- 3113 - NEUTRON STARS - We have much more to learn about Neutron Stars. Each property shows itself a little differently depending on our observations and the instruments we use to make the discoveries. It is possible that Neutron Stars become Quark Stars before they become Black Holes.
- ----------------------- 3113 - NEUTRON STARS
- All stars, depending on their size, are destined to evolve into one of these three :
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------------------ (1) White Dwarf
------------------ (2) Neutron Star
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------------------ (3) Black Hole
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- The White Dwarf goes through a giant Red Dwarf stage before it collapses but it is not large enough to go supernova. The Neutron Star and Black Hole both evolve after a giant Supernova explosion.
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------------------ (1) White Dwarf - If a star is Sun size or up to 7 times the mass of our Sun than it will evolve into a White Dwarf. The maximum mass a White Dwarf can have after the Red Dwarf sheds much of its mass into outer space is 1.4 Solar Mass. This is called the “Chandrasekliar limit“, after the physicist who first developed the theory.
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------------------ (2) Neutron Star - If a star is between 8 Solar Mass and 25 Solar Mass it will explode as a Supernova and the remnant core will be a Neutron Star of between 1.4 Solar Mass and 3 Solar Mass. A 3 Solar Mass is the upper limit for a Neutron Star. All the other prior star mass must be ejected into outer space with the Supernova explosion.
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------------------ (3) Black Hole - If the star is greater than 26 Solar Mass the same Supernova explosion occurs but the remnant remaining afterwards is so large it becomes a Black Hole. When the stellar core is greater than 3 Solar Mass the collapsed star has an escape velocity than can exceed the speed of light. Nothing escapes and the star remnant disappears into a Black Hole.
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- “Neutron Stars” are exotic objects that have many strange properties. Depending on which property we are observing these stars have been called:
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------------------ (a) Pulsars
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------------------ (b) Gamma Ray Bursters
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------------------ (c) X-ray Bursters
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------------------ (d) Magnetars
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------------------ (e) Soft Gamma Ray Repeaters
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------------------ (f) Millisecond Radio Pulsars
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- The neutron itself was not discovered until 1932. But, within a year two astronomers, Fritz Zwicky and Walter Baade, proposed a theory that a massive star could collapse into a Neutron Star.
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- Their theory predicted that protons and electrons could be collapsed into neutrons by the massive gravity that would squeeze the core to a density of 10^18 kilograms per meter^3.
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- A star with a 3 Solar Mass would end up as a Neutron Star only 17 kilometers in diameter and have a density so great that a sugar cube, centimeter^3, would weigh 2,470,000,000 tons.
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--------------------------------------------
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------------------ Density = Mass / Volume
- Inserting the mass of the Sun and the volume of a sphere:
------------------ Density = 3 * 1.989*10^30 kilograms / 4/3pi*(8.6*10^3 m )^3
------------------ Density = 2.24 * 10^18 kg/m^3
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-------------------------------------------
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- No astronomer at the time expected to ever find such a small, dense object in the vast Universe.
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- Then in 1967 Jocelyn Bell at Cambridge University detected radio pulses that had a regular period of exactly 1.3373011 seconds. In 1968 astronomers found the first Pulsar in the center of the Crab Nebula in the Constellation, Taurus the Bull.
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- Later a pulsar neutron star was discovered in the Veil Nebula in the Constellation Cygnus the Swan. It is 1,500 lightyears away and went supernova 10,000 years ago during Earth’s Ice Age.
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- Another in the Gum Nebula in the Constellation Vela spans 60 degrees across the sky. At its nearest it is 300 lightyears away, but it has a diameter of 2,300 lightyears. It’s supernova occurred 11,000 years ago. Its pulsar period is .089 seconds.
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- Puppis A is another nebula with a neutron star at its center. These nebulae are extremely beautiful and worth your time to look them up on the internet and see a Hubble Space Telescope picture. The colors vary from pink hydrogen gas, green sulfur, to blue oxygen gas all powered by a Neutron Star.
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- Today there have been over 2000 Pulsar Neutron Stars discovered. The average Pulsars has a 1 second period (60 rpm) and a 10^-15 second per second spin down rate. The average Pulsar is 1,000,000 years old and has a magnetic flux strength of 10^12 gauss.
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- The magnetic fields of Neutron Stars can very from 100,000,000 times that on Earth to 100,000,000,000,000 stronger that Earth’s field. It is believed that the spinning star inside this magnetic field is what is causing it to loose energy and slow down. But, not by much, 10^-15 second per second equates to 0.03 seconds per 1 million years.
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- Often this powerful spinning magnetic field has an axis that is offset from the stars spin axis. An intense beam of radiation shines in a narrow cone outwardly from the magnetic poles. The beam sweeps around the sky like a light house beacon. If the Earth happens to be located in the right direction the beam flashes as it whips past our line of sight. These are the pulses we see in radio waves, X-rays, and gamma rays.
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- The radiating beam gets generated by the spinning Neutron Star’s magnetic field acting like a giant generator. The intense electric fields generated accelerate the charged protons and electrons located near the stars surface. The charged particles become channeled and pour out the north and south magnetic poles to be accelerated into outer space.
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- The Crab Nebula Pulsar flashes at us 30 times per second. .033 seconds per rotation. The Crab Nebula is a beautiful object to see in outer space. It is in the Constellation Taurus 6,500 lightyears away.
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- There are three main stars that outline the “V” shape of the Taurus: Nath, Aldebaran, and Zeta. The Crab Nebula is next to the star Zeta. It is the remnants of a Supernova explosion that occurred in the year 1054.
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- The nebula that we see today is the escaping gas and dust that is lit up by the radiation and Pulsar wind from the Neutron Star at its center. The nebula is 7,600 lightyears across. The Neutron Star at its center is only 20 kilometers in diameter and spinning at 30 times per second.
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----------------------------------------------------------------
The math and physics is between the dashed lines. If you do not want to do the math just skim through to the next dashed line and continue learning.
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- The Crab Nebula measures 4 arc minutes or 240 arc seconds across. Its diameter can be calculated using the formula:
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------------------ Arc seconds = 206,265 * diameter / distance.
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------------------ 240 = 206,265 * diameter / 6500 LY / 3.26 LY / parsec
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------------------ Diameter = 2.32 parsec * 3.26 LY/parsec
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------------------ Diameter = 7.56 lightyears.
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- If the diameter is 7.56 lightyears today and the nebula is expanding at an average of 12,000 kilometers per second when did the supernova explode?
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------------------ Time = distance / rate
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------------------ Time = 7.56/2 lightyears radius * 9.4605*10^15 meters/LY / 12*10^5 meters/second.
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------------------ Time = 2.98 *10^10 seconds / 3.16*10^7 seconds / year
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------------------ Time = .943 *10^3
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- Time was 943 years ago, or the year 1062. The actual year was 1054 recorded in Chinese history as being visible during the day for three weeks.
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--------------------------------------------------
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- The Crab Supernova started out as a star 7 Solar Mass when it ran out of fuel and exploded as a Supernova 952 years ago. The remnant of 3 Solar Mass collapsed down to 17 kilometers in diameter.
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- We know the diameter of a Neutron Star from the calculation that the force of gravity must overcome the nuclear forces that keep the matter from collapsing. Matter does not compress easily. Matter is made up of atoms and atoms are made up of proton nuclei and orbiting electrons.
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- If the mass is great enough and the gravity is strong enough it can overcome the resistance of the electrons to collapse into the nucleus. This electron force is known as degenerative pressure.
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- If we set the pressure from the force of gravity equal to the degenerative pressure and solve for the volume of the sphere remaining we can determine the radius of the Neutron Star sphere.
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---------------------------------
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- Gravitational Force = Gravitational Constant * product of Masses / distance between them squared.
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------------------ Force of Gravity = G*m^2/r^2
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- G is the constant of proportionality depending on the units used in the measurements. In our units G = 6.67*10^-11 meter^3/kilogram/seconds^2.
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- A star is made up of a certain number of protons and each proton has a mass of 1.67 * 10^-27 kilograms. Since the mass of the electron is almost 2000 times smaller it is ignored in these calculations. Since the star is star is neutral charge there are the same number of protons as electrons, and the same number of neutrons.
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------------------- Force of Gravity = G*(N*m)^2/r^2
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- Gravitational pressure is the force of gravity per unit area. In this case it is the surface area of a sphere which is equal to 4*pi*r^2.
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------------------ Gravitational pressure = G*(N*m)^2/r^2 * (4*pi*r^2)
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------------------ Gravitational pressure = G*(N*m)^2/ (4*pi*r^4)
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------------------ The volume of a sphere, V = 4/3*pi*r^3
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------------------ r^3 = 3*V/4*pi
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------------------ r^4 = (3*V/4*pi)^4/3
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- Substituting this back into the equation for gravitational pressure:
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------------------ Gravitational pressure = G*(N*m)^2/ (4*pi*(3*V/4*pi)^4/3)
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------------------ Gravitational pressure = .537 *G*(N*m)^2/ (*V)^4/3
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- Since the gravitational pressure directed inward varies throughout the star and our calculation only dealt with the surface area a more rigorous calculation yields a pressure 32% of the number/volume ratio instead of 53.7%:
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------------------ Gravitational pressure = .32 *G*(N*m)^2/ (*V)^4/3
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----------------------------------------------------
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- The negative pressure, or degeneracy pressure due to the electrons refusal to collapse, is calculated as the ratio of the change in energy to the change in volume:
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------------------ Degeneracy pressure = Change in energy / Change in volume
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------------------ Degeneracy pressure = -dE / dV
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- This calculation is omitted because it is too complicated. The result shows the pressure as a function of the number of neutrons per total volume of the star:
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-----------------------------------------
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Degeneracy pressure = (Planck’s Constant^2/5*M) * (3*pi^2)^2/3 * (N / V)^5/3
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Where: Planck’ Constant = 1.05*10^-34 joule * seconds
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------------------ N = number of neutrons = number of electrons = number of protons
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------------------ N = total mass = 3 Solar Mass / mass of a neutron
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------------------ M = mass of a neutron = 1.67*10^-27 kilograms
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------------------ Solar Mass = 1.989*10^30 kg
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------------------ N = 3 * 1.989*10^30 kg / 1.67*10^-27 kilograms
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------------------ N = 3.573 * 10^57 neutrons
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----------------------------
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- Solving these equations for a 3 Solar Mass star and setting the two pressures equal to each other:
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------------------ Degeneracy pressure = (1.05*10^-34 joule * sec)^2/5*1.67*10^-27 kg)* 9.569 * (3.573 * 10^57 / V)^5/3
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------------------ Degeneracy pressure = 10.545*10^54 / V^5/3 joule^2 * sec^2/ kg
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------------------ Gravitational pressure = .32 *G*(N*m)^2/ (V)^4/3
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------------------ G = gravitational constant = 6.67 *10^-11 m^3/(kg *sec^2)
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------------------ Gravitational pressure = .32 * 6.67 *10^-11 m^3/(kg *sec^2) *(3 * 1.989*10^30 kg )^2/ (V)^4/3
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------------------ Gravitational pressure = 75.843*10^49 /v^4/3 m^3*kg/sec^2
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------------------ Gravitational pressure = Degeneracy pressure
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------------------ 75.843*10^49 /V^4/3 m^3*kg/sec^2 = 10.545*10^54 / V^5/3 joule^2 * sec^2/ kg
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------------------ V^1/3 = .1390*10^5 meters
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------------------ Volume = 4/3*pi*r^3
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------------------ 4/3*pi*r^3^1/3 = .1390*10^5 meters
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------------------ Radius = 8.6 kilometers
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-----------------------------------
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- The diameter of the 10 Solar Mass star collapses to 17.2 kilometers. The star collapsed from a radius of 700,000,000 meters to a Neutron Star radius of 8,600 meters in less than one second.
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- The bounce that occurs at the core sends a tremendous shockwave back into space blowing away most of the mass and leaving a remnant of 3 Solar Mass. The scattered mass becomes the interstellar medium that lights in the colorful expanding nebula.
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- The neutron core will have temperatures in the millions degree Kelvin and a magnetic field a trillion times stronger than Earth. The angular momentum has to be conserved in the collapse of this star so when the radius is reduced the angular spin velocity must increase to keep the momentum constant.
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- Before the collapse the star was rotating once every 57 days. After the collapse it was spun up to .00074 seconds per rotation, or 1,345 rotations per second. An rpm of 81,000. That is really having your engine revved up.
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--------------------------------------
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------------------ Angular momentum = mass * angular velocity * radius^2
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- To have the same angular momentum before and after:
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------------------- 3 Solar Mass * 2*pi/57days * (7*10^8 m)^2 = 3 Solar Mass * 2*pi/period * (8.6*10^3 m)^2
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------------------ Period = 7.433*10^-4 seconds per cycle
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- The Neutron Star is rotating 1,345 times per second.
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------------------------------------------
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If the Neutron Star is spinning 1,345 rotations per second and the radius is 8.6 kilometers the velocity at the surface is 24% the speed of light.
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------------------------------------------
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------------------ Velocity = 1345/second * 2*pi* 8.6 km
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------------------ Velocity = 72,678 kilometers / second
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- Light travels at 299,800 kilometers / second , so this 24% the speed of light.
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-------------------------------------------
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- If a particle is orbiting just above the surface of a Neutron Star its speed is 39% the speed of light:
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------------------------------------------
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- Kepler’s law for orbiting bodies is the ratio of the square of the periods and the cube of the radius are the same.
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------------------ Period^2 = (Radius Neutron Star / Radius of Earth)^3 * (Mass of Sun/Mass of Neutron Star)
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------------------ Period^2 = (8.6 km / 1.5*10^8 km)^3 * (1 Solar Mass/ 1.4 Solar Mass)
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------------------ Period^2 = 210.4*10^-24 years
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------------------ Period = 14.5 *10^-12 years * 3.15*10^7 seconds / year
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------------------ Period = 45.69*10^-5 seconds
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------------------ Velocity = 2*pi*radius / period
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------------------ Velocity = 2*pi*8.6 km / 45.69*10^-5 seconds
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------------------ Velocity = 1.18 *10^5 km/sec
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- 118,000 km/sec with the speed of light 299,800 km/sec means that the particle orbiting just above the surface is traveling at 39% the speed of light. If it were traveling 100% the speed of light it would be a Black Hole and not a Neutron Star.
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----------------------------------------------------
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- Over 2000 Pulsars have been discovered. By plotting the spin-down rates versus the periods of rotation these Pulsars can be grouped into categories of Neutron Stars that have certain properties. Pulsars tend to slow down as they loose energy.
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- For example, the Crab Pulsar rotates once every 0.033 seconds, but it is slowing down at the rate of 0.000000364 seconds per day. This is an equivalent spin-down rate of 0.4213*10^-12 seconds per seconds which puts the Crab Pulsar as a younger Pulsar above the middle of the pack.
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- The full range of spin-down rates is from 10^-21 seconds per second to 10^-9 seconds per second versus their periods ranging from .001 seconds per rotation to 100 seconds per rotation.
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- The Pulsars with 5, 10, 100 second periods have the most intense magnetic fields. They are known as Magnetars and they pulse only X-rays rather than radio waves. They are also know as X-ray Pulsars.
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- The crust of the Pulsar Neutron Star is composed of a rigid, superdense form of iron that quivers in response to a changing magnetic field. Enormous stresses in the crust cause it to crack, creating star quakes and releasing blasts of gamma rays. These Neutron Stars are known as Gamma Ray Bursters, or Soft Gamma Ray Repeaters.
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- Many Neutron Stars are binaries and the more massive star can feed off the less massive star. An accretion disk can form with infalling gas adding energy to the Neutron Star spinning it even faster. The gas in the accretion disk heats up and emits a torrent of X-rays. These are known as X-ray Bursters.
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- The oldest Pulsars have radiated most of their energy and settled down to become Millisecond Radio Pulsars that are extraordinarily stable. With spin-down rates of 10^-20 seconds per second their pulses are more stable than our best atomic clocks here on Earth.
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- We have much more to learn about Neutron Stars. Each property shows itself a little differently depending on our observations and the instruments we use to make the discoveries.
-
- It is possible that Neutron Stars become Quark Stars before they become Black Holes. Regardless the more massive Neutron Stars are at the edge of evolving into Black Holes.
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- Because most everything disappears they are less exotic than Neutron Stars. Their mass, event horizon, and spin are the only three things we have to describe them, so far. This is just a pebble of knowledge on the shore of a whole ocean of the unknown to be explored.
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- March 30, 2021 NEUTRON STARS 625 3113
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--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
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--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
--------------------- --- Wednesday, March 31, 2021 ---------------------------
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