Tell me about the physics of material "falling onto a neutron star and emitting hard x-rays"

TauZero , 11 months ago

Roche limit is not really relevant here. That’s for orbiting bodies, like a satellite around a Jupiter-like planet whose orbit spirals inward due to tidal forces, and eventually crosses the Roche limit, whereby the moon disintegrates into a cloud of rocks that spreads out and forms a ring. Yes, the hyperbolic orbit of the collision trajectory here is a “type” of orbit, but really the video is about the collision itself. There is not enough time for the planet to meaningfully disintegrate under the neutron star’s gravity. “What’s that? The ground is kinda shaking. Could that be the tidal force from that neutron st-ACK!!!”.

In the video you can see the surface of the Earth bulge out towards the star under its gravity in the last second, but most of the kinetic energy of the explosion is imparted by direct physical interaction (i.e. electromagnetic) between the matter of the earth and the matter of the star, and in particular between the matter of the earth that has already been accelerated and the matter of the earth lying farther out.

Or at least it would be if the impactor really was just a chunk of iron with the density slider cranked up. This fluid simulator can’t imagine anything else of course, but you are right that it remains a question of whether a neutron star or a black hole could impart any kinetic energy onto the greater earth at all. Maybe it will just pass through and leave a circular hole, sweeping the material in front of it onto itself. The tunnel would immediately collapse, and the crust would be messed up from tidal sloshing, but maybe the ball of the earth itself will remain intact.

The hard x-rays I believe is a reference to thermal radiation of infalling matter. Just like a bullet that hits a wall while staying intact is hot to the touch because its kinetic energy got 100% converted into heat, or a meteoroid that hits the Moon creates a flash of light visible from Earth because for a second the cloud of collision debris is as hot as the filament of a lamp, the earth material impacting the surface of the star gets really hot. The impact velocity is at minimum the escape velocity of the star, which is thousands of km/s, which means the peak of thermal radiation is in the x-ray range.

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.