Medium-resolution spectroscopic study of the intermediate-mass pre-main sequence binary $\theta^1$ Ori E

$\theta^1$ Ori E is a very young and relatively massive pre-main sequence (PMS) spectroscopic and eclipsing binary with nearly identical components. We analyze \'Echelle spectra of the system obtained over fifteen years and report 91 radial velocities measured from cross-correlating the observations with a suitable synthetic spectrum. The spectra of individual binary components are indistinguishable from each other, with a composite spectral type around G4 III. The projected equatorial velocity is estimated to be $v \sin{i} = 32\pm 3~km~s^{-1}$, consistent with rotational synchronization. We find that the circular orbit has $P_{\rm orb} = 9.89522 \pm 0.00003~d$, $K_1 = 83.36 \pm 0.29~km~s^{-1}$, $K_2 = 84.57 \pm 0.28~km~s^{-1}$, and $asini = 32.84\pm0.08\ R_\odot$. The mass ratio is $q = 0.9856 \pm 0.0047$, indicating nearly identical but significantly different masses. The systemic velocity of the binary, $\gamma = 29.7 \pm 0.2~km~s^{-1}$, is similar to that of other Trapezium members. Using Spitzer light curves and our results, we derive $M_1 = 2.755\pm0.043\ M_{\odot}$, $M_2 = 2.720\pm0.043\ M_{\odot}$, $R_1=6.26\pm0.31R_{\odot}$ and $R_2=6.25\pm0.30R_{\odot}$. Together with our estimate of the effective temperature, $T_{\rm eff}=5150\pm200\ K$, a bolometric luminosity of $28.8\pm4.6\ L_{\odot}$ is derived for each component. Compared to evolutionary models of PMS stars, the binary age turns out to be less than or equal to $\sim 10^5$ years. Its components are probably the most massive stars known with masses determined with precision better than 2 percent, with both being PMS stars.