Self-similarity of the magnetic field at different scales: The case of G31.41+0.31

Context. Dust polarization observations of the massive protocluster G31.41+0.31 carried out at similar to 1 '' (3750 au) resolution with the SMA at 870 mu m have revealed one of the clearest examples to date of an hourglass-shaped magnetic field morphology in the high-mass regime. Additionally, similar to O.'' 24 (similar to 900 au) resolution observations with ALMA at 1.3 mm have confirmed these results. The next step is to investigate whether the magnetic field maintains its hourglass-shaped morphology down to circumstellar scales. Aims. To study the magnetic field morphology toward the four (proto)stars A, B, C, and D contained in G31.41+0.31 and examine whether the self-similarity observed at core scales (1 '' and 0.'' 24 resolution) still holds at circumstellar scales, we carried out ALMA observations of the polarized dust continuum emission at 1.3 mm and 3.1 mm at an angular resolution of similar to 0.'' 068 (similar to 250 au), sufficient to resolve the envelope emission of the embedded protostars. Methods. We used ALMA to perform full polarization observations at 233 GHz (Band 6) and 97.5 GHz (Band 3) with a synthesized beam of 0.'' 072 x 0.'' 064. We carried out polarization observations at two different wavelengths to confirm that the polarization traces magnetically aligned dust grains and is not due to dust self-scattering. Results. The polarized emission and the direction of the magnetic field obtained at the two wavelengths are basically the same, except for an area between the embedded sources C and B. In such an area, the emission at 1.3 mm could be optically thick and affected by dichroic extinction. In the rest of the core, the similarity of the emission at the two wavelengths suggests that the polarized emission is due to magnetically aligned grains. The polarized emission has been successfully modeled with a poloidal field with a small toroidal component on the order of 10% of the poloidal component, with a position angle phi = -63 degrees, an inclination i = 50 degrees, and a mass-to-flux ratio lambda = 2.66. The magnetic field axis is oriented perpendicular to the NE-SW velocity gradient detected in the core. The strength of the plane-of-the-sky component of the mean magnetic field, estimated using both the Davis-Chandrasekhar-Fermi and the polarization-intensity gradient methods, is in the range similar to 10-80 mG, for a density range 1.4 x 10(7)-5 x 10(8) cm(-3). The mass-to-flux ratio is in the range lambda similar to 1.9-3.0, which suggests that the core is "supercritical". The polarization-intensity gradient method indicates that the magnetic field cannot prevent gravitational collapse inside the massive core. The collapse in the external part of the core is (slightly) sub-Alfvenic and becomes super-Alfvenic close to the center. Conclusions. Dust polarization measurements from large core scales to small circumstellar scales, in the hot molecular core G31.41+0.31 have confirmed the presence of a strong magnetic field with an hourglass-shaped morphology. This result suggests that the magnetic field could have a relevant role in regulating the star-forming process of massive stars at all scales, although it cannot prevent the collapse. However, it cannot be ruled out that the large opacity of the central region of the core may hinder the study of the magnetic field at circumstellar scales. Therefore, high-angular resolution observations at longer wavelengths, tracing optically thinner emission, are needed to confirm this self-similarity.