stellaR: A Package to Manage Stellar Evolution Tracks and Isochrones

We present the R package stellaR, which is designed to access and manipulate publicly available stellar evolutionary tracks and isochrones from the Pisa low-mass database. The procedures for extracting important stages in the evolution of a star from the database, for constructing isochrones from stellar tracks and for interpolating among tracks are discussed and demonstrated. Due to the advance in the instrumentation, nowadays astronomers can deal with a huge amount of high-quality observational data. In the last decade impressive improvements of spectroscopic and photometric observational capabilities made available data which stimulated the research in the globular clusters field. The theoretical effort of recovering the evolutionary history of the clusters benefits from the computation of extensive databases of stellar tracks and isochrones, such as Pietrinferni et al. (2006); Dotter et al. (2008); Bertelli et al. (2008). We recently computed a large data set of stellar tracks and isochrones, “The Pisa low-mass database” (Dell’Omodarme et al., 2012), with up to date physical and chemical inputs, and made available all the calculations to the astrophysical community at the Centre de Données astronomiques de Strasbourg (CDS)1, a data center dedicated to the collection and worldwide distribution of astronomical data. In most databases, the management of the information and the extraction of the relevant evolutionary properties from libraries of tracks and/or isochrones is the responsibility of the end users. Due to its extensive capabilities of data manipulation and analysis, however, R is an ideal choice for these tasks. Nevertheless R is not yet well known in astrophysics; up to December 2012 only seven astronomical or astrophysical-oriented packages have been published on CRAN (see the CRAN Task View Chemometrics and Computational Physics). The package stellaR (Dell’Omodarme and Valle, 2012) is an effort to make available to the astrophysical community a basic tool set with the following capabilities: retrieve the required calculations from CDS; plot the information in a suitable form; construct by interpolation tracks or isochrones of compositions different to the ones available in the database; construct isochrones for age not included in the database; extract relevant evolutionary points from tracks or isochrones. Get stellar evolutionary data The Pisa low-mass database contains computations classified according to four parameters: the metallicity z of the star, its initial helium value y, the value of α-enhancement of the heavy elements mixture with respect to the reference mixture and the mixing-length parameter αml used to model external convection efficiency. The values of the parameters available in the database can be displayed using the function showComposition(): > showComposition() Mixing-length values: 1.7, 1.8, 1.9 alpha-enhancement values: 0, 1 (i.e. [alpha/Fe] = 0.0 [alpha/Fe] = 0.3) Chemical compositions: z y.1 y.2 y.3 y.4 y.5 y.6 1e-04 0.249 0.25 0.27 0.33 0.38 0.42 2e-04 0.249 0.25 0.27 0.33 0.38 0.42 3e-04 0.249 0.25 0.27 0.33 0.38 0.42 4e-04 0.249 0.25 0.27 0.33 0.38 0.42 5e-04 0.250 0.25 0.27 0.33 0.38 0.42 6e-04 0.250 0.25 0.27 0.33 0.38 0.42 7e-04 0.250 0.25 0.27 0.33 0.38 0.42 8e-04 0.250 0.25 0.27 0.33 0.38 0.42 9e-04 0.250 0.25 0.27 0.33 0.38 0.42 1e-03 0.250 0.25 0.27 0.33 0.38 0.42 1via anonymous ftp from ftp://cdsarc.u-strasbg.fr or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/ A+A/540/A26 The R Journal Vol. 5/1, June ISSN 2073-4859 CONTRIBUTED RESEARCH ARTICLES 109 2e-03 0.252 0.25 0.27 0.33 0.38 0.42 3e-03 0.254 0.25 0.27 0.33 0.38 0.42 4e-03 0.256 0.25 0.27 0.33 0.38 0.42 5e-03 0.258 0.25 0.27 0.33 0.38 0.42 6e-03 0.260 0.25 0.27 0.33 0.38 0.42 7e-03 0.262 0.25 0.27 0.33 0.38 0.42 8e-03 0.264 0.25 0.27 0.33 0.38 0.42 9e-03 0.266 0.25 0.27 0.33 0.38 0.42 1e-02 0.268 0.25 0.27 0.33 0.38 0.42 The table of chemical compositions presents all the y values available for a given z. For a set of parameters, the track files are identified specifying the mass of the desired model (in the range [0.30 1.10] M (M = 1.99 · 1033 g is the mass of the Sun), in steps of 0.05 M ), while the age (in the range [8.0 15.0] Gyr, in steps of 0.5 Gyr) is required for the isochrones. Upon specification of the aforementioned parameters, the stellaR package can import data from CDS (via anonymous ftp) over an active Internet connection. The CDS data are stored in ASCII format and include a header with calculation metadata, such as the metallicity, the initial helium abundance, and the mixing-length. The import is done via a read.table() call, skipping the header of the files. The following data objects can be downloaded from the database site: • Stellar track: a stellar evolutionary track computed starting from Pre-Main Sequence (PMS) and ending at the onset of helium flash (for masses M ≥ 0.55 M ) or at the exhaustion of central hydrogen (for 0.30 M ≤ M ≤ 0.50 M ). The functions getTrk() and getTrkSet() can be used to access such data; they respectively return objects of classes "trk" and "trkset". • Stellar ZAHB: Zero-Age Horizontal-Branch models. The function getZahb() can be used to access such data; it returns an object of class "zahb". • HB models: computed from ZAHB to the onset of thermal pulses. The functions getHb() and getHbgrid() can be used to access such data; they respectively return objects of classes "hb" and "hbgrid". • Stellar isochrones: computed in the age range [8.0 15.0] Gyr. The functions getIso() and getIsoSet() can be used to access such data; they respectively return objects of classes "iso" and "isoset". Readers interested in details about the computation procedure are referred to Dell’Omodarme et al. (2012). The data gathered from CDS are organized into objects of appropriate classes. The package includes print and plot S3 methods for the classes "trk", "trkset", "zahb", "hb", "hbgrid", "iso", and "isoset". As an example, we illustrate the recovering of the stellar track for a model of mass M = 0.80 M , metallicity z = 0.001, initial helium abundance y = 0.25, mixing-length αml = 1.90, α-enhancement [α/Fe] = 0.0. > track track Stellar track Mass = 0.8 Msun Z = 0.001 , Y = 0.25 Mixing length = 1.9 [alpha/Fe] = 0 > names(track) [1] "mass" "z" "y" "ml" "alpha.enh" "data" > class(track) [1] "trk" "stellar" The function getTrk() returns an object of class "trk", which is a list containing the track metadata, i.e. the star mass, the metallicity, the initial helium abundance, the mixing-length and the α-enhancement, and the computed data in the data frame data. Track data contains the values of 15 variables: > names(track$data) [1] "mod" "time" "logL" "logTe" "mass" "Hc" "logTc" "logRHOc" [9] "MHEc" "Lpp" "LCNO" "L3a" "Lg" "radius" "logg" The included variables are: mod the progressive model number; time the logarithm of the stellar age (in yr); logL the logarithm of the surface luminosity (in units of solar luminosity); logTe the logarithm of The R Journal Vol. 5/1, June ISSN 2073-4859 CONTRIBUTED RESEARCH ARTICLES 110 the effective temperature (in K); mass the stellar mass (in units of solar mass); Hc the central hydrogen abundance (after hydrogen exhaustion: central helium abundance); logTc the logarithm of the central temperature (in K); logRHOc the logarithm of the central density (in g/cm3); MHEc the mass of the helium core (in units of solar mass); Lpp the luminosity of pp chain (in units of surface luminosity); LCNO the luminosity of CNO chain (in units of surface luminosity); L3a the luminosity of triple-α burning (in units of surface luminosity); Lg luminosity of the gravitational energy (in units of surface luminosity); radius the stellar radius (in units of solar radius); logg the logarithm of surface gravity (in cm/s2). Similarly the part of the track starting from ZAHB and ending at the onset of thermal pulses can be downloaded with the call: > hbtk hbtk Stellar track from ZAHB Mass = 0.8 Msun Mass RGB = 0.8 Msun Z = 0.001 , Y = 0.25 Mixing length = 1.9 [alpha/Fe] = 0 > names(hbtk) [1] "mass" "massRGB" "z" "y" "ml" "alpha.enh" [7] "data" > class(hbtk) [1] "hb" "stellar" Function getHb() returns an object of class "hb", which differs from an object of class "trk" only for the presence of the variable massRGB, i.e. the Red-Giant Branch (RGB) progenitor mass. Usually a set of tracks with different mass and/or metallicity values are needed for computations. The package stellaR provides the function getTrkSet(), which can download a set of tracks with different values for mass, metallicity, initial helium abundance, mixing-length and α-enhancement. As an example the whole set of masses (from 0.30 to 1.10 M , in steps of 0.05 M ), for metallicity z = 0.001, initial helium abundance y = 0.25, mixing-length αml = 1.90, and α-enhancement [α/Fe] = 0.0 can be downloaded as follows: > mass trks trks [[1]] Stellar track Mass = 0.3 Msun Z = 0.001 , Y = 0.25 Mixing length = 1.9 [alpha/Fe] = 0