Measuring the mass-radius relation of neutron stars to determine the Equation of State (EOS) of ultra-dense matter
The labeled curves show mass-radius (M-R) relations from several different EOS as well as the limits on M and R obtainable with Constellation-X (based on 4U 1636-53, 582 Hz spin frequency; see also Strohmayer 2004). The elliptical confidence regions are derived from fitting the pulse profiles of burst oscillations. The model for the pulsations is an expanding hot spot on the rotating neutron star surface. The contours denote the statistical quality achievable with one burst (the big ellipse), and six bursts (the small ellipse). The dashed diagonal line (labeled z = 0.35) denotes the constraint from centroiding absorption lines, and the solid portion of the line gives an estimate of the accuracy in R from measuring the line widths
Neutron stars contain the highest density matter known in the Universe and their structure depends on the physics of the interactions between fundamental particles: protons, neutrons and their constituent quarks. The theory of such interactions, Quantum Chromodynamics (QCD), is not yet sufficiently constrained to accurately predict the state of matter at such extremes. The only way to constrain the low temperature high-density regime of QCD is with precise measurements of both the masses and radii of neutron stars. Accurate masses for some neutron stars have been obtained from observations of young neutron star pulsars in binary systems, but essentially nothing is known about the radii.
Accreting neutron stars in binary systems provide several unique opportunities to probe the structure of neutron stars: 1) A continuous supply of fresh metals allows higher atmospheric abundances of the line producing elements (such as Fe) to be present than in isolated (non-accreting) neutron stars, increasing the likelihood for the formation of a detectable absorption line spectrum. 2) Accretion also leads to thermonuclear X-ray bursts; brief but bright flashes of thermal X-ray radiation shining through the neutron star atmosphere, during which the spin rate of the neutron star can be observed directly (so called "burst oscillations"). These old neutron stars have also gained enough mass to probe the mass-radius relation in a different regime than the young pulsars. This leads to the possibility of obtaining mass-versus-radius curves for neutron stars, telling us a great deal about the state of matter at extreme densities (see Figure; Lattimer & Prakash 2001).
Constellation-X will be the first X-ray observatory with the capability of making simultaneous high spectral resolution and fast timing measurements of X-ray bursts. One may then simultaneously use several independent methods to constrain mass and radius, providing important checks on any systematic errors associated with either method.
Read more about the neutron star measurements possible with Constellation-X: