Metallicity and absolute magnitude calibrations for UBV photometry

Calibrations are presented here for metallicity ([Fe/H]) in terms of the ultraviolet excess, [ δ( U − B ) at B − V = 0.6 , hereafter δ 0.6 ], and also for the absolute visual magnitude ( M V ) and its difference with respect to the Hyades (Δ M H V ) in terms of δ 0.6 and ( B − V ) , making use of high‐resolution spectroscopic abundances from the literature and Hipparcos parallaxes. The relation [Fe/H]–δ 0.6 has been derived for dwarf plus turn‐off stars, and also for dwarf, turn‐off, plus subgiant stars classified using the M V –( B − V ) 0 plane of Fig. 11, which is calibrated with isochrones from Bergbusch & VandenBerg (and also VandenBerg & Clem). The [Fe/H]–δ 0.6 relations in our equations (5) and (6) agree well with those of Carney, as can be seen from Fig. 5(a). Within the uncertainties, the zero‐points, +0.13(±0.05) of equation (5) and +0.13(±0.04) of equation (6), are in good agreement with the photometric ones of Cameron and of Carney, and close to the spectroscopic ones of Cayrel et al. and of Boesgaard & Friel for the Hyades open cluster. Good quantitative agreement between our estimated [Fe/H] abundances with those from uvby –β photometry and spectroscopic [Fe/H] spec values demonstrates that our equation (6) can be used in deriving quality photometric metal abundances for field stars and clusters using UBV data from various photometric surveys. 11MV− ( B − V ) 0 for the 514 stars in our sample to which the Lutz–Kelker corrections have been applied. Solid lines show the isochrones for the range of −2.31 ≤[Fe/H]≤−0.30 . The 12‐Gyr isochrones of BV& VC with [α/Fe]=+0.30 for [Fe/H]≤−0.60 and with [α/Fe]= 0.00 for [Fe/H] > −0.60 have been used. Stars which fall in between the dashed lines are assumed to be subgiant stars. Stars which lie below and to the left‐hand side of the lower dashed line are classified as turn‐off and dwarf stars for the range of −2.31 ≤[Fe/H]≤−0.30 . Stars between the dashed lines which lie to the left‐hand side of the [Fe/H]=−2.31 isochrone are included in this work as subgiants. Stars to the right‐hand side of the [Fe/H]=−0.30 isochrone and below the lower dashed line are included as turn‐off and dwarf stars. The 42 stars above the upper dashed line are excluded from this work as probable giant stars on the basis of these isochrones.5(a) The relation of [Fe/H] spec −δ 0.6 from the binning of the dependent variable shown in Figs 3(a) and 4(a). Equations (5) and (6) are plotted as filled dots (subgiant, dwarf, plus turn‐off stars) and plus signs (dwarf plus turn‐off stars), respectively. Solid and dashed lines show the relations from Carney (1979) and Cameron (1985), respectively. Open triangles plot the relation of Sandage & Fouts (1987), and the synthetic relation of Buser & Kurucz (1992) is shown with diamond symbols. The relations of equations (5) and (6) are close to that of Carney (1979). Note that the zero‐point, [Fe/H] spec for δ 0.6 = 0.0 , of Sandage & Fouts (1987) is larger than the others. (b) The relation of [Fe/H] spec −δ 0.6 from the binning of the independent variable shown in Figs 6(a) and 7(a). Equations (7) and (8) are plotted as filled dots (subgiant, dwarf plus turn‐off stars) and plus signs (dwarf plus turn‐off stars), respectively. For dwarf and turn‐off stars, a new hybrid M V calibration is presented, based on Hipparcos parallaxes with σ π /π≤ 0.1 and with a dispersion of ±0.24 in M V . This hybrid M V calibration contains δ 0.6 and ( B − V ) terms, plus higher order cross‐terms of these, and is valid for the ranges of +0.37 ≤ ( B − V ) 0 ≤+0.88, − 0.10 ≤δ 0.6 ≤+0.29 and 3.44 ≤ M V ≤ 7.23 . For dwarf and turn‐off stars, the relation for Δ M H V is revised and updated in terms of ( B − V ) and δ 0.6 , for the ranges of −0.10 ≤δ 0.6 ≤+0.29 , and +0.49 ≤ ( B − V ) 0 ≤+0.89 , again making use of Hipparcos parallaxes with σ π /π≤ 0.1 . These parallaxes for metal‐poor dwarf and turn‐off stars in our sample reveal that the difference of Δ M H V ( B − V ) relative to Hyades at ( B − V ) =+0.70 should be 1.37 mag, instead of the 1.58 mag given by Laird et al. In general, Hipparcos parallaxes are larger than ground‐based ones, causing a divergence of our Δ M H V ( B − V , δ 0.6 ) relation (the solid line in Fig. 15b), from the one of Laird et al. (the dashed line) for the range +0.10 ≤δ 0.6 ≤+0.29 ; our absolute magnitudes are fainter, as has been confirmed for local subdwarfs by Reid. Our final calibrations for Δ M H V ( B − V , δ 0.6 ) , equations (16) and (17), are third‐order polynomials in δ 0.6 , pass through the origin, and provide photometric distances in reasonable agreement with those obtained directly from Hipparcos parallaxes ( Fig. 18). 15(a) Δ M H V versus δ 0.6 for 257 dwarfs and turn‐off stars (shown with circles) for the ranges of −0.10 ≤δ 0.6 ≤+ 0.29 , and +0.49 ≤ ( B − V ) 0 ≤+ 0.89 . The Δ M H V values of the 257 stars are corrected to ( B − V ) =+0.70 . (b) The solid line shows the third‐order polynomial of equation (15), which fits binned values of Δ M H V for 241 stars with Hipparcos parallaxes and smaller residuals. A dashed line shows the Δ M H V (δ 0.6 ) relation from the equation (4a) of LCL88. Big open squares show mean Δ M H V values for each δ 0.6 bin (0.01 mag in size). Combined error bars, , are also plotted. The final residuals of 241 stars are plotted as a function of Δ M H V and δ 0.6 in the panels (c) and (d), respectively; a residual means an observation minus its estimate. Open triangles show the relation of Δ M H V (δ 0.6 ) at ( B − V ) =+0.70 constructed from the 6‐Gyr isochrones of BV&VC, with [α/Fe]=+0.00 for [Fe/H] > −0.60 , and [α/Fe]=+0.30 for [Fe/H]≤−0.60 (see column 9 of Table 10).18Comparisons of the differences in distance between those from the LCL88, M V calibration and those from our equations (10) and (17), as a function of the Hipparcos distances, d Hip . (a) Δ d Hip‐equation 17 = d Hip − d equation 17 , (b) Δ d Hip‐LCL88 = d Hip − d LCL88 , (c) Δ d Hip‐equation 10 = d Hip − d equation 10 (d) Δ d equation 17‐LCL88 = d equation 17 − d LCL88 (e) Δ d equation 10‐equation 17 = d equation 10 − d equation 17 . All distances are in parsec (pc), and all comparisons are made for the 257 stars over the ranges of −0.10 ≤δ 0.6 ≤+ 0.29 and +0.49 ≤ ( B − V ) 0 ≤+ 0.89 .