If hot gaseous galactic halo coronae contain multi-million-Kelvin plasma, then why wouldn't such gas undergo fusion, and thereby generate gamma-rays ? Prof. Lawson claims:

 

[math]P \approx 1.4 \times 10^{-34} n^2 T^{1/2} \frac{watts}{cm^3}[/math]

 

[math]L = P V \approx \frac{P V^2 m_H^2}{V m_H^2} watts \approx \frac{ 1.4 \times 10^{-34} M^2 T^{1/2} }{ \frac{4 \pi}{3} R^3 m_H^2 } watts [/math]

 

For galaxy clusters, the estimated fusion luminosity, of the cluster halo gas, could be considerable:

 

[math]\approx 4 \times 10^{11} \left( \frac{ \left( \frac{M}{100 T M_{\odot}} \right)^2 \left( \frac{T}{100 MK}\right)^{1/2} }{ \left( \frac{R}{Mpc} \right)^3 }\right) L_{\odot} [/math]

 

[math]\approx 40 \left( \frac{ \left( \frac{M}{100 T M_{\odot}} \right)^2 \left( \frac{T}{100 MK}\right)^{1/2} }{ \left( \frac{R}{Mpc} \right)^3 }\right) L_{*} [/math]

 

where [math]L_{*} \equiv 10^{11} L_{\odot}[/math] is a characteristic (big, spiral) galaxy luminosity. Prof. Sarazin seems to say, that the total x-ray luminosity, of galaxy cluster halo gas [math]\approx 10^{44.5} \frac{erg}{s} \approx L_{*}[/math]. So, this estimate, for fusion-generated luminosity, could account, for observed luminosities, or even exceed the same.

 

 

 

Against this, because collisions in the IGM would be rare, perhaps inter-mediate fusion products (D,T,He-3) would decay back into H, before they re-collided, and fused into He-4 ?

 

 

 

 

Were the fusion to occur, then the mass production rate, of He-4, in galaxy cluster coronae, would be:

 

[math]L \times \frac{m_{He}}{4.23 \times 10^{-12} J} \approx \frac{4 GM_{\odot}}{Gyr}[/math]

 

times all the factors in the parentheses. In the age of the universe (10 Gyr), that translates to [math]\approx 40 G M_{\odot}[/math], implying a metallicity of [math]\frac{4e10}{e14} = 4e-4[/math], which is negligible, and probably allot less than the errors in estimates of cluster halo gas metallicity.

 

 

 

Q: does fusion occur, in gaseous galaxy (cluster) coronae ?

 

more simply, our sun converts 10% of its mass to He-4, in 10Gyr.

 

So, 4e11 L_sun ----> 10% x 4e11 M_sun / 10 Gyr = 4e9 M_sun / Gyr

 

oops: L* = 1e10 L_sun

If hot gaseous galactic halo coronae contain multi-million-Kelvin plasma, then why wouldn't such gas undergo fusion, and thereby generate gamma-rays ? Prof. Lawson claims:

 

[math]P \approx 1.4 \times 10^{-34} n^2 T^{1/2} \frac{watts}{cm^3}[/math]

 

[math]L = P V \approx \frac{P V^2 m_H^2}{V m_H^2} watts \approx \frac{ 1.4 \times 10^{-34} M^2 T^{1/2} }{ \frac{4 \pi}{3} R^3 m_H^2 } watts [/math]

 

 

I don't see L=PV in the link; L has a different definition. Where does that come from? Isn't that just total energy? Why are you using [math]{ \frac{4 \pi}{3} R^3 [/math] for a shell volume?

 

I don't follow your other calculations at all. It looks like you're using total mass instead of coronal mass.

L = luminosity = energy per time

 

P = "luminosity density" = energy per time per volume

 

standardized definitions would be better; if "P" = "power" (J / s), then "P" = "L" = energy per time...

 

for want of worthier symbols, i stuck w/ the "P" from the link, and tossed in "L" from astronomy

 

conceptually, the former is the spatial density of the latter (Power per volume vs. Power total)

 

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Hypothetically, if fusion could occur, in diffuse space plasmas; then those plasmas would accumulate the products of fusion, such as D,T. So, those plasmas would not necessarily be "pristine" / "primordial", but would have undergone some fusion phenomena. In some sense, the whole of the universe, is like the inside, of a vast cosmic-scale star, some super-diffuse super-O/B/A super-blue giant. D/T/He3/He4 could have been accumulating therein, for the lifetime of the universe. Observed abundances of such intermediate fusion nuclei need not indicate pristine/primordial/unprocessed abundances, from the Big Bang.