Investigating the System Configuration of Kepler-451 through Orbital Period Variations: Dynamical and Magnetic Interpretations

Abstract We present an analysis of eclipse timing variations in Kepler-451 using data spanning 2004–2024 from both ground- and space-based observations. Using two data sets, Data Set A (DS-A) and Data Set B (DS-B), we constructed updated O–C diagrams. By modeling both data sets with various light-travel time (LTT) configurations, we tested for the presence of circumbinary companions. For DS-A, the two-companion model (LTT34) provides the best fit with rms = 3.23 s and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>1.23</mml:mn> </mml:math> , while adding a fifth body (LTT345) does not improve the fit (rms = 3.24 s, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>1.28</mml:mn> </mml:math> ). For DS-B, the three-companion model (LTT345) yields the best fit (rms = 2.31 s, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>1.01</mml:mn> </mml:math> ), although the semiamplitude of the inner companion (1.34 s) is smaller than the systematic error (1.81 s), suggesting it may originate from observational or calibration systematics. Applegate-mechanism tests indicate that most signals exceed the available energy budget, while the outer LTT terms in both data sets remain consistent with the Standard Model and may have a magnetic origin. Removing these magnetic terms yields dynamically stable configurations for at least 10 7 yr. These findings support the presence of a second-generation circumbinary planet at ∼3.4 au around Kepler-451, while the origin of the remaining LTT signals remains uncertain.