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A Code to Measure Stellar Atmospheric Parameters and Their Covariance from Spectra

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A Code to Measure Stellar Atmospheric Parameters and Their Covariance from Spectra MNRAS 467, 971–984 (2017) doi:10.1093/mnras/stx144 Advance Access publication 2017 January 19 ZASPE: a code to measure stellar atmospheric parameters and their covariance from spectra Rafael Brahm,1,2‹ Andres´ Jordan,´ 1,2 Joel Hartman3 and Gasp´ ar´ Bakos3†‡ 1 Instituto de Astrof´ısica, Facultad de F´ısica, Pontificia Universidad Catolica´ de Chile, Av. Vicuna˜ Mackenna 4860, 7820436 Macul, Santiago, Chile Downloaded from https://academic.oup.com/mnras/article-abstract/467/1/971/2929275 by Princeton University user on 28 November 2018 2Millennium Institute of Astrophysics, Santiago, Chile 3Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA Accepted 2017 January 17. Received 2017 January 13; in original form 2015 December 7 ABSTRACT We describe the Zonal Atmospheric Stellar Parameters Estimator (ZASPE), a new algorithm, and its associated code, for determining precise stellar atmospheric parameters and their uncertainties from high-resolution echelle spectra of FGK-type stars. ZASPE estimates stellar atmospheric parameters by comparing the observed spectrum against a grid of synthetic spectra only in the most sensitive spectral zones to changes in the atmospheric parameters. Realistic uncertainties in the parameters are computed from the data itself, by taking into account the systematic mismatches between the observed spectrum and the best-fitting synthetic one. The covariances between the parameters are also estimated in the process. ZASPE can in principle use any pre-calculated grid of synthetic spectra, but unbiased grids are required to obtain accurate parameters. We tested the performance of two existing libraries, and we concluded that neither is suitable for computing precise atmospheric parameters. We describe a process to synthesize a new library of synthetic spectra that was found to generate consistent results when compared with parameters obtained with different methods (interferometry, asteroseismology, equivalent widths). Key words: methods: data analysis – techniques: spectroscopic – stars: fundamental parame- ters – planetary systems. tems. Long baseline optical interferometry has been used on bright 1 INTRODUCTION sources with known distances to measure their physical radii The determination of the physical parameters of stars is a fundamen- (Boyajian et al. 2012, 2013) and precise stellar densities have been tal requirement for studying their formation, structure and evolution. obtained using asteroseismology on stars observed by Kepler and Additionally, the physical properties of extrasolar planets depend CoRoT (e.g. Silva Aguirre et al. 2015). Unfortunately, for the rest strongly on how well we have characterized their host stars. In the of the stars, including the vast majority of planetary hosts, physical case of transiting planets, the measured transit depth is related to parameters cannot be measured and indirect procedures have to be the ratio of the planet to stellar radii. Similarly, for radial velocity adopted in which the atmospheric parameters, such as the effective planets, the semi-amplitude of the orbit is a function of both the temperature (Teff), surface gravity (log g) and metallicity ([Fe/H]), mass of the star and the mass of the planet. In the case of directly are derived from stellar spectra by using theoretical model atmo- imaged exoplanets, their estimated masses depend on the age of spheres. Stellar evolutionary models are then compared with the the systems. With more than 3000 planets and planetary candidates estimated atmospheric parameters in order to determine the physi- discovered, mostly by the Kepler mission (e.g. Howard et al. 2012; cal parameters of the star. Burke et al. 2014), homogeneous and accurate determination of the The amount of information about the properties of the stellar physical parameters of the host stars are required for linking their atmosphere contained in its spectrum is enormous. Current state- occurrence rates and properties with different theoretical predictions of-the-art high-resolution echelle spectrographs are capable of de- (e.g. Howard et al. 2010; Buchhave et al. 2014). tecting subtle variations of spectral lines that, in principle, can be Direct determinations of the physical properties of single stars translated into the determination of the physical atmospheric con- (mass, radius and age) are limited to a couple dozens of sys- ditions of a star with exquisite precision. However, there are several factors that reduce the precision that can be achieved. On one side, there are many other properties of a star that can produce changes E-mail: [email protected] on the absorption lines. For example, velocity fields on the surface † Alfred P. Sloan Research Fellow. of the star, which include the stellar rotation (which may be dif- ‡ Packard Fellow. ferential) and the micro- and macroturbulence, modify the shape C 2017 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society 972 R. Brahm et al. of the absorption lines. Non-solar abundances change the partic- uncertainties and correlations in the parameters are computed from ular strength of the lines of each element. Therefore, in order to the data itself and include the systematic mismatches due to the obtain precise atmospheric parameters, all of these variables have imperfect nature of the theoretical spectra. The structure of the pa- to be considered. However, even when all the significant variables per is as follows. In Section 2, we describe the method that ZASPE of the problem are taken into account, the precision in the param- uses for determining the stellar parameters and their covariance ma- eters becomes limited by modelling uncertainties, e.g. imperfect trix, including details on the synthesis of a new synthetic library to modelling of the stellar atmospheres and spectral features due to overcome limitations of the existing libraries for stellar parameter unknown opacity distribution functions, uncertainties in the prop- estimation. In Section 3, we summarize the performance of ZASPE erties of particular atomic and molecular transitions, effects arising on a sample of stars with measured stellar parameters, and we com- Downloaded from https://academic.oup.com/mnras/article-abstract/467/1/971/2929275 by Princeton University user on 28 November 2018 from the assumed geometry of the modelled atmosphere and non- pare our uncertainties with those produced by STARFISH. Finally, in local thermodynamic equilibrium (LTE) effects. These sources of Section 4, we summarize and conclude. error are unavoidable and are currently the main problem for obtain- ing reliable uncertainties in the estimated stellar parameters. Most 2 THE METHOD of the actual algorithms that compute atmospheric parameters from high-resolution stellar spectra do not consider in detail this factor In order to determine the atmospheric stellar parameters of a star, for obtaining the uncertainties. The problem is that if the reported ZASPE compares an observed continuum normalized spectrum uncertainties are unreliable, then they propagate to the planetary against synthetic spectra using least-squares minimization by per- parameters and can bias the results or hide potential trends in the forming an iterative algorithm that explores the complete parameter properties of the system under study that, if detectable, could lead space of FGK-type stars. For simplicity, we assume first that we are to deeper insights into their formation and evolution. able to generate an unbiased synthetic spectrum with any set of stel- A widely used procedure for obtaining the atmospheric param- lar atmospheric parameters (Teff,logg and [Fe/H]). By unbiased, eters of a star consists in comparing the observed spectra against we mean that there are no systematic trends in the level of mismatch synthetic models and adopts the parameters of the model that pro- of the synthesized and real spectra as a function of the stellar param- duces the best match as the estimated atmospheric parameters of the eters, but there can be systematic mismatches that are not a function observed star. This technique has been implemented in algorithms of stellar parameters. If Fλ is the observed spectrum and Sλ(θ)is such as SME (Valenti & Piskunov 1996), SPC (Buchhave et al. 2012) the synthesized spectrum with parameters θ ={Teff , log g,[Fe/H]}, and ISPEC (Blanco-Cuaresma et al. 2014) to derive parameters of the quantity that we minimize is planetary host stars. Thanks to the large number of spectral features X2(θ) = (F − S (θ))2. (1) used, this method has been shown to be capable of dealing with λ λ λ spectra having low signal-to-noise ratio (SNR), moderate resolu- tion and a wide range of stellar atmospheric properties. However, In equation (1), we have not included the weights coming from one of the major drawbacks of spectral synthesis methods for the the uncertainties in the observed flux because we are assuming that estimation of the atmospheric parameters is the determination of the SNR of the data is high enough for the uncertainties in the their uncertainties. This problem arises because the source of error parameters to be governed by the systematic mismatches between is not the Poisson noise of the observed spectrum, but instead is usu- the data and the models. ally dominated by imperfections in the synthesized model spectra, The synthesized spectrum needs to have some processing done which produce highly correlated residuals. In such cases, standard in order to compare it against the observed one.
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