Most-likely DCF Estimates of Magnetic Field Strength
The Davis–Chandrasekhar–Fermi (DCF) method is widely used to evaluate magnetic fields in star-forming regions. Yet it remains unclear how well DCF equations estimate the mean plane-of-the-sky field strength in a map region. To address this question, five DCF equations are applied to an idealized clo...
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IOP Publishing
2024-01-01
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| Series: | The Astrophysical Journal |
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| Online Access: | https://doi.org/10.3847/1538-4357/ad1596 |
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| author | Philip C. Myers Ian W. Stephens Simon Coudé |
| author_facet | Philip C. Myers Ian W. Stephens Simon Coudé |
| author_sort | Philip C. Myers |
| collection | DOAJ |
| description | The Davis–Chandrasekhar–Fermi (DCF) method is widely used to evaluate magnetic fields in star-forming regions. Yet it remains unclear how well DCF equations estimate the mean plane-of-the-sky field strength in a map region. To address this question, five DCF equations are applied to an idealized cloud map. Its polarization angles have a normal distribution with dispersion σ _θ , and its density and velocity dispersion have negligible variation. Each DCF equation specifies a global field strength B _DCF and a distribution of local DCF estimates. The “most-likely” DCF field strength B _ml is the distribution mode, for which a correction factor β _ml ≡ B _ml / B _DCF is calculated analytically. For each equation, β _ml < 1, indicating that B _DCF is a biased estimator of B _ml . The values of β _ml are β _ml ≈ 0.7 when ${B}_{\mathrm{DCF}}\propto {\sigma }_{\theta }^{-1}$ due to turbulent excitation of Alfvénic MHD waves, and β _ml ≈ 0.9 when ${B}_{\mathrm{DCF}}\propto {\sigma }_{\theta }^{-1/2}$ due to non-Alfvénic MHD waves. These statistical correction factors β _ml have partial agreement with correction factors ${\beta }_{\mathrm{sim}}$ obtained from MHD simulations. The relative importance of the statistical correction is estimated by assuming that each simulation correction has both a statistical and a physical component. Then the standard, structure function, and original DCF equations appear most accurate because they require the least physical correction. Their relative physical correction factors are 0.1, 0.3, and 0.4 on a scale from 0 to 1. In contrast, the large-angle and parallel- δ B equations have physical correction factors 0.6 and 0.7. These results may be useful in selecting DCF equations, within model limitations. |
| first_indexed | 2024-03-08T05:11:14Z |
| format | Article |
| id | doaj.art-7c0651e9ffb243f4b60a5194201a2a89 |
| institution | Directory Open Access Journal |
| issn | 1538-4357 |
| language | English |
| last_indexed | 2024-03-08T05:11:14Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
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| series | The Astrophysical Journal |
| spelling | doaj.art-7c0651e9ffb243f4b60a5194201a2a892024-02-07T09:39:47ZengIOP PublishingThe Astrophysical Journal1538-43572024-01-0196216410.3847/1538-4357/ad1596Most-likely DCF Estimates of Magnetic Field StrengthPhilip C. Myers0https://orcid.org/0000-0002-2885-1806Ian W. Stephens1https://orcid.org/0000-0003-3017-4418Simon Coudé2https://orcid.org/0000-0002-0859-0805Center for Astrophysics , Harvard and Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA ; pmyers@cfa.harvard.eduDepartment of Earth, Environment, and Physics, Worcester State University , Worcester, MA 01602, USADepartment of Earth, Environment, and Physics, Worcester State University , Worcester, MA 01602, USAThe Davis–Chandrasekhar–Fermi (DCF) method is widely used to evaluate magnetic fields in star-forming regions. Yet it remains unclear how well DCF equations estimate the mean plane-of-the-sky field strength in a map region. To address this question, five DCF equations are applied to an idealized cloud map. Its polarization angles have a normal distribution with dispersion σ _θ , and its density and velocity dispersion have negligible variation. Each DCF equation specifies a global field strength B _DCF and a distribution of local DCF estimates. The “most-likely” DCF field strength B _ml is the distribution mode, for which a correction factor β _ml ≡ B _ml / B _DCF is calculated analytically. For each equation, β _ml < 1, indicating that B _DCF is a biased estimator of B _ml . The values of β _ml are β _ml ≈ 0.7 when ${B}_{\mathrm{DCF}}\propto {\sigma }_{\theta }^{-1}$ due to turbulent excitation of Alfvénic MHD waves, and β _ml ≈ 0.9 when ${B}_{\mathrm{DCF}}\propto {\sigma }_{\theta }^{-1/2}$ due to non-Alfvénic MHD waves. These statistical correction factors β _ml have partial agreement with correction factors ${\beta }_{\mathrm{sim}}$ obtained from MHD simulations. The relative importance of the statistical correction is estimated by assuming that each simulation correction has both a statistical and a physical component. Then the standard, structure function, and original DCF equations appear most accurate because they require the least physical correction. Their relative physical correction factors are 0.1, 0.3, and 0.4 on a scale from 0 to 1. In contrast, the large-angle and parallel- δ B equations have physical correction factors 0.6 and 0.7. These results may be useful in selecting DCF equations, within model limitations.https://doi.org/10.3847/1538-4357/ad1596Interstellar magnetic fieldsStar formation |
| spellingShingle | Philip C. Myers Ian W. Stephens Simon Coudé Most-likely DCF Estimates of Magnetic Field Strength The Astrophysical Journal Interstellar magnetic fields Star formation |
| title | Most-likely DCF Estimates of Magnetic Field Strength |
| title_full | Most-likely DCF Estimates of Magnetic Field Strength |
| title_fullStr | Most-likely DCF Estimates of Magnetic Field Strength |
| title_full_unstemmed | Most-likely DCF Estimates of Magnetic Field Strength |
| title_short | Most-likely DCF Estimates of Magnetic Field Strength |
| title_sort | most likely dcf estimates of magnetic field strength |
| topic | Interstellar magnetic fields Star formation |
| url | https://doi.org/10.3847/1538-4357/ad1596 |
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