GAPS IN PROTOPLANETARY DISKS AS SIGNATURES OF PLANETS. II. INCLINED DISKS

We examine the observational appearance of partial gaps being opened by planets in protoplanetary disks, considering the effects of the inclination relative to the line of sight. The gap's trough is darkened by both shadowing and cooling, relative to the uninterrupted disk. The gap's outer wall is brightened by direct illumination and also by heating, which puffs it up so that it intercepts more starlight. In this paper, we examine the effects of inclination on resolved images of disks with and without gaps at a wide range of wavelengths. The scattering surface's offset from the disk midplane creates a brightness asymmetry along the axis of inclination, making the disk's near side appear brighter than the far side in scattered light. Finite disk thickness also causes the projected distances of equidistant points on the disk surface to be smaller on the near side of the disk as compared to the far side. Consequently, the gap shoulder on the near side of the disk should appear brighter and closer to the star than on the far side. However, if the angular resolution of the observation is coarser than the width of the brightened gap shoulder, then the gap shoulder on the far side may appear brighter because of its larger apparent size. We present a formula to recover the scale height and inclination angle of an imaged disk using simple geometric arguments and measuring disk asymmetries. Resolved images of circumstellar disks have revealed clearings and gaps, such as the transitional disk in LkCa 15. Models created using our synthetic imaging attempting to match the morphology of observed scattered light images of LkCa 15 indicate that the H-band flux deficit in the inner $\sim0.5\arcsec$ of the disk can be explained with a planet of mass greater than 0.5 Jupiter mass.

[1]  Sarah E. Dodson-Robinson,et al.  TRANSITIONAL DISKS AS SIGNPOSTS OF YOUNG, MULTIPLANET SYSTEMS , 2011, 1106.4824.

[2]  J. Pety,et al.  Resolving the inner dust disks surrounding LkCa 15 and MWC 480 at mm wavelengths , 2006, astro-ph/0610200.

[3]  D. Wilner,et al.  A CLOSER LOOK AT THE LkCa 15 PROTOPLANETARY DISK , 2011, 1110.3865.

[4]  Marshall D. Perrin,et al.  RULING OUT STELLAR COMPANIONS AND RESOLVING THE INNERMOST REGIONS OF TRANSITIONAL DISKS WITH THE KECK INTERFEROMETER , 2009, 0912.0846.

[5]  G. Bryden,et al.  A HOT GAP AROUND JUPITER'S ORBIT IN THE SOLAR NEBULA , 2011, 1110.4166.

[6]  A. Morbidelli,et al.  On the width and shape of gaps in protoplanetary disks , 2006 .

[7]  H. McAlister,et al.  A Tale of Two Herbig Ae Stars, MWC 275 and AB Aurigae: Comprehensive Models for Spectral Energy Distribution and Interferometry , 2008, 0808.1728.

[8]  Beth Biller,et al.  A LIKELY CLOSE-IN LOW-MASS STELLAR COMPANION TO THE TRANSITIONAL DISK STAR HD 142527 , 2012, 1206.2654.

[9]  Johns Hopkins University,et al.  Disk Accretion onto High-Mass Planets , 1999 .

[10]  High-Resolution Near-Infrared Images and Models of the Circumstellar Disk in HH 30 , 2001, astro-ph/0104066.

[11]  L. Hartmann,et al.  On the Diversity of the Taurus Transitional Disks: UX Tauri A and LkCa 15 , 2007, 0710.2892.

[12]  Subaru Telescope,et al.  IMAGING OF A TRANSITIONAL DISK GAP IN REFLECTED LIGHT: INDICATIONS OF PLANET FORMATION AROUND THE YOUNG SOLAR ANALOG LkCa 15 , 2010, 1005.5162.

[13]  C. Dominik,et al.  Full two-dimensional radiative transfer modelling of the transitional disk LkCa 15 , 2010, 1001.2146.

[14]  C. Dominik,et al.  UvA-DARE ( Digital Academic Repository ) Flaring vs . self-shadowed disks : The SEDs of Herbig Ae / Be stars , 2004 .

[15]  Catherine Espaillat,et al.  RESOLVED IMAGES OF LARGE CAVITIES IN PROTOPLANETARY TRANSITION DISKS , 2011, 1103.0284.

[16]  Jonathan P. Williams,et al.  SUBMILLIMETER ARRAY OBSERVATIONS OF THE RX J1633.9-2442 TRANSITION DISK: EVIDENCE FOR MULTIPLE PLANETS IN THE MAKING , 2012, 1204.5722.

[17]  S. Wolf,et al.  Tracing large-scale structures in circumstellar disks with ALMA , 2012, 1212.1793.

[18]  S. Lubow,et al.  Three-dimensional calculations of high- and low-mass planets embedded in protoplanetary discs , 2003, astro-ph/0301154.

[19]  Dynamical Masses of T Tauri Stars and Calibration of Pre-Main-Sequence Evolution , 2000, astro-ph/0008370.

[20]  Catherine Espaillat,et al.  Confirmation of a Gapped Primordial Disk around LkCa 15 , 2008, 0807.2291.

[21]  J. Papaloizou,et al.  On disc protoplanet interactions in a non-barotropic disc with thermal diffusion , 2008, 0804.4547.

[22]  Matthew R. Bate,et al.  Gas accretion on to planetary cores: three-dimensional self-gravitating radiation hydrodynamical calculations , 2008, 0811.1259.

[23]  H. Jang-Condell.  PLANET SHADOWS IN PROTOPLANETARY DISKS. II. OBSERVABLE SIGNATURES , 2009, 0906.1375.

[24]  A. Quillen,et al.  The vertical structure of planet-induced gaps in protoplanetary discs , 2007, 0709.1649.

[25]  M. Ireland,et al.  LkCa 15: A YOUNG EXOPLANET CAUGHT AT FORMATION? , 2011, 1110.3808.

[26]  Jonathan P. Williams,et al.  880 μm IMAGING OF A TRANSITIONAL DISK IN UPPER SCORPIUS: HOLDOVER FROM THE ERA OF GIANT PLANET FORMATION? , 2012, 1205.3545.

[27]  Hannah Jang-CondellAlan P. Boss.  Signatures of Planet Formation in Gravitationally Unstable Disks , 2007 .

[28]  Hannah Jang-Condell,et al.  GAPS IN PROTOPLANETARY DISKS AS SIGNATURES OF PLANETS. I. METHODOLOGY AND VALIDATION , 2012, 1202.3465.

[29]  M. de Val-Borro,et al.  A comparative study of disc–planet interaction , 2006 .

[30]  Searching for the sub-stellar companions in the LkCa15 proto-planetary disk , 2010, 1004.3487.

[31]  Olivier Guyon,et al.  POLARIMETRIC IMAGING OF LARGE CAVITY STRUCTURES IN THE PRE-TRANSITIONAL PROTOPLANETARY DISK AROUND PDS 70: OBSERVATIONS OF THE DISK , 2012, 1208.2075.

[32]  D. Padgett,et al.  Probing dust grain evolution in IM Lupi's circumstellar disc. Multi-wavelength observations and mo , 2008, 0808.0619.

[33]  L. C. Henyey,et al.  Diffuse radiation in the Galaxy , 1940 .

[34]  A. Dutrey,et al.  Probing the structure of protoplanetary disks: a comparative study of DM Tau, LkCa 15, and MWC 480 , 2007, astro-ph/0701425.

[35]  Sebastian Wolf,et al.  On the Observability of Giant Protoplanets in Circumstellar Disks , 2004, astro-ph/0410064.

[36]  A. J. Weinberger,et al.  THE 0.5–2.22 μm SCATTERED LIGHT SPECTRUM OF THE DISK AROUND TW Hya: DETECTION OF A PARTIALLY FILLED DISK GAP AT 80 AU , 2013, 1306.2969.

[37]  G. Chauvin,et al.  A companion candidate in the gap of the T Chamaeleontis transitional disk , 2011, 1102.4982.

[38]  C. Lada,et al.  The structure of brown dwarf circumstellar discs , 2004, astro-ph/0403276.

[39]  Disk temperature variations and effects on the snow line in the presence of small protoplanets , 2004, astro-ph/0404590.

[40]  H. Jang-Condell.  Planet Shadows in Protoplanetary Disks. I. Temperature Perturbations , 2008, 0801.4561.

[41]  J. Carpenter,et al.  STRUCTURE AND EVOLUTION OF PRE-MAIN-SEQUENCE CIRCUMSTELLAR DISKS , 2009, 0906.2227.

[42]  A. Frank,et al.  Observational Properties of Protoplanetary Disk Gaps , 2005, astro-ph/0508630.

[43]  D. Sasselov,et al.  Radiative Transfer on Perturbations in Protoplanetary Disks , 2003, astro-ph/0304330.