The Low-Energy Spectral Index of Gamma-ray Burst Prompt Emission from Internal Shocks
The prompt emission of most gamma-ray bursts (GRBs) typically exhibits a non-thermal Band component. The synchrotron radiation in the popular internal shock model is generally put forward to explain such a non-thermal component. However, the low-energy photon index <inline-formula><math xml...
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MDPI AG
2021-09-01
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| Series: | Galaxies |
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| Online Access: | https://www.mdpi.com/2075-4434/9/3/68 |
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| author | Kai Wang Zi-Gao Dai |
| author_facet | Kai Wang Zi-Gao Dai |
| author_sort | Kai Wang |
| collection | DOAJ |
| description | The prompt emission of most gamma-ray bursts (GRBs) typically exhibits a non-thermal Band component. The synchrotron radiation in the popular internal shock model is generally put forward to explain such a non-thermal component. However, the low-energy photon index <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∼</mo><mo>−</mo><mn>1.5</mn></mrow></semantics></math></inline-formula> predicted by the synchrotron radiation is inconsistent with the observed value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∼</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>. Here, we investigate the evolution of a magnetic field during propagation of internal shocks within an ultrarelativistic outflow, and revisit the fast cooling of shock-accelerated electrons via synchrotron radiation for this evolutional magnetic field. We find that the magnetic field is first nearly constant and then decays as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>B</mi><mo>′</mo></msup><mo>∝</mo><msup><mi>t</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, which leads to a reasonable range of the low-energy photon index, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>3</mn><mo>/</mo><mn>2</mn><mo><</mo><mi>α</mi><mo><</mo><mo>−</mo><mn>2</mn><mo>/</mo><mn>3</mn></mrow></semantics></math></inline-formula>. In addition, if a rising electron injection rate during a GRB is introduced, we find that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> reaches <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>2</mn><mo>/</mo><mn>3</mn></mrow></semantics></math></inline-formula> more easily. We thus fit the prompt emission spectra of GRB 080916c and GRB 080825c. |
| first_indexed | 2024-03-10T07:40:01Z |
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| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-03-10T07:40:01Z |
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| spelling | doaj.art-d0ff75a64f674372a76d0e95d31864882023-11-22T13:10:49ZengMDPI AGGalaxies2075-44342021-09-01936810.3390/galaxies9030068The Low-Energy Spectral Index of Gamma-ray Burst Prompt Emission from Internal ShocksKai Wang0Zi-Gao Dai1Department of Astronomy, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, ChinaDepartment of Astronomy, University of Science and Technology of China, Hefei 230026, ChinaThe prompt emission of most gamma-ray bursts (GRBs) typically exhibits a non-thermal Band component. The synchrotron radiation in the popular internal shock model is generally put forward to explain such a non-thermal component. However, the low-energy photon index <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∼</mo><mo>−</mo><mn>1.5</mn></mrow></semantics></math></inline-formula> predicted by the synchrotron radiation is inconsistent with the observed value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∼</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>. Here, we investigate the evolution of a magnetic field during propagation of internal shocks within an ultrarelativistic outflow, and revisit the fast cooling of shock-accelerated electrons via synchrotron radiation for this evolutional magnetic field. We find that the magnetic field is first nearly constant and then decays as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>B</mi><mo>′</mo></msup><mo>∝</mo><msup><mi>t</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, which leads to a reasonable range of the low-energy photon index, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>3</mn><mo>/</mo><mn>2</mn><mo><</mo><mi>α</mi><mo><</mo><mo>−</mo><mn>2</mn><mo>/</mo><mn>3</mn></mrow></semantics></math></inline-formula>. In addition, if a rising electron injection rate during a GRB is introduced, we find that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> reaches <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>2</mn><mo>/</mo><mn>3</mn></mrow></semantics></math></inline-formula> more easily. We thus fit the prompt emission spectra of GRB 080916c and GRB 080825c.https://www.mdpi.com/2075-4434/9/3/68gamma rays burstsradiation mechanismsnon-thermal |
| spellingShingle | Kai Wang Zi-Gao Dai The Low-Energy Spectral Index of Gamma-ray Burst Prompt Emission from Internal Shocks Galaxies gamma rays bursts radiation mechanisms non-thermal |
| title | The Low-Energy Spectral Index of Gamma-ray Burst Prompt Emission from Internal Shocks |
| title_full | The Low-Energy Spectral Index of Gamma-ray Burst Prompt Emission from Internal Shocks |
| title_fullStr | The Low-Energy Spectral Index of Gamma-ray Burst Prompt Emission from Internal Shocks |
| title_full_unstemmed | The Low-Energy Spectral Index of Gamma-ray Burst Prompt Emission from Internal Shocks |
| title_short | The Low-Energy Spectral Index of Gamma-ray Burst Prompt Emission from Internal Shocks |
| title_sort | low energy spectral index of gamma ray burst prompt emission from internal shocks |
| topic | gamma rays bursts radiation mechanisms non-thermal |
| url | https://www.mdpi.com/2075-4434/9/3/68 |
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