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The Eclipsing System V404 Lyr: Light-Travel Times and Gamma Doradus Pulsations

We present the physical properties of V404 Lyr exhibiting eclipse timing variations and multiperiodic pulsations from all historical data including the Kepler observations. Detailed analyses of 2,922 minimum epochs showed that the orbital period has varied through a combination with an upward-opening parabola and two sinusoidal variations, with periods of $P_3$=649 d and $P_4$=2,154 d and semi-amplitudes of $K_3$=193 s and $K_4$=49 s, respectively. The secular period increase could be interpreted as a combination of the secondary to primary mass transfer and angular momentum loss. The most reasonable explanation for both sinusoids is a pair of light-travel-time effects due to two circumbinary objects with projected masses of $M_3$=0.47 M$_\odot$ and $M_4$=0.047 M$_\odot$. The third-body parameters are consistent with those calculated using the W-D binary code. For the orbital inclinations higher than 43$^\circ$, the fourth component has a mass within the hydrogen-burning limit of $\sim$0.07 M$_\odot$, which implies that it is a brown dwarf. A satisfactory model for the Kepler light curves was obtained through applying a cool spot to the secondary component. The results demonstrate that the close eclipsing pair is in a semi-detached, but near-contact, configuration; the primary fills approximately 93% of its limiting lobe and is larger than the lobe-filling secondary. Multiple frequency analyses were applied to the light residuals after subtracting the synthetic eclipsing curve from the Kepler data. This revealed that the primary component of V404 Lyr is a $γ$ Dor type pulsating star, exhibiting seven pulsation frequencies in the range of 1.85$-$2.11 d$^{-1}$ with amplitudes of 1.38$-$5.72 mmag and pulsation constants of 0.24$-$0.27 d. The seven frequencies were clearly identified as high-order low-degree gravity-mode oscillations which might be excited through tidal interaction.