(Shortened) CONTEXT: [...] AIMS: Motivated by the relation proposed by Amati and collaborators, we look within the ``fireshell'' model for a relation between the peak energy E_p of the νF_νtotal time-integrated spectrum of the afterglow and the total energy of the afterglow E_{aft}, which in our model encompasses and extends the prompt emission. METODS: [...] Within the fireshell model [...] We can then build two sets of ``gedanken'' GRBs varying the total energy of the electron-positron plasma E^{e^\pm}_{tot} and keeping the same baryon loading B of GRB050315. The first set assumes for the effective CBM density the one obtained in the fit of GRB050315. The second set assumes instead a constant CBM density equal to the average value of the GRB050315 prompt phase. RESULTS: For the first set of ``gedanken'' GRBs we find a relation E_p\propto (E_{aft})^a, with a = 0.45 \pm 0.01, whose slope strictly agrees with the Amati one. Such a relation, in the limit B \to 10^{-2}, coincides with the Amati one. Instead, in the second set of ``gedanken'' GRBs no correlation is found. CONCLUSIONS: Our analysis excludes the Proper-GRB (P-GRB) from the prompt emission, extends all the way to the latest afterglow phases and is independent on the assumed cosmological model, since all ``gedanken'' GRBs are at the same redshift. The Amati relation, on the other hand, includes also the P-GRB, focuses on the prompt emission only, and is therefore influenced by the instrumental threshold which fixes the end of the prompt emission, and depends on the assumed cosmology. This may well explain the intrinsic scatter observed in the Amati relation.
Variation of the Amati Relation with the Cosmological Redshift: a Selection Effect or an Evolution Effect?
由于伽马射线暴（GRB）的红移和光谱的数量有限，所有目前的研究GRB变量之间的相关性使用的红移跨越一个非常大的范围内的爆发样本。因此，进化和选择效应被忽略了，这可能对结果有重要影响。在这封信中，我们将Amati（2006，2007）观测到的48个长时γ暴按红移由低到高分为四组，每组包含12个γ暴。然后我们用Amati关系式$\log E_\iso = a + b \log E_\p$拟合每个群，并检查参数$a$和$b$是否随GRB红移而演化。我们发现，$a$和$b$随各组伽玛暴的平均红移而发生系统而显著的变化。蒙特卡罗模拟表明，只有$\sim 4$百分比的机会，变化是由选择效应所引起的通量限制。因此，我们的结果可能表明，伽玛暴强烈的宇宙学红移的演变。
A Note on "Probing the existence of the $E_{peak}$-$E_{iso}$ correlation in long Gamma Ray Bursts" by Ghirlanda et al. - astro-ph/0502186
在Nakar & Piran（2004）中，我们已经证明了很大一部分BATSE爆发不能满足伽马暴各向同性能量-峰值能量之间的Amati关系。Band and Preece（2005）进行的进一步分析证实了我们的结果。最近Ghirlanda等人（2005）声称，当考虑Amati关系周围的散射的精确分布时，BATSE样本与Amati关系一致。我们发现BATSE样本与Amati关系（包括散射）一致的概率，正如Ghirlanda等人（2005）对23个已知红移的爆发样本所发现的那样，是非常小的。
Confirmation of the $\eps$ -- $\eiso$ (Amati) relation from the X-ray flash XRF 050416A observed by Swift/BAT
We report Swift Burst Alert Telescope (BAT) observations of the X-ray Flash (XRF) XRF 050416A. The fluence ratio between the 15-25 keV and 25-50 keV energy bands of this event is 1.5, thus making it the softest gamma-ray burst (GRB) observed by BAT so far. The spectrum is well fitted by the Band function with E^{ \rm obs}_{ \rm peak} of 15.0_{-2.7}^{+2.3} keV. Assuming the redshift of the host galaxy (z = 0.6535), the isotropic-equivalent radiated energy E_{\rm iso} and the peak energy at the GRB rest frame (E^{ \rm src}_{ \rm peak}) of XRF 050416A are not only consistent with the correlation …
Reconstructing the Cosmic Expansion History up to Redshift z=6.29 with the Calibrated Gamma-Ray Bursts
最近，伽马射线暴（GRB）被认为是Ia型超新星（SNIa）的补充宇宙学探测器。自从几个经验的伽玛暴光度关系被提出作为距离指示器以来，伽玛暴一直被提倡作为标准烛光。然而，在直接使用伽玛暴时存在所谓的循环问题。最近，一个新的想法，以完全宇宙学无关的方式校准伽玛暴已被提出，并解决了圆度问题。在目前的工作中，按照梁{ \it et al.}提出的方法，我们用307个SNIa用Amati关系标定了70个伽玛暴。然后，按照Shafieloo { \it et al.}提出的方法，我们用标定的伽玛暴平滑地重建了直到红移$z=6.29$的宇宙膨胀历史。我们在重建结果中发现了一些新的特征。
