J/A+A/666/A60 Stellar Models and Limb Darkening (Kostogryz+, 2022)
Stellar limb darkening.
A new MPS-ATLAS library for Kepler, TESS, CHEOPS, and PLATO passbands.
Kostogryz N.M., Witzke V., Shapiro A.I., Solanki S.K., Maxted P.F.L.,
Kurucz R.L., Gizon L.
<Astron. Astrophys. 666, A60 (2022)>
=2022A&A...666A..60K 2022A&A...666A..60K (SIMBAD/NED BibCode)
ADC_Keywords: Models, atmosphere ; Photometry ; Optical
Keywords: radiative transfer - methods: numerical - Sun: atmosphere -
stars: atmospheres
Abstract:
The detection of the first exoplanet paved the way for the era of
transit-photometry space missions with revolutionary photometric
precision, whose aim is to discover new exoplanetary systems around
different types of stars. With this high precision, it is possible to
derive the radii of exoplanets very accurately, which is crucial for
constraining their type and composition. However, it requires an
accurate description of their host stars, especially their
center-to-limb variation of intensities (so-called limb darkening) as
it affects the planet-to-star radius ratio determination.
We aim to improve the accuracy of limb-darkening calculations for
stars with a wide range of fundamental parameters.
We used the recently developed 1D Merged Parallelized Simplified ATLAS
(MPS-ATLAS) code to compute model atmosphere structures and to
synthesize stellar limb darkening on a very fine grid of stellar
parameters. For the computations, we utilized the most accurate
information on chemical element abundances and mixing-length
parameters, including convective overshoot. The stellar limb darkening
was fitted using the two most accurate limb darkening laws: the
power-2 and 4-parameter nonlinear laws.
We present a new extensive library of stellar model atmospheric
structures, the synthesized stellar limb darkening curves, and the
coefficients of parameterized limb-darkening laws on a very fine grid
of stellar parameters in the Kepler, TESS, CHEOPS, and PLATO
passbands. The fine grid allows the sizable errors, introduced by the
need to interpolate, to be overcome. Our computations of solar limb
darkening are in a good agreement with available solar measurements at
different view angles and wavelengths. Our computations of stellar limb
darkening agree well with available measurements of Kepler stars. A
new grid of stellar model structures, limb darkening, and their fitted
coefficients in different broad passbands are provided.
Description:
We present stellar model atmospheric structures, limb darkening, and
limb darkening coefficients according to the description in Table 3 of
our paper.
files/tablee1.txt and files/tablee2.txt contain the entire grid of our
atmospheric structures.
First line in each structure gives the corresponding stellar parameters.
Second line gives the number of depth points for the structure.
Then we provide the structure which is described in Description of file
In the end of the each structure we give the input parameters used to
compute the structure (see description in Witzke et al.,
2021A&A...653A..65W 2021A&A...653A..65W).
A phython program is provided to read
files/tablee3.txt and files/tablee4.txt.
def readlimbdarkening_curves(filename: str, mh: float, teff: float, logg: float, passband: str):
mh_grid, teff_grid, logg_grid, i0 = np.loadtxt(filename, usecols=(0, 1, 2, 4), unpack = True)
clv = np.loadtxt(filename, usecols=(range(5,28)))
passbands_grid = np.array(["Kepler", "TESS", "CHEOPS", "PLATO"])
ind_pb = np.squeeze(np.argwhere(passbands_grid≡passband))
Nmh = len(np.unique(mh_grid))
Nteff = len(np.unique(teff_grid))
Nlogg = len(np.unique(logg_grid))
Npb = len(passbands_grid)
mh_grid = mh_grid.reshape((Nmh, Nteff,Nlogg, Npb))[:, 0, 0, ind_pb]
teff_grid = teff_grid.reshape((Nmh, Nteff, Nlogg, Npb))[0, :, 0, ind_pb]
logg_grid = logg_grid.reshape((Nmh, Nteff, Nlogg, Npb))[0, 0, :, ind_pb]
i0 = i0.reshape((Nmh, Nteff, Nlogg, Npb))[:, :, :, ind_pb]
clv = clv.reshape((Nmh, Nteff, Nlogg, Npb, clv.shape[1]))[:,:,:,ind_pb,:]
indMH = np.argmin((abs(mh_grid - mh)))
indTeff = np.argmin((abs(teff_grid - teff)))
indLogg = np.argmin((abs(logg_grid - logg)))
return mh_grid[indMH], teff_grid[indTeff], logg_grid[indLogg], i0[indMH, indTeff, indLogg], clv[indMH, indTeff, indLogg, :]
This function can be called for the given stellar parameters and
passband, and it returns the closest stellar parameters in our grid,
absolute value of intensity at the disk center, and the corresponding
stellar limb darkening curves at 24 disk positions.
A phython program is provided to read files/tablee5.txt and
files/tablee6.txt.
def readlimbdarkening_coefficients(filename: str, mh: float, teff: float, logg: float, passband: str, ld_law: str):
mh_grid, teff_grid, logg_grid, c, alpha, a1, a2, a3, a4 =np.loadtxt(filename, usecols=(0, 1, 2, 4, 5, 6, 7, 8, 9), unpack = True)
passbands_grid = np.array(["Kepler", "TESS", "CHEOPS", "PLATO"])
ind_pb = np.squeeze(np.argwhere(passbands_grid≡passband))
Nmh = len(np.unique(mh_grid))
Nteff = len(np.unique(teff_grid))
Nlogg = len(np.unique(logg_grid))
Npb = len(passbands_grid)
mh_grid = mh_grid.reshape((Nmh, Nteff, Nlogg, Npb))[:, 0, 0, ind_pb]
teff_grid = teff_grid.reshape((Nmh, Nteff, Nlogg, Npb))[0, :, 0, ind_pb]
logg_grid = logg_grid.reshape((Nmh, Nteff, Nlogg, Npb))[0, 0, :, ind_pb]
indMH = np.argmin((np.min(mh_grid - mh)))
indTeff = np.argmin((abs(teff_grid - teff)))
indLogg = np.argmin((abs(logg_grid - logg)))
if ld_law ≡ "4_coefficients":
a1 = a1.reshape((Nmh, Nteff, Nlogg, Npb))[:, :, :, ind_pb]
a2 = a2.reshape((Nmh, Nteff, Nlogg, Npb))[:, :, :, ind_pb]
a3 = a3.reshape((Nmh, Nteff, Nlogg, Npb))[:, :, :, ind_pb]
a4 = a4.reshape((Nmh, Nteff, Nlogg, Npb))[:, :, :, ind_pb]
return mh_grid[indMH], teff_grid[indTeff], logg_grid[indLogg], a1[indMH, indTeff, indLogg], a2[indMH, indTeff, indLogg], a3[indMH, indTeff, indLogg], a4[indMH, indTeff, indLogg]
c = c.reshape((Nmh, Nteff, Nlogg, Npb))[:, :, :, ind_pb]
alpha = alpha.reshape((Nmh, Nteff, Nlogg, Npb))[:, :, :, ind_pb]
return mh_grid[indMH], teff_grid[indTeff], logg_grid[indLogg], c[indMH, indTeff, indLogg], alpha[indMH, indTeff, indLogg]
This function can be called for the given stellar parameters,
passband(["Kepler","TESS","CHEOPS","PLATO"]), and limb darkening laws
("power-2" or "4-coefficients"), and it returns the closest stellar
parameters in our grid and the corresponding limb-darkening
coefficients.
File Summary:
--------------------------------------------------------------------------------
FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
list.dat 97 6 List of the tables (table3 of the paper)
files/* . 6 Individual tables in original format
tablee3.dat 241 136640 Set1 of stellar CLVs in different passbands
tablee4.dat 241 136640 Set2 of stellar CLVs in different passbands
tablee5.dat 79 136640 Set1 of stellar limb darkening coefficients
tablee6.dat 79 136640 Set1 of stellar limb darkening coefficients
--------------------------------------------------------------------------------
Description of file: files/table1.txt, files/table2.txt
For each blok of data:
------------------------------------------------------------------------------
Bytes Format Units Label Explanations
------------------------------------------------------------------------------
2- 14 E13.12 g/cm2 rhox Column mass
18- 24 F6.1 K Tgas Gas temperature
26- 35 E10.4 erg/cm3 Pgas Gas pressure
37- 46 E10.4 cm-1 ne Electron number density
48- 57 E10.4 cm2/g kRoss Mean Rosseland opacity
59- 68 E10.4 erg/cm3 Prad Radiation pressure
70- 79 E10.4 cm/s vturb Turbulent velocity
------------------------------------------------------------------------------
Byte-by-byte Description of file: list.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 11 A11 --- FileName Name of the file, in subdirectory files (1)
13- 91 A79 --- Title Description of the table
93- 97 A5 --- Set Grid set
--------------------------------------------------------------------------------
Note (1): For files tablee3.txt, tablee4.txt, tablee5.txt and tablee6.txt,
versions for the python programs.
--------------------------------------------------------------------------------
Byte-by-byte Description of file: tablee3.dat tablee4.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 5 F5.2 --- M/H [-5.0/1.5] Metallicity
7- 10 I4 K Teff [3500/9000] Effective
temperature
12- 14 F3.1 [cm/2] logg [3.0/5.0] gravity
16- 21 A6 --- passband Instrumental passband
(CHEOPS, Kepler, PLATO, TESS)
23- 34 E12.6 10-7W/(cm3*s*sr) I(1.0) Disk center intensity
36- 43 F8.6 --- I(0.9)/I(1.0) Limb darkening at mu=0.9
45- 52 F8.6 --- I(0.8)/I(1.0) Limb darkening at mu=0.8
54- 61 F8.6 --- I(0.7)/I(1.0) Limb darkening at mu=0.7
63- 70 F8.6 --- I(0.6)/I(1.0) Limb darkening at mu=0.6
72- 79 F8.6 --- I(0.5)/I(1.0) Limb darkening at mu=0.5
81- 88 F8.6 --- I(0.4)/I(1.0) Limb darkening at mu=0.4
90- 97 F8.6 --- I(0.35)/I(1.0) Limb darkening at mu=0.35
99-106 F8.6 --- I(0.3)/I(1.0) Limb darkening at mu=0.3
108-115 F8.6 --- I(0.25)/I(1.0) Limb darkening at mu=0.25
117-124 F8.6 --- I(0.22)/I(1.0) Limb darkening at mu=0.22
126-133 F8.6 --- I(0.2)/I(1.0) Limb darkening at mu=0.2
135-142 F8.6 --- I(0.17)/I(1.0) Limb darkening at mu=0.17
144-151 F8.6 --- I(0.15)/I(1.0) Limb darkening at mu=0.15
153-160 F8.6 --- I(0.12)/I(1.0) Limb darkening at mu=0.12
162-169 F8.6 --- I(0.1)/I(1.0) Limb darkening at mu=0.1
171-178 F8.6 --- I(0.09)/I(1.0) Limb darkening at mu=0.09
180-187 F8.6 --- I(0.08)/I(1.0) Limb darkening at mu=0.08
189-196 F8.6 --- I(0.07)/I(1.0) Limb darkening at mu=0.07
198-205 F8.6 --- I(0.06)/I(1.0) Limb darkening at mu=0.06
207-214 F8.6 --- I(0.05)/I(1.0) Limb darkening at mu=0.05
216-223 F8.6 --- I(0.03)/I(1.0) Limb darkening at mu=0.03
225-232 F8.6 --- I(0.02)/I(1.0) Limb darkening at mu=0.02
234-241 F8.6 --- I(0.01)/I(1.0) Limb darkening at mu=0.01
--------------------------------------------------------------------------------
Byte-by-byte Description of file: tablee5.dat tablee6.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 5 F5.2 [-] M/H [-5.0/1.5] Metallicity
7- 10 I4 K Teff [3500/9000] Effective temperature
12- 14 F3.1 [cm/s] logg [3.0/5.0] gravity
16- 21 A6 --- passband Instrumental passband
(CHEOPS, Kepler, PLATO, TESS)
23- 30 F8.6 --- c coefficient of power-2 limb darkening law
32- 39 F8.6 --- alpha coefficient of power-2 limb darkening law
41- 49 F9.6 --- a1 coefficient of 4-coefficients limb darkening law
51- 59 F9.6 --- a2 coefficient of 4-coefficients limb darkening law
61- 69 F9.6 --- a3 coefficient of 4-coefficients limb darkening law
71- 79 F9.6 --- a4 coefficient of 4-coefficients limb darkening law
--------------------------------------------------------------------------------
Acknowledgements:
Nadiia Kostogryz, kostogryz(at)mps.mpg.de
(End) [CDS] 09-Sep-2022