Significance of Rotational Kinetic Energy in space

Rotational kinetic energy is always considered to be a very petty quantity, and for good reason too. Our sun only has about 1.5∗1036 Joules of rotational kinetic energy. Our sun outputs 3.8 ∗ 1026 Watts of power and it it were to use it’s rotational kinetic energy, it would stop spinning in just 125 years! This might be a very convincing argument for showing the pettiness of rotational kinetic energy, but it can be quite significant in some circumstances circumstances.

When a star dies by exploding into a supernova, it has 3 choices: white dwarf, black hole, a neutron star. The procedure of selecting its afterlife is not in the scope of this article, though ` is a great to-the-point explanation on that topic. A little information on the formation of neutron stats:

When a star like our sun dies(but over 10 times more massive), all of its mass “falls in” as gravity takes over. When it falls in, the gravitational potential energy of the mass gets converted into kinetic energy, and all the mass speeds up while falling to the core, a very basic concept. What’s not so intuitive is that the density at the centre becomes so concentrated that all the mass literally BOUNCES OFF into space with velocities in the order of 10,000 km/s. Not only does the star lose a colosall amount of mass, it also loses an immense amount of energy in the form of kinetic energy that the (bounced off) mass carries away. The star then becomes a neutron star, it is condensed into a sphere having a mere 10km radius, but saying that the neutron star has an IMMENSE amount of energy is still an understatement.

Apart from the energy emitted on formation, these stars also have a very high power output in the form of loads and loads of radiation. The crab pulsar(a neutron star) outputs energy at a rate 100,000 times that of our sun (link), this is truly an incomprehensible number. But what is quite noticeable is that the sun has about 5 BILLION times the surface area of this neutron star, it is a well known fact that stars emit energy due to deuterium(hydrogen) fusion at the surface, so how does it emit so much energy with such a small surface area? The secret lies in a different source than just hydrogen fusion (in fact, neutron stars are mostly made of iron), the real deal is in the spin of this neutron star.

These neutron stars have extremely fast rotations, the fastest neutron star rotates about 700 times in 1 second. On the equator, the speeds reach 25% the speed of light. This clearly indicates that they have an enormous amount of rotational kinetic energy, and in fact, this amount is a quite significant part of the total power output.

How the rotational kinetic energy is converted to other forms of energy and radiation is not a mystery anymore. In brief, the pulsar(the neutron star) is spinning so fast, that its heart sends out amazingly powerful stellar winds. These winds combined with the tremendously powerful magnetic fields that it generates excite and accelerate photons to thousands of Giga ElectroVolts of energy. But this phenomenon has a toll on the star’s rotation, rotational kinetic energy being converted into radiation directly means that the star’s rotation is slowing down. Taking the example of the crab pulsar (another neutron star), this neutron star emits 150,000 times the energy our sun does as previously stated above. The period of rotation of the crab pulsar in October of the year 1999 was 33.5 milliseconds, the important fact here is that this period was increasing everyday by ap- proximately 36 nanoseconds. This almost exactly translates to the amount of energy being released if we perform the calculation:

The key point to notice here is that almost ALL of the energy comes from the rotational kinetic energy. This energy is a very large number and s

uggests that the neutron star will stop in about 10 centuries if the rate remains the same. But, the rate of slowing depends on several properties apart, and also on what scientists call irregular ‘glitches’, in short, crab pulsar will not be stopping any soon thanks to its gargantuan rotational kinetic energy reserve. Anyone willing to go down this rabbit hole may use this resource.

Picture credit: Chandra X-ray Observatory, Harvard University