KIC 12602250: A low-amplitude Double-mode $\delta$ Scuti star with Amplitude Modulation

We propose for the first time that KIC 12602250 is a low-amplitude radial double-mode $\delta$ Scuti star with amplitude modulation. The detailed frequency analysis is given for the light curve of KIC 12602250 which is delivered from the Kepler mission. The Fourier analysis of the long cadence data (i.e. Q0 - Q17, spanning 1471 days) reveals that the variations of the light curve are dominated by the strongest mode with frequency F0 = 11.6141 $\rm{d^{-1}}$, suggesting that KIC 12602250 is a $\delta$ Scuti star. The other independent mode F1 = 14.9741 $\rm{d^{-1}}$ is newly detected. The amplitude of the light variations of \target is $\sim$ 0.06 mag, which indicates that this is a low-amplitude $\delta$ Scuti star, but the ratio of F0/F1 is estimated as 0.7756 which is typical of HADS, and a slow amplitude growth is detected in F1 and $f_{3}$, which could be due to stellar evolution, suggesting that KIC 12602250 could be a post main sequence $\delta$ Scuti which is crossing the instability strip for the first time.