Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# Magnetic field morphology in interstellar clouds with the velocity gradient technique

## Abstract

Magnetic fields, while ubiquitous in many astrophysical environments, are challenging to measure observationally. Based on the properties of anisotropy of eddies in magnetized turbulence, the velocity gradient technique is a method synergistic to dust polarimetry that is capable of tracing plane-of-the-sky magnetic fields, measuring the magnetization of interstellar media and estimating the fraction of gravitational collapsing gas in molecular clouds using spectral line observations. Here, we apply this technique to five low-mass star-forming molecular clouds in the Gould Belt and compare the results to the magnetic field orientation obtained from polarized dust emission. We find that the estimates of magnetic field orientations and magnetization for both methods are statistically similar. We estimate the fraction of collapsing gas in the selected clouds. By using the velocity gradient technique, we also present the plane-of-the-sky magnetic field orientation and magnetization of the Smith Cloud, for which dust polarimetry data are unavailable.

## Access options

\$32.00

All prices are NET prices.

## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author and other co-authors upon reasonable request.

## Code availability

The code for the VGT algorithm is available at https://github.com/wisYue/Survey.git.

## References

1. Planck Collaboration Planck intermediate results. XXXV. Probing the role of the magnetic field in the formation of structure in molecular clouds. Astron. Astrophys. 586, A138 (2016).

2. Larson, R. B. Turbulence and star formation in molecular clouds. Mon. Not. R. Astron. Soc. 194, 809–826 (1981).

3. McKee, C. F. & Tan, J. C. The formation of massive stars from turbulent cores. Astrophys. J. 585, 850–871 (2003).

4. Seifried, D. & Walch, S. The impact of turbulence and magnetic field orientation on star-forming filaments. Mon. Not. R. Astron. Soc. 452, 2410–2422 (2015).

5. Bromm, V., Coppi, P. S. & Larson, R. B. Forming the first stars in the Universe: the fragmentation of primordial gas. Astrophys. J. Lett. 527, L5–L8 (1999).

6. Hill, T. et al. Filaments and ridges in Vela c revealed by Herschel: from low-mass to high-mass star-forming sites. Astron. Astrophys. 533, A94 (2011).

7. Brandenburg, A. & Lazarian, A. Astrophysical hydromagnetic turbulence. Space Sci. Rev. 178, 163–200 (2013).

8. Andersson, B.-G., Lazarian, A. & Vaillancourt, J. E. Interstellar dust grain alignment. Annu. Rev. Astron. Astrophys. 53, 501–539 (2015).

9. Planck Collaboration Planck 2018 results. III. High Frequency Instrument data processing and frequency maps. Preprint at https://arxiv.org/abs/1807.06207 (2018).

10. Li, H.-B. et al. Self-similar fragmentation regulated by magnetic fields in a region forming massive stars. Nature 520, 518–521 (2015).

11. Lazarian, A. Magnetic fields via polarimetry: progress of grain alignment theory. J. Quant. Spectrosc. Radiat. Transf. 79, 881 (2003).

12. Lazarian, A. & Hoang, T. Subsonic mechanical alignment of irregular grains. Astrophys. J. 669, L77–L80 (2007).

13. Hoang, T., Cho, J. & Lazarian, A. Alignment of irregular grains by mechanical torques. Astrophys. J. 852, 129 (2018).

14. Davis, L. The strength of interstellar magnetic fields. Phys. Rev. 81, 890–891 (1951).

15. Chandrasekhar, S. & Fermi, E. Magnetic fields in spiral arms. Astrophys. J. 118, 113 (1953).

16. Crutcher, R. M., Wandelt, B., Heiles, C., Falgarone, E. & Troland, T. H. Magnetic fields in interstellar clouds from Zeeman observations: inference of total field strengths by Bayesian analysis. Astrophys. J. 725, 466–479 (2010).

17. Taylor, A. R., Stil, J. M. & Sunstrum, C. A rotation measure image of the sky. Astrophys. J. 702, 1230–1236 (2009).

18. González-Casanova, D. F. & Lazarian, A. Velocity gradients as a tracer for magnetic fields. Astrophys. J. 835, 41 (2017).

19. Yuen, K. H. & Lazarian, A. Tracing interstellar magnetic field using velocity gradient technique: application to atomic hydrogen data. Astrophys. J. 837, L24 (2017).

20. Lazarian, A. & Yuen, K. H. Tracing magnetic fields with spectroscopic channel maps. Astrophys. J. 853, 96 (2018).

21. Yuen, K. H. et al. Statistical tracing of magnetic fields: comparing and improving the techniques. Astrophys. J. 865, 54 (2018).

22. Goldreich, P. & Sridhar, S. Toward a theory of interstellar turbulence. 2: strong Alfvénic turbulence. Astrophys. J. 438, 763–775 (1995).

23. Lazarian, A. & Vishniac, E. T. Reconnection in a weakly stochastic field. Astrophys. J. 517, 700–718 (1999).

24. Cho, J. & Vishniac, E. T. The anisotropy of magnetohydrodynamic Alfvénic turbulence. Astrophys. J. 539, 273–282 (2000).

25. Maron, J. & Goldreich, P. Simulations of incompressible magnetohydrodynamic turbulence. Astrophys. J. 554, 1175–1196 (2001).

26. Beresnyak, A. & Lazarian, A. Scaling laws and diffuse locality of balanced and imbalanced magnetohydrodynamic turbulence. Astrophys. J. Lett. 722, L110–L113 (2010).

27. Beresnyak, A. & Lazarian, A. in Magnetic Fields in Diffuse Media (eds Lazarian, A., de Gouveia Dal Pino, E. M. & Melioli, C.) 163–226 (Springer, 2015).

28. Hsieh, C.-h. et al. Tracing magnetic field morphology using the velocity gradient technique in the presence of CO self-absorption. Astrophys. J. 873, 16 (2019).

29. Lazarian, A. et al. Distribution of velocity gradient orientations: mapping magnetization with the velocity gradient technique. Astrophys. J. 865, 46 (2018).

30. Hu, Y., Yuen, K. H. & Lazarian, A. Improving the accuracy of magnetic field tracing by velocity gradients: principal component analysis. Mon. Not. R. Astron. Soc. 480, 1333–1339 (2018).

31. Ostriker, E. C., Stone, J. M. & Gammie, C. F. Density, velocity, and magnetic field structure in turbulent molecular cloud models. Astrophys. J. 546, 980–1005 (2001).

32. Xu, S. & Lazarian, A. Magnetohydrodynamic turbulence and turbulent dynamo in partially ionized plasma. New J. Phys. 19, 065005 (2017).

33. Smith, G. P. A peculiar feature at lII = 40°.5, bII = − 15°.0. Bull. Astron. Institutes Netherlands 17, 203 (1963).

34. Hill, A. S., Mao, S. A., Benjamin, R. A., Lockman, F. J. & McClure-Griffiths, N. M. Magnetized gas in the Smith High Velocity Cloud. Astrophys. J. 777, 55 (2013).

35. Betti, S. K. et al. Constraining the magnetic field of the Smith High-Velocity Cloud using Faraday rotation. Astrophys. J. 871, 215 (2019).

36. Goldsmith, P. F. et al. Large-scale structure of the molecular gas in Taurus revealed by high linear dynamic range spectral line mapping. Astrophys. J. 680, 428–445 (2008).

37. Ridge, N. A. et al. The complete survey of star-forming regions: phase I data. Astrophys. J. 131, 2921–2933 (2006).

38. Lin, S.-J. et al. The intrinsic abundance ratio and X-factor of CO isotopologues in L 1551 shielded from FUV photodissociation. Astrophys. J. 826, 193 (2016).

39. Bieging, J. H., Revelle, M. & Peters, W. L. The Arizona Radio Observatory CO mapping survey of galactic molecular clouds. IV. The NGC 1333 cloud in Perseus in CO J = 2−1 and 13CO J = 2−1. Astrophys. J. Suppl. Ser. 214, 7 (2014).

40. Burleigh, K. J., Bieging, J. H., Chromey, A., Kulesa, C. & Peters, W. L. The Arizona Radio Observatory CO mapping survey of galactic molecular clouds. III. The Serpens cloud in CO J = 2−1 and 13CO J = 2−1 emission. Astrophys. J. Suppl. Ser. 209, 39 (2013).

41. Lazarian, A. & Pogosyan, D. Velocity modification of H I power spectrum. Astrophys. J. 537, 720–748 (2000).

42. Cho, J. & Lazarian, A. Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications. Mon. Not. R. Astron. Soc. 345, 325–339 (2003).

43. Yuen, K. H. & Lazarian, A. Tracing interstellar magnetic field using the velocity gradient technique in shock and self-gravitating media. Preprint at https://arXiv.org/abs/1703.03026 (2017).

44. Falceta-Gonçalves, D., Lazarian, A. & Kowal, G. Studies of regular and random magnetic fields in the ISM: statistics of polarization vectors and the Chandrasekhar-Fermi technique. Astrophys. J. 679, 537 (2008).

45. Zhang, Q., Wang, K., Lu, X. & Jiménez-Serra, I. Fragmentation of molecular clumps and formation of a protocluster. Astrophys. J. 804, 141 (2015).

46. Ballesteros-Paredes, J., Klessen, R. S., Mac Low, M.-M. & Vazquez-Semadeni, E. in Protostars and Planets V (eds Reipurth, B., Jewitt, D. & Keil, K.) 63–80 (Univ. Arizona Press, 2007).

47. Sugitani, K. et al. Near-infrared-imaging polarimetry toward Serpens South: revealing the importance of the magnetic field. Astrophys. J. 734, 63 (2011).

48. Bland-Hawthorn, J. et al. The Smith cloud: H i associated with the Sgr dwarf? Mon. Not. R. Astron. Soc. 299, 611–624 (1998).

49. Lockman, F. J., Benjamin, R. A., Heroux, A. J. & Langston, G. I. The Smith Cloud: a high-velocity cloud colliding with the Milky Way. Astrophys. J. Lett. 679, L21–L24 (2008).

50. Wakker, B. P. et al. Distances to galactic high-velocity clouds. I. Cohen Stream, Complex GCP, cloud g1. Astrophys. J. 672, 298–319 (2008).

51. Lazarian, A. & Pogosyan, D. Studying velocity turbulence from Doppler-broadened absorption lines: statistics of optical depth fluctuations. Astrophys. J. 686, 350–362 (2008).

52. Lazarian, A., Pogosyan, D. & Esquivel, A. Quest for H i turbulence statistics: new techniques. In Seeing Through the Dust: The Detection of H i and the Exploration of the ISM in Galaxies, Astronomical Society of the Pacific Conference Series (eds Taylor, A. R., Landecker, T. L. & Willis, A. G.) 276, 182 (2002).

53. Clark, S. E., Peek, J. E. G. & Miville-Deschênes, M. A. The physical nature of neutral hydrogen intensity structure. Preprint at https://arXiv.org/abs/1902.01409 (2019).

54. Yuen, K. H., Hu, Y., Lazarian, A. & Pogosyan, D. Comment on Clark et al. (2019) “The physical nature of neutral hydrogen intensity structure”. Preprint at https://arXiv.org/abs/1904.03173 (2019).

## Acknowledgements

A.L. acknowledges the support of National Science Foundation (NSF) grants AST 1715754 and 1816234, and NASA grant NNX14AJ53G. The research of P.F.G. was carried out at the Jet Propulsion Laboratory, which is operated for NASA by the California Institute of Technology. We acknowledge M. Heyer for a number of valuable suggestions in improving our paper. We acknowledge the COordinated Molecular Probe Line Extinction Thermal Emission Survey of Star Forming Regions (COMPLETE) for providing a range of data for the Perseus region and the Arizona Radio Observatory for providing the data of the Serpens region and NGC 1333. The Green Bank Observatory is a facility of the NSF operated under a cooperative agreement by Associated Universities, Inc. This work is based on observations obtained with Planck (http://www.esa.int/Planck), an ESA science mission with instruments and contributions directly funded by the ESA Member States, NASA and Canada.

## Author information

Authors

### Contributions

All authors discussed the results, commented on the manuscript and contributed to the writing of the manuscript. Y.H., K.H.Y. and A.L. conceived the project, Y.H., K.H.Y. and K.W.H. performed calculations, while Y.H., K.H.Y., V.L. and A.L. analysed the results and wrote the original manuscript. R.A.B. provided suggestions on how the VGT technique might be applied to the Smith Cloud. The data on the Taurus cloud were provided by P.F.G. and data on the Smith Cloud were provided by A.S.H. and F.J.L.

### Corresponding author

Correspondence to Yue Hu.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Journal peer review information: Nature Astronomy thanks Andrea Bracco, Kate Pattle and Thomas H. Troland for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

### Supplementary Information

Supplementary Figures 1–5, Supplementary Table 1 and Supplementary References 1–18.

## Rights and permissions

Reprints and Permissions

Hu, Y., Yuen, K.H., Lazarian, V. et al. Magnetic field morphology in interstellar clouds with the velocity gradient technique. Nat Astron 3, 776–782 (2019). https://doi.org/10.1038/s41550-019-0769-0

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41550-019-0769-0

• ### Magnetic fields from turbulent gas motions

• Kate Pattle

Nature Astronomy (2019)