← the band experiments · method
All four parameters free Teff , log g, helium and metallicity, fitted together. The sample spans He II 4686 strength on purpose, from sdB with the line absent to He-sdOB where it is the strongest feature in the blue, because the question was whether that line is what makes Z measurable.
18 stars
17 / 18 Z determined
0.18 median error on Z [dex]
14 / 18 chi² improved
-0.0 0.5 1.0 20000 30000 40000 50000 Teff [K] J10233+0759 |corr(Teff, Z)| 0.98 J07439+3727 |corr(Teff, Z)| 0.53 J08161+4803 |corr(Teff, Z)| 0.23 J12564+2742 |corr(Teff, Z)| 0.27 J18328+6309 |corr(Teff, Z)| 0.04 J16237+1229 |corr(Teff, Z)| 0.25 J07333+1744 |corr(Teff, Z)| 0.41 J07334+3652 |corr(Teff, Z)| 0.73 J08251-6314 |corr(Teff, Z)| 0.53 J07403+2049 |corr(Teff, Z)| 0.37 J17083+3001 |corr(Teff, Z)| 0.35 J11047+0925 |corr(Teff, Z)| 0.50 J21107+0001 |corr(Teff, Z)| 0.72 J22174+1216 |corr(Teff, Z)| 0.79 J16387+6728 |corr(Teff, Z)| 0.43 J09099+6229 |corr(Teff, Z)| 0.72 J22071+1257 |corr(Teff, Z)| 0.23 J22226+0051 |corr(Teff, Z)| 0.91 J10233+0759 |corr(log g, Z)| 0.81 J07439+3727 |corr(log g, Z)| 0.40 J08161+4803 |corr(log g, Z)| 0.36 J12564+2742 |corr(log g, Z)| 0.24 J18328+6309 |corr(log g, Z)| 0.27 J16237+1229 |corr(log g, Z)| 0.14 J07333+1744 |corr(log g, Z)| 0.06 J07334+3652 |corr(log g, Z)| 0.33 J08251-6314 |corr(log g, Z)| 0.14 J07403+2049 |corr(log g, Z)| 0.17 J17083+3001 |corr(log g, Z)| 0.20 J11047+0925 |corr(log g, Z)| 0.32 J21107+0001 |corr(log g, Z)| 0.30 J22174+1216 |corr(log g, Z)| 0.37 J16387+6728 |corr(log g, Z)| 0.63 J09099+6229 |corr(log g, Z)| 0.25 J22071+1257 |corr(log g, Z)| 0.64 J22226+0051 |corr(log g, Z)| 0.30 J10233+0759 |corr(helium, Z)| 0.73 J07439+3727 |corr(helium, Z)| 0.12 J08161+4803 |corr(helium, Z)| 0.04 J12564+2742 |corr(helium, Z)| 0.00 J18328+6309 |corr(helium, Z)| 0.16 J16237+1229 |corr(helium, Z)| 0.13 J07333+1744 |corr(helium, Z)| 0.14 J07334+3652 |corr(helium, Z)| 0.05 J08251-6314 |corr(helium, Z)| 0.18 J07403+2049 |corr(helium, Z)| 0.01 J17083+3001 |corr(helium, Z)| 0.20 J11047+0925 |corr(helium, Z)| 0.13 J21107+0001 |corr(helium, Z)| 0.46 J22174+1216 |corr(helium, Z)| 0.04 J16387+6728 |corr(helium, Z)| 0.36 J09099+6229 |corr(helium, Z)| 0.16 J22071+1257 |corr(helium, Z)| 0.37 J22226+0051 |corr(helium, Z)| 0.37 eff
How correlated metallicity is with each of the other three. Temperature is the one it cannot be told apart from; helium, which was the worry, is the one it can. -0 2000 4000 6000 -0.0 0.5 1.0 |correlation(Teff, Z)| J07439+3727 corr 0.53 moves 800 K J07334+3652 corr 0.73 moves 6 K J10233+0759 corr 0.98 moves 1027 K J12564+2742 corr 0.27 moves 4 K J08161+4803 corr 0.23 moves 46 K J07333+1744 corr 0.41 moves 217 K J16237+1229 corr 0.25 moves 21 K J18328+6309 corr 0.04 moves 37 K J08251-6314 corr 0.53 moves 501 K J07403+2049 corr 0.37 moves 542 K J17083+3001 corr 0.35 moves 39 K J11047+0925 corr 0.50 moves 41 K J09099+6229 corr 0.72 moves 2812 K J21107+0001 corr 0.72 moves 957 K J22174+1216 corr 0.79 moves 57 K J22226+0051 corr 0.91 moves 5507 K J22071+1257 corr 0.23 moves 121 K J16387+6728 corr 0.43 moves 673 K And the correlation says what it costs. Past 0.5 the temperature moves by hundreds of kelvin when Z is freed; below it, by tens. -0.00 0.10 0.20 0.30 -0.0 1.0 2.0 W(He II 4686) [Å] J07439+3727 W -0.13 e(Z) 0.08 J07334+3652 W -0.08 e(Z) 0.31 J10233+0759 W 0.02 e(Z) 2.42 off the top J12564+2742 W 0.03 e(Z) 0.26 J08161+4803 W -0.09 e(Z) 0.12 J07333+1744 W -0.01 e(Z) 0.20 J16237+1229 W -0.08 e(Z) 0.20 J18328+6309 W -0.18 e(Z) 0.17 J08251-6314 W 0.42 e(Z) 0.19 J07403+2049 W 0.34 e(Z) 0.08 J17083+3001 W 0.42 e(Z) 0.12 J11047+0925 W 0.58 e(Z) 0.18 J09099+6229 W 1.28 e(Z) 0.13 J21107+0001 W 0.46 e(Z) 0.19 J22174+1216 W 0.61 e(Z) 0.23 J22226+0051 W 0.43 e(Z) 0.19 J22071+1257 W 2.31 e(Z) 0.12 J16387+6728 W 2.42 e(Z) 0.13 The hypothesis this was built to test: that He II 4686 carries the metal signal, so Z would be undetermined without it. There is no such relation — the stars with the line absent do as well as the rest. -2 -1 0 +1 20000 30000 40000 50000 Teff [K] J07439+3727 Z +0.94 +- 0.08 J07334+3652 Z -0.72 +- 0.31 J10233+0759 Z -2.00 +- 2.42 J12564+2742 Z +0.03 +- 0.26 J08161+4803 Z +0.41 +- 0.12 J07333+1744 Z +0.68 +- 0.20 J16237+1229 Z +0.56 +- 0.20 J18328+6309 Z +0.71 +- 0.17 J08251-6314 Z +0.44 +- 0.19 J07403+2049 Z +0.68 +- 0.08 J17083+3001 Z +0.06 +- 0.12 J11047+0925 Z -0.03 +- 0.18 J09099+6229 Z +0.86 +- 0.13 J21107+0001 Z +0.53 +- 0.19 J22174+1216 Z +0.03 +- 0.23 J22226+0051 Z +0.91 +- 0.19 J22071+1257 Z +0.63 +- 0.12 J16387+6728 Z +0.92 +- 0.13 The fitted metallicity, with its error. Above the standard sdB pattern almost everywhere, as both earlier experiments found by other means. What is degenerate with what pair median |corr| worst helium ↔ Z 0.14 0.46 temperature ↔ Z 0.43 0.91 gravity ↔ Z 0.30 0.64
Freeing Z moves the temperature by a median of 800 K in the 7 stars with |corr(Teff , Z)| > 0.5, and 46 K in the 10 below it. That split comes out of the covariance, not out of the shifts it predicts.
Every star star class W4686 Teff 3p Teff 4p ΔT log n(He)/n(H) Z ± He↔Z T↔Z χ² 3p χ² 4p J10233+0759 sdB +0.02 17894 18921 +1027 -1.77 -2.00 2.42 +0.73 -0.98 1.40 1.34 J07439+3727 sdB -0.13 21386 22186 +800 -2.30 +0.94 0.08 -0.12 +0.53 2.51 1.97 J08161+4803 sdB -0.09 24208 24254 +46 -3.08 +0.41 0.12 +0.04 +0.23 1.78 1.73 J12564+2742 sdB +0.03 25649 25645 -4 -4.00 +0.03 0.26 -0.00 -0.27 1.24 1.24 J18328+6309 sdB -0.18 26825 26788 -37 -2.44 +0.71 0.17 +0.16 +0.04 1.36 1.26 J16237+1229 sdB -0.08 28318 28339 +21 -2.98 +0.56 0.20 +0.13 +0.25 1.27 1.22 J07333+1744 sdB -0.01 30158 30375 +217 -2.00 +0.68 0.20 +0.14 +0.41 1.30 1.24 J07334+3652 sdB -0.08 32149 32155 +6 -2.49 -0.72 0.31 +0.05 -0.73 2.61 2.41 J08251-6314 sdOB +0.42 32823 33324 +501 -1.62 +0.44 0.19 +0.18 +0.53 3.65 3.60 J07403+2049 sdOB +0.34 34147 34689 +542 -1.59 +0.68 0.08 +0.01 +0.37 1.90 1.57 J17083+3001 sdOB +0.42 36819 36858 +39 -1.67 +0.06 0.12 -0.20 +0.35 1.31 1.31 J11047+0925 sdO +0.58 38271 38230 -41 -2.29 -0.03 0.18 -0.13 +0.50 1.29 1.29 J21107+0001 sdO +0.46 39713 40670 +957 -2.52 +0.53 0.19 -0.46 +0.72 1.53 1.48 J22174+1216 sdO +0.61 41619 41676 +57 -2.40 +0.03 0.23 -0.04 +0.79 1.19 1.19 J16387+6728 He-sdOB +2.42 46137 46810 +673 +0.95 +0.92 0.13 +0.36 +0.43 3.05 2.82 J09099+6229 sdO +1.28 47720 50532 +2812 -1.74 +0.86 0.13 -0.16 +0.72 1.61 1.35 J22071+1257 He-sdOB +2.31 53699 53820 +121 +0.50 +0.63 0.12 +0.37 +0.23 2.01 1.92 J22226+0051 sdO +0.43 48372 53879 +5507 -3.24 +0.91 0.19 -0.37 +0.91 1.23 1.16
The row in accent is the one star whose metallicity is not determined: the coolest in the sample, where Z runs to the edge of the delivered range and everything is correlated with everything. Z is bounded to that range, so a value at −2 or +1 exactly is the bound and not a measurement.