We use X-ray and infrared observations to study the properties of three classes of young stars in the Carina Nebula: intermediate-mass (2--8M$_odot$) pre-main sequence stars (IMPS; i.e. intermediate-mass T Tauri stars), late-B and A stars on the zero-age main sequence (AB), and lower-mass T Tauri stars (TTS). We divide our sources among these three sub-classifications and further identify disk-bearing young stellar objects versus diskless sources with no detectable infrared (IR) excess emission using IR (1--8 $mu$m) spectral energy distribution modeling. We then perform X-ray spectral fitting to determine the hydrogen absorbing column density ($N_{rm H}$), absorption-corrected X-ray luminosity ($L_{rm X}$), and coronal plasma temperature ($kT$) for each source. We find that the X-ray spectra of both IMPS and TTS are characterized by similar $kT$ and $N_{rm H}$, and on average $L_{rm X}$/$L_{rm bol} sim4times10^{-4}$. IMPS are systematically more luminous in X-rays (by $sim$0.3 dex) than all other sub-classifications, with median $L_{rm X} = 2.5times10^{31}$ erg s$^{-1}$, while AB stars of similar masses have X-ray emission consistent with TTS companions. These lines of evidence converge on a magneto-coronal flaring source for IMPS X-ray emission, a scaled-up version of the TTS emission mechanism. IMPS therefore provide powerful probes of isochronal ages for the first $sim$10 Myr in the evolution of a massive stellar population, because their intrinsic, coronal X-ray emission decays rapidly after they commence evolving along radiative tracks. We suggest that the most luminous (in both X-rays and IR) IMPS could be used to place empirical constraints on the location of the intermediate-mass stellar birth line.
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