Linear nonadiabatic properties of SX phoenicis variables

We present a detailed linear, nonadiabatic pulsational scenario for oscilla ting blue stragglers (BSs)/SX Phe variables in Galactic globular clusters ( GGCs) and in Local Group (LG) dwarf galaxies. The sequences of models were constructed by adopting a wide range of input parameters and properly cover the region of the H-R diagram in which these objects are expected to be pu lsationally unstable. Current calculations together with more metal-rich mo dels already presented by Gilliland et al. suggest that the pulsation prope rties of SX Phe variables are partially affected by metal content. In fact, the pulsation periods for the first three modes are marginally affected wh en moving from Z=0.0001 to 0.006, whereas the hot edges of the instability region move toward cooler effective temperatures by approximately 300-500 K . The inclusion of a metallicity term in the period-luminosity-color (P-L-C ) relations causes a substantial decrease in the intrinsic scatter and in t he individual error of the coefficients. This supports the result recently brought out by Petersen & Christensen-Dalsgaard for delta Scuti stars. More over, we find that the discrepancy between our relation and similar theoret ical and empirical relations available in the literature is typically small er than 5%. The comparison between theory and observations in the plane as well as in the luminosity amplitude-log P plane does not help to disentangl e the M-V-log P long-standing problem of mode identification among SX Phe s tars. However, our calculations suggest that the secular period change seem s to be a good observable to identify the pulsation mode of cooler SX Phe v ariables. Together with the previous models we also constructed new sequenc es of models by adopting selected effective temperatures and luminosities a long two evolutionary tracks characterized by the same mass value and metal content (M/M-circle dot = 1.2, Z = 0.001) but different He contents in the envelope, namely, Y = 0.23 and 0.30. The He content in the latter track wa s artificially enhanced soon after the central H exhaustion to mimic, with a crude approximation, the collisional merging between two stars. Interesti ngly enough, we find that the He-enhanced models present an increase in the pulsation period and a decrease in the total kinetic energy of the order o f 20% when compared with the canonical ones. At the same time, the blue edg e of the fundamental mode for the He-enhanced models is approximately 1000 K cooler than for canonical ones. Moreover, we find that the secular period change for He-enhanced models is approximately a factor of 2 larger than f or canonical ones. According to this evidence, we suggest that the pulsatio n properties of SX Phe variables can be soundly adopted to constrain the ev olutionary history of BSs and in turn to single out the physical mechanisms that trigger their formation.