The circumgalactic medium (CGM) of the Milky Way is mostly obscured by nearby gas in position-velocity space because we reside inside the Galaxy. Substantial biases exist in most studies on the Milky Ways CGM that focus on easier-to-detect high-velocity gas. With mock observations on a Milky-Way analog from the FOGGIE simulation, we investigate four observational biases related to the Milky Ways CGM. First, QSO absorption-line studies probe a limited amount of the CGM mass: only 35% of the mass is at high Galactic latitudes $|b|>20$ degrees, of which only half is moving at $|v_{rm LSR}|gtrsim100$ km s$^{-1}$. Second, the inflow rate ($dot{M}$) of the cold gas observable in HI 21cm is reduced by a factor of $sim10$ as we switch from the local standard of rest to the galaxys rest frame; meanwhile $dot{M}$ of the cool and warm gas does not change significantly. Third, OVI and NV are promising ions to probe the Milky Ways outer CGM ($rgtrsim$15 kpc), but CIV may be less sensitive. Lastly, the scatter in ion column density is a factor of 2 higher if the CGM is observed from inside-out than from external views because of the gas radial density profile. Our work highlights that observations of the Milky Ways CGM, especially those using HI 21cm and QSO absorption lines, are highly biased. We demonstrate that these biases can be quantified and calibrated through synthetic observations with simulated Milky-Way analogs.
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