The Param Expansion Response Function (\(\zeta_\uparrow\)): A Unified Secular Stability Criterion for Roche Lobe Overflow
P. M. Deshmukh *
Department of Physics, Dr. Vishwanath Karad MIT World Peace University, Pune, Maharashtra, India.
*Author to whom correspondence should be addressed.
Abstract
Aims: This study introduces the Param Expansion Response Function (\(\zeta_\uparrow\)) to refine the secular stability criteria for Roche lobe overflow in low-mass binary systems.
Study Design: Theoretical derivation and empirical calibration using high-precision eclipsing binary data. Methodology: We integrate magnetic braking, tidal synchronization, and non-conservative mass transfer into a unified orbital response exponent. The model is calibrated using M-R data for M-dwarfs from Chaturvedi et al. (2018) to account for the "radius anomaly."
Results: The unified function identifies a critical mass ratio qcrit \(\approx\) 0.62, significantly more restrictive than the classic values of \(\approx\) 0.75 found in conservative frameworks. This explains the stability gap observed in short-period binaries.
Conclusion: The \(\zeta_\uparrow\) framework provides a robust tool for predicting mass transfer outcomes and the precursors of common envelope evolution.
Keywords: Binary stars, Roche Lobe Overflow, magnetic braking, secular stability, M-dwarfs