To investigate the spatial distribution of the intracluster medium temperature in galaxy clusters in a quantitative way and probe the physics behind it, we analyze the X-ray spectra from a sample of 50 clusters that were observed with the Chandra ACIS instrument over the past 15 years and measure the radial temperature profiles out to 0.45r500. We construct a physical model that takes into consideration the effects of gravitational heating, thermal history (such as radiative cooling, active galactic nucleus feedback, and thermal conduction), and work done via gas compression, and use it to fit the observed temperature profiles by running Bayesian regressions. The results show that in all cases our model provides an acceptable fit at the 68% confidence level. For further validation, we select nine clusters that have been observed with both Chandra (out to ≳0.3r500) and Suzaku (out to ≳1.5r500) and fit their Chandra spectra with our model. We then compare the extrapolation of the best fits with the Suzaku measurements and find that the model profiles agree with the Suzaku results very well in seven clusters. In the remaining two clusters the difference between the model and the observation is possibly caused by local thermal substructures. Our study also implies that for most of the clusters the assumption of hydrostatic equilibrium is safe out to at least 0.5r500 and the non-gravitational interactions between dark matter and its luminous counterparts is consistent with zero.
