Millisecond Pulsars

Millisecond pulsars were discovered several years after the x-ray binaries. These are neutron stars that are usually found in binary systems and have rotation rates between 100 and 1000 times per second.

Just imagine a 1.4 solar mass neutron star with its magnetic poles perpendicular to its rotation axis rotating approximately 500 times per second. How many things are you aware of on a macro level that can rotate 500 times per second? The more common unit of macro rotation rate is rotations per minute. The millisecond pulsar rotates approximately 30,000 times per minute. This is considerably faster than most automobile engines.

There are few things that can get up to millisecond rotation rates. For a 5 mile radius neutron star, the material near the surface at the equator is rotating at 2*pi*R*500 = 3000*R = 15,000 miles per second, or just under 10% of the speed of light (186,000 mps). This places an upper limit of about 50 miles where material co-rotating with the neutron star would actually be traveling very close to the speed of light. This is a limit because we can not observe anything traveling faster than c (speed of light).

General Characteristics of Millisecond Pulsars

Most millisecond pulsars are found in binary systems, where the companion is an old star or white dwarf.

A disproportionate percentage of millisecond pulsars are found in globular clusters, which consist entirely of old main sequence stars. No giants are in the globular clusters, And the density of globular clusters is many times that found anywhere else in the galaxy.

Interestingly, in order to explain the existence of these binary millisecond pulsars in globular clusters, standard scientific explanations are forced to resort to the NS-Capture theory.

i.e. the current theory of supernovas creating neutron stars, or “NS-Creation theory”, fails to be able to account for millisecond pulsars in globular clusters, and as described in the core NS-Capture theory, if the NS-Creation theory fails, the NS-Capture theory must be invoked.

Therefore, we now have a situation where:

1. The NS-Creation theory requires the NS-Capture theory to explain at least some situations.
2. The NS-Capture theory does not need, and, in fact proves, that the NS-Creation theory is generally incorrect.

SIde note: The NS-Creation theory, could also be called the NS-Collapse theory, because the basic mechanism involved in this theory is that a neutron star is formed by the gravitational collapse of a star that has sufficiently cooled down that its interior can accumulate enough mass in a small enough space that gravitational collapse is spontaneous. The other mechanism that could produce a collapse is if a giant star simultaneously explodes in a supernova and simultaneously implodes causing enough pressure to compress enough mass such that gravitational collapse is spontaneous, creating a neutron star.

The NS-Capture theory does not use either of these mechanisms because the NS-Capture theory assumes a population of pre-existing neutron stars that are ejected from galactic black hole nuclei, along with the material used to create ordinary stars. These notions are pre-mature to discuss in any detail at this point of the analysis, so we will return to general analysis of the millisecond pulsars.

More about neutron stars

A good, but somewhat advanced, reference for all the material we are discussing on this site is a 124-page paper, entitled:

“Formation and Evolution of Binary and Millisecond Pulsars“,
by D. Bhattacharya and E.P.J. van den Heuvel
(Physics Reports (Review Section of Physics Letters) 203, Nos. 1&2 (1991) 1-124.
North Holland

This paper is not free, but I have found it well worth the price to purchase it. Some of the discussion points on millisecond pulsars will refer to this reference to avoid going into unnecessary detail which might slow down the overall presentation of this information.

One remarkable property of neutron stars is that they all seem to have a mass of about 1.4 times the mass of the Sun. Therefore, the Sun can never “evolve” to become a neutron star, because it does not have enough mass. The same is true for more than 90% of the stars in the Milky Way galaxy.

The properties of neutron stars are most clearly understood by observing them as pulsars in binary systems. The orbits can be studied in detail, and their mass can also be calculated in detail based on the properties of the orbit and the properties of the binary companion. It is based on these analyses that it has been determined that most, if not all, neutron stars weigh in at 1.4 M-Sun.

A second, even more remarkable, property of neutron stars is that even when they are orbiting in a close binary trajectory right in the atmosphere of the companion, and despite their huge gravitational field attracting huge amounts of mass from the companion, it turns out that the neutron star does not seem to become any more massive!

The reason for this is that as particles are accelerated toward the surface of the neutron star, those particles emit radiation, X-rays, as well as other wavelengths, and what happens is that the radiation pressure becomes so great, pushing the material away from the neutron star, that it overwhelms the gravitational force attracting the material to the neutron star.

This phenomenon results in a value, called the Eddington limit (discussed at length in Bhattacharya), that restricts the amount of mass per unit time that can “accreted” onto the neutron star. The maximum amount of mass that can be accreted for a 1.4 solar mass neutron star is 1.5×10**-8 M-Sun per year.

Therefore, in a typical spin-up time, of say, 10 million years, only 0.15 M-Sun can be accreted, which is approximately 10 % of the original mass of the neutron star. Considering that in the process, jets of material are ejected from the neutron star along the pulsar rotation axis, it may turn out that even significantly less than this amount actually reaches the surface of the neutron star.

Basically, it appears that a neutron star can rip apart its binary companion, leaving nothing behind except remnants blowing away from the pulsar wind radiation, while the neutron star, itself, remains essentially unchanged, except for the fact that it is left rotating about 500 times per second.

Millisecond Pulsars and the P/P-dot Diagram

The P/P-dot diagram is the main tool used in the analysis of pulsars. Unfortunately, it does not include the X-Ray binaries, but it easily could by providing a negative P-dot axis, which would show the pulsars that are spinning up.

Interestingly, these pulsars would be on a trajectory to join the millisecond pulsars in the lower left portion of the P/P-dot diagram that has the lowest P-values (highest spin rates), and the lowest P-dot values (the slowest spin deceleration (slow-down) rates).

One will also notice in the P/P-dot diagram that most, if not all, of the millisecond pulsars (MSPs) in the lower left quadrant are in binary systems. The binary companions of these MSPs are generally relatively low mass white dwarfs (< 1 M-Sun). Some have even been measured to be as low mass as 0.02 M-Sun.

The very slow spin-down rates of the MSPs has been attributed to their somehow having lost the strength of their magnetic fields (which would mean less radiation, and thus smaller loss of angular momentum, and therefore slower spin-down rates). In addition the spin-down rates are so slow that it has been assumed that the MSPs are billions of years old, as opposed to the slower isolated pulsars that have spin-down rates that puts their age into the thousands or millions of years categories. These assumptions are consistent with the NS-Creation/Collapse theory, which requires their age to be billions of years in order to keep the neutron star populations in globular clusters low enough to be consistent with the ability to produce these binary MSPs at a rate consistent with NS-Creation by supernova populations. i.e. the creation rate of neutron stars by supernova explosions in globular clusters is relatively small, so the rate of creation of MSP binaries is also relatively small. Therefore, if the NS-Creation of binary MSPs by NS-Capture is the explanation of the origins of the binary MSPs, then the binary MSPs must be extremely long-lived in order to account for their extremely high abundance in globular clusters.

The above paragraph may be a lot to absorb all at once, but it basically says that for the NS-Creation theory to work, the lifetime of binary MSPs must be billions of years to account for their large abundance in globular clusters.

Consequently, the location of the binary MSPs on the P/P-dot diagram, forces the NS-Creation theory to assert that the magnetic fields of these neutron stars must have become small and their spin-down rates accordingly are correspondingly extremely slow, making the binary MSPs extremely long-lived.

The NS-Capture theory, globally applied to globular clusters, implies that, by contrast, there pre-existed a very high number of neutron stars in the globular clusters that were there from the beginning of the existence of the globular clusters.

As a result, the NS-Capture theory predicts a much higher rate of creation of binary MSPs in the globular clusters, and therefore enables another process that may be seen to explain the extremely slow spin-down rates observed in the MSPs.

The solution to this situation is very straight-forward, and it says that if an MSP has a binary companion, then the MSP’s high spin rate is maintained by continuing interaction with the remains of the original star that has been reduced to a white dwarf by blowing its atmosphere away leaving only a dense core.

However, this dense core is also going to be disrupted by the presence of the MSP, which will provide and ongoing source of fuel to keep the MSP spinning. Since the MSP is likely spinning at its maximum Eddington limit rate, we basically have an equilibrium situation, which will exist until the companion is completely evaporated, after which the MSP will rapidly slow down and join the main body of slowing down pulsars in the middle of the P/P-dot diagram.

According to the Bhatacharya paper, ref’d above, this evaporation will likely take place on the order of millions of years. Now we have a situation where there needs to be a mechanism to create binary MSPs much more frequently than the NS-Creation theory can account for, but the NS-Capture theory provides naturally, since there are many more neutron stars in the cluster, which causes a much higher binary-MSP creation rate, than the NS-Creation theory can produce.

Therefore the main difference between the NS-Creation theory and NS-Capture theory is that:

1. The NS-Capture theory naturally explains the existence of the population of binary MSPs in globular clusters, using exactly the same mechanism as was proved logically necessary in the case to the giant stars and their supernova explosions.
2. The NS-Creation theory is hard-pressed to explain the binary MSPs, and requires new assertions about declining magnetic fields without physical basis for making the assertions, plus it requires a long slow-down rate, while ignoring the presence of a close companion, which, in general will cause the NS to spin-up not spin-down.

Therefore we conclude that the NS-Capture theory works for both giant-star binary pulsars and small white dwarf millisecond pulsars, while at the same time the NS-Creation theory requires assertions with little physical basis to explain either the giant star binary pulsars or the binary MSPs.

The work of this web site will be to try to pin down this logic to firmly rule out the NS-Creation theory, which will force the assertion of the NS-Capture theory, which is ready-made to explain all the observed phenomena. i.e. force the assertion of the existence of 5 trillion neutron stars in the Milky Way Galaxy.