Frequency analysis of KIC 1573174 : shedding light on the nature of HADS stars

We propose that KIC 1573174 is a quadruple-mode $\delta$ Scuti star with pulsation amplitudes between those of the HADS (high-amplitude Delta Scuti star) group and average low-amplitude pulsators. The radial modes detected in this star provide a unique opportunity to exploit asteroseismic techniques up to their limits. Detailed frequency analysis is given for the light curve from the Kepler mission. The variation of the light curve is dominated by the strongest mode with a frequency of F0 = 7.3975 $\rm{d^{-1}}$, as shown by Fourier analysis of long cadence data (Q1-Q17, spanning 1460 days), indicating that the target is a $\delta$ Scuti star. The other three independent modes with F1 = 9.4397 d$^{-1}$, F2 = 12.1225 d$^{-1}$ and F3 = 14.3577 d$^{-1}$, have ratios of $P_{1}$ / $P_{0}$, $P_{2}$ / $P_{0}$ and $P_{3}$ / $P_{0}$ estimated as 0.783, 0.610 and 0.515, which indicate that KIC 1573174 is a quadruple-mode $\delta$ Scuti star. A different approach has been used to determine the $O-C$ through the study of phase modulation. The change of period $(1/P)~dP/dt$ is obtained resulting in $-1.14 \times 10^{-6}~\text{yr}^{-1}$ and $-4.48 \times 10^{-6}~\text{yr}^{-1}$ for F0 and F1 respectively. Based on frequency parameters (i.e., F0, F1, F2, and F3), a series of theoretical models were conducted by employing the stellar evolution code MESA. The ratio of observed $f_{1}/f_{2}$ is larger than that of the model, which may be caused by the rotation of the star. We suggest high-resolution spectral observation is highly desired in the future to further constrain models.