Warped Disc Instability: analytical predictions and numerical simulations

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

Eğri Disk Kararsızlığı: Analitik Öngörüler ve Nümerik Simülasyonlar

Öz

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.

Anahtar Kelimeler

• toplanma
• kara delik fiziği
• hidrodinamik
• kararsızlıklar

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