Modeling of Two Low-amplitude Radially Pulsating <i>δ</i> Scuti Stars: KIC 12602250 and KIC 5768203

Abstract In this research, we conducted systematic photometric, spectroscopic, and theoretical modeling analyses of two δ Scuti stars—KIC 12602250 and KIC 5768203—that pulsate only in radial modes. We collected their relevant photometric and spectroscopic parameters from multiple catalogs and estimated the absolute luminosities of both stars. Using high-precision time-series data from Kepler and TESS, we performed in-depth analysis of the periodic modulation in pulsation frequency phases, successfully determining the orbital periods and companion mass distribution ranges for these binary systems. Additionally, we thoroughly investigated the temporal evolution characteristics of pulsation periods and amplitudes. Based on calculations using Modules for Experiments in Stellar Astrophysics stellar evolution models, we determined that KIC 12602250 has a mass of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>M</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.6</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.07</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.05</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> with metallicity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>Z</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.03</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>9</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.010</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.018</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and is currently in the main-sequence evolutionary stage. For KIC 5768203, we derived precise parameters through rigorous constraints: mass M = 2.09 ± 0.01 M ⊙ , metallicity Z = 0.024 ± 0.003, and radius R = 3.19 ± 0.01 R ⊙ . Theoretical models reveal that this star has already crossed the first main-sequence turn-off point and entered the late-main-sequence evolutionary stage. Through comparative studies with typical High Amplitude δ Scuti stars, we believe that the primary reason for the low radial pulsation amplitudes in these two stars likely stems from their specific evolutionary states.