2)    Atlas of the Universe. Patrick Moore Phillips, London, 1994.






Dim? Star erupts and brightens to thousands of time than normal state, lasts days, months at most, fade back into obscruity.

Result of an out burst of the white dwarf component of a binary system – Other star is a normal star not yet evolved to white dwarf, relatively low density. The white dwarf draws material away from other and forms ‘accretion disk’, temp rises, lower part: mild nuclear reactions lanketed by non reacting material above, temp rises until violent explostion material outward, speeds up to 1500 km per sec. Reverts to original state but loads of Energy, 1 million billion nuclear bombs. White dwarf has only lost a tiny fraction of its mass. Some become very brilliant.

Recurrent novae Blaze Star T Coronae Borealis in the Northern crown   80 yrs between flares. P Cygni in the Swam



Estimated to be 1000 years old, the Cat’s Eye Nebula, or NGC 6543,  is a visual “fossil record” of the dynamics and late evolution of a dying star

What do distant galaxies, interstellar clouds of gas and dust, and faint star clusters have in common? When seen through a small or medium-sized telescope, all tend to look like faint, unresolved clouds. The brightest of these so-called nebulae (the Latin word for “clouds”) can even be glimpsed with the naked eye. The Orion Nebula, for instance, can be found in the sword of the constellation Orion on any clear winter evening, and the grand Andromeda Galaxy is a treat in the autumn sky.

By the beginning of this century, more than 10,000 nebulae had been catalogued. A number had been identified as interstellar clouds or star clusters, but most still remained a mystery. Not until Edwin Hubble, observing with the 100-inch telescope on Mt. Wilson in the 1920s, spotted individual stars in the Andromeda Galaxy (then known as the “Great Nebula”) did their true nature come out. Hubble found that these nebulae were huge galaxies in their own right, enormously expanding our view of the size and contents of the universe.



Origin and Scale of Neutron Stars

A neutron star has roughly the mass of our Sun crammed in a ball ten kilometers in radius. Its density is therefore a hundred trillion times the density of water; at that density, all the people on Earth could be fit into a teaspoon! Neutron stars are born during supernova, and are held up by neutron degeneracy pressure. These stars are relatively rare: only about 10^8 in our galaxy, or one in a thousand stars, so the nearest one is probably at least 40 light years away.

Neutron Stars and Extreme Physics

Neutron stars therefore have states of matter that cannot be duplicated in laboratories. Study of them helps us test our theories, and perhaps discover new physics. But how can we observe neutron stars? 

Observing Neutron Stars

We see a normal star by the light it gives off during fusion. Neutron stars are very hot, more than 100,000 K for most of their lifetimes, so this sounds promising but most of the energy comes out as X-rays (not visible light). Also, neutron stars are so small that at typical distances they are ten billion times fainter than you can see with your naked eye, which is too faint for even the Hubble Space Telescope. We need some other way to see neutron stars.

One way is to see them as radio pulsars. Another way is if the neutron star is one member of a binary, in which case the gravity of the neutron star can strip gas off its companion. The gas from the companion falls onto the neutron star, and emits fantastic power in X-rays: as much as 50,000 times the luminosity the Sun produces. This is a tremendously efficient way to generate energy. Dropping a kilogram of matter onto the surface of a neutron star releases as much energy as a five megaton hydrogen bomb!

Since the neutron star is a very small target, astronomically speaking, gas can't fall onto it directly. Instead, gas spirals around the neutron star, and friction with itself releases huge amounts of energy in what is called an accretion disk. Studying the X-rays from accretion disks can give us hints about the star: for example, how does matter behave at extremely high densities?









The Equation of State

As mentioned above, we want to know the properties of the extremely dense matter in the center of neutron stars. One way to characterize the matter is by its equation of state.

The equation of state can be pictured as the relation between the density of matter and its pressure. Consider a glass of water. The shape of the water in the glass can be changed easily (e.g., by sloshing it around), but the volume, and hence the density, of the water is extremely difficult to change. Even if you apply a huge amount of pressure to the water, for example by a piston, the density changes hardly at all; this is the basis of hydraulic presses. Water may therefore be said to have a stiff equation of state. In contrast, the volume of air in an empty glass can be changed easily, with little pressure, so air may be said to have a soft equation of state. So, a knowledge of the equation of state tells us, essentially, how squeezable the matter is.

In the case of a neutron star, knowledge of both the mass and radius of a particular neutron star would tell us the equation of state. This is because gravity squeezes the star, and the more mass the star has the more gravity squeezes it. If the star has a large radius (meaning, say, 15~km!), it was relatively successful in resisting gravity and thus has a very stiff equation of state. If the star has a small radius (say, 8~km), it was not as successful in resisting gravity and it has a softer equation of state. We therefore need to estimate the mass and radius of neutron stars.

Estimating NS Masses and Radii

No easy task, this. Astronomical measurements are often challenging, because we can't go to a star and experiment on it. Neutron stars are especially tough, because they are relatively small and far away: even the closest one would appear to be the size of a bacterium on the Moon, so we have to find other ways to determine the mass or radius of a neutron star.

One way to do this is to use Kepler's laws. If we can figure out how far two stars in a binary are from each other, and the duration of their orbital period, we know something about their masses. Only for neutron stars in binaries do we have even a rough estimate of the mass, and in only a few of those cases do we know the mass accurately.

Estimating the radius is much more difficult than estimating the mass. Unlike the mass, the radius doesn't have any strong effects on what we can observe. From astronomical observations alone, neutron stars could have radii from 5~km to 30~km (although most of that range, all but about 7~km to 20~km, is ruled out by what we know of nuclear physics).

So, we need some kind of breakthrough in the evidence to allow us to further constrain the radii of neutron stars.

An Unexpected Discovery

We can only discover what our instruments can detect, so many times in astrophysics a breakthrough in our understanding has come from an improvement in instrumental capabilities.

Such was the case when the Rossi X-ray Timing Explorer was launched on December 30, 1995. Its many outstanding properties include an unprecedented sensitivity to very rapid variations of the X-ray intensity of accreting neutron stars, i.e., neutron stars stripping mass from their stellar companions. This led to the discovery of a completely unexpected phenomenon: fast intensity oscillations, sometimes more than a thousand times per second!

Kilohertz Intensity Oscillations

Figure 1 shows the X-ray brightness from one neutron star system, as a function of time. The intensity goes up and down nearly 1000 times per second. There are at least 10 known neutron stars that show this, and we have discovered that:

The dramatic change in frequency means that it can't be something simple like the spin frequency of the neutron star, since the star can't easily be spun up or down. However, the common occurrence of this phenomenon and its other properties mean that it is telling us something fundamental about the flow of matter onto neutron stars.


Key Points


Accretion disk:  the pattern of flow of matter from a normal star to a neutron star or black hole, which is flattened and thus disk-like.

Degeneracy pressure:  a quantum-mechanical phenomenon; fermions, such as electrons or neutrons, obey Pauli's exclusion principle, so that no two fermions can occupy the same state. Thus, if fermions are squeezed together they resist even if there is no temperature and no energy generation. This resistance to squeezing is degeneracy pressure.

Equation of state:  the relation between the pressure and density of a given type of matter, which is an indication of how the matter resists squeezing. If the matter resists squeezing strongly (e.g., water), the equation of state is stiff; if it resists squeezing only weakly (e.g., air), the equation of state is soft.

Event horizon:  in a black hole, the point beyond which events cannot be detected. This is the point of no return; an object that falls inside the event horizon can't get out.

Kepler's laws:  rules for the orbital motion of planets or anything else bound by gravity. The law of most interest here is that the square of the orbital period is proportional to the cube of the orbital separation, and inversely proportional to the mass. Thus, if we see an orbital period, we can estimate the mass or orbital separation and therefore constrain the mass and radius of a neutron star.

Singularity:  in a black hole, the "center point", at which densities, tidal forces, and other physical quantities become infinite. Our current physical theories break down at this point.

Tidal force:  the force an object feels because of the differential pull of gravity at different distances.

Related Web Resources
Moderately technical guide to various aspects of neutron star physics
Robert Nemiroff's page on virtual trips to black holes and neutron stars. Neat animation showing gravitational light bending!
Black hole FAQ at Berkeley. Accurate, yet accessible