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In this work, the photometric data from the American Association of VariableStar Observers are collected and analyzed on the SX Phoenicis star DY Pegasi(DY Peg). From the frequency analysis, we get three independent frequencies:$f_0 = 13.71249\ \rm{c\ days^{-1}}$, $f_1 = 17.7000\ \rm{c\ days^{-1}}$, and$f_2 =18.138\ \rm{c\ days^{-1}}$, in which $f_0$ and $f_1$ are the radialfundamental and first overtone mode, respectively, while $f_2$ is detected forthe first time and should belong to a nonradial mode. The $O-C$ diagram of thetimes of maximum light shows that DY Peg has a period change rate$(1/P_0)(\mathrm{d} P_0/\mathrm{d} t) = -(5.87 \pm 0.03) \times 10^{-8} \\mathrm{yr^{-1}}$ for its fundamental pulsation mode, and should belong to abinary system that has an orbital period $P_{\mathrm{orb}} = 15425.0 \pm 205.7\ \mathrm{days}$. Based on the spectroscopic information, single starevolutionary models are constructed to fit the observed frequencies. However,some important parameters of the fitted models are not consistent with thatfrom observations. Combing with the information from observation andtheoretical calculation, we conclude that DY Peg should be an SX Phoenicis starin a binary system and accreting mass from a dust disk, which was the residueof its evolved companion (most probably a hot white dwarf at the present stage)produced in the asymptotic giant branch phase. Further observations are neededto confirm this inference, and it might be potentially a universal formationmechanism and evolutionary history for SX Phoenicis stars.

DY Pegasi: An SX Phoenicis Star in a Binary System with an Evolved Companion