2008A&A...487L..37G -
Astronomy and Astrophysics, volume 487, L37-40 (2008/8-4)
The Amati relation in the ``fireshell'' model.
GUIDA R., BERNARDINI M.G., BIANCO C.L., CAITO L., DAINOTTI M.G. and RUFFINI R.
Abstract (from CDS):
The cosmological origin of gamma-ray bursts (GRBs) has been firmly established, with redshifts up to z=6.29. They are possible candidates for use as ``distance indicators'' for testing cosmological models in a redshift range hardly achievable by other cosmological probes. Asserting the validity of the empirical relations among GRB observables is now crucial for their calibration. Motivated by the relation proposed by Amati and collaborators, we look within the ``fireshell'' model for a relation between the peak energy Ep of the νFν total time-integrated spectrum of the afterglow and the total energy of the afterglow Eaft, which in our model encompasses and extends the prompt emission. The fit within the fireshell model, as for the ``canonical'' GRB 050315, uses the complete arrival time coverage given by the Swift satellite. It is performed simultaneously, self-consistently, and recursively in the four BAT energy bands (15-25keV, 25-50keV, 50-100keV, and 100-150keV), as well as in the XRT one (0.2-10keV). It uniquely determines the two free parameters characterizing the GRB source, the total energy Ee±tot of the e± plasma and its baryon loading B, as well as the effective CircumBurst Medium (CBM) distribution. We can then build two sets of ``gedanken'' GRBs varying the total energy of the electron-positron plasma Ee±tot and keeping the same baryon loading B of GRB 050315. The first set assumes the one obtained in the fit of GRB 050315 for the effective CBM density. The second set assumes instead a constant CBM density equal to the average value of the GRB 050315 prompt phase. For the first set of ``gedanken'' GRBs we find a relation Ep∝(Eaft)a, with a=0.45±0.01, whose slope strictly agrees with the Amati one. Such a relation, in the limit B⟶10–2, coincides with the Amati one. Instead, no correlation is found in the second set of ``gedanken'' GRBs. Our analysis excludes the proper GRB (P-GRB) from the prompt emission, extends all the way to the latest afterglow phases, and is independent of the assumed cosmological model, since all ``gedanken'' GRBs are at the same redshift. The Amati relation, on the other hand, includes the P-GRB, focuses only on the prompt emission, being therefore influenced by the instrumental threshold that fixes the end of the prompt emission, and depends on the assumed cosmology. This might explain the intrinsic scatter observed in the Amati relation.
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Syntax of coordinates is : "ra dec (wtype) [error ellipse] quality bibcode" :
ra dec : right ascension and declination (unit and frame defined according to your Output Options)
Grey values are increasing the original precision due to the computation of frame transformations
(wtype) : wavelength class for the origin of the coordinates (Rad, mm, IR, Optical, UV, Xray, Gam)
[error ellipse] : measurement uncertainty, on (ra,dec) if the positional angle is 90 degrees, on (majaxis,minaxis) otherwise (in mas at defined epoch in the original catalogue),
position angle (in degrees North celestial pole to East)
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D : 1-10" (and some old data)
C : 0.1-1"
B : 0.01-0.1" + 2MASS, Tyc
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(ep=B1950 eq=1950) :
20 22 30.494 -42 45 52.13
[
500 500 90
]
Syntax of coordinates is : "ra dec (wtype) [error ellipse] quality bibcode" :
ra dec : right ascension and declination (unit and frame defined according to your Output Options)
Grey values are increasing the original precision due to the computation of frame transformations
(wtype) : wavelength class for the origin of the coordinates (Rad, mm, IR, Optical, UV, Xray, Gam)
[error ellipse] : measurement uncertainty, on (ra,dec) if the positional angle is 90 degrees, on (majaxis,minaxis) otherwise (in mas at defined epoch in the original catalogue),
position angle (in degrees North celestial pole to East)
quality : flag of quality
E ≥ 10"
D : 1-10" (and some old data)
C : 0.1-1"
B : 0.01-0.1" + 2MASS, Tyc
A : VLBI, Hipparcos
bibcode : bibcode of the coordinates reference
Gal
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(ep=J2000) :
358.177351 -34.826143
[
500 500 90
]
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References (211 between 1850 and 2023) (Total 211)
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