In the 1980s, while working at Berkeley Lab's Bevatron/Bevalac, Norman Glendenning of the Nuclear Sciences Division found his thoughts turning to neutron stars.

Norman Glendenning

Researchers were using the Bevalac to study nuclear "equations of state" — the way nuclear matter changes when subjected to extremes of pressure, density, or temperature. Some hoped the Bevalac could create nuclear densities great enough to free quarks from their imprisonment within protons, neutrons, and other hadrons (an accomplishment that hasn't been claimed even yet, although researchers at Brookhaven's Relativistic Heavy Ion Collider may be close). Although they failed to liberate quarks, the Bevalac investigators did observe fleeting states of matter with up to three times the density of the nucleus.

"But when I considered what one could learn from the interior of a neutron star, with ten times nuclear density, I rather lost interest in the accelerators of that era," says Glendenning. Speculating on what forms the densest matter in the universe might take, Glendenning soon began raising startling questions and proposing equally startling answers. Theorists and observers are still grappling with his ideas today.

The nativity of neutron stars

In 1934 astronomers Walter Baade and Fritz Zwicky coined new terms for the brightest exploding stars, suggesting that supernovae were powered by the collapse of the cores of large ordinary stars into neutron stars — objects only 10 to 20 kilometers across, made entirely of neutrons, and so dense that gravity at their surface would be 100 billion times greater than Earth's.

Jocelyn Bell with the Cambridge University radiotelescope that discovered the first pulsar.

This was a bold proposal, the neutron itself having been discovered only two years earlier. The existence of neutron stars wasn't proved until 1967, when Jocelyn Bell (Burnell), a graduate student of Cambridge radio astronomer Antony Hewish, discovered the self-advertising, spinning neutron stars called pulsars.

Although their net charge must be neutral, however, neutron stars aren't made solely of neutrons. The binding of gravity inside a neutron star is many times greater than the nuclear binding that holds atomic nuclei together; pressure and density vary with depth, and neutron stars depend on many kinds of particles to cope with these extreme and changeable conditions: neutrons, of course, but also protons, electrons, and other, weirder species. How they arrange themselves depends on a number of variables including the star's mass, its diameter, and how fast it's spinning.

Moving toward the center, density increases; matter is crushed ever closer together, until at some point quarks become "deconfined," popping out of their little hadron bags to form a soup of free quarks and gluons (gluons are the bosons that carry the strong force and normally keep quarks stuck together).

Theorists were long in the habit of thinking of this phase change — from the confined-quark to the deconfined-quark stage — as analogous to phase changes in water, for example from liquid water to ice. In the case of a neutron star, it was assumed, pressure increases smoothly with depth, until at some point neutron matter makes a smooth transition to quark matter.

If phase changes in water occurred in a system with two oppositely charged components, instead of freezing from the top down, spheres of ice would form.

But phase changes in water, says Glendenning, "are first-order transitions with only one independent component" — namely water itself. "In the real world, this kind of transition is far from typical. The situation is much more interesting for substances with two or more components."

Going through a phase

The stuff of a neutron star, for example. One of the two components that vary in neutron-star phase changes is electric charge. While neutron stars are globally neutral, local regions could have excesses of positive or negative charge.

A second component is baryon number, which must also be conserved. Hadrons have positive baryon numbers, while their antiparticles have negative baryon numbers.

There is no simple correspondence between electric charge and baryon number. A neutron has a positive baryon number but no electric charge; up and down quarks both have a fractional baryon number (plus 1/3), but an up quark's electric charge is plus 2/3, and a down quark's is minus 1/3.

Because of this two-component system — the hadronic matter and the quark matter — the stuff of a neutron star can make trade-offs locally to maintain overal global electrical neutrality and conserve baryon number. Between the star's outer, quark-confined regions and its innermost, quark-deconfined regions, there will be mixed phases, mixed hadronic and quark matter that take on fantastic geometries.

Hadron regions like to maintain an equal number of neutrons and protons. This is not possible globally but is approachable locally, where hadronic matter begins to mix with quark matter, because under extreme pressure neutrons can become protons by transferring electric charge to quarks — changing up quarks into down or strange quarks, for example. The result is a region of positively charged nuclear matter with negatively charged quark matter embedded in it.

Glendenning uses a vivid metaphor to describe how different a two-component phase change is from the one-component phase changes of water: "Suppose water had two independent components and one of them was electric charge, with opposite charge on the ice than on the water. Then a lake would not freeze over starting with a sheet of ice on top, but ice spheres would form throughout the volume of the lake, of slightly different size and spacing from top to bottom, because of the pressure gradient."

Glendenning theorizes that in a neutron star of the right mass and density, a crystal of hadronic and quark matter in mixed geometric configurations occupies the region between outer nuclear matter and inner quark matter.

Likewise, where hadronic matter and quark matter are mixed, if quark matter is in the minority the quarks are segregated as droplets in a crystalline array, each droplet at a lattice point. As the pressure increases the proportion of quark matter increases and the droplets elongate to rods; still more pressure means still more free quarks, and the rods join into slabs.

As pressure continues to increase, quark matter becomes the dominant phase, and the hadrons inside it form slabs, rods, and finally droplets, just before the system turns to pure quark matter. Glendenning jokingly refers to this as a pasta model: "Drops like orzo, rods like spaghetti, slabs like lasagna."

The picture of neutron star interiors based on two-component phase transitions is not intuitive (nothing about neutron stars is), and while Glendenning says he's astonished everybody before him missed it, he admits it took him five years to realize it himself.

But is there any way this theoretical understanding can ever be tested experimentally?

Putting a spin on the ball

In the early 1970s, nuclear physicists at Berkeley Lab and elsewhere observed that when certain rapidly spinning rare-earth nuclei like erbium and holmium are created in accelerator experiments, there is a moment when they temporarily slow down before spinning faster again. The explanation of this "backbending" spin seemed to be that while individual spinning protons or neutrons in the nucleus like to pair with others, forces induced by the spin of the nucleus as a whole break up some of these pairs. Inertia momentarily increases until the spins realign.

Tiny atomic nuclei aren't much like neutron stars, but Glendenning found the analogy striking: a change of state in one part of a rotating mixed system, the nucleon pairs, had a noticeable if temporary effect on the spin rate of the whole nucleus. He realized that the mixed states of hadronic matter and quark matter in a neutron star offered a comparable way for changes in part of the star to affect the spin rate of the whole.

Two conditions that can effect the spin of a neutron star, once its initial spin rate has been established in the collapse of the star that formed it, are drag and mass accretion. A pulsar is a neutron star with a strong magnetic field not aligned with its rotation axis; the moving magnetic field creates a broad band of electromagnetic radiation, including radio waves, which led to the discovery of the first pulsar in 1967. Radiation drags on the pulsar and gradually slows it down.

On the other hand, a neutron star that slowly sucks matter from a companion star becomes more massive and, like a spinning ice skater who pulls in her arms, spins increasingly faster.

If a spinning neutron star's magnetic field is not aligned with its rotation axis, the drag of electromagnetic radiation slows it down (foreground). A neutron star that accretes matter from a companion star becomes more massive and spins ever faster (background).

Because of centrifugal forces, the faster a star spins, the less the pressure in its interior, and vice versa. Phase change boundaries — where hadronic matter mixes with quark matter — migrate as the star's rotation rate changes.

If a pulsar spins slower, pressure increases, and pure quark matter may form or increase at its center. Quark matter is incredibly dense. So if the star as a whole is slowing down, like a spinning skater extending her arms, then adding more quark matter at its center would be like a massive tiny skater inside the big one, a set of spinning Russian dolls in which the innermost is pulling in her arms and forcing the whole cluster to spin up again — temporarily.

The same glitch happens in reverse. A star that's accreting matter and spinning faster will relieve internal pressure, which will cause a quark-matter core to move to a less dense mixed phase — temporarily causing the star to slow down.

"Neutron stars are relativistic objects in which extremes of gravity exaggerate these effects through frame-dragging," says Glendenning. "The massive spinning core causes the rest of the star to spin faster than it otherwise would."

"Backbending" as neutron stars spin faster or slower should be detectable as an increase in the number of neutron stars spinning at certain rates, among a population of neutron stars whose spin rates otherwise vary smoothly. A preliminary catalog of x-ray neutron stars showed just such a spike; unfortunately the compiler of the catalog later withdrew this result. Until more catalogs of neutron-star spin are compiled, and include more kinds of neutron stars, the question remains open.

How the matter in a neutron star arranges itself through phase changes is a subject of continuing lively interest. Astronomers are using new kinds of measurements to determine the mass and radius of neutron stars by observation, and theorists argue over what exotica may be found within them. Norman Glendenning's studies are an inevitable part of the continuing intellectual ferment.

Additional information

• More about Norman Glendenning's work on neutron stars and pulsars
• More about observational techniques for measuring the mass and radius of neutron stars