Interfacial Dynamics in Protoplanetary Accretion Disks BERN 2017

Transcription

1 DEPARTMENT OF EARTH SCIENCES, RAYMOND AND BEVERLY SACKLER FACULTY OF EXACT SCIENCES Interfacial Dynamics in Protoplanetary Accretion Disks BERN 2017 Author: Ron Yellin-Bergovoy Supervisors: Prof. Eyal Heifetz Dr. Orkan M. Umurhan

2 Motivation Outline 1 Motivation 2 introduction 3 The potential vorticity (PV) perspective 9 2 Vorticity waves propagation in protoplanetary discs 17 3 Future Research 32 Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

3 Introduction Motivation introduction Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

4 Motivation introduction The angular momentum problem Observations shows that new stars accrete material. v θ v kep = GM r L = mvr = m GM r. ν kinematic is insufficient ν = αc s H v turb l turb (Shakura and Sunyaev,1973). Cold disks do not support the magnetorotational instability (MRI). Disks Keplerian shear profile is linear stable (i.e., the Rayleigh (Rayleigh, 1880) and the Fjørtoft (Fjørtoft, 1953) conditions), so where does the turbulence come from? Many different instabilities with different degree transport and some connection to planet formation. Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

5 Motivation introduction The angular momentum problem Observations shows that new stars accrete material. v θ v kep = GM r L = mvr = m GM r. ν kinematic is insufficient ν = αc s H v turb l turb (Shakura and Sunyaev,1973). Cold disks do not support the magnetorotational instability (MRI). Disks Keplerian shear profile is linear stable (i.e., the Rayleigh (Rayleigh, 1880) and the Fjørtoft (Fjørtoft, 1953) conditions), so where does the turbulence come from? Many different instabilities with different degree transport and some connection to planet formation. Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

6 Observations Motivation introduction Atacama Large Millimeter/submillimeter Array (ALMA) Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

7 Observational data Motivation introduction (a) HL Touri system, band 6(1mm) dust emissions (ALMA website, 2015). (b) HD system emission, band7(0.85mm) dust emissions (Casassus et al., 2013). (c) SAO system, band9(0.45mm) dust emission (Perez et al., 2014). Figure: Observational images of PPD systems Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

8 Motivation introduction Numerical young disk density profiles Estrada et al., 2015 Lin 2012b density gradients profiles Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

9 Motivation The potential vorticity (PV) perspective The potential vorticity (PV) perspective So what is missing? What is the basic mechanism/s of the instabilities? Additional questions Which profiles go unstable? and why? What is the role of stratification and shear? how does self gravity (SG) contribute to the dynamics? Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

10 Motivation The potential vorticity (PV) perspective The potential vorticity (PV) perspective So what is missing? What is the basic mechanism/s of the instabilities? Additional questions Which profiles go unstable? and why? What is the role of stratification and shear? how does self gravity (SG) contribute to the dynamics? To get answers we look at analogous systems in GFD which also include shear, rotation and stratification, in which the PV perspective was used in order to understand the instability as emerging from interacting Rossby waves Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

11 Motivation The potential vorticity (PV) perspective Vorticity and cross stream displacementpositive correlation Heifetz et al Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

12 Motivation The potential vorticity (PV) perspective Rossby wave resonance type instability ω m Ω 0 Q r < 0 +q q +q q q q Q r > 0 +q ω m Ω 0 Shear Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

13 Motivation The potential vorticity (PV) perspective Rossby wave resonance type instability ω m Ω 0 Q r < 0 +q q +q q q q Q r > 0 +q ω m Ω 0 Shear stable!! action at a distance Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

14 Motivation The potential vorticity (PV) perspective Rossby wave resonance type instability ω m Ω 0 Q r < 0 +q q +q q q q Q r > 0 +q ω m Ω 0 Shear stable!! action at a distance Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

15 Motivation Density interfaces and vorticity The potential vorticity (PV) perspective Gravity vorticity waves (Rabinovich et al. 2011) Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

16 Motivation The potential vorticity (PV) perspective Interfaces and vorticity waves resonance type instability Also in: Buoyancy and Rossby-Gravity vorticity waves (Harnik et al. 2008; Rabinovich et al. 2011). MHD and vorticity Alfven vorticity waves (Heifetz et al. 2015). Surface tension and capillary vorticity waves (Heifetz et al. 2014). Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

17 Vorticity waves propagation in protoplanetary discs Outline 1 Motivation 2 2 Vorticity waves propagation in protoplanetary discs 17 3 Future Research 32 Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

18 Vorticity waves propagation in protoplanetary discs Basic equations Du Dt v 2 r + 2Ω kv Dv v Dt + u r + 1 r 2 Ω k r r = 1 ρ = 1 ρr p r + ϕ r, p θ + ϕ r θ, where the Lagrangian time derivative is given as: D Dt = t + u + Ω k r ˆθ = t + u v r + r + Ω k θ. and, 2 ϕ = 4πG grav ρ. u = 1 r r (ru) + 1 r v θ = 0 Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

19 Vorticity waves propagation in protoplanetary discs Vorticity generation D L q Dt = u r q + 1 r (r 2 Ω k ) r 1 ρ p r ρ 2 θ r ρ r p, θ q q u q + δ q The Rossby term Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

20 Vorticity waves propagation in protoplanetary discs Baroclinic torque and vorticity generation D L q Dt = u r q + 1 r (r 2 Ω k ) r 1 r ρ 2 ρ θ p r ρ r p, θ p ρ + δρ q ρ p + δp The Boussinesq term Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

21 Vorticity waves propagation in protoplanetary discs Baroclinic torque and vorticity generation D L q Dt = u r q + 1 r (r 2 Ω k ) r 1 r ρ 2 ρ θ p r ρ p r θ, p ρ ρ + δρ q ρ p +q p + δp p + δp ρ + δρ The Boussinesq term The non-boussinesq term Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

22 Vorticity waves propagation in protoplanetary discs What is self gravity (SG)? basic state equation: 1 ρ p r = ϕ r + v 2Ω k + v, r Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

23 Vorticity waves propagation in protoplanetary discs Vorticity waves propagation the dispersion relation: ω m Ω 0 = 1 Q + ρ Q 4m ρ 2 ρ + ± 1 Q + ρ Q 4m ρ ρ 1 2mr 1 ρ p r r 0 r 0 + πg grav ρ m 2 1/2 together with the generic vorticity displacement ratio: ω ˆq 0 = 2m m Ω 0 ˆξ 0 wave propagation r 0 instability Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

24 Vorticity waves propagation in protoplanetary discs Vorticity waves propagation the dispersion relation: ω m Ω 0 = 1 Q + ρ Q 4m ρ 2 ρ + ± 1 Q + ρ Q 4m ρ ρ 1 2mr 1 ρ p r r 0 r 0 + πg grav ρ m 2 1/2 together with the generic vorticity displacement ratio: ω ˆq 0 = 2m m Ω 0 ˆξ 0 wave propagation and the sufficient condition for instability for a single edge wave is ρ p < 2r 0 ρ Q + ρ Q 2 + πg grav r r 0 m 4 ρ ρ 2 instability Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36 r 0 r 0

25 Vorticity waves propagation in protoplanetary discs Vorticity waves propagation Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

26 Results There are two azimuthally propagating edge gravity waves corresponding to the density interface,which move opposite to one another with respect to the local basic state rotation rate at the interface. The vorticity interface correspond to a Rossby like wave which is counter propagating in respect to the mean flow.

27 Results There are two azimuthally propagating edge gravity waves corresponding to the density interface,which move opposite to one another with respect to the local basic state rotation rate at the interface. The vorticity interface correspond to a Rossby like wave which is counter propagating in respect to the mean flow. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified), which is a a strictly Boussinesq effect.

28 Results There are two azimuthally propagating edge gravity waves corresponding to the density interface,which move opposite to one another with respect to the local basic state rotation rate at the interface. The vorticity interface correspond to a Rossby like wave which is counter propagating in respect to the mean flow. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified), which is a a strictly Boussinesq effect. In the non-boussinesq term, self-gravity acts as a wave stabilizer irrespective of the stratification of the system.

29 Results There are two azimuthally propagating edge gravity waves corresponding to the density interface,which move opposite to one another with respect to the local basic state rotation rate at the interface. The vorticity interface correspond to a Rossby like wave which is counter propagating in respect to the mean flow. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified), which is a a strictly Boussinesq effect. In the non-boussinesq term, self-gravity acts as a wave stabilizer irrespective of the stratification of the system. Self-gravity also alters the dynamics via the radial main pressure gradient, which is a Boussinesq effect.

30 Results There are two azimuthally propagating edge gravity waves corresponding to the density interface,which move opposite to one another with respect to the local basic state rotation rate at the interface. The vorticity interface correspond to a Rossby like wave which is counter propagating in respect to the mean flow. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified), which is a a strictly Boussinesq effect. In the non-boussinesq term, self-gravity acts as a wave stabilizer irrespective of the stratification of the system. Self-gravity also alters the dynamics via the radial main pressure gradient, which is a Boussinesq effect. The non-boussinesq effects also contribute to the wave propagation through an asymmetric term ( 1 4m ρ ρ Q ), which correlates to the vorticity mass flux across the interface. back

31 Results There are two azimuthally propagating edge gravity waves corresponding to the density interface,which move opposite to one another with respect to the local basic state rotation rate at the interface. The vorticity interface correspond to a Rossby like wave which is counter propagating in respect to the mean flow. Instability only occurs if the radial pressure gradient is opposite to that of the density jump (unstably stratified), which is a a strictly Boussinesq effect. In the non-boussinesq term, self-gravity acts as a wave stabilizer irrespective of the stratification of the system. Self-gravity also alters the dynamics via the radial main pressure gradient, which is a Boussinesq effect. The non-boussinesq effects also contribute to the wave propagation through an asymmetric term ( 1 4m ρ ρ Q ), which correlates to the vorticity mass flux across the interface. back

32 Future Research Outline 1 Motivation 2 2 Vorticity waves propagation in protoplanetary discs 17 3 Future Research 32 Instability 43 Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

33 Future Research In this research we will consider: Gaseous disk rotating around a central mass. Self gravity. Incompressible. basic state axisymmetrical.

34 Future Research In this research we will consider: Gaseous disk rotating around a central mass. Self gravity. Incompressible. basic state axisymmetrical. We will start studying simple setups and continue to more complex and realistic ones. Taylor Caulfield setup (same sign). Taylor Caulfield setup (opposite sign). Holmboe setup (Umurhan and Heifetz, 2007).

35 THANK YOU!!

36 Future Research Studies have shown that the emergence of axisymmetric structures in young PPDs are associated with the following processes: Ice line/snow cone, other lines. Mean-motion orbital resonances (e.g. Kirkwood gaps). Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

37 Future Research Studies have shown that the emergence of axisymmetric structures in young PPDs are associated with the following processes: Ice line/snow cone, other lines. Mean-motion orbital resonances (e.g. Kirkwood gaps). Gap opening by Planets (Lin and Papaloizou, 1986; Koller et al., 2003; de Val-Borro et al., 2007). Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

38 Future Research Studies have shown that the emergence of axisymmetric structures in young PPDs are associated with the following processes: Ice line/snow cone, other lines. Mean-motion orbital resonances (e.g. Kirkwood gaps). Gap opening by Planets (Lin and Papaloizou, 1986; Koller et al., 2003; de Val-Borro et al., 2007). Magnetorotational Instability transition zones (Varniere and Tagger,2006; Lyra et al., 2009; Regaly et al., 2012; Flock et al., 2014). Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

39 Future Research Studies have shown that the emergence of axisymmetric structures in young PPDs are associated with the following processes: back Ice line/snow cone, other lines. Mean-motion orbital resonances (e.g. Kirkwood gaps). Gap opening by Planets (Lin and Papaloizou, 1986; Koller et al., 2003; de Val-Borro et al., 2007). Magnetorotational Instability transition zones (Varniere and Tagger,2006; Lyra et al., 2009; Regaly et al., 2012; Flock et al., 2014). Pressure maxima and drug dynamics resulting in gas over density via drift and/or secular instabilities (Goodman and Pindor, 2000; Youdin at el., 2005; Meru, 2014; Takahashi and Inutska, 2014; Lyra and Kuchner, 2013). Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

40 Future Research Studies have shown that the emergence of axisymmetric structures in young PPDs are associated with the following processes: back Ice line/snow cone, other lines. Mean-motion orbital resonances (e.g. Kirkwood gaps). Gap opening by Planets (Lin and Papaloizou, 1986; Koller et al., 2003; de Val-Borro et al., 2007). Magnetorotational Instability transition zones (Varniere and Tagger,2006; Lyra et al., 2009; Regaly et al., 2012; Flock et al., 2014). Pressure maxima and drug dynamics resulting in gas over density via drift and/or secular instabilities (Goodman and Pindor, 2000; Youdin at el., 2005; Meru, 2014; Takahashi and Inutska, 2014; Lyra and Kuchner, 2013). Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

41 Future Research Vorticity waves propagation the dispersion relation: ω m Ω 0 = 1 Q + ρ Q 4m ρ 2 ρ + ± 1 Q + ρ Q 4m ρ ρ 1 2mr 1 ρ p r r 0 r 0 + πg grav ρ m 2 1/2 together with the generic vorticity displacement ratio: ω ˆq 0 = 2m m Ω 0 ˆξ 0 r 0 Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

42 Future Research Vorticity waves propagation the dispersion relation: ω m Ω 0 = 1 Q + ρ Q 4m ρ 2 ρ + ± 1 Q + ρ Q 4m ρ ρ 1 2mr 1 ρ p r r 0 r 0 + πg grav ρ m 2 1/2 together with the generic vorticity displacement ratio: ω ˆq 0 = 2m m Ω 0 ˆξ 0 and the sufficient condition for instability for a single edge wave is ρ p < 2r 0 ρ Q + ρ Q 2 + πg grav r r 0 m 4 ρ ρ 2 r 0 r 0 Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

43 Future Research Instability Modified Rayleigh-Taylor instability ρ r > 0 p r < 0 +ξ, ρ q ξ, +ρ +q +ξ, ρ q ξ, +ρ back Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

44 Future Research Instability PV inversion, Greens function and the velocity field Rabinovich et al back Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

45 Rossby waves Future Research Instability ω m Ω 0 Q r < 0 ξ +q, +ξ +ξ q, ξ ξ +q, +ξ +ξ q, ξ ξ Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

46 Future Research Instability Boussinesq gravity waves ω m Ω 0 ρ r < 0 p r < 0 +ξ, +ρ +q q ξ, ρ +ξ, +ρ +q +q +q q q ξ, ρ Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

47 Future Research Instability non-boussinesq gravity waves ω m Ω 0 ρ r < 0 Q > 0 +ξ, p +q +ξ, p +q +q q +q q ξ, +p q ξ, +p r 0 Q0 u 0 = p θ ρ Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36

48 Future Research Instability non-boussinesq self gravity waves ω m Ω 0 ρ r < 0 +ξ, p +q, φ q, +φ ξ, +p +ξ, p +q, φ +q +q q q, +φ ξ, +p p 0 = 2π m r 0G grav ρ 0 ρ 0 ξ dispersion relation Ron Yellin-Bergovoy (TAU) Interfacial Dynamics in PP-disks February 21, / 36