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Fig. 5.

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Visual representation of the problem of binning surface-brightness (SX) bins into temperature-profile (kT) bins. Left: SX profile of RXJ0856.1+3756 in the [0.3–2] keV band, extracted in 3 . $ \overset{\prime \prime }{.} $3 circular radial bins. Centre: Signal-to-noise ratio (S/N) in each bin of the SX profile as a function of the bin index. Right: Innermost vs outermost SX bin indexes, overplotted on the S/N obtained from placing the range of SX bins indicated by the axes into one single kT bin. The green line delineates a 30σ S/N requirement. Two SX example binning schemes are also shown (solid step curves). These correspond to a fixed binning of two input SX bins (small fixed width steps), and a logarithmic binning of the SX profile (continuously increasing step size).

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