  Power density spectra (PDSs) of long gamma-ray bursts provide useful
information on GRBs, indicating their self-similar temporal structure. The best
power-law PDSs are displayed by the longest bursts (T_90 > 100 s) in which the
range of self-similar time scales covers more than 2 decades. Shorter bursts
have apparent PDS slopes more strongly affected by statistical fluctuations.
The underlying power law can then be reproduced with high accuracy by averaging
the PDSs for a large sample of bursts. This power-law has a slope alpha\approx
-5/3 and a sharp break at 1 Hz.
  The power-law PDS provides a new sensitive tool for studies of gamma-ray
bursts. In particular, we calculate the PDSs of bright bursts in separate
energy channels. The PDS flattens in the hard channel (h\nu > 300 keV) and
steepens in the soft channel (h\nu < 50 keV), while the PDS of bolometric light
curves approximately follows the -5/3 law.
  We then study dim bursts and compare them to the bright ones. We find a
strong correlation between the burst brightness and the PDS slope. This
correlation shows that the bursts are far from being standard candles and dim
bursts should be intrinsically weak. The time dilation of dim bursts is
probably related to physical processes occurring in the burst rather than to a
cosmological redshift.
  Finally, we test the internal shock model against the observed PDS. We
demonstrate how the model can reproduce the -5/3 power law.

Astrophysics