Revisiting the distance to radio Loops I and IV using Gaia and
  radio/optical polarization data
  Galactic synchrotron emission exhibits large-angular-scale features known as
radio spurs and loops. Determining the physical size of these structures is
important for understanding the local interstellar structure and for modeling
the Galactic magnetic field. However, the distance to these structures is
either under debate or entirely unknown. We revisit a classical method of
finding the location of radio spurs by comparing optical polarization angles
with those of synchrotron emission as a function of distance. We consider three
tracers of the magnetic field: stellar polarization, polarized synchrotron
radio emission, and polarized thermal dust emission. We employ archival
measurements of optical starlight polarization and Gaia distances, and
construct a new map of polarized synchrotron emission from WMAP and Planck
data. We confirm that synchrotron, dust emission, and stellar polarization
angles all show a statistically significant alignment at high Galactic
latitude. We obtain distance limits to three regions towards Loop I of
112$\pm$17 pc, 135$\pm$20 pc, and $<105$ pc. Our results strongly suggest that
the polarized synchrotron emission towards the North Polar Spur at $b >
30^\circ$ is local. This is consistent with the conclusions of earlier work
based on stellar polarization and extinction, but in stark contrast with the
Galactic center origin recently revisited on the basis of X-ray data. We also
obtain a distance measurement towards part of Loop IV (180$\pm$15 pc) and find
evidence that its synchrotron emission arises from chance overlap of structures
located at different distances. Future optical polarization surveys will allow
the expansion of this analysis to other radio spurs.
