In your post, you stateThis is actually a really cool question. My guess is that the intracluster medium is probably sparse enough that one wouldn't need to worry. A little back of the envelope math here:
dearplanetaryastronomermike. blogspot.com/2009/03/dark- matter-stars-and-gas-wheres. html
"Now, this gas is actually the material from which stars are created. Its most ubiquitous form throughout a galaxy is as a hot diffuse medium (somewhere around 10,000K)"
"Eventually, a whole cluster of galaxies is created, surrounded by a massive cloud of unused, superheated hydrogen gas (in the incredibly hot 100 million K range) known as the intracluster medium (ICM)."
Could human spaceships fly through these? I guess they may be hot, but the density is very low, so how much heat would the spaceship absorb and could it radiate the heat away?
- Let's say there's 500 galaxies in a cluster, each at around 10^12 solar masses (or about 2 x 10^45 g) so that gives us a total mass of around 10^48 g for the cluster's galaxies. The Intracluster Medium (ICM) should be about 10 times that, or about 10^49 g.
- However, the cluster is huge...if the milky way is roughly 25 kiloparsecs in diameter, a fair estimate for the cluster size is on the order of a megaparsec in radius. That translates to a volume of roughly [(10^6)(3 x10^18 cm)]^3 = 3 x 10^73 cm^3. That leaves us with a pretty low density of about 4 x 10^-25 g/cm^3. We throw in Avogadro's number for good measure, and assume pure hydrogen, and we end up getting about 1 hydrogen atom for every 5 cm^3...it's actually kinda weird how those huge numbers end up canceling so well.
So, yeah, a given atom will be crazy energetic - temperature scales linearly with kinetic energy - but there's so few of them I don't think it would be a huge issue heat-wise. The radiative constant of the ship should easily compensate for the occasional high-energy atom.
I think the concern would be more of a sputtering problem - at these energies, I'd worry about slow ionization of the ship's outer hull. Each hyper-energetic hydrogen atom the spaceship ran into might strip molecules from the crystal lattice of whatever alloy the spaceship was composed of. Sometimes it'll strip multiple molecules per collision, sometimes none, so let's just do an order of magnitude estimate and say 1 molecule stripped per collision. At 1 hydrogen atom per 5 cm^3, it doesn't seem like a big deal, but I think as it starts to cover spaceship-sized distances it might be an issue. Let's consider this in terms of cross-section:
For each square centimeter of spaceship hull surface hurtling through the cluster, a molecule of the hull will be stripped every 5 cm. If we want to travel from the edge to the center, we're talking about 3 x 10^24 cm, or roughly 6 x 10^23 molecules stripped. Again, weird that we just happen to hit on Avogadro's number again - roughly 1 mole of material per square centimeter will be stripped.
Assuming we're talking about, say, iron here, that's a molecular weight of 56, so 56 g/mole. So, behind each square centimeter of hull, 56 grams will be stripped traveling to the center of the cluster. With iron at a density of 8 g/cm^3, that would mean a 7 cm thickness would be stripped traveling to the center.
So, I guess the answer here is that if you add 7 cm of hull thickness (at least to the front of your spaceship) as an ablative shield, you should be okay. You actually probably want to double that, since presumably you'd like to leave the cluster at some point, too.