Stacking Spectra in Protoplanetary Disks: Detecting Intensity Profiles from Hidden Molecular Lines in HD 163296

We introduce a new stacking method in Keplerian disks that (1) enhances signal-to-noise ratios (S/N) of detected molecular lines and (2) that 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 de-correlated. Stacked and aligned spectra, thus, have a higher S/N. We apply our method to 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/N of the originally detected DCN (3-2), DCO+ (3-2), and 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 3 sigma. These dramatically enhanced S/N allow us to measure intensity distributions in all lines with high significance. The principle of our method can not only be applied to Keplerian disks but also to any systems with ordered kinematic patterns.