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 .
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 \times 10 ^ { -8 } { erg cm ^ { -2 } s ^ { -1 } } , while the remaining ( non-radius expansion ) bursts reached 4.5 \times 10 ^ { -8 } { erg 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 time scale of \simeq 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 \simeq 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 R _ { NS } = 10 km ) , with the uncertainty arising from the probable range of the neutron star mass M _ { NS } = 1.4 –2 M _ { \sun } .