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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2509.04572 |
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| _version_ | 1866918136022827008 |
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| author | Lai, Paul C. W. Li, Kaye J. Yap, Y. X. Jane Wu, Kinwah Kong, Albert K. H. |
| author_facet | Lai, Paul C. W. Li, Kaye J. Yap, Y. X. Jane Wu, Kinwah Kong, Albert K. H. |
| contents | For synchrotron radiation from relativistic electrons having a power-law energy distribution with a power-law index $p$ in an optically thin medium with a locally uniform magnetic field, it is generally adopted that the spectral index $α= (p-1)/2$ and the degree of linear polarisation $Π_{\rm L,pl} = (p +1)/(p+7/3)$, and hence that $Π_{\rm L,pl} = (α+1)/(α+5/3)$. These ($α$, $Π_{\rm L,pl}$; $p$) relations are derived assuming that the electrons have an isotropic momentum distribution and a power-law energy distribution, and they have been used, almost universally, in the interpretation of polarimetry observations. In this study, we assess the validity of the ($α$, $Π_{\rm L,pl}$; $p$) relations in different scenarios, such as anisotropic electron momenta and non-power-law distributions of electron energy. We calculate the synchrotron radiation and polarisation spectra for power-law, kappa and log-parabola electron-energy distributions, with isotropic and two anisotropic (beamed and loss cone) electron-momentum distributions. Our calculations show that when the electron momenta are isotropic, the usual ($α$, $Π_{\rm L,pl}$; $p$) relations are generally applicable. However, if the electrons are anisotropic, the usual ($α$, $Π_{\rm L,pl}$; $p$) relations could break down. Applying the usual ($α$, $Π_{\rm L,pl}$; $p$) relations indiscriminately without caution on anisotropy in the electron momentum distribution, would lead to incorrect interpretations of polarimetry data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectropolarimetry of synchrotron radiation from relativistic electrons with anisotropic pitch-angle and various energy distributions Lai, Paul C. W. Li, Kaye J. Yap, Y. X. Jane Wu, Kinwah Kong, Albert K. H. High Energy Astrophysical Phenomena For synchrotron radiation from relativistic electrons having a power-law energy distribution with a power-law index $p$ in an optically thin medium with a locally uniform magnetic field, it is generally adopted that the spectral index $α= (p-1)/2$ and the degree of linear polarisation $Π_{\rm L,pl} = (p +1)/(p+7/3)$, and hence that $Π_{\rm L,pl} = (α+1)/(α+5/3)$. These ($α$, $Π_{\rm L,pl}$; $p$) relations are derived assuming that the electrons have an isotropic momentum distribution and a power-law energy distribution, and they have been used, almost universally, in the interpretation of polarimetry observations. In this study, we assess the validity of the ($α$, $Π_{\rm L,pl}$; $p$) relations in different scenarios, such as anisotropic electron momenta and non-power-law distributions of electron energy. We calculate the synchrotron radiation and polarisation spectra for power-law, kappa and log-parabola electron-energy distributions, with isotropic and two anisotropic (beamed and loss cone) electron-momentum distributions. Our calculations show that when the electron momenta are isotropic, the usual ($α$, $Π_{\rm L,pl}$; $p$) relations are generally applicable. However, if the electrons are anisotropic, the usual ($α$, $Π_{\rm L,pl}$; $p$) relations could break down. Applying the usual ($α$, $Π_{\rm L,pl}$; $p$) relations indiscriminately without caution on anisotropy in the electron momentum distribution, would lead to incorrect interpretations of polarimetry data. |
| title | Spectropolarimetry of synchrotron radiation from relativistic electrons with anisotropic pitch-angle and various energy distributions |
| topic | High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2509.04572 |