Astronomy & Astrophysics manuscript no. bc c ESO 2019 October 22, 2019 YBC, a stellar bolometric corrections database with variable extinction coefficients: an application to PARSEC isochrones Yang Chen1,?, Léo Girardi2, Xiaoting Fu3, Alessandro Bressan4, Bernhard Aringer1, Piero Dal Tio1; 2, Giada Pastorelli1, Paola Marigo1, Guglielmo Costa4, and Xing Zhang5 1 Dipartimento di Fisica e Astronomia Galileo Galilei, Università di Padova, Vicolo dell’Osservatorio 3, I-35122 Padova, Italy 2 Osservatorio Astronomico di Padova – INAF, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy 3 The Kavli Institute for Astronomy and Astrophysics at Peking University, Beijing, China 4 SISSA, via Bonomea 365, I-34136 Trieste, Italy 5 Department of Astronomy, University of Science and Technology of China, Chinese Academy of Sciences, Hefei, Anhui 230026, China Received .... / Accepted ..... ABSTRACT We present the YBC database of stellar bolometric corrections (BCs), available at http://stev.oapd.inaf.it/YBC. We ho- mogenise widely-used theoretical stellar spectral libraries and provide BCs for many popular photometric systems, including the Gaia filters. The database can be easily extended to additional photometric systems and stellar spectral libraries. The web interface allows users to transform their catalogue of theoretical stellar parameters into magnitudes and colours of selected filter sets. The BC tables can be downloaded or also be implemented into large simulation projects using the interpolation code provided with the database. We compute extinction coefficients on a star-by-star basis, hence taking into account the effects of spectral type and non- linearity dependency on the total extinction. We illustrate the use of these BCs in PARSEC isochrones. We show that using spectral-type dependent extinction coefficients is quite necessary for Gaia filters whenever AV & 0:5 mag. BC tables for rotating stars and tables of limb-darkening coefficients are also provided. Key words. Hertzsprung-Russell and C-M diagrams – dust, extinction – open clusters: individual: NGC 2425 – open clusters: individual: Melotte 22 1. Introduction One of the obvious advantages of having a homogeneous database for BCs would be to facilitate the comparison between Bolometric corrections (BCs) are usually applied to the abso- stellar models and the observations. Indeed, besides the differ- lute magnitude of a star to obtain its bolometric absolute magni- ences in the theoretical quantities such as log L=L and Teff of tude or luminosity, or conversely, to predict the magnitudes of a various stellar models, additional deviations are often introduced model star in a given set of filters. Most modern versions of BCs from different authors using different BC tables. The possibil- are usually based on theoretical stellar spectral libraries, e.g. Gi- ity of testing the difference from those originally applied will rardi et al. (2002); Casagrande & VandenBerg (2014, 2018a). In become more critical with forthcoming facilities providing pho- some cases empirical stellar spectral libraries are also used for tometry of much higher precision: considering, for instance, the this purpose, however, they require additional calibration from ∼ 10−4 mag errors expected for Gaia sources with G < 12 mag the theoretical atmosphere models and are always limited by the and > 100 CCD transits, for a nominal mission with perfect cal- coverage of stellar spectral type and wavelength range (Sánchez- ibrations (see figure 9 in Evans et al. 2018), and the systematic Blázquez et al. 2006; Rayner et al. 2009; Chen et al. 2014b). errors smaller than 0.005 mag planned for LSST single visits In practice, BCs are often provided along with, or can be eas- (Ivezic´ et al. 2019). Another aspect to consider is the differ- ily computed from the spectral libraries obtained from the mod- ent ways of handling the interstellar extinction in the models, elling of stellar atmospheres. In the present day, the widely used which is especially crucial when using either UV filters (as in theoretical stellar spectral libraries include ATLAS9 (Castelli & GALEX) or very broad passbands (such as the Gaia, TESS, and arXiv:1910.09037v1 [astro-ph.SR] 20 Oct 2019 Kurucz 2003) and PHOENIX (Allard et al. 2012) for generic HST/WFC3/UVIS extremely wide filters). In these cases, fixed types of stars, MARCS (Gustafsson et al. 2008) for cool or inter- extinction coefficients are no longer valid and the effect of stellar mediate temperature stars, COMARCS for K/M/S/C stars (Aringer spectral types becomes critical (Girardi et al. 2008). et al. 2009, 2016, 2019), and PoWR for Wolf-Rayet (WR) stars (Gräfener et al. 2002, and refs. therein). These libraries, with In this work, we build a database where we assemble existing different solar abundance, offer large grids of models covering popular stellar spectral libraries to compute BC tables homoge- neously for a wide variety of photometric systems. The web in- different stellar parameters (metallicity, Teff and log g). How- ever, currently there is a lack of a single, homogeneous, public terface of this database provides a convenient way for the users database to synthesise these libraries and provide BC tables for to transform their theoretical stellar catalogues into magnitudes a large set of photometric systems. and colours, and hence to compare them with observations. It has the flexibility to choose different stellar spectral libraries, ? e-mail: [email protected] thus allowing their differences to be easily investigated. The ex- Article number, page 1 of 14 A&A proofs: manuscript no. bc tinction coefficients have been computed on a star-by-star basis, Usually, synthetic spectral libraries provide the stellar flux therefore the variation with spectral type has been taken into ac- at the stellar radius R. This flux Fλ is related to the effective count. The non-linearity as a function of AV has been included, temperature Teff of the star by which is important for highly attenuated targets. Z 1 In this paper, we introduce the definitions of the BCs in sec- 4 Fbol ≡ Fλdλ = σTeff; (3) tion 2, the available stellar spectral libraries in section 3 and our 0 C/Python code package in section 4. We compare some of our re- sults with the literature in section 5. In section 6, we discuss the where σ is the Stefan-Boltzmann constant. By placing the star at spectral type dependent extinction coefficients. Section 7 sum- 10 pc from the earth, the flux we receive is marises the main results. !2 R −0:4Aλ fλ,10pc = Fλ10 ; 2. Bolometric corrections 10pc In this section, we recall some basic relations concerning the where Aλ is the assumed extinction between the star and the bolometric correction which are necessary for the discussion. We observer. Therefore, the absolute magnitude Mi for a photon- refer the readers to Kurucz (1979), Bessell et al. (1998), and Gi- counting photometric system is rardi et al. (2002) for a more exhaustive discussion. 2R λ2 3 First, we recall the definition of magnitude. Assuming we 6 λ fλ,10pcS λ,idλ7 6 λ1 7 (at earth) receive a radiation flux fλ (or fν) from a source, the Mi = −2:5log 6 7 + mi;0 46 R λ2 0 57 λ f S λ,idλ magnitude in a certain filter band i with transmission curve S λ,i λ1 λ is 2 R λ 3 2 2 −0:4Aλ 6 ! λFλ10 S λ,idλ7 6 R λ1 7 2 R λ2 3 − 6 7 λ f S dλ = 2:5log 6 R λ 7 + mi;0: (4) 6 λ λ λ,i 7 46 10pc 2 0 57 6 1 7 λ f S λ,idλ mi = −2:5log 6 7 + mi;0: (1) λ1 λ 46R λ2 0 57 λ f S λ,idλ λ1 λ The definition of bolometric magnitude Mbol is 0 In this equation, fλ is the flux of the reference spectrum and mi;0 is the corresponding reference magnitude. These two quantities Mbol = Mbol; − 2:5log(L=L ) 2 depend on the photometric system and will be discussed later. λ1 = Mbol; − 2:5log(4πR Fbol=L ): (5) and λ2 denote the lower and upper wavelength limits of the filter transmission curve, respectively. The above equation is valid for According to the IAU 2015 resolution (Mamajek et al. 2015), the present-day photon-counting devices (CCDs or IR arrays). For absolute bolometric magnitude for the nominal solar luminosity 26 more traditional energy-integrating systems the above equation (3:828 × 10 W) is Mbol; = 4:74 mag. should be changed to Given an absolute magnitude Mi in a given filter band i for a star of absolute bolometric magnitude M , the bolometric cor- 2 R λ2 3 bol 6 fλS λ,idλ 7 rection BCi is: 6 λ1 7 mi = −2:5log 6 7 + mi;0: (2) 46R λ2 0 57 f S λ,idλ λ1 λ BCi = Mbol − Mi: (6) 0 0 Depending on the reference spectra fλ (or fν ), commonly By combing equations (4), (5) and (6), we have used magnitude systems are: 2 ! 4πσ(10pc) 4 – Vega magnitude systems. The spectrum of Vega (α Lyr) is BCi =Mbol; − 2:5log − 2:5log(Teff) used as the reference spectrum. The reference magnitudes L 2R λ 3 are set so that Vega has a magnitude equal to, or slightly 2 −0:4Aλ 6 λFλ10 S λ,idλ7 different from zero. By default, we use the latest Vega spec- 6 λ1 7 − + 2:5log 6 R λ 7 mi;0: (7) trum1 from the CALSPEC database (Bohlin et al. 2014). 46 2 0 57 λ λ fλ S λ,idλ – AB magnitude systems (Oke 1974). The reference spectrum 1 0 48:60 −1 −2 −1 has a constant value of fν = 10 −2:5 erg s cm Hz . The The advantage of using the above equation to compute BCs is reference magnitudes thus are set to −48.60 mag.