkening coefficient (Filter v)
45- 51 F7.4 --- b Limb-darkening coefficient (Filter b)
54- 60 F7.4 --- y Limb-darkening coefficient (Filter y)
63- 69 F7.4 --- U Limb-darkening coefficient (Filter U)
72- 78 F7.4 --- B Limb-darkening coefficient (Filter B)
81- 87 F7.4 --- V Limb-darkening coefficient (Filter V)
90- 96 F7.4 --- R Limb-darkening coefficient (Filter R)
99-105 F7.4 --- I Limb-darkening coefficient (Filter I)
109-115 F7.4 --- J Limb-darkening coefficient (Filter J)
119-125 F7.4 --- H Limb-darkening coefficient (Filter H)
129-135 F7.4 --- K Limb-darkening coefficient (Filter K)
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Byte-by-byte Description of file: sunmon.dat vegamon.dat
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Bytes Format Units Label Explanations
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3- 11 F9.2 nm lambda wavelength
19- 23 F5.2 [cm/s+2] logg Surface gravity
25- 30 F6.0 K Teff Effective temperature
32- 35 F4.1 [Sun] log[M/H] log [metal/H]
40- 45 F6.3 --- A1 Monochromatic Limb-darkening coefficient a1
48- 53 F6.3 --- A2 Monochromatic Limb-darkening coefficient a2
55- 61 F7.3 --- A3 Monochromatic Limb-darkening coefficient a3
64- 69 F6.3 --- A4 monochromatic Limb-darkening coefficient a4
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Byte-by-byte Description of file: atlasco.dat phoenixc.dat
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Bytes Format Units Label Explanations
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1 A1 --- Coeff Limb-darkening coefficients
(u, (a,b) (c,d) (e,f) (G1) (1)
4 I1 km/s VT Microturbulent velocity
5- 9 F5.2 [cm/s+2] logg Surface gravity
11- 16 F6.0 K Teff Effective temperature
18- 21 F4.1 [Sun] log[M/H] log [metal/H]
24- 30 F7.4 --- u Linear Limb-darkening coefficient (Filter u)
33- 39 F7.4 --- v Linear Limb-darkening coefficient (Filter v)
42- 48 F7.4 --- b Linear Limb-darkening coefficient (Filter b)
51- 57 F7.4 --- y Linear Limb-darkening coefficient (Filter y)
60- 66 F7.4 --- U Linear Limb-darkening coefficient (Filter U)
69- 75 F7.4 --- B Linear Limb-darkening coefficient (Filter B)
78- 84 F7.4 --- V Linear Limb-darkening coefficient (Filter V)
87- 93 F7.4 --- R Linear Limb-darkening coefficient (Filter R)
96-102 F7.4 --- I Linear Limb-darkening coefficient (Filter I)
106-112 F7.4 --- J Linear Limb-darkening coefficient (Filter J)
116-122 F7.4 --- H Linear Limb-darkening coefficient (Filter H)
126-132 F7.4 --- K Linear Limb-darkening coefficient (Filter K)
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Note (1): Limb-darkening coefficients:
(u) linear Limb-darkening coefficients
(a, b) quadratic Limb-darkening coefficients
(c, d) square root Limb-darkening coefficients
(e, f) logarithmic Limb-darkening coefficients
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Byte-by-byte Description of file: atlasb.dat phoenixb.dat
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Bytes Format Units Label Explanations
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1- 3 F3.0 km/s VT microturbulent velocity
6- 10 F5.2 cm/s+2 logg Surface gravity
13- 18 F6.0 K Teff Effective temperature
20- 24 F5.2 [Sun] log[M/H] log [metal/H]
28- 33 F6.3 --- A1 Bolometric Limb-darkening coefficient a1
36- 41 F6.3 --- A2 Bolometric Limb-darkening coefficient a2
44- 49 F6.3 --- A3 Bolometric Limb-darkening coefficient a3
52- 57 F6.3 --- A4 Bolometric Limb-darkening coefficient a4
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Byte-by-byte Description of file: atlasbco.dat phoenibc.dat
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Bytes Format Units Label Explanations
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1 A1 --- Coeff [a-f u] Limb-darkening coefficient (G1)
4 I1 km/s VT microturbulent velocity
5- 9 F5.2 [cm/s+2] logg Surface gravity
11- 16 F6.0 K Teff Effective temperature
18- 21 F4.1 [Sun] log[M/H] log [metal/H]
24- 30 F7.4 --- Limb Limb-darkening coefficient (1)
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Note (1): Limb-darkening coefficients:
For Coeff = u , (u) linear limb-darkening coefficients,
For Coeff = a or b, (a, b) quadratic limb-darkening coefficients,
For Coeff = c or d, (c, d) square root limb-darkening coefficients,
For Coeff = e or f, (e, f) logarithmic limb-darkening coefficients,
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Global notes:
Note (G1): Note on linear, quadratic, square root and logarithmic fittings
Linear I(µ)/I(1)=1-u(1-µ) (1)
Quadratic I(µ)/I(1)=1-a(1-µ)-b(1-µ)2 (2)
Square root I(µ)/I(1)=1-c(1-µ)-d(1-sqr(µ)) (3)
Logarithmic I(µ)/I(1)=1-e(1-µ)-fµln(µ) (4)
Non-linear law I(µ)/I(1) = 1 - a1*(1-µ**.5) - a2*(1-µ) -
a3*(1-µ**1.5) - a4*(1-µ**2) (6)
Where I(1) is the specific intensity at the center of the disk,
u, a, b, c, d, e, f are the corresponding limb-darkening coefficients and
µ=cos(γ), γ being the angle between the line of sight and
the emergent intensity
The present calculations were performed using all available µ points:
17 µ points ⟹ ATLAS
16 µ points ⟹ PHOENIX
Acknowledgements: Antonio Claret Dos Santos
References:
Claret, Studies on stellar rotation. II. Gravity-darkening: 2000A&A...359..289C 2000A&A...359..289C
(End) Patricia Bauer [CDS] 12-Dec-2000