# NS-Capture Explanation of SNEs

## General Description

The NS-Capture theory explains SNE’s as follows:

- An NS (neutron star) is captured by an RS (regular star)
- Through repeated interactions between the NS and the atmosphere of the RS, the orbit of the NS around the RS becomes circular.
- At this point the X-rays from the NS gravitationally drawing in material from the RS are generating on the order of 10**38 ergs/sec.
- These x-rays are absorbed by the atmosphere of the RS causing the RS to get hotter at the rate of 10**38 ergs/sec.
- After 10**5 years, the RS may possibly have absorbed:

10**38 e/s 10**5 y 3*10**7 s/y = 10**50 ergs - The gravitational self binding energy is roughly proportional to the mass of the RS.

E-binding Sun = 10**48 ergs

E-binding 10 solar mass RS ~ 10*10**48 ergs = 10**49 ergs - Therefore, in 10**5 years an RS with a captured NS may absorb s much or more energy than the self-binding energy of the RS itself.
- At some point the RS is effectively just a cloud of unbound gas containing an NS that is generating at least 10**38 ergs/sec, thus blowing the unbound gas in all directions forming a gas nebula.
- This gas nebula plus the NS near its center is exactly what a Supernova Event appears as: for example: the Crab Nebula Supernova remnant.

Conventional theory (NS-Creation) would have us believe that a Supernova is a result of an RS imploding in a gravitational collapse, with opposite exploding gas, where the implosion results in the creation of an NS rotating upwards of 100 time/sec, and travelling through the remnants with a proper motion of approximately 200 km/sec. The proper motion is attributed to an asymmetric Supernova explosion which “kicks” the NS out of the center of the remnants with this velocity.

By contrast, the NS-Capture theory has a well-explained cause and effect of all the major pulsar properties:

- There is an observed mechanism for spinning up an NS in Cen X-3 and other x-ray pulsar observations. (see ref [10] of that page for original Cen X-3 data).
- The observed luminosity (L) of Cen X-3 is:

L(Cen X-3) = 3*10**5 L(Sun) = 3*10**5 * 3.8*10**26 W * 10**7 (ergs/Watt-sec)

= 1.14*10**39 ergs/sec

which gives the order of magnitude of the energy being absorbed by the RS companion of the Cen X-3 pulsar.

The RS companion is a 20 M Sun supergiant O-star, which has an approximate self-binding energy of 2*10**49 ergs.

Thus, we can make a rough prediction that Cen X-3 may blow up in a Supernova within the next:

2*10**49/1.1*10**39 sec ~ 2*10**10 sec ~ 6*10**2 years = 600 years - The orbital velocity of the Cen X-3 pulsar around its RS companion is calculated from its observed orbital period of ~ 2.1 days and its orbital radius of ~ 7*10**5 km:

velocity of pulsar ~ 10**7 km / 1.7 10**4 sec ~ 5.8*10**2 km/sec.

This velocity is more than enough to account for the proper motion of the pulsar through the SN remants. - Finally, the NS-Capture theory has no need to “create” a neutron star since there is already one there.

## Neutron Star <-> Regular Star Collision Rates

With the NS-Capture theory it is assumed that there are many more neutron stars than regular stars. This means that at any time every single star in the galaxy will have some number (e.g. 25) of neutron stars in its vicinity, where its vicinity is roughly the average interstellar distance: for example 2 light years.

This means that each star can be regarded as being contained in an 8 cubic light year cube, along with 25 neutron stars.

Consider interstellar proper motion to be on the order of 20 km/sec. That means in this cube that there are 25 neutron stars traveling in random directions in the cube. Some neutron stars may leave the cube and others may enter but the average number in the cube will be some specific number, such as 25.

This will be the case for all star densities. If the average interstellar distance in a more dense region of the galaxy, say 1 light year, then each regular star in this region will have 25 neutron stars within a 1 cubic light year cube. i.e. the assumption is that the relative density of #NS/#RS is a constant.

We can consider the chance of a collision between a normal star and a neutron star to be simply the ratio of their cross-sections for a binding collision. Think of the cube as a shooting gallery where each “shot” is traversing the cube at 20 km/sec, and the chance of the NS hitting the RS is basically the ratio of the 2 circular cross sections divided by the area of a side of the cube.

Therefore, in our example of a 2 light year cube let’s consider the cross-sectional area of the RS to be 1 Solar Radius (700,000 km, which we can round up to 10**6 km). We can use the same radius for the NS as well. So, if when we shoot the NS through the cube then there will be a binding collision if the centers of mass of the two stars come within 2,000,000 km of each other.

A light year is approximately 10 trillion km = 10**13 km. Therefore, one side of the 2ly cube has an area of 4*10**26 km**2.

The area of the cross-sectional overlap is roughly 4*10**12 km**2.

Therefore the chance of the neutron star “hitting” the regular star with a binding collision is roughly:

4*10**12 / 4* 10**26 = 10**-14

i.e. the chance of hitting the RS is one in 10**14 = one in one-hundred-trillion.

By comparison, in the denser region, where there is a 1ly cube, we have the same cross-sectional overlap, but the side of the cube is smaller by a factor of 4.

The other parameter is the rate of collisions. In the 2ly cube the time it takes for one shot across the cube is:

2ly/(2km/sec) = 2*10**13 / 2*10**2 seconds = 10**11 sec

A year is roughly 10**7 sec, so the time in years is roughly:

the traversal time is approximately 10**4 = 10,000 years.

So, in 10,000 years we have 25 NS’s “shooting” at the RS and each one has a 1*10**-14 chance of making a collision so the chance in one cube is 25/10**14.

Now, there are about 200 billion stars in the Milky Way Galaxy: i.e. 2*10**11 stars in MWG. So the chance in 10,000 years of a single binding collision occurring in the MWG is:

25*2*10**11/10**14 = 5*10**12/10**14 = 5*10**-2 = 5/100 = 1 in 20.

Therefore, in 20*10,000 years = 200,000 years, we expect 1 binding collision to occur in the MWG.

The above is “back of the envelope” calculation, but it shows how to calculate the rate for a given star density in a given volume.

## Gravitational Factor

There is a significant factor that needs to be added to the size of the target star cross-section. From the time the NS begins its approach to the RS (i.e. when it enters the 2ly-cube), there will be a gravitational attraction that effectively makes the target larger than its physical size, because the NS and RS are pulled together by gravity.

A way to model this is to put the RS at the center of the cube, and have the NS enter the cube perpendicular to the face of the cube. This gives an initial set of conditions for calculating the effective radius of the target:

- velocity of the NS (ex. 20 km/sec)
- initial “impact distance”, r, equal to the distance of the NS to the center of the face of the cube where it enters
- distance from the face of the cube to the RS at the center (1/2 length of side of cube)
- mass of NS (1.4 M-sun)
- mass of RS (1 <-> 25 M-sun)

We can use the simulation of NS-Capture to empirically calculate the effective size of the target. Basically use the initial conditions above as input to the Euler approximation used to produce the charts on the simulation page.

## Supernova Types

With the NS-Capture theory model of how neutron stars become bound to ordinary stars, we have not yet considered all the different types of stars that are targets of this uniform collection on neutron stars.

It turns out that even though the number of giant stars is much less than the number of regular stars, the cross-sectional overlap of the giants makes them much easier targets to hit. A rough estimate is that the total cross-sectional area of all the giants in the MWG is on the same order of magnitude as the total cross-sectional area of all the regular stars in the MWG.

What this means is that roughly half the binding collisions in the MWG are between an NS and giant, so at any time, we expect there to be roughly the same number of close binary x-ray emitting giants as there are close binary x-ray emitting regular stars.

So, for supernova types we will assume the following:

- Giants with NS companion produce Type II supernovae
- Younger, larger regular stars with NS companion produce Type I supernovae
- Older, smaller regular stars with NS companions do not produce a supernova, but instead, evaporate their companion RS

It is theorized that he 3rd type of NS-RS-binary that prdduces milli-second pulsars. Also, it is expected that because the stellar density of globular clusters is so high and that GC’s contain mostly older,smaller stars, that this accounts for the high number of binary neutron star pulsars in GC’s with white dwarf companions.

It is theorized that Cen X-3 is an example of a pre-SN-II type explosion.

It is theorized the Her X-1 is an example of a pre-SN-I type explosion