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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?

Basics

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

Photoionisation equilibrium

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)

Other useful representations (same data as previous slide)

Differencesphoto-ionisationmodels(Mrk 509 SED)

Differences photoionisation models(NGC 5548 obscured case)

Photoionisationmodelling

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

Pressure equilibrium? No!

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)

Time-dependent photoionisation

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

Time-dependentSEDsMrk 509(Kaastra et al. 2012, paper VIII)

Predictedsignal

Simplified case: predicted change transmission forinstantaneous 0.1 dexincrease L, at spectralresolution EPIC/pn

Signal is weak (1% level) but detectable

Time-dependentcalculation

Total

Soft X

Hard X

Time evolution ion concentrations ni:

dni/dt = Aij(t) nj

Aij(t) contains t-dependentionisation & recombinationrates

Limitsdistance

- Recombination time scaledensity n
- Using ξ=L/nr2r=√(L/ ξn)
- No variabilityseen: lower limit r
- Variabilityseen, but sparse data: upper limit r

- Using measured column densityN=nΔr withΔrthicknesslayer & Δr <r r<L/Nξ
- [O III] 5007 has been imaged (Phillips et al. 1986) (r=3 kpc)

Summary distance limit methodsfor 5 components in Mrk 509

Results: where is the outflow?(Kaastra et al. 2012, paper VIII)

Abundancesoutflow(Steenbrugge et al. 2011, paper VII)

- Relative metal abundances close to Solar
- Absolute abundancesawait new COS data withhydrogenLymanseries
- Onlydoableaftercarefullphotoionisationmodelling

Surprise: very low soft X-ray flux

Appearance of lowly ionised gas

Obscuring stream

- Two components:
- Main: log ξ = -1.2, NH=1026 m-2, fcov=0.86 (X-ray) and ~0.3 in UV; produces UV BAL
- Second: almost neutral, NH=1027m-2, fcov=0.3 (X-ray) and <0.1 in UV
- Partial covering inner BLR, v up to 5000 km/s, inside WA distance few light days (~1014 m, 0.003 pc)
- Obscuration already 3 years ongoing

Importance for feedback(Murray et al. 1995)

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