Magnetar as Central Engine of Gamma-Ray Bursts: Quasi-Universal Jet, Event Rate and X-ray Luminosity Function of Dipole Radiations. (arXiv:2003.11278v1 [astro-ph.HE])

Magnetar as Central Engine of Gamma-Ray Bursts: Quasi-Universal Jet, Event Rate and X-ray Luminosity Function of Dipole Radiations. (arXiv:2003.11278v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Xie_W/0/1/0/all/0/1">Wen-Jin Xie</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Zou_L/0/1/0/all/0/1">Le Zou</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Liu_H/0/1/0/all/0/1">Hong-Bang Liu</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Wang_S/0/1/0/all/0/1">Shan-Qin Wang</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Liang_E/0/1/0/all/0/1">En-Wei Liang</a> (GXU)

Early shallow-decaying X-ray afterglows of gamma-ray bursts (GRBs) may be
attributed to the dipole radiations of newly-born magnetars. Assuming that the
GRB jets powered by magnetars are quasi-universal, we find that the jet
structure can be parameterized as a uniform jet with a luminosity of $log
L_{rm j}/{rm erg s^{-1}}=52.68^{+0.76}_{-0.33}$ (1$sigma$) and an opening
angle $theta_{rm j}=2.10_{-1.28}^{+1.90}$ (50% confidence level),
surrounding by a power-law decay component with an index of
${-4.00^{+0.27}_{-0.37}}$ (1$sigma$). The inferred local GRB rate is
$rho=9.6$ Gpc$^{-3}$ yr$^{-1}$ by including both the typical GRBs and LL-GRBs
as the same population. The typical viewing angle is $3.3^{o}$, and may be
$20^{o}sim30^{o}$ for LL-GRBs. The X-ray luminosity function of the dipole
radiation wind can be empirically described by a broken power-law function with
indices $beta_1=0.78^{+0.16}_{-0.15}$ and $beta_2>1.6$ broken at $log L_{b,
w}/{rm erg s^{-1}}=48.51^{+0.53}_{-0.65}$. In case of that the wind outflow
is collimated and co-axial with the GRB jet, we find that the wind structure is
similar to the GRB jet, i.e., $log L_{rm c, w}/{rm erg
s^{-1}}=48.38^{+0.30}_{-0.48}$, $theta_{rm c,
w}={2.65^{o}}_{-1.19^{o}}^{+0.1.73^{o}}$, and $k_{rm w}=4.57^{+1.21}_{-0.75}$.
The observed correlation between the prompt gamma-ray luminosity and X-ray
luminosity of the wind may be resulted from the viewing angle effect in such a
jet-wind system. Discussion on survey with the X-ray instruments on board the
{em Einstein Probe} mission in the soft X-ray band for the jet and wind
emission is also presented.

Early shallow-decaying X-ray afterglows of gamma-ray bursts (GRBs) may be
attributed to the dipole radiations of newly-born magnetars. Assuming that the
GRB jets powered by magnetars are quasi-universal, we find that the jet
structure can be parameterized as a uniform jet with a luminosity of $log
L_{rm j}/{rm erg s^{-1}}=52.68^{+0.76}_{-0.33}$ (1$sigma$) and an opening
angle $theta_{rm j}=2.10_{-1.28}^{+1.90}$ (50% confidence level),
surrounding by a power-law decay component with an index of
${-4.00^{+0.27}_{-0.37}}$ (1$sigma$). The inferred local GRB rate is
$rho=9.6$ Gpc$^{-3}$ yr$^{-1}$ by including both the typical GRBs and LL-GRBs
as the same population. The typical viewing angle is $3.3^{o}$, and may be
$20^{o}sim30^{o}$ for LL-GRBs. The X-ray luminosity function of the dipole
radiation wind can be empirically described by a broken power-law function with
indices $beta_1=0.78^{+0.16}_{-0.15}$ and $beta_2>1.6$ broken at $log L_{b,
w}/{rm erg s^{-1}}=48.51^{+0.53}_{-0.65}$. In case of that the wind outflow
is collimated and co-axial with the GRB jet, we find that the wind structure is
similar to the GRB jet, i.e., $log L_{rm c, w}/{rm erg
s^{-1}}=48.38^{+0.30}_{-0.48}$, $theta_{rm c,
w}={2.65^{o}}_{-1.19^{o}}^{+0.1.73^{o}}$, and $k_{rm w}=4.57^{+1.21}_{-0.75}$.
The observed correlation between the prompt gamma-ray luminosity and X-ray
luminosity of the wind may be resulted from the viewing angle effect in such a
jet-wind system. Discussion on survey with the X-ray instruments on board the
{em Einstein Probe} mission in the soft X-ray band for the jet and wind
emission is also presented.

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