Using Chandra we have obtained imaging X-ray spectroscopy of the 10 to 16 Myr old F-star binary HD 113766. We individually resolve the binary components for the first time in the X-ray and find a total 0.3 to 2.0 keV luminosity of 2.2e29 erg/sec, consistent with previous RASS estimates. We find emission from the easternmost, infrared-bright, dusty member HD 113766A to be only 10% that of the western, infrared-faint member HD 113766B. There is no evidence for a 3rd late-type stellar or sub-stellar member of HD113766 with Lx > 6e25 erg s-1 within 2 arcmin of the binary pair. The ratio of the two stars Xray luminosity is consistent with their assignments as F2V and F6V by Pecaut et al. (2012). The emission is soft for both stars, kTApec = 0.30 to 0.50 keV, suggesting X-rays produced by stellar rotation and/or convection in young dynamos, but not accretion or outflow shocks which we rule out. A possible 2.8 +/- 0.15 (2{sigma}) hr modulation in the HD 113766B X-ray emission is seen, but at very low confidence and of unknown provenance. Stellar wind drag models corresponding to Lx = 2e29 erg s-1 argue for a 1 mm dust particle lifetime around HD 113766B of only 90,0000 years, suggesting that dust around HD 113766B is quickly removed, whereas dust around HD 113766A can survive for > 1.5e6 yrs. At 1e28 to 1e29 erg s-1 luminosity, astrobiologically important effects, like dust warming and X-ray photolytic organic synthesis, are likely for any circumstellar material in the HD 113766 systems.
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