Quantitative polarimetry of the disk around HD 169142

Context. Many scattered light images of protoplanetary disks have been obtained with the new generation of adaptive optics (AO) systems at large telescopes. The measured scattered radiation can be used to constrain the dust that forms planets in these disks. Aims. We want to constrain the dust particle properties for the bright, pole-on transition disk around HD 169142 with accurate measurements and a quantitative analysis for the polarization and intensity of the scattered radiation. Methods. We investigate high resolution imaging polarimetry of HD 169142 taken in the R′ and I′ bands with the SPHERE/ZIMPOL AO instrument. The geometry of this pole-on disk is close to rotational symmetry, and we can use azimuthally averaged radial profiles for our analysis. We describe the dependence of the disk polarimetry on the atmospheric turbulence, which strongly impacts the AO point spread function (PSF). With non-coronagraphic data we can analyze the polarimetric signal of the disk simultaneously with the stellar PSF and determine the polarization of the disk based on simulations of the PSF convolution. We also extract the disk intensity signal and derive the fractional polarization for the R′ and I′ bands. We compare the scattered flux from the inner and outer disk rings with the corresponding thermal dust emissions measured in the IR and estimate the ratio between scattered and absorbed radiation. Results. We find for the inner and outer disk rings of HD 169142 mean radii of 170 ± 3 mas and 522 ± 20 mas, respectively, and the same small deviations from a perfect ring geometry as previous studies. The AO performance shows strong temporal variation because of the mediocre seeing of about 1.1″; this produces PSF peak variations of up to a factor of four and strongly correlated changes for the measured disk polarization of about a factor of two for the inner disk ring and about 1.2 for the more extended outer disk. This variable PSF convolution effect can be simulated and accurately corrected, and we obtain ratios between the integrated disk polarization flux and total system flux ($ \widehat{Q}_\phi/I_{\mathrm{tot}} $) of 0.43 ± 0.01% for the R′ band and 0.55 ± 0.01% for the I′ band. This indicates a reddish color for the light reflection by the dust. The inner disk ring contributes about 75% and the outer disk about 25% to the total disk flux. The extraction of the scattered intensity of the disk is only possible for the bright, narrow, inner disk ring, and the obtained fractional polarization $ \widehat{p} $ for the scattered radiation is 23.6 ± 3.5% for the I′ band and 22.0 ± 5.9% for the R′ band. The ratio between scattered disk flux and star flux ($ \widehat{I}_{\mathrm{disk}}/I_{\star} $) is about 2.3 ± 0.3%. This is much smaller than the derived IR excess FfIR/F⋆ = 17.6% for the disk components observed in scattered light. This indicates that only a small fraction of the radiation illuminating the disk is scattered; most is absorbed and reemitted in the IR. Conclusions. We demonstrate the feasibility of accurate quantitative photo-polarimetry of a circumstellar disk with a radius of less than 0.2″, observed with ground-based AO systems, if the PSF convolution effects can be properly taken into account. Accurate measurements are a pre-requisite for finding differences in the dust properties for different disks. The derived fractional polarization of about 23% in the R′ and I′ bands for the compact (20 AU) inner disk of HD 169142 is lower than the measurement for the more extended disk HD 142527 for the same wavelength range and significantly lower than the estimates for near-IR data of other extended protoplanetary disks