Editing 2413: Pulsar Analogy

{{comic
| number    = 2413
| date      = January 18, 2021
| title     = Pulsar Analogy
| image     = pulsar_analogy.png
| titletext = The #2 cause of astronomer hand injuries is trying to do vector math when the second axis points off to the right.
}}

==Explanation==

{{w|Pulsar}}s are a kind of old, shrunken, fast-spinning star.  They are usually {{w|neutron stars}}.  They no longer shine in all directions, but instead produce beams of radiation out of their magnetic poles, which blip by us in rapid pulses as they spin.

[[Ponytail]], an astronomer in this comic, explains a pulsar's fast rotation with an analogy about a tape measure retracting.  The analogies that Ponytail picks are incredibly poor ones, as seen in [[2094: Short Selling]].

Since the analogy does result in something that spins, the reader might think that, while they don't immediately see how it helps in understanding pulsars, they're willing to reserve judgment to see what is then done with the analogy; Cueball's response may suggest this sort of wait-and-see attitude.  However, the analogy is likely to be useless or misleading, as the tape measure starts to rotate because the retracting tape is not moving only in a radial (in/out) direction. As a star collapses into a pulsar, its natural rotation rate is greatly amplified by its shrinking moment of inertia.

Further elaborations of the analogy, rather than clarifying matters, are successively more surreal.  More misleading than the tape-measure is the idea of a laser measure being "exactly" like the emissions of a pulsar, which, although both pulse, are produced in entirely different ways and are at best simply helping the mind hold the concept.

When a tape measure retracts, the part of the tape outside the tape measure is not going directly towards the tape measure's center but rather towards a hole in the side. This means the tape possesses some angular momentum relative to the tape measure. In addition, when the tape measure retracts, the part of the tape inside the tape measure rotates around a spool (which pulls the part of the tape outside the tape measure inside), so it also has angular momentum relative to the tape measure. When the tape is completely retracted, the tape can no longer rotate relative to the tape measure. Because of the conservation of rotational momentum, the tape measure will start spinning at this point.

While pulsars also rotate quickly due to the conservation of angular momentum, the exact {{w|Pulsar#Formation,_mechanism,_turn_off|mechanism}} is completely different. Pulsars are formed when stars collapse due to no longer performing enough fusion to produce enough heat and energy to cancel out gravity. This causes the star to contract, which causes its mass, on average, to be closer to its axis of rotation, which causes the rotational inertia (also called the moment of inertia) to decrease. If the star's angular velocity stayed constant, this would cause the angular momentum to decrease, so the star's angular velocity must increase in order to offset the decrease in rotational inertia, i.e. the star (which is now a pulsar) spins faster. This is demonstrated [https://www.youtube.com/watch?v=_eMH07Tghs0 here]. This method requires an initial rotation, which comes from the star. (The star's rotation comes from the dynamics of the gas cloud which forms the solar system in the first place.)

Some tape measures have a built-in {{w|laser line level}} and others have a built-in {{w|laser rangefinder}}. Pulsars emit electromagnetic radiation out of their magnetic poles, which is similar to a laser, but unlike the laser of a tape measure, the pulsar beam is emitted through the axis of the magnetic field.  The pulsing nature of a pulsar comes from when the axis of rotation is not precisely aligned with the axis of the magnetic field, and the location of the viewer as the beam sweeps by.  In the tape measure analogy the beam is at a right angle to the axis of rotation, so as long as the viewing angle isn't parallel with the rotation axis, the viewer would see the laser increase and decrease periodically as it the rotating tape measure points towards or away from the viewer.

While pulsars do demonstrate incredible {{w|Quake_(natural_phenomenon)#Starquake|starquakes}} and rotational {{w|Glitch_(astronomy)|glitches}}, neutron degeneracy is part of the mechanisms in which they are originally formed. During the formation of a neutron star, usually in the form of an initial inward implosion, the neutron degeneracy (basically the impossibility of neutron of occupying the same space because of fundamental constraints in physics that are studied by quantum mechanics) stops the implosion and redirects the shockwave outwards, thus producing a Supernova explosion. The analogy is with a tape measurer that hits a hand (the constraint) during its rapid rotation due to its retracting tape (the implosion) thus redirecting part of the energy towards the hand (the supernova energy is redirected outside).

However, astronomers do not usually let go of laser tape measures frequently, so they are probably not the top cause of any type of hand injuries, contrary to what Ponytail said.

The title text mentions the {{w|right-hand rule}} in three-dimensional space. In a typical 3D coordinate system the Y-axis will point counterclockwise to the X-axis when looking down from the positive Z-axis.  In academia, students are often taught to remember a number of mathematical conventions by using their actual physical right and left hands to align the axes.  When the axes are in a different order, the left hand can be used instead of the right, but there are a number of common operations in engineering and physics that use the {{w|cross product}} in systems where the first axis might point in absolutely any direction relative to the viewer.  Using the hand rules, the thumb is aimed along the first axis, the forefinger along the second, and the middle finger along the third — all at ninety degrees.  So, when the first axis points off to the right, the right wrist is torqued to its full extension to make the thumb point that way while the other two fingers don't.  During exams, students can be seen performing this feat.  People who learn cross products early in their life may develop other approaches for remembering these things, that don't stretch the hands as much, but then adopt the common approach once taught it. This rule has been previously mentionned in [[199: Right-Hand Rule]].

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Cueball and Ponytail are standing next to each other.]
:Cueball: Why do pulsars spin so ''fast?''
:Ponytail: Hmm, let me think of an analogy...

:[A tape measure is retracting above Ponytail's head. To the right of her head a tape measure is spinning rapidly.]
:Ponytail: You know how when you retract a tape measure and let go, it leaves it spinning?
:Ponytail: It's like that.
:Cueball (off-panel): Oh, I see.

:[A tape measure with a laser instead of a measuring tape is spinning slowly.]
:Cueball (off-panel): And if the tape measure is the kind with a laser level, that's the beam of radiation?
:Ponytail (off-panel): Exactly!

:[Cueball and Ponytail are walking next to each other.]
:Ponytail: And when the tape whips around and smacks your hand, that's the neutron degeneracy shockwave.
:Cueball: Sounds painful!
:Ponytail: Top cause of astronomer hand injuries.

{{comic discussion}}
[[Category:Astronomy]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]