Plumbing the depths of neutron stars

28 March 2013

New techniques developed by the ISOLTRAP collaboration are allowing investigations of a possible birthplace of the heavy elements.

An illustration of the depth profile

Imagine the mass of the entire Sun squeezed into a radius of just 10 km. This is about the density of a neutron star – the highest density known in the cosmos. These extremely dense objects are the residues of core-collapse supernova explosions, so a significant fraction of the stars in the universe finish their lives this way. They are often present as binary systems that eventually merge, in principle radiating detectable gravity waves. Another tantalizing possibility is that the ejecta from these events might enrich the interstellar medium with heavy elements, created by a rapid neutron-capture process (the r process). The composition of neutron stars is therefore important yet the description of these ultracompact objects remains one of the biggest challenges facing nuclear and particle physics today.

As the name implies, neutron stars are essentially – but not wholly – composed of neutrons. As figure 1 shows, neutron stars are thought to consist of three layers: a homogeneous core and two concentric shells (Lattimer and Prakash 2004). The surface of the star contains only nuclei that are stable under natural terrestrial conditions. Below this “outer crust”, however, the rapidly increasing internal densities form nuclei that are increasingly neutron-rich, eventually reaching the “drip line”, or the brink of nuclear stability. This marks the transition to the “inner crust”, which is an inhomogeneous assembly of neutron–proton clusters and unbound neutrons that is neutralized by a quasi-uniform electron gas. Deeper into the star, the clusters start to smooth out, giving way to the inner core whose structure is the source of much debate.

Magic numbers

A landmark paper in 1971 presented a model for neutron stars that assumed cold, catalysed matter in which increasingly heavy and neutron-rich nuclides (resulting from electron capture) exist in a state of equilibrium for beta-decay processes (Baym, Pethick and Sutherland, 1971). The effects of the shell structure of nuclei mean that the nuclides residing in neutron-star crusts will cluster around the “magic” neutron numbers, N = 50 and 82, which correspond to closed shells (see figure 2). Indeed, one of the outstanding questions in nuclear physics is whether these magic numbers retain their “supernatural” characteristics in nuclides far from stability. The most exotic N = 50 and N = 82 species are therefore the priority for many experiments in nuclear physics.

Chart of nuclides

Neutron-star crusts present a situation in which solid-state physics is combined with nuclear physics and relativistic gravitation. Although it will remain impossible to create such conditions in the laboratory, recent developments in nuclear theory are now providing consistent and accurate knowledge of nuclear binding energies and a nuclear equation of state that can help to place the composition of the outer crust on firm ground. In analogy with ice cores, scientists can “drill” into the neutron star to determine the most abundant species in each layer. Using known masses, the composition of the outer crust has been well determined to a depth of about 215 m (for the star shown in figure 1) but deeper knowledge relies on theoretical models of nuclear masses. However, different state-of-the-art mass models do not predict the same composition and they can be tested only by high-precision mass measurements on further exotic species.

Unlike many scenarios in nucleosynthesis, where astrophysical uncertainties dominate those resulting from nuclear physics, those of the neutron-star crust are relatively robust. This is because of its likeness to a crystalline semiconductor in a sea of charge-carriers, except that the crust is a lattice of neutron-rich nuclides surrounded by neutrons. The lattice and thermodynamic conditions are therefore well defined, so the crustal composition will depend mainly on the nuclear binding energies.

The ISOLTRAP Penning-trap mass spectrometer at CERN’s ISOLDE radioactive-beam facility has pioneered the art of online precision mass measurements

The ISOLTRAP Penning-trap mass spectrometer at CERN’s ISOLDE radioactive-beam facility has pioneered the art of online precision mass measurements. It uses static electric and magnetic fields to confine ions in an unperturbed environment to weigh accurately the exotic nuclides produced by ISOLDE. Recently, an advance in mass spectrometry with the ISOLTRAP experiment combined with the state-of-the-art purification techniques at ISOLDE, have enabled a first measurement of the mass of 82Zn, an exotic nuclide predicted to reside in neutron-star crusts (Wolf et al. 2013).

The ISOLDE facility produces exotic zinc isotopes by fission in a uranium-carbide target bombarded by the 1.4 GeV proton beams from CERN’s PS-Booster (PSB). Because protons also induce transmutation through the process of spallation, other neutron-deficient elements having the same mass number (isobars) are also produced. Isobaric contamination is the worst enemy of exotic nuclides because their intensity can be up to a million times higher than that of the isobar being sought.

The first line of defence against this is a special version of an ISOLDE target that includes a tungsten convertor unit. Instead of aiming for the target itself, the PSB operators bear left, to hit the converter. The result is an effusion of slow neutrons that induce fission in the nearby target material but without producing the isobaric contamination that would result from direct spallation reactions. Having produced only neutron-rich isobars, the next line of defence is a highly selective, three-step laser excitation tuned to ionize only zinc isotopes. Yet another trick is then pulled from ISOLDE’s sleeve to eliminate residual surface-ionized isobars: a temperature-controlled quartz transfer-line between the target and the ion source. Nevertheless, despite these state-of-the-art precautions, more than 6000 ions per second of 82Rb were still present in the beam delivered to ISOLTRAP in comparison to just a few ions of zinc, making this one of the most challenging measurements of exotic nuclides to date.

To measure 82Zn, yet another type of ion trap was integrated into the suite of Paul and Penning traps comprising ISOLTRAP’s mass spectrometer. The multi-reflection time-of-flight mass separator (MR-ToF MS), shown in figure 3 (overleaf), allowed residual 82Rb+ contaminants to be separated in time after multiple reflections between electrostatic mirrors. The advantage over purification in Penning traps is a mass-resolving power in excess of 100,000, obtained in about only 15 ms. From the MR-ToF MS, the short-lived 82Zn+ ions were sent through an electronic beam gate, opened quickly for 82Zn but otherwise closed to block the contaminants. The purified sample was transferred to the first of two Penning traps situated in individual superconducting solenoids, where the ions were cooled in a helium buffer-gas in preparation for the final mass measurement in the second, hyperbolic high-precision Penning trap. There, the standard time-of-flight ion cyclotron-resonance technique was used to determine the mass. This successful implementation of the MR-ToF MS represents a pioneering advance in mass spectrometry.

Drilling deeper

Probing neutron-star composition requires solving relativistic equations, known as the Tolman-Oppenheimer-Volkov (TOV) equations, that govern hydrostatic equilibrium in neutron-degenerate matter. The TOV equations relate pressure and mass-energy to the neutron-star radius and therefore require an equation of state. Stable- and radioactive-beam facilities have provided substantial information about the equations of state of finite nuclei but even the most exotic systems studied have proton fractions of 25–30%, which is far larger than the few per cent found in neutron stars. With this in mind, a Brussels-Montréal collaboration has developed a model for predicting nuclear binding energies based on the Skyrme force – an effective interaction between nucleons that also provides an equation of state – within the same theoretical framework (Pearson et al. 2011).

Multi-reflection time-of-flight mass separator

With the new 82Zn mass, calculations were performed to “drill” deeper into the neutron-star crust. This was done by minimizing the Gibb’s free energy per nucleon, where the total pressure at a given depth can be determined by the electron pressure and the lattice pressure. The abundances of all neighbouring nuclides were calculated for an array of nucleon densities and pressures. Last, the depths of the crust at which the nuclides are formed can be found using the TOV equations. Figures 1 and 2 illustrate the results. Because the new mass is considerably less bound than the predictions of the mean-field model HFB-19, 82Zn is no longer present in the neutron-star crust. The nuclide 80Zn remains but its presence is now constrained experimentally – deeper in the core than predicted by HFB-19. This result has extended knowledge of the crust composition of neutron stars to new depths.

This composition may have relevance for the nucleosynthesis of heavy elements by the r process, named for the series of rapid neutron captures that are involved (Arnould et al. 2007). The decompression of a neutron star’s matter brought about by tidal effects from a merger with a black hole or another neutron star, allows an r process to occur as the ejected clump vaporizes into the interstellar medium. While the total ejected mass per event is relatively low, it can still explain the total enrichment of r nuclei in the Galaxy; moreover, the calculated abundance distribution is tantalizingly close to that observed in the Solar System. The robustness of these predictions to the variation of input parameters makes the composition of neutron stars one of the most promising situations for addressing the important question of the origin of the elements.

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