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High precision radial velocity (RV) measurements in the near infrared are on high demand, especially in the context of exoplanet search campaigns shifting their interest to late type stars in order to detect planets with ever lower mass or targeting embedded pre-main-sequence objects. ESO is offering a new spectrograph at the VLT -- CRIRES -- designed for high resolution near-infrared spectroscopy with a comparably broad wavelength coverage and the possibility to use gas-cells to provide a stable RV zero-point. We investigate here the intrinsic short-term RV stability of CRIRES, both with gas-cell calibration data and on-sky measurements using the absorption lines of the Earths atmosphere imprinted in the source spectrum as a local RV rest frame. Moreover, we also investigate for the first time the intrinsic stability of telluric lines at 4100 nm for features originating in the lower troposphere. Our analysis of nearly 5 hours of consecutive observations of MS Vel, a M2II bright giant centred at two SiO first overtone band-heads at 4100 nm, demonstrates that the intrinsic short-term stability of CRIRES is very high, showing only a slow and fully compensateable drift of up to 60 m/s after 4.5 hours. The radial velocity of the telluric lines is constant down to a level of approx. +/- 10 m/s (or 7/1000 of one pixel). Utilising the same telluriclines as a rest frame for our radial velocity measurements of the science target, we obtain a constant RV with a precision of approx. +/- 20 m/s for MS Vel as expected for a M-giant.
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