================================================================================
      A new  non-linear limb-darkening law  for LTE stellar atmosphere models:
      Calculations for -5.0  < log [M/H] < +1,  2000 K < T$_{eff}$ < 50000 K 
      at several surface gravities 
      CLARET A.
      Astron. Astrophys.  363, 1081-1190  (2000)
================================================================================

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 2000 K-50000 K. 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($\mu$) at any part of the 
disk for any filter or wavelength, log g, effective temperature, metallicity 
and microturbulent velocity.  

The results are presented in 46 tables for the 12 filters (bolometric) and 
can be retrieved from   the CDS. Due to the size of the remaining tables, 
mainly the monochromatic, these are available only on request (CD ROMs).

Keywords:  
stars- atmospheres: Limb-Darkening 
stars- binaries: eclipsing
stars: Brown dwarfs
stars: Abundances

File Summary:
--------------------------------------------------------------------------------
  FileName      Lrecl  Records   Explanations
--------------------------------------------------------------------------------
ReadMe             80      398       This file

table1             80      54         GRIDS

table2            131     1549   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -5.0, v.tu=2 km/s
table3            131     1573   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -4.5, v.tu=2 km/s
table4            131     1573   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -4.0, v.tu=2 km/s
table5            131     1593   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -3.5, v.tu=2 km/s
table6            131     1617   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -3.0, v.tu=2 km/s
table7            131     1609   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -2.5, v.tu=2 km/s
table8            131     1609   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -2.0, v.tu=2 km/s
table9            131     1625   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -1.5, v.tu=2 km/s
table10           131     1641   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -1.0, v.tu=2 km/s
table11           131     1645   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -0.5, v.tu=2 km/s
table12           131     1645   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -0.3, v.tu=2 km/s
table13           131     1645   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -0.2, v.tu=2 km/s
table14           131     1645   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = -0.1, v.tu=2 km/s
table15           131     1909   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = 0.0, v.tu=2 km/s
table16           131     1569   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = +0.1, v.tu=2 km/s
table17           131     1621   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = +0.2, v.tu=2 km/s
table18           131     1597   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = +0.3, v.tu=2 km/s
table19           131     1585   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = +0.5, v.tu=2 km/s
table20           131     1505   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] = +1.0, v.tu=2 km/s
table21           131     1921   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] =  0.0, v.tu=0 km/s
table22           131     1945   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                 ATLAS models, log [M/H] =   0.0, v.tu=1 km/s
table23           131     1865   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] =  0.0, v.tu=4 km/s
table24           131     1829   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models, log [M/H] =  0.0, v.tu=8 km/s
table25           131        9   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  SUN (ATLAS),  log [M/H] = 0.0, v.tu=1.5 km/s
table26           131        9   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  VEGA (ATLAS), log [M/H] =-0.5, v.tu=  0 km/s
table27            69     1102   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  SUN (ATLAS),  log [M/H] = 0.0, monochromatic
table28            69     1102   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  VEGA (ATLAS), log [M/H] =-0.5, monochromatic
table29            57     9555   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  ATLAS models - bolometric, 
                                  -5.0 < log [M/H] < +1.0,v.tu=2,0,1,4,8 km/s 
table30           132      9556   (u) linear limb-darkening coefficients
                                  ATLAS models, all metallicities,
                                  v.tu=2,0,1,4,8 km/s 
table31           132     19107   (a, b) quadratic limb-darkening coefficients
                                  ATLAS models, all metallicities,
                                  v.tu=2,0,1,4,8 km/s 
table32           132     19107   (c, d) square root limb-darkening coefficients
                                  ATLAS models, all metallicities,
                                  v.tu=2,0,1,4,8 km/s 
table33           132     19107   (e, f) logarithmic limb-darkening coefficients
                                  ATLAS models, all metallicities,
                                  v.tu=2,0,1,4,8 km/s 
table34            38     9555   (u) linear limb-darkening coefficients
                                  ATLAS models, all metallicities,
                                  v.tu=2,0,1,4,8 km/s, bolometric 
table35            38     9555   (a, b) quadratic limb-darkening coefficients
                                  ATLAS models, all metallicities,
                                  v.tu=2,0,1,4,8 km/s, bolometric 
table36            38     9555   (c, d) square root limb-darkening coefficients
                                  ATLAS models, all metallicities,
                                  v.tu=2,0,1,4,8 km/s, bolometric 
table37            38     9555   (e, f) logarithnmic limb-darkening coefficients
                                  ATLAS models, all metallicities,
                                  v.tu=2,0,1,4,8 km/s, bolometric 
table38           131      565   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  PHOENIX models,log [M/H] = 0.0, v.tu= 2 km/s
table39            57      144   (a_1,a_2,a_3,a_4) limb-darkening coefficients
                                  PHOENIX models-  bolometric,  
                                  log [M/H] = 0.0, v.tu= 2 km/s
table40           132      144    (u) linear limb-darkening coefficients
                                  PHOENIX models,log [M/H] = 0.0, v.tu= 2 km/s
table41           132      285    (a, b) cuadratic limb-darkening coefficients
                                  PHOENIX models,log [M/H] = 0.0, v.tu= 2 km/s
table42           132      285    (c, d) square root  limb-darkening coefficients
                                  PHOENIX models,log [M/H] = 0.0, v.tu= 2 km/s
table43           132      285    (e, f) logarithmic limb-darkening coefficients
                                  PHOENIX models,log [M/H] = 0.0, v.tu= 2 km/s
table44            29      144   (u) linear limb-darkening coefficients
                                  PHOENIX models-  bolometric,  
                                  log [M/H] = 0.0, v.tu= 2 km/s
table45            30      284   (a, b) quadratic limb-darkening coefficients
                                  PHOENIX models-  bolometric,  
                                  log [M/H] = 0.0, v.tu= 2 km/s
table46            30      284   (c, d) square root limb-darkening coefficients
                                  PHOENIX models-  bolometric,  
                                  log [M/H] = 0.0, v.tu= 2 km/s
table47            30      284   (e, f) logarithmic limb-darkening coefficients
                                  PHOENIX models-  bolometric,  
                                  log [M/H] = 0.0, v.tu= 2 km/s
--------------------------------------------------------------------------------

Byte-by-byte Description of files: TABLE2-TABLE26 and TABLE38 (EQUATION 6)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
   1-  2  A3            Coeff  [a_i,i=1,4] Limb-darkening coefficients(1)
   4-  8  F5.2   cm/s+2  logg     Surface gravity
  10- 15  F6.0     K     Teff     Effective temperature
  17- 20  F4.1           log Z    log [metal/H]
  23- 29  F7.4   ---     u     Limb-darkening coefficient (Filter u)
  32- 38  F7.4   ---     v     Limb-darkening coefficient (Filter v)
  41- 47  F7.4   ---     b     Limb-darkening coefficient (Filter b)
  50- 56  F7.4   ---     y     Limb-darkening coefficient (Filter y)
  59- 65  F7.4   ---     U     Limb-darkening coefficient (Filter U)
  68- 74  F7.4   ---     B     Limb-darkening coefficient (Filter B)
  77- 83  F7.4   ---     V     Limb-darkening coefficient (Filter V)
  86- 92  F7.4   ---     R     Limb-darkening coefficient (Filter R)
  95- 101 F7.4   ---     I     Limb-darkening coefficient (Filter I)
 105- 111 F7.4   ---     J     Limb-darkening coefficient (Filter J)
 115- 121 F7.4   ---     H     Limb-darkening coefficient (Filter H)
 125- 131 F7.4   ---     K     Limb-darkening coefficient (Filter K)
--------------------------------------------------------------------------------

Byte-by-byte Description of files: TABLE27 - TABLE 28 (EQUATION 6)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
   6- 11  F6.2   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           log Z    log [metal/H]
  40- 45  F6.3   ---     A1     Monochromatic Limb-darkening coefficient a_1
  48- 53  F6.3   ---     A2     Monochromatic Limb-darkening coefficient a_2
  56- 61  F6.3   ---     A3     Monochromatic Limb-darkening coefficient a_3
  64- 69  F6.3   ---     A4     monochromatic Limb-darkening coefficient a_4
--------------------------------------------------------------------------------

Byte-by-byte Description of files: TABLE29 and TABLE39 (EQUATION 6)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
  1-  3   F2.0   km/s    VT     microturbulent velocity
  6- 10   F5.2   cm/s+2  logg   Surface gravity
  13-18   F6.0     K     Teff   Effective temperature
  20- 23  F5.2           log Z  log [metal/H]
  28- 33  F6.3   ---     A1     Bolometric Limb-darkening coefficient a_1
  36- 41  F6.3   ---     A2     Bolometric Limb-darkening coefficient a_2
  44- 49  F6.3   ---     A3     Bolometric Limb-darkening coefficient a_3
  52- 57  F6.3   ---     A4     Bolometric Limb-darkening coefficient a_4
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE30 and TABLE40 (EQUATION 1)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
   1-     A1             Coeff  (u) linear Limb-darkening coefficients
   4-     I.1   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           log Z  log [metal/H]
  24- 30  F7.4   ---     u     Linear Limb-darkening coefficient (u) (Filter u)
  33- 39  F7.4   ---     v     Linear Limb-darkening coefficient (u) (Filter v)
  42- 48  F7.4   ---     b     Linear Limb-darkening coefficient (u) (Filter b)
  51- 57  F7.4   ---     y     Linear Limb-darkening coefficient (u) (Filter y)
  60- 66  F7.4   ---     U     Linear Limb-darkening coefficient (u) (Filter U)
  69- 75  F7.4   ---     B     Linear Limb-darkening coefficient (u) (Filter B)
  78- 84  F7.4   ---     V     Linear Limb-darkening coefficient (u) (Filter V)
  86- 92  F7.4   ---     R     Linear Limb-darkening coefficient (u) (Filter R)
  96- 102 F7.4   ---     I     Linear Limb-darkening coefficient (u) (Filter I)
 106- 112 F7.4   ---     J     Linear Limb-darkening coefficient (u) (Filter J)
 116- 122 F7.4   ---     H     Linear Limb-darkening coefficient (u) (Filter H)
 126- 132 F7.4   ---     K     Linear Limb-darkening coefficient (u) (Filter K)
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE31 and TABLE41 (EQUATION 2)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
   1-     A1             Coeff  (a, b) quadratic Limb-darkening coefficients
   4-     I.1   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           log Z  log [metal/H]
  24- 30  F7.4   ---     u  Quadratic Limb-darkening coeff  (a, b) (Filter u)
  33- 39  F7.4   ---     v  Quadratic Limb-darkening coeff  (a, b) (Filter v)
  42- 48  F7.4   ---     b  Quadratic Limb-darkening coeff  (a, b) (Filter b)
  51- 57  F7.4   ---     y  Quadratic Limb-darkening coeff  (a, b) (Filter y)
  60- 66  F7.4   ---     U  Quadratic Limb-darkening coeff  (a, b) (Filter U)
  69- 75  F7.4   ---     B  Quadratic Limb-darkening coeff  (a, b) (Filter B)
  78- 84  F7.4   ---     V  Quadratic Limb-darkening coeff  (a, b) (Filter V)
  86- 92  F7.4   ---     R  Quadratic Limb-darkening coeff  (a, b) (Filter R)
  96- 102 F7.4   ---     I  Quadratic Limb-darkening coeff  (a, b) (Filter I)
 106- 112 F7.4   ---     J  Quadratic Limb-darkening coeff  (a, b) (Filter J)
 116- 122 F7.4   ---     H  Quadratic Limb-darkening coeff  (a, b) (Filter H)
 126- 132 F7.4   ---     K  Quadratic Limb-darkening coeff  (a, b) (Filter K)
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE32 and TABLE42 (EQUATION 3)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
   1-     A1             Coeff  (c, d) square root Limb-darkening coefficients
   4-     I.1   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           log Z  log [metal/H]
  24- 30  F7.4   ---     u  Square root Limb-darkening coeff.  (c, d) (Filter u)
  33- 39  F7.4   ---     v  Square root Limb-darkening coeff.  (c, d) (Filter v)
  42- 48  F7.4   ---     b  Square root Limb-darkening coeff.  (c, d) (Filter b)
  51- 57  F7.4   ---     y  Square root Limb-darkening coeff.  (c, d) (Filter y)
  60- 66  F7.4   ---     U  Square root Limb-darkening coeff.  (c, d) (Filter U)
  69- 75  F7.4   ---     B  Square root Limb-darkening coeff.  (c, d) (Filter B)
  78- 84  F7.4   ---     V  Square root Limb-darkening coeff.  (c, d) (Filter V)
  86- 92  F7.4   ---     R  Square root Limb-darkening coeff.  (c, d) (Filter R)
  96- 102 F7.4   ---     I  Square root Limb-darkening coeff.  (c, d) (Filter I)
 106- 112 F7.4   ---     J  Square root Limb-darkening coeff.  (c, d) (Filter J)
 116- 122 F7.4   ---     H  Square root Limb-darkening coeff.  (c, d) (Filter H)
 126- 132 F7.4   ---     K  Square root Limb-darkening coeff.  (c, d) (Filter K)
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE33 and TABLE43 (EQUATION 4)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
   1-     A1             Coeff  (c, d) logarithmic Limb-darkening coefficients
   4-     I.1   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           log Z  log [metal/H]
  24- 30  F7.4   ---     u Logarithmic Limb-darkening coeff.  (e, f) (Filter u)
  33- 39  F7.4   ---     v Logarithmic Limb-darkening coeff.  (e, f) (Filter v)
  42- 48  F7.4   ---     b Logarithmic Limb-darkening coeff.  (e, f) (Filter b)
  51- 57  F7.4   ---     y Logarithmic Limb-darkening coeff.  (e, f) (Filter y)
  60- 66  F7.4   ---     U Logarithmic Limb-darkening coeff.  (e, f) (Filter U)
  69- 75  F7.4   ---     B Logarithmic Limb-darkening coeff.  (e, f) (Filter B)
  78- 84  F7.4   ---     V Logarithmic Limb-darkening coeff.  (e, f) (Filter V)
  86- 92  F7.4   ---     R Logarithmic Limb-darkening coeff.  (e, f) (Filter R)
  96- 102 F7.4   ---     I Logarithmic Limb-darkening coeff.  (e, f) (Filter I)
 106- 112 F7.4   ---     J Logarithmic Limb-darkening coeff.  (e, f) (Filter J)
 116- 122 F7.4   ---     H Logarithmic Limb-darkening coeff.  (e, f) (Filter H)
 126- 132 F7.4   ---     K Logarithmic Limb-darkening coeff.  (e, f) (Filter K)
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE34 and TABLE44 (EQUATION 1)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
  1-  3   F2.0   km/s    VT     microturbulent velocity
  4-  8   F5.2   cm/s+2  logg   Surface gravity
  10- 15  F6.0     K     Teff   Effective temperature
  17- 20  F4.1           log Z  log [metal/H]
  23- 29  F7.4   ---     u      Linear bolometric Limb-darkening coefficient 
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE35 (EQUATION 2)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
  1-  3   F2.0   km/s    VT     microturbulent velocity
  4-  8   F5.2   cm/s+2  logg   Surface gravity
  10- 15  F6.0     K     Teff   Effective temperature
  17- 20  F4.1           log Z  log [metal/H]
  23- 29  F7.4   ---     a    Quadratic bolometric Limb-darkening coefficient 
  32- 38  F7.4   ---     b    Quadratic bolometric Limb-darkening coefficient 
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE36 (EQUATION 3)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
  1-  3   F2.0   km/s    VT     microturbulent velocity
  4-  8   F5.2   cm/s+2  logg   Surface gravity
  10- 15  F6.0     K     Teff   Effective temperature
  17- 20  F4.1           log Z  log [metal/H]
  23- 29  F7.4   ---     c    Sq. root bolometric Limb-darkening coefficient 
  32- 38  F7.4   ---     d    Sq. root bolometric Limb-darkening coefficient 
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE37 (EQUATION 4)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
  1-  3   F2.0   km/s    VT     microturbulent velocity
  4-  8   F5.2   cm/s+2  logg   Surface gravity
  10- 15  F6.0     K     Teff   Effective temperature
  17- 20  F4.1           log Z  log [metal/H]
  23- 29  F7.4   ---     e    Logar. bolometric Limb-darkening coefficient 
  32- 38  F7.4   ---     f    Logar. bolometric Limb-darkening coefficient 
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE45 (EQUATION 2)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
  1       A1       -     Coeff  Quadratic limb-darkening coef. 
  4-  4   I2     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           log Z  log [metal/H]
  24- 31  F7.4   ---    (a, b)  Quadratic bolometric Limb-darkening coefficient 
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE46 (EQUATION 3)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
  1       A1       -     Coeff  Square root limb-darkening coef. 
  4-  4   I2     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           log Z  log [metal/H]
  24- 31  F7.4   ---    (c, d)  Quadratic bolometric Limb-darkening coefficient 
--------------------------------------------------------------------------------
Byte-by-byte Description of files: TABLE47 (EQUATION 4)
--------------------------------------------------------------------------------
   Bytes Format  Units   Label  Explanations
--------------------------------------------------------------------------------
  1       A1       -     Coeff  Logarithmic limb-darkening coef. 
  4-  4   I2     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           log Z  log [metal/H]
  24- 31  F7.4   ---    (e, f)  Quadratic bolometric Limb-darkening coefficient 
--------------------------------------------------------------------------------

(1)Note: I(mu)/I(1) = 1 - a_1+(1 - mu**.5) - a_2*(1 - mu) - a_3*(1 - mu**1.5) 
      -  a_4*(1 - mu**2) 

Note on linear, quadratic, square root and logarithmic fittings.  
The present calculations were performed using all available \mu points:
17 \mu points  ==> ATLAS
16 \mu points  ==> PHOENIX         

================================================================================



See also:
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)
J/A+A/359/289 :  Studies on stellar rotation.II.Gravity-darkening (Claret 2000)
