ALMA Imprint of Intergalactic Dark Structures in the Gravitational Lens SDP.81

We present an analysis of the ALMA long baseline science verification data of the gravitational lens system SDP.81. We fit the positions of the brightest clumps at redshift z=3.042 and a possible AGN component of the lensing galaxy at redshift z=0.2999 in the band 7 continuum image using a canonical lens model, a singular isothermal ellipsoid plus an external shear. Then, we measure the ratio of fluxes in some apertures at the source plane where the lensed images are inversely mapped. We find that the aperture flux ratios of band 7 continuum image are perturbed by 10-20 percent with a significance at 2 ~ 3 sigma level. Moreover, we measure the astrometric shifts of multiply lensed images near the caustic using the CO(8-7) line. Using a lens model best-fitted to the band 7 continuum image, we reconstruct the source image of the CO(8-7) line by taking linear combination of inverted quadruply lensed images. At the 50th channel (rest-frame velocity 28.6 km/s) of the CO(8-7) line, we find an imprint of astrometric shifts of the order of 0.01 arcsec in the source image. Based on a semi-analytic calculation, we find that the observed anomalous flux ratios and the astrometric shifts can be explained by intergalactic dark structures in the line of sight. A compensated homogeneous spherical clump with a mean surface mass density of the order of 10^8 solar mass h^-1 arcsec^-2 can explain the observed anomaly and astrometric shifts simultaneously.