Context : Polarized continuum emission at millimeter/sub-millimeter wavelengths is usually attributed to thermal emission from dust grains aligned through radiative torques with the magnetic field .
However , recent theoretical work has shown that under specific conditions polarization may arise from self-scattering of thermal emission and by radiation fields from a nearby stellar object .

Aims : We use multi-frequency polarization observations of a circumbinary disk to investigate how the polarization properties change at distinct frequency bands .
Our goal is to discern the main mechanism responsible for the polarization through comparison between our observations and model predictions for each of the proposed mechanisms .

Methods : We used the Atacama Large Millimeter/submillimeter Array to perform full polarization observations at 97.5 GHz ( Band 3 ) , 233 GHz ( Band 6 ) and 343.5 GHz ( Band 7 ) .
The ALMA data have a mean spatial resolution of 28 AU .
The target is the Class I object BHB07-11 , which is the youngest object in the Barnard 59 protocluster .
Complementary Karl G. Jansky Very Large Array observations at 34.5 GHz were also performed and revealed a binary system at centimetric continuum emission within the disk .

Results : We detect an extended and structured polarization pattern remarkably consistent among all three bands .
The distribution of polarized intensity resembles a horseshoe shape with polarization angles following this morphology .
From the spectral index between bands 3 and 7 , we derive a dust opacity index \beta \sim 1 consistent with maximum grain sizes larger than expected to produce self-scattering polarization in each band .
The polarization morphology and the polarization levels do not match predictions from self-scattering .
On the other hand , marginal correspondence is seen between our maps and predictions from radiation field assuming the brightest binary component as main radiation source .
Previous molecular line data from BHB07-11 indicates disk rotation .
We used the DustPol module of the ARTIST radiative transfer tool to produce synthetic polarization maps from a rotating magnetized disk model assuming combined poloidal and toroidal magnetic field components .
The magnetic field vectors ( i. e. , the polarization vectors rotated by 90 \degr ) are better represented by a model with poloidal magnetic field strength about 3 times the toroidal one .

Conclusions : The similarity of our polarization patterns among the three bands provides a strong evidence against self-scattering and radiation fields .
On the other hand , our data are reasonably well reproduced by a model of disk with toroidal magnetic field components slightly smaller than poloidal ones .
The residual is likely due to the internal twisting of the magnetic field due to the binary system dynamics , which is not considered in our model .