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 mini-spirals, 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 ($J=3\rightarrow2$) transition from this region into individual clustered cloud components and find the polarization observed at different wavelengths might be tracing completely different layers of dust along the line-of-sight (LOS). We use modified Davis-Chandrasekhar-Fermi methods to estimate the $B$-field from the observations. From our analysis we find the mean strength of the plane-of-sky $B$-field ($B_{{}_{\mathrm{POS}}}$) of the CND and the mini-spirals, probed at 53 $\mu$m to be of the order of $\sim2$ mG. The magnetic field is lowest close to the Galactic Centre, in the region of the ionized mini-cavity within the CND with $B_{{}_{\mathrm{POS}}}<1$ mG, 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 6 mG. The $B$-field has the least strength along the Eastern Arm of the mini-spiral, which is also the only region with $\mathcal{M}_{\mathrm{A}}>1$ and a mass-to-flux ratio of $\lambda\gtrsim1$. The similarity between the $B_{{}_{\mathrm{POS}}}$ estimates of the 53 $\mu$m and 850 $\mu$m observations might indicate them originating from the same depth along the LOS, mostly from the CND and its foreground cloud features, including the negative-longitude extension.