Non-linear behaviour of warped discs around a central object with a quadrupole moment
ABSTRACT The non-linear behaviour of low-viscosity warped discs is poorly understood. We verified a non-linear bending-wave theory, in which fluid columns undergo affine transformations, with direct 3D hydrodynamical simulations. We employed a second-order Godunov-type scheme, meshless finite mass (...
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Veröffentlicht in: | Monthly notices of the Royal Astronomical Society 2022-04, Vol.512 (4), p.6078-6092 |
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creator | Deng, Hongping Ogilvie, Gordon I |
description | ABSTRACT
The non-linear behaviour of low-viscosity warped discs is poorly understood. We verified a non-linear bending-wave theory, in which fluid columns undergo affine transformations, with direct 3D hydrodynamical simulations. We employed a second-order Godunov-type scheme, meshless finite mass (MFM), and also the smoothed particle hydrodynamics (SPH) method, with up to 128 million particles. For moderate non-linearity, MFM maintains well the steady non-linear warp predicted by the affine model for a tilted inviscid disc around a central object with a quadrupole moment. However, numerical dissipation in SPH is so severe that even a low-amplitude non-linear warp degrades at a resolution where MFM performs well. A low-amplitude arbitrary warp tends to evolve towards a non-linear steady state. However, no such state exists in our thin disc with an angular semithickness H/R = 0.02 when the outer tilt angle is beyond about 14°. The warp breaks tenuously and reconnects in adiabatic simulations, or breaks into distinct annuli in isothermal simulations. The breaking radius lies close to the location with the most extreme non-linear deformation. Parametric instability is captured only in our highest resolution simulation, leading to ring structures that may serve as incubators for planets around binaries. |
doi_str_mv | 10.1093/mnras/stac858 |
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The non-linear behaviour of low-viscosity warped discs is poorly understood. We verified a non-linear bending-wave theory, in which fluid columns undergo affine transformations, with direct 3D hydrodynamical simulations. We employed a second-order Godunov-type scheme, meshless finite mass (MFM), and also the smoothed particle hydrodynamics (SPH) method, with up to 128 million particles. For moderate non-linearity, MFM maintains well the steady non-linear warp predicted by the affine model for a tilted inviscid disc around a central object with a quadrupole moment. However, numerical dissipation in SPH is so severe that even a low-amplitude non-linear warp degrades at a resolution where MFM performs well. A low-amplitude arbitrary warp tends to evolve towards a non-linear steady state. However, no such state exists in our thin disc with an angular semithickness H/R = 0.02 when the outer tilt angle is beyond about 14°. The warp breaks tenuously and reconnects in adiabatic simulations, or breaks into distinct annuli in isothermal simulations. The breaking radius lies close to the location with the most extreme non-linear deformation. Parametric instability is captured only in our highest resolution simulation, leading to ring structures that may serve as incubators for planets around binaries.</description><identifier>ISSN: 0035-8711</identifier><identifier>EISSN: 1365-2966</identifier><identifier>DOI: 10.1093/mnras/stac858</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>Monthly notices of the Royal Astronomical Society, 2022-04, Vol.512 (4), p.6078-6092</ispartof><rights>2022 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society 2022</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c270t-aa08a0309b0d3834ee7e61ac4a1aebb27be89bd0b284f00bbdfb2478eae390783</citedby><cites>FETCH-LOGICAL-c270t-aa08a0309b0d3834ee7e61ac4a1aebb27be89bd0b284f00bbdfb2478eae390783</cites><orcidid>0000-0001-6858-1006 ; 0000-0002-7756-1944</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,1598,27903,27904</link.rule.ids><linktorsrc>$$Uhttps://dx.doi.org/10.1093/mnras/stac858$$EView_record_in_Oxford_University_Press$$FView_record_in_$$GOxford_University_Press</linktorsrc></links><search><creatorcontrib>Deng, Hongping</creatorcontrib><creatorcontrib>Ogilvie, Gordon I</creatorcontrib><title>Non-linear behaviour of warped discs around a central object with a quadrupole moment</title><title>Monthly notices of the Royal Astronomical Society</title><description>ABSTRACT
The non-linear behaviour of low-viscosity warped discs is poorly understood. We verified a non-linear bending-wave theory, in which fluid columns undergo affine transformations, with direct 3D hydrodynamical simulations. We employed a second-order Godunov-type scheme, meshless finite mass (MFM), and also the smoothed particle hydrodynamics (SPH) method, with up to 128 million particles. For moderate non-linearity, MFM maintains well the steady non-linear warp predicted by the affine model for a tilted inviscid disc around a central object with a quadrupole moment. However, numerical dissipation in SPH is so severe that even a low-amplitude non-linear warp degrades at a resolution where MFM performs well. A low-amplitude arbitrary warp tends to evolve towards a non-linear steady state. However, no such state exists in our thin disc with an angular semithickness H/R = 0.02 when the outer tilt angle is beyond about 14°. The warp breaks tenuously and reconnects in adiabatic simulations, or breaks into distinct annuli in isothermal simulations. The breaking radius lies close to the location with the most extreme non-linear deformation. Parametric instability is captured only in our highest resolution simulation, leading to ring structures that may serve as incubators for planets around binaries.</description><issn>0035-8711</issn><issn>1365-2966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNqF0D1PwzAQh3ELgUQpjOweWUzPcV6cEVW8SRUsdI7O9kVNlcTBTqj49gTanemk00__4WHsVsK9hFKtuj5gXMURrc70GVtIlWciKfP8nC0AVCZ0IeUlu4pxDwCpSvIF2775XrRNTxi4oR1-NX4K3Nf8gGEgx10TbeQY_NQ7jtxSPwZsuTd7siM_NONu_n5O6MI0-JZ457uZXLOLGttIN6e7ZNunx4_1i9i8P7-uHzbCJgWMAhE0goLSgFNapUQF5RJtihLJmKQwpEvjwCQ6rQGMcbVJ0kITkiqh0GrJxHHXBh9joLoaQtNh-K4kVL9Nqr8m1anJ7O-O3k_DP_QHl1dnBg</recordid><startdate>20220419</startdate><enddate>20220419</enddate><creator>Deng, Hongping</creator><creator>Ogilvie, Gordon I</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-6858-1006</orcidid><orcidid>https://orcid.org/0000-0002-7756-1944</orcidid></search><sort><creationdate>20220419</creationdate><title>Non-linear behaviour of warped discs around a central object with a quadrupole moment</title><author>Deng, Hongping ; Ogilvie, Gordon I</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-aa08a0309b0d3834ee7e61ac4a1aebb27be89bd0b284f00bbdfb2478eae390783</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Deng, Hongping</creatorcontrib><creatorcontrib>Ogilvie, Gordon I</creatorcontrib><collection>CrossRef</collection><jtitle>Monthly notices of the Royal Astronomical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Deng, Hongping</au><au>Ogilvie, Gordon I</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Non-linear behaviour of warped discs around a central object with a quadrupole moment</atitle><jtitle>Monthly notices of the Royal Astronomical Society</jtitle><date>2022-04-19</date><risdate>2022</risdate><volume>512</volume><issue>4</issue><spage>6078</spage><epage>6092</epage><pages>6078-6092</pages><issn>0035-8711</issn><eissn>1365-2966</eissn><abstract>ABSTRACT
The non-linear behaviour of low-viscosity warped discs is poorly understood. We verified a non-linear bending-wave theory, in which fluid columns undergo affine transformations, with direct 3D hydrodynamical simulations. We employed a second-order Godunov-type scheme, meshless finite mass (MFM), and also the smoothed particle hydrodynamics (SPH) method, with up to 128 million particles. For moderate non-linearity, MFM maintains well the steady non-linear warp predicted by the affine model for a tilted inviscid disc around a central object with a quadrupole moment. However, numerical dissipation in SPH is so severe that even a low-amplitude non-linear warp degrades at a resolution where MFM performs well. A low-amplitude arbitrary warp tends to evolve towards a non-linear steady state. However, no such state exists in our thin disc with an angular semithickness H/R = 0.02 when the outer tilt angle is beyond about 14°. The warp breaks tenuously and reconnects in adiabatic simulations, or breaks into distinct annuli in isothermal simulations. The breaking radius lies close to the location with the most extreme non-linear deformation. Parametric instability is captured only in our highest resolution simulation, leading to ring structures that may serve as incubators for planets around binaries.</abstract><pub>Oxford University Press</pub><doi>10.1093/mnras/stac858</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0001-6858-1006</orcidid><orcidid>https://orcid.org/0000-0002-7756-1944</orcidid></addata></record> |
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title | Non-linear behaviour of warped discs around a central object with a quadrupole moment |
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