https://journaliaarj.com/index.php/IAARJ <p style="text-align: justify;"><strong>International Astronomy and Astrophysics Research Journal</strong> aims to publish high-quality papers (<a href="http://www.journaliaarj.com/index.php/IAARJ/general-guideline-for-authors">Click here for Types of paper</a>) in all areas of Astronomy and Astrophysics. By not excluding papers based on novelty, this journal facilitates the research and wishes to publish papers as long as they are technically correct and scientifically motivated. The journal also encourages the submission of useful reports of negative results. This is a quality controlled, OPEN peer-reviewed, open-access INTERNATIONAL journal.</p> <p style="text-align: justify;">This is an open-access journal which means that all content is freely available without charge to the user or his/her institution.</p> International Astronomy and Astrophysics Research Journal en-US International Astronomy and Astrophysics Research Journal 2456-9119 https://journaliaarj.com/index.php/IAARJ/article/view/121 <p><strong>Aims:</strong> 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.</p> <p><strong>Study Design:</strong> 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 <em>M-R</em> data for M-dwarfs from Chaturvedi et al. (2018) to account for the "radius anomaly."</p> <p><strong>Results:</strong> The unified function identifies a critical mass ratio <em>q_crit</em> \(\approx\) 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.</p> <p><strong>Conclusion:</strong> The \(\zeta_\uparrow\) framework provides a robust tool for predicting mass transfer outcomes and the precursors of common envelope evolution.</p> P. M. Deshmukh Copyright (c) 2026 Author(s). The licensee is the journal publisher. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2026-03-23 2026-03-23 8 1 1 11 10.9734/iaarj/2026/v8i1121