Abstract
A revision of the orbital parameters of the spectroscopic binary Cepheid TX Del, often classified as a BL Her subtype of T2 variables, has been carried out. The pulsation radius is determined from two series of photometric observations, including Gaia DR3: \(\langle R\rangle\approx 22.4\pm 0.8\,R_{\odot}\) for the ( \(B,V\) ) bands and \(\langle R\rangle\approx 20.6\pm 0.6\,R_{\odot}\) for the ( \(BP,RP\) ) bands, respectively. The amplitude of the radius variations is about \(2\,R_{\odot}\) . The new radius estimates are significantly smaller than the previous estimates, which were in the range of 37 to 60 \(R_{\odot}\) . Using the Bayesian distance, \(\langle D\rangle\approx 1064\pm 25\) pc, the absolute values of TX Del are estimated to be \(\langle M_{V}\rangle_{I}\approx{-}1.31\pm 0.04\) mag and \(\langle M_{G}\rangle_{I}\approx{-}1.40\pm 0.03\) mag, respectively. The absolute magnitude and mean radius of TX Del are in excellent agreement with the predictions of the ‘‘period–luminosity’’ and ‘‘period–radius’’ relations for T2 Cepheids with a period of \(P_{\textrm{pls}}\approx 6.1662\) days; TX Del is approximately \(2\overset{\textrm{m}}{.}2\) fainter than classical Cepheids with the same period. It is shown that for orbital plane inclination angles \(20^{\circ}<i<(30{-}35)^{\circ}\) the satellite can be more massive than the main component, which leads to an evolutionary scenario with mass exchange. The current Roche sphere filling degree is \(37{-}55\%\) . The orbit of the binary system TX Del calculated based on astrometric data from Gaia DR3 and radial velocity is limited by a \(|z|<0.42\) kpc torus with the inner and outer radii equal to 7.2 and 8.3 kpc, respectively, while the vertical velocity is \(|V_{z}|\leq 38\) km s \({}^{-1}\) ; the period of galactovertical oscillations is about 77 Myrs. The tangential velocity is 220–255 km s \({}^{-1}\) . The high metallicity and kinematic characteristics allow us to refer TX Del to the population of the old disk of the Milky Way with a vertical scale \(H_{z}\approx 0.3\) kpc (or to a thick disk with \(H_{z}\approx 0.85\) kpc). At the same time, in terms of pulsation characteristics (period, luminosity, and position in the instability strip), TX Del is close to Population II Cepheids with \(\textrm{[Fe/H]}<{-}1\) (including globular cluster Cepheids) that are at the evolutionary stage after the horizontal branch. To finally clarify the evolutionary status of such variables, additional evolutionary and pulsation calculations are required over a wider range of periods and luminosities.
