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Photoionized plasma analysis. Jelle Kaastra. Introduction. What is a photoionised plasma?. Plasma where apart from interaction with particles also interaction with photons occurs Photon spectrum needs to affect the particles (e.g. heating)

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## Photoionized plasma analysis

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**Photoionized plasma analysis**Jelle Kaastra**What is a photoionised plasma?**• Plasma where apart from interaction with particles also interaction with photons occurs • Photon spectrum needs to affect the particles (e.g. heating) • Thus, plasma with resonant scattering has photons involved but is not photoionised (although resonance scattering also occurs in photoionised plasmas)**It is all about the optical depth**• Optical depth τ = 0: collisional • Optical depth τ≠ 0 but not τ >> 1: classical photoionised plasma • Optical depth τ >>1: more atmosphere-like or stellar interior-like, not discussed here • Note: optical depth depends on photon energy – the above is rather crude**Examples of photoionised plasmas**• Accreting sources: • Galactic X-ray binaries • Active galactic nuclei • Tenuous gas (like some components of the ISM/IGM) • Nova shells**Feeding the monster**• Gas transported from 1020 to 1012 m scale • Disk forms due to viscosity / B-fields / loss angular momentum • Only few Msun/year reach black hole**Outflowsfrom the monster**• Notall gas reaches black hole • Outflowsthroughmagnetised jets, disk winds, outflowsfrom torus surrounding disk • Gives feedback tosurroundings, but howmuch?**Something to think about**• Most important line features: • O-lines (1s-np of O I – O VIII) • Fe UTA & other n = 1-2 transitions • Fe-K • Si lines (see e.g. NGC 3783) • Multiple absorption components • Blending with foreground galactic features (example: Mrk 509 O IV with Galactic O I) • Contamination by emission lines**Key parameter: ionisation parameter**• Spectrum depends on ratio photons / particles • Common used (Xstar, SPEX): ξ = L / nr2 with: • L = ionising luminosity between 1 – 1000 Ryd (13.6 eV – 13.6 keV; note the upper boundary!) • n is hydrogen density (NB, different from ne!) • r is distance from ionising source • Alternative (Cloudy): UH = QH / 4πcnr2 with: • QH number of H-ionising photons (13.6 Ryd – ∞)**Photoionisedplasmas**• Irradiated plasma • Twobalanceequations: Photons: Photo-ionisation Heatingbyphoto-electrons Electrons: Radiative recombination (electron capture) Cooling by collisional excitation (followed by line radiation)**Photoionisationmodelling**• Radiation impacts a volume (layer) of gas • Different interactionsof photonswithatomscauseionisation, recombination, heating & cooling • In equilibrium,ionisation state of the plasma determinedby: • spectral energy distributionincomingradiation • chemicalabundances • ionisation parameterξ=L/nr2withLionisingluminosity, ndensityandrdistancefromionising source; ξessentially ratio photondensity / gas density**First balance equation: ionisation stages (1)**• Same rates as for CIE plasmas: • Collisional ionisation • Excitation auto-ionisation • Radiative recombination • Dielectronic recombination • At low T, charge transfer ionisation & recombination**First balance equation: ionisation stages (2)**• New for PIE plasmas: • Photoionisation • Compton ionisation (Compton scattering of photons on bound electrons; for sufficient large energy transfer this leads to ionisation)**Second balance equation: energy**• Balance: heating = cooling • Take care how heating etc is defined: we use here heating/cooling of the free electrons • For instance, for e-+ione-+ion++e-we assign the ionisation energy I to the cooling of the free electrons**Heating processes**• Compton scattering (photon looses energy) • Free-free absorption • Photo-electrons • Compton ionisation • Auger electrons • Collisional de-excitation**Cooling processes**• Inverse Compton scattering (photon gains energy) • Electron ionisation • Recombination • Free-free emission (Bremsstrahlung) • Collisional excitation**Heating & cooling (NGC 5548 in 2013)**Inverse Compton Recombination Free-free emission Collisional excitation Electron ionisation ------------------- Compton scatter Photoelectrons Auger electrons Compton ionisation (Coll. de-excitation) (Free-free absorption)**Heating & cooling (NGC 5548 obscured)**Inverse Compton Recombination Free-free emission Collisional excitation Electron ionisation ------------------- Compton scatter Photoelectrons Auger electrons Compton ionisation (Coll. de-excitation) (Free-free absorption)**Performance (151 grid points)**• Same run on NGC 5548 obscured SED: • XSTAR: 40 hours (& crashed for kT > 10 keV) • Cloudy: 4 hours • SPEX: 5 minutes • Okay the above may depend on optimalisation flags etcetc, but ….**Performance**• Often people make a grid of models as function of few parameters table grid feed into favorite fitting program • SPEX pion model allows fast instantaneous calculation & simultaneous fitting of the continuum of any shape; multiple stacked layers**Stabilityphoto-ionisationequilibrium(examplesfromDetmers et**al. 2011) Ξ = Fion/nkTc= ξ/4πckT Stable equilibrium fordT/d Ξ> 0**Stability curves differhere case NGC 5548 (Mehdipour et al.**2014)**Practical examples from SPEX (1)**• Most simple model: slab • Input: • Set of ionic column densities (arbitrary, no physics involved) • Outflow velocity • Line broadening • Covering fraction fc • Transmission: T(E) = (1 – fc) + fc e-τ(E) with τ(E) containing all physics of absorption • Emission needs to be modelled separately**Practical examples from SPEX (2)**• next simple model: xabs • Input: • Set of ionic column densities pre-calculated using real photoionisation code • Ionisation parameter ξ = L/nr^2 • Outflow velocity • Line broadening • Covering fraction fc • Transmission: T(E) = (1 – fc) + fc e-τ(E) with τ(E) containing all physics of absorption • Emission needs to be modelled separately**Practical examples from SPEX (3)**• next simple model: warm • Input: • Set of ionic column densities pre-calculated using real photoionisation code • Absorption measure distribution dNH(ξ)/dξ, parametrized by powerlaw segments • Outflow velocity • Line broadening • Covering fraction fc • Transmission: T(E) = (1 – fc) + fc e-τ(E) with τ(E) containing all physics of absorption • Emission needs to be modelled separately**Practical examples from SPEX (4)**• latest model: pion • Input: • Arbitrary SED (using SPEX emission components, or file, or …) • Does self-consistent photoionisation calculations • Ionisation parameter ξ = L/nr^2 • Outflow velocity • Line broadening • Covering fraction fc • Transmission: T(E) = (1 – fc) + fc e-τ(E) with τ(E) containing all physics of absorption • Emission (still) needs to be modelled separately**Future extensions of the pion model**• Include also emission (using SPEX plasma code core; several processes need updates) • Cooling at low T not yet accurate enough (Rolf Mewe’s CIE model stopped at K-like ions or higher) • Thicker layers (simple radiation transport using escape factors) • NB only the Titan code takes full radiative transfer into account**AbsorptionMeasure Distribution**Discrete components Emission measure Column density Continuous distribution Ionisation parameter ξ Temperature**Decomposition into separate ξ**• Early example: NGC 5548 (Steenbrugge et al. 2003) • Use column densities Fe ions from RGS data • Measured Nion as sum of separate ξ components • Need at least 5 components**Separate components in pressure equilibrium, or continuous?**Discrete components in pressure equilibrium? Continuous NH(ξ) distribution? Krongold et al. 2003 Steenbrugge et al. 2005**Discrete ionisationcomponents in Mrk 509?Detmers et al. 2011**paper III • Fitting RGS spectrum with 5 discrete absorber components (A-E) • Gives excellent fit**Continuous AMD model?Mrk 509, Detmerset al. 2011**• Fit columns withcontinuous (spline) model • C & D discrete components! • FWHM <35% & <80% • B (& A) toopoorstatisticsto prove ifcontinuous • E harder determined: correlationξ & NH • Discrete components D E C B**A comparison between sources**• All Seyfert 1s show similar trend • NH increases with ξlike power law • High ξ cut-off? • Same behaviour in Seyfert 2s (NGC 1068, Brinkman et al. 2002)**Why study time-dependent photoionisation?**• Because most photoionised sources are time-variable • Gives opportunity to determine distance of gas from ionising source mass loss, kinetic luminosity etc**“The” recombination time scale**• Pure recombination equilibrium: 0 = dni/dt = niRi-1 + ni+1Ri • This leads, with Ri = neαi to characteristic time trec = 1 / [ne (ni+1/ni – αi-1/αi)] • Thus, we see that trec~1/ne • However, there is always a point where ni(ξ) and ni+1(ξ) are such that trec∞, and this point is usually close to where ni(ξ) peaks!**Density estimates: line ratios**• ξ = L/nr2 • C III has absorption lines near 1175 Å from metastable level • Combined with absorption line from ground (977 Å) this yields n • n = 3x104 cm-3 in NGC 3783 (Gabel et al. 2004) r~1 pc • Onlyappliesforsome sources, low ξ gas • X-rayssimilarlines, sensitivetohighern (e.g. O V, Kaastra et al. 2004); no convincing case yet (in AGN, but Fe linesfromexcited levels are seen in X-raybinaries**Density estimates: reverberation**• If L increases for gas at fixed n and r, then ξ=L/nr² increases • change in ionisation balance • column density changes • transmission changes • Gas has finite ionisation/recombination time tr (density dependent as ~1/n) • measuring delayed response yields trnr**LightcurveMrk 509 during100 days(Kaastra et al. 2011, paper**I) • Factor ~2 increase in soft X-ray • Correlated with UV • No correlation with hard X-ray UV Soft X-ray Hard X-ray

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