Angular momentum transport in the boundary layers of accretion disks

1. Angular momentum transport in the boundary layers of accretion disks Roman Rafikov (Princeton) Mike Belyaev, Jim Stone, Alexander Philippov

2. Inogamov & Sunyaev 1999 Boundary layer – working definition BL –the inner disk region in contact with the stellar surface where the angular velocity of the disk material rapidly decreases to match the stellar rotation speed

3. Disk vs magnetospheric accretion 10^8 G - neutron star 10^5 G – CV 10^3 G - YSO

4. Observational evidence BL disk BL disk Revnivtsev & Gilfanov 2006 Revnivtsev & Gilfanov 2006 Neutron stars

5. Promise of SRG-eRosita • More accurate observations of bright NSs, accreting at high Mdot, when spreading layer is expected to form • Larger sample of low luminosity NSs with hot, optically thin BLs • New observations of dwarf nova systems

6. BL Inogamov & Sunyaev 1999, 2011 BL star star disk disk Theory: BL geometry • BL in the disk • BL inside the star • Spreading layer Popham & Narayan 1993, 1995 Kippenhahn & Thomas 1976

7. g v v Angular momentum transport in the BL • Magnetorotational instability does not work • Shear instabilities (Kelvin-Helmholtz) are expected • Derived in incompressible limit – not valid in BL! • Other types of instabilities – baroclinic, Tayler-Spruit, etc. have not been shown to operate under the BL conditions

8. Trapped acoustic modes

9. We simulate supersonic flow in a Keplerian disk over the gaseous stellar surface using Athena • 2D, equatorial plane of the disk only (i.e. cylindrical R - phi coordinates) • Rotation is fully accounted for • We fully resolve non-axisymmetric structures responsible for the angular momentum transport • Pure hydro, no B-field effects at the moment, no radiation pressure (are being included now!) • Isothermal EOS, constant sound speed everywhere – interested only in dynamical features of the flow Belyaev, Rafikov, & Stone 2012

10. Initial setup

11. Initial stages of the BL development Oblique shocks going into star, spinning up its outer layers

12. Quasi-steady state • Pattern: crossing shocks in the disk and vortices in the BL • Static in a frame rotating with • Persists for hundreds of orbital periods

13. BL BL broadens and attains a quasi-stationary width, which is much larger than the initial width

14. Vortices are waves propagating in the BL • Deflect supersonic flow – sound waves are launched • Waves nonlinearly evolve and shock • Reflect at some radius in the disk and come back to the BL, reinforcing the waves in the BL

15. star disk ILR OLR CR dispersion relation Lindblad resonance Acoustic modes do not propagate between the LRs

16. AM and mass transport by acoustic modes • BL radiates acoustic modes carrying negative AM • As a result, BL gains AM, stellar surface spins up • Pattern of shocks spins slower than the disk fluid • Upon hitting the shock disk fluid decelerates, loses AM (absorbs negative AM of the wave), goes in • Resonant cavity gets slowly depleted as mass goes into the star • This leads to inward AM flux

17. M=6, full 2*pi

18. Preliminary: 3D, with MHD

19. Summary • We came up with a novel mechanism of the angular momentum transport and variability in astrophysical BLs • It relies on operation of the global instability involving corotation amplification and a feedback loop, which gives rise to a quasi-stationary system of sonic modes • Nonlinear evolution of these acoustic modes results in weak shocks and provides a mechanism of angular momentum exchange between the different parts of the system • This gives rise to mass transfer onto the star and variability associated with rotating mode pattern