- #1
zhermes
- 1,255
- 3
I'm wondering how to calculate the neutrino diffusion time-scale from a neutron star---just to an order of magnitude or so accuracy.
Based on a 10km, 1.4 solar-mass star, and a cross section [tex] \sigma_{\mu n} \approx 10^{-42}[/tex] cm^2; I found the mean-free path to be
[tex]l \approx 10^{14}cm[/tex].
Then using
[tex] t \approx \frac{R^2}{l c} = 10^{-12} s [/tex]
which is about 13 orders of magnitude too small... why?
The neutrinos are so relativistic that using the speed of light should be fine.
One clear problem is that in the limit that [tex]l \rightarrow \infty[/tex], the time-scale goes to zero----while it seems like it should simply approach R/c.
I was looking at a powerpoint (i.e. without thorough explanations), which showed a timescale
[tex]
t_D = \frac{3}{\pi^2} \frac{\partial Y_L}{\partial Y_\nu} \frac{R^2}{c l_{\nu e}}
[/tex]
Can anyone explain this?
Based on a 10km, 1.4 solar-mass star, and a cross section [tex] \sigma_{\mu n} \approx 10^{-42}[/tex] cm^2; I found the mean-free path to be
[tex]l \approx 10^{14}cm[/tex].
Then using
[tex] t \approx \frac{R^2}{l c} = 10^{-12} s [/tex]
which is about 13 orders of magnitude too small... why?
The neutrinos are so relativistic that using the speed of light should be fine.
One clear problem is that in the limit that [tex]l \rightarrow \infty[/tex], the time-scale goes to zero----while it seems like it should simply approach R/c.
I was looking at a powerpoint (i.e. without thorough explanations), which showed a timescale
[tex]
t_D = \frac{3}{\pi^2} \frac{\partial Y_L}{\partial Y_\nu} \frac{R^2}{c l_{\nu e}}
[/tex]
Can anyone explain this?