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I once read that the solar wind is more or less blowing a "bubble" into the interstellar medium. However, the numbers I found while trying to verify this don't give me a clear picture yet:

What I did not find was the density of the interstellar medium directly around the solar system. I know that the solar wind is interacting with the interstellar medium, which is responsible for the termination shock, but I'm wondering if the density difference is large enough that one can say that the sun is actually blowing a "bubble" into the interstellar medium.

So, is the density inside the heliosphere much less than directly outside of it?

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At the moment, the Solar System is inside the Local Interstellar Cloud (which is itself within the Local Bubble). The LIC has a neutral hydrogen number density of $\sim0.1\text{ cm}^{-3}$, which is a bit lower than the mean galactic neutral hydrogen number density. The Local Bubble itself is less dense than the LIC, by about one or two orders of magnitude. On the whole, this region of space is less dense than the ISM, on average.

So, if we take atomic hydrogen density to be a good benchmark, then the LIC and surrounding regions are in fact less dense than the Solar System on average.

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