1. Tidal Stripping of Star Close to Massive Black Holes
Lixin (Jane) Dai
(KIPAC/Stanford)
+ Roger Blandford
Peter Eggleton
Jane Dai

2. Black Hole Spin Probe Accretion Disc Jet Close Stars
Iron Lines (Reynolds & Nowak 03)
Multi-temperature black body method
(e.g. Yuan, Quataert & Narayan 04; Gou et al 11)
Jet
Complicated models (Blandford & Znajek 77)
Close Stars
tidal events
Jane Dai

3. Tidal Disruption Unbound / eccentric / parabolic Pros: bright
Cons: short, hard to model with high precision for spin
Might be able to detect fastly spinning holes
e.g. Komossa 99, Zauderer 11, Bloom 11, Gezari 09, 12, van Velsen 11
Jane Dai

4. Tidal Stripping Circular, equatorial orbit Cons: Not as luminous
Pros: long, easier to model with precision for a/M
Dai, Blandford & Eggleton 2011a
Dai & Blandford 2011b
Jane Dai

5. Close Binary Systems
Newtonian framework (e.g. Hjellming & Webbink 87, Soberman et al. 97):
- Cataclysmic variables
- Low Mass X-ray Binaries
SMBH-star binary:
Relativistic -> Spin!
Jane Dai

6. Relativistic Model No accurate enough GR framework
-Hameury et. al. 1994
GR Modifications near ISCO:
Gravitational Radiation Power: 20%
Roche Volume: 40%
Mass Accretion Rate: 50%
Dai, Blandford & Eggleton 2011a
Dai & Blandford 2011b
Jane Dai

7. Newtonian Roche Volume
(Frank et al 2002) L1 L2
(Dai & Blandford 2011b)
Jane Dai

8. Relativistic Roche Volume
(Dai & Blandford 2011b)
0.368
0.456
0.683
0.503
Riemann -> local tidal tensor.
Evaluate volume within critical equi-potential
Jane Dai

9. Comparison 20-40% difference! non-rotating stars co-rotating stars
Fishbone 73 /Hameury 94: sphere, no spin, no stellar rotation
20-40% difference!
non-rotating stars
(Dai & Blandford 2011b)
co-rotating stars
Jane Dai

10. Star: Adiabatic Evolution
- Local entropy conserved (tdyn<< ttransfer << tKelvin ) - Orbital period ~-1/2
(Dai & Blandford 2011a)
Jane Dai

11. Relativistic P-M
(Dai & Blandford 2011b)
Jane Dai

12. Relativistic Roche Evolution
Lower main-sequence star
107 M Schwarzschild hole
(Dai & Blandford 2011b)
Newtonian
Stable
Relativistic
Jane Dai

13. RE J1034+396 XMM-Newton z=0.042 Seyfert Lbol ~ 1044 erg s-1
1 hr QPO with 20 cycles
~7% sinusoidal profile
(Gierlinski et al. 2008)
Jane Dai

14. Simulated Hotspot Emission
Dai & Blandford 2011b
Jane Dai

15. X-ray AGN QPOs XMM-Newton: ~100 AGN, only 1 QPO (RE J1034)
(Gonzalez-Martin & Vaughan 12)
Chandra: Not good for timing analysis due to pile-up
Suzaku / RXTE: ~100 AGN each, unevenly sampled data
Jane Dai

16. Suzaku IC4329a
Jane Dai

17. Take-aways Why are we interested in tidal stripping?
-“QPOs” from AGN as probe of SMBH spin.
How is the model different from X-ray binaries?
-Different stellar evolution.
-Rigorous GR
Observations?
- RE J
- Search Suzaku/RXTE archives for QPOs with P~0.1-10hr.
Jane Dai

18. Dai, Blandford & Eggleton 2011a Dai & Blandford 2011b
Jane Dai

19. Jane Dai

20. Jane Dai

21. Stars near SMBH MBH ~ 4106 M (Ghez et al. 2008) Rg~ 20 light sec
ISCO ~ light min
Closest observed stellar orbit ~ 10 light hr ~180 Rg
- Tidal radius RstarMstar-1/3  Mstar0.5
Jane Dai

22. Orbits Rapidly Circularize
(Peters 1964)
Jane Dai

23. Simulated Hotspot Emission
Dai & Blandford 2011b
Jane Dai

24. Pre-Roche: Gravitational Inspirals
(Finn & Thorne 2000)
- Gravitational radiation dominates
- Need PPN (Parametrized Post-Newtonian) corrections to torque
- Torque = - dL/dt
Jane Dai

25. Relativistic Correction Tau
0.00
1.65
1.00
(Dai & Blandford 2011b)
Jane Dai

26. Roche radii for various stars
(Dai & Blandford 2011a)
Jane Dai

27. Relativistic Roche Volume
(Dai & Blandford 2011b)
Jane Dai

28. Stellar adiabatic evolution
Local entropy S(m) conserved
(tdyn<< ttransfer << tKelvin )
Perfect gas: S/N~Cv ln(P/), =5/3
EOS: dP/dm = - Gm / 4pr4
dr/dm = 1/ 4pr2
New boundary conditions
Jane Dai

29. Upper and Lower main-sequence stars
Zero age main sequence star models with metalicity 0.01
(Peter Eggleton’s simulation)
Jane Dai

30. Red Giants
Jane Dai

31. White dwarfs R(m) ~(m/ Mch)-1/3 (1 - (m/Mch)4/3)1/2, Mch = 1.459 M
Jane Dai

32. Brown dwarfs
P~ 1013 rconstant S(m)
Jane Dai

33. Planets Solid planets: density no change
Liquid planets: radius constant
Jane Dai

34. Newtonian Roche Evolution
Stellar parameter :
 = ln/lnm > 6 dynamical instability
star moves out
<0 star moves in
Stellar orbit evolution:
- Sun, upper main sequence, giants spiral in and then out;
- Lower main sequence, white dwarf, brown dwarf, liquid planet spiral out;
- Solid planet stays on the same orbit.
Jane Dai

35. Newtonian P-M (Dai & Blandford 2011b) Jane Dai Upper main sequence
Earth
Sun
Jupiter
Red giant
Upper main sequence
White Dwarf
Brown dwarf
Lower main sequence
(Dai & Blandford 2011b)
Jane Dai

36. X-ray observations Maximum efficiency: a ~ m PR ~ PISCO RE J1034: 1hr
Liberal mass loss
ISCO ->Spin
Wind
Equatorial viewing
Luminosity ~ D4
D~2?
RE J1034: 1hr
- BH: Msun ,
- Star: M-dwarf-Sun
- Not enough power
- How to fix that?
Jane Dai

37. Probe of Spin Hot Spot Light Curve P-Pdot Analysis:
10,000 years observation
Similar to Pulsars
Jane Dai

38. Vision? Coincidence? Time-traveller?
“You should work on SMBH tidal problems. It is nothing now but will become something big within two years.”
- Roger Blandford (2009)
Vision? Coincidence?
Time-traveller?
Jane Dai

39. Future work Inclined or elliptical stellar orbit?
Interactions with other stars? (Exo-planets)
GW-EM coupled signals
Jets?
3D relativistic dynamical simulations
Jane Dai

40. Jane Dai

41. Jane Dai

42. Post-Roche Evolution After mass transfer orbit expands
P ~ m-h/2
~ m-1.1 for low mass star
t-tR=4100M6-2/3 P2.7[(P/PR)3.6-1] yr; [~ 10000yr]
Conservative Mass loss
~ -m7.9 eventually till ttransfer > tKelvin
Dynamical complications
Holding pattern?
Interactions, drag
Jane Dai
21 v 2009
CFA

43. Other observations 17 min IR QPO frm SgrA* (Genzel)
GRB burst tidal disruption
12yr period in OJ287??
Binary black holes??? (Lehto & Valtonen)
LISA harbingers
Discover incipient EMRI, coalescence
Predictable evolution with degree position!
Seek electromagnetic signal in phase with ~10-9 power
eg LSST.
Jane Dai
21 v 2009
CFA