Neutron stars are presumed to contain the densest matter in the cosmos. These remnants of core-collapse supernovae pack more than the Sun’s mass (M ⊙) into a sphere less than 30 km across. There is considerable uncertainty about the character of matter squeezed to such ultrahigh densities, which cannot be reproduced in the laboratory.
As the name implies, much of a neutron star’s interior is probably just neutrons packed together at a density of about 1015 g/cm3—a few times that of a typical nucleus. The protons and electrons of the progenitor material have mostly merged into neutrons by inverse beta decay.
Theorists speculate, however, that at the highest densities near the cores of the most massive neutron stars there may be phase boundaries that enclose more exotic states: free-quark matter rich in strange quarks, Bose–Einstein condensates of K mesons, or simply nuclear matter in which a significant fraction of the neutrons have become hyperons (baryons harboring strange quarks).
But now much of that speculation has abruptly been laid to rest by a single astrophysical weighing. Using the National Radio Astronomy Observatory’s 100-meter-diameter telescope in Green Bank, West Virginia, NRAO’s Paul Demorest and coworkers have measured the highest neutron-star mass ever determined in a precision weighing.1 The neutron star in the binary-pulsar system J1614−2230, they report, has a mass of 1.97 ± 0.04 M ⊙. The previous record was 1.67 ± 0.01 M ⊙.
Ruling out exotic cores
Now we know for the first time that neutron stars can be twice as massive as the Sun. So what? “Actually, it’s quite amazing how much that simple fact tells you,” says NRAO team member Scott Ransom. To begin with, it rules out most of the proposed equations of state (EOSs) that predict exotic phases for sufficiently compressed nuclear matter.
Every putative EOS is characterized by some maximum neutron-star mass M max beyond which collapse to a black hole would be inevitable. It turns out that the predicted M max is generally smaller for EOSs that allow transitions to exotic phases than for those that don’t. In effect, the extra degrees of freedom introduced by the possibility of such transitions make the star less resistant to contraction.
Both nuclear and quark matter are fermionic systems of spin-1⁄2 particles for which the Pauli exclusion principle dictates that increasing compression requires increasing particle momenta. Conjectures of exotic fermionic phases with abundant hyperons or strange quarks are speculative attempts to lower ground-state energies by mitigating the exclusion principle’s energy cost. So is the introduction of bosonic meson condensates.
For various classes of proposed EOSs, figure 1 shows the range of predicted M max and, below those upper limits, the dependence of a neutron star’s radius on its mass. For almost all EOSs that yield exotic hadronic matter (hyperons, kaonic Bose condensates, and the like) the mass–radius tracks terminate well below the newly measured J1614 mass, and they are therefore ruled out by that measurement.
Some EOSs that yield strange-quark matter are barely consistent with the new record mass, but only if the quarks, far from being “free,” interact almost as strongly as they do in hadrons. Such detailed implications of the record neutron-star mass are discussed in a follow-up paper by Feryal Özel (University of Arizona) and two other theorists, in collaboration with the NRAO observers.2
A spinning neutron star usually generates a radio beam along its magnetic-field axis. If that axis is misaligned with the star’s spin axis, the radio beam sweeps out a lighthouse pattern, and a fortunately situated observer sees the neutron star made manifest as a radio pulsar whose pulse frequency is the star’s spin rate.
The binary pulsar J1614 was discovered in 2003, at a distance of about 3000 light-years. Its rapid spin yields a very stable pulse period of 3.15 milliseconds. The neutron star and its lighter, white-dwarf companion orbit the system’s center of mass with a period of about nine days. The orbit is evident in the pulsar’s nine-day Doppler-shift period. But that’s not enough for a mass determination of the neutron star or its companion.
For binary-pulsar pairs of neutron stars in tight, highly eccentric orbits, one can often exploit the general-relativistic precession or decay of those orbits to measure both masses with high precision. The many neutron-star masses thus measured in recent decades cluster in the range 1.25–1.4 M ⊙ (see the yellow band in figure 1). But that narrow range probably reflects a bias introduced by requiring double-neutron-star binaries.
Therefore radio astronomers, in their search for heavier neutron stars, have been looking at heterostellar binaries like J1614, with orbits too large and circular for good measurement of decay or precession. Instead, they aim to exploit another observational consequence of general relativity, which went unnoticed until 1964.
In that year, Irwin Shapiro pointed out—and soon demonstrated with radar beams bounced off planets—a general-relativistic increase in the travel time of light passing by a massive object. The Shapiro effect is above and beyond that due simply to increased path length from gravitational bending. In the case of a felicitously oriented binary-pulsar system, radio pulses from the neutron star would be delayed for a few microseconds whenever in the orbital cycle they pass close to a sufficiently compact companion on their way to the observer (see the cartoon orbits in figure 2). White dwarfs, though not nearly as compact as neutron stars, are 105 times denser than the Sun.
A good measurement of how the Shapiro delay varies over an orbital cycle would yield the masses of both the pulsar and its companion. But a random pulsar with a white-dwarf companion in our corner of the Milky Way would exhibit only a very weak Shapiro signal. The amplitude of the periodic signal is proportional to the companion’s mass, and the sharpness of its peak depends sensitively on the inclination of the orbital plane to the line of sight. The effect is strongest when the orbital plane is seen edge-on.
”Low-resolution timing measurements of J1614 over the years suggested it might yield a fairly decent Shapiro signal,” recalls Demorest. “But what we found in our recent high-resolution nine-day observation [shown in figure 2] was spectacular beyond all expectation.”
J1614 turned out to be the most nearly edge-on binary pulsar yet seen. The data revealed an angle of 89.17 ± 0.02° between the orbital plane’s normal and the line of sight. The strength and clarity of the observed signal also benefit from two other fortunate circumstances, one natural, the other instrumental: The companion’s mass, 0.500 ± 0.006 M ⊙, is three times that of a typical white dwarf in a binary-pulsar system. And the observation owes much to GUPPI, the innovative Green Bank Ultimate Pulsar Processing Instrument installed on the radio telescope shortly before the nine-day observation last March.
Performing ultrahigh-speed computer processing of each pulse as it arrives, GUPPI provides a fourfold improvement in the telescope’s timing resolution. It also corrects for signal smearing due to dispersion by interstellar electrons.
As a function of orbital phase in the nine-day circuits of the pulsar and its companion, figure 2 plots the measured delay of the pulse arrivals relative to what one would expect in the absence of the Shapiro effect. The zero of the orbital phase is taken to be the moment when the white dwarf is closest to our line of sight to the pulsar.
Demorest and company took a large fraction of their data near that moment of “orbital conjunction,” where one expects the strongest and most rapidly varying Shapiro delay. The cusped curve shows the best theoretical fit to the single-orbit GUPPI measurements plus auxiliary longer-term Doppler data. That fit yields the impressively precise determinations of the two masses and our viewing angle of their orbital plane.
Merging neutron stars
Beyond ruling out most proposed scenarios for exotic matter in neutron stars, the new record mass has other important implications.2 Among them is a possible answer to the long-standing puzzle of what causes the short-duration minority subclass of gamma-ray bursts (see PHYSICS TODAY, November 2005, page 17 ). There’s much evidence that short GRBs signal the cataclysmic merger of two neutron stars into a black hole. But short GRBs typically last a second or two, which is much too long for the naive dynamical time scale of such mergers.
But now that we know that neutron stars can be heavier than 1.8 M ⊙, Özel and company argue, two scenarios for prolonging the GRB become possible: The merged system might be momentarily supported by centrifugal forces that take about a second to dissipate and allow the final collapse. Alternatively, the formation of the black hole might not be delayed, but in the process a massive accretion disk could form and be devoured in something like a second.
Neutron-star mergers are also expected to be a principal source of gravitational-wave signals recorded by ground-based detectors in the near future. A later generation, capable of recording such signals at frequencies beyond a kilohertz, should reveal much about the inner characteristics of the merging neutron stars. But how much can one learn from the lower-frequency components to which LIGO and the next generation of detectors are limited?
In that regard, the existence of 2-M ⊙ neutron stars is encouraging. If neutron stars had the highly condensed cores expected for exotic matter, little information about their interiors would be encoded at frequencies below 600 Hz by tidal deformation during a merger. But having largely ruled out such condensed cores, the collaboration concludes that the detection of gravitational waves, even at low frequencies, “will allow accurate measurements of the equation of state of neutron-star matter in the near future.”2