Modeling Supercritical Accretion FlowShin Mineshige (Kyoto) & Ken Ohsuga (RIKEN)
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
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?
. . m Supercritical stateSlim disk (with outflow) ~10% LE ~ LE State transition in BH binary Esin et al. (1997) Very high state High/soft state Intermediatestate Low/hard state Quiescence Standard disk+corona Standard disk Radiatively inefficient flow (ADAF/CDAF/MHD Flow)
radiation pressure accreting gas accreting gas Shakura & Sunyaev (1973) Diskaccretion may achieve L>LE Super-Eddington flux (F>LE/4πr2) is possible in the z-direction becauseofradiationanisotropy(!?) .
. rtrap~ (Mc2/LE)rs What is Photon trapping? Begelman (1978), Ohsuga et al. (2002) When photon diffusion time,tdiff~Hτ/c, exceeds accretion time tacc~r/|vr|, photons are trapped. Low-energy photons Low-energy photons BH radiative diffusion & accretion High-energy photons trapped photons (c) K. Ohsuga
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?
L=LE log L/LE . . logm≡logM/(LE/c2) Slim disk modelAbramowicz et al. (1988); Watarai et al. (2000) • Basics This occurs within trapping radius rtrap~(Mc2/LE)rs • Model One-dim. model (in r direction) with radiation entropy advection accretion energy trapped photons . viscous radiative heating cooling
. M/(LE/c2)=1,10,102,103MBH=105Msun 3rS Slim disk structureBeloborodov (1998), Mineshige, Manmoto et al. (2002) Wang & Zhou (1999), Watarai & Fukue (1999) Case of non-spinning BHs: Low M rin～3rS ;Teff∝r-3/4 High M rin～rS;Teff∝r-1/2 . . Slim-disk signatures1.smallinnermostradius 2.flatter temp. profile (=rms)
1.Small innermost radius(Abramowicz, Kato, … Watarai & Mineshige 2003) potential minimum Classical argument: Circular orbits of a test particle become unstable atr<rms(=3rSfornospin 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<rms. Same is true for ADAF. slim-disk solutions The disk inner disk is not always at rin=rms.
2.Flatter temperature profile Standard disk: Constant fraction of grav. energy is radiated away. Slim disk: Fraction of energy which is radiated away decreases inward: Qrad/Qvis~tacc/tdiff∝r/rtrap∝r
Spectral properties(e.g. Kato et al. 1998,2008) Disk spectra = multi-color blackbody radiation Temp. profiles affect spectra: Fν∝∫Bν(T(r))2πrdr T∝r-p ⇒ Fν∝ν3-(2/p) ・standard disk (p=3/4) ⇒Fν∝ν1/3 ・slim disk (p=1/2) ⇒Fν∝ν-1 Fν ν1/3 (smallr) hν ν-1 Fν (smallr) hν
IC342 galaxy UltraLuminousX-raysources(ULXs)Colbert & Mushotzky (1999), Makishima et al. (2000), van der Karel (2003) • Bright (>~1040ergs-1) compact X-ray sources • Successively found in off-center regions of nearby galaxies. • If L<LE, black hole mass should be > 100 Msun. LE~1038(M/Msun) erg s-1 • Two possibilities • Sub-critical accretion onto intermediate-mass BHs (M>100Msun). • Super-critical accretion onto stellar-mass BHs (M~3-30Msun).
Extended disk-blackbody model(Mitsuda et al. 1984; Mineshige et al. 1994) Fitting with superposition of blackbody (Bν) spectra: Three fitting parameters: Tin= temp.of innermost region (～max.temp.) rin = size of the region emitting with Bν(Tin) p= temperature gradient (=0.75 in disk-blackbody model) Corrections: Real inner edge is at ～ ξrin with ξ～0.4 Higher color temp.; Tc=κTin with κ～1.7 ⇒ Good fits to the Galactic BHs with p=0.75
Spectralfitting1.Conventionalmodel(Miller et al. 2004, Roberts et al. 2005) Fitting with disk blackbody (p=0.75) + power-law We fit XMM-Newton data of several ULXs ⇒ lowTin～0.2keVandphoton index ofΓ=1.9 If we set rin~3rS, BH mass is MBH~300Msun. log conts NGC5204X-1 However, PL comp. entirely dominates over DBB comp. loghν
Spectralfitting2.Extended DBB model(Vierdayanti, SM, Ebisawa, Kawaguchi 2006) Model fitting, assuming T∝r-p We fit the same ULX data with extended DBB model ⇒highTin~2.5keVandp=0.50±0.03(noPLcomp.) MBH~12Msun & L/LE~1, supporting slim disk model. log conts NGC5204X-1 loghν
Temperature-Luminosity diagram(Vierdayanti et al. 2006, PASJ 58, 915) logLx Newmodelfitting gives MBH <30Msun. Low-temperature results should be re-examined!! DBB + PL ext.DBB logkT (keV)
outflow disk wind BH accreting gas accretion Rsp spherization radius, Rsp~ rtrap ⇒ Similar effects are expected. Comment on outflow(Shakura & Sunyaev 1973; Poutanen et al. 2007) ・ ・ Standard disk with outflow Set L(r)≡2πr2F(r)=LE→M(r)∝r(∵F∝M(r)/r3) Same as that of slim disks!!
3.Radiation-hydro. simulation The slim-disk model is one-dimensional model, although multi-dimensional effects, such as outflow, could be important when L >~ LE. We thus perform radiation-hydrodynamic (RHD) simulations. ・What are the multi-dimensional effects? ・What can we understand them?
500 z/rs Injection 500 BH r/rs Our global 2D RHD simulationsOhsuga, Mori, Nakamoto, SM (2005, ApJ 628, 368) • First simulations of super-critical accretion flows in quasi-steady regimes. • Matter (with0.45Keplerianang. mom. at 500rS) is continuously added through the outer boundary → disk-outflow structure • Flux-limited diffusion adopted. • αviscosity (α=0.1), MBH=10Msun • Mass input rate:1000(LE/c2) →luminosity of~3LE gas density Initiallyemptydisk
outflow z/rs disk flow BH r/rs density contours & velocity fields Overview of 2D super-critical flow Ohsuga et al. (2005) Case of M=10Msun and M=1000LE/c2 ・ gas density radiation energy density (c) K. Ohsuga
Why is supercritical accretion feasible? Ohsuga & S.M. (2007, ApJ 670, 1283) Radiation energy density is high;Erad ≫EE≡LE/4πr2c, but Why is then radiation pressure force so weak? Note radiation energy flux is Frad∝(κρ)-1∇Erad. → Because of relatively flat Eradprofile. fast outflow slow accretion SteepEradprofile yield super-Eddington flux.
Photon trapping Fr=radiation flux in the rest frame F0r=radiation flux in the comoving frame is Fr~F0r+vrE0 z/rs Photon trapping also helps reducing radiation pressure force. BH Radiation flux (Fr) is inward! r/rs (c) K. Ohsuga
BH Density contours Significantradiationanisotropy luminosity 12 our simulations 4D2F()/LE 8 4 0 viewing angle The observed luminosity is sensitive to the viewing-angle; Maximum L ~ 12 LE!! ⇒ mild beaming (c) K. Ohsuga
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?
Our global 2D RMHD simulationsOhsuga, 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), MBH=10Msun Model A (0=100g/cm3) : supercritical accretion Model B (0=10-4g/cm3) : standard-disk type accretion Model C (0=10-8g/cm3) : radiatively inefficient accretion z/rs non-radiative MHD simulation for 4.5 rotation periods turn on radiation terms r/rs
Model A： Supercritical accretion（ｌog ρ0=1 g/cm3) log /0 v/vesc z/rs z/rs r/rs r/rs
Model B： Standard-disk type accretion（ｌog ρ0=10-4 g/cm3) log /0 v/vesc z/rs z/rs r/rs r/rs
Model C： Radiatively inefficient accretion（ｌog ρ0=10-8 g/cm3) log /0 v/vesc z/rs z/rs r/rs r/rs
accretion rate/（LE/c2） Model A (supercritical) outflow rate/（LE/c2） luminosity/LE Model B (standard) Not yet in a quasi- steady state. Model C (RIAF) ~ 1 sec (c) K. Ohsuga
SummaryofRMHDsimulations Model A: similar to the results of RHD simulations Model B: moderate variations and outflow (??) Model C: similar to the results of MHD simulations
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. • 2DRHDsimulationsofsupercriticalflowshowsuper- Eddingtonluminosity,significant radiation anisotropy (beaming), high-speed outflow etc. L can be>~10LE!! • 2D RMHD simulations are in progress. We can basically reproduce three different regimes of accretion flow.