Improved Ep-TL-Lp Diagram and a Robust Regression Method
Abstract
The accuracy and reliability of gamma-ray bursts (GRBs) as distance indicators are strongly restricted by their systematic errors, which are larger than the statistical errors. These systematic errors might come from either intrinsic variations of GRBs, or systematic errors in observations. In this paper, we consider the possible origins of systematic errors in the following observables: (i) the spectral peak energies (Ep) estimated by the cut-off power law (CPL) function and (ii) the peak luminosities (Lp) estimated by 1 s in observer time. By removing or correcting them we can reveal the true intrinsic variation of the Ep-TL-Lp relation of GRBs. Here, TL is the third parameter of GRBs, defined as TL ≡ Eiso / Lp. Not only the time resolution of Lp is converted from the observer time to the GRB rest frame time, the time resolution with the largest likelihood is sought. After removing any obvious origin of systematic errors in the observation mentioned above, there still seems to remain some outliers. For this reason, we take of account another origin of the systematic error, as below: (iii) the contamination of short GRBs or other populations. To estimate the best-fit parameters of the Ep-TL-Lp relations from data including outliers, we develop a new method which combines robust regression and an outlier identification technique. Using our new method for 18 GRBs with σEp / Ep < 0.1, we detected 6 outliers, and found that the Ep-TL-Lp relation becomes tightest at around 3 s.
- Publication:
-
Publications of the Astronomical Society of Japan
- Pub Date:
- August 2011
- DOI:
- 10.1093/pasj/63.4.741
- arXiv:
- arXiv:1106.5373
- Bibcode:
- 2011PASJ...63..741T
- Keywords:
-
- gamma rays: bursts;
- gamma rays: cosmology;
- gamma rays: observations;
- Astrophysics - Cosmology and Nongalactic Astrophysics
- E-Print:
- 24 pages, 7 figures, accepted for publication in PASJ