The properties of the inner disk around HL Tau: Multi-wavelength modeling of the dust emission

¹ Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
e-mail: yliu@mpia.de
² Purple Mountain Observatory, Chinese Academy of Sciences, 2 West Beijing Road, Nanjing 210008, PR China
³ Key Laboratory for Radio Astronomy, Chinese Academy of Sciences, 2 West Beijing Road, Nanjing 210008, PR China
⁴ Instituto de Radioastronomía y Astrofísica UNAM, Apartado Postal 3-72 (Xangari), 58089 Morelia, Michoacán, México
⁵ National Radio Astronomy Observatory, PO Box O, 1003 Lopezville Road, Socorro, NM 87801-0387, USA
⁶ Max Planck Institute for Radioastronomy Bonn, Auf dem Hügel 69, 53121 Bonn, Germany
⁷ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁸ European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching bei München, Germany
⁹ INAF–Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
¹⁰ Excellence Cluster “Universe”, Boltzmann-Str. 2, 85748 Garching bei München, Germany

Received: 25 September 2016
Accepted: 25 July 2017

Abstract

We conducted a detailed radiative transfer modeling of the dust emission from the circumstellar disk around HL Tau. The goal of our study is to derive the surface density profile of the inner disk and its structure. In addition to the Atacama Large Millimeter/submillimeter Array images at Band 3 (2.9 mm), Band 6 (1.3 mm), and Band 7 (0.87 mm), the most recent Karl G. Jansky Very Large Array (VLA) observations at 7 mm were included in the analysis. A simulated annealing algorithm was invoked to search for the optimum model. The radiative transfer analysis demonstrates that most radial components (i.e., >6 AU) of the disk become optically thin at a wavelength of 7 mm, which allows us to constrain, for the first time, the dust density distribution in the inner region of the disk. We found that a homogeneous grain size distribution is not sufficient to explain the observed images at different wavelengths simultaneously, while models with a shallower grain size distribution in the inner disk work well. We found clear evidence that larger grains are trapped in the first bright ring. Our results imply that dust evolution has already taken place in the disk at a relatively young (i.e., ~1 Myr) age. We compared the midplane temperature distribution, optical depth, and properties of various dust rings with those reported previously. Using the Toomre parameter, we briefly discussed the gravitational instability as a potential mechanism for the origin of the dust clump detected in the first bright ring via the VLA observations.