Warped Disc Instability: analytical predictions and numerical simulations

Year 2023, , 28 - 33, 31.12.2023

Suzan Doğan

https://doi.org/10.55064/tjaa.1200157

Abstract

Both theoretical models and observational findings indicate that accretion discs are generally warped. According to our detailed stability analysis of the warped disc equations, if the warp of a disc exceeds the critical amplitude, the disc cannot remain stable. The instability, which appears in the form of anti-diffusion of the surface density and the warp amplitude, can lead to a
separating of the disc into two or several discrete planes. To test our analytical predictions, we perform 3-dimensional hydrodynamical simulations of accretion discs that are misaligned to the rotation of a spinning black hole and thus precess due to the Lense–Thirring effect. We vary the disc parameters,
including the viscosity parameter, the disk angular semi-thickness, and the inclination of the disc, with respect to the rotation axis of the black hole. According to our numerical investigation, i) highly inclined discs are more susceptible to disc tearing than those with lower inclination; ii) lower values of the disc viscosity parameter lead to instability at lower warp amplitudes; iii) the disc thickness can play a key role in
determining how vulnerable the disc is to instability. These findings are consistent with instability analysis of the warped discs. Disc tearing has the capacity to dramatically alter the instantaneous accretion rate and the observable properties of the discs in X-ray binaries and Active Galactic Nuclei on short time-scales.

Keywords

accretion, black hole physics, hydrodynamics, instabilities

Project Number

117F280

Eğri Disk Kararsızlığı: Analitik Öngörüler ve Nümerik Simülasyonlar

Abstract

Hem kuramsal modeller hem de gözlemsel bulgular astrofiziksel toplanma disklerinin genellikle eğri bir yapı sergilediğine işaret etmektedir. Eğri disk dinamiğine ilişkin analitik incelememize göre, kritik eğrilik değerine ulaşan diskler kararlılığını koruyamaz. Yoğunluğun ve eğriliğin anti-difüzyonu formunda beliren kararsızlık, diskin halkalara ayrılmasına neden olur. Bu çalışmada, kararsızlık analizinden elde ettiğimiz analitik öngörüleri test etmek amacıyla, dönen bir kara delik etrafında Lense - Thirring etkisi nedeniyle presesyon yapan disklerin kararlılığına ilişkin yüksek çözünürlüklü ve 3-boyutlu hidrodinamik simülasyonlar yapıldı. Diskin açısal momentum vektörü ile kara deliğin spin vektörü arasındaki açı (eğiklik), kalınlık ve viskozitenin eğri disk evrimi üzerindeki etkileri araştırıldı. Simülasyon sonuçlarına göre, (i) eğikliği büyük olan diskler kararsız kalmaya daha eğilimlidir; (ii) viskozitesi düşük diskler daha küçük eğrilik değerlerinde kararsız kalmaktadır; (iii) kalınlık, eğri disk evriminde belirleyici rol üstlenmektedir. Bu sonuçlar, kararsızlık analizinden türettiğimiz analitik öngörüleri doğrulamaktadır. Disklerde parçalanma süreci, toplanma oranlarını dramatik bir biçimde değiştiren ve X-ışın çiftleri ile Etkin Gökada Özeklerinde kısa zaman ölçeklerinde gözlenebilir özellikleri açıklama potansiyeli taşıyan bir süreç olarak karşımıza çıkmaktadır.

Keywords

toplanma, kara delik fiziği, hidrodinamik, kararsızlıklar

Supporting Institution

TÜBİTAK

Project Number

117F280

Thanks

Bu çalışmanın bir kısmı 117F280 nolu TÜBİTAK projesi tarafından desteklenmiştir.

References

• Bardeen J.~M., Petterson J.~A.: The Lense-Thirring Effect and Accretion Disks around Kerr Black Holes. Astrophysical Journal Letters {\bf 195} (1975) L65.
• Bate, M.~R., Lodato, G., \& Pringle, J.~E.: Chaotic star formation and the alignment of stellar rotation with disc and planetary orbital axes. Monthly Notices of the Royal Astronomical Society {\bf 401} (2010) 1505--1513
• Do{\u{g}}an, S., Nixon, C.~J.:\ Instability of non-Keplerian warped discs.\ Monthly Notices of the Royal Astronomical Society {\bf 495} (2020) 1148-1157.
• Do{\v g}an, S., Nixon, C.~J., King, A.~R., \& Pringle, J.~E.: Instability of warped discs. Monthly Notices of the Royal Astronomical Society {\bf 476} (2018) 1519--1531
• Do{\u g}an, S., Nixon, C., King, A., \& Price, D.~J.: Tearing up a misaligned accretion disc with a binary companion. Monthly Notices of the Royal Astronomical Society {\bf 449} (2015) 1251--1258
• Fragner, M.~M., Nelson, R.~P.:\ Evolution of warped and twisted accretion discs in close binary systems.\ Astronomy and Astrophysics {\bf 511} (2010) 23.
• Gerend, D., \& Boynton, P.~E.: Optical clues to the nature of Hercules X-1/HZ Herculis. Astrophysical Journal {\bf 209} (1976) 562--573
• Heap, S.~R., Lindler, D.~J., Lanz, T.~M., et al.: Space Telescope Imaging Spectrograph Coronagraphic Observations of $\beta$ Pictoris. Astrophysical Journal {\bf 539} (2000) 435--444
• Katz, J.~I.: Thirty-five-day Periodicity in Her X-1. Nature Physical Science {\bf 246} (1973) 87--89
• Kraus S., Kreplin A., Young A.~K., Bate M.~R., Monnier J.~D., Harries T.~J., Avenhaus H., et al.: A triple-star system with a misaligned and warped circumstellar disk shaped by disk tearing. Science {\bf 369} (2020) 1233.
• Larwood, J.~D., Nelson, R.~P., Papaloizou, J.~C.~B., Terquem, C.:\ The tidally induced warping, precession and truncation of accretion discs in binary systems: three-dimensional simulations. Monthly Notices of the Royal Astronomical Society {\bf 282} (1996) 597-613.
• {Lense}, J. and {Thirring}, H.: Über den Einflu{\ss} der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift {\bf 19} (1918) 156
• Lightman, A.~P., \& Eardley, D.~M.: Black Holes in Binary Systems: Instability of Disk Accretion. Astrophysical Journal {\bf 187} (1974) L1
• Liska, M. and 6 colleagues: Disc tearing and Bardeen-Petterson alignment in GRMHD simulations of highly tilted thin accretion discs.\ Monthly Notices of the Royal Astronomical Society {\bf 507} (2021) 983-990.
• Lodato, G., Pringle, J.~E.\ 2007.\ Warp diffusion in accretion discs: a numerical investigation.\ Monthly Notices of the Royal Astronomical Society {\bf 381} (2007) 1287-1300.
• Lodato, G., \& Price, D.~J.: On the diffusive propagation of warps in thin accretion discs. Monthly Notices of the Royal Astronomical Society {\bf 405} (2010) 1212--1226
• Lucas, W.~E., Bonnell, I.~A., Davies, M.~B., \& Rice, W.~K.~M.: Misaligned streamers around a Galactic Centre black hole from a single cloud's infall. Monthly Notices of the Royal Astronomical Society {\bf 433} (2013) 353--365
• Margon, B.: Observations of SS 433. Annual review of astronomy and astrophysics {\bf 22} (1984) 507--536
• Marino, S., Perez, S., and Casassus, S.: The Astrophysical Journal {\bf 798} (2015) L44.
• Nelson, R.~P., Papaloizou, J.~C.~B.: Hydrodynamic simulations of the Bardeen-Petterson effect. Monthly Notices of the Royal Astronomical Society {\bf 315} (2000) 570-586.
• Nixon, C., King, A., and Price, D.: Tearing up the disc: misaligned accretion on to a binary. Monthly Notices of the Royal Astronomical Society {\bf 434} (2013) 1946.
• Nixon, C., King, A., Price, D., and Frank, J.: Tearing up the Disk: How Black Holes Accrete. The Astrophysical Journal Letters {\bf 757} (2012) L24
• Ogilvie, G.~I.:\ The non-linear fluid dynamics of a warped accretion disc.\ Monthly Notices of the Royal Astronomical Society {\bf 304} (1999) 557-578.
• Papaloizou, J.~C.~B., \& Terquem, C.: On the dynamics of tilted discs around young stars. Monthly Notices of the Royal Astronomical Society {\bf 274} (1995) 987--1001
• Papaloizou, J.~C.~B., \& Pringle, J.~E.: The time-dependence of non-planar accretion discs. Monthly Notices of the Royal Astronomical Society {\bf 202} (1983) 1181
• Price, D.~J. and 26 colleagues. Phantom: A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics.\ Publications of the Astronomical Society of Australia {\bf 35} (2018) e031.
• Pringle, J.~E.: Self-induced warping of accretion discs. Monthly Notices of the Royal Astronomical Society {\bf 281} (1996) 357-361
• Raj, A., Nixon, C.~J., Do{\u{g}}an, S.: Disk Tearing: Numerical Investigation of Warped Disk Instability. The Astrophysical Journal {\bf 909} (2021) 81.
• Raj, A., Nixon, C.~J.:Disk Tearing: Implications for Black Hole Accretion and AGN Variability.\ The Astrophysical Journal {\bf 909} (2021) 82.
• Roberts, W.~J.: A slaved disk model for Hercules X-1. Astrophysical Journal, {\bf 187} (1974) 575 - 584