Calculation Frameworkof X-ray Radiation basedon Monte Carlo SimulationsMONACOMONte 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 2011June 26-30, 2011 at Berlin

Acknowledgement

Spectral modeling of accretion-powered pulsarsKazuo Makishima

Polarization calculationPaolo Coppi

Cross section data of scattering by helium atomEugine Churazov

• XMM-Newton, Chandra (1999-)High-resolution grating spectrometer E/ΔE~100-1000 for point sourcesLine intensity, Doppler broadening/shift

• Suzaku (2005-)Wide-band, low background → Hard X-ray information with high S/N

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Modern X-ray Observationshave brought high-quality data containing detailed physical information

Evans+ (2009)

NASA

NGC 1068AGN outflow

Chandra←Image

Spectrum→

Radiative TransferInterpretation of such high-quality data requires more precise astrophysical models. We have to solve a problem of radiative transfer.

optical thickness

Optically thickOptically thin

easy

Statistical approachcontinuous approximation

diffusion approximation→differential equation

Reprocessing of X-ray photonsIt is necessary to treat• discrete processes of photons,• competing processes,• multiple interactions.

Moreover, it depends on geometry.

Black body if very thicke.g. standard accretion disk

Monte Carlo approach

τ � 1 τ � 1τ ∼ 1

Monte Carlo Simulation

(E1,!1, t1,x1)

(E0,!0, t0,x0)

X-ray sourceinitial condition

emissionthe last interaction

to an observer(escaping)

cloud

Tracking photons by calculating their propagation and interactions based on Monte Carlo method

Process of one event:1) generate a photon, record initial conditions2) calculate the next interaction point3) invoke the interaction, reprocess photons4) repeat 2-35) record the last interaction information if a photon 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

• Initial conditions of photons (Source function)

•Observerʼs direction

•Time of observation

•Distance of the source

MC SimulationGeometry building (Geant4)Particle tracking (Geant4)

Physical processes (original)

Analysis (Convolution)Observation (Imaging/spectroscopy)

Output event list

Observed spectra/Images

• Initial conditions of photons for simulation

•Geometry

•Physical conditions of matter

• 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 ProcessesMONACO has extensible structure;you can (easily) add new physical processes.We have implemented:

State of matter Processes Applications

Hot plasma (Inverse) Compton scatteringAccretion flows

Hot coronaearound compact objects

Photoionized plasma

PhotoionizationPhotoexciation

Stellar winds in X-ray binaries

AGN outflows

Neutral matter PhotoabsorptionScattering by bound electrons

X-ray reflection nebulae (molecular clouds)

AGN tori

Comptonization in Accretion Flow

Lab frame

Bulk motionʼsframe

Target electronʼs frame

•determine the next interaction point

•see the bulk motion

•select the target electron

•see the thermal motion

Lorentz transformation

•calculate scattering by a rest electron

pµ

Using Lorentz transformation

p�µ p��µ

p��µ1p�µ

1pµ1

Lorentz transformation

supersonicflow

subsonicflow

neutron star magnetic pole

X-rayX-ray

Thermal & bulk ComptonizationBecker & Wolff (2007)

optically thick Analytical/numerical methods are effective.

not optically thickcomplicated geometry

high energy bandThe process is essentially discrete.→Monte Carlo approach is suitable.

Magnetic field effects can be included.

Comptonized Spectrum

Energy [keV]-210 -110 1 10 210

]-1

[keV

keV

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Energy [keV]2 3 4 5 6 7 8 9 10 20 30 40 50 60

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33

Pure thermal Comptonization✓ Spherical cloud of different Thomson

depths✓ Temperature: 6.4 keV✓ Seed: monochromatic 0.64 keV✓ For large τ, the spectrum agrees with

the theoretical spectrum of saturated Comptonization.

Accretion Column Model✓ Assuming Vela X-1’s column✓ Temperature: 6 keV✓ Seed: thermal bremsstrahlung✓ Column radius: 200 m✓ Magnetic field effect included approximately✓ Successfully generated a power law with a

quasi-exponential cutoff.Odaka et al. in prep. & Suzaku conference poster in July at Stanford.

Photoionized Plasma

Stellar wind in an HMXB is thebest laboratory to study photoionized plasmas.

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).

B-type star

Neutron Star

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Energy [keV]1.7 1.72 1.74 1.76 1.78 1.8 1.82 1.84 1.86 1.88 1.90

50

100

150

200

250

300

Energy [keV]1.7 1.72 1.74 1.76 1.78 1.8 1.82 1.84 1.86 1.88 1.90

50

100

150

200

250

300

turbulent velocity: 0 km s-1

turbulent velocity: 100 km s-1

Be-likeB-likeC-likeN-likeO-like

Monte Carlo simulation is a powerful tool to simulate effects of turbulence on a line spectrum.

First attempt to reproduce Si-K complex of Vela X-1 spectrum obtained by Chandra.Model parameters are not optimized yet.

Turbulence suppresses Auger-resonance destruction.

Vela X-1 (orbital phase = 0.5)Chandra HETG

Simulation

X-ray Reflection Nebula

Giant molecular cloud Sgr B2 hasbeen reflecting a past outburstof SMBH Sgr A*, displaying strongFe fluorescence at 6.4 keV.It shows strong time variabilityover a few year scale.

Such objects are good probesof molecular clouds themselves and the black hole activity.

We have to consider multiple scatterings and structure of the cloud. → Monte Carlo simulation

Koyama+ (2008)

Diagnostics of Molecular Clouds

cloud. Table 8.1 shows parameters of our cloud models in the simulation. We prepared

four models of di!erent n0 values corresponding to total cloud masses from 2.5! 105M!

to 2! 106M" (Models 1–4). In Models 1–4, the power-law index ! = 1 was assumed, as

radio observations have reported values of 2 (Lis & Goldsmith, 1990) or 0.87 (de Vicente

et al., 1997). To investigate e!ects of di!erent density profiles, we built a model with

! = 0 (Model 5) and a model with ! = 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

di!erent 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

F (E) # exp($NH"abs(E))E"! (1 keV < E < 400 keV), (8.2)

where NH = 6 ! 1022 cm"2 is an equivalent hydrogen column density of the surrounding

di!use component, and "abs(E) is the photoelectric absorption cross section at energy E

per hydrogen. The photon index # of the initial spectrum is 1.8, which is consistent with

flares of Sgr A* or X-ray emission from Seyfert galaxies.

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Figure 8.1: Geometrical setup of the simulation. We assumed three di!erent positions ofthe Sgr B2 cloud, fixing the projected distance from Sgr A* to 100 pc.

129

Parameters:• line-of-sight position of the cloud• mass • density profile• chemical compositionImaging results show very different between the iron line and hard X-rays.

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Figure 8.4: Time evolution of the morphology of the iron line (left panels) and the hardX-ray (right panels) for Model 2 from the brightest moment at intervals of five years.The observation time is marked at the top of each image and the cloud position alongthe line of sight is marked at the left of each row. The colors are mapped on a linearscale common to all the images of the same energy band.

In order to evaluate the spectra quantitatively, we extracted the hard-X-ray flux (20–

60 keV), the iron line flux, the equivalent width of the iron line, and the shoulder-to-peak

ratio of the Compton shoulder as a function of time. The iron line was divided into

a peak and a shoulder. The peak flux and shoulder flux are integrated over energy

ranges between 6.0 keV and 6.38 keV, and 6.38 keV and 6.42 keV, respectively. A

continuum is evaluated by fitting to a power law over a range between 5.5 keV and 6.8

keV without several fluorescent line energies, and is then subtracted from both the fluxes.

The equivalent width and the shoulder-to-peak ratio were calculated by these values thus

obtained.

Figure 8.6 shows the spectral parameters as a function of time elapsed since the end of

the Sgr A* flare. After t = 303 yr, the hard-X-ray and iron line fluxes gradually decrease

while the equivalent width and shoulder-to-peak ratio increase with time. Although the

iron line flux is almost independent of the cloud mass in the brightest phase, its decay

speed depends on the mass because of absorption. The equivalent width of the iron

line keeps constant and does not depend on the cloud mass when the whole cloud is

illuminated. In the fading phase, however, its variation significantly depends on the

mass; it shows rapid increase in the dense clouds. One reason for this is a di!erence

of photoelectric absorption probability (Sunyaev & Churazov, 1998). In a dense cloud,

continuum photons around 6 keV are largely absorbed but hard X-rays of about 10 keV

133

2000 2005 2010 2015 2000 2005 2010 2015

Odaka+ (2011)

Sgr A*

Earth

100 pc

Iron line (6.4 keV) Hard X-rays (20-60 keV)behind+100 pc

center0 pc

before-100 pc

ASTRO-H Observatory

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Scheduled for launch in 2014 Micro-calorimeterEnergy res. ΔE = 5 eV at 6 keVHard X-ray mirror + imagerImaging spectroscopy up to 80 keV

Energy [keV]5 6 7 8

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ts s

-310

-210

-110

1

X-ray reflection from Sgr B2 (200 ks simulation)

Compton

High S/N data obtained by ASTRO-H will open high-precision physics experiments at cosmic laboratories.Our MC framework based on accurate treatment of X-ray radiative transfer enables evaluation of systematic errors due to astrophysical objects.

SuzakuASTRO-H SXS

Suzaku CCD

Large effective area = Good statistics

Imaging Polarimetry

-100 -50 0 50 100310×

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a photon index of 1.5 in an energy range between 0.3 keV and 30 keV.

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Fig. 1.— Geometrical setup of the clumpy wind in the LS 5039 system for the volume filling factorf = 0.03 and the clump size coe!cient a = 0.05. The two figures have the same model parametersbut di"erent random seeds for position determination of clumps. The grey circle at the centerrepresents the O-type star and the three red squares show the di"erent positions of the X-rayemitter. Only wind clumps which intersect with a region of !2" 1011 cm < z < +2" 1011 cm aredrawn as black circles to avoid filling up.

3. Results

We extracted spectra from the simulation outputs for each wind model and each position ofthe X-ray emitter. Figure 2 shows an example of the spectra obtained by the simulation. Since anobserved spectrum is attenuated by interstellar medium (ISM) absorption, we applied the e"ect tothe simulation results by multiplying exp(!NH,ISM!abs(E)), where NH,ISM = 7 " 1021 cm!2 is anequivalent hydrogen column density of the ISM and !abs(E) is a photo-absorption cross section. Wefitted these spectra including the ISM absorption e"ect to a single power law attenuated by photo-absorption, i.e. f(E) = A exp(!NH,total!abs(E))E!! , which well agrees with X-ray observationsof LS 5039 (Bosch-Ramon et al. 2007; Takahashi et al. 2009). In the fitting, the photon index" and the normalization A are fixed to the values of the initial spectrum. Thus, the equivalenthydrogen column density NH,total is an only free parameter. To evaluate the e"ective column densityoriginating from the wind absorption, we used NH,wind = NH,total ! NH,ISM for each wind model.The NH,wind values were averaged over all the 24 simulations which have the same wind parameter,and their standard deviation was adopted as an estimate of their uncertainties.

Simple model of clumpy stellar wind

Summary of MONACO

We have been developing a new calculation framework of X-ray radiation based on Monte Carlo method.

It is multi-purpose, easy to use, and extensible.

This MC framework will enable us to interpret high S/N data obtained by modern/future X-ray observatories.

We are going to prepare to open it to the public.