Eddington-limited X-ray Bursts as Distance Indicators. I. Systematic Trends and Spherical Symmetry in Bursts from 4u 1728−34

We investigate the limitations of thermonuclear X-ray bursts as a distance indicator for the weaklymagnetized accreting neutron star 4U 1728−34. We measured the unabsorbed peak flux of 81 bursts in public data from the Rossi X-Ray Timing Explorer. The distribution of peak fluxes was bimodal: 66 bursts exhibited photospheric radius expansion (presumably reaching the local Eddington limit) and were distributed about a mean bolometric flux of 9.2 × 10 erg cm s, while the remaining (non-radius expansion) bursts reached 4.5× 10 erg cm s, on average. The peak fluxes of the radius-expansion bursts were not constant, exhibiting a standard deviation of 9.4% and a total variation of 46%. These bursts showed significant correlations between their peak flux and the X-ray colors of the persistent emission immediately prior to the burst. We also found evidence for quasi-periodic variation of the peak fluxes of radius-expansion bursts, with a time scale of ≃ 40 d. The persistent flux observed with RXTE/ASM over 5.8 yr exhibited quasi-periodic variability on a similar time scale. We suggest that these variations may have a common origin in reflection from a warped accretion disk. Once the systematic variation of the peak burst fluxes is subtracted, the residual scatter is only ≃ 3%, roughly consistent with the measurement uncertainties. The narrowness of this distribution strongly suggests that i) the radiation from the neutron star atmosphere during radius-expansion episodes is nearly spherically symmetric, and ii) the radius-expansion bursts reach a common peak flux which may be interpreted as a standard candle intensity. Adopting the minimum peak flux for the radius-expansion bursts as the Eddington flux limit, we derive a distance for the source of 4.4–4.8 kpc (assuming RNS = 10 km), with the uncertainty arising from the probable range of the neutron star mass MNS = 1.4–2 M⊙. Subject headings: stars: neutron — X-rays: bursts — nuclear reactions — equation of state — stars: individual (4U 1728-34) — X-rays: individual (4U 1728-34)