Spectroscopic Disentangling Revealed the Tertiary Component in the Multiple System EM Boo

We present a comprehensive photometric and spectroscopic study of the triple stellar system EM\,Boo. The system is composed of detached, low-mass components, and for the first time in the literature, the spectrum of the tertiary component has been successfully disentangled from the composite spectrum using the \texttt{KOREL} code. Synthetic spectra were generated for each disentangled component, allowing determination of their atmospheric parameters. The depth of the H$_\alpha$ line in the tertiary spectrum indicates that it is an intermediate-temperature star, consistent with spectral types between A and F, and its effective temperature was determined to be 7000~K. By analyzing the radial velocity and light curves simultaneously, the fundamental physical parameters of the system were derived, and its detailed evolutionary status was investigated using \texttt{MESA} models. The \textit{HIPPARCOS} trigonometric parallax ($\varpi_{\rm Hip}=1.33\pm1.45$ mas) and \textit{Gaia} DR3 trigonometric parallax ($\varpi_{\rm Gaia}=3.9699\pm0.1812$ mas) show a significant discrepancy, most likely related to the system's multiplicity and the limitations of single-star astrometric solutions. To provide independent distance estimates, we modeled the spectral energy distribution (SED) using multi-wavelength flux data, yielding $E(B-V)=0.05$ mag and a trigonometric parallax $\varpi_{\rm SED}=3.2$ mas, corresponding to $d_{\rm SED}=313$ pc. Furthermore, photometric distance estimates based on the components' absolute magnitudes yield $d_{1}=299$ pc and $d_{2}=301$ pc, in good agreement with the SED-based distance. Both the SED-based and photometric distances converge around $d=300$ pc, indicating that the \textit{Gaia} trigonometric parallax underestimates the true distance of EM\,Boo.