Period Change of the Binary System WR+O V444 Cyg: Updated Ephemeris Formula

TL;DR

This study targets the orbital-period evolution of the WR+O eclipsing binary V444 Cyg, driven by mass loss from the Wolf-Rayet wind. By compiling times of primary minimum from independent original light curves and applying a uniform Hertzsprung-method analysis, the authors construct a comprehensive $O-C$ dataset and fit a quadratic ephemeris to extract a period-change rate of $\\dot{P}=0.134\pm0.003$ s/yr. Using the standard wind-mass-loss relation $\\dot{M}_{WR}=\\frac{\\dot{P}}{2P}(M_{WR}+M_O)$ together with spectroscopic mass estimates and inclination, they derive $\\dot{M}_{WR}=(6.82\pm0.26)\times10^{-6} M_\odot$/yr, representing the most reliable dynamical WR wind mass-loss constraint to date. The work addresses historical biases by prioritizing independent data sources and uniform processing, providing an updated ephemeris $Min I (HJD)=E_0+P n + A n^2$ with $E_0=2441164.333\pm0.001$, $P=4.2124550\pm0.0000005$ d, and $A=(8.94\pm0.21)\times10^{-9}$ d, and it offers a robust foundation for future WR wind studies.

Abstract

V444 Cyg is a WN5+O6 V eclipsing binary system that exhibits a secular variation in its orbital period due to the loss of matter from the Wolf-Rayet star through its powerful stellar wind. This makes it possible to obtain a dynamical estimate of the WR star mass-loss rate with minimal modeling assumptions. Numerous studies have been published on this topic. Unfortunately, over time, they have accumulated various flaws due to the authors' differing use of previously published light curves. In this paper, we have critically analyzed all published data, added new data obtained by us, and present a table containing all currently known times of the primary minimum, found in a uniform manner and based on independent original data. Using this table, we updated the value of the parameters of the quadratic formula describing the times of the primary minimum. The found rate of orbital period change is $\dot{P} = 0.134\pm 0.003$ s/year, and the corresponding value of the WR star mass-loss rate is $\dot{M}_{\rm WR} = (6.82 \pm 0.26) \times 10^{-6} M_\odot$/year.

Figures (2)

• Figure 1: ($O-C$) values obtained for the times of primary minimum from Table \ref{['tab:moments']} (dots with error bars), as well as ($O-C$) values computed directly from the data of Semeniuk~sem68 (the date interval $\sim$ 2430000$-$2439000, shown by green circles), Janiashvili and Urushadze~jan16 ($\sim$ 2448182, the purple circle), Eris and Ekmeksi~eris11 ($\sim$ 2454328, the blue circle). The corresponding ($O-C$) values based on times of primary minimum from Table \ref{['tab:moments']}, and calculated using the same original data by Khaliullin et al. khal84 and Shaposhnikov shap23, are shown in red. All ($O-C$) values were calculated using the linear formula for the times of primary minimum given in the text.
• Figure 2: Approximation of the ($O-C$) values by a quadratic function. Only the ($O-C$) calculated from the values from Table \ref{['tab:moments']} were used.