标题：Erratum: “An Origin of Multiple Ring Structure and Hidden Planets in HL Tau: A Unified Picture by Secular Gravitational Instability” (2016, AJ, 152, 184)
摘要：Apart from the above typographical errors, we used an incorrect equation for the dust diffusion by the turbulence to calculate the dispersion relations. We underestimated (overestimated) the diffusion of dust particles with small (large) Stoke number. The secular GI is stabilized when we use the corrected equation with the exponential cutoff surface density model with the parameters given in the original paper, since the secular GI was marginally unstable with the parameters used in the original paper. Thus, we show the alternative results whose strength of the turbulence α are 2/3 times smaller than that used in the original paper. The fiducial value of α in the original paper is observationally suggested by Pinte et al. (2016). Since this α value is required from the observed sharp ring structure, this value should be regarded as an upper limit. Thus, the observation of the continuum emission of the disk around HL Tau can be explained by α=2×10 −4 , with which the secular GI grows.
