Stellar Remnants: Neutron Stars and Black Holes

At right are the results of a numerical simulation of a black hole/black hole collision and the gravitational radiation which is produced (much as the manner in which water waves are generated by disturbances and in the manner in which EM waves are generated by electrical charges).

Reading: Chapter 18 (The Bizarre: Stellar Graveyard)

The remnants left from Type II SN are the compact objects known as neutron stars for lower mass massive stars and black holes for higher mass massive stars. Both neutron stars and black holes are bizarre objects:
Neutron stars are roughly the mass of the Sun (around 1.4 solar masses) with diameters of only 10 to 15 kilometers, the size of a city, say Eugene. As their name implies, they are made primarily of neutrons with a small amount of protons and neutrons. They have monstrous densities, more than 10¹⁴ g per cubic centimeter, comparable to the density and atomic nucleus. Neutron stars are essentially giant atomic nuclei held together by gravity.
Black Holes: In the 1600s, Issac Newton developed his Universal Theory of Gravitation and his three laws of motion. This way of looking at the Universe works quite nicely for the motions of the planets and most of our everyday experiences. However, under certain circumstances, this picture is inadequate. To fix-up some problems, Albert Einstein developed his Special and General Theories of Relativity which brought a new persepctive to our thinking about space, time, and gravitation. Based on the theories of relativity, an unusual kind of star was possible, Black Holes, stars for which the escape speed from their surfaces (the Event Horizon is the speed of light! Because the speed of light is the maximum speed to which an object can be aceelerated, nothing can escape from a black hole, not even light.

In this section, we go over some of the properties and recent observations of neutron stars and black holes.

I. Neutron Stars
The existence of neutron stars was predicted soon after the neutron was discovered by Chadwick in 1932, and how they might be formed in Type II SN as predicted in a prescient paper by Baade and Zwicky in 1934. However, it wasn't until 1967 that neutron stars were discovered when Jocelyn Bell and Anthony Hewish discovered what are called pulsars. Pulsars are rapidly rotating (some spinning more than 600 times per second), strongly magnetic (the strongest having fields of order 100 billion Tesla) neutron stars. A typical MRI machine on Earth has a magnetic field of several Tesla!
Produced in 1054 but only discovered in 1968, the Crab pulsar (rotating neutron star) found in the Crab Nebula (supernova remnant) is a prime example of a pulsar. The Crab pulsar pulses 30 times a second in the γ-rays all the way to the radio; it is one of the few pulsars to blink in the optical.
The pulsation of the Crab pulsar is interpreted within the standard model for a pulsar. Pulsars are modeled as rapidly rotating strongly magnetic neutron stars, the neutron star in the Crab pulsar spins 30 times a second with intense magnetic fields, the neutron star in the Crab pulsar is thought to have a field of strength 10⁸ Tesla. Outside of these properties, the neutron star in the Crab pulsar has typical properties of a neutron star, mass around 1.4 times that of the Sun and radius of 10 to 15 km.
If the Crab pulsations are indeed caused by the spin of the star in the Crab, then the Crab pulsar must contain a neutron star rather say, a normal star or a white dwarf. Its high rate of spin means that in order for a star to hold itself together against the centrifugal force arising from the rotation, the density of the star must be greater than 100 billion grams per cubic centimeter. This density is larger than that of a main sequence star or a white dwarf but is comfortably below that of a neutron star.

The burst of neutrinos detected from SN1987A by the Kamiokande and IMB experiments showed that a neutron star was produced during the explosion of SN987A. Because of this many searches were launched in attempts to find the neutron star. Despite many attempts, the neutron star thought to lie in the center of SN1987A remained elusive. In the last few years, however, indirect evidence that a neutron star lurks in the heart of SN1987A has been found using the Webb telescope. Astronomers have noted the signal due to singly ionized Argon (ArII) shown in the upper right image (the bright spot in the center) must be the result of an energetic source of emission at the center of the SN1987A. The type of source most consistent with the data is a neutron star. This result is tantalizing but further lines of inquiry (and evidence) must be developed to make an air-tight argument that the long sought-after neutron star has indeed been found.

II. Black Holes
The idea of a Black Hole although formally flowing from Einstein's theories, nonetheless has its origins in the late 1700s, well before Einstein's time. Michell (1784) and Laplace (1799) independently suggested the idea for dark stars

Imagine we have four stars, each of 1 solar mass, that is, each star has the mass of the Sun. From upper left, moving clockwise, we have images of the Sun, a white dwarf, a black hole, and a neutron star. Each object has different radius. The Sun has 7x10⁸m, the white dwarf 6x10⁶ m, the neutron star 10⁴ m, and the black hole 3x10³ m
What is the escape speed from each object? Well the escape speed is how fast must an object move to escape the gravitational pull of the body.

For the Sun, we find that the escape speed is 600 km per second

What do you think the escape from the white dwarf will be? larger or smaller than that from the Sun? Well, the mass is the same so that doesn't affect anything. Hmm, the radius is smaller so that we are closer to the center of the white dwarf and so we would expect that its escape speed would be larger. Indeed it is. The escape speed from the white dwarf is about 7,000 km per second.

What do you think the escape speed from the neutron star will be? larger or smaller than the white dwarf? It will be larger and is about 200,000 km per second, nearly the speed of light which is 300,000 km per second!
Interestingly, all of the escape speeds are less than the speed of light. This is good, because in our Universe, it is physically impossible to accelerate an object to the speed of light in our Universe. Consequently, objects will travel slower than the speed of light and so, in principle, none of the aforementioned stars can trap particles of light.
The last entries in the game are the black holes. It turns out, that if the radius of a one solar mass star is less than 3 kilometers then their escape speeds are greater than the speed of light. This means that nothing, not even light will be able to escape from their surfaces. Michell and Laplace essentially made this argument in the late 1700s to suggest that there should be dark stars, that is, stars from which light cannot escape. Today we would call such stars black holes.

The surface of a black hole is referred to as the Event Horizon, because this is the surface from which the escape speed is the speed of light. The radius of the Event Horizon is the Schwarzshild radius. Anything inside of the Event Horizon cannot escape from the black hole and so is cut-off from our Universe. Things outside of the Event Horizon can reach the rest of the Universe (communicate with the Universe). The Event Horizon is not a material surface, the matter inside of a black hole has all streamed into the very center where it is crammed into a point with zero volume and so has infinite density. This bizarre point is known as the singularity.

To get a feel for some of Einstein's ideas, we must start thinking about the space-time of the Universe. Suppose that I tell you that Astronomy 122 meets in 100 Willamette Hall. Is this enough to get you to class? Well, no, because I didn't tell you when the class meets, namely, 14:00-14:50 on MWF. In order for you to show up for class, you must know not only where it meets but also when it meets. This is true for all events in the Universe; you must know not only where the event occurs (its spatial position) but also when the event occurs (its temporal position). The space and time positions are equally important and we should think about events in the Universe in terms of their space-time positions.
An interesting property of this space-time is that it has structure* and is not rigid.*

Question: What are some consequences of viewing the Universe in this manner?

The path an object rolling on a table top follows is determined by the shape of the surface (it rolls on the table top). The table top defines the space-time for the rolling object. For objects rolling in the Universe, a similar idea holds in that the paths of objects follow the shape of the shape-time.
Locally, the space-time in this room is fairly flat and so, unless you push on an object, its free motion (unforced motion) is in a straight line. If I were to place a large chunk of mass into the room, the mass would distort the shape of the space-time. In two-dimensions, this is easy to visualize. Imagine a rubber sheet onto which you place a bb. The bb causes a depression to form in the rubber sheet.

This is analogous to what mass does to the structure of space-time. It causes a depression to form so that if an object rolls toward it, it falls into the pit and is captured. (This, by the way, is how Einstein envisioned how gravity works. Mass distorts the space-time causing particles to roll toward the mass. Note that the objects follow the shape of the space-time and in this sense are following an unforced motion! That is, there is no gravitational force, objects are simply following their natural motions.)
Return to the rubber sheet analogy. If I drop a bb on the sheet and it bounces, ripples in the sheet are produced which propagate away from the disturbance. These ripples in the space-time are referred to as gravitational waves.

Gravitational waves from compact stars and other Celestial Objects. Below is shown the Laser Interferometer Gravitational-Wave Observatory (LIGO) located in Hanford, WA which announced the discovery of gravitational waves in 2015 from GW150914, produced by the merger of two orbiting black holes (Abbott et al. 2016). This important work earned the 2017 Nobel Prize in Physics for Rainer Weiss, Barry C. Barish and Kip S. Thorne for "decisive contributions to the LIGO detector and the observation of gravitational waves." Note that there was an earlier indirect detection of gravitational waves for which the Nobel Prize in Physics 1993 was aswarded to Russell A. Hulse and Joseph H. Taylor Jr. for "the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation."

Comment: The opening of the sky to the study of gravitational waves was huge, but opening ot the sky to the combination of gravitational and the Electro-magnetic (EM) spectrum and the study of other forms of emissions from Celestial objects would be huge. Examples for such GW/EM sourfes are supernovae, $gamma;-ray bursters (merging neutron stars or black holes), unstable rotating neutron stars, close binary white dwarf stars... .
The exciting discovery of gravitational waves from merging neutron stars in the form of a γ-ray burst has verified that indeed, gravitational waves with electromagnetic radiation are produced by a broad range of astrophysical sources. The recent detetion by LIGO of a γ-ray burst source has substantially enhanced our understanding of the heavy element production in the Universe: