This study made extensive use of the computing facilities offered by the Calcul en Midi-Pyrénées (CALMIP) project and the Centre Informatique National de l'Enseignement Supérieur (CINES), France. Some of the spectroscopic observations reported here were obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution.

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The Mont4kccd QE curve as well as the filter transmission curves can be found on the following webpage: http:james.as.arizona.edu/~psmith/61inch/instruments.html

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... envelope

Note that the parameter $M_{\rm env}$ commonly used in extreme horizontal branch stellar evolution includes the mass of hydrogen contained in the thin He/H transition zone, whereas the parameter M(H) used in our envelope models does not. They can be related with $\log{[M_{\rm env}/M_{\ast}]}=\log{[M(H)/M_{\ast}]}+C$ , where C is a small positive term slightly dependent on the model parameters that can be computed from the converged model using the mass of hydrogen present in the transition zone itself.

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... 0911+456

Note that the asteroseismic mass determination is robust. We carried out additional searches in parameter space forcing the mass to the canonical value of 0.47 $M_{\odot}$ and found that the resulting best fit solution presented an unacceptably bad period match with a dispersion of $\langle\Delta P/P \rangle=1.5$ % or $\Delta P=2.5$ s (compared to $\langle \Delta P/P \rangle=0.26$ % for the optimal model). Moreover, the mode identification inferred was less than convincing, the only radial mode being assigned to one of the lowest amplitude pulsations. The period fit was improved only marginally by varying the mass in the 0.46-0.48 $M_{\odot}$ range.

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