J/MNRAS/407/2075 Gamma-ray bursts spectral peak estimator (Shahmoradi+, 2010)
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Hardness as a spectral peak estimator for gamma-ray bursts.
Shahmoradi A., Nemiroff R.J.
=2010MNRAS.407.2075S
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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:
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FileName Lrecl Records Explanations
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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
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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.
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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
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Bytes Format Units Label Explanations
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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
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Note (1): The model are as follows:
BAND = empirical GRB model by Band et al., 1993ApJ...413..281B
with 2 exponents {alpha} and {beta} for low/high energy
COMP = Comptonized Model, where
f(E) = A(E/Eb)^{alpha}^exp((-E(2+{alpha}))/Ep)
SBPL = Smoothly Broken Power Law, with power coefficients {lambda}_1_
for the low energies and {lambda}_2_ for high energies; the
break scale {Lambda} 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.
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Byte-by-byte Description of file: table3.dat
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Bytes Format Units Label Explanations
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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
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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).
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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 {sigma}_a_=0.02 and {sigma}_b_=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 {sigma}_a_=0.02
and {sigma}_b_=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 {sigma}_a_=0.01 and
{sigma}_b_=0.04 No attempt was made to keep the significant digits.
Values are rounded off at the 2nd decimal places.
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History:
From electronic version of the journal
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(End) Patricia Vannier [CDS] 07-Mar-2011