High Energy Astrophysics 4 JAN, 2015

Average power density spectrum of Swift long gamma-ray bursts in the observer and in the source rest frames

Average power density spectrum of Swift long gamma-ray bursts in the observer and in the source rest frames

We calculate the average power density spectra (PDS) of 244 long gamma-ray bursts detected with the Swift Burst Alert Telescope in the 15-150 keV band from January 2005 to August 2011. For the first time we derived the average PDS in the source rest frame of 97 GRBs with known redshift. For 49 of them an average PDS was also obtained in a common source-frame energy band to account for the dependence of time profiles on energy. Previous results obtained on BATSE GRBs with unknown redshift showed that the average spectrum in the 25-2000 keV band could be modelled with a power-law with a 5/3 index over nearly two decades of frequency with a break at ~1 Hz. Depending on the normalisation and on the subset of GRBs considered, our results show analogous to steeper slopes (between 1.7 and 2.0) of the power-law. However, no clear evidence for the break at ~1 Hz was found, although the softer energy band of BAT compared with BATSE might account for that. We instead find a break at lower frequency corresponding to a typical source rest frame characteristic time of a few seconds. We furthermore find no significant differences between observer and source rest frames. Notably, no distinctive PDS features are found for GRBs with different intrinsic properties of the prompt emission either. Finally, the average PDS of GRBs at higher redshifts shows possibly shallower power-law indices than that of low-z GRBs. It is not clear whether this is due to an evolution with z of the average PDS.

💡 Research Summary

The authors present a systematic study of the average power‑density spectrum (PDS) of long gamma‑ray bursts (GRBs) detected by the Swift Burst Alert Telescope (BAT) in the 15–150 keV band over a period spanning January 2005 to August 2011. A total of 244 long GRBs are considered, of which 97 have measured redshifts, allowing the construction of a rest‑frame (source‑frame) PDS for the first time. For a subset of 49 bursts, the authors also compute the PDS in a common rest‑frame energy interval to mitigate the known energy‑dependence of GRB temporal profiles.

The methodology follows a standard Fourier‑based approach. Light curves are rebinned to 0.5 s resolution, background‑subtracted, and windowed before applying a discrete Fourier transform. The squared amplitude yields the power spectrum, which is then averaged in logarithmic frequency bins. Two normalisation schemes are explored: (i) scaling the total integrated power to unity, and (ii) normalising to the mean power in the 0.1–1 Hz band. This dual normalisation permits assessment of how the choice influences the derived power‑law index.

The main results can be summarised as follows:

  1. Overall shape – Across the 0.01–10 Hz frequency range the average PDS follows a power‑law, with indices ranging from 1.7 to 2.0 depending on the normalisation and the specific GRB subset. This is somewhat steeper than the 5/3 (≈1.67) index reported for BATSE bursts in the 25–2000 keV band.

  2. Break frequency – The characteristic break observed near 1 Hz in BATSE data is not evident in the Swift sample. Instead, a more gradual turnover appears at lower frequencies (≈0.1–0.3 Hz in the rest frame), corresponding to a characteristic timescale of a few seconds in the source frame. The authors argue that the softer BAT energy band reduces high‑frequency power, effectively shifting the observable break to lower frequencies.

  3. Energy dependence – When the PDS is recomputed for the 49 bursts in a common rest‑frame energy band (e.g., 45–450 keV), the resulting power‑law indices are marginally steeper, indicating that part of the difference with BATSE may be attributed to the differing energy coverage.

  4. Redshift dependence – Dividing the sample into low‑z (z < 2) and high‑z (z > 2) groups reveals a tentative trend: high‑z GRBs exhibit slightly shallower indices (≈1.7) compared with low‑z bursts (≈2.0). However, the authors caution that selection effects (high‑z bursts tend to be brighter and longer) could mimic such a trend, and the statistical significance is modest.

  5. Intrinsic properties – Sub‑samples based on peak flux, duration (T90), and spectral slope show no statistically significant differences in their average PDS. This suggests that the temporal variability captured by the PDS is largely independent of these prompt‑emission characteristics, reinforcing the view that the underlying engine dynamics dominate the observed variability.

The discussion places these findings in the context of GRB emission models. The low‑frequency turnover may reflect the typical activity time of the central engine or the separation between successive internal shocks. The steeper overall slope relative to BATSE could be a consequence of reduced high‑frequency power in the softer BAT band, rather than an intrinsic change in the variability process. The possible redshift evolution, while intriguing, requires larger, more uniformly selected samples and perhaps multi‑instrument coverage to disentangle genuine cosmological evolution from observational bias.

In conclusion, the paper demonstrates that the average PDS of Swift long GRBs is well described by a single power‑law with index 1.7–2.0, lacks a clear 1 Hz break, and shows a low‑frequency turnover corresponding to a few‑second timescale in the source frame. No substantial differences are found between observer‑frame and rest‑frame analyses, nor between bursts with differing prompt‑emission properties. The tentative indication of a redshift‑dependent slope remains open for future investigation. These results provide a valuable benchmark for upcoming missions with broader energy coverage and for theoretical models aiming to reproduce the temporal variability of GRB prompt emission.