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We present the first degree-scale tomography map of the dusty magnetized interstellar medium (ISM) from stellar polarimetry and distance measurements. We used the RoboPol polarimeter at Skinakas Observatory to conduct a survey of the polarization of starlight in a region of the sky of about four square degrees. We propose a Bayesian method to decompose the stellar-polarization source field along the distance to invert the three-dimensional (3D) volume occupied by the observed stars. We used this method to obtain the first 3D map of the dusty magnetized ISM. Specifically, we produced a tomography map of the orientation of the plane-of-sky component of the magnetic field threading the diffuse, dusty regions responsible for the stellar polarization. For the targeted region centered on Galactic coordinates (l,b) ≈ (103.3°, 22.3°), we identified several ISM clouds. Most of the lines of sight intersect more than one cloud. A very nearby component was detected in the foreground of a dominant component from which most of the polarization signal comes and which we identified as being an intersection of the wall of the Local Bubble and the Cepheus Flare. Farther clouds, with a distance of up to 2 kpc, were similarly detected. Some of them likely correspond to intermediate-velocity clouds seen in HIspectra in this region of the sky. We found that the orientation of the plane-of-sky component of the magnetic field changes along distance for most of the lines of sight. Our study demonstrates that starlight polarization data coupled to distance measures have the power to reveal the great complexity of the dusty magnetized ISM in 3D and, in particular, to provide local measurements of the plane-of-sky component of the magnetic field in dusty regions. This demonstrates that the inversion of large data volumes, as expected from the PASIPHAEsurvey, will provide the necessary means to move forward in the modeling of the Galactic magnetic field and of the dusty magnetized ISM as a contaminant in observations of the cosmic microwave background polarization. 

We present the first Bayesian method for tomographic decomposition of the plane-of-sky orientation of the magnetic field with the use of stellar polarimetry and distance. This standalone tomographic inversion method presents an important step forward in reconstructing the magnetized interstellar medium (ISM) in three dimensions within dusty regions. We develop a model in which the polarization signal from the magnetized and dusty ISM is described by thin layers at various distances, a working assumption which should be satisfied in small-angular circular apertures. Our modeling makes it possible to infer the mean polarization (amplitude and orientation) induced by individual dusty clouds and to account for the turbulence-induced scatter in a generic way. We present a likelihood function that explicitly accounts for uncertainties in polarization and parallax. We develop a framework for reconstructing the magnetized ISM through the maximization of the log-likelihood using a nested sampling method. We test our Bayesian inversion method on mock data, representative of the high Galactic latitude sky, taking into account realistic uncertainties from Gaia and as expected for the optical polarization survey P ASIPHAE according to the currently planned observing strategy. We demonstrate that our method is effective at recovering the cloud properties as soon as the polarization induced by a cloud to its background stars is higher than ~0.1% for the adopted survey exposure time and level of systematic uncertainty. The larger the induced polarization is, the better the method’s performance, and the lower the number of required stars. Our method makes it possible to recover not only the mean polarization properties but also to characterize the intrinsic scatter, thus creating new ways to characterize ISM turbulence and the magnetic field strength. Finally, we apply our method to an existing data set of starlight polarization with known line-of-sight decomposition, demonstrating agreement with previous results and an improved quantification of uncertainties in cloud properties.