The formation of EL CVn-type binaries

EL CVn-type binaries are eclipsing binaries that contain an A-or F-type dwarf star and a very low mass (similar to 0.2 M-circle dot) helium white dwarf precursor (proto-He WD). A number of such objects have been discovered in the Wide Angle Search for Planets and Kepler photometric surveys. Here, we have studied the formation of EL CVn-type binaries and give the properties and the space density of this population of stars in the Galaxy. We show that EL CVn binaries cannot be produced by common envelope evolution as previously believed because this process leads to merging of the components when giants have such low-mass cores. Stable mass transfer in low-mass binaries, from more than 65 000 runs of Population I binary evolution, may well reproduce the properties of EL CVn stars such as the evolutionary phase, mass ratios and the WD mass-period (M-WD-P) relation. The study shows that the most common donor mass range for producing the observed EL CVn-type stars is 1.15-1.20 M-circle dot and that the lifetime of such objects increases dramatically with decreasing proto-He WD mass. This leads to an intrinsic peak mass around the minimum mass of proto-He WDs of similar to 0.16 M-circle dot. The most probable proto-He WD mass is 0.17-0.21 M-circle dot after selection effects included. We estimated the number of EL CVn stars with P <= 2.2 d to be 2-5 x 10(6) in the Galaxy, indicating a local density of 4-10 x 10(-6) pc-(3). We conclude that many more EL CVn-type binaries remain to be discovered and that these binaries will be predominantly low-mass systems in old stellar populations.