The Pulsating Eclipsing Binary TIC 309658221 in a 7.59 Day Orbit

We present a new eclipsing binary (EB) showing multiperiodic oscillations using the first three sectors of {\it TESS} photometry. The eclipse and pulsation light curves of TIC 309658221 were modeled using an iterative method to obtain a consistent photometric solution. The {\it TESS} target is a circular-orbit, detached binary system with a mass ratio of 0.349, an inclination angle of 80.42 deg, and a temperature difference of 847 K between the components. The primary component of the system lies near the red edge of the $\delta$ Sct instability region on the main-sequence band in the Hertzsprung-Russell diagram. Multiple frequency analyses were applied to the eclipse-subtracted residuals after removing the binary effects in the observed data. These resulted in the detection of 26 frequencies, of which $f_1-f_6$ were independent pulsation frequencies. The 20 other frequencies could be mainly caused by orbital harmonics ($f_8$ and $f_{11}$) or combination frequencies. The period ratios and pulsation constants of the $f_1-f_6$ frequencies are in the ranges of $P_{\rm pul}/P_{\rm orb}$ = 0.010$-$0.013 and Q = 0.027$-$0.036 days, respectively, which are typical of $\delta$ Sct type. The results reveal that TIC 309658221 is an eclipsing $\delta$ Sct star with an orbital period of 7.5952 days and pulsation frequencies of 9.94$-$13.01 day$^{-1}$. This work demonstrates that the 2-min cadence observations of {\it TESS} are very useful for the study of pulsating EBs with multiple frequencies and low amplitudes.