  We present the results from the Suzaku satellite of the surrounding region of
a galaxy cluster, A2744, at $z=0.3$. To search for oxygen emission lines from
the warm-hot intergalactic medium (WHIM), we analyzed X-ray spectra from two
northeast regions 2.2-3.3 and 3.3-4.4 Mpc from the center of the cluster, which
offers the first test on the presence of a WHIM near the typical accretion
shock radius ($\sim 2r_{200}$) predicted by hydrodynamical simulations. For the
2.2-3.3 Mpc region, the spectral fit significantly (99.2% significance)
improved when we include OVII and OVIII lines in the spectral model. A
comparable WHIM surface brightness was obtained in the 3.3-4.4 Mpc region and
the redshift of OVIII line is consistent with $z=0.3$ within errors. The
present results support that the observed soft X-ray emission originated from
the WHIM. However, considering both statistical and systematic uncertainties,
OVIII detection in the northeast regions was marginal. The surface brightness
of the OVIII line in ${\rm 10^{-7} photons\,cm^{-2}s^{-1}arcmin^{-2}}$ was
measured to be $2.7\pm 1.0$, $2.1 \pm 1.2$ for the 2.2-3.3, 3.3-4.4 Mpc
regions, giving the upper limit on the baryon overdensity of $\delta = 319
(<443)$, $283 (<446)$, respectively. This is comparable with previous
observations of cluster outskirts and their theoretical predictions. The future
prospect for WHIM detection using the Athena X-IFU micro-calorimeter is briefly
discussed here. In addition, we also derived the ICM temperature distribution
of A2744 to detect a clear discontinuity at the location of the radio relic.
This suggests that the cluster has undergone strong shock heating by mass
accretion along the filament.
