1. Modeling Supercritical Accretion Flow Shin Mineshige (Kyoto) & Ken Ohsuga (RIKEN)

2. Outline Introduction Basics of supercritical (super-Eddington) accretion Slim disk model for ULXs Properties of “slim” disks Spectral fits to ULXs Global radiation-hydrodynamic simulations Multi-dimensional effects Why is supercritical accretion feasible? Global radiation-magnetohydrodynamic simulations Three different regimes of accretion flow

3. 1. Introduction Binary black holes show distinct spectral states, (probably) depending on the mass accretion rate. ・ What happens at high accretion rates? ・ What physical processes are important there?

4. State transition in BH binary State transition in BH binary Esin et al. (1997) Standard disk+corona Standard disk Radiatively inefficient flow (ADAF/CDAF/MHD Flow) Very high state High/soft state Intermediate state Low/hard state Quiescence m.. Supercritical state Slim disk (with outflow) ~10% L E ~ L E

5. 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 Shakura & Sunyaev (1973)

6. 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.

7. 2. Slim disk model for ULXs Slim disk model was proposed for describing high luminosity, supercritical accretion flows. We examined the XMM/Newton data of several ULXs based on the slim disk model. ・ What is the slim disk model? ・ What features are unique to the slim disk? ・ What did we find in ULX data?

8. Basics This occurs within trapping radius r trap ~ (Mc 2 /L E ) r s Model One-dim. model (in r direction) with radiation entropy advection 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. viscous radiative heating cooling

9. Slim disk structure Slim disk structure Beloborodov (1998), 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) Case of non-spinning BHs: (=r ms )

10. 1. Small innermost radius 1. Small innermost radius (Abramowicz, Kato, … Watarai & Mineshige 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: The classical argument can- not apply because the disk is not in force balance. The inner edge can be at r < r ms. Same is true for ADAF. The disk inner disk is not always at r in = r ms. potential minimum slim - disk solutions

11. Standard disk: Constant fraction of grav. energy is radiated away. Slim disk: Fraction of energy which is radiated away decreases inward: Q rad /Q vis ~ t acc /t diff ∝ r/r trap ∝ r 2. Flatter temperature profile

12. Disk spectra = multi-color blackbody radiation Temp. profiles affect spectra: F ν ∝ ∫B ν (T (r ) ) 2πrdr T ∝ r -p ⇒ F ν ∝ ν 3-(2/p) ・ standard disk (p =3/4) ⇒ F ν ∝ ν 1/3 ・ slim disk (p =1/2) ⇒ F ν ∝ ν -1 Spectral properties Spectral properties (e.g. Kato et al. 1998,2008) ν 1/3 ν -1 hνhν FνFν hν hν FνFν (small r)

13. Ultra Luminous X-ray sources (ULXs) Ultra Luminous X-ray sources (ULXs) Colbert & Mushotzky (1999), 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

14. Extended disk-blackbody model Extended disk-blackbody model (Mitsuda et al. 1984; Mineshige et al. 1994) Fitting with superposition of blackbody (B ν ) spectra: Three 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 (=0.75 in disk-blackbody model) 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 BHs with p =0.75

15. 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 (Miller et al. 2004, Roberts et al. 2005) NGC 5204 X-1 log hν log conts However, PL comp. entirely dominates over DBB comp.

16. Model fitting, assuming T ∝ r -p We fit the same ULX data with 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

17. log kT (keV) log L x Temperature-Luminosity diagram Temperature-Luminosity diagram (Vierdayanti et al. 2006, PASJ 58, 915) New model fitting gives M BH <30M sun. Low-temperature results should be re-examined!! DBB + PLext. DBB

18. Standard disk with outflow Set L (r ) ≡ 2πr 2 F (r ) = L E → M (r ) ∝ r ( ∵ F ∝ M (r )/r 3 ) Comment on outflow Comment on outflow (Shakura & Sunyaev 1973; Poutanen et al. 2007) ・ Same as that of slim disks !! BH outflow disk wind accreting gas accretion ・ spherization radius, R sp ~ r trap R sp ⇒ Similar effects are expected.

19. 3.Radiation-hydro. simulation The slim-disk model is one-dimensional model, although multi-dimensional effects, such as outflow, could be important when L >~ L E. We thus perform radiation-hydrodynamic (RHD) simulations. ・ What are the multi-dimensional effects? ・ What can we understand them?

20. Our global 2D RHD simulations Our global 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 ang. mom. at 500 r S ) is continuously added through the outer boundary → disk-outflow structure Flux-limited diffusion adopted. α viscosity (α=0.1), M BH =10M sun 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 gas density

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

22. Why is supercritical accretion feasible? Ohsuga & S.M. (2007, ApJ 670, 1283) Steep E rad profile yield super-Eddington flux. Radiation energy density is high; E rad ≫ E E ≡ L E /4πr 2 c, but Why is then radiation pressure force so weak ? Note radiation energy flux is F rad ∝ (κρ) -1 ∇ E rad. → Because of relatively flat E rad profile. fast outflow slow accretion

23. (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 reducing radiation pressure force. F r =radiation flux in the rest frame F 0 r =radiation flux in the comoving frame is F r ~F 0 r +v r E 0

24. 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 0 viewing angle

25. 4.Global radiation-magneto- hydrodynamic simulations Alpha viscosity adopted in RHD simulations is not so realistic. We have just obtained preliminary results of 2-dim. global RMHD simulations of black hole accretion flows. ・ Can we reproduce different spectral states?

26. Our global 2D RMHD simulations Our global 2D RMHD simulations Ohsuga, Mori, SM (2008, in preparation) Extension of MHD simulations to incorporate radiation effects (through flux-limited diffusion). Start with a torus threaded weak poloidal fields: Three different regimes (  0 =density normalization), M BH =10 M sun Model A (  0 =10 0 g/cm 3 ) : supercritical accretion Model B (  0 =10 -4 g/cm 3 ) : standard-disk type accretion Model C (  0 =10 -8 g/cm 3 ) : radiatively inefficient accretion non-radiative MHD simulation for 4.5 rotation periods turn on radiation terms z /rsz /rs r /rsr /rs

27. log  /  0 v / v esc Model A ： Supercritical accretion （ ｌ og ρ 0 =1 g/cm 3 ) r /rsr /rs r /rsr /rs z /rsz /rs z /rsz /rs

28. v / v esc Model B ： Standard-disk type accretion （ ｌ og ρ 0 =10 -4 g/cm 3 ) log  /  0 r /rsr /rs r /rsr /rs z /rsz /rs z /rsz /rs

29. v / v esc Model C ： Radiatively inefficient accretion （ ｌ og ρ 0 =10 -8 g/cm 3 ) log  /  0 r /rsr /rs r /rsr /rs z /rsz /rs z /rsz /rs

30. (c) K. Ohsuga luminosity/L E accretion rate/ （ L E /c 2 ） outflow rate/ （ L E /c 2 ） Model A (supercritical) Model B (standard) Model C (RIAF) Not yet in a quasi- steady state. ~ 1 sec

31. Summary of RMHD simulations Modeldensity & temperature luminosity, L /L E energeticskin. luminosity, L kin /L Model A (supercritical) ρ~10 -2 g/cm 3 T ~10 8 K ~10 0 Erad >> Egas >~ Emag ~0.2 Model B (standard) ρ~10 -5 g/cm 3 T ~10 6 K ~10 -2 Egas ~ Emag ~ Erad ~0.003 Model C (RIAF) ρ~10 -9 g/cm 3 T ~10 10 K ~10 -8 Egas > Emag >> Erad ~3 Model A: similar to the results of RHD simulations Model B: moderate variations and outflow (??) Model C: similar to the results of MHD simulations

32. Conclusions Near- or supercritical accretion flows seem to occur in some systems (ULXs…?). Slim disk model predicts flatter temperature profile. Spectral fitting with variable p (temp. gradient) proves the presence of supercritical accretion in some ULXs. 2D RHD simulations of supercritical flow show super- Eddington luminosity, significant radiation anisotropy (beaming), high-speed outflow etc. L can be >~ 10 L E !! 2D RMHD simulations are in progress. We can basically reproduce three different regimes of accretion flow.