1. Super-Critical Accretion? Shin Mineshige (Kyoto Univ.) with K. Ohsuga, K. Vierdayanti, K. Ebisawa, T. Kawaguchi TIARA Workshop (29/11/2006) 1.General introduction 2.Slim disk model (simplified model) 3.Observational tests - Case of ULXs 4.Multi-dimensional effects

2. 1. Introduction (background) There are some objects which seem to undergo super-critical (or super-Eddington) accretion. ・ What are ULXs? What are NLS1s? ・ What do we know from observations? ・ What is key physics in super-critical accretion?

3. Ultra Luminous X-ray sources (ULXs) Ultra Luminous X-ray sources (ULXs) Makishima et al. (2000), van der Karel (2003) Bright (~10 40 erg s -1 ) compact X-ray sources Successively found in off-center regions of nearby galaxies. If L 100 M sun. L E ~ 10 38 (M/M sun ) erg s -1 Two possibilities Sub-critical accretion onto intermediate-mass BHs (M>100M sun ). Super-critical accretion onto stellar-mass BHs (M~3-30M sun ). IC342 galaxy

4. Arguments in favor of intermediate-mass BH (IMBH) Luminosities sometimes exceed ~ 10 40 erg s -1 (=L E of 100 M sun ) Some ULXs show kT ~ 0.1 keV, indicating large M BH (> 100 M sun ) Do ULXs contain IMBHs? Do ULXs contain IMBHs? Miller et al. (2003, 2004) log L x 0.1 keV 1.0 keV low L & highT =stellar-mass BHs log kT (keV) 10 40 erg/s 10 37 erg/s 10M sun 100M sun high L & lowT =IMBHs (?)

5. What determines disk temperature? Energetics (Newtonian version) grav.energy: half → radiation energy half → rotation energy That is, (1/2)E grav = E rad For r ~ 3 r S, we have ⇒ BH 1 keV for 10 M sun BH, 0.1 keV for 10 5 M sun BH

6. Narrow-line Seyfert 1 galaxies (NLS1s) What are NLS1s? Narrow “broad lines” (< 2000 km s -1 ) Seyfert 1 type X-ray features Extreme soft excess & variability Seem to contain less massive BHs Good analogy with stellar-mass BHs in their very high (large L ) state. High T bb ( ∝ M BH -1/4 ) ⇒ large soft excess Small (GM BH /R BLR ) 1/2 ⇒ narrow line width NLS1s = high L/L E system Boller et al. (NewA 44, 2000)

7. Spherical accretion system cannot shine at L > L E. What is the Eddington luminosity? What is the Eddington luminosity? radiation pressure accreting gas accreting gas Gravity > rad. pressure ⇒ GM/r 2 >κF/c ⇒ L < L E =4πCGM/κ ( ∵ F=L/4πr 2 )

8. Super-Eddington flux (F > L E /4πr 2 ) is possible in the z-direction because of radiation anisotropy (!?). Disk accretion may achieve L>L E Disk accretion may achieve L>L E radiation pressure accreting gas accreting gas

9. BH Low- energy photons trapped photons Low- energy photons High- energy photons radiative diffusion & accretion (c) K. Ohsuga What is Photon trapping? Begelman (1978), Ohsuga et al. (2002) When photon diffusion time,t diff ~Hτ/c, exceeds accretion time t acc ~r/v r, photons are trapped. r trap ~ (Mc 2 /L E ) r s.

10. 2. Slim disk model Slim disk model was proposed for describing high luminosity flows as an extension of the standard disk. ・ What is distinct from the standard disk model? ・ What are its observational signatures?

11. Basics This occurs within trapping radius r trap ~ (Mc 2 /L E ) r s Model Radially 1-D model with radiation entropy advection Spectrum τ ≫ 1 → multicolor blackbody but with higher T Slim disk model Slim disk model Abramowicz et al. (1988); Watarai et al. (2000) log L/L E L=L E log m ≡ log M/(L E /c 2 ).. accretion energy trapped photons.

12. Slim-disk structure Slim-disk structure Mineshige, Manmoto et al. (2002) Low M r in ～ 3r S ;T eff ∝ r -3/4 High M r in ～ r S ; T eff ∝ r -1/2 3 rS3 rS. M/(L E /c 2 )=1,10,10 2,10 3 M BH =10 5 M sun.. Slim-disk signatures 1.small innermost radius 2.flatter temp. profile Wang & Zhou (1999), Watarai & Fukue (1999)

13. What determines the inner edge of a disk? What determines the inner edge of a disk? Watarai & Mineshige (PASJ 55, 959, 2003) Classical argument: Circular orbits of a test particle become unstable at r < r ms (=3 r S for no spin BH) Case of slim disk: Usual stability analysis cannot apply because of no force balance. Same is true for ADAF. The disk inner disk is not always at r in = r ms. potential minimum slim - disk solutions

14. Standard disk: Constant fraction of grav. energy is radiated away. Slim disk: Fraction of energy which is radiated away decreases inward: t diff =t acc → Mc 2 /L E ~r/r trap ∝ r What determines temp. profile?.

15. Disk spectra = multi-color blackbody radiation Temperature profiles affect spectra T ∝ r -p ⇒ F ∝ ν 3-(2/p) ・ standard disk (p =3/4) ⇒ F ∝ ν 1/3 ・ slim disk (p =1/2) ⇒ F ∝ ν -1 Spectral properties Spectral properties (e.g. Kato et al. 1998) ν 1/3 ν -1 hνhν FνFν hν hν FνFν (small r)

16. 3. Observational tests: Case of ULXs We examined the XMM/Newton data of several ULXs which were suggested to contain intermediate-mass black holes. ・ How to test the theory? ・ What did we find?

17. Extended disk-blackbody model Extended disk-blackbody model (Mitsuda et al. 1984; Mineshige et al. 1994) Fitting with superposition of blackbody (B ν ) spectra: Fitting parameters: T in = temp.of innermost region ( ～ max. temp.) r in = size of the region emitting with B ν (T in ) p = temperature gradient Corrections: Real inner edge is at ～ ξr in with ξ ～ 0.4 Higher color temp.; T c =κT in with κ ～ 1.7 ⇒ Good fits to the Galactic BBHs with p=0.75

18. Fitting with disk blackbody (p=0.75) + power-law We fit XMM-Newton data of several ULXs ⇒ low T in ～ 0.2 keV and photon index ofΓ=1.9 If we set r in ~ 3 r S, BH mass is M BH ~ 300 M sun. Spectral fitting 1. Conventional model Spectral fitting 1. Conventional model (Roberts et al. 2005) NGC 5204 X-1 log hν log conts

19. Spectral decomposition of DBB & PL components DBB comp. is entirely dominated by PL comp. Can we trust values derived from the minor component? Problem with DBB+PL fitting log hν log conts NGC 5204 X-1

20. Model fitting, assuming T ∝ r -p We fit the same data but with the extended DBB model ⇒ high T in ~ 2.5 keV and p =0.50 ±0.03 (no PL comp. ) M BH ~ 12 M sun & L/L E ~ 1, supporting slim disk model. Spectral fitting 2. Extended DBB model Spectral fitting 2. Extended DBB model (Vierdayanti, SM, Ebisawa, Kawaguchi 2006) NGC 5204 X-1 log hν log conts

21. Why can both models give good fits? Because the spectral shapes are similar below ~10 keV. Both show f ν ∝ ν -1 in 0.1~10keV range. power-law (Γ=2) extended DBB with p=0.5

22. log kT (keV) log L x Temperature-Luminosity diagram Temperature-Luminosity diagram (Vierdayanti et al. 2006, PASJ 58, 915) No evidence of IMBHs so far New model fitting gives M BH <30M sun. Low-temperature results should be re-examined!! The same test is needed for NLS1s DBB + PLext. DBB

23. Fate of Prad-driven instability Radiation pressure-dominated SS disk is unstable. (1) relaxation oscillation? Honma et al. (1991), Szuszkiewicz & Miller (1998) (2) soft-to-hard transition? Takeuchi & Mineshige (1998), Gu & Lu (2000) (3) strongly clumped disk? Krolik (1998) (4) disk-corona structure? Nakamura & Osaki (1993), Svensson & Zdziarski (1994) Σ M ・ (1) (2)

24. Bursting behavior of micro-quasar Bursting behavior of micro-quasar (Yamaoka, Ueda & Inoue 2002) GRS 1915+105 exhibits state transitions between peak (slim disk) and valley (thin disk) log r in log T in time counts (T ∝ r -1/2 ) (T ∝ r -3/4 )

25. 4. Multi-dimensional effects The slim-disk model applies only to the flow with L ~ L E. For even higher L, we need to perform radiation-hydrodynamical (RHD) simulations. ・ What are the multi-dimensional effects? ・ What can we understand them?

26. A simple model A simple model (Ohsuga et al. 2002, ApJ 574, 315; 2003, ApJ 596, 429) Problem with the slim-disk formulation Radiative cooling rate is evaluated as ~ 4σT 4 /3τ (at same r) Consider a part of the disk which is moving inward Dynamics is given. Solve radiation transfer in z-direction. Can approximately evaluate 2D photon trapping effects. BH accretion radiative diffusion

27. The slim-disk model overestimates the luminosity. The frequency of the SED peak first increases then decreases with increase of mass-accretion rate. (c) K. Ohsuga Photon trapping: observable effects Luminosity [L/L E ] Slim disk Our results (Photon-trapping) Mass-accretion rate m=10 ・ m=100 ・ 30 m=10 ・ MCD Luminosity SED Variations Photon- trapping Slim disk Ohsuga et al. 2003Ohsuga et al. 2002

28. Our 2D RHD simulations Our 2D RHD simulations Ohsuga, Mori, Nakamoto, SM (2005, ApJ 628, 368) First simulations of super-critical accretion flows in quasi-steady regimes. Matter with 0.45 Keplerian A.M. is continuously added through the outer boundary → disk-outflow structure Flux-limited diffusion adopted. α viscosity with α=0.1. Mass input rate: 1000 (L E /c 2 ) → luminosity of ~3 L E Injection BH r/rs r/rs z/rs z/rs 500 Initially empty disk

29. (c) K. Ohsuga Overview of 2D super-critical flow Overview of 2D super-critical flow Ohsuga et al. (2005, ApJ 628,368) gas energy radiation energy density density BH r/rs r/rs z/rs z/rs density contours & velocity fields disk flow outflow Case of M =10 M sun & M =1000 L E /c 2 ・

30. Why is accretion possible? Why is accretion possible? Ohsuga & S.M. (2006, submitted) Low ρ and steep E rad profile yields super-Eddington flux. Radiation energy density is high; E rad ≫ E E ≡ L E /4πr 2 c. Then why is the radiation pressure force so weak? Note radiation energy flux is F rad ∝ (κρ) -1 ∇ E rad. → Because of high ρ and relatively flat E rad profile.

31. (c) K. Ohsuga Photon trapping Photon trapping BH z/rs z/rs r/rs r/rs Radiation flux (F r ) is inward! Photon trapping also helps reduced radiation pressure force. F r =radiation flux in the rest frame F 0 r =radiation flux in the comoving frame F r ~F 0 r +v r E 0

32. The observed luminosity is sensitive to the viewing- angle; Maximum L ~ 12 L E !! luminosity BH  Density contours 12 8 4 4  D 2 F(  )/L E our simulations (c) K. Ohsuga Significant radiation anisotropy Significant radiation anisotropy ⇒ mild beaming Ohsuga et al. (2005, ApJ 628,368) 0 viewing angle

33. Why beaming? Photon energy increases as θ decreases, why? - Because we see photons from deeper, hot region. - Because of Doppler effect. Why photon number increases as θ decreases, why? - Because of anisotropic gas distribution. - Because I ν /ν 3 is Lorentz invariant & hν increases. radiation gas Heinzeller, S.M. & Ohsuga (2006, MNRAS 372, 1208,)

34. Future issue Interaction with magnetic fields Magnetic fields are essential ingredients in disks Photon-bubble instability (Begelman 2002) Magnetic tower jet → global RHD+MHD simulations necessary (Kato, SM, & Shibata 2004)

35. Conclusions Near- and super-critical accretion flows seem to occur in some systems (ULXs, NLS1s…?). Slim disk model predicts flatter temperature profile. Spectral fitting with variable p proves the presence of supercritical accretion in ULXs. How about NLS1s? 2D RHD simulations of super-critical flow show super- Eddington luminosity, significant radiation anisotropy (beaming), high-speed outflow, large absorption, etc. L can be ~10 L E !! Issues: magnetic fields, line spectra, instability,…