The warm-hot intergalactic medium ( WHIM ) at temperatures 10 ^ { 5 } -10 ^ { 7 } K is believed to contain 30-50 % of the baryons in the local universe .
However , all current X-ray detections of the WHIM at redshifts z > 0 are of low statistical significance ( \lower 2.0 pt \hbox { $ \buildrel \scriptstyle < \over { \scriptstyle \sim } $ } 3 \sigma ) and/or controversial .
In this work , we aim to establish the detection limits of current X-ray observatories and explore requirements for next-generation X-ray telescopes for studying the WHIM through X-ray absorption lines .
We analyze all available grating observations of Mrk 421 and obtain spectra with signal-to-noise ratio ( S/N ) of \sim 90 and 190 per 50 mÅ spectral bin from Chandra and XMM-Newton observations , respectively .
Although these spectra are two of the best ever collected with Chandra and XMM-Newton , we can not confirm the two WHIM systems reported by Nicastro et al .
in 2005 .
Our bootstrap simulations indicate that spectra with such high S/N can not constrain the WHIM with O VII column densities N _ { OVII } \approx 10 ^ { 15 } ~ { } { cm ^ { -2 } } ( corresponding to an equivalent widths of 2.5 mÅ for a Doppler velocity of 50 ~ { } { km~ { } s ^ { -1 } } ) at \lower 2.0 pt \hbox { $ \buildrel \scriptstyle > \over { \scriptstyle \sim } $ } 3 \sigma significance level .
The simulation results also suggest that it would take > 60 Ms for Chandra and 140 Ms for XMM-Newton to measure the N _ { OVII } at \geq 4 \sigma from a spectrum of a background QSO with flux of \sim 0.2 mCrab ( 1 Crab = 2 \times 10 ^ { -8 } ~ { } { erg~ { } s ^ { -1 } ~ { } cm ^ { -2 } } at 0.5-2 keV ) .
Future X-ray spectrographs need to be equipped with spectral resolution R \sim 4000 and effective area A \geq 100 ~ { } { cm ^ { 2 } } to accomplish the similar constraints with an exposure time of \sim 2 Ms and would require \sim 11 Ms to survey the 15 QSOs with flux \lower 2.0 pt \hbox { $ \buildrel \scriptstyle > \over { \scriptstyle \sim } $ } 0.2 mCrab along which clear intergalactic O VI absorbers have been detected .