Comprehensive analysis of CM Draconis: eclipse timing variations driven by either a third body or stellar magnetic activity

The CM Draconis system is a well-studied, double-lined spectroscopic binary that is totally eclipsing and exhibits strong magnetic activity. Nearly one million photometric measurements have been collected across multiple wavelengths over more than half a century. In addition to showing frequent flare activity and apsidal motion, CM Dra also hosts a distant white dwarf and has been proposed to harbor a Jupiter-sized circumbinary companion. At only 47 light-years from Earth, it remains one of the most observationally rich and dynamically intriguing low-mass binary systems. We present a comprehensive photometric and spectroscopic analysis of the system using new ground-based observations and data from 19 sectors of the \textit{TESS} mission. We derive precise fundamental parameters for both components: $M_1 = 0.2307 \pm 0.0008\,M_\odot$, $M_2 = 0.2136 \pm 0.0008\,M_\odot$, $R_1 = 0.2638 \pm 0.0011\,R_\odot$, $R_2 = 0.2458 \pm 0.0010\,R_\odot$, $L_1 = 0.0060 \pm 0.0005\,L_\odot$, and $L_2 = 0.0050 \pm 0.0004\,L_\odot$. The derived distance ($14.4 \pm 0.6$ pc) is consistent with \textit{Gaia} DR3 measurements. Eclipse timing variations (ETVs) spanning over five decades were analyzed in detail. A long-period ($\sim$56 yr) modulation was identified, which may be attributed either to the light-time effect of a possible circumbinary companion or to magnetic activity cycles. While the Bayesian Information Criterion statistically favors the model involving a light-time effect from a planetary companion, stellar activity remains a viable alternative that cannot yet be ruled out. Our results demonstrate that CM Dra is a valuable test case for studying both stellar activity and the potential presence of circumbinary companions in multiple-star systems. Continued long-term monitoring will be essential to distinguish between these competing scenarios.