After a rapid introduction about the models of comptonization, we present
some simulations that underlines the expected capabilities of Simbol-X to
constrain the presence of this process in objects like AGNs or XRB.Comment: 5 pages, 6 figures, invited talk at 'Simbol-X: the hard X-ray
  universe in focus', Bologna (Italy), 14-16 May, 2007. To appear in Memorie
  della SAI

Petrucci, Pierre-Olivier

English

arXiv

International audienceAfter a rapid introduction about the models of comptonization, we present some simulations that underlines the expected capabilities of Simbol-X to constrain the presence of this process in objects like AGNs or XR

Petrucci, P. O.

Hal - Université Grenoble Alpes

Models of comptonization.

HAL-INSU

5 pages, 6 figures, invited talk at 'Simbol-X: the hard X-ray universe in focus', Bologna (Italy), 14-16 May, 2007. To appear in Memorie della SAItAfter a rapid introduction about the models of comptonization, we present some simulations that underlines the expected capabilities of Simbol-X to constrain the presence of this process in objects like AGNs or XRB

Models of Comptonization

Models of ComptonizationPierre-Olivier PetrucciTo cite this version:Pierre-Olivier Petrucci. Models of Comptonization. 5 pages, 6 figures, invited talk at ’Simbol-X: the hard X-ray universe in focus’, Bologna (Italy).. 2008. <hal-00242665>HAL Id: hal-00242665https://hal.archives-ouvertes.fr/hal-00242665Submitted on 6 Feb 2008HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.hal-00242665, version 1 - 6 Feb 2008Mem. S.A.It. Vol. 75, 282c© SAIt 2004 Memorie dellaModels of ComptonizationP.O. PetrucciLaboratoire d’Astrophysique de Grenoble, UJF/CNRS, 414 rue de la Piscine, 38041Grenoble Cedex 9, FRANCEe-mail: pierre-olivier.petrucci@obs.ujf-grenoble.frAbstract. After a rapid introduction about the models of comptonization, we present somesimulations that underlines the expected capabilities of Simbol-X to constrain the presenceof this process in objects like AGNs or XRBKey words. Radiation mechanisms: general1. The Comptonization processThe Compton effect was diskovered by A.H.Compton in 1923 and corresponds to the gainor loss of energy of a photon when it interactswith matter (usually electrons). For an electronat rest, the photon loss of energy is of the order∆E = E′ − E≃ −E2mec2(1 − cos θ)where θ is the photon scattering angle (see Fig.1).For a on-stationnary electron part of the elec-tron energy can be taken away by the photons(i.e. ∆E > 0). This corresponds to the inverseCompton process.1.1. Thermal ComptonizationThermal comptonization corresponds to thecase where seed photons (the ”cold” phase) arecomptonized by a thermal plasma (the ”hot”phase) of electron. This thermal plasma is char-acterized by a temperature Te and an opticalSend offprint requests to: P. O. PetrucciFig. 1. A photon of energy E comes in from theleft, collides with a target (usually an electron)at rest, and a new photon of energy E’ emergesat an angle θ.depth τ. In this case, the mean relative en-ergy gain per collision ∆EEand the mean num-ber of scatterings can be easily computed (e.g.Petrucci: Models of Comptonization 2830.01 0.1 1 10 100 100010−1210−11Flux (Arbitrary Units)Energy (keV)0.01 0.1 1 10 100 100010−1210−11Flux (Arbitrary Units)Energy (keV)a) b)Fig. 2. a) Thermal comptonization spectra for the same plasma temperature and optical depth butdifferent geometry: blue: cylindrical, red: slab, black: spherical. b) We fix the plasma temperaturebut change its optical depth in order to have roughly the same spectral index in the 2-10 keV band.This exemplifies the ”geometrical” degeneracy of the thermal comptonization spectrum.(Rybicki & Lightman, 1979)):∆EE≃(4kTemec2)+ 16(kTemec2)2for E ≪ kTeandN ≃ (τ + τ2) (1)Then we define the Compton parametery =∆EEN. Large values of y means that theComptonization process is efficient and modi-fies noticeably the seed spectrum.1.1.1. Thermal ComptonizationspectrumWhile thermal comptonization spectra havebeen computed since more than two decades,important effects like the anisotropy of the softphoton field were precisely taken into accountin the beginning of the 90’s by the pioneeringworks of Haardt (1993); Stern et al. (1995) andPoutanen & Svensson (1996). These effectsappear far from being negligible. Noticeably,for a given set of plasma temperature and opti-cal depth, the spectral shape is significantly dif-ferent for different disk-corona geometries (cf.Fig. 2a) but also for different viewing angle,this last dependence being crucial for a cor-rect interpretation of X-ray spectra. These ef-fects underline the differences between realis-tic thermal comptonization spectra and the cut-off power law approximation generally used tomimic them. Moreover, the relation betweenthe photon index Γ and the plasma tempera-ture and optical depth can be strongly degener-ated (”spectral” degeneracy) , different couples(τ, Te) giving, for the same disk-corona geom-etry, the same Γ. A ”geometrical” degeneracyalso exists and is exemplifies in Fig. 2b wherethe same high energy spectrum is reproducedwith different set of parameters and with dif-ferent geometries. These degeneracies compli-cate the fitting procedure and high S/N dataover broad band energy intervals are requiredto break them.1.1.2. Radiative BalanceIn a disk-corona system, the Comptonizing re-gion and the source of soft photons are cou-pled, as the optically thick disk necessarily re-processes and reemits part of the Comptonizedflux as soft photons which are the seeds forComptonization. The system must then satisfyequilibrium energy balance equations, whichdepend on geometry and on the ratio of di-rect heating of the disk to that of the corona.284 Petrucci: Models of ComptonizationIn the limiting case of a ”passive” disk (i.e.non intrinsically radiative, it radiates what itabsorbs from the hot phase), the amplificationof the Comptonization process, determined bythe Compton parameter y, is fixed by geometryonly (Haardt & Maraschi, 1991; Stern et al.,1995). Therefore, if the corona is in energy bal-ance, the temperature and optical depth mustsatisfy a relation which can be computed fordifferent geometries of the disk+corona config-uration (cf. Fig. 3). It is then theoretically pos-sible to constrain the geometry of the systemand verify the selfconsistency of the model,provided that the plasma temperature and op-tical depth Te and τ are known with sufficientprecision.1.2. Non-thermal ComptonizationIn the case of non-thermal particles the energytransfert between the elctron and the photon isvery efficient. For an electron with a Lorentzfactor γ it is of the order:∆E ≃ γ2E (2)Consequently the comptonization of a mo-noenergetic seed photon field by a non-thermaldistribution of electrons n(γ) ∝ γ−s producesFig. 3. Different theoretical relationship, cor-responding to different disk-corona geometry,between the corona temperature and opticaldepth in the case of energy balance betweenthe hot and cold phases.a non-thermal spectrum F(ν) ∝ ν− s−12 (e.g.Rybicki & Lightman 1979).2. What can we expect withSIMBOL-X?The comptonization process play a role in allSIMBOL-X science cases,– AGNs (thermal comptonization in Seyfertgalaxies, non-thermal comptonization inBlazars)– X-ray binaries (thermal comptonization inthe hard state, non-thermal(?) comptoniza-tion in the Intermediate and Soft states)– X-ray background– Galaxy clusters– Supernovae remnants– GRBsWe detailed below some simulations of comp-tonization spectra showing the advances thatwe can expect with Simbol-X.Fig. 4. Contour plots τ-kTe for simulations ofdifferent exposures (red: 1ks, blue: 5 ks andblack: 50 ks). The simulated data correspondto a thermal comptonization spectrum withL2−10keV = 10−11 erg.s−1.cm−2, kTe = 250keV, τ = 0. Only the long exposure simulationenable to break the τ-kTe degeneracy charac-teristic of thermal comptonization spectra.Petrucci: Models of Comptonization 285Fig. 5. Left: 500 sec. simulated Simbol-X data of Cyg X-1 assuming L2−10keV = 10−9 erg.s−1.cm−2kTe = 100 keV, τ = 1.7 and R = 0.3. Right: the corresponding τ-kTe contour plot.2.1. Simu. N◦ 1: the case of a SeyfertgalaxyWe simulate the spectrum of a Seyfert galaxy(NGC 5548) with different exposure time as-suming L2−10keV = 10−11 erg.s−1.cm−2, kTe =250 keV, τ = 0.1 and R = 1. We assume aslab geometry. Then we fit the faked data withthe model used for the simulations. The corre-sponding contour plots τ-kTe are plotted in Fig.4. If, for small exposure time (1 ks, red contourplot) the contour is very elongated, this ”spec-tral” degeneracy is broken for exposures of afew tens of ks (see the black contours that cor-respond to 50 ks). However we underline thefact that the real data generally show the pres-ence of complex reflection/absorption featuresthat can strongly limit the data analysis and theprecise study of the underlying continuum.It is worth noting that a few tens of kscorresponds to the orbiting timescale at a fewSchwarzschild radii around a 108 solar massesblack hole. It means that it should be possiblewith Simbol-X to follow the time evolution ofthe temperature and optical deth of the coronaon a dynamical timescale. However simula-tions show that breaking the geometrical de-generacy will require very long (> 100 ks) ex-posure with Simbol-X.2.2. Simu. N◦2: the case of amicroquasarWe simulate the X-ray spectrum of the mi-croquasar Cyg X-1, with L2−10keV = 10−9erg.s−1.cm−2 kTe = 100 keV, τ = 1.7 andR = 0.3. Good constraints of the spectral pa-rameters can be obtained in a few hundred ofseconds (cf. Fig. 5).2.3. Simu. N◦3: the case of a blazarWe also simulate the X-ray spectrim of theblazar Mkn 421 (cf. Fig. 6). The spectrum isvery well determine in 1 ks ! But in orderto have constrains on the Synchrotron Self-Compton process multi-λ observations (radio,Optical, IR, X and γ) are needed.3. Conclusions– Simbol-X should bring strong constrainson comptonization spectra on dynamicaltime scale for AGNs, and on very shorttime scale in XrBs.– However this can be complicated by thepresence of complex absorption/emissionfeatures– The broadest energy range is neededand multi-wavelength observations are rec-ommended (CTA, GLAST, HERSCHEL,ALMA, LOWFAR, WSO-UV, ...).286 Petrucci: Models of ComptonizationFig. 6. Left: Typical Synchrotron Self-Compton spectrum of a blazar. Right: Simbol X simulationof the blazar Mkn 421 in 1ks.Acknowledgements. I am very grateful to theCEA/DSM/DAPNIA/SAp for its financial support.ReferencesHaardt, F. 1993, ApJ, 413, 680Haardt, F. & Maraschi, L. 1991, ApJ, 380, L51Poutanen, J. & Svensson, R. 1996, ApJ, 470,249Rybicki, G. B. & Lightman, A. P. 1979, in AWiley-Interscience Publication, New York:Wiley, 1979Stern, B. E., Poutanen, J., Svensson, R., Sikora,M., & Begelman, M. C. 1995, ApJ, 449,L13+

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