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I have read on the webpage of NASA that there is a massive hot gas halo around our galaxy. Its temperature is between 100,000 and 1 million Kelvins or more. I do not understand why is it so hot. The temperature of the cosmic background radiation is only 2.7 Kelvins. The stars of our galaxy warm it up or one (or more) process in the gas?

UPDATE: The question is about circumgalactic medium (CGM) not about the gases within our galaxy.

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The cosmic background microwave radiation is composed of photons which interact with the electromagnetic field. The interstellar medium is composed of matter in various forms, as is this gas halo. Locally, where the halo is the interaction of the gas with the mwb is weak and the gas cannot be "cooled" by it . At most the microwaves will be dispersed within the gas and disappear as an independent observable. – anna v Oct 23 '12 at 7:09
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The article linked in the question refers to the hot gas surrounding the galaxy, in what is known as the circumgalactic medium (CGM). The CGM, in turn, draws in gas that has undergone gravitational collapse and shock-heating during the process of structure formation.

Older version of answer concerning the gas within the galaxy:

The hottest regions of the galaxy are most likely heated by supernovae. A classic paper that describes how the three thermal phases of the interstellar medium ("cold," "warm", and "hot") are maintained, and invoking a connection between the hot phase and supernovae, is McKee and Ostriker 1977. See also this page for some helpful visuals. The high-velocity gas ejected in a supernova explosion collides with the gas in the surrounding interstellar medium, shocks, and heats up to millions of Kelvin.

Finally, some of the supernova-heated gas can flow back out of the galaxy and into the CGM, causing it to harbor metals which could only be produced by stellar evolution.

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You want to read this. A quick excerpt from it:

The ISM (Interstellar Medium) is usually far from thermodynamic equilibrium. Collisions establish a Maxwell-Boltzmann distribution of velocities, and the 'temperature' normally used to describe interstellar gas is the 'kinetic temperature', which describes the temperature at which the particles would have the observed Maxwell-Boltzmann velocity distribution in thermodynamic equilibrium.

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