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Mass of a Neutron Star Determined

September 13, 2004

The radius and mass of a neutron star have been determined. Astrophysicists Tod Strohmayer of the NASA Goddard Space Flight Center and Adam Villarreal of the University of Arizona have determined the radius and mass of the neutron star in the x-ray binary system EXO 0748-676. The radius and mass constrain the theories for the composition of neutron stars. Strohmayer and Villarreal presented their work at the meeting in New Orleans, Louisiana, USA of the High-Energy Astrophysics Division (HEAD) of the American Astronomical Society on September 8.

The binary system EXO 0748-676 is a transient x-ray burst source belonging to the class of x-ray binary called the Low-Mass X-ray Binary (LMXB).1 It has an orbital period of 3.82 hours, and it is observed in both the optical and the x-ray energy bands. Its light curve, which is the intensity of the source as a function of time, shows an eclipse of the neutron star in the system is eclipsed by its companion. The light curve also has a dip caused by the eclipse of the neutron star by the region of the accretion disk that is struck by the material streaming from the companion. The eclipses imply that the orbital system axis is inclined by 73°–83° to the observer, with the precise angle dependent on the mass and radius of the neutron star.

In a previous observation with the European Space Agency's XMM-Newton satellite, Jean Cottan of the NASA Goddard Space Flight Center and his colleagues observed narrow absorption lines that show evidence of a gravitational redshift,2 from which one can derive the ratio of a star's mass to its radius.

To find independent values of mass and radius requires a second piece of data. Strohmayer and Villard say that they have this through their discovery of a 47 Hertz variability in the x-ray light curve observed with the NASA Rossi X-Ray Timing Explorer, a satellite orbiting Earth. They state this frequency is a consequence of the rotation of the neutron star, and it is equal to the rotation frequency. The width of an absorption line is partially set by the motion of the emission region towards and away from the observer as the star rotates, and it therefore a measure of the rotation velocity of the emission region. Combining a velocity derived from a model fit to the line with the rotation rate derived from the variability of the light curve gives the distance of the emission region from the rotation axis of the neutron star. If the emission region is at the equator, then this distance equals the radius of the neutron star. Strohmayer and Villard find a radius in the range of 9.5 and 15 km, with a best estimate of 11.5 km. With this radius, the offset of the absorption line center gives a gravitational redshift that is consistent with a stellar mass of 1.5 and 2.3 solar masses, with a best value of 1.75 solar masses.

The importance of finding both the mass and the radius of a neutron star is that with these values one can constrain the theories for the composition of the neutron star's interior. The densities at the core of a neutron star are the highest for any star in the universe. For the values given above, and ignoring the effects of general relativity, one finds an average density of 3 × 1014 gm cm-3. In comparison, the average density of Earth is 5.5 gm cm-3. At these densities, the interior of the neutron star is expected to be composed of free neutrons, protons, and electrons; the interior is too dense for individual atomic nuclei to survive.

Currently the only information available is from the press release, which does not discuss the analysis of the data, so an independent evaluation of their analysis is not yet possible. The modeling of absorption lines is a tricky business, because the shape and position of a line is dependent not only on the rotation of the star and the gravitational potential at the star's surface, but also on the temperature and motion of the emitting gas. The latitude at which the emission occurs and the orientation of the star's rotation axis both affects the value found for the radius, so a model dependence is introduced in deriving a value for the stellar radius. One presumes this is the source of the broad range of values for the radius.

1 Binary systems in the Low-Mass X-ray Binary (LMXB) class consist of a neutron star and a low-mass main-sequence star that are in a tight orbit. The atmosphere of the main-sequence star is pulled by the neutron star's gravity into orbit around the neutron star, forming an accretion disk. The accretion disk gradually releases gravitational potential energy, which is radiated away as as light at the infrared, optical, ultraviolet, and x-ray energies. As the gas looses energy, it slowly moves to lower orbits until it flows into the neutron star's atmosphere. Over time, the atmosphere of the neutron star builds up a thick layer of hydrogen and helium that is under high pressure. This layer is unstable to a thermonuclear runaway, and eventually it detonates, producing a massive x-ray burst.

2 The absorption of light by an atom occurs at specific characteristic energies. These characteristic energies can be changed if the atom is in motion and if the atom is at a different gravitational potential than the observer. The motion of an atom produces a doppler shift of the lines. Atoms have a thermal motion and they have a motion from the bulk motion of the medium they are in. The thermal motion produces a broadening of an absorption line, with a line's width set by the temperature of the medium. The bulk motion can either red shift (a shift to lower energy) or blue shift (a shift to higher energy) a line if there is only one velocity for the medium. When the absorbing medium is characterised by many bulk velocities, the line is not only shifted in energy, it is also broadened. For instance, if the emission is spread over the surface of a rotating star, the radiation emitted at the limb of the star moving towards the observer is blue shifted, that emitted at the limb moving away from the observer is red shifted, and the total effect is the broadening of the line.

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