estimateBin {SCEPtERbinary}

Age estimates for the supplied binary systems

Description

The function computes the grid-based estimates of the age for the supplied binary systems.

Usage

    estimateBin(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 18 columns, containing in each row the observational data of the stellar objects.

sigma

a vector of 14 elements, containing the error on observational data. The error on mass and radius are expressed as relative error. If the errors on the observables of the two stars are identical, it is possible to provide a vector of length 7.

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 the observables for primary and secondary stars. In order, it should contains 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), the age (if known), and the relative age (if known). Identical quantities for the secondary stars should follows. sigma should contain, in the same order, the uncertainties on the observational quantities.

estimateBin 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 object matrix adopted for the estimate; the independent star estimate of the primary mass M1 (in solar units), radius R1 (in solar units), age age1 (in Gyr); the corresponding independent estimates for the secondary (M2, R2, age2); the joint-likelihood estimates of these quantities obtained explicitly assuming coevality (M1b, R1b, age1b, M2b, R2b, age2b); the relative age r of the primary star (0 = ZAMS; 1 = TAMS); the best estimate of the age of the system ageBin under coevality assumption; the mean of the age of the two independent estimates of the stellar ages.

Age estimates are obtained by a maximum likelihood technique. 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.

G. Valle, M. Dell'Omodarme, P.G. Prada Moroni, and S. Degl'Innocenti (2014). Grid-based estimates of stellar ages in binary systems. SCEPtER: Stellar CharactEristics Pisa Estimation gRid. A&A, submitted.

Examples

require(SCEPtER)
data(stdGrid)
ogrid <- stdGrid[ do.call(order, as.data.frame(stdGrid[,1])), ]

## observational constraint: Teff, [Fe/H], M, R
vsel <- c(1,0,1,0,0,1,1)
sigma <- c(100, 0.25, 0.1, 0.025, 0.05, 0.01, 0.005)

## syntetic sample of 10 bynary systems
bl <- block(stdGrid)
sam <- sampleBinStar(10, stdGrid, bl, restrict=TRUE)

## add Gaussian noise to the observations
starbp <- errorObsBin(sigma, sam)

resB <- estimateBin(ogrid, starbp, sigma, 3, vsel, parallel=FALSE)


## An observed system: PK Peg
## observation from Clausen et al. (2010). A&A, 516, A42.

obs <- c(6265,NA,-0.12,NA,NA,1.414,1.988,NA,NA, 6320,NA,-0.12,NA,NA,1.257,1.474,NA,NA)
sigma <- c(85,0,0.07,0,0,0.007/1.414,0.008/1.988, 90,0,0.07,0,0,0.005/1.257,0.017/1.474)

## for sensible estimate adopt at least nrow=10000
star <- matrix(obs, nrow=100, ncol=18, byrow=TRUE)

## add Gaussian noise
starp <- errorObsBin(sigma, star)

resB <- estimateBin(ogrid, starp, sigma, 3, vsel, parallel=FALSE)

quantile(resB$ageBin, c(0.16, 0.5, 0.84))