TauZero , 11 months ago

As a quick calculation using the Boltzman formula:

<pre style="background-color:#ffffff;">
<span style="color:#323232;">E = 3/2 k_B T
</span>

Say we imagine that the entire kinetic energy of bulk material from Earth (let’s say iron) impacting the star at 10000km/s is converted into thermal kinetic energy of individual iron atoms (atomic weight 56).

<pre style="background-color:#ffffff;">
<span style="color:#323232;">1/2 m v**2 = 3/2 k_B T
</span><span style="color:#323232;">T = 1/3 m v**2 / k_B
</span><span style="color:#323232;">k_B = 1.38e-23 J/K
</span><span style="color:#323232;">m = 0.056 kg / 6.02e23
</span><span style="color:#323232;">v = 1e7 m/s
</span><span style="color:#323232;">T = 1/3 * .056/6.02e23 * 1e7**2 / 1.38e-23
</span><span style="color:#323232;">
</span><span style="color:#323232;">T = 225 GK
</span>

Looking at the black body temperature chart that 225 gigakelvin corresponds precisely to gamma rays from neutron star collisions.