Quasi-periodic oscillations (QPOs) observed in the giant flares of magnetars
are of particular interest due to their potential to open up a window into the
neutron star interior via neutron star asteroseismology. However, only three
giant flares have been observed. We therefore make use of the much larger data
set of shorter, less energetic recurrent bursts. Here, we report on a search
for QPOs in a large data set of bursts from the two most burst-active
magnetars, SGR 1806-20 and SGR 1900+14, observed with the Rossi X-ray Timing
Explorer (RXTE). We find a single detection in an averaged periodogram
comprising 30 bursts from SGR 1806-20, with a frequency of 57 Hz and a width of
5 Hz, remarkably similar to a giant flare QPO observed from SGR 1900+14. This
QPO fits naturally within the framework of global magneto-elastic torsional
oscillations employed to explain the giant flare QPOs. Additionally, we uncover
a limit on the applicability of Fourier analysis for light curves with low
background count rates and strong variability on short timescales. In this
regime, standard Fourier methodology and more sophisticated Fourier analyses
fail in equal parts by yielding an unacceptably large number of false positive
detections. This problem is not straightforward to solve in the Fourier domain.
Instead, we show how simulations of light curves can offer a viable solution
for QPO searches in these light curves.Comment: accepted for publication in ApJ; 12 pages, 7 figures; code +
instructions at https://github.com/dhuppenkothen/MagnetarQPOSearchPaper ;
associated data products at
http://figshare.com/articles/SGR_1900_14_RXTE_Data/1184101 (SGR 1900+14) and
http://figshare.com/articles/SGR_1806_20_Bursts_RXTE_data_set/1184427 (SGR
1806-20