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Section 8: Superfluidity on a Cosmic Scale

We conclude this unit with an introduction to some truly high Tc superfluids—the neutron superfluids found in the crust and core of a neutron star, for which Tc can be as large as 600,000 K. As we will see, the remarkable behavior of these superfluids not only enables us to study their emergent behavior by observing pulsars located many light-years away, but also establishes that these represent the most abundant superfluids in our universe.

The first director of the Los Alamos National Laboratory, Robert Oppenheimer (ca. 1944) was a brilliant theoretical physicist and inspired teacher who became famous for his remarkably effective leadership of the Manhattan Project.

Figure 27: The first director of the Los Alamos National Laboratory, Robert Oppenheimer (ca. 1944) was a brilliant theoretical physicist and inspired teacher who became famous for his remarkably effective leadership of the Manhattan Project.

Source: © Los Alamos National Laboratory. More info

Russian physicist Arkady Migdal suggested in the 1960s that cosmic hadron superfluids might exist in neutron stars. If the neutron stars studied by Robert Oppenheimer in 1939 existed, he reasoned, then in light of the fact that nuclei in the outer shells of terrestrial nuclei exhibited superfluid behavior, the neutrons these stars contained would surely be superfluid. Not long afterwards, Vitaly Ginzburg and David Kirshnitz argued that neutron stars, if indeed they existed, would surely rotate, in which case their rotation should be described in terms of the quantized vortex lines seen in liquid He.

An image taken by the Chandra X-ray telescope of the Vela supernova remnant that shows dramatic bow-like structures produced by the interaction of radiation and electron beams coming from the  rapidly rotating neutron star in its center with its immediate environment.

Figure 28: An image taken by the Chandra X-ray telescope of the Vela supernova remnant that shows dramatic bow-like structures produced by the interaction of radiation and electron beams coming from the rapidly rotating neutron star in its center with its immediate environment.

Source: © NASA, PSU, G. Pavlov et al., courtesy of Chandra X-ray Observatory. More info

The issue of such cosmic superfluidity remained a gleam in the theorist's eye until 1967. In that year, Cambridge graduate student Jocelyn Bell, who was studying atmospheric-produced scintillations of radio signals in Antony Hewish's radio astronomy laboratory, discovered pulsars. Astronomers soon identified these objects as rotating neutron stars which slowed down in remarkably regular fashion as they transferred their rotational energy into electromagnetic waves and accelerated electron beams.

Two years later, V. Radhakrishnan and Richard Manchester, using a radiotelescope in Australia, and Paul Reichley and George Downs, based at Caltech's Jet Propulsion Laboratory, independently observed that a comparatively young and fast pulsar, the Vela pulsar with an 89 ms period of rotation, "glitched." First, instead of continuing a remarkably regular spin-down produced by the transformation of its rotational energy into the beams of radio emission observed on Earth, it sped up by a few parts in a million.

Then, over some days to weeks, the sudden spin-up decayed. That a sudden spin-up of a tiny astronomical object with a radius of about 10 kilometers but a mass of the order of our Sun should occur at all is remarkable. Indeed, astronomers might have treated the glitch report as a malfunction of an observing radio telescope had not observers working independently in Australia and California both seen it. But perhaps more remarkable is the fact that astronomers could actually observe a glitch, since a response time for ordinary neutron matter would be about 10-4 seconds, the time it takes a sound signal to cross the star. So, under normal circumstances, a glitch and its response would be gone in less time than the twinkling of an eye.

Radiotelescope observations of postglitch behavior in the Vela pulsar.

Figure 29: Radiotelescope observations of postglitch behavior in the Vela pulsar.

Source: © Sarah Buchner, Hartebeesthoek Radio Astronomy Observatory, South Africa. More info

The explanation was soon forthcoming: The slow decay time provided unambiguous evidence for the presence of superfluid neutrons in the pulsar. The reason was that these can change their angular momentum only by the postglitch motion of the vortex lines they carry and that process could easily be imagined to take days to months.

Why glitches occur

 This recent image from the Chandra X-ray telescope shows the Crab Nebula, the remnant of a supernova explosion seen on Earth in 1054 AD that accompanied the formation of a rapidly rotating neutron star at its center.

Figure 30: This recent image from the Chandra X-ray telescope shows the Crab Nebula, the remnant of a supernova explosion seen on Earth in 1054 AD that accompanied the formation of a rapidly rotating neutron star at its center.

Source: © NASA, CXC, and SAO. More info

Theorists initially thought that the origin of the glitch was extrinsic to the neutron superfluid. They envisioned a starquake in which part of the stellar crust crumbled suddenly in response to the forces produced by changes in the star's shape induced by pulsar spindown. But the observation of a second glitch in the Vela pulsar quickly ruled out that explanation for Vela pulsar glitches, since an elementary calculation showed that the expected time between such massive starquakes would be some thousands of years. Typical intervals between Vela pulsar glitches are some two years. It should be noted that for the much smaller glitches (a few parts in 100 million) seen in very young pulsars, such as that located in the Crab Nebula, whose age is less than 1,000 years, starquakes continue to provide a plausible explanation of their origin.

In 1975, Philip Anderson and Naoki Itoh came up with what astrophysicists now recognize as the correct explanation of the frequent pulsar glitches seen in the Vela and other older pulsars. Glitches, they argued, are an intrinsic property of the crustal neutron superfluid and come about because the vortex lines that carry the angular momentum of the crustal superfluid are pinned to the crustal nuclei with which they coexist. As a result, the superfluid's angular velocity, which can change only through the motion of its vortices, will lag that of the crust. The lag will persist until a sufficiently large number of vortices are pinned, at which point these unpin catastrophically, bringing about a sudden jump in the angular momentum of the star—a glitch—while their subsequent motion determines the postglitch behavior produced by superfluid response to the glitch.

An illustration of two possible regimes of pinning for superfluid vortices in the crust of a neutron star. Left: the weak pinning expected when the size of the normal core,  of a vortex in the crustal neutron superfluid vortex is comparable to that of a crustal nucleus. Right the superweak pinning expected for a much larger vortex normal core.

Figure 31: An illustration of two possible regimes of pinning for superfluid vortices in the crust of a neutron star. Left: the weak pinning expected when the size of the normal core, of a vortex in the crustal neutron superfluid vortex is comparable to that of a crustal nucleus. Right the superweak pinning expected for a much larger vortex normal core.

Source: © Reproduced by permission of the AAS. Courtesy of M.A. Alpar, P.W. Anderson, D. Pines, and J. Shaham, 1983. More info

Unexpectedly, perhaps, careful study of the range of pinning possibilities and the nonlinear response of the superfluid to unpinning events has made it possible to identify the distinct pinning regions in the stellar crust shown in Figure 30 by their different response to a glitch and to explain the characteristic response times identified in the postglitch behavior of the Vela and other pulsars. Still more surprising, a careful analysis of the glitch magnitude and the superfluid postglitch response of a given pulsar now makes it possible to predict with some accuracy (roughly tens of days, say, for glitches separated by intervals of order years) the time to its next glitch.

A summary of our present theoretical understanding of the components of a neutron star is given in Figure 32, while some recent observations of the two best-known neutron stars, those found in the Crab and Vela constellations, are illustrated in Figures 28 and 30.

Superfluids in the stars

Based on the roughly 25 glitching pulsars observed so far, we can easily establish that the amount of cosmic neutron superfluid observed thus far is several solar masses, or some 1034 grams. That far exceeds the quantity of terrestrial superfluid ever produced or observed. Further, the amount of cosmic neutron superfluid contained in neutron stars that have yet to be seen to glitch is likely an order of magnitude larger.

A cross section of a neutron star shows the rich variety of emergent quantum matter expected in its crust and core.

Figure 32: A cross section of a neutron star shows the rich variety of emergent quantum matter expected in its crust and core.

Source: © Dany Page. More info

Interestingly, glitch observations also provide us with important information on the hadron equation of state, since one that is too soft will not yield a crust sufficiently thick (~ 1 km) to support the region of pinned crustal superfluid we need to explain glitches. On combining this with information from direct measurements of pulsar masses in binary systems, theorists now conclude that the hadron equation of state that describes the behavior of matter in the inner core of the star depicted in Figure 32, is sufficiently stiff that one will not find quark or other proposed exotic forms of matter there.

Developing an emergent perspective

While the author was receiving radiation treatment for prostate cancer at UCSF in San Francisco in the spring of 1999, with time on his hands following his early morning irradiations, he arranged to visit Stanford two days a week to discuss with his colleague Bob Laughlin various issues relating to the then newly formed Institute for Complex Adaptive Matter.

What emerged from those discussions was a paper, "The Theory of Everything." In it, we pointed out the obvious—that there can be no "theory of everything" in an emergent universe in which it is impossible to calculate with precision the result of bringing more than a dozen or so particles together, to say nothing of the difficulties in dealing with the living matter (discussed in Unit 9). We then called attention to the not so obvious; that despite this, one knows many examples of the existence of higher organizing principles in nature—gateways to emergence that lead to protected behavior in the form of exact descriptions of phenomena that are insensitive to microscopic details.

In this unit, we have considered a number of well-established quantum protectorates: the low-energy excitation spectrum of a conventional crystalline insulator, which consists of transverse and longitudinal sound, regardless of microscopic details; the low energy screening of electron interactions in quantum plasmas; the low-energy behavior of a Landau Fermi liquid; and the low-energy excitation spectrum of a conventional superconductor which is characterized by a handful of parameters that may be determined experimentally but cannot be computed from first principles. We have also considered a newly discovered candidate protectorate, the emergence of the Kondo liquid in heavy electron materials.

In "The Theory of Everything," we emphasized the importance of developing an emergent perspective on science, a perspective espoused years earlier by P. W. Anderson in his seminal article, "More is Different." The importance of acquiring and applying that emergent perspective—the realization that we have to study the system as a whole and search for the organizing principles that must be at work to bring about the observed emergent behavior—is arguably the most important takeaway message of this unit.

An emergent perspective is also needed as we confront emerging major societal challenges—human-induced climate change, terrorism, our current global economic meltdown. These are all caused by humans; and in searching for an appropriate emergent response, we begin by seeking to identify their origins in societal behavior. But now there is a difference. Because these emerging challenges have no unique cause, it follows that there is no unique or even "best" solution. So we must try many different partial solutions, invent many new institutions, and, above all, experiment, experiment, experiment, as we address the various candidate causes, hoping (and expecting) that in the process some of these experiments will work. If all goes well, because everything is pretty much connected to everything else, a set of related solutions that begin to produce the desired result will emerge over time.

The selection of the examples of emergent behavior in quantum matter to be discussed in this unit has been a quite personal one. There are so many interesting examples of emergent behavior in quantum matter that the unit could easily have been 10 times its present length; in choosing which to present, the author decided to focus on examples drawn from his personal experience. He hopes the reader/viewer will be inspired to explore a number of other important examples on her/his own. Among those highly recommended are the discovery and explanation of quantum Hall states, metal-insulator transitions, dynamical mean field theory, quantum critical behavior, the recently discovered topological insulators, and the emerging fields of spintronics, nanoscience and nanotechnology, and quantum information.