NS-Capture and the Empirical Spin-up Process

The empirical NS spin-up process is the evolutionary process by which neutron stars spin-up in a binary system from an initial non-spinning state to a final spun-up state in the midst of a supernova explosion or in a tight binary as a millisecond pulsar with a white dwarf or helium core companion. The core WD or He companion may be regarded as the remains of a star that was destroyed by the NS through the process of accretion. Similarly, the SNR of the SNE was the final destabilization of the companion of a binary x-ray pulsar that spun up as long as there was material to accrete, but was stopped short of becoming a MSP because of the destabilization of the companion star.

The reason for describing the “empirical NS spin-up process” as “empirical” is because we define the process based on observations of the behavior of the NS in terms of the P/P-dot diagram. The empirical spin-up process is shown in the bottom half of the diagram below in the section labelled “Spinning-Up Pulsars”:

The diagram above is a full P/P-dot diagram that characterizes both the conventional spinning-down pulsars P/P-dot diagram shown in the top half, joined with the new spinning-up pulsars diagram shown in the lower half. The origin of this diagram has been described in the section: How the NS-Capture Theory explains the P/P-dot Diagram.

The NS Spin-Up Process has 4 fairly distinct phases, which may be characterized by the spin period of the pulsar in the binary system when the pulsar is in that phase. The phases are sequential and are listed in order beginning with the longest (slowest) observed spin periods (seconds per cycle) and ending with the shortest (fastest) observed spin periods. Each phase is characterized by a range of spin periods.

Phase 1: spin period range: 10.0 sec -> 1000.0 sec+; This is from the time of initial capture through the Be X-ray Binary phase (the Be X-ray binaries are the main examples of this phase of the spin-up process).
Phase 2: spin period range: 0.1 sec -> 10.0 sec: This is the close binary circular eclipsing phase (examples: Cen X-3, Her X-1, SMC X-1; these stars may experience a SNE, in which case the NS-pulsar would become an isolated magnetar in the spinning-down part of the P/P-dot diagram).
Phase 3: spin period range: 0.02 sec -> 0.1 sec: This is the common envelope phase (these are stars that often experience an SNE; examples tbd; these are the NS’s that become the main body of spinning down pulsars in the island portion of the spinning-down P/P-dot diagram).
Phase 4: spin period range: 0.001 sec -> 0.02 sec: This is the Millisecond Pulsar (MSP) phase (examples include: serveral x-ray binary millisecond pulsars, which are the end of the spin up process and when the accretion material is exhausted move to the spin-down process as isolated and binary MSP’s with WD or He core remains of star the did not experience SNE in phase 3).

Note: the focus of the examples above is primarily of the high mass types of x-ray binaries (HMXB’s), although examples of low mass x-ray binaries (LMXB’s) are presumed in NS-Capture theory to go through the same basic phases.

Note: the use of terms describing the spin rate and spin-up and spin-down rates can be confusing. Here are some definitions to try to help:

spin rate: (rotations per second (aka: the frequency)) of a pulsar: a very high spin rate means a very short spin period; this quantity is associated with a steady amount of angular momentum. As long as the spin-rate (= 1/spin-period) remains constant the angular momentum of the pulsar is constant. Note: the “spin-period” (aka seconds per rotation) is denoted by “P” and is the “P” on the P/P-dot diagram.
spin-down rate: ((seconds per rotation) per second) of a pulsar: this quantity is a deceleration; i.e. the spin-rate is slowing down and the spin period is getting longer. It indicates the rate of loss of angular momentum of the pulsar; i.e. the pulsar is steadily rotating slower implying it is losing angular momentum; it loses the angular momentum by generating electromagnetic waves as its magnetic field rotates like a light house beacon. The spin-down rate is represented by “dP/dt” (or P-dot) on the P/P-dot diagram. It is implicitly a negative quantity, but is generally displayed by its positive absolute value on the conventional P/P-dot diagram, which only shows spin-down rates.
spin-up rate: ((seconds per rotation) per second) of a pulsar: this quantity is an acceleration; i.e. the spin-rate is speeding up and the spin period is getting shorter. It indicates the rate of gain of angular momentum of the pulsar; i.e. the pulsar is steadily rotating faster implying it is gaining angular momentum; it gains the angular momentum by its gravitational field pulling material onto itself from its binary companion along its magnetic field lines. The spin-up rate is also represented by “dP/dt” (or P-dot) on the “combined P/P-dot diagram”, which shows both spin-down and spin-up rates on the upper and lower half of the diagram, respectively. The spin-up rate is implicitly a positive quantity, and has not been included on the standard P/P-dot diagrams that only represent spinning-down pulsars. The diagram on this page shows both spinning-up and spinning-down pulsars.

Spin-up Process: Phase 1: Be X-ray Binaries

During the past 50 years, possibly the most interesting area in X-ray astronomy has been the discovery of the Be X-ray Binaries. These are binary systems containing a Be star and a slowly spinning (10 sec -> 1000+ sec) neutron star pulsar, in a generally highly elliptical orbit that has close contact at periastron (distance of closest approach).

Based on spin-orbit analysis, we have shown that time evolution of these systems goes from highly elliptical, very slowly spinning neutron star pulsars to circular orbit faster spinning pulsars, which cover the range of phase 1 spin periods (1000+ sec -> ~10 sec (i.e. as time goes by the spin period gets shorter (i.e. the pulsar is spinning faster)), which at the low end of the spin period range leaves the binary x-ray pulsar system entering phase 2 of the spin-up process.

In addition, an article reviewed in astrobites.com by Matthew Green has shown additional spin period behavior that further supports the evolutionary trend of phase 1 from slower (longer) spin period pulsar to faster (shorter) spin period pulsar.

In the diagram above, we can see a definite trend from the upper right to the lower left. The reason why we can say the trend is in this direction is because the vertical axis, which shows the absolute value of the spin-down rate (red points) or spin-up rate (blue points) is related to the magnetic field strength of the pulsar. In particular, the higher the spin-up rate or spin-down rate implies the stronger the magnetic field. i.e. if the magnetic field is stronger at a given spin rate the pulsar with the stronger magnetic field will spin down faster than the pulsar with the weaker magnetic field, because more electromagnetic energy will be transmitted per rotation for the pulsar with the stronger field, which will result in a greater loss of rotational energy per rotation. This works both for spin-down and spin-up (in terms of the absolute value, which is always positive). In the case of spin-up, the torque exerted on the pulsar with the stronger magnetic field will be greater during accretion than the torque exerted on the pulsar with the weaker magnetic field and thus will spin-up faster.

Therefore, in the lower left of the diagram above, the magnetic field of the pulsar is the weakest, whereas in the upper right the magnetic field of the pulsar is the strongest, because the magnitude of the spin-down or spin-up rate is a higher value in the upper part of the diagram. Since the changes in the magnetic field are due to accretion, which weakens the magnetic field (see Bhattacharya 1991), it becomes obvious that when the pulsar passes at periastron, the result will be that the accretion both spins up the pulsar to shorter spin period and weakens the magnetic field such that the spin-down rate decreases when the pulsar is away from periastron and not accreting matter. The net effect is that the periastron passages cause the magnetic field to weaken and the spin rate to increase, which means this process can only proceed in the upper right to lower left direction and not the other way around (i.e. there is no known physical mechanism which could make the magnetic field of the pulsar stronger, which would be the only way the pulsar could move up on the diagram).

Note that the figure shows both spin-up rates (blue) and spin-down rates (red). Both take place primarily because of the wide elliptical orbits during which there is generally no significant accretion taking place and the pulsar tends to slow down by emitting electromagnetic pulses. However, at periastron passage direct Roche-lobe accretion of substantial amounts of matter can take place which will spin-up the pulsar.

So, which will win? The spin-up forces of accretion or the spin-down forces of electromagnetic radiation? The chart, itself, provides one plausible answer: because the faster spin rates in the lower left are where there is a weaker magnetic field, and it is accretion that causes the magnetic field to weaken, then the magnetic field can only get weaker as time passes and more periastron passages further weaken the field. Therefore, we see that for the weaker fields, we have the faster spin rates (shorter periods), and the precursor to such a state must be from a slower spin rate and a stronger field. So, the pulsars must spin-up and the field must weaken over long periods of time.

Note: although the data points on diagram are each for different pulsars, the trend is clear that all the pulsars are eventually moving to the lower left regardless of whether they are momentarily spinning-up or spinning-down. i.e. the spin-up to shorter spin periods and the magnetic field weakening which results in slower spin-up rates or spin-down rates are the physical trends that are driven by the force of accretion and in particular, the physical effect of magnetic field weaken in non-reversible, which results in the trend from the upper right to the lower left.

Spin-up Process: Phase 2: Eclipsing, Close Circular Orbit X-ray Binaries

This is the part of the empirical spin-up process that was first discovered in 1971 with Cen X-3 and Her X-1. (Note: Rich Levinson is co-author of both the Cen X-3 binary spin-up discovery paper and the Her X-1 binary spin-up discovery paper.)

As described in the section “Binary Pulsars Don’t Slow Down“, the NS-Capture Theory was derived based primarily on analysis of Cen X-3, Her X-1, and the Crab pulsar, and therefore phase 2 is extremely important, in and of itself, in that it reveals the process that is required to explain the spin-down and spin-up P/P-dot diagrams. That process has been revealed empirically with the combined diagrams above showing how the binary systems evolve from an initial neutron star capture event, which ultimately results in either a full scale supernova explosion (in any of phases 1,2 or 3) sending the spun-up pulsar from the lower half of the diagram to the island in the upper half of the diagram, or in the case of no SNE, the process evolves to phase 4, where the move to the upper diagram is less dramatic.

Cen X-3 and Her X-1 are examples of pulsars that are mature in phase 2 and showing signs of entering phase 3. In particular, these x-ray pulsars are in close binary orbits with their companions from which they are steadily accreting material while at the same time pumping in x-ray energy into their companions at rates up to 10**37 -> 10**38 ergs/sec. This is in comparison to the total luminosity of the Sun of 3.8 x 10**33 ergs/sec. i.e. the x-ray energy emitted by these pulsars is on the order of 10,000 times the total luminosity of the Sun, and they actually located in the upper atmosphere of their companions.

As a result of this intense input of energy to the companion, the companion will heat up and ultimately expand and envelop the neutron star pulsar within its atmosphere, at which point the binary system enters the common envelope phase 3. In addition, the magnetic fields of the pulsars are on the order of 10**12 Gauss which is consistent with the magnetic fields of the isolated pulsars in the island of the P/P-dot diagram. Therefore, it is consistent to assert that if a spinning-up binary pulsar in late phase 2 or early phase 3 were to result in its companion blowing up in a supernova event, the pulsar would be left in a state matching that of the pulsars in the main island of the spinning-down portion of the P/P-dot diagram.

Spin-up Process: Phase 3: Common Envelope Binary

This is the part of the empirical spin-up process where the x-ray pulsar becomes invisible to the outside world because all the x-ray radiation is absorbed by the “common envelope atmosphere” that encloses both the x-ray pulsar and the core of its companion. It may also be thought of as a normal star that has a neutron star burrowing around inside of it.

Systems like Cen X-3 and Her X-1 are destined to enter this phase within a time that can be projected roughly by the spin-up rate of the pulsars. When the pulsar spin period gets down to the below the one-second range we can expect it to soon disappear into a common envelope. That is because we do not see x-ray binaries with a pulsar spinning faster than a few rotations per second, and since they will inevitably be forced to higher spin rates by accretion, the only plausible explanation is that they have become immersed in a common envelope.

In addition, references such as Bhattacharya and van den Heuval 1991 explain that “We see no way how a Be/X-ray binary can avoid spiral-in when the Be star becomes a red giant or red supergiant.”.

Altogether this means that even though we cannot directly observe x-ray pulsars during the common envelope phase that they must exist because of the large collection of HMXB progenitors that are observed that are destined to end up in the common envelope phase.

Therefore, we can now consider what happens during phase 3.

First of all the neutron star is not going anywhere, it is tightening its orbit around the companion’s stellar core and continuing to disrupt the common envelope by pumping in x-ray energy at a rate upwards of 10**38 ergs/second. That is more than 30,000 times the total energy emitted by the Sun happening within the atmosphere of the companion star, and being absorbed by that atmosphere.
At some point the heat absorbed by the atmosphere will become so large that the atmosphere will just up and blow away becoming gravitationally unbound from the system.
Another alternative is that the atmosphere will become unbound and the gravitational stability of the core will also become unbound (Bhattacharya and van den Heuval 1991) and the whole star will blow away in a supernova leaving an isolated spun-up pulsar that moves to the top P/P-dot diagram in the section labelled “Supernova Remnant Associated”.
This can happen because the energy absorbed by the companion from a neutron star x-ray pulsar emitting energy at 10**39 ergs/sec, can absorb as much energy as the total gravitational self binding energy of the companion which is on the order of 10**48 ergs in a few hundred years (1 yr ~3×10**7 sec).
Finally, there is the alternative that the common envelope blows away, but the core of the companion remains intact. This is the case where the system enters phase 4 as a millisecond pulsar in a close binary system with white dwarf or He star companion.

In summary, phase 3 is an inevitable consequence of phases 1 and 2, and is the precursor to both the phase 4 result of a binary hovering millisecond pulsar or the isolated spinning-down pulsar that is a result of a supernova explosion that sends the pulsar to the top half of the P/P-dot diagram containing the spinning-down pulsars.

Spin-up Process: Phase 4: Binary Millisecond Pulsars

A second major discovery during the last 50 years was the existence of millisecond pulsars (MSP). These are neutron stars that spin up to hundreds of rotations per second, an order of magnitude faster than the Crab Pulsar that spins 30 times per second. Many of these MSP’s are found in binary systems, where the companion is typically a white dwarf or the He core of a star that no longer has an outer atmosphere. The generally accepted model of how these MSP’s come into existence is that they were part of a low mass x-ray binary, where the neutron star was embedded in the atmosphere of its companion and spun up to these extreme high rotation rates while ripping apart and ultimately blowing away the outer atmosphere of the companion. Often when the outer atmosphere was blown away, the remains of the core would collapse into a white dwarf or simply the helium core of the original companion.

In addition, several accreting x-ray binary millisecond pulsars (AMPs) have been discovered since 1998. These AMPs represent the “X-ray Binary MSP’s” section in the upper left corner of the lower Spinning-up pulsars half of the full P/P-dot diagram represented at the top of this page.

With these observations in phase 4, the empirical spin-up process is now complete with one harmonious evolutionary model from original capture as observed in elliptical Be X-ray binaries of phase 1, to the circularized close binaries of phase 2, through the well-documented existence of common envelope binaries in phase 3, and finally the accreting x-ray binaries in phase 4.

Note that in any of the first three phases, the companion can destabilize gravitationally and have its remains blown away in what is typically observed in supernova remnants. These SNE’s are represented by the 3 upward pointing vertical arrows in the combined spin-up/spin-down P/P-dot diagram shown above.

Relation between Empirical and Diagrammatic Processes

In the section Diagrammatic Proof of NS-Capture, we showed using the diagram below, how columns 3 and 4 represent the full spin-up and spin-down parts of the evolution of pulsars and their relation to supernova explosions. Basically, the lower half of the combined P/P-dot diagram is represented by the empirical spin-up process that corresponds to column 3 of the diagrammatic proof diagram. In addition the empirical spin-down process is represented by column 4 of the diagrammatic proof diagram below. (The empirical data is represented by the green cells in the diagram.)

Another factor that needs to be mentioned is that it is generally accepted that the magnetic field of the neutron stars decay while the neutron star goes through the spin-up process. This means that the faster spinning pulsars in the top 2 rows of the diagrammatic proof diagram have much weaker fields than the slower spinning pulsars in the 3rd and 4th rows of that diagram. That also indicates that in order to represent 3 vertical arrows in the combined P/P-dot diagram at the top of this page that we would need to have horzontal cross arrows going directly from cells (4,3)->(4,4) for phase 1 SNE, from cells (3,3)->(3,4) for phase 2 SNE, and from cells (2,3)->(2,4) for phase 3 SNE. This would not change the sense of the diagram, but is only noted to show how to directly relate the diagrammatic proof diagram directly above to the combined empirical proof P/P-dot diagram at the top of this page.

The implication again is that this shows a contradiction in the NS-Creation theory, which is represented by column 2 in the diagram, because NS-Creation produces a fast spinning pulsar that has a weaker magnetic field than those found in the slower x-ray pulsars such as Cen X-3 and Her X-1. Therefore, in addition to the spin contradiction found in the NS-Creation theory, there is also a magnetic field contradiction, in that there would need to be a manner to strengthen the magnetic field as the NS-Creation created pulsar spun down to the slow spin rates of Cen X-3 and Her X-1.

i.e. the forces of accretion-driven spin-up and accretion-driven magnetic field weakening make it physically impossible for the NS-Creation theory process in column 2 to occur. i.e. you can’t go down the up escalator.

In other words NS-Creation requires column 2 evolution which in addition to needing a mechanism to slow down the fast pulsars created at the top of column 2, while they are in a binary environment that tends to make the pulsar go faster, also requires a mechanism to strengthen the magnetic field of the pulsar in order reach the bottom of column 2.

These required mechanisms are further contradicted by the empirical evidence of column 3, the empirical spin-up process. We therefore conclude that NS-Capture theory provides a mechanism to resolve these contradictions, and should provide sufficient motivation to begin the search for the nearby neutron stars that are implied by the NS-Capture theory.

Additional comments on “binary pulsars don’t slow down”

This page has been intended to explain the reason why the statement that “Pulsars in binary systems do not slow down.” is both true and the fundamental reason why the NS-Capture Theory must also be true. This statement is partially explained here.

The statement is intended to communicate the inescapable conclusion that an x-ray pulsar in a binary system will inevitably spin-up, but not necessarily that at every point in time would the pulsar be spinning up, because there is ample evidence that for short intervals, that a pulsar in a binary system may slow down. Examples where pulsars in binary systems momentarily spin down include:

The situation where the pulsar is in a part of an elliptical orbit where there is no accretion taking place, when the pulsar is most distant from its companion, the pulsar can temporarily be spinning down.
The situation where a pulsar is spinning faster than its equilibrium period, such as when the accretion is being provided by a stellar wind instead of the close binary Roche-lobe overflow condition (so-called propeller spin-down).
The situation where a millisecond pulsar is orbiting the core of a star that it has already fundamentally destroyed, such as a white dwarf or a helium core.

These situations arise during the spin-up life cycle of an NS-Capture binary system, but the overall inevitable trend of the binary is that these situations are special cases when the main Roche-lobe accretion in a circular close binary spins up the pulsar essentially from zero spin at the time of capture, right through to the eventual supernova sending the pulsar into the main island of the P/P-dot diagram, or, if supernova never occurs, then to the final state of millisecond pulsar + stellar core binary found in the lower left of the spin-down section of the P/P-dot diagram.