The warm-hot intergalactic medium (WHIM) at temperatures 105-107?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 ( 3σ) 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 ratios (S/Ns) of ~90 and 190 per 50?m? 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 cannot confirm the two WHIM systems reported by Nicastro et?al. in 2005. Our bootstrap simulations indicate that spectra with such high S/N cannot constrain the WHIM with O VII column densities (corresponding to an equivalent width of 2.5?m? for a Doppler velocity of 50 km s–1) at 3σ significance level. The simulation results also suggest that it would take 60?Ms for Chandra and 140?Ms for XMM-Newton to measure the at ≥4σ from a spectrum of a background QSO with flux of ~0.2?mCrab (1 Crab = 2 × 10–8 erg s–1 cm–2 at 0.5-2?keV). Future X-ray spectrographs need to be equipped with spectral resolution R ~ 4000 and effective area A ≥ 100 cm2 to accomplish the similar constraints with an exposure time of ~2?Ms and would require ~11?Ms to survey the 15 QSOs with flux 0.2?mCrab along which clear intergalactic O VI absorbers have been detected.
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