Context. Despite recent observational and theoretical advances in mapping the magnetic fields associated with molecular clouds, their three-dimensional (3D) morphology remains unresolved. Multi-wavelength and multi-scale observations will allow us to paint a comprehensive picture of the magnetic fields of these star-forming regions. Aims. We reconstructed the 3D magnetic field morphology associated with the Perseus molecular cloud and compared it with predictions of cloud-formation models. These cloud-formation models predict a bending of magnetic fields associated with filamentary molecular clouds. We compared the orientation and direction of this field bending with our 3D magnetic-field view of the Perseus cloud. Methods. We used previous line-of-sight and plane-of-sky magnetic field observations as well as Galactic magnetic field models to reconstruct the complete 3D magnetic field vectors and morphology associated with the Perseus cloud. Results. We approximated the 3D magnetic field morphology of the cloud as a concave arc that points in the decreasing longitude direction in the plane of the sky (from our point of view). This field morphology preserves a memory of the Galactic magnetic field. In order to compare this morphology to cloud-formation model predictions, we assume that the cloud retains a memory of its most recent interaction. After incorporating velocity observations, we find that the line-of-sight magnetic field observations are consistent with predictions of shock-cloud-interaction models. Conclusions. To our knowledge, this is the first time that the 3D magnetic fields of a molecular cloud have been reconstructed. We find the 3D magnetic field morphology of the Perseus cloud to be consistent with the predictions of the shock-cloud-interaction model that describes the formation mechanism of filamentary molecular clouds.

Magnetic fields permeate the interstellar medium and are important in the star formation process. Determining the three-dimensional (3D) magnetic fields of molecular clouds will allow us to better understand their role in the evolution of these clouds and the formation of stars. We fully reconstruct the approximate 3D magnetic field morphology of the Orion A molecular cloud (on scales of a few to ∼100 pc) using Galactic magnetic field models, as well as available line-of-sight and plane-of-sky magnetic field observations. While previous studies identified the 3D magnetic field morphology of the Orion A cloud as an arc shape, in this study we provide the orientation of this arc-shaped field and its plane-of-sky direction for the first time. We find that this 3D field is a tilted, semi-convex (from our point of view) structure and mostly points in the direction of decreasing latitude and longitude on the plane of the sky from our vantage point. The previously identified bubbles and events in this region were key in shaping this arc-shaped magnetic field morphology.