Volume 568, August 2014
|Number of page(s)||13|
|Published online||03 September 2014|
In this section we describe the 3D fitting algorithm developed to maximize the probability for one star to belong to a point of the theoretical grid in the [m1] − [c1] − Hβ space. We took into account the photometric errors in the three indexes that form the so-called ellipsoid of errors, as well as the distance between the star (s) and the point of the grid (g): (A.1)with Dsg,x = [c1] s − [c1] g, Dsg,y = [m1] s − [m1] g, and Dsg,z = [Hβ] s − [Hβ] g being the distances in each of the axes, and ξ − ξg being the distance along the axis between the star and the point of the grid.
The propagated photometric error in the direction between the star and the point of the grid (Dse) is computed as the distance between the location of the star and the surface of the ellipsoid of errors in the ξ direction (see Fig. A.1)
Schema of the ellipsoid of errors that shows how to compute the σsg between the star and any point of the grid from the individual errors of the three photometric indexes.
|Open with DEXTER|
with a = 5σ[c1], b = 5σ[m1], and c = 5σHβ. It is computed from the equation of the ellipsoid and the equation of a line in the ξ direction, that is, The 5σ photometric error between the star and the ellipsoid in the given direction is (A.2)From this, the probability for one star to belong to a point of the grid is computed centered on the star, with the standard deviation being Dse: (A.3)For each star, we computed the probability P for all the points of the grid to find the point with higher probability Pmax. In Fig. A.2 we show, for a single star, the probability for all the points of the grid in a [c1]–[m1] and a [c1]–Hβ diagrams.
[c1]–[m1] and a [c1]–Hβ diagram. The color shows the corresponding probability P for a star with ([c1], [m1], Hβ) = (0.96, 0.15, 2.96).
|Open with DEXTER|
The original grids are discretized in steps of 0.5 or 0.25 in log g and 250 K, 500 K, or 1000 K in Teff. To develop our 3D fit the grids were interpolated in steps of 10 K in Teff and 0.01 in log g.
A significant fraction of the young stars in our survey can be binaries, either visual or physical. For physical binaries, some tests were developed to estimate the change in their photometric indexes and in turn the error introduced when ignoring binarity. Their binarity ratio is debated, but according to Arenou (2010) 1) it can reach up to 80% for the more massive stars; and 2) the mass ratio between the stars has a probability peak around M2/M1 = 0.6, with about 10% of cases with a mass ratio higher than M2/M1 = 0.8.
Differences in [c1] (top) and Hβ (bottom) between the primary and the binary system. Left: the color shows the Teff of the primary. Right: the color shows the mass ratio between the primary and the secondary.
|Open with DEXTER|
Simulations were made to estimate the change on the photometric indexes for different mass ratios. Different main-sequence-type stars from B0 to F0 were selected as primaries (checking all the cases, without considering the initial mass function). Then, for each primary, different secondaries were assumed, as well as their physical parameters. We assigned to each star the corresponding photometric indexes ((b − y), m1, c1, Hβ) according to the Castelli & Kurucz (2004) grids, and the assumed Teff and log g = 4.2. Then the fluxes for the primary and the secondary stars were combined. Figure B.1 shows the differences in the photometric indexes between the primary and the combined system for different Teff of the primary and different mass ratios. For primary stars with Teff> 7000 K, the bias reaches values up to 008 in [c1], up to 002 in [m1], and up to 004 in Hβ, which also leads to possible misclassifications. As is known, the effect on absolute magnitude MV is highest when the two stars have equal luminosities, yielding an error of 075 (i.e., 30% error in distance for this extreme case).
The transformation coefficients obtained for the new calibration after modifying the primary standard list are provided in Table C.1. These values have to be compared with those from Tables A.3 and A.4 from Paper I. Equation numbers refer to those from Paper I. The new photometric indexes have also been uploaded to the CDS archive.
Standard transformation coefficients for the new calibration.
In Table D.1 we describe the columns available for the SPP catalog of our anticenter survey. The complete catalog can be found at the CDS data archive. First an identifier and RA-Dec coordinates for the star are given, as well as the photometric indexes (with the new value of Hβ) and their errors. Then all the SPP from the MB and EC methods are listed, also with the errors and flags. For the MB, the (B) SPP obtained from the second maxim probability at the other side of the gap between early- and late-type regions are also provided. Only the 13687 stars with either Teff> 7000 K from MB or classified as O-A9 by EC methods are included in the catalog. The physical parameters for stars with Teff< 7000 K (either as a secondary (B) SPP or for stars differently classified by the two methods) are only tentative, and they must be used with caution.
Description of the columns available for the SPP catalog.
© ESO, 2014
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.