2016ApJ...832..204Y

We introduce a new stacking method in Keplerian disks that (1) enhances signal-to-noise ratios (S/Ns) of detected molecular lines and (2) makes visible otherwise-undetectable weak lines. Our technique takes advantage of the Keplerian rotational velocity pattern. It aligns spectra according to their different centroid velocities at their different positions in a disk and stacks them. After aligning, the signals are accumulated in a narrower velocity range as compared to the original line width without alignment. Moreover, originally correlated noise becomes decorrelated. Stacked and aligned spectra thus have a higher S/N. We apply our method to Atacama Large Millimeter/Submillimeter Array (ALMA) archival data of DCN (3-2), DCO⁺ (3-2), N₂D⁺ (3-2), and H₂CO (3_0,3-2_0,2), (3_2,2-2_2,1), and (3_2,1-2_2,0) in the protoplanetary disk around HD 163296. As a result, (1) the S/Ns of the originally detected DCN (3-2), DCO⁺ (3-2), H₂CO (3_0,3-2_0,2), and N₂D⁺ (3-2) lines are boosted by a factor of >=4-5 at their spectral peaks, implying one order of magnitude shorter integration times to reach the original S/N; and (2) the previously undetectable spectra of the H₂CO (3_2,2-2_2,1) and (3_2,1-2_2,0) lines are materialized at more than 3σ. These dramatically enhanced S/Ns allow us to measure intensity distributions in all lines with high significance. The principle of our method can be applied not only to Keplerian disks but also to any systems with ordered kinematic patterns.