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Doppler beaming factors for white dwarfs, main sequence stars, and giant stars. Limb-darkening coefficients for 3D (DA and DB) white dwarf models

Claret, A. and Cukanovaite, E. and Burdge, K. and Tremblay, P.-E. and Parsons, S. and Marsh, T. R. (2020) Doppler beaming factors for white dwarfs, main sequence stars, and giant stars. Limb-darkening coefficients for 3D (DA and DB) white dwarf models. Astronomy and Astrophysics, 641 . Art. No. A157. ISSN 0004-6361. doi:10.1051/0004-6361/202038436.

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Context. Systematic theoretical calculations of Doppler beaming factors are scarce in the literature, particularly in the case of white dwarfs. Additionally, there are no specific calculations for the limb-darkening coefficients of 3D white dwarf models. Aims. The objective of this research is to provide the astronomical community with Doppler beaming calculations for a wide range of effective temperatures, local gravities, and hydrogen/metal content for white dwarfs as well as stars on both the main sequence and the giant branch. In addition, we present the theoretical calculations of the limb-darkening coefficients for 3D white dwarf models for the first time. Methods. We computed Doppler beaming factors for DA, DB, and DBA white dwarf models, as well as for main sequence and giant stars covering the transmission curves of the Sloan, UBVRI, HiPERCAM, Kepler, TESS, and Gaia photometric systems. The calculations of the limb-darkening coefficients for 3D models were carried out using the least-squares method for these photometric systems. Results. The input physics of the white dwarf models for which we have computed the Doppler beaming factors are: chemical compositions log [H/He] = −10.0 (DB), −2.0 (DBA), and He/H = 0 (DA), with log g varying between 5.0 and 9.5 and effective temperatures in the range 3750–100 000 K. The beaming factors were also calculated assuming non-local thermodynamic equilibrium for the case of DA white dwarfs with T_(eff) >  40 000 K. For the mixing-length parameters, we adopted ML2/α = 0.8 (DA case) and 1.25 (DB and DBA). The Doppler beaming factors for main sequence and giant stars were computed using the ATLAS9 version, characterized by metallicities ranging from [−2.5, 0.2] solar abundances, with log g varying between 0 and 5.0 and effective temperatures between 3500 and 50 000 K. The adopted microturbulent velocity for these models was 2.0 km s⁻¹. The limb-darkening coefficients were computed for three-dimensional DA and DB white dwarf models calculated with the CO5BOLD radiation-hydrodynamics code. The parameter range covered by the three-dimensional DA models spans log g values between 7.0 and 9.0 and T_(eff) between 6000 and 15 000 K, while He/H = 0. The three-dimensional DB models cover a similar parameter range of log g between 7.5 and 9.0 and T_(eff) between 12 000 and 34 000 K, while log H/He = −10.0. We adopted six laws for the computation of the limb-darkening coefficients: linear, quadratic, square root, logarithmic, power-2, and a general one with four coefficients. Conclusions. The beaming factor calculations, which use realistic models of stellar atmospheres, show that the black body approximation is not accurate, particularly for the filters u, u′, U, g, g′, and B. The black body approach is only valid for high effective temperatures and/or long effective wavelengths. Therefore, for more accurate analyses of light curves, we recommend the use of the beaming factors presented in this paper. Concerning limb-darkening, the distribution of specific intensities for 3D models indicates that, in general, these models are less bright toward the limb than their 1D counterparts, which implies steeper profiles. To describe these intensities better, we recommend the use of the four-term law (also for 1D models) given the level of precision that is being achieved with Earth-based instruments and space missions such as Kepler and TESS (and PLATO in the future).

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Claret, A.0000-0002-4045-8134
Cukanovaite, E.0000-0002-3184-3428
Burdge, K.0000-0002-7226-836X
Tremblay, P.-E.0000-0001-9873-0121
Marsh, T. R.0000-0002-2498-7589
Additional Information:© ESO 2020. Received: 18 May 2020 Accepted: 27 July 2020. We thank the referee S. Bloemen for his helpful suggestions and comments. The Spanish MEC (ESP2017-87676-C5-2-R, PID2019-107061GB-C64, and PID2019-109522GB-C52) is gratefully acknowledged for its support during the development of this work. A. C. also acknowledges financial support from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award for the Instituto de Astrofísica de Andalucía (SEV-2017-0709). The research leading to these results has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme n. 677706 (WD3D). SGP acknowledges the support of a Science and Technology Facilities Council (STFC) Ernest Rutherford Fellowship. This research has made use of the SIMBAD database, operated at the CDS, Strasbourg, France, and of NASA’s Astrophysics Data System Abstract Service.
Funding AgencyGrant Number
Ministerio de Educación y Ciencia (MEC) ESP2017-87676-C5-2-R
Ministerio de Educación y Ciencia (MEC) PID2019-107061GB-C64
Ministerio de Educación y Ciencia (MEC) PID2019-109522GB-C52
Severo OchoaSEV-2017-0709
European Research Council (ERC)677706
Science and Technology Facilities Council (STFC)UNSPECIFIED
Subject Keywords:white dwarfs / binaries: eclipsing / stars: atmospheres
Record Number:CaltechAUTHORS:20200925-104734525
Persistent URL:
Official Citation:Doppler beaming factors for white dwarfs, main sequence stars, and giant stars - Limb-darkening coefficients for 3D (DA and DB) white dwarf models A. Claret, E. Cukanovaite, K. Burdge, P.-E. Tremblay, S. Parsons and T. R. Marsh A&A, 641 (2020) A157 DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105552
Deposited By: George Porter
Deposited On:25 Sep 2020 20:00
Last Modified:16 Nov 2021 18:44

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