SINTERING-INDUCED DUST RING FORMATION IN PROTOPLANETARY DISKS: APPLICATION TO THE HL TAU DISK

<jats:title>ABSTRACT</jats:title> <jats:p>The latest observation of HL Tau by ALMA revealed spectacular concentric dust rings in its circumstellar disk. We attempt to explain the multiple ring structure as a consequence of aggregate sintering. Sintering is known to reduce the sticking efficiency of dust aggregates and occurs at temperatures slightly below the sublimation point of the constituent material. We present a dust growth model that incorporates sintering and use it to simulate global dust evolution due to sintering, coagulation, fragmentation, and radial inward drift in a modeled HL Tau disk. We show that aggregates consisting of multiple species of volatile ices experience sintering, collisionally disrupt, and pile up at multiple locations slightly outside the snow lines of the volatiles. At wavelengths of 0.87–1.3 mm, these sintering zones appear as bright, optically thick rings with a spectral slope of <jats:inline-formula> <jats:tex-math> <?CDATA $\approx 2$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>≈</mml:mo> <mml:mn>2</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj522900ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, whereas the non-sintering zones appear as darker, optically thinner rings of a spectral slope of <jats:inline-formula> <jats:tex-math> <?CDATA $\approx 2.3$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>≈</mml:mo> <mml:mn>2.3</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj522900ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>–2.5. The observational features of the sintering and non-sintering zones are consistent with those of the major bright and dark rings found in the HL Tau disk, respectively. Radial pileup and vertical settling occur simultaneously if disk turbulence is weak and if monomers constituting the aggregates are <jats:inline-formula> <jats:tex-math> <?CDATA $\sim 1\;\mu {\rm{m}}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> <mml:mspace width="0.25em" /> <mml:mi>μ</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj522900ieqn3.gif" xlink:type="simple" /> </jats:inline-formula> in radius. For the radial gas temperature profile of <jats:inline-formula> <jats:tex-math> <?CDATA $T=310{(r/1\mathrm{au})}^{-0.57}\;{\rm{K}}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mn>310</mml:mn> <mml:msup> <mml:mrow> <mml:mo stretchy="true">(</mml:mo> <mml:mi>r</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mn>1</mml:mn> <mml:mspace width="0.25em" /> <mml:mi>au</mml:mi> <mml:mo stretchy="true">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.57</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em" /> <mml:mi mathvariant="normal">K</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj522900ieqn4.gif" xlink:type="simple" /> </jats:inline-formula>, our model perfectly reproduces the brightness temperatures of the optically thick bright rings and reproduces their orbital distances to an accuracy of <jats:inline-formula> <jats:tex-math> <?CDATA $\lesssim 30\%$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>≲</mml:mo> <mml:mn>30</mml:mn> <mml:mo>%</mml:mo> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj522900ieqn5.gif" xlink:type="simple" /> </jats:inline-formula>.</jats:p>