Studying Matter at Extreme Densities

Pulsars can be used to study the strong nuclear force. The density of matter at the center of neutron stars is one or two orders of magnitude larger than the density of atomic nuclei. The behavior (i.e., the exact relation between pressure and density, known as equation of state, or EOS) of "cold" matter under such conditions is not known. Understanding the behavior of matter at very high densities is one of the priorities for research in astrophysics outlined in the report of the National Academies entitled From Quarks to the Cosmos: Eleven Science Questions for the New Century (Board on Physics and Astronomy, 2003, National Academies Press).

Most massive pulsar ever!

One way to learn about the EOS is by measuring the masses of recycled pulsars, which have accreted matter for a long period of time. Very "soft" EOSs predict lower pressures for a given density, i.e., highly compressible matter. This results in very small, compact stars with very high gravitational fields, these are very close to forming black holes. Most of these EOSs predict upper limits for the mass of a neutron star of about 1.6 solar masses (above that limit, the star implodes and forms a black hole). If one can find a more massive star, we can exclude such "soft" EOSs.

Mass-mass plot for PSR J0751+1807


Constraints on pulsar and secondary masses from the general relativistic timing model. Confidence limits of 68% and 95% are shown. The shaded region in the lower left is disallowed by the Keplerian mass function.  Dashed lines show constraints from the orbital decay alone. A dotted line indicates an inclination of 60 degrees.

A recent Arecibo experiment has important implications for this study. Nice et al. 2005 have recently published the results of the long-term timing of PSR J0751+1807, a 3.48-ms pulsar in a tight binary system with a white dwarf companion. The measurement of the Shapiro delay and orbital decay of this system indicate that its mass is 2.1 +/- 0.2 solar masses (see figure above). If more precise measurements can confirm this high value, then many model EOSs for dense matter can be ruled out. In this case, matter at the cores of neutron stars is highly incompressible.

Fastest pulsar ever!

Another way of studying the behavior of super-dense matter is to find fast pulsars. This excludes "stiff" EOSs, which predict that matter is highly incompressible. That would produce very large stars that can not withstand large spin frequencies without breaking apart. Until recently, the fastest known pulsar was PSR B1937+21, the first millisecond pulsar (MSP) to be discovered. This object rotates 642 times per second, its discovery in 1982 at the Arecibo Observatory excluded some very stiff EOSs.

Pulse profile of Terzan 5 ad


Pulse profile for PSR J1748-2446ad, repeated for clariy, for the best detection of this pulsar. The apparent interpulse has high statistical significance, particularly in plots where the best observations are co-added.

Paulo Freire, an Arecibo Observatory Staff member, is part of an international team that is using the S-band receiver of the Green Bank Telescope to search for millisecond pulsars in globular clusters. So far, a total of 50 MSPs have been found by this project (Ransom et al. 2006), 30 of these in the globular cluster Terzan 5 (for the first 21 discoveries in that cluster, see Ransom et al. 2005, see also the list of pulsars in globular clusters which includes these 50 new objects). One of the recent discoveries, Terzan 5 ad, has a spin frequency of 716 Hz, i.e., it is now the most rapidly spinning pulsar known (Hessels et al. 2006). This is not yet fast enough to introduce significant constraints on the EOS, but it constrains models of neutron stars crusts and models of the emission of gravitational waves by the star's rotation. It also opens up the possibility that faster pulsars might be found in the future.