Time-integrated polarizations in the prompt phase of gamma-ray bursts via the multi-window interpretation

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Table 1.

Spectral parameters and polarization properties of the 23 GRBs.

GRB	PD_obs(%)	α_B	β_B	z	Instrument(Polarization)	PD_cal, a(%)	PD_cal, t(%)	PD_int(%) ^(a)
100826A	$27_{- 11}^{+ 11}$ $27_{-11}^{+11}$	$- 0 . 785_{- 0.022}^{+ 0.022}$ $-0.785_{-0.022}^{+0.022}$	$- 1 . 895_{- 0.024}^{+ 0.024}$ $-1.895_{-0.024}^{+0.024}$	–	GAP	21.87	48.48	$36 . 72_{- 0.57}^{+ 0.57}$ $36.72_{-0.57}^{+0.57}$
110301A	$70_{- 22}^{+ 22}$ $70_{-22}^{+22}$	$- 0 . 864_{- 0.019}^{+ 0.019}$ $-0.864_{-0.019}^{+0.019}$	$- 2 . 723_{- 0.055}^{+ 0.055}$ $-2.723_{-0.055}^{+0.055}$	–	GAP	52.48	52.48	$47 . 8_{- 0.61}^{+ 0.59}$ $47.8_{-0.61}^{+0.59}$
110721A	$84_{- 28}^{+ 16}$ $84_{-28}^{+16}$	$- 1 . 137_{- 0.019}^{+ 0.019}$ $-1.137_{-0.019}^{+0.019}$	$- 1 . 932_{- 0.053}^{+ 0.053}$ $-1.932_{-0.053}^{+0.053}$	0.382	GAP	49.79	51.85	$38 . 8_{- 1.07}^{+ 1.12}$ $38.8_{-1.07}^{+1.12}$
161218B	$13_{- 13}^{+ 28}$ $13_{-13}^{+28}$	$- 0 . 597_{- 0.016}^{+ 0.016}$ $-0.597_{-0.016}^{+0.016}$	$- 3 . 131_{- 0.206}^{+ 0.206}$ $-3.131_{-0.206}^{+0.206}$	–	POLAR	43.64	41.57	$27 . 2_{- 0.32}^{+ 0.34}$ $27.2_{-0.32}^{+0.34}$
170101B	$60_{- 36}^{+ 24}$ $60_{-36}^{+24}$	$- 0 . 526_{- 0.062}^{+ 0.062}$ $-0.526_{-0.062}^{+0.062}$	$- 2 . 301_{- 0.132}^{+ 0.132}$ $-2.301_{-0.132}^{+0.132}$	–	POLAR	50.43	51.30	$32 . 42_{- 2.37}^{+ 2.32}$ $32.42_{-2.37}^{+2.32}$
170114A	$10 . 1_{- 7.4}^{+ 10.5}$ $10.1_{-7.4}^{+10.5}$	$- 0 . 928_{- 0.045}^{+ 0.045}$ $-0.928_{-0.045}^{+0.045}$	$- 2 . 040_{- 0.075}^{+ 0.075}$ $-2.040_{-0.075}^{+0.075}$	–	POLAR	11.68	54.16	$39 . 92_{- 2.08}^{+ 2.1}$ $39.92_{-2.08}^{+2.1}$
170206A	$13 . 5_{- 8.6}^{+ 7.4}$ $13.5_{-8.6}^{+7.4}$	$- 0 . 406_{- 0.042}^{+ 0.042}$ $-0.406_{-0.042}^{+0.042}$	$- 2 . 427_{- 0.100}^{+ 0.100}$ $-2.427_{-0.100}^{+0.100}$	–	POLAR	38.54	39.12	$16 . 03_{- 1.95}^{+ 1.91}$ $16.03_{-1.95}^{+1.91}$
170207A	$5 . 9_{- 5.9}^{+ 9.6}$ $5.9_{-5.9}^{+9.6}$	$- 0 . 953_{- 0.025}^{+ 0.025}$ $-0.953_{-0.025}^{+0.025}$	$- 2 . 433_{- 0.226}^{+ 0.226}$ $-2.433_{-0.226}^{+0.226}$	–	POLAR	45.33	46.47	$36 . 05_{- 2.30}^{+ 1.93}$ $36.05_{-2.30}^{+1.93}$
170210A	$11 . 4_{- 9.7}^{+ 35.7}$ $11.4_{-9.7}^{+35.7}$	$- 1 . 025_{- 0.015}^{+ 0.015}$ $-1.025_{-0.015}^{+0.015}$	$- 2 . 448_{- 0.116}^{+ 0.116}$ $-2.448_{-0.116}^{+0.116}$	–	POLAR	45.66	45.91	$38 . 06_{- 0.78}^{+ 0.77}$ $38.06_{-0.78}^{+0.77}$
170305A ^(b)	$40_{- 25}^{+ 25}$ $40_{-25}^{+25}$	$- 0 . 242_{- 0.197}^{+ 0.197}$ $-0.242_{-0.197}^{+0.197}$	$- 1 . 879_{- 0.083}^{+ 0.083}$ $-1.879_{-0.083}^{+0.083}$	–	POLAR	51.27	52.63	$26 . 19_{- 6.44}^{+ 6.04}$ $26.19_{-6.44}^{+6.04}$
160325A	< 45.02	$- 0 . 868_{- 0.064}^{+ 0.064}$ $-0.868_{-0.064}^{+0.064}$	$- 2 . 068_{- 0.123}^{+ 0.123}$ $-2.068_{-0.123}^{+0.123}$	–	AstroSat	55.63	56.28	$44 . 34_{- 3.85}^{+ 3.24}$ $44.34_{-3.85}^{+3.24}$
160802A	< 51.89	$- 0 . 632_{- 0.023}^{+ 0.023}$ $-0.632_{-0.023}^{+0.023}$	$- 2 . 387_{- 0.075}^{+ 0.075}$ $-2.387_{-0.075}^{+0.075}$	–	AstroSat	49.63	54.44	$40 . 11_{- 0.86}^{+ 0.27}$ $40.11_{-0.86}^{+0.27}$
160821A	< 33.87	$- 0 . 988_{- 0.004}^{+ 0.004}$ $-0.988_{-0.004}^{+0.004}$	$- 2 . 253_{- 0.018}^{+ 0.018}$ $-2.253_{-0.018}^{+0.018}$	–	AstroSat	5.44	44.76	$36 . 56_{- 0.16}^{+ 0.16}$ $36.56_{-0.16}^{+0.16}$
170527A	< 36.46	$- 1 . 089_{- 0.013}^{+ 0.013}$ $-1.089_{-0.013}^{+0.013}$	$- 3 . 858_{- 1.270}^{+ 1.270}$ $-3.858_{-1.270}^{+1.270}$	–	AstroSat	48.22	47.39	$37 . 38_{- 0.58}^{+ 0.57}$ $37.38_{-0.58}^{+0.57}$
171010A	< 30.02	$- 1 . 117_{- 0.005}^{+ 0.005}$ $-1.117_{-0.005}^{+0.005}$	$- 2 . 246_{- 0.013}^{+ 0.013}$ $-2.246_{-0.013}^{+0.013}$	0.3285	AstroSat	55.94	56.72	$55 . 4_{- 0.3}^{+ 0.22}$ $55.4_{-0.3}^{+0.22}$
171227A	< 55.62	$- 0 . 811_{- 0.007}^{+ 0.007}$ $-0.811_{-0.007}^{+0.007}$	$- 2 . 436_{- 0.035}^{+ 0.035}$ $-2.436_{-0.035}^{+0.035}$	–	AstroSat	42.72	44.27	$32 . 15_{- 0.56}^{+ 0.56}$ $32.15_{-0.56}^{+0.56}$
180120A	$62 . 37_{- 29.79}^{+ 29.79}$ $62.37_{-29.79}^{+29.79}$	$- 1 . 031_{- 0.018}^{+ 0.018}$ $-1.031_{-0.018}^{+0.018}$	$- 2 . 497_{- 0.053}^{+ 0.053}$ $-2.497_{-0.053}^{+0.053}$	–	AstroSat	58.77	60.22	$56 . 18_{- 0.55}^{+ 0.47}$ $56.18_{-0.55}^{+0.47}$
180427A	$60 . 01_{- 22.32}^{+ 22.32}$ $60.01_{-22.32}^{+22.32}$	$- 0 . 317_{- 0.044}^{+ 0.044}$ $-0.317_{-0.044}^{+0.044}$	$- 3 . 037_{- 0.102}^{+ 0.102}$ $-3.037_{-0.102}^{+0.102}$	–	AstroSat	47.04	46.48	$28 . 28_{- 3.48}^{+ 3.2}$ $28.28_{-3.48}^{+3.2}$
180806A	< 95.8	$- 0 . 922_{- 0.029}^{+ 0.029}$ $-0.922_{-0.029}^{+0.029}$	$- 2 . 141_{- 0.103}^{+ 0.103}$ $-2.141_{-0.103}^{+0.103}$	–	AstroSat	50.30	51.75	$40 . 68_{- 1.7}^{+ 1.41}$ $40.68_{-1.7}^{+1.41}$
180914A	< 33.55	$- 0 . 632_{- 0.044}^{+ 0.044}$ $-0.632_{-0.044}^{+0.044}$	$- 2 . 084_{- 0.086}^{+ 0.086}$ $-2.084_{-0.086}^{+0.086}$	–	AstroSat	50.90	51.27	$38 . 26_{- 1.43}^{+ 1.26}$ $38.26_{-1.43}^{+1.26}$
190530A	$46 . 85_{- 18.53}^{+ 18.53}$ $46.85_{-18.53}^{+18.53}$	$- 0 . 973_{- 0.004}^{+ 0.004}$ $-0.973_{-0.004}^{+0.004}$	$- 3 . 680_{- 0.146}^{+ 0.146}$ $-3.680_{-0.146}^{+0.146}$	0.9386	AstroSat	42.40	42.95	$37 . 87_{- 0.68}^{+ 0.1}$ $37.87_{-0.68}^{+0.1}$
200311A	< 45.41	$- 0 . 963_{- 0.027}^{+ 0.027}$ $-0.963_{-0.027}^{+0.027}$	$- 4 . 962_{- 7.550}^{+ 7.550}$ $-4.962_{-7.550}^{+7.550}$	–	AstroSat	43.09	44.14	$35 . 03_{- 1.05}^{+ 1.09}$ $35.03_{-1.05}^{+1.09}$
200412A	< 53.84	$- 0 . 636_{- 0.030}^{+ 0.030}$ $-0.636_{-0.030}^{+0.030}$	$- 2 . 429_{- 0.090}^{+ 0.090}$ $-2.429_{-0.090}^{+0.090}$	–	AstroSat	49.31	49.23	$39 . 59_{- 1.34}^{+ 1.29}$ $39.59_{-1.34}^{+1.29}$

Notes.

^(a)

PD_int represents the results obtained in Guan & Lan (2023).

^(b)

The variation in the electron Lorentz factor is a single power law with g = −1 for the aligned-field case, and it is g = −1.5 for the toroidal-field case.

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