Issue 
A&A
Volume 568, August 2014



Article Number  A119  
Number of page(s)  13  
Section  Stellar atmospheres  
DOI  https://doi.org/10.1051/00046361/201423703  
Published online  03 September 2014 
Online material
Appendix A: 3D fitting algorithm
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 [m_{1}] − [c_{1}] − Hβ space. We took into account the photometric errors in the three indexes that form the socalled ellipsoid of errors, as well as the distance between the star (s) and the point of the grid (g): (A.1)with D_{sg,x} = [c_{1}] _{s} − [c_{1}] _{g}, D_{sg,y} = [m_{1}] _{s} − [m_{1}] _{g}, and D_{sg,z} = [Hβ] _{s} − [Hβ] _{g} being the distances in each of the axes, and ξ − ξ_{g} 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 (D_{se}) 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)
Fig. A.1
Schema of the ellipsoid of errors that shows how to compute the σ_{sg} between the star and any point of the grid from the individual errors of the three photometric indexes. 

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with a = 5σ_{[c1]}, b = 5σ_{[m1]}, and c = 5σ_{Hβ}. 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 D_{se}: (A.3)For each star, we computed the probability P for all the points of the grid to find the point with higher probability P_{max}. In Fig. A.2 we show, for a single star, the probability for all the points of the grid in a [c_{1}]–[m_{1}] and a [c_{1}]–Hβ diagrams.
Fig. A.2
[c_{1}]–[m_{1}] and a [c_{1}]–Hβ diagram. The color shows the corresponding probability P for a star with ([c_{1}], [m_{1}], Hβ) = (0.96, 0.15, 2.96). 

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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 T_{eff}. To develop our 3D fit the grids were interpolated in steps of 10 K in T_{eff} and 0.01 in log g.
Appendix B: Binarity effect
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 M_{2}/M_{1} = 0.6, with about 10% of cases with a mass ratio higher than M_{2}/M_{1} = 0.8.
Fig. B.1
Differences in [c_{1}] (top) and Hβ (bottom) between the primary and the binary system. Left: the color shows the T_{eff} of the primary. Right: the color shows the mass ratio between the primary and the secondary. 

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Simulations were made to estimate the change on the photometric indexes for different mass ratios. Different mainsequencetype 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), m_{1}, c_{1}, Hβ) according to the Castelli & Kurucz (2004) grids, and the assumed T_{eff} 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 T_{eff} of the primary and different mass ratios. For primary stars with T_{eff}> 7000 K, the bias reaches values up to 008 in [c_{1}], up to 002 in [m_{1}], and up to 004 in Hβ, which also leads to possible misclassifications. As is known, the effect on absolute magnitude M_{V} is highest when the two stars have equal luminosities, yielding an error of 075 (i.e., 30% error in distance for this extreme case).
Appendix C: New transformation coefficients
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.
continued.
Appendix D: Catalog of young stars
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 RADec 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 latetype regions are also provided. Only the 13687 stars with either T_{eff}> 7000 K from MB or classified as OA9 by EC methods are included in the catalog. The physical parameters for stars with T_{eff}< 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
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