estimate {SCEPtER}

Mass, radius, and age estimates for the supplied objects

Description

The function computes the grid-based estimates of the mass, radius, and age for the supplied objects.

Usage

    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.

Value

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

# 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))