Quantitative Polarimetry for the Transition Disk in RX J1604.3-213010

Context. The characterization of the dust in protoplanetary disks is important for a better understanding of the resulting composition of forming planets and the dust particle evolution in these systems. Aims. We aim to accurately characterize the properties of the dust in the face-on transition disk around RX J1604.3-213010 (RX J1604) by analyzing the multiwavelength scattered light intensity and polarization images obtained with the ZIMPOL and IRDIS subinstruments of VLT/SPHERE. Methods. We used archival data of RX J1604 from the ESO archive and carefully corrected the polarization signal for instrumental effects, also taking the interstellar polarization into account. We measured the radial profiles of the disk for the azimuthal polarization, Q(phi)(r), in the R, J, and H bands and describe variations in our data due to the seeing and other effects. We derived the intrinsic polarization profiles of the disk, (Q) over cap (phi)(r), by comparing the data with rotationally symmetric models convolved with the point spread functions of the observations. We also measured the disk intensity, I-disk(r), with reference star differential imaging for the J and H bands. This provides the disk-integrated polarized intensity, (Q) over cap (phi)/I-*, for the R, J, and H bands and the averaged fractional polarization, <(P) over cap (phi)>, for the J and H bands. We investigated the azimuthal dependence of the scattered light and the shadows produced by hot dust near the star. The derived results were finally compared with model calculations to constrain the scattering properties of the reflecting dust in RX J1604. Results. RX J1604 is a dipper source, and the data show different kinds of variability. However, a detailed analysis of repeated measurements shows that the results are not affected by dipping events or atmospheric seeing variations. We derive accurate radial disk profiles for the intrinsic polarized intensity, (Q) over cap (phi)/I-*, and measure different profile peak radii for different bands because of the wavelength dependence of the dust opacity. The disk-integrated polarization is (Q) over cap (phi)/I-* = 0.92 +/- 0.04% for the R band and 1.51 +/- 0.11% for the J band, indicating a red color for the polarized reflectivity of the disk. The intensity of the disk is I-disk/I-* = 3.9 +/- 0.5% in the J band, and the fractional polarization is <(P) over cap (phi)> = 38 +/- 4% for the J band and 42 +/- 2% for the H band. The comparison with the IR excess for RX J1604 yields an apparent disk albedo of about Lambda(I) approximate to 0.16 +/- 0.08. We also find that previously described shadows seen in the R band data are likely affected by calibration errors. We derive, using dust scattering models for transition disks, approximate J band values for the scattering albedo omega approximate to 0.5, scattering asymmetry g approximate to 0.5, and scattering polarization p(max) approximate to 0.7 for the dust. Conclusions. The bright disk of RX J1604 has a very simple axisymmetric structure and is therefore well suited as a benchmark object for accurate photo-polarimetric measurements. We derive values for the disk polarization, <(P) over cap (phi)>, and the apparent disk albedo, Lambda(I), for the J band. Because. <(P) over cap (phi)> and Lambda(I) depend predominantly on dust scattering parameters and only weakly on the disk geometry, these parameters define tight relations for the dust scattering parameters between omega and p(max) and between omega and g. The positive R to J band color for the polarized reflectivity, ((Q) over cap (phi)/I-*)(J) approximate to 1.64 center dot ((Q) over cap (phi)/I-*)(R), is mainly a result of the wavelength dependence of dust parameters because the scattering geometry is expected to be very similar for different colors. This work demonstrates the potential of accurate photo-polarimetric measurements of the circumstellar disk RX J1604 for the determination of dust scattering parameters that strongly constrain the physical properties of the dust.