‘Every Pulsar has a Story’… Novel Insights to Pulsar Phenomenology through Glitch and Timing Noise Analysis

This is an image of a pulsar, which is a rotating neutron star. It is emitting electromagnetic energy while spinning.
Rotating Neutron Star (Pulsar) emitting energy — Astronomy Magazine

Neutron stars have long been an exciting celestial body for astrophysicists and astronomers trying to understand the cosmos. Neutron stars are most commonly seen as pulsars, which are highly magnetized rotational neutron stars. Observations of pulsars, whose pulses are produced by a narrow beam of coherent radio emissions reveal the timing noise and pulsar glitch rotational anomalies. Such a serendipitous discovery such as pulsars are detected using radiotelescopy, through which their signatures are registered. From Earth, Pulsars appear as blinking stars, although this appearance is truly an illusion from the emission of energy on the polar sides of the pulsar appearing as light. Currently, astronomers and astrophysicists have discovered close to 3,000 pulsars, with pulsar PSR J0108–1431 being the closest observable pulsar to Earth. With each pulsar releasing radio waves from each pole, they exhibit different rotations. This phenomenology refers to how each pulsar is unique as its rotational manifestation is not constant. There are normal pulsars that exhibit normal rotation speeds, and millisecond or fast pulsars that rotate within the millisecond, or at exponentially swifter speeds. Their rotations are also variable due to a pulsar glitch, which is an astronomical phenomenon in which the rotational frequency of pulsars sporadically increases, the cause of which still remains unknown. Studies of pulsars, understanding their glitch morphologies, glitch populations, determining phenomenology, and conducting rotational and/or substructural analyses are all studies that can aid in understanding the obscure astrophysical natures of pulsars. Understanding pulsars will provide insights into neutron star interiors, pulsar glitch causes, superfluidity, and timing noise calculations. This potential for substructure is extremely important in elaborating upon existing astrophysics principles.

Pulsars, discovered by Antony Hewish and Jocelyn Bell Burnell in 1967, exhibit strong magnetic fields, thus exuding electromagnetic energy, naturally-induced spin rotation, and extreme densities. Pulsars have been discovered in our galaxy, and are additional exclusively found in different sizes of Magellanic Clouds, two irregular dwarf galaxies visible within the Southern Celestial Hemispheres, and Local Group Milky Way Galaxy orbits. These clouds are anomalous and hold over 30 billion stars, and exhibited a massive supernova detonation in 1987, which was the brightest in 300 years. The byproducts of the explosion are still being explored amidst its rapid expansion and evolution. Pulsars, in specificity, are derivatives of neutron stars, whose physiology is described as:

Current theory and equations of state suggest that neutron star radius decreases with increasing mass and that the maximum possible mass is around 3M⊙. Pulsars are believed to consist of two main components: the crystalline crust and a liquid neutron interior, with the boundary defined by the radius at which the density is that of nuclear matter (2.7 x 10¹⁴ g cm-³). The crust is an extremely rigid lattice of iron nuclei; at the neutron drip point (4 x 10¹¹ g cm-³), nuclei become embedded in a neutron fluid formed when electrons penetrate the most massive, unstable nuclei. This transition gives way to a neutron superfluid with a smaller proton superfluid component, which rotates through an array of discrete vortices, and importantly, can rotate decoupled from the rest of the star. At the center of the neutron star, the behavior is matter is poorly understood and may form a solid core, or dissolve into an elementary state of quarks and gluons. The diversity and extreme densities of pulsars effectively make them a crucial laboratory for the high-density matter.

In order to properly observe young non-recycled pulsars with spin-down energies 10³⁵ erg/s (Johnson, Smith, Karastigou, Kramer), radiofrequency (RF) oscillation rate comprehension or gamma-ray spectroscopy forms is used, typically in 1GHz to reduce any possible complications in pulsar ‘sight’. Pulsars are a type of neutron star, a celestial object created by supernovas of massive stars, with the ferrous core of what was once a stable medium to high mass star becomes the pulsar by densely collapsing, and the neutron star is sustained by the localized gravity created by neutron degeneracy pressure. Neutron star’s morphology resembles that of scaled atomic nuclei, as it’s the average density of 6.7 x 10¹⁴ g cm-³ is almost identical to that of nuclear matter. A newborn neutron star’s opaque outer core effectively traps neutrinos, an elementary particle and neutral subatomic particle with no charge, half-integral spin, and negligible mass. The neutrinos are effectively discharged within seconds of the phase, and the energy of the neutrino remains inside of the core of the star to heat it up to 250+ billion Kelvin. Over Millenium, neutron stars cool and will eventually become inactive, but perpetually undying, becoming gelid and barely emitting radiation by discharging additional neutrinos. The core of the neutron star is it’s heart, as it holds the quantity of initial angular momentum, which is what causes the star to acquire macro rotation. The characteristic radiation emitted by Pulsars is likely due to neutron star rotation, as it's subsequent electric field catalyzes charged particles and causes them to excite in the magnetic field. This mechanism creates conical electromagnetic energy observables. It is important to note that only newly-formed pulsars can be observed through radio frequencies, due to old pulsars eventually experiencing death as they spin-down under electromagnetic torque. Highly energetic pulsars, such as PSR J0437–4715 can be determined by the medium of remains of a supernova explosion or plerion, which are pulsar wind nebulae that are found inside of supernova remnant shell locations, and is powered through the release of the pulsar wind from the central pulsar, with a nebula being an interstellar cloud of ionized gases. As they age, they shy from the galactic plane ( 200-300 km s-¹), effectively deviating locations within the galaxy, a conglomerate of compact objects, stars, and other bodies within an isolated system experiencing spontaneous increasing entropy, and are not accepting of respective nebulae as they move away from them.

It is important to note that pulsars can also be timed.

Figure 1: showing intergalactic background light frequencies graphically It has each one in different colors for indication.
Figure 1: Graphical display of intergalactic background light frequencies within the energy signature spectrum

In keeping with discovering pulsars, nearby pulsars, populations, and binary pulsar companion related cosmic structures, such as main-sequence and dwarf stars can also be observed in infrared (IR), ultraviolet (UV), and optical wavelengths, as shown in Figure 1 (not the data, but the energy classification on the graph are to be understood) above. Accretion-powered (a phenomenon in which an astronomical object gravitationally attracts more typically gaseous matter to grow and form in an accretion disk) and luminescent pulsars are discovered through gamma-ray and X-ray imaging. These surveys of pulsars typically help with discovery, but can also help in modeling substructure. Telescopy is also a commonly used device of surveying, through which observations can be made by sifting through data and searching for pulsar signals or indication. This methodology is called the Fourier transform-method and uses a uniquely-dubbed combing technique to optimize efficiency and the likelihood of correctness. This method also uses rotating radio transients (RRAT) — that are actually pulses but are considered by some to be abnormal weak pulsars with different pulse-to-pulse variability — as a reference case for classifying isolated radio pulses. Separating radio frequency interference or any other cause of incoherence of pulsar understanding is additionally vital when conducting analytical experiments of pulsars, especially in using machine learning/neural network models within the pulse de-dispersion surveyance process. Galactic electron distribution is also another determinant within a pulsar system, especially when surveying and accounting for the distribution/dispersion process, and can be used to factor and quantify the distance to a particular pulsar, such as how through an effect called parallax, along with accompanying information, Astro scientists were able to approximate that the Crab Pulsar (J0534+2200) is 7,175 light-years away.

Pulsar timing is a certain scrutinization over a pulsar, in which it is consistently monitored with regard to its spin tendencies. This regular monitoring is done, once again, by the use of tracking radio pulses. Pulsar timing is a method with longevity, as well, as it unambiguously accounts for every rotation of up to decades, allowing for the easy identification of a glitch or other sort of foreign or internal spin deviation. It can also be used to determine a dying pulsar. Timing pulsars requires a high-accuracy threshold, as they record the times of radio pulses. The timing ‘scientific’ method goes as follows: discover → observe → de-disperse → record → correct. The corrections are made to the time-of-arrival, or TOAs, that are recorded through the timing, as it is necessary to compensate Earth elliptical motion due to sun rotation ‘systemography’ (within the 3 standard methods, but this is a natural occurrence), relativistic Shapiro delay, and to optimize the quantification of the pulse. Results are also subject to the Doppler Shift in second-order special relativity (SR), an effect that is the change in frequency relative to an observer perspective, expressed as f ’= [(v + v.)/v ]f to describe the observed frequency, among other possible variables that could skew results. Pulsar TOAs can then be fitted precisely to a third-order Taylor polynomial, which encompasses the period, electromagnetic torque, and magnetic braking over time.

Timing solution expression. Sorry, this equation is too difficult to detail in words, but please use dictation!
Timing pulsar noise solution expression

The timing solution above presents a calculation to incorporate many parameters, including predicted TOAs for pulses, magnetic field permeability μ, pulsar characteristic age, magnetic field potency, and the long-term braking index which has a commonly assumed value in spin-down torque systems, or dramatic reversals. Timing solutions are extremely vital in astrophysics, although the relatively inconclusive nature of these studies make it difficult to circumvent anomalies.

But does every pulsar truly have a story? This is determined by studying possible pulsar phenomenology, which is the proposition of what makes each and every pulsar differ from one another. However, in order to qualify phenomenology, it is imperative that the phenomena behind it are understood. This includes a comprehensiveness of pulsar glitches or spin-ups, a phenomenon first detected in the J0835–4510 Vela Pulsar of 1969, which was couple years after the first pulsar was discovered. The microglitch phenomena as shown in pulsar MSP PSRJ1824–2425, display a clear discrepancy in millisecond pulsar glitches, even from young recycled pulsars, clearly deviating from the standard, especially in glitch size. More works within machine learning and statistic data-intensive research indicate that other pulsar may be capable of exhibiting this similar unique behavior of glitching. Glitch reversals are also possible underlying phenomena, in which an anti glitch occurs, which is named for its inverse spin-down effect. This phenomenon has mainly been observed specifically in magnetars and accreting X-ray pulsars, which may reveal more models in the substructure of anti glitch populations to a similar vein of micro glitches. Originally, the models built to study the pulsar proposed that the glitch was a byproduct of the rigid neutron star crust, a crystal lattice. During this event, the spin-down of electromagnetic energy, the star would have a tendency to retreat to an oblate (elliptical spheroid), which amasses considerable strain in the neutron star crust, which in turn results in a starquake — an astronomical earthquake of a star that is present in magnetars, powerful 1000x magnetic field neutron stars, and pulsars, in which the change in the massiveness or shape of a pulsar quickly disrupts pulse rate or radiation levels — , which causes a drastic change in the moment of inertia I = mr² (I moment of inertia equals mass times the square of perpendicular distance from the rotational axis of the pulsar originally) that results in the pulsar ‘glitching’. A well-known ideated theory on glitches is that the interior of a pulsar is superfluid, meaning that it is liquid that flows with zero viscosity. As superfluids rotate by means of quantized vortices that have angular momentum, as the angular velocity of the fluid at any point is proportional to vortex density, when the pulsar sping down at the electromagnetic rotational equivalent of linear force, or torque from the cone of radiation, the vorticose must relocate or terminate; plausibly, vortexes can attach to ions within the magnetic flux tubes or neutron star crystal lattice crust, via a process called ion-track pinning, which prevents the superfluid from being affected by spin-down, and store kg m²/s¹ rotational momentum that is likely to be released during a pulsar glitch.

Hydrodynamics of superfluid pulsars give new functions and definitions to glitches. The novelization of this quantum cosmology modeled by Khomenko and Haskell is now serving as a fortified blueprint for de obfuscating pulsar glitch morphological structure. The superfluid theory [elaborated on above] has accumulated the popular vote in the astrophysics and astrochemistry community, especially due to it being able to qualify the more aggravated glitches of J0537-6910, J0908, J0835-4510, and other young pulsars that feature extreme and frequent glitches. However, even with the current theories, there is no standard glitch trigger to date, effective September 8th, 2020, though it is likely that an explanation will be provided with the coming years, according to recent exposition. Three models of the possible glitch trigger for unpinning and angular momentum transfer that have strong, falsifiable, and foolproof predictions for glitches are the “snowplow” model, starquakes, and the vortex avalanche. Below is the explanation for each of these phenomenal models that offer coherent explanations to pulsar glitches.

A 3D animation of the ideated “crunchy crust” of neutron star, and squishy or solid quantum fluid in it. A lot blues, greens.
A 3D animation of the ideated “crunchy crust” of neutron star pulsars, and “squishy or solid” quantum fluid.

1. Starquakes: The pinning force on a vortex produces a shear force on the star’s crystalline lattice, which is only balanced by the crust’s elasticity. Thus, over time, as the differential rotation log increases, the crust is subjected to ever-increasing strain. Once a critical strain is released, the crust would break and the moment of inertia would redistribute, triggering a glitch event. This model is best suited for younger pulsars and smaller glitches. Similar to quakes and tectonic activity on Earth, one would expect scale-invariant statistics and possible pre-shocks/aftershocks.

2. “Snowplow” Model: As the pulsar rotates, differential lag builds up through the pinning of vortices, which prevents the superfluid from slowing; over time, vortices unpin from the interior where the pinning force is weaker, and re-pin in regions with stronger pinning force. During this process, vortices migrate outwards until, at the region where pinning force is at its maximum, a critical lag is reached and vortices unpin catastrophically, transferring angular momentum in a glitch. This model predicts periodic behavior with a set maximum size.

3. Vortex Avalanches: This model is based on a self-organized critical system, and considers local unpinning and vortex interactions. Theoretical work suggests it may be possible for regions of increased Magnus force to exist within the superfluid, such that random unpinning processes on a local scale can lead to vortex avalanches and regional unpinning; these are referred to as nearest-neighbor avalanches. In coherent-noise avalanches, over time vortices tend to pin to homogeneously-distributed sites with stronger pinning forces, and avalanches are triggered in response to global Magnus force. This model predicts aftershocks and spikes at the upper and lower ends of the distribution of glitch sizes.

Spontaneous glitch activity, especially when scrutinized in a glitch population is an extremely notable pulsar event that still remains in obscuration, like many astronomy-based discoveries.

So do pulsars have phenomenology? The answer is IDK! I mean, yes, it is probable that all pulsars are different, but we’ll never know… I do know this, however: Pulsars have — objectively — become some of the most useful heavenly bodies that are used in high-energy astrophysics to observe and understand the cosmic universe and dimensions of space. I can’t wait to see what astronomically amazing discoveries are found because of their brilliant presence.

***If you didn’t get this article, don’t worry. Sometimes I get lost in my own writing! Just make sure to look up all of the italicized words, and brush up with your astrophysics theories! Oh yeah, don’t forget math either. Make sure to look at some calc too. If you’re totally new to this, again, don’t sweat it! Any knowledge is good knowledge, even if you don’t get it holistically. Remember that when I write my next article about Pulsars detailing how I used neural network computation to fully determine their plausible substructure. Oooooooooh… coming soon! — Okezue

ma ’23 + tks ’22 | bio @sickkidstoronto | ml @hansonrobotics | ml collaborator @ibm | https://okezuebell.com

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store