We present a systematic analysis of 43 nearby galaxy groups (kT500 = 0.7–2.7 keV or M500 = 1013–1014 h−1 M☉, 0.012 0.15 r500 and are consistent with a "universal temperature profile." We present the K–T relations at six characteristic radii (30 kpc, 0.15 r500, r2500, r1500, r1000, and r500), for 43 groups from this work and 14 clusters from the Vikhlinin et al. (2008) sample. Despite large scatter in the entropy values at 30 kpc and 0.15 r500, the intrinsic scatter at r2500 is much smaller and remains the same (∼ 10%) to r500. The entropy excess at r500 is confirmed, in both groups and clusters, but the magnitude is smaller than previous ROSAT and ASCA results. We also present scaling relations for the gas fraction. It appears that the average gas fraction between r2500 and r500 has no temperature dependence, ∼ 0.12 for 1–10 keV systems. The group gas fractions within r2500 are generally low and have large scatter. This work shows that the difference of groups from hotter clusters stems from the difficulty of compressing group gas inside of r2500. The large scatter of the group gas fraction within r2500 causes large scatter in the group entropy around the center and may be responsible for the large scatter of the group luminosities. Nevertheless, the groups appear more regular and more like clusters beyond r2500 from the results on gas fraction and entropy. Therefore, mass proxies can be extended into low-mass systems. The M500–T500 and M500–YX,500 relations derived in this work are indeed well behaved down to at least 2 ×1013 h−1 M☉.
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