Measurements of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>-mode polarization of the cosmic microwave background from 500 square degrees of SPTpol data

We report a $B$-mode power spectrum measurement from the cosmic microwave background (CMB) polarization anisotropy observations made using the SPTpol instrument on the South Pole Telescope. This work uses $500\text{ }\text{ }{\mathrm{deg}}^{2}$ of SPTpol data, a five-fold increase over the last SPTpol $B$-mode release. As a result, the bandpower uncertainties have been reduced by more than a factor of two, and the measurement extends to lower multipoles: $52&lt;\ensuremath{\ell}&lt;2301$. Data from both 95 and 150 GHz are used, allowing for three cross-spectra: $95\text{ }\mathrm{GHz}\text{ }\ifmmode\times\else\texttimes\fi{}\text{ }95\text{ }\mathrm{GHz}$, $95\text{ }\mathrm{GHz}\text{ }\ifmmode\times\else\texttimes\fi{}\text{ }150\text{ }\mathrm{GHz}$, and $150\text{ }\mathrm{GHz}\text{ }\ifmmode\times\else\texttimes\fi{}\text{ }150\text{ }\mathrm{GHz}$. $B$-mode power is detected at very high significance; we find $P(BB&lt;0)=5.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}71}$, corresponding to a $18.1\ensuremath{\sigma}$ detection of power. With a prior on the galactic dust from Planck, WMAP and BICEP2/Keck observations, the SPTpol $B$-mode data can be used to set an upper limit on the tensor-to-scalar ratio, $r&lt;0.44$ at 95% confidence (the expected $1\ensuremath{\sigma}$ constraint on $r$ given the measurement uncertainties is 0.22). We find the measured $B$-mode power is consistent with the Planck best-fit $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model predictions. Scaling the predicted lensing $B$-mode power in this model by a factor ${A}_{\mathrm{lens}}$, the data prefer ${A}_{\mathrm{lens}}=1.17\ifmmode\pm\else\textpm\fi{}0.13$. These data are currently the most precise measurements of $B$-mode power at $\ensuremath{\ell}&gt;320$.