The mass of the neutron star in SMC X-1

1. The mass of the neutron star in SMC X-1 A.K.F Val Baker, A.J. Norton & H. Quaintrell Department of Physics and Astronomy, The Open University, Walton Hall, Milton Keynes, MK7 6AA Introduction • X-ray pulsars are accreting X-ray binary systems where compact object is a highly magnetized rotating neutron star. • Direct measurement of neutron star mass if system is eclipsing. • If their masses can be measured to high accuracy, the equation of state for nuclear matter may be constrained. • Only 7 eclipsing X-ray binary pulsars currently known. The mass ratio qis defined as: A value forican be found from the following geometrical approximation: where Mx is the mass of the neutron star, Mo is the mass of the optical companion, Kx is the semi amplitude of the neutron star’s radial velocity curve, which can be found from pulse timing delays and Ko is the semi-amplitude of the optical stars radial velocity curve, which can be found from optical spectroscopy. where a is the separation of the centres of mass of the two stars, qe is the eclipse half angle andb is the ratio of radius of the optical companion to that of its Roche-lobe, RL. RL has been found to be reasonably well fitted by the expression: For a circular orbit it can be shown that: where A, B and C are constants that depend on W, the ratio of rotational period of the giant star to the orbital period (Rappaport & Joss1983). and similarly, where iis the inclination of the orbital plane to the line of sight and P is the period of the orbit. History of SMC X-1 • SMC X-1 is an eclipsing X-ray pulsar located in the Small Magellanic Cloud (SMC). • Optical counterpart is the B0I supergiant Sk 160. • Long quasi stable period of 50-60 days - believed to be result of quasi periodic obscuration of the neutron star by a precessing accretion disk. • Mode of mass transfer believed to have significant contributions from Roche-lobe overflow, as the stellar winds observed in Sk 160 are not strong enough to power accretion from the secondary onto the primary. • Mass of the neutron star was first found using image-tube photographic spectroscopy. • Reynolds et al. (1993) were the first to account for heating of the donor star by the X-ray flux from the neutron star. • van Kerkwijk et al. (1995) pointed out the uncertainties introduced in this approach by not allowing for an accretion disk and suggested that corrections for heating effects may be an over estimation. • van der Meer et al. (2005) found a low value for the mass of the neutron star - did not account for heating corrections. Observations • August/September 2000 • 1.9m Radcliff telescope. • Sutherland Observatory in South Africa (SAAO). • The grating spectrograph – resolution of 0.5/Å pixel. • 56 usable spectra spanning the wavelength range 4300 – 5100Å Analysis • Each spectrum of Sk160 was cross-correlated against the median spectrum of HR1174. • Resulting radial velocities were heliocentric corrected. • A simple sinusoid was fitted to a combination of our data and Reynolds et al.’s data. • Using the semi-amplitude found from this fit, the masses of the two stellar components were found. • Monte Carlo methods were used to determine the uncertainties on the inferred values. • An upper limit for the mass was obtained by assuming Sk 160 fills its Roche-lobe. • A lower limit for the mass was obtained by assumingi = 90o. Median spectrum of Sk 160 Raw radial velocity curve and best fit X-ray heating corrections • Radial velocity measurements of the optical companion in a binary system reflect its motion about the centre of light. • In Keplerian orbits the centre of light should be approximately coincident with the centre of mass. • Heating of the optical companion by the X-ray source can lead to a variation between the centre of light and the centre of mass. • Due to the heating and temperature dependence of spectral lines, the shift in line centre may vary significantly. • In this study we only used the helium lines for cross-correlation, so these effects can be ignored. • To correct for the heating effects we ran models using the sophisticated light-curve synthesis program LIGHT2 (Hill 1988). • The program generates non-Keplerian velocity corrections by averaging a velocity based on contributions from weighted elements of the giant stars projected stellar disk. • The code was required to run through 3 iterations before convergence. Heating corrected radial velocity curve and best fit Discussion • Our final value for the systemic velocity of SMC X-1, g =179.2±1.5 km s-1 is in excellent agreement with previously obtained values (e.g. Hutchings et al. 1977). • Our raw value for Koand the corresponding upper limit on the neutron star mass, 1.020.10 Mסּ, are both comparable with those found by van der Meer et al. (2005). • Previous studies assume the giant star is Roche-lobe filling, thus giving only upper limits to the stellar masses. • Effects of X-ray heating on the inner hemisphere of Sk 160 are present but not dramatic (Reynolds et al. 1993). • Non-Keplerian corrections, for Her X-1, found from both a diskless model and a disk model are in good agreement (Reynolds et al. 1997), so we assume the lack of a disk in LIGHT2 does not affect our results significantly. • We conclude that the mass of the neutron star in SMC X-1 lies in the range 0.92±0.09 Mסּ≥Mx≥ 1.22±0.10 Mסּ. 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