Synchrotron Break Frequencies of Mildly to Highly Relativistic Outflows Observed Off-axis
We consider the synchrotron spectrum produced by mildly to highly relativistic collisionless shocks. Simple analytic formulae are derived for the break frequencies (peak frequency, self-absorption frequency, synchrotron, and inverse Compton cooling frequencies) of the emission produced by postshock...
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2024-01-01
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| Online Access: | https://doi.org/10.3847/1538-4357/ad9684 |
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| author | Gilad Sadeh |
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| collection | DOAJ |
| description | We consider the synchrotron spectrum produced by mildly to highly relativistic collisionless shocks. Simple analytic formulae are derived for the break frequencies (peak frequency, self-absorption frequency, synchrotron, and inverse Compton cooling frequencies) of the emission produced by postshock plasma elements propagating at an angle θ _e relative to the observer’s line of sight. These formulae reproduce well the results of earlier exact analytic calculations valid for ultrarelativistic shocks and also hold for γ < 10 and for “off-axis” propagation (deviating from the ultrarelativistic results by approximately 1 order of magnitude). Our results will improve parameter estimation accuracy from future observations of synchrotron emission produced by collisionless shocks driven by the relativistic ejected material from compact object mergers and jetted tidal disruption events. The improved accuracy for mildly relativistic velocities is essential since most events will be observed off-axis, with γ < 10 outflows dominating the synchrotron emission (due to relativistic beaming). For GW170817, our results imply that (i) the Lorentz factor of the plasma emitting the observed radiation is bounded by 2.6 < γ at t ∼ 10 days and by γ < 12 at t > 16 days, (ii) the interstellar medium (ISM) density, n , and the fraction of internal energy density held by magnetic fields, ε _B , are bounded by n · ε _B ≲ 3 × 10 ^−7 cm ^−3 . In future merger events in higher-density ISM, the peak and cooling frequencies may be identified in the radio and X-ray bands; consequently, γ , n · ε _B could be measured as opposed to the case of GW170817, where these frequencies are out of the observable range. |
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| id | doaj-art-82d831065686407ba642bbb092a1100b |
| institution | DOAJ |
| issn | 1538-4357 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
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| series | The Astrophysical Journal |
| spelling | doaj-art-82d831065686407ba642bbb092a1100b2025-08-20T02:50:23ZengIOP PublishingThe Astrophysical Journal1538-43572024-01-01977218110.3847/1538-4357/ad9684Synchrotron Break Frequencies of Mildly to Highly Relativistic Outflows Observed Off-axisGilad Sadeh0https://orcid.org/0009-0003-0141-6171Department of Particle Physics & Astrophysics, Weizmann Institute of Science , Rehovot 76100, IsraelWe consider the synchrotron spectrum produced by mildly to highly relativistic collisionless shocks. Simple analytic formulae are derived for the break frequencies (peak frequency, self-absorption frequency, synchrotron, and inverse Compton cooling frequencies) of the emission produced by postshock plasma elements propagating at an angle θ _e relative to the observer’s line of sight. These formulae reproduce well the results of earlier exact analytic calculations valid for ultrarelativistic shocks and also hold for γ < 10 and for “off-axis” propagation (deviating from the ultrarelativistic results by approximately 1 order of magnitude). Our results will improve parameter estimation accuracy from future observations of synchrotron emission produced by collisionless shocks driven by the relativistic ejected material from compact object mergers and jetted tidal disruption events. The improved accuracy for mildly relativistic velocities is essential since most events will be observed off-axis, with γ < 10 outflows dominating the synchrotron emission (due to relativistic beaming). For GW170817, our results imply that (i) the Lorentz factor of the plasma emitting the observed radiation is bounded by 2.6 < γ at t ∼ 10 days and by γ < 12 at t > 16 days, (ii) the interstellar medium (ISM) density, n , and the fraction of internal energy density held by magnetic fields, ε _B , are bounded by n · ε _B ≲ 3 × 10 ^−7 cm ^−3 . In future merger events in higher-density ISM, the peak and cooling frequencies may be identified in the radio and X-ray bands; consequently, γ , n · ε _B could be measured as opposed to the case of GW170817, where these frequencies are out of the observable range.https://doi.org/10.3847/1538-4357/ad9684Relativistic fluid dynamicsNeutron starsGravitational wave sourcesRadio transient sourcesGamma-ray transient sourcesX-ray transient sources |
| spellingShingle | Gilad Sadeh Synchrotron Break Frequencies of Mildly to Highly Relativistic Outflows Observed Off-axis The Astrophysical Journal Relativistic fluid dynamics Neutron stars Gravitational wave sources Radio transient sources Gamma-ray transient sources X-ray transient sources |
| title | Synchrotron Break Frequencies of Mildly to Highly Relativistic Outflows Observed Off-axis |
| title_full | Synchrotron Break Frequencies of Mildly to Highly Relativistic Outflows Observed Off-axis |
| title_fullStr | Synchrotron Break Frequencies of Mildly to Highly Relativistic Outflows Observed Off-axis |
| title_full_unstemmed | Synchrotron Break Frequencies of Mildly to Highly Relativistic Outflows Observed Off-axis |
| title_short | Synchrotron Break Frequencies of Mildly to Highly Relativistic Outflows Observed Off-axis |
| title_sort | synchrotron break frequencies of mildly to highly relativistic outflows observed off axis |
| topic | Relativistic fluid dynamics Neutron stars Gravitational wave sources Radio transient sources Gamma-ray transient sources X-ray transient sources |
| url | https://doi.org/10.3847/1538-4357/ad9684 |
| work_keys_str_mv | AT giladsadeh synchrotronbreakfrequenciesofmildlytohighlyrelativisticoutflowsobservedoffaxis |