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A Comprehensive Study of Bright Fermi-GBM Short Gamma-ray Bursts: I. Multi-Pulse Lightcurves and Multi-Component Spectra

Department of Physics, Nanchang University, Nanchang 330031, Mainland china

^*

Author to whom correspondence should exist addressed.

Bookish Editors: Andrea Melandri and Silvia Piranomonte

Universe 2022, 8(3), 159; https://doi.org/10.3390/universe8030159 (registering DOI)

Received: 11 Feb 2022 / Revised: 28 February 2022 / Accepted: 1 March 2022 / Published: 2 March 2022

Abstract

Sorted by the photon fluences of short Gamma-ray Bursts (SGRBs) detected by the Fermi-Gamma Ray Burst Monitor (GBM), 9 brightest bursts are selected to perform a comprehensive assay. All GRB lightcurves are fitted well by 1 to 3 pulses that are modelled by fast-rising exponential decay contour (FRED), within which the resultant ascension fourth dimension is strongly positive-correlated with the full time width at half maxima (FWHM). A photon spectral model involving a cutoff power-law function and a standard blackbody office (CPL + BB) could reproduce the spectral energy distributions of these SGRBs well in the bursting phase. The CPL's peak energy is establish strongly positive-correlated with the BB's temperature, which indicates they might be from the same physical origin. Possible concrete origins are discussed to business relationship for these correlations.

one. Introduction

Gamma-ray Bursts (GRBs) are the most energetic transient events in the universe, which is only after the bing bang. Short Gamma-ray Outburst (SGRB) is an important astrophysical phenomena to shed calorie-free on the properties of the stellar physics, especially on the merger events of ii compact objects in the gravitational-moving ridge era, such as two neutron stars (NS-NS), which is firstly proved in SGRB 170817A [1]. During the short emission timescale of such consequence, i.e., less than ii seconds in the prompt stage, SGRB typically consists of several pulses in its lightcurve (LC) and multiple spectral components in its spectral energy distribution (SED). The radiation procedure accounted for these properties during the prompt emission of SGRBs is yet cryptic, which nonetheless can revel some aspects of GRB, such every bit the primal engine, the outflow composition and the structures of the relativistic jet [2,iii,4,5,6]. For pulses of those LCs, it is found that the rising time width and the full time width are positively correlated with each other in well-nigh of the long GRBs (LGRBs) detected by the Burst and Transient Source Experiment (BATSE) on board Compton Gamma Ray Observatory (CGRO) [7,8,9]. However, such pulses in nigh BATSE SGRBs have not enough high count rates to be decomposed. For the SEDs represented by the nonthermal models in most SGRBs [10], 2 bright SGRBs (GRB 120323A and GRB 170206A) with the standard blackbody component detection both in their time-integrated and fourth dimension-resolved spectra are reported in the literatrue [11,12], while the multiple blackbody component (mBB, a not-standard thermal component) is found in several redshift-measured SGRBs [thirteen]. In order to talk over the possible physical origins in SGRBs, 9 fluence-selected brightest SGRBs amongst 522 Fermi-Gamma Burst Monitor (GBM) as of 2021 December are selected to perform the comprehensive analysis, in which both the LCs and SEDs are fitted. In Section 2, nosotros describe the method. The results and possible correlaions are presented in Section 3. The word on these correlations is presented in Section iv. Nosotros nowadays the summary and conclusion in Department 5.

2. Data Assay

In this section, nosotros present the sample option and the full general method for the lightcurve fitting and spectral energy distribution plumbing fixtures, employing the Fermi/GBM observations.

two.one. Sample Selection

Fermi/GBM has 2 types of scintillation detectors, such as 12 Sodium Iodide (NaI) units named from 'n0' to 'n9', 'na' and 'nb', and two Bismuth Germanate (BGO) units named 'b0' and 'b1'. NaIs embrace the photon energy betwixt about 8 keV and 1 MeV while BGOs between about 200 keV and 40 MeV. Amidst 522 SGRBs detected by the Fermi-GBM as of 2021 December, nine are selected with l–300 keV free energy fluence

$S_{50–300\mathrm{keV}}$

in a higher place seven

$\times {10}^{-6}$ $\mathrm{erg}{\mathrm{cm}}^{-\mathrm{ii}}$

and GBM

$T_{\mathrm{ninety}}$

less than 2 s. GBM

$T_{\mathrm{ninety}}$

is between GBM

$T_{05}$

and

$T_{95}$

, that are the times when 5% and 95% of the total GRB energy fluence is accumulated respectively. For each GRB, we selected four detectors in the following analysis, which are closest to the best-localizaion GRB position as shown in the Tabular array 1. Their data can be downloaded from the public data site of Fermi/GBM https://heasarc.gsfc.nasa.gov/FTP/fermi/data/gbm/bursts/, accessed on xv November 2021.

2.two. Method

two.2.1. Lightcurve Plumbing fixtures

GBM Time-Tagged Issue (TTE, ii µs temporal resolution) data of iii NaI detectors is employed, which were binned into 10 ms in our lightcurve fitting except for GRB 171108A, which takes 2 ms bins for its very short

$T_{90}$

of 32 ms. The energy band is selected ranging from 50 keV to 300 keV. GRB lightcurves are usually irregular, but could be decomposed every bit several pulses, virtually of which are described as the fast-ascension exponential-decay profile (FRED). FRED can be presented same as that in [14],

$$S\left(t\right|A,T_{\mathrm{commencement}},T_{\mathrm{ascension}},\xi )=A{e}^{-\xi \left(\frac{t-T_{\mathrm{start}}}{T_{\mathrm{rise}}}+\frac{T_{\mathrm{rise}}}{t-T_{\mathrm{starting\; time}}}-2\right)}$$

(one)

where A is the amplitude,

$T_{\mathrm{offset}}$

is offset fourth dimension of the pulse and

$T_{\mathrm{rise}}$

is the ascent time interval before the peak,

$\xi$

is an disproportion parameter to represent the skewness of the FRED pulse. The disuse time interval can exist calculated by

$T_{\mathrm{decay}}=\frac{\mathrm{one}}{2}{T}_{\mathrm{ascent}}{\xi }^{-1}[{(1+4\xi )}^{1/\mathrm{two}}+1]$

[15]. Therefore, we perform the plumbing equipment with several FRED pulses to nine GRBs in our sample, normally with 1, ii or 3 FRED pulses which are named single-pulse SGRB, double-pulse SGRB and triple-pulse SGRB respectively. The maximum likelihood statistical method is employed in the LC plumbing fixtures.

2.ii.2. Spectral Energy Distribution Fitting

GBM TTE data of all detectors in Table 1 are used in our spectral analysis. Instrument response files are selected with

$rsp\mathrm{two}$

files, nosotros fit the background with an automobile-selected orders polynomials using the Nelder-Mead method. Photons with energy ranging from 8 to 900 keV for NaIs are selected while from 200 keV to 40 MeV for BGOs.

We select iv models to fit the gamma-ray spectra, eastward.grand., the Band-function model (Ring), the cutoff power-law part model (CPL) and 2 blackbody function (BB)-included models, such as BAND + BB and CPL + BB. In society to distinguish from the single BAND model and the single CPL model higher up, we named the BAND component and the BB component in the BAND + BB model while the CPL component and BB component in CPL + BB model. Ring model is written every bit the so-chosen Ring function [x], such as

$$\begin{array}{c}\hfill \mathrm{Northward}{\left(E\right)}_{\mathrm{BAND}}=N_{0,\mathrm{Band}}\left\{\begin{array}{cc}{\left(\frac{E}{E_{\mathrm{piv}}}\right)}^{\alpha }{\mathrm{east}}^{[-E/E_0]},\hfill & \mathrm{Due\; east}\le (\alpha -\beta ){\mathrm{East}}_0\hfill \\ \\ {\left(\frac{(\alpha -\beta )E_0}{E_{\mathrm{piv}}}\right)}^{(\alpha -\beta )}{e}^{(\beta -\alpha )}{\left(\frac{\mathrm{East}}{E_{\mathrm{piv}}}\right)}^{\beta },\hfill & \mathrm{East}\ge (\alpha -\beta )E_0\hfill \end{array}\right.\end{array}$$

(2)

where

$\alpha$

,

$\beta$

is the photon index before and later the typical free energy of

$(\alpha -\beta )E_0$

, and

$E_0$

is the break energy in the

$F_E(=\mathrm{Eastward}{N}_E)$

spectrum, note that the summit free energy in the

$\mathrm{Due\; east}{F}_{\mathrm{Due\; east}}(=E^2{N}_{\mathrm{Due\; east}})$

spectrum

${\mathrm{Due\; east}}_{\mathrm{peak}}=(2+\alpha )E_0$

[xv]. CPL could be regarded as the lower energy segment of the BAND model but with an exponential cutoff-power-police decay in the high-energy band, such as

$$N_E\left(\mathrm{CPL}\right)={\mathrm{Due\; north}}_{0,\mathrm{CPL}}{\left(\frac{\mathrm{East}}{E_{\mathrm{piv}}}\right)}^{\mathrm{\Gamma }}{\mathrm{eastward}}^{-\mathrm{East}/E_{\mathrm{c}}},$$

(three)

where

$\mathrm{\Gamma }$

is the photon alphabetize and

${\mathrm{East}}_{\mathrm{c}}$

is the cutoff energy.

$E_{\mathrm{piv}}$

in both models is the pivot energy and stock-still at 100 keV, which is most to adopt the observations. BB component is usually modified by the standard Planck spectrum, which is given past the photon flux,

$$N_E\left(\mathrm{BB}\right)=N_{0,\mathrm{BB}}\frac{E^2}{\mathrm{eastward}\mathrm{10}p[E/kT]-\mathrm{i}},$$

(iv)

where k is the Boltzmann's constant, and the joint parameter

$kT$

as a output parameter in common. The BB component is the condiment spectral compoennt in our spectral analysis, such as Ring + BB and CPL + BB. In all spectral models,

$N_0$

is the normalisation.

For each spectral plumbing equipment, a likelihood value

$\mathrm{50}(\overrightarrow{\theta })$

as the function of the complimentary parameters

$\overrightarrow{\theta }$

is derived. The value of the Bayesian Information Criterion (BIC; [sixteen]), defined as BIC = −2ln

$L(\overrightarrow{\theta })$

+

$\mathrm{yard}lnn$

, are calculated, where grand is the number of free parameters to exist estimated and n is the number of observations (the sum of the selected GBM free energy channels). In this work, the Multi-Mission Maximum Likelihood parcel (3ML; [17]) are employed to acquit out all the spectral analysis and the parameter estimation, with the emcee sampling method.

3. Upshot

three.1. Multiple Pulses

Results of the lightcurve fitting are presented in Table ii. For the single-pulse GRBs,

$T_{\mathrm{rise}}$

is about 0.03 s and 0.05 s for GRB 171108A and GRB 120323A respectively, while well-nigh 0.27 southward and 0.59 due south for GRB 171126A and GRB 140209A respectively. For 4 GRBs with two FRED pulses (double-pulse SGRB), it is found that they take the similar design of the ascension time, such as the second rising fourth dimension

$T_{\mathrm{rise},2}$

is virtually 1 to 3 times the beginning rising fourth dimension

$T_{\mathrm{rise},\mathrm{one}}$

. For the merely GRB with three FRED pulses (triple-pulse SGRB), GRB 170206A has the most energetic flux in the sample. Its first two rising times are compared, e.thousand., 0.xvi due south, 0.12 southward respectively. Its last ascension time is 0.54 s, which is longer than that in the quondam two pulses.

Figure 1 shows the observational lightcurves and the plumbing fixtures curves of nine GRBs in our sample. The ruddy histograms represent lightcurves, and solid black lines are the best fittings by FRED profiles.

Tabular array 2. Derived parameters of GRB FRED pulses.

Table 2. Derived parameters of GRB FRED pulses.

GRB	Models
	${\mathit{Pulse}}_{\mathbf{ane}}$			${\mathit{Pulse}}_{\mathbf{2}}$			${\mathit{Pulse}}_{\mathbf{three}}$
	${\mathit{T}}_{\mathrm{start},1}$ (southward)	${\mathit{T}}_{\mathrm{rise},\mathrm{i}}$ (southward)	${\mathit{FWHM}}_{\mathbf{one}}$ (s)	${\mathit{T}}_{\mathrm{outset},2}$ (south)	${\mathit{T}}_{\mathrm{ascent},\mathrm{two}}$ (southward)	${\mathit{FWHM}}_{\mathbf{2}}$ (s)	${\mathit{T}}_{\mathrm{start},\mathrm{three}}$ (south)	${\mathit{T}}_{\mathrm{rise},3}$ (southward)	${\mathit{FWHM}}_{\mathbf{three}}$ (s)
090227B	$-0.03\pm 0.03$	$0.04\pm 0.01$	$0.06\pm 0.02$	$-0.02\pm 0.02$	$0.07\pm 0.04$	$0.05\pm 0.04$	-	-	-
120323A	$-0.03\pm 0.01$	$0.05\pm 0.01$	$0.13\pm 0.01$	-	-	-	-	-	-
140209A	$1.03\pm 0.02$	$0.59\pm 0.03$	$0.44\pm 0.03$	-	-	-	-	-	-
150819B	$-0.05\pm 0.01$	$0.05\pm 0.01$	$0.04\pm 0.01$	$0.45\pm 0.01$	$\mathrm{0.fourteen}\pm 0.02$	$\mathrm{0.xiii}\pm 0.02$	-	-	-
170206A	$0.30\pm 0.01$	$0.16\pm 0.01$	$0.27\pm 0.03$	$0.57\pm 0.02$	$0.12\pm 0.02$	$0.24\pm 0.06$	$\mathrm{0.sixty}\pm 0.03$	$0.54\pm 0.03$	$0.22\pm 0.02$
171108A	$-0.04\pm 0.01$	$0.03\pm 0.01$	$0.02\pm 0.01$	-	-	-	-	-	-
171126A	$-\mathrm{0.eleven}\pm 0.02$	$0.27\pm 0.03$	$0.48\pm 0.08$	-	-	-	-	-	-
180703B	$-0.19\pm 0.01$	$0.35\pm 0.01$	$0.24\pm 0.01$	$\mathrm{0.seventy}\pm 0.01$	$0.51\pm 0.01$	$0.42\pm 0.01$	-	-	-
181222B	$-0.03\pm 0.01$	$0.09\pm 0.01$	$0.21\pm 0.01$	$-0.03\pm 0.01$	$0.23\pm 0.01$	$0.11\pm 0.01$	-	-	-

In club to analyze the relationship between the rising time (

$T_{\mathrm{rise}}$

) phase and the whole pulse fourth dimension width, total time with in half maximum (FWHM) is measured, which is as well presented in Table 2. And then we test the correlation betwixt FWHM and

$T_{\mathrm{rise}}$

by the linear plumbing equipment in logarithmic space, such as

$$lo\mathrm{one\; thousand}\left(\mathrm{FWHM}\right)=\mathrm{one\; thousand}+nlog\left(T_{\mathrm{rise}}\right)$$

(5)

where thousand and n are the free parameters. This fitting is performed past the basic linear regression analysis in the popular

$Origi\mathrm{due\; north}$

scientific package, which can give the coefficient of determination

$R^2$

(

$0<R^2<\mathrm{i}$

). For the linear fit, two variables, such every bit FWHM and

$T_{\mathrm{ascension}}$

in this section, are positively correlated if the Pearson-correlation coefficient R (

$-1<R<\mathrm{ane}$

) is close to i. For example, a strong correlation can be claimed when R > 0.viii while a moderate correlation can exist claimed when 0.v

$<R<$

0.8 [18]. We likewise calculate the probability p of the zilch hypothesis, which can exist described equally the confidence level of i

$-p$

for the correlation.

For the private pulse in our sample, we found that

$T_{\mathrm{rise}}$

and FWHM are strongly correlated with each other, which is plotted in Figure 2, with R = 0.82, chiliad =

$-0.17\pm 0.14$

and n =

$0.78\pm 0.15$

. The best fit for the correlation is written as

$$log\left(\mathrm{FWHM}\right)=(-0.17\pm 0.14)+(0.78\pm \mathrm{0.fifteen})lo\mathrm{thousand}\left(T_{\mathrm{rise}}\right),$$

(6)

p is about 1.9 × x

${}^{-4}$

, which as well favors a strong positive correlation. This strong correlaiton implies those pulses are emitted within one impulsive explosion.

3.2. Multiple Spectral Components

Nosotros obtained the resultant spectral parameters of each GRB besides as the BIC values, presented in Table 3. Firstly, BIC value of one model is enough smaller than that in other mdoels, i.e.,

$\mathrm{\Delta }$

BIC

$>6$

, is selected every bit the all-time-fit model [19]. If ii or more models have the

$\mathrm{\Delta }$

BIC

$<\mathrm{half-dozen}$

with each other, so we named them the compareable models. Secondly, we will pass up a model if the resultant parameters in a candidate model are unreasonable, such as

$\mathrm{yard}T$

is less than eight keV, which is the minimum photon free energy nosotros selected. For each model, we plot 3 GRBs equally the example in Effigy three.

• For GRB 090227B, CPL, Band + BB and CPL + BB models are the compared models.

• For GRB 120323A, CPL + BB model is the best-fit model.

• For GRB 140209A, Band and BAND + BB models are the compared models.

• For GRB 150819B, CPL and CPL + BB models are the compared models.

• For GRB 170206A, CPL + BB model is the all-time-fit model.

• For GRB 171108A, Band, CPL and CPL + BB models are the compared models.

• For GRB 171126A, BAND and CPL models are the compared models.

• For GRB 180703B, BAND, CPL and CPL + BB models are the comared models.

• For GRB 181222B, BAND model is the best model.

Amid four candidate models, the CPL + BB model is all-time model in two GRBs, such as GRB 120323A and GRB 170206A, and is the compared models in GRBs 090227B, 150819B, 171108A, 180703B. For other 3 GRBs, although the CPL + BB model is not the best/compared model, the resultant

$kT$

is well constrained. In gild to test the possible correlation betwixt the multiple spectral components, we thus choose the spectral fittings that are modelled by CPL + BB model in the post-obit analysis.

Tabular array 3. Resultant parameters by the spectral fitting.

Table three. Resultant parameters by the spectral fitting.

$\mathbf{GRB}$	$\mathit{Model}$	$\mathit{BIC}$	$\mathit{\alpha }/\mathbf{\Gamma }$	${\mathit{E}}_{\mathit{peak}}/{\mathit{Eastward}}_{\mathit{c}}$ (keV)	$\mathit{\beta }$	$\mathit{kT}$ (keV)
090227B	BAND	1692	$-0.12\pm 0.03$	$\mathrm{g}\pm 4$	$-2.10\pm 0.05$	-
	CPL	1517	$-0.46\pm 0.02$	$1400\pm 66$	-	-
	BAND + BB	1522	$-0.42\pm 0.04$	$950\pm 58$	$-2.20\pm 0.10$	$490\pm 29$
	CPL + BB	1522	$-0.55\pm 0.06$	$1600\pm 180$	-	$270\pm 66$
120323A	Band	2151	$-0.84\pm 0.07$	$72\pm 5$	$-\mathrm{two.10}\pm 0.02$	-
	CPL	2310	$-\mathrm{1.forty}\pm 0.02$	$350\pm 21$	-	-
	BAND + BB	2158	$-0.81\pm 0.11$	$71\pm 7$	$-\mathrm{two.10}\pm 0.02$	$1\pm \mathrm{i}$
	CPL + BB	2097	$-1.40\pm 0.03$	$530\pm 57$	-	$12\pm 1$
140209A	Band	3194	$-0.52\pm 0.05$	$150\pm \mathrm{vi}$	$-\mathrm{2.forty}\pm 0.08$	-
	CPL	3248	$-0.69\pm 0.03$	$140\pm \mathrm{half-dozen}$	-	-
	Band + BB	3191	$-0.33\pm \mathrm{0.xv}$	$160\pm 11$	$-2.50\pm 0.09$	$10\pm \mathrm{i}$
	CPL + BB	3220	$-\mathrm{0.lxx}\pm 0.07$	$170\pm 18$	-	$16\pm 2$
150819B	Ring	2670	$-\mathrm{1.ten}\pm 0.03$	$540\pm 38$	$-\mathrm{3.xxx}\pm 0.21$	-
	CPL	2663	$-\mathrm{1.ten}\pm 0.03$	$600\pm 55$	-	-
	BAND + BB	2672	$-1.00\pm 0.12$	$510\pm 66$	$-\mathrm{iii.20}\pm 0.24$	$8\pm 2$
	CPL + BB	2665	$-1.10\pm \mathrm{0.eleven}$	$570\pm 96$	-	$6\pm 6$
170206A	Band	3056	$-\mathrm{0.xxx}\pm 0.04$	$340\pm \mathrm{xiv}$	$-2.6\pm 0.13$	-
	CPL	3054	$-0.40\pm 0.03$	$240\pm 11$	-	-
	Band + BB	3062	$-0.54\pm \mathrm{0.xiv}$	$430\pm 85$	$-\mathrm{three.00}\pm 0.39$	$38\pm \mathrm{ix}$
	CPL + BB	3048	$-0.57\pm 0.06$	$370\pm 44$	-	$41\pm 4$
171108A	BAND	6	$0.15\pm \mathrm{0.xx}$	$92\pm 6$	$-3.30\pm 0.21$	-
	CPL	2	$-0.03\pm 0.19$	$51\pm 7$	-	-
	Band + BB	12	$0.49\pm 0.61$	$100\pm 23$	$-\mathrm{iii.thirty}\pm 0.26$	$10\pm \mathrm{x}$
	CPL + BB	7	$0.32\pm 0.44$	$45\pm 10$	-	$\mathrm{viii}\pm 5$
171126A	BAND	2988	$-0.38\pm 0.08$	$88\pm 4$	$-\mathrm{iii.00}\pm 0.23$	-
	CPL	2989	$-0.49\pm 0.07$	$62\pm 5$	-	-
	BAND + BB	2999	$-0.37\pm 0.12$	$\mathrm{xc}\pm \mathrm{five}$	$-\mathrm{iii.10}\pm 0.23$	$1\pm \mathrm{i}$
	CPL + BB	2995	$-0.49\pm 0.11$	$65\pm 9$	-	$8\pm 6$
180703B	Ring	3482	$-0.65\pm 0.04$	$140\pm 5$	$-3.10\pm 0.22$	-
	CPL	3481	$-0.70\pm 0.03$	$110\pm 4$	-	-
	Ring + BB	3487	$-0.63\pm 0.06$	$140\pm 10$	$-3.10\pm 0.28$	$\mathrm{viii}\pm 7$
	CPL + BB	3483	$-0.67\pm 0.06$	$120\pm 8$	-	$12\pm 2$
181222B	BAND	2677	$-0.58\pm 0.01$	$350\pm \mathrm{six}$	$-\mathrm{three.ten}\pm 0.11$	-
	CPL	2719	$-0.61\pm 0.01$	$270\pm 6$	-	-
	BAND + BB	2687	$-0.58\pm 0.02$	$350\pm \mathrm{vii}$	$-3.10\pm 0.10$	$1\pm 1$
	CPL + BB	2721	$-0.66\pm 0.04$	$290\pm 20$	-	$\mathrm{twoscore}\pm 16$

Effigy 3. Examples for the SED fitting by iv models. (a) + (b) + (c): Ring; (d) + (east) + (f): CPL; (g) + (h) + (i): Band + BB; (j) + (k) + (50): CPL + BB.

Figure 3. Examples for the SED fitting by four models. (a) + (b) + (c): Band; (d) + (east) + (f): CPL; (g) + (h) + (i): Ring + BB; (j) + (thousand) + (l): CPL + BB.

In guild to compare the multiple spectral components, we select the CPL + BB model to examination the correlation betwixt the peak energy

$E_{\mathrm{peak}}$

=

$(2+\mathrm{\Gamma })E_c$

in the CPL component and the temperature

$\mathrm{one\; thousand}T$

in the BB component using the linear fit in logarithmic infinite aforementioned as above. Excluding GRB 150819B, whose median value of

$\mathrm{grand}T$

= 6 keV is less than 8 keV, we plant that

${\mathrm{Due\; east}}_{\mathrm{peak}}$

is strongly correlated with

$kT$

with R = 0.97, g =

$-\mathrm{ane.40}\pm 0.31$

and n =

$1.11\pm 0.12$

. The all-time fit for the correlation is written as

$$\mathrm{50}o\mathrm{1000}\left(E_{\mathrm{meridian}}\right)=(-\mathrm{one.xl}\pm 0.31)+(\mathrm{ane.xi}\pm 0.12)log\left(kT\right),$$

(7)

p is about i.0 × x

${}^{-4}$

, which favors a potent correlation, as seen in Figure iv. This potent correlation implies those two spectral components might share the same origins.

4. Discussion

iv.1. Bias on the Transition Process of SGRBs

As seen in previous sections, in that location are 3 types of SGRBs, such as with single-pulse SGRB, double-pulse SGRB and triple-pulse SGRB, which might be continued with different types of energy dissipation. Transition process within one impulsive explosion, that is from a fireball to a Poynting-flux-dominated outflow, has been plant in several LGRBs, e.chiliad., GRB 160625B and GRB 160626B [20,21,22]. When the multiple-pulse SGRBs can be clearly separated, it could be the apparent evidence to constrain the transition times, such as the GRB 150819B and GRB 180703B in this work. Although such bias exists in individual SGRBs, the positive correlation between the FWHM and the rising fourth dimension still hold in our sample, which might due to the very short

$T_{90}$

duration and a small SGRB sample. This dispersion might exist resolved when with more and more SGRBs detected in distinct types of pulses, which could divide this correlation into ii or more subclass.

4.ii. Implications for the Simultaneous Thermal and Non-Thermal Spectral Components

More than and more GRB spectra were discovered deviating from the typical Band model, while the model comprising a PL/CPL (nonthermal) and an additional BB (thermal) is constitute beingness fitted well in several GRBs [23,24,25,26,27,28]. The nonthermal component was well described within the context of synchrotron radiation from particles in the jet, while the thermal component was interpreted by the emission from the jet photosphere, encounter [27] and references therein. The PL component was claimed to originate most likely from the inverse-Compton process as well as the CPL component, whose seed photons are usually the synchrotron-induced photons. The loftier-energy exponential cutoff in the latter component (CPL) is naturally interpreted as anything betwixt the high-free energy photons and the depression-energy photons [29,30]. The correlation found in this work, such as CPL's peak energy

${\mathrm{Due\; east}}_{pea\mathrm{one\; thousand}}$

is in proportion to BB's temperature

$kT$

(

$E_{peak}\propto \mathrm{grand}{T}^{1.1}$

), would imply that despite the different pulse-type SGRBs in our sample, the prompt broadband gamma-ray radiation could originate from the similar structures of the region, such as the same jet structures and outflow compositions in the different types of SGRBs. As seen in [28], both the leptonic model and hadronic model could produce the simultaneous thermal and not-thermal spectral components, more extensive physical explanations are required in future.

five. Summary and Conclusions

In this work, nine most vivid SGRBs accept been analyzed both in the LCs and SEDs. Of these bursts, the pulses in the LCs are all best-fitted by the FRED profiles. The resultant rising fourth dimension width (

$T_{\mathrm{rising}}$

) is constitute to be strongly positive-correlated with the full time width at one-half maxima (FWHM), which implies those pulses are emitted within 1 impulsive explosion. This correlation might be divided into two or more subclass if more and more SGRBs in different pulse types are detected in hereafter. The correlation of spectral parameter found in this work, such as CPL'due south peak energy

$E_{p\mathrm{eastward}ak}$

is in proportion to BB's temperature

$\mathrm{chiliad}T$

(

${\mathrm{East}}_{peak}\propto k{T}^{\mathrm{ane.1}}$

), would imply that despite the different pulse-type SGRBs in our sample, the prompt broadband gamma-ray radiation could originate from the like structures of the region.

Writer Contributions

Writing—review and editing, P.-Due west.Z. and Q.-Westward.T. All authors have read and agreed to the published version of the manuscript.

Funding

Q.-W.T. was funded by National Nature Science Foundation of China grant numbers 11903017 and 12065017.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data available on reasonable asking to the authors.

Conflicts of Interest

The authors declare no conflict of interest.

References

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Figure i. Observaional lightcurves in the energy ring from 50 keV to 300 keV and the best-fit lines modelled past the FRED functions. For top pannel of each GRB, the red histogram represents fifty–300 keV observational lightcurve, and solid blackness line is the best fit with the empirical role (FRED). The bottom pannel in ecah GRB is the residual between the observation and the fitting model.

Figure 1. Observaional lightcurves in the energy band from 50 keV to 300 keV and the best-fit lines modelled by the FRED functions. For elevation pannel of each GRB, the carmine histogram represents l–300 keV observational lightcurve, and solid black line is the all-time fit with the empirical role (FRED). The bottom pannel in ecah GRB is the rest between the observation and the fitting model.

Effigy 2. Correlation of the rising fourth dimension (

$T_{\mathrm{rise}}$

) and the total width at one-half maxima (FWHM) of private pulses in all selected short GRBs. 95% and 99.7% confidence leverls are plotted by low-cal blueish dotted line and greenish dashed line respectively.

Figure 2. Correlation of the rise time (

$T_{\mathrm{rise}}$

) and the full width at half maxima (FWHM) of individual pulses in all selected short GRBs. 95% and 99.7% confidence leverls are plotted by calorie-free blue dotted line and green dashed line respectively.

Figure 4. Correlation of acme energy

$E_{peak}$

in CPL function and temperature

$kT$

in the standard BB function when GRB spectrum is fitted by CPL + BB model.

Figure 4. Correlation of peak energy

${\mathrm{East}}_{peak}$

in CPL function and temperature

$\mathrm{chiliad}T$

in the standard BB function when GRB spectrum is fitted by CPL + BB model.

Table ane. GRB sample.

GRB	${\mathit{T}}_{90}$ (south)	${\mathit{T}}_{05}$ (s)	${\mathit{T}}_{95}$ (s)	Detetor	${\mathit{S}}_{50–300\mathbf{keV}}$ (${10}^{-\mathrm{six}}$$\mathbf{erg}{\mathbf{cm}}^{-\mathrm{ii}}$)
090227B	0.304	−0.016	0.288	'n0','n1','n2','b0'	eleven.1$\pm$0.1
120323A	0.384	0	0.384	'n0','n3','n4','b0'	10.four$\pm$0.1
140209A	1.408	i.344	ii.752	'n9','na','nb','b1'	ix.0$\pm$0.1
150819B	0.96	−0.064	0.896	'n2','n9','na','b1'	8.1$\pm$0.1
170206A	one.168	0.208	one.376	'n9','na','nb','b1'	x.2$\pm$0.2
171108A	0.032	−0.016	0.016	'n9','na','nb','b1'	10.4$\pm$0.6
171126A	1.472	0	1.472	'n0', 'n1','n2','n3'	7.two$\pm$0.1
180703B	1.536	0.128	1.664	'n0','n1','n3','b0'	8.eight$\pm$0.1
181222B	0.576	0.032	0.608	'n3','n4','n7','b0'	36.2$\pm$0.i

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