2. 1 Indiana 3D Hydro Group The Effects of Envelope Irradiation on Gravitational Instabilities in Embedded Protoplanetary Disks Kai Cai Astronomy Department Indiana University May 18, 2006 (Now at: McMaster University) Richard H. Durisen Annie C. Mejía (Univ. of Washington) Megan K. Pickett (Purdue Univ. Calumet) Aaron C. Boley Scott Michael

3. 2 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 2 Gravitational Instabilities in Embedded Disks Gravitational Instabilities (GIs) in Disks Toomre’s stability parameter for Q = c s  /  G  < 1  ring instability for Q < 1.5 - 1.7  spiral instability Several class 0/I disks have low Q’s e.g. HL Tau, L1551 IRS5 Why? Disks are massive @ earlier times Disks are smaller @ earlier times This Study: Effects of Envelope Irradiation

4. 3 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 3 3D Hydro Code Numerical Characteristics: 2 nd order in space and time Eulerian Fixed cylindrical grid (r, ,z) (256,128,32) to (512,512,64) ~ millions of cells ! Runs in parallel on SMP machines r = 512 z = 64  = 128

5. 4 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 4 Radiative Cooling: Mejía (2004) & Cai (2006) – Radiative cooling in the atmosphere (  R <2/3) – Flux-limited diffusion in the disk interior (  R  2/3) – Envelope irradiation: blackbody flux with T env – D’Alessio et al. (2001) mean opacities (dust grains): a max can vary (n(a) ~ a -3.5, a min = 0.005  m) z (AU) Atmosphere (  < 2/3) Interior (  ≥ 2/3) 0 816243240 8 0 r (AU) Envelope Irradiation

6. 5 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 5 Initial Axisymmetric Model Initial model for radiative cooling simulations Initial model for radiative cooling simulations R = 40 AU M d = 0.07 M  M  = 0.5 M   (r)  r -1/2 Q min =1.5 R = 40 AU M d = 0.07 M  M  = 0.5 M   (r)  r -1/2 Q min =1.5

7. 6 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 6 The Disk Evolution: four phases Irr 15K

8. 7 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 7 The Effects of Envelope Irradiation Irr 15K Irr 25K No Irr. 14 ORPs 3500 yr Irr 50K Simulations compared during the asymptotic phase  A  = 1.51 Global t cool = 2.7 ORPs  A  = 1.01 Global t cool = 5 ORPs  A  = 1.16 Global t cool = 3.2 ORPs  A   0.40 Global t cool ~ 9 ORPs Cai et al. (2007, in prep.)

9. 8 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 8 Total Nonaxisymmetry A sum of the amplitudes of all m’s, then averaged temporally   A  (13 - 14  ORPs) No-Irr: 1.51 Irr 15K: 1.16 Irr 25K: 1.01 Irr 50K: 0.40 - continues to damp Boss (2002) reported a similar effect when he raised outer disk T.

10. 9 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 9 Envelope Irradiation: Q(r) At 14.9 ORPs (= 3725 yrs)

11. 10 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 10 Total Energies … ∇·F∇·F   ∫(∇· F)dVdt ∫  dVdt cooling heating

12. 11 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 11 The Luminosity of the Envelope Irradiation L env =  T env 4  2  R d 2 = total energy input rate of the envelope irradiation on the disk Stellar luminosity L  =  T  4  4  R  2 (T  = 4000 K, R  = 2 R  ) In all cases, net disk luminosity L disk ~ 5×10 30 erg/s 1.3×10 33 1/350K 7.2×10 31 2.2×10 -2 25K 8.6×10 30 2.8×10 -3 15K L env (erg/s) L env / L  T env

13. 12 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 12 Vertical Structure  Irradiation tends to make the disk isothermal vertically No-Irr Irr @ 25K  T

14. 13 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 13 Mass Transport, Modes & Torques Gravitational torques (A. Boley) Average mass transport over the last 3 ORPs

15. 14 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 14 L1551 IRS 5 system Osorio et al. (2003) Lim & Takakuwa (2005) A triple?

16. 15 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 15 L1551 IRS 5 : model fit Osorio et al. (2003)

17. 16 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 16 A new initial model M  = 0.3 M , M d = 0.2 M , R = 15 AU,  (r)  r -1, Q min <1 - close to L1551 IRS 5 northern disk Setup: T env = 120K, a max =200  m L env ~ L ⋆ of T Tau star (T= 4000K, R= 2R ๏ ) 2 AU

18. 17 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 17 Simulating a L1551 IRS 5 Disk Disk expands  R final ~ 30 AU: unrealistic Very high midplane  & long radiative cooling time

19. 18 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 18 Q(r) and the Correction Factor Corrected Q min = (1 + k mu h)Q 0 ~ 1.4-1.5

20. 19 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 19 Analytic Analyses Rafikov (2005)    min   inf [f(  )] 1/5, T mid  T min  T inf [f(  )] 2/5, etc. 0.07 M  disk (at 20 AU) :  inf  201 g cm -2, T inf  39 K, but [f(  )] 1/5 might be large (~1.5) For L1551 IRS 5 disk (at 10 AU):  inf  1220 g cm -2 and T inf  65.6 K, but [f(  )] 1/5 ~ 5.3  Despite simplifications, Rafikov (2005)’s analytic arguments may be valid out to ~ 20 AU for our disk. Matzner & Levin (2005): o nly discussed SLING as global GIs

21. 20 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 20 Conclusions Envelope irradiation tends to suppress GIs – it cannot be ignored ! No dense clumps produced, so direct giant formation by GIs unlikely. GIs  fragmentation! Mild irradiation preferentially suppresses high-order modes Future Stellar irradiation – T irr (r) ~ r -1/2 Consider the gravitational effect of a binary companion – e.g., Mayer et al. (2005), Boss (2006) -> Roche potential Mass infall onto the disk - e.g., Mayer et al. (2004), Banerjee et al. (2004), Vorobyov & Basu (2005) ……

22. 21 Indiana University - Purdue University Calumet 3D Hydro Group Indiana University - Purdue University Calumet 3D Hydro Group Click to edit Master subtitle style Click to edit Master title style 21 Thank you!