# Mass, radius, and age estimates for the supplied objects The function computes the grid-based estimates of the mass, radius, and age for the supplied objects. ```r estimate(data, STAR, sigma, thr, sel, parallel=FALSE) ``` ## Arguments - `data`: the matrix estimation grid. The matrix should be sorted according to the values in the first column (the stellar effective temperature). - `STAR`: a matrix of 7 columns, containing in each row the observational data of the stellar objects. - `sigma`: a vector of 7 elements, containing the error on observational data. The error on seismic parameters are expressed as relative error. - `thr`: the threshold for the selection of cases over which the computation of likelihood is performed. - `sel`: a vector of 7 elements, containing 1 or 0 for inclusion or exclusion of a observational data from the likelihood computation. - `parallel`: logical flag indicating if the estimations should be performed in parallel on a multi-core architecture. ## Returns `STAR` should contains in order: the stellar effective temperature, the logarithm of the surface gravity, the metallicity [Fe/H], the average large frequency separation (in micro Hz), the maximum oscillation power (in micro Hz), the mass (in solar units), the radius (in solar units). `sigma` should contain, in the same order, the uncertainties on the observational quantities. `estimate` returns a data frame obtained with the estimates of stellar parameters for each row of the input matrix `STAR`. In the columns of the data frame there are: the identifier `id` of the row of the input matrix adopted for the estimate; the mass estimate `M` (in solar units); the radius estimate `R` (in solar units); the age estimate `age` (in Gyr). Mass, radius, and age estimates are obtained by a maximum likelihood technique widely adopted in literature. Details on the technique can be found in the references reported below. ## References G. Valle, M. Dell'Omodarme, P.G. Prada Moroni, and S. Degl'Innocenti (2014). **Uncertainties in grid-based estimates of stellar mass and radius. SCEPtER: Stellar CharactEristics Pisa Estimation gRid**. A&A, 561, A125. G. Valle, M. Dell'Omodarme, P.G. Prada Moroni, and S. Degl'Innocenti (2014). **Uncertainties in asteroseismic grid-based estimates of stellar ages. SCEPtER: Stellar CharactEristics Pisa Estimation gRid**. A&A, accepted. S. Basu, G.A. Verner, W.J. Chaplin, and Y. Elsworth (2012). **Effect of Uncertainties in Stellar Model Parameters on Estimated Masses and Radii of Single Stars**. The Astrophysical Journal, 746, 76. N. Gai, S. Basu, W.J. Chaplin, and Y. Elsworth (2011). **An In-depth Study of Grid-based Asteroseismic Analysis**. The Astrophysical Journal, 730, 63. ## Examples ```r # Solar seismic data from Thiery et al. (2000) Dnisun <- 134.8 nimaxsun <- 3034 # Observational data for alpha Cent B from: # Kjeldsen et al. (2005), Porto de Mello et al. (2008) # Observed mass and radius: 0.935 +- 0.006, 0.863 +- 0.005 # from Miglio & Montalban (2005) acenB <- c(5316, 0, 0.25, 161.5/Dnisun, 4100/nimaxsun, 0.935, 0.863) sigmaCen <- c(30, 0, 0.04, 0.01, 0.05, 0.006/0.935, 0.005/0.863) # Load the standard estimation grid data(stdGrid) # order standard grid by effective temperature (required by estimate) ii <- do.call(order, as.data.frame(stdGrid[,1])) oGrid <- stdGrid[ii, ] # For accurate estimates adopt at least NUM=10000 NUM <- 200 # obtain NUM copies of the object and add Gaussian perturbations star <- matrix(acenB, byrow=TRUE, nrow=NUM, ncol=7) starp <- errorObs(sigmaCen, star) # select the observational constraints # using Teff, [Fe/H], Delta nu, nu_max vsel <- c(1,0,1,1,1,0,0) # call the estimation routines res <- estimate(oGrid, starp, sigmaCen, 3, vsel) quantile(res$M, c(0.16, 0.5, 0.84)) quantile(res$R, c(0.16, 0.5, 0.84)) ```

estimate function