Earnest Guest said:I'm not sure what all that has to do with the estimation of cluster gas mass from X-Ray radiation. Could you connect the dots for me?
I don't want this discussion to devolve into a MOND vs LCDM discussion because I don't believe in either, but as long as you brought up failures, perhaps you should do some reading about LUX, the LHC and the Standard Model of Quantum Physics. LCDM works great except for the part where there's no candidates left for dark matter particles. Short story: if it existed at any of the possible energy levels, we would have found it by now in the LHC. If it interacted with matter, it would have sparked up the tank at LUX.Torbjorn_L said:Are you asking me about 'all that' (figures for rapid reading)? My comment should be self explanatory, but I'll repeat:
1. There are many clusters, so presumably many mutual failures in tests of MOND.
2. LambdaCDM is better than MOND or any other theory on structures at all scales, including those that MOND was ad hoc constructed to do a fair job on. (So why bother with the failures?)
Okay. But Newton's second law of motion is one of those things that is true by definition. It is a definition of what we mean when we used the word "force" in a Newtonian context. I don't think it's possible to get it wrong within the regime where Newtonian mechanics holds, which it definitely does here.Earnest Guest said:Don't put words in my mouth. I mean the Second Law of Motion isn't accurate. The failure of MOND is related to their attempt to fix gravity, which works just fine.
If you have the volume of the gas, you can calculate the pressure. This requires some assumptions about the extent of the cluster along the line of sight. One common assumption is to just assume it's spherical.Earnest Guest said:OK, so then (1) how do you calculate the pressure and (2) will doubling the pressure double the temperature?
Sort of. A self gravitating cloud of gas increases in temperature as it releases energy. This is why stars are hot, for example. As the cloud releases energy, it collapsed in on itself, reducing is volume and increasing its pressure. Because there is now more matter in a smaller volume, the gravitational attraction between the atoms in the gas also increases.Earnest Guest said:Yes, I see that now, but I still can't get my head around this basic physical fact: if the energy is not renewed, then the X-Ray radiation will cool down to the CMBR. Why do we assume that the radiation is from braking (which is a one-time energy output) and not from the pressure exerted on the gas by gravity (which would be a constant source of energy)?
So to wrap it up, the P = n k T relation isn't needed because the flux and the temperature can have only one density and you simply multiply that density by the volume to get the mass. So if you doubled the pressure, you'd double the flux, but the temperature would stay the same?Chalnoth said:You can slow or stop the collapse by having some process dump energy into it. Stars stop collapsing for this reason: the nuclear furnace at their core provides a steady source of information. Presumably the formation of galaxies within a cluster likewise slow the collapse of the cluster gas, particularly when AGN's turn on.
Not quite. As I said earlier: it depends upon how the pressure is doubled. Would this be an isothermal process? An adiabatic process?Earnest Guest said:So to wrap it up, the P = n k T relation isn't needed because the flux and the temperature can have only one density and you simply multiply that density by the volume to get the mass. So if you doubled the pressure, you'd double the flux, but the temperature would stay the same?