Moreover, I have considered clusters with evidence of a large cooling flow and the Coma cluster ROR: rpn00, exposure time: In Table 1 , I quote the results obtained by fitting the azimuthally averaged profiles of the surface brightness between 0 and R out , where the brightness value is larger than three times the uncertainty in that radial bin. I perform the following fits see Fig.
Best-fitting results using the models discussed in the text. The core cooling radii are in The values for the F-test represent the level of significance. Where a two-phase model provides a significantly better fit, I find that the F-test shows no statistical improvement with a six-parameter fit cf.
Table 1. Therefore, I use in the following considerations the best-fitting results obtained with a five-parameter fit, i. This is not in contradiction with the present observational results. Allen quotes the cooling radii obtained from deprojection analysis of 30 cooling flow clusters images. The distribution of the ratio, r c r cool , has a median value of 1. For the clusters in exam here, I measure a r c r cool ratio of 1. I remind, however, that I am using a different definition of r cool than the one adopted in the standard spatial analysis: in the latter, r cool is the radius where the cluster cooling time first exceeds the Hubble time, whereas in this work r cool defines the boundary of the central cool phase of the gas.
The use of this physically meaningful model allows us to directly handle each of the two gas distributions, one that describes the profile of the gas related to the cooling flow and the other that model the ambient gas.
As shown above, there is no statistical justification for using the six-parameter fit. Therefore, I consider hereafter the case r c r cool. In the equations above, both the function f and F have to be smaller than 1 by definition. Their behaviour, however, depends strongly upon X , the radius in unit of r cool up to where the outer phase extends and can be represented with a single temperature.
Plot of the functions f diamonds and F squares versus X. The dashed lines represent A, the dotted ones A The error-bars are overplotted to each point. The agreement is remarkably good with the results of Markevitch and collaborators and White, which assume a two-phase gas for their spectral model in a way similar to the one I have adopted for the physical framework described above. Note that Markevitch et al. On the other hand, the disagreement with the results of Allen and collaborators can be explained with the more complex model that they adopt, where an absorption intrinsic to the cluster is combined with the cooling flow only.
The errors are at the In the observational data, these come from the propagation of the error on the temperature estimates. The error on the F function is computed after Monte Carlo fit of the original surface brightness profile. References for the observational data:  Allen et al.
The typical relative errors on the ratio of luminosities, gas and total masses are of about 1 per cent and come from Monte Carlo replications of the observed surface brightness profile and emission-weighted temperature.
I have presented a new analytic formula to model the total surface brightness profile of clusters of galaxies where a two-phases intracluster gas can be assumed. This scenario is consistent with the present results of spectral analyses of the central regions of clusters that harbour a cooling flow. The use of this formula allows to properly disentangle the contribution of the cooling flow to the cluster emissivity using only the spatial distribution of the X-ray photons. After removing the contamination from the cooling flow, I show how some relevant physical parameters are affected, like, for example, the ambient gas temperature see Table 2.
In a forthcoming paper, I will investigate the systematic changes in the temperature, luminosity and mass cf. Table 3 of a sample of clusters of galaxies and how these variations affect the relations among these quantities. I thank Anna, Sara and Carlo.
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I acknowledge the support of the Royal Society. Andy Fabian and David White are thanked for a useful reading of the manuscript, and the anonymous referee for comments which improved this work. Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Sign In or Create an Account.
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Matter and Energy in Clusters of Galaxies. Bowyer, Stuart; Hwang, Chorng-Yuan.
The insignificance of "heating flows" in "cooling flow" clusters of galaxies
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