Bayesian Approach to Equipartition Estimation of Magnetic Field Strength
Magnetic fields, together with cosmic rays (CRs), play an important role in the dynamics and evolution of galaxies, but are difficult to estimate. Energy equipartition between magnetic fields and CRs provides a convenient way to approximate magnetic field strength from radio observations. We present...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2025-01-01
|
| Series: | The Astrophysical Journal Supplement Series |
| Subjects: | |
| Online Access: | https://doi.org/10.3847/1538-4365/ad98f5 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841526985250045952 |
|---|---|
| author | Adam A. Zychowicz Krzysztof T. Chyży |
| author_facet | Adam A. Zychowicz Krzysztof T. Chyży |
| author_sort | Adam A. Zychowicz |
| collection | DOAJ |
| description | Magnetic fields, together with cosmic rays (CRs), play an important role in the dynamics and evolution of galaxies, but are difficult to estimate. Energy equipartition between magnetic fields and CRs provides a convenient way to approximate magnetic field strength from radio observations. We present a new approach for calculating the equipartition magnetic field strength based on Bayesian methods. In this approach, the magnetic field is a random variable that is distributed according to a posterior distribution conditional on synchrotron emission and the size of the emitting region. It allows for the direct application of the general formulas for total and polarized synchrotron radiation without the need to invert these formulas, which has limited the equipartition method to highly simplified cases. We have derived the equipartition condition for the case of different low-energy breaks, slopes, and high-energy cutoffs of power-law spectra of the CR proton and electron distributions. The derived formalism was applied in the general case of a magnetic field consisting of both uniform and randomly oriented field components. The applied Bayesian approach naturally provides the uncertainties in the estimated magnetic field strengths resulting from the uncertainties in the observables and the assumed values of the unknown physical parameters. In the examples presented, we used two different Markov Chain Monte Carlo methods to generate the posterior distribution of the magnetic field. We have also developed a web application called BMAG that implements the described approach for different models and observational parameters of real sources. |
| format | Article |
| id | doaj-art-d57cd31e75494e649a0d1d547db1d41f |
| institution | Kabale University |
| issn | 0067-0049 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal Supplement Series |
| spelling | doaj-art-d57cd31e75494e649a0d1d547db1d41f2025-01-16T09:20:30ZengIOP PublishingThe Astrophysical Journal Supplement Series0067-00492025-01-0127624110.3847/1538-4365/ad98f5Bayesian Approach to Equipartition Estimation of Magnetic Field StrengthAdam A. Zychowicz0https://orcid.org/0009-0004-2544-0632Krzysztof T. Chyży1https://orcid.org/0000-0002-6280-2872Astronomical Observatory of the Jagiellonian University , ul. Orla 171, 30-244 Kraków, Poland; Jagiellonian University , Doctoral School of Exact and Natural Sciences, ul. Prof. St. Łojasiewicza 11, 30-348 Kraków, Poland ; adam.zychowicz@doctoral.uj.edu.plAstronomical Observatory of the Jagiellonian University , ul. Orla 171, 30-244 Kraków, PolandMagnetic fields, together with cosmic rays (CRs), play an important role in the dynamics and evolution of galaxies, but are difficult to estimate. Energy equipartition between magnetic fields and CRs provides a convenient way to approximate magnetic field strength from radio observations. We present a new approach for calculating the equipartition magnetic field strength based on Bayesian methods. In this approach, the magnetic field is a random variable that is distributed according to a posterior distribution conditional on synchrotron emission and the size of the emitting region. It allows for the direct application of the general formulas for total and polarized synchrotron radiation without the need to invert these formulas, which has limited the equipartition method to highly simplified cases. We have derived the equipartition condition for the case of different low-energy breaks, slopes, and high-energy cutoffs of power-law spectra of the CR proton and electron distributions. The derived formalism was applied in the general case of a magnetic field consisting of both uniform and randomly oriented field components. The applied Bayesian approach naturally provides the uncertainties in the estimated magnetic field strengths resulting from the uncertainties in the observables and the assumed values of the unknown physical parameters. In the examples presented, we used two different Markov Chain Monte Carlo methods to generate the posterior distribution of the magnetic field. We have also developed a web application called BMAG that implements the described approach for different models and observational parameters of real sources.https://doi.org/10.3847/1538-4365/ad98f5Galaxy magnetic fieldsMagnetic fieldsRadio astronomySupernova remnantsCosmic raysRadio continuum emission |
| spellingShingle | Adam A. Zychowicz Krzysztof T. Chyży Bayesian Approach to Equipartition Estimation of Magnetic Field Strength The Astrophysical Journal Supplement Series Galaxy magnetic fields Magnetic fields Radio astronomy Supernova remnants Cosmic rays Radio continuum emission |
| title | Bayesian Approach to Equipartition Estimation of Magnetic Field Strength |
| title_full | Bayesian Approach to Equipartition Estimation of Magnetic Field Strength |
| title_fullStr | Bayesian Approach to Equipartition Estimation of Magnetic Field Strength |
| title_full_unstemmed | Bayesian Approach to Equipartition Estimation of Magnetic Field Strength |
| title_short | Bayesian Approach to Equipartition Estimation of Magnetic Field Strength |
| title_sort | bayesian approach to equipartition estimation of magnetic field strength |
| topic | Galaxy magnetic fields Magnetic fields Radio astronomy Supernova remnants Cosmic rays Radio continuum emission |
| url | https://doi.org/10.3847/1538-4365/ad98f5 |
| work_keys_str_mv | AT adamazychowicz bayesianapproachtoequipartitionestimationofmagneticfieldstrength AT krzysztoftchyzy bayesianapproachtoequipartitionestimationofmagneticfieldstrength |