J/MNRAS/407/2075 Gamma-ray bursts spectral peak estimator (Shahmoradi+, 2010)
Hardness as a spectral peak estimator for gamma-ray bursts. Shahmoradi A., Nemiroff R.J. <Mon. Not. R. Astron. Soc., 407, 2075-2090 (2010)> =2010MNRAS.407.2075S
ADC_Keywords: Gamma rays Keywords: gamma-ray burst: general Abstract: Simple hardness ratios are found to be a good estimator for the spectral peak energy in gamma-ray bursts (GRBs). Specifically, a high correlation strength is found between the nuFnu peak in the spectrum of Burst and Transient Source Experiment (BATSE) GRBs, Ep,obs and the hardness of GRBs, inline image, as defined by the fluences in channels 3 and 4, divided by the combined fluences in channels 1 and 2 of the BATSE Large Area Detectors (LADs). The correlation is independent of the type of the burst, whether long-duration GRB (LGRB) or short-duration (SGRB) and remains almost linear over the wide range of the BATSE energy window (20-2000KeV). Based on Bayes theorem and Markov Chain Monte Carlo techniques, we also present multivariate analyses of the observational data while accounting for data truncation and sample incompleteness. Prediction intervals for the proposed inline image relation are derived. Results and further simulations are used to compute Ep,obs estimates for nearly the entire BATSE catalogue: 2130 GRBs. File Summary:
FileName Lrecl Records Explanations
ReadMe 80 . This file table1.dat 79 249 *Summary of the spectral properties of 249 BATSE GRBs used to calibrate the linear HRH-EpObs relation in Sect. 2.2. table3.dat 123 2130 *Ep,obs estimates for 2130 GRBs in the BATSE catalog
Note on table1.dat: The hardness ratios are calculated via the BATSE catalog data (Cat. IX/20), while the rest of spectral parameters are taken from Kaneko et al. (2006, Cat. J/ApJS/166/298). Note on table3.dat: Overall, we recommend the use of either Ep,obs estimates from OLS(Ep,obs|HRH) (EpMe1) or the expected Ep,obs estimates from the simulation (EpMe) together with the 90% upper and lower prediction intervals given in (E_EpMe, e_EpMe). Ep,obs by the OLS-bisector (EpMe2) might be useful in cases where both HRH and Ep,obs need to be treated impartially (e.g. Shahmoradi & Nemiroff 2009, submitted (arXiv:0904.1464); Isobe et al. 1990ApJ...364..104I). The model-dependent simulation-based estimates of Ep,obs (EpMo*) might be used only in cases where the best fit spectral model of the GRB is known independently. In general, the 90% lower and upper prediction intervals on the estimated Ep,obs should always be reported and considered in analyses.
See also: IX/20 : The Fourth BATSE Burst Revised Catalog (Paciesas+ 1999) J/ApJS/166/298 : Spectral cat. of bright BATSE gamma-ray bursts (Kaneko+, 2006) Byte-by-byte Description of file: table1.dat
Bytes Format Units Label Explanations
1- 4 I4 --- TrigNo Burst's trigger number as reported in the BATSE catalog 6- 9 A4 --- Model [BAND COMP SBPL] Model (1) 11- 16 F6.2 --- HRH Hardness Ratio (G1) 18- 21 F4.2 --- e_HRH rms uncertainty on HRH 23- 27 F5.2 0.10ph/s/cm2 A Normalization factor of the assumed spectral model for each GRB 29- 33 F5.2 0.10ph/s/cm2 e_A rms uncertainty on A 35- 38 I4 keV Ep Observed spectral peak energy 40- 43 I4 keV e_Ep rms uncertainty on Ep 45- 49 F5.2 --- alpha Low-energy photon index (3) 51- 54 F4.2 --- e_alpha rms uncertainty on alpha 56- 61 F6.2 --- beta ? High-energy photon index (4) 63- 66 F4.2 --- e_beta ? rms uncertainty on beta 68- 70 I3 keV Eb ? Spectral break energy (5) 72- 74 I3 keV e_Eb ? rms uncertainty on Eb 75- 79 F5.2 --- Lambda ? Break scale of SBPL model for GRBs best described by SBPL
Note (1): The model are as follows: BAND = empirical GRB model by Band et al., 1993ApJ...413..281B with 2 exponents α and β for low/high energy COMP = Comptonized Model, where f(E) = A(E/Eb)αexp((-E(2+α))/Ep) SBPL = Smoothly Broken Power Law, with power coefficients λ1 for the low energies and λ2 for high energies; the break scale Λ is the fifth parameter of this model Note (3): alpha represents the low-energy photon index of the Band model for GRBs best described by the Band model, and the low-energy photon index of SBPL model for GRBs best described by SBPL, also the photon index of COMP model for GRBs best described by COMP. Note (4): beta represents the high-energy photon index of the Band model for GRBs best described by the Band model, and the low-energy photon index of SBPL model for GRBs best described by SBPL. Note (5): Ebreak represents the break-energy of the Band model for GRBs best described by the Band model, and the break-energy of SBPL model for GRBs best described by SBPL.
Byte-by-byte Description of file: table3.dat
Bytes Format Units Label Explanations
1- 4 I4 --- TrigNo Burst trigger number as reported in the BATSE catalog 5 A1 --- n_TrigNo [*] * for GRBs used to derive the regression lines in Sect 2.2. 6- 12 F7.2 --- HRH Hardness ratio (G1) 14- 19 F6.2 --- e_HRH ? rms uncertainty on HRH 20 A1 --- n_HRH [A] large uncertainties (2) 22- 28 F7.2 keV EpMe1 ? Mean OLS(Y|X) peak energy Ep,obs (3) 30- 34 F5.2 keV E_EpMe1 ? Error on EpMe1, upper limit 36- 40 F5.2 keV e_EpMe1 ? Error on EpMe1,obs, lower limit 42- 49 F8.2 keV EpMe2 ? Mean OLS bisector peak energy Ep,obs (4) 51- 56 F6.2 keV E_EpMe2 ? Error on EpMe2, upper limit 58- 63 F6.2 keV e_EpMe2 ? Error on EpMe2, lower limit 65- 68 I4 keV EpMo1 Band model peak energy Ep,obs (5) 70- 73 I4 keV E_EpMo1 Error on EpMo1, upper limit 75- 78 I4 keV e_EpMo1 Error on EpMo1, lower limit 80- 83 I4 keV EpMo2 COMP(CPL) model peak energy Ep,obs (6) 85- 89 I5 keV E_EpMo2 Error on EpMo2, upper limit 91- 94 I4 keV e_EpMo2 Error on EpMo3, lower limit 96- 99 I4 keV EpMo3 SBPL model peak energy Ep,obs (7) 101-104 I4 keV E_EpMo3 Error on EpMo3, upper limit 106-108 I3 keV e_EpMo3 Error on EpMo3, lower limit 110-113 I4 keV EpMe ? Weighted average of peak energy Ep,obs (8) 115-118 I4 keV E_EpMe ? Error on EpMe, upper limit 120-123 I4 keV e_EpMe ? Error on EpMe, lower limit
Note (2): For 262 dim, low S/N GRBs marked by A, the uncertainties in the fluences are greater than their reported fluences in BATSE catalog. Therefore, for these GRBs, the error propagation also results in HRH uncertainties that are larger than the value of HRH. In these cases, the Gaussian approximation to the uncertainties is not a good assumption and therefore, the uncertainties on HRH are not reported. Note (3): Mean response of OLS(Ep,obs|HRH) (Eq. 1) with the corresponding 1sigma uncertainties on the mean response. No attempt was was made to keep the significant digits. Values are rounded off at the 2nd decimal places. Note (4): Mean response of OLS-bisector (Eq. 3) with the corresponding 1sigma uncertainties on the mean response. No attempt was made to keep the significant digits. Values are rounded off at the 2nd decimal places. Note (5): Most probable Ep,obs with 90% Prediction Interval (PI) derived from simulation in case of the Band model as the best spectral fit. Note (6): Most probable Ep,obs with 90% PI derived from simulation in case of the COMP (CPL) model as the best spectral fit. Note (7): Most probable Ep,obs with 90% PI derived from simulation in case of the SBPL model as the best spectral fit. Note (8): The weighted average of Ep,obs of the three GRB models with 90% PI derived from simulation according to Eqs. (20)-(23).
Global notes: Note (G1): HRH represents Hardness Ratio as defined in Sect. 2.2: Log(Ep/300[keV])=0.10+0.63Log(HRH/10) for OLS(Y|X), with intercept and slope uncertainties of σa=0.02 and σb=0.05 (OLS: Ordinary-Least-Squares) Log(Ep/300[keV])=0.15+0.87Log(HRH/10) for OLS(X|Y), with intercept and slope uncertainties of σa=0.02 and σb=0.002 (OLS: Ordinary-Least-Squares) Log(Ep/300[keV])=0.12+0.75Log(HRH/10) for the bisector line, with intercept and slope uncertainties of σa=0.01 and σb=0.04 No attempt was made to keep the significant digits. Values are rounded off at the 2nd decimal places.
History: From electronic version of the journal
(End) Patricia Vannier [CDS] 07-Mar-2011
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