Re-analysis of polarization in the γ-ray flux of GRB 021206

A previous analysis of the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observation of GRB 021206 found that the gamma-ray flux was 80 +/- 20 per cent polarized. We re-examine these data and find no signal that can be interpreted as due to polarization. First, we find that the number of scattering events suitable for measuring polarization - having been scattered from one detector to another, with a count produced in both - is considerably lower than estimated by Coburn & Boggs, by a factor of 10 (830 +/- 150, versus 9840 +/- 96). The signal-to-noise ratio of the data set is thus too low to produce a detection, even from a 100 per cent polarized source. None the less, we develop a polarization-detection analysis limited in sensitivity only by Poisson noise, which does not require a spacecraft mass model to detect polarization, as in Coburn & Boggs. We find no signal which might be interpreted as due to polarization of GRB 021206. Separately, we reproduce the Coburn & Boggs signal and show that it is not due to polarization. Rather, the Coburn & Boggs signal is consistent with the previously neglected systematic uncertainty in the 'null light curve' used for detection. Due to the low signal-to-noise ratio of the RHESSI data, our Poisson noise-limited analysis results in an upper limit consistent with 100 per cent polarization of the gamma-ray flux from GRB 021206. Thus, no observational constraint on the polarization of GRB 021206 can be derived from these data.