Power density spectrum of nonstationary short-lived light curves

Details Power density spectrum of nonstationary short-lived light curves Power density spectrum of nonstationary short-lived light curves

2011-04-28

arxiv.org/abs/1104.5308v1

2011, MNRAS, 415, 3561

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

11 pages, 5 figures, accepted to MNRAS

Scientific paper

10.1111/j.1365-2966.2011.18969.x

The power density spectrum of a light curve is often calculated as the average of a number of spectra derived on individual time intervals the light curve is divided into. This procedure implicitly assumes that each time interval is a different sample function of the same stochastic ergodic process. While this assumption can be applied to many astrophysical sources, there remains a class of transient, highly nonstationary and short-lived events, such as gamma-ray bursts, for which this approach is often inadequate. The power spectrum statistics of a constant signal affected by statistical (Poisson) noise is known to be a chi2(2) in the Leahy normalisation. However, this is no more the case when a nonstationary signal is also present. As a consequence, the uncertainties on the power spectrum cannot be calculated based on the chi2(2) properties, as assumed by tools such as XRONOS powspec. We generalise the result in the case of a nonstationary signal affected by uncorrelated white noise and show that the new distribution is a non-central chi2(2,lambda), whose non-central value lambda is the power spectrum of the deterministic function describing the nonstationary signal. Finally, we test these results in the case of synthetic curves of gamma-ray bursts. We end up with a new formula for calculating the power spectrum uncertainties. This is crucial in the case of nonstationary short-lived processes affected by uncorrelated statistical noise, for which ensemble averaging does not make any physical sense.

Affiliated with

Also associated with

No associations

Rating

Power density spectrum of nonstationary short-lived light curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Power density spectrum of nonstationary short-lived light curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Power density spectrum of nonstationary short-lived light curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-448989