Abstract
The mass of a star is the most fundamental parameter for its structure, evolution, and final fate. It is particularly important for any kind of stellar archaeology and characterization of exoplanets. There exist a variety of methods in astronomy to estimate or determine it. In this review we present a significant number of such methods, beginning with the most direct and model-independent approach using detached eclipsing binaries. We then move to more indirect and model-dependent methods, such as the quite commonly used isochrone or stellar track fitting. The arrival of quantitative asteroseismology has opened a completely new approach to determine stellar masses and to complement and improve the accuracy of other methods. We include methods for different evolutionary stages, from the pre-main sequence to evolved (super)giants and final remnants. For all methods uncertainties and restrictions will be discussed. We provide lists of altogether more than 200 benchmark stars with relative mass accuracies between \([0.3,2]\%\) for the covered mass range of \(M\in [0.1,16]\,M_\odot\), \(75\%\) of which are stars burning hydrogen in their core and the other \(25\%\) covering all other evolved stages. We close with a recommendation how to combine various methods to arrive at a “mass-ladder” for stars.
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(Figure credit: Stassun et al. 2018)
(Figure credit: Moya et al. 2018)
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Notes
More than 4360, as of October 9, 2020. Source: exoplanet.eu.
Noticeable exceptions are the most massive globular clusters (\(>10^6\,M_\odot\)), such as \(\omega\) Centauri, which display spreads in age and [Fe/H] (e.g., Villanova et al. 2007).
A regularly updated catalogue of binary CSPNe is maintained by David Jones and can be found at http://www.drdjones.net/bcspn/.
See, however the recent redetermination of masses by Reindl et al. (2020).
In detail, (n, \(\ell\)) determines a multiplet of \(2\ell +1\) modes that are degenerate in frequency for spherical stars. When the symmetry is broken, e.g., by rotation, the different components of the multiplet show up in the oscillation spectrum, with each component identified by the azimuthal number \(m = -\ell , -\ell +1,\ldots ,\ell -1, \ell\).
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Acknowledgements
We thank the Lorentz Center and its staff for making it possible to organize a workshop in November 2018. This review resulted from the intense and pleasant onsite discussions during this meeting and follow-up collaborations. The contribution of the Lorentz Center staff in stimulating suggestions, giving feedback and taking care of all practicalities, helped us to focus on our research and to organize a meeting of high scientific quality. The authors are much indebted to all colleagues participating in the workshop, even though they were not involved in the textual contributions for this review paper. A.S. acknowledges support from Grants ESP2017-82674-R and PID2019-108709GB-I00 (MICINN) and 2017-SGR-1131 (AGAUR). C.A., J.S.G.M., and M.G.P. received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement no. 670519: MAMSIE) and from the KU Leuven Research Council (grant C16/18/005: PARADISE). M.B. is supported through the Lise Meitner grant from the Max Planck Society and acknowledges support by the Collaborative Research centre SFB 881 (projects A5, A10), Heidelberg University, of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). V.S.A. acknowledges support from the Independent Research Fund Denmark (Research grant 7027-00096B) and the Carlsberg foundation (Grant agreement CF19-0649). Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant agreement No. DNRF106). D.B., J.C.M., and I.R. acknowledge support from the Spanish Ministry of Science, Innovation and Universities (MICIU), and the Fondo Europeo de Desarrollo Regional (FEDER) through Grants ESP2016-80435-C2-1-R and PGC2018-098153-B-C33, as well as the support of the Generalitat de Catalunya (CERCA programme). N.B. gratefully acknowledge financial support from the Royal Society (University Research Fellowships) and from the European Research Council (ERC-CoG-646928, Multi-Pop). A.E. acknowledges support from the Research Foundation Flanders (FWO) under contract ZKD1501-00-W01 (Grant no. 792848). D.K.F. acknowledges funds from the Alexander von Humboldt Foundation in the framework of the Sofia Kovalevskaja Award endowed by the Federal Ministry of Education and Research and grant 2016-03412 from the Swedish Research Council. D.G. gratefully acknowledges financial support from the CRT foundation under Grant no. 2018.2323 “Gaseous or rocky? Unveiling the nature of small worlds”. L.G. acknowledges funding from LSST-Italy and from project MITiC 2015. N.L. was financially supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under Grant number AYA2015-69350-C3-2-P. A.M. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 749962 (project THOT). B.N. is supported by Fundação para a Ciência e a Tecnologia (FCT, Portugal) under Grant PD/BD/113744/2015 from PhD::SPACE, an FCT PhD program, and by the Alexander von Humboldt Foundation. Further support from FEDER – Fundo Europeu de Desenvolvimento Regional funds through the COMPETE 2020 – Operacional Programme for Competitiveness and Internationalisation (POCI), and by Portuguese funds through FCT – Fundação para a Ciência e a Tecnologia in the framework of the Project POCI-01-0145-FEDER-030389 is also acknowledged. K.P. acknowledges support from the Croatian Science Foundation (HRZZ research Grant IP-2014-09-8656). P-E.T. has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme n. 677706 (WD3D). The authors thank our colleagues G. Bono, T.L. Campante, M.S. Cunha, P. Das, C. Johnston, F. Kiefer, P. Maxted, M.J.P.F.G. Monteiro, Th. Rodrigues, V. Schaffenroth, M. Vučković for helpful comments and useful discussions. This work presents results from the European Space Agency (ESA) space mission Gaia and from the American National Aeronautics and Space Administration (NASA) space missions Kepler and TESS.
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Serenelli, A., Weiss, A., Aerts, C. et al. Weighing stars from birth to death: mass determination methods across the HRD. Astron Astrophys Rev 29, 4 (2021). https://doi.org/10.1007/s00159-021-00132-9
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DOI: https://doi.org/10.1007/s00159-021-00132-9