J/A+A/676/A50 2D synthetic spectra for fast rotating stars (Lazzarotto+, 2023)
Photometric determination of rotation axis inclination, rotation rate and mass
of rapidly rotating intermediate mass stars.
Lazzarotto A., Hui-Bon-Hoa A., Rieutord M.
<Astron. Astrophys. 676, A50 (2023)>
=2023A&A...676A..50L 2023A&A...676A..50L (SIMBAD/NED BibCode)
ADC_Keywords: Models ; Stars, activity ; Spectroscopy
Keywords: stars: fundamental parameters - stars: rotation
Abstract:
Intermediate-mass stars are often fast rotators, and hence are
centrifugally flattened and notably affected by gravity darkening. To
analyse this kind of stars properly, one must resort to 2D models to
compute the visible radiative flux and to take the geometrical effect
of the star inclination into account.
Assuming a given stellar age and chemical composition, our aim is to
derive the mass and rotation rates of main sequence fast rotating
stars, along with their inclination, from photometric quantities
influenced by gravity darkening.
We chose three observables that vary with mass, rotation, and
inclination: the temperature derived by the infrared flux method
TIRFM, the Stroemgren c1 index, and a second index c2 built in the
same way as the c1 index, but sensitive to the UV side of the Balmer
jump. These observables are computed from synthetic spectra produced
with the PHOENIX code and rely on a 2D stellar structure from the
ESTER code. These quantities are computed for a grid of models in the
range 2 to 7M☉ and rotation rates from 30% to 80% of the
critical rate. Then, for any triplet (TIRFM, c1, c2), we try to
retrieve the mass, rotation rate, and inclination using a
Levenberg-Marquardt scheme, after a selection step to find the most
suitable starting models.
Hare-and-hound tests showed that our algorithm can recover the mass,
rotation rate, and inclination with a good accuracy. The
difference between input and retrieved parameters is negligible for
models lying on the grid and is less than a few percent otherwise. An
application to the real case of Vega showed that the u filter is
located in a spectral region where the modelled and observed spectra
are discrepant, and led us to define a new filter. Using this new
filter and subsequent index, the Vega parameters are also retrieved
with satisfactory accuracy.
This work opens the possibility to determine the fundamental
parameters of rapidly rotating early-type stars from photometric space
observations.
Description:
A new 2D models for rotating star is given for stars with Solar
abundances at ZAMS and with Vega abundances from Royer F., Gebran M.,
Monier R., et al. 2014A&A...562A..84R 2014A&A...562A..84R, with a core/envelope
hydrogen ratio Xc of 0.271. Files info_sol.dat and info_veg.dat
summarize ESTER outputs for models, respectively, with a solar and
vega composition and age. Files obs_sol.dat and obs_veg.dat summarize
computed observable according inclination for models, respectively,
with a solar and vega composition and age. Files sm*o*.dat and
vm*o*.dat are the model spectra according the inclination where the
first letter stands for the solar composition (s) and Vega
composition (v) and numbers following m and o stand for the mass of
the model given in solar mass, and the rotation rate given as
percentage.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
info_sol.dat 505 36 Solar ESTER model information
info_veg.dat 505 99 Vega ESTER model information
obs_sol.dat 60 684 Observable according inclination for model
with solar composition and age
obs_veg.dat 62 1881 Observable according inclination for model
with Vega composition and age
files/* . 135 Individual ESTER/PHX spectrum according
inclination files
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Byte-by-byte Description of file: info_sol.dat info_veg.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 11 E11.6 g Mass Mass
13- 14 I2 --- RotRate Rotation rate given as percentage
16- 26 E11.6 cm Rp Polar radius
28- 38 E11.6 cm Re Equatorial radius
40- 45 F6.3 --- eps Flatness
47- 57 E11.6 10-7W L Luminosity (erg/s)
59- 65 F7.1 K TeffP Polar effective temperature
67- 73 F7.1 K TeffE Equatorial effective temperature
75- 80 F6.4 [cm/s2] log(geff)P Logarithm of the polar effective gravity
82- 87 F6.4 [cm/s2] logg(eff)E Logarithm of the
equatorial effective gravity
89- 96 E8.3 km/s veq Equatorial velocity
98-108 E11.6 rad/s OmegaP Polar rotational speed
110-120 E11.6 rad/s OmegaE Equatorial rotational speed
122-132 E11.6 rad/s OmegaC Critical rotational speed
134-140 F7.5 d PeriodP ?=- Polar period (- for infinity)
142-148 F7.5 d PeriodE ?=- Equatorial period (- for infinity)
150-156 F7.5 d PeriodC ?=- Critical period (- for infinity)
158-167 E10.5 10-7J.s Lz Angular momentum (erg*s)
169-179 E11.6 cm2/s j Lz/M
181-191 E11.6 g.cm2 Iz Axial moment of inertia
193-203 E11.6 g.cm2 Ic Central moment of inertia
205-216 E12.6 --- J2 First multipolar coefficient of the
gravitational field from inertia moments
218-229 E12.6 --- J2-bis First multipolar coefficient of the
gravitational field direct calculation
231-242 E12.6 10-7J T Kinetic energy
244-255 E12.6 --- T/W Ratio between rotational kinetic energy
and gravitational binding energy
257-267 E11.6 yr Tkh Kelvin-Helmoltz time
269-279 E11.6 g Mc Mass of the core
281-291 E11.6 cm Rpc Polar radius of the core
293-303 E11.6 cm Rec Equatorial radius of the core
305-310 F6.3 --- epsc Flatness of the core
312-321 E10.5 10-7J.s Lzc Angular momentum of the core (erg*s)
323-328 F6.4 --- Xc Fraction of the hydrogen abundance present
in the convective core. Hydrogen
abundance in the core is thus X=X0.Xc
330-340 E11.6 K Tc Central temperature
342-352 E11.6 g/cm3 rhoc Central density
354-364 E11.6 dyn/cm2 pc Central pressure
366-371 F6.4 --- X0 Mass fraction of hydrogen
373-378 F6.4 --- Y0 Mass fraction of helium
380-385 F6.4 --- Z0 Mass fraction of metals
387-397 E11.6 cm Rpc2 Polar radius of the core
399-409 E11.6 cm Rec2 Equatorial radius of the core
411-416 F6.3 --- epsc2 Flatness of the core
418-419 I2 --- ndom Number of domains
421 I1 --- ndomc Number of domains in convective core
423-424 I2 --- npts Number of points in each domains
426-429 I4 --- nr Number of radial points in external domain
431-432 I2 --- nth Number of latitudinal points
434 I1 --- nex Number of radial points in external domain
436-439 A4 --- opa Opacity
441-444 A4 --- eos Equation of state
446-451 A6 --- nuc Type of nuclear reactions
453-458 A6 --- atm Type of atmosphere
460-463 F4.2 --- surff If different from unity, coefficient
modifying boundary conditions to
truncate the stellar model
465 I1 --- core-convec [0/1] values enable/disable convection
in core
467-477 E11.6 cm min-core-size Impose a minimum core size
479 I1 --- env-convec [0/1] values enable/disable convection
in envelope
481-492 E12.6 --- Virial-test Normalized residual resulting from the
Virial theorem
494-505 E12.6 --- Energy-test Relative difference between the luminosity
of the star obtained as the integral
over the volume of the energy generation
rate and that obtained as the integral of
the energy flux at the surface
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Byte-by-byte Description of file: obs_sol.dat obs_veg.dat
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Bytes Format Units Label Explanations
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1- 3 F3.1 Msun Mass Star mass
5- 7 F3.1 --- RotRate Rotaion rate given as percentage
9- 12 F4.1 deg i Inclinaition
14- 21 F8.2 K Tirfm Effective temperature computed with
Infrared Method Flux
23- 30 F8.6 mag c1 Stromgren color index
32- 40 F9.6 mag c1p Stromgren color index with shifter u-filter
42- 49 F8.6 mag c2 Color index build with HST filters
51- 62 A12 --- FileName File name in subdirectory files
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Byte-by-byte Description of file: files/*
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 7 F7.1 0.1nm lambda Wavelength
9- 20 E12.6 10mW/m2/nm Flux0 Flux for i=0 degrees (in erg/s/cm2/Å)
22- 33 E12.6 10mW/m2/nm Flux5 Flux for i=5 degrees (in erg/s/cm2/Å)
35- 46 E12.6 10mW/m2/nm Flux10 Flux for i=10 degrees (in erg/s/cm2/Å)
48- 59 E12.6 10mW/m2/nm Flux15 Flux for i=15 degrees (in erg/s/cm2/Å)
61- 72 E12.6 10mW/m2/nm Flux20 Flux for i=20 degrees (in erg/s/cm2/Å)
74- 85 E12.6 10mW/m2/nm Flux25 Flux for i=25 degrees (in erg/s/cm2/Å)
87- 98 E12.6 10mW/m2/nm Flux30 Flux for i=30 degrees (in erg/s/cm2/Å)
100-111 E12.6 10mW/m2/nm Flux35 Flux for i=35 degrees (in erg/s/cm2/Å)
113-124 E12.6 10mW/m2/nm Flux40 Flux for i=40 degrees (in erg/s/cm2/Å)
126-137 E12.6 10mW/m2/nm Flux45 Flux for i=45 degrees (in erg/s/cm2/Å)
139-150 E12.6 10mW/m2/nm Flux50 Flux for i=50 degrees (in erg/s/cm2/Å)
152-163 E12.6 10mW/m2/nm Flux55 Flux for i=55 degrees (in erg/s/cm2/Å)
165-176 E12.6 10mW/m2/nm Flux60 Flux for i=60 degrees (in erg/s/cm2/Å)
178-189 E12.6 10mW/m2/nm Flux65 Flux for i=65 degrees (in erg/s/cm2/Å)
191-202 E12.6 10mW/m2/nm Flux70 Flux for i=70 degrees (in erg/s/cm2/Å)
204-215 E12.6 10mW/m2/nm Flux75 Flux for i=75 degrees (in erg/s/cm2/Å)
217-228 E12.6 10mW/m2/nm Flux80 Flux for i=80 degrees (in erg/s/cm2/Å)
230-241 E12.6 10mW/m2/nm Flux85 Flux for i=85 degrees (in erg/s/cm2/Å)
243-254 E12.6 10mW/m2/nm Flux90 Flux for i=90 degrees (in erg/s/cm2/Å)
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Acknowledgements:
Axel Lazzarotto, axel.lazzarotto(at)irap.omp.eu
References:
Royer et al. 2014A&A...562A..84R 2014A&A...562A..84R, Vega abundancies
Blackwell et Shallis 1977MNRAS.180..177B 1977MNRAS.180..177B, IRFM
(End) Patricia Vannier [CDS] 14-Jun-2023