Figure2. 1. Cross-sections slice of ingas Run density 26 (Lin the x y plane through z =0ofRun4attimet =0.25t B =0.2 10 4 X /L Edd =0.01) Figureshowing 2. Zoom-in the inner the 30inner pc 4the pc [x y] of the planethroughz [x y] planethroughz yr, overplotted =0atatimet =0atatimet =2.047 =2.047 Myr. Myr in Run 26 (L X /L Edd =0.01). Th with The the gasvelocity density vector is inarrows. the top-left panel, temperature represent in the gas top-right, density in photoionization the top-left, temperature parameter in inthe thebottom-left, top-right, photoionization and Mach number parameter in the bottom-left, and Machnu in the bottom-right, overplotted with the velocity thevector bottom-right. arrows. It It showscolder, stretching denser of the filament-like colder clumps structures, as they with fallhotter, intoward less-dense thecenter. Theyremaindenser, howeverget he gas in between, both components accreting in (with at r<1pc,mostlybyadiabaticcompression.note the colder phase moving in faster), all of whichthat hasthe been color caused scheme by non-spherical in this cross-section has been changed and it has been cooling and fragmentation. This and all the other without cross-section the velocity 10 images 29 vectors, in this paper have been generated using SPLASH (Price 2007). Run04 Run05 in order to show the small-scale features clearly. Run01 Run06 Run02 Gas Accretion onto a Supermassive Black Hole: 10 29 Mass Inflow Rate into r in (g / s) 10 28 a step to modeling AGN feedback in cosmological simulations 10 27 Mass Inflow Rate into r in (g / s) 10 26 10 29 10 28 0.0 0.2 0.4 0.6 0.8 1.0 1.2 time (10 4 yr) 10 Collaborators: 27 10 26 Mass Inflow Rate into r in (g / s) 10 28 10 27 Ken 10 26 Nagamine 0.0 0.5 1.0 1.5 2.0 2.5 3.0 time (10 4 yr) Univ. of Nevada, 10 Las Vegas (UNLV) 29 Run07 0 1 2 3 4 5 6 time (10 4 yr) Mass Inflow Rate into r in (g / s) 10 28 Run08 Run03 10 Paramita 27 Barai (UNLV / INAF Trieste) 10 26 0 2 4 6 8 10 12 Daniel 14 Proga (UNLV) Figure 3. Mass inflow rate at the inner boundary as a function of time for the first eight runs in Table 1. Each panel hasc a different 0000 RAS, outermnras 000, 000 000 radius: r out =5(top-left),10(top-right),20(bottom-left),50pc(bottom-right), as the time coverage becomes longer. The top-right panel shows different particle numbers: N =64 3 (Run 05) and c 0000 128 3 (Run RAS, 06) MNRAS for the Bondi 000, IC. 000 000 In addition, the top row and bottom-right panels show the results of the Bondi IC (Runs 04, 05, 06, 08), together with the uniform IC runs (Runs 01, 02, 03). The Bondi mass accretion rate (marked as the dash-dot-dot-dot horizontal line in each panel) is reproduced for a limited time duration. time (10 4 yr)
Outline Intro / Motivation The simplest case: spherical Bondi accretion Include radiative cooling / heating -- radiative feedback by X-rays Barai, Proga, KN, 2011, MNRAS, in press (arxiv:1102.3925) Non-spherical accretion flow, fragmentation due to thermal instability Conclusions Barai, Proga, KN, 2011, in prep. (Paper II)
Motivation Small-scale sims Cosmological sims Gap (e.g. Ohsuga, Proga, ) (e.g. Di Matteo+, Booth & Schaye, ) Still a large gap btw small-scale sims & cosmological sims. ( pc) (~kpc - 10 Mpc) Cosmo sims uses ad-hoc AGN accretion models as sub-grid physics. How well can a cosmological SPH code (e.g. GADGET) handle accretion onto a SMBH?
The Bondi Accretion Problem Spherically symmetric accretion onto a central mass (Bondi 1952) Gas is at rest at infinity, with ρ & p. Increase in the central mass is ignored. Two equations are solved: Ṁ = 4πr 2 ρv =constant. ( ) v 2 γ 2 + p γ 1 ρ [ ( ρ ρ ) γ 1 1 ] (Continuity Eq.) = GM BH r, (Bernoulli s Eq.) One of the solutions: Ṁ B =4πλ c (GM BH ) 2 Characteristic scales: c 3 s, ( ) ρ, λ c = ( 1 2) (γ+1) ( ) 2(γ 1) 5 3γ (3γ 5) 2(γ 1). 4 R B = GM ( BH 5 3γ Bondi radius:. Sonic radius: c 2 R s = s, 4 ) R B. Bondi time: t B = R B c s = GM BH c 3 s,.
Simplest Case: Spherical Bondi Accretion Flow onto a SMBH GADGET-3: 3-d cosmological SPH/ N-body code (Springel 05) Central SMBH 10 8 M represented by a pseudo- Newtonian Paczynsky & Wiita (1980) potential rout=5-20 pc, Nptcl=64 3-128 3 Set IC to uniform/spherical Bondi flow w/ γ=1.01, ρ =10-19 g/cm 3, T =10 7 K, Tinit=T Corresponding Bondi solution: RB=3pc, Rsonic=1.5pc, tb=7.9e3yr 3-d spherical volume, vacuum boundary condition Run r out N b IC M tot,ic c M part d t end e No. [pc] [M ] [M ] [10 4 yr] 1 5 64 3 Uniform i 3.96 10 5 1.51 3 2 10 64 3 Uniform 6.19 10 6 23.61 7.2 3 50 128 3 Uniform 7.73 10 8 368.60 20 4 5 64 3 Bondi j 1.81 10 6 6.89 2 5 10 64 3 Bondi 9.76 10 6 37.23 8 6 10 128 3 Bondi 9.76 10 6 4.65 8 7 20 128 3 Bondi 6.24 10 7 29.75 8 7a k 20 128 3 Bondi 6.24 10 7 29.75 80 7b l 20 128 3 Bondi 6.24 10 7 29.75 100 8 50 128 3 Bondi 8.48 10 8 404.35 16 9 20 128 3 ρ B,v init =0 6.24 10 7 29.75 8 10 20 128 3 Uniform 4.95 10 7 23.60 8 11 20 128 3 Hernquist m 6.24 10 7 29.75 7.2 12 n 20 128 3 Bondi 6.24 10 7 29.75 8 All runs: rin=0.1pc, γ=1.01
Example: Properties of Particles 1000 10 8 Run 7: rout=20 pc, Nptcl=128 3 Snap at t=2tb=1.6e4 yr Follows the Bondi solution (red curve) well except the very inner part Inner part: supersonic (M~6), outerpart: subsonic Mach = v / c s v r (km/s) a = sqrt(a x 2 + ay 2 + az 2 ) 0-1000 -2000-3000 10.00 1.00 0.10 0.01 10 8 10 7 10 6 10 5 10 4 10 3 v B 0.1 1.0 10.0 Mach # Radial Vel Rs~1.5 pc 0.1 1.0 10.0 Acceleration 0.1 1.0 10.0 T ( o K)! (g/cm 3 ) h Smoothing (pc) 10 7 10 6 10-16 10-17 10-18 10-19 10-20 1.0 0.1 0.1 1.0 10.0! B Temperature almost isothermal ( γ=1.01) Density 0.1 1.0 10.0 Smoothing Length hmin~0.15 pc 0.1 1.0 10.0
. Mass Inflow Rates at rin 10 26 the larger rout, the longer duration of Bondi inflow rate If started from a Bondi flow, Bondi rate is achieved quickly. After a while, the inflow rate decreases due to the artificial outflow at the outer boundary. Greater sim. volume reduces this effect on mass inflow. Mass Inflow Mass Inflow Rate into r in (g / s) 10 10 29 10 28 10 27 10 26 0.0 0.2 0.4 0.6 0.8 1.0 1.2 time (10 4 yr) Run07 rout=20 pc Bondi rate 0 1 2 3 4 5 6 time (10 4 yr) Figure 3. Mass inflow rate at the inner boundary as a function of time reproducing Bondi rate well. radius: r out =5(top-left),10(top-right),20(bottom-left),50pc(bot due to outflow problem at panel shows different particle numbers: N =64 3 (Run outer 05) BC and 128 3 (Ru panels show the results of the Bondi IC (Runs 04, 05, 06, 08), togethe accretion rate (marked as the dash-dot-dot-dot horizontal line in each p
Radiative Heating & Cooling Xray emitting corona irradiates the accretion flow L X = f X L Edd, L Edd = 4πcGm pm BH, Flux: F X = L X σ e 4πr. 2 Approx. analytic heating/cooling rates from Blondin 94; opt-thin gas illuminated by a 10 kev bremsstrahlung. net rate: ρl = n 2 (G Compton + G X L b,l ) [erg cm 3 s 1 ], Compton h/c rate: Net Xray photoioniz. heating and recomb. cooling rate: Brems. and line cooling rate: (Opt-thin: δ=1) G Compton =8.9 10 36 ξ (T X 4T ) [ergcm 3 s 1 ]. ( ) G X =1.5 10 21 ξ 1/4 T 1/2 1 T [erg cm 3 s 1 ]. T X L b,l = 3.3 10 27 T 1/2 + [ 1.7 10 18 exp ( 1.3 10 5 /T ) ξ 1 T 1/2 +10 24] δ [erg cm 3 s 1 ]. TX=1.16x10 8 K (=10keV, Blondin 94)
Runs with radiative cooling/heating Table 2. Simulations of Spherical Accretion with Radiative Heating and Co Run r out N M tot,ic M part γ init T R B ρ T init L X t end No. [pc] [M ] [M ] [K] [pc] [g/cm 3 ] [L Edd ] [10 5 yr] 13 20 128 3 5.81 10 5 0.277 1.4 10 7 2.19 10 21 T 0.5 1.0 14 50 128 3 8.23 10 6 3.92 1.4 10 7 2.19 10 21 T 0.5 2.9 15 20 128 3 5.81 10 1 2.77 10 7 1.4 10 7 2.19 10 27 T 0.5 1.0 16 20 256 3 5.81 10 1 3.46 10 8 1.4 10 7 2.19 10 27 T 5 10 4 1.9 17 20 128 3 5.81 10 5 0.277 1.4 10 7 2.19 10 21 b T rad 5 10 4 2.9 18 20 128 3 5.65 10 5 0.269 5/3 10 7 1.84 10 21 T rad 5 10 4 3.0 19 20 128 3 1.47 10 7 7.0 5/3 10 5 183.9 10 21 T rad 5 10 4 1.5 20 200 256 3 1.33 10 9 79.09 5/3 10 5 183.9 10 21 T rad 5 10 4 6.5 21 200 256 3 4.95 10 8 29.50 5/3 10 7 1.84 10 21 T rad 5 10 4 8.7 22 200 128 3 1.33 10 7 6.33 5/3 10 5 183.9 10 23 T rad 5 10 4 70 23 200 256 3 1.33 10 7 0.791 5/3 10 5 183.9 10 23 T rad 5 10 4 20 24 c 200 1.24 10 7 9.77 10 6 0.791 5/3 10 5 183.9 10 23 T Run23 5 10 5 19 25 200 1.24 10 7 9.77 10 6 0.791 5/3 10 5 183.9 10 23 T Run23 5 10 3 21 26 200 1.24 10 7 9.77 10 6 0.791 5/3 10 5 183.9 10 23 T Run23 1 10 2 22 27 200 1.24 10 7 9.77 10 6 0.791 5/3 10 5 183.9 10 23 T Run23 2 10 2 25 28 200 1.24 10 7 9.77 10 6 0.791 5/3 10 5 183.9 10 23 T Run23 5 10 2 50
Ptcl properties w/ radiative heating & cooling Representative run: M in Rate (r in ) (g / s) red: free-fall scaling blue: ZEUS-2d result Near the inner radius, excess heating by artificial viscosity is seen. Inflow rate is enhanced above Bondi rate, due to lower gas temp: T(rout) <10 5 K, T =10 5 K 10 26 10 25 Run23 0 50 100 150 200 time (10 4 yr) v r (km/s) T ( o K) 0-500 -1000-1500 -2000 v ff v ZEUS -2500 0.1 1.0 10.0 100.0 10 8 10 7 10 6 10 5 10 4 Run #23: t=1myr, LX=5e-4LEdd, γ=5/3 T ZEUS T ff,a 0.1 1.0 10.0 100.0 rout=200pc, 256 3 ptcls T ff,ar (g/cm 3 ) Mach = v / c s 10-18 10-19 10-20 10-21 10-22 10-23 100.0 10.0 1.0 0.1 ZEUS 0.1 1.0 10.0 100.0 0.1 1.0 10.0 100.0 green: free-fall scaling w/ only adiabatic term ff Mach ff,ar Tff,ar: solving internal energy eq. w/ both radiative & adiabatic term
Impact of varying Lx on inflow rates Restart Run #23 at t=1.4 Myr, Lx/LEdd=5e-4 orig. Runs 24-28: increase Lx Dramatic decrease in Ṁ in at Lx/LEdd>0.01 --- transition from net inflow to net outflow M in Rate (r in ) (g / s) 10 26 10 25 10 24 10 23 10 22 Run24 Run23 Run25 Run26 Run27 Run28 Lx/LEdd 5e-5 5e-4 5e-3 0.01 0.02 0.05 0.0 0.5 1.0 1.5 2.0 2.5 time (Myr) net outflow; non-spherical fragmentation observed. Thermal instability due to rad. feedback
Non-spherical outflow: Run 26: rout=200pc, Lx/LEdd=0.01 due to rad. feedback Temperature Density inner ±40pc inner ±4pc
Ptcl Properties: impact of rad feedback Run 26: rout=200pc, Lx/LEdd=0.01, t=2.0 Myr Density Large scatter due to thermal instability --- cold inflow and hot outflow Radial Vel Temperature Mach # Cold component Photoionization parameter: ξ 4πF X n = L X r 2 n, Photoi. param inner region Radiative equil. outer region Outflowing gas near outer BC
Time Evolution of a Single Ptcl Run 26: rout=200pc, Lx/LEdd=0.01, t=2.0 Myr Start (triangle): r=53 pc, t=1.4 Myr Velocity (km / s) 0-200 -400-600 v! v " v r v ff ~ r -0.5 0.1 1.0 10.0 100.0 # (g/cm 3 ) 10-20 10-21 10-22 # ff ~ r -1.5 0.1 1.0 10.0 100.0 End (square): r=1pc, t=1.8 Myr + symbol: dt=0.004 Myr T ( o K) 10 6 10 5 10 4 T ff,a ~ r -1 0.1 1.0 10.0 100.0 Entropy = P / # $ (cgs) 10 28 10 27 10 26 0.1 1.0 10.0 100.0 10 6 T rad 10 6 T rad T ( o K) 10 5 T ( o K) 10 5 10 4 10 100 1000 % (erg cm / s) 10 4 1 10 100 &
Non-spherical outflow: Run 27: rout=200pc, Lx/LEdd=0.02 due to rad. feedback Temperature Density ± 200pc inner ±60pc
Ptcl Properties: impact of rad feedback Run 27: rout=200pc, Lx/LEdd=0.02 Density Radial Vel Mach # Temperature Photoi. param inner region outer region
Non-spherical outflow: Run 28: rout=200pc, Lx/LEdd=0.05 due to rad. feedback Temperature Density ± 200pc
Run 28 log ρgas rout=200pc, Lx/LEdd=0.05 log T t=1.8 Myr t=3.0 Myr Figure 8. Time evolution of gas in Run 28 (L X /L Edd =0.05) showing the whole computational volume 200 pc of the [y z] plane
Conclusions GADGET-3 SPH code can reproduce the spherical Bondi accretion rate properly, but with some limitations. spurious heating by Artificial Viscosity near r in & artificial outflow at rout due to outer BC are problems for SPH. non-spherical in/outflow develops due to rad. feedback via thermal instability, even in the simplest situation that we studied --- connection with NLR? (Paper II) Future work: include rad. pressure, rotation, diff geometry, comparison w/ NLR obs, connect with cosmological sim
Run 26: rout=200pc, Lx/LEdd=0.01 ± 30 pc range (t = 2.047 Myr) colder, denser filament-like structures due to non-spherical fragmentation Figure 1. Cross-sections in Run 26 (L X /L Edd =0.01) showing the inner 30 pc of the [x y] planethroughz =0atatimet =2.047 Myr. The gas density is in the top-left panel, temperature in the top-right, photoionization parameter in the bottom-left, and Mach number in the bottom-right, overplotted with the velocity vector arrows. It shows colder, denser filament-like structures, with hotter, less-dense Sunday, November gas in between, 13, 2011 both components accreting in (with the colder phase moving in faster), all of which has been caused by non-spherical
Run 26: rout=200pc, Lx/LEdd=0.01 Zoom-in: inner 4 pc Figure 2. Zoom-in of the inner 4 pc of the [x y] planethroughz =0atatimet =2.047 Myr in Run 26 (L X /L Edd =0.01). The panels represent gas density in the top-left, temperature in the top-right, photoionization parameter in the bottom-left, and Machnumberin
Run 27 log ρgas log T rout=200pc, Lx/LEdd=0.02 t=1.86 Myr t=2.12 Myr t=2.46 Myr