The Hardness-intensity Correlation of Photospheric Emission from a Structured Jet for Gamma-Ray Bursts. (arXiv:2203.00882v2 [astro-ph.HE] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Song_X/0/1/0/all/0/1">Xin-Ying Song</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Meng_Y/0/1/0/all/0/1">Yan-Zhi Meng</a>
For many gamma-ray bursts (GRBs), hardness-intensity correlation (HIC) can be
described by a power-law function, $E_{rm p}propto F^{kappa}$, where $E_{rm
p}$ is the peak energy of $nu F_{nu}$ spectrum, and $F$ is the instantaneous
energy flux. In this paper, HIC of the non-dissipative photospheric emission
from a structured jet is studied in different regimes. An intermediate
photosphere, which contains both of unsaturated and saturated emissions is
introduced, and we find positive $kappa<1/4$ in this case. The same conclusion
could be generalized to the photospheric emission from a hybrid jet without
magnetic dissipations, or that with sub-photospheric magnetic dissipations and
fully thermalized. This may imply that the contribution peaking at $sim1/2$ in
the distribution of observed $kappa$ are mainly from the prompt emission of
GRBs with synchrotron origin. Besides, emissions of the intermediate
photosphere could give a smaller low-energy photon index $alpha$ than that in
the unsaturated regime, and naturally reproduce anti-correlation in
$alpha-E_{rm p}$ in a GRB pulse.
For many gamma-ray bursts (GRBs), hardness-intensity correlation (HIC) can be
described by a power-law function, $E_{rm p}propto F^{kappa}$, where $E_{rm
p}$ is the peak energy of $nu F_{nu}$ spectrum, and $F$ is the instantaneous
energy flux. In this paper, HIC of the non-dissipative photospheric emission
from a structured jet is studied in different regimes. An intermediate
photosphere, which contains both of unsaturated and saturated emissions is
introduced, and we find positive $kappa<1/4$ in this case. The same conclusion
could be generalized to the photospheric emission from a hybrid jet without
magnetic dissipations, or that with sub-photospheric magnetic dissipations and
fully thermalized. This may imply that the contribution peaking at $sim1/2$ in
the distribution of observed $kappa$ are mainly from the prompt emission of
GRBs with synchrotron origin. Besides, emissions of the intermediate
photosphere could give a smaller low-energy photon index $alpha$ than that in
the unsaturated regime, and naturally reproduce anti-correlation in
$alpha-E_{rm p}$ in a GRB pulse.
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