Comparing submillimeter polarized emission with near-infrared
  polarization of background stars for the Vela C molecular cloud
  We present a large-scale combination of near-infrared (near-IR) interstellar
polarization data from background starlight with polarized emission data at
submillimeter (sub-mm) wavelengths for the Vela C molecular cloud. The near-IR
data consist of more than 6700 detections probing a range of visual extinctions
between $2$ and $20\,$mag in and around the cloud. The sub-mm data was
collected in Antartica by the Balloon-borne Large Aperture Submillimeter
Telescope for Polarimetry (BLASTPol). This is the first direct combination of
near-IR and sub-mm polarization data for a molecular cloud aimed at measuring
the "polarization efficiency ratio" ($R_{\mathrm{eff}}$), a quantity that is
expected to depend only on grain intrinsic physical properties. It is defined
as $p_{500}/(p_{I}/\tau_{V})$, where $p_{500}$ and $p_{I}$ are polarization
fractions at $500\,\mu$m and $I$-band, respectively, and $\tau_{V}$ is the
optical depth. To ensure that the same column density of material is producing
both polarization from emission and from extinction, we conducted a careful
selection of near-background stars using 2MASS, $Herschel$ and $Planck$ data.
This selection excludes objects contaminated by the Galactic diffuse background
material as well as objects located in the foreground. Accounting for
statistical and systematic uncertainties, we estimate an average
$R_{\mathrm{eff}}$ value of $2.4\pm0.8$, which can be used to test the
predictions of dust grain models designed for molecular clouds when such
predictions become available. $R_{\mathrm{eff}}$ appears to be relatively flat
as a function of the cloud depth for the range of visual extinctions probed.
