Magnetic Field at the Galactic Centre from Multi-Wavelength Dust Polarization

We have mapped the magnetic field ($B$-field) for a region of about 30 pc around the centre of our Galaxy, which encompasses the circumnuclear disk (CND), the minispiral, and the 20 km s$^{-1}$ and 50 km s$^{-1}$ molecular clouds, using thermal dust polarization observations obtained from SOFIA/HAWC+ and JCMT/SCUPOL. We decompose the spectra of $^{12}$CO ($J\!=\!3\!\rightarrow\!2$) transition from this region into individual cloud components and find the polarization observed at different wavelengths might be tracing completely different layers of dust along the line of sight. We use modified Davis-Chandrasekhar-Fermi methods to measure the strength of $B$-field projected in the plane of the sky ($B_{{}_{\mathrm{POS}}}$). The mean $B_{{}_{\mathrm{POS}}}$ of the CND and the minispiral, probed at 53 $\mu$m is of the order of $\sim\!2$ mG. $B_{{}_{\mathrm{POS}}}\!\!\!<\!1$ mG close to the Galactic Centre, in the region of the ionized mini-cavity within the CND, and increases outwards. However, the longer wavelength polarization at 216 $\mu$m appears to come from a dust layer that is cooler and behind the CND and has a stronger $B$-field of about 7 mG. The $B$-field strength is lowest along the Eastern Arm of the minispiral, which is also the only region with Alfv\'en Mach number, $\mathcal{M}_{\mathrm{A}}>1$ and mass-to-flux ratio, $\lambda\!\gtrsim\!1$. Such an observed weak $B$-field could be a result of the low resolution of the observation, where the tangled $B$-fields due to the strong turbulence in the high density clumps of the CND are lost within the beam size of the observation.