Calculation Framework of X-ray Radiation based on Monte Carlo Simulations MONACO MONte Carlo simulation for Astrophysics and COsmology Hirokazu Odaka (ISAS/JAXA) Shin Watanabe, Yasuyuki Tanaka, Dmitry Khangulyan, Tadayuki Takahashi (ISAS/JAXA), Masao Sako (Penn), Felix Aharonian (Dublin Institute for Advanced Studies) The X-ray Universe 2011 June 26-30, 2011 at Berlin Acknowledgement Spectral modeling of accretion-powered pulsars Kazuo Makishima Polarization calculation Paolo Coppi Cross section data of scattering by helium atom Eugine Churazov • • Wide-band,low background (2005-)Suzaku Doppler broadening/shift Line intensity, E/ High-resolutiongrating spectrometer Chandra(1999-) XMM-Newton, havebrought high-quality datacontaining detailedphysical information Δ X- E~100-1000for point sources Modern X-ray Observations X-ray Modern AGN outflow NGC 1068 NASA ← Spectrum Image Chandra → Hard X-ray information withhigh S/N 4 Evans et al. → Counts s−1 Å−1 Counts s−1 Å−1 Counts s−1 Å−1 02×10 −3 4×10 −3 05×10 −3 0.01 0 0.01 0.02 Fe K Fe 20 21 22 2311 24 12 25 13 26 14 27 15 28 16 17 18 19 N VII γ 2 3 4 5 6 7 8 9 10 Ne IX γ α Ne IX β Fe XXII N VII β Ne X α r O VII O i Fe XX f Ne IX r i f O VIII RRC O Wavelength (Å) Wavelength SI Kα Si XIII 3p–1s Si XIV O VIII γ α r O VIII O Si XIII NVII α f Si K Evans+(2009) β α RRC VII O Mg XI β Fe XVII O VII δ Mg XII α O VII γ Mg XI r i f NVII RRC O VII β O VIII O α Ne X β N VII δ Ne IX RRC Figure 2. Co-added Chandra HETG MEG and HEG gratings spectrum of NGC 1068 from the entire 440-ks data set. Shown are the principal transitions from H- and He-like species, together with RRCs. Radiative Transfer Interpretation of such high-quality data requires more precise astrophysical models. We have to solve a problem of radiative transfer. τ 1 τ 1 τ 1 ∼ Optically thin Optically thick Reprocessing of X-ray photons It is necessary to treat Statistical approach discrete processes of photons, • continuous approximation competing processes, • diffusion approximation easy multiple interactions. • →differential equation Moreover, it depends on geometry. Black body if very thick e.g. standard accretion disk optical thickness Monte Carlo approach Monte Carlo Simulation Tracking photons by calculating their Process of one event: propagation and interactions based 1) generate a photon, record on Monte Carlo method initial conditions to an observer emission (escaping) the last interaction 2) calculate the next (E1, Ω1,t1, x1) interaction point 3) invoke the interaction, reprocess photons 4) repeat 2-3 5) record the last interaction X-ray source initial condition information if a photon cloud (E0, Ω0,t0, x0) escapes from the system. A MC simulation generates a list of events containing a response of the system. Convolution of this event list with the initial conditions produces the final spectrum/image. (similar to methods of Greenʼs function) Odaka+ (2011) The MONACO Framework MC Simulation •Geometry Geometry building (Geant4) •Physical conditions of matter Particle tracking (Geant4) Physical processes (original) •Initial conditions of photons Output event list for simulation •Initial conditions of photons Analysis (Convolution) (Source function) Observation (Imaging/spectroscopy) •Observerʼs direction •Time of observation Observed spectra/Images •Distance of the source • Building geometry and tracking particles: Geant4 toolkit library ←Sophisticated treatment of complicated geometry (e.g. radiation detector simulation) • Physical processes: original implementation ←Existing codes have been inadequate to treat binding effects of atoms and gas motion (Doppler effect of thermal/bulk/micro-turbulent motions). We also extend the Geant4 geometry builder for astrophysical objects. Physical Processes MONACO has extensible structure; you can (easily) add new physical processes. We have implemented: State of matter Processes Applications Accretion flows Hot plasma (Inverse) Compton scattering Hot coronae around compact objects Stellar winds in X-ray Photoionized Photoionization binaries plasma Photoexciation AGN outflows X-ray reflection nebulae Photoabsorption Neutral matter (molecular clouds) Scattering by bound electrons AGN tori Comptonization in Accretion Flow optically thick Analytical/numerical methods are effective. not optically thick The process is essentially discrete. complicated geometry →Monte Carlo approach is suitable. high energy band supersonic Using Lorentz transformation flow Lab Bulk motionʼs Target electronʼs frame frame frame •determine the •select the target •calculate scattering next interaction electron by a rest electron X-ray point •see the thermal •see the bulk motion X-ray subsonic motion flow µ µ µ p p p magnetic pole Lorentz Lorentz neutron star transformation transformation µ µ µ Thermal & bulk Comptonization p1 p1 p1 Becker & Wolff (2007) Magnetic field effects can be included. Comptonized Spectrum Pure thermal Comptonization 1 ✓ Spherical cloud of different Thomson 10-1 ] depths -1 ✓ Temperature: 6.4 keV 10-2 [keV keV i ✓ Seed: monochromatic 0.64 keV F 10-3 ✓ For large τ, the spectrum agrees with the theoretical spectrum of saturated 10-4 Comptonization. 10-2 10-1 1 10 102 Energy [keV] 3 Accretion Column Model 1 ✓ Assuming Vela X-1’s column 10-1 ✓ Temperature: 6 keV -1 10-2 ✓ Seed: thermal bremsstrahlung keV -2 cm -3 ✓ Column radius: 200 m -1 10 ✓ Magnetic field effect included approximately 10-4 photons s ✓ Successfully generated a power law with a 10-5 quasi-exponential cutoff. Odaka et al. in prep. & Suzaku conference 10-6 2 3 4 5 6 7 8 9 10 20 30 40 50 60 Energy [keV] poster in July at Stanford. Photoionized Plasma Stellar wind in an HMXB is the B-type star best laboratory to study photoionized plasmas. Neutron Star Radiation from a photoionized plasma can be regarded as reprocessed emissions from illuminated matter. →MC simulation is suitable. Our MC simulation successfully reproduced Vela X-1 spectrum for lines of H, He-like ions (Watanabe+ 2006). We recently extended this code to L-shell ions (Li-, Be-...like). Vela X-1 (orbital phase = 0.5) 4 turbulent velocity: 0 km s-1 Chandra HETG 300 3.5 Be-like Simulation 250 3 Fe B-like 2.5 200 C-like 2 150 N-like 1.5 100 O-like 1 0.5 50 0 0 0 2 4 6 8 10 1.7 1.72 1.74 1.76 1.78 1.8 1.82 1.84 1.86 1.88 1.9 Energy [keV] He-like triplet f+Li-like turbulent velocity: 100 km s-1 4 300 Turbulence suppresses Auger-resonance 3.5 H-like 250 3 destruction. 200 2.5 i r 150 2 L-ions 1.5 100 1 50 0.5 0 0 1.7 1.72 1.74 1.76 1.78 1.8 1.82 1.84 1.86 1.88 1.9 1.7 1.75 1.8 1.85 1.9 1.95 2 2.05 2.1 Energy [keV] First attempt to reproduce Si-K complex of Monte Carlo simulation is a powerful tool Vela X-1 spectrum obtained by Chandra. to simulate effects of turbulence on a line Model parameters are not optimized yet. spectrum. X-ray Reflection Nebula Giant molecular cloud Sgr B2 has been reflecting a past outburst of SMBH Sgr A*, displaying strong Fe fluorescence at 6.4 keV. It shows strong time variability over a few year scale. Koyama+ (2008) Such objects are good probes of molecular clouds themselves and the black hole activity. We have to consider multiple scatterings and structure of the cloud. → Monte Carlo simulation cloud. Table 8.1 shows parameters of our cloud models in the simulation. We prepared 5 four models of different n0 values corresponding to total cloud masses from 2.5 10 M × ! to 2 106M (Models 1–4). In Models 1–4, the power-law index α = 1 was assumed, as × " radio observations have reported values of 2 (Lis & Goldsmith, 1990) or 0.87 (de Vicente et al., 1997). To investigate effects of different density profiles, we built a model with α = 0 (Model 5) and a model with α = 2 (Model 6), fixing the total mass to 5 105M . × ! While we assumed a metal abundance of 1.5 protosolar value in Models 1–6 as a standard value in the GC region (Nobukawa et al., 2010), we additionally checked two models of different values of 1.0 protosolar (Model 7) and 2.0 protosolar (Model 8). We ignored the third component surrounding the dense envelope to reduce computation costs; instead we introduced absorption of the initial spectrum by the third component as γ F (E) exp( N σ (E))E− (1 keV <E<400 keV), (8.2) ∝ − H abs 22 2 where N =6 10 cm− is an equivalent hydrogen column density of the surrounding H × diffuse component, and σabs(E) is the photoelectric absorption cross section at energy E per hydrogen. The photon index γ of the initial spectrum is 1.8, which is consistent with flares of Sgr A* or X-rayDiagnostics emission from Seyfert galaxies. of Molecular Clouds 89;>&:?&@90%$&'". Odaka+ (2011) '53446&7344. Parameters: !)ABC • line-of-sight position of the cloud '53446&4. /0#&12 0"8"-$9-&8:;09$<=>&'!. • mass !)D4C !"#$%& Sgr A* • density profile 344&,- 100 pc • chemical composition '53446&5344. !)3EBC Imaging results show very different between the iron line and hard X-rays. !"#$%&'()*&+,-.Earth 5*67$.089$1234 ()*+$,'*)-$./#'0#$1234 Figure 8.1: Geometrical setup of the simulation. We assumed three different positions of :;0$-* Iron :0"$-*line (6.4:00$-* keV) ::"$-* :;0$-*Hard X-rays:0"$-* (20-60:00$-* keV)::"$-* the Sgr B2 cloud, fixing the projected distance from Sgr A* to 100 pc.