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 weakly magnetized 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 (RXTE). 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 x 10(-8) ergs cm(-2) s(-1), while the remaining ( non - radius expansion) bursts reached 4.5 x 10(-8) ergs cm(-2) s(-1), 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 timescale of similar or equal to40 days. The persistent flux observed with RXTE/ASM over 5.8 yr exhibited quasiperiodic variability on a similar timescale. 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 similar or equal to3%, roughly consistent with the measurement uncertainties. The narrowness of this distribution strongly suggests that ( 1) the radiation from the neutron star atmosphere during radius expansion episodes is nearly spherically symmetric and ( 2) the radius expansion bursts reach a common peak flux that 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 R-NS = 10 km), with the uncertainty arising from the probable range of the neutron star mass M-NS = 1.4 - 2M(.).