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)
• 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
6
Outflows from the monster
• Not all gas reaches black hole
• Outflows through magnetised jets, disk winds,
outflows from torus surrounding disk
• Gives feedback to surroundings, but how much?
7
Basics
9
10
11
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 – ∞)
Photoionised plasmas
• Irradiated plasma
• Two balance equations:
Photons:
Electrons:
Photo-ionisation
Radiative
recombination
(electron capture)
Heating by photoelectrons
Cooling by collisional
excitation (followed
by line radiation)
15
Photoionisation modelling
• Radiation impacts a volume (layer) of gas
• Different interactions of photons with atoms
cause ionisation, recombination, heating &
cooling
• In equilibrium, ionisation state of the plasma
determined by:
– spectral energy distribution incoming radiation
– chemical abundances
– ionisation parameter ξ=L/nr2 with L ionising
luminosity, n density and r distance from ionising
source; ξ essentially ratio photon density / gas density
16
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-+ione-+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 etc etc, 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
Stability photo-ionisation equilibrium
(examples from Detmers et al. 2011)
• Ξ = Fion/nkTc
= ξ/4πckT
• Stable equilibrium
for dT/d Ξ > 0
26
Stability curves differ
here case NGC 5548 (Mehdipour et al. 2014)
Other useful representations
(same data as previous slide)
105
104
Fe XXV
Fe XVII
Fe XXV
x
1000
Fe XVII
Fe IX
100
Fe IX
10
1
1
10
X
100
Differences photo-ionisation models
(Mrk 509 SED)
29
Differences photoionisation models
(NGC 5548 obscured case)
Photoionisation modelling
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
Absorption measure distribution (AMD)
Emission measure
Column density
Absorption Measure Distribution
Discrete components
Continuous
distribution
Ionisation parameter ξ
Temperature
38
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
39
Separate components in pressure
equilibrium, or continuous?
Discrete components in
pressure equilibrium?
Continuous NH(ξ)
distribution?
Krongold et al. 2003
Steenbrugge et al. 2005
40
Discrete ionisation components in Mrk 509?
Detmers et al. 2011 paper III
• Fitting RGS spectrum
with 5 discrete
absorber components
(A-E)
• Gives excellent fit
41
Continuous AMD model?
Mrk 509, Detmers et al. 2011
• Fit columns with
continuous (spline) model
• C & D discrete
components!
• FWHM <35% & <80%
• B (& A) too poor statistics
to prove if continuous
• E harder determined:
correlation ξ & NH
•  Discrete components
D
E
C
B
42
Pressure equilibrium? No!
43
A comparison between sources
• All Seyfert 1s show
similar trend
• NH increases with ξ
like 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 timevariable
• 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
• Only applies for some sources, low ξ gas
• X-rays similar lines, sensitive to higher n (e.g. O V,
Kaastra et al. 2004); no convincing case yet (in
AGN, but Fe lines from excited levels are seen in Xray binaries
48
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
trnr
49
Lightcurve Mrk 509 during 100 days
(Kaastra et al. 2011, paper I)
UV
Soft X-ray
Hard X-ray
• Factor ~2 increase in
soft X-ray
• Correlated with UV
• No correlation with
hard X-ray
50
Spectral energy distribution
(Mehdipour et al. 2011, paper IV)
DBB
Soft excess
Power law
51
Time-dependent SEDs Mrk 509
(Kaastra et al. 2012, paper VIII)
52
Predicted signal
Simplified case:
predicted change
transmission for
instantaneous 0.1
dex increase L, at
spectral resolution
EPIC/pn
 Signal is weak
(1% level) but
detectable
53
Time-dependent calculation
Total
Soft X
Hard X
Time evolution ion concentrations ni:
dni/dt = Aij(t) nj
Aij(t) contains t-dependent ionisation & recombination rates
54
Limits distance
• Recombination time scale  density n
– Using ξ=L/nr2 r=√(L/ ξn)
– No variability seen: lower limit r
– Variability seen, but sparse data: upper limit r
• Using measured column density N=nΔr
with Δr thickness layer & Δr <r  r<L/Nξ
• [O III] 5007 has been imaged (Phillips et
al. 1986) (r=3 kpc)
55
Summary distance limit methods
for 5 components in Mrk 509
Component
Method
Lower limit
Method
Upper limit
A
Direct imaging [O III]
Direct imaging [O III]
B
(UV)
C
pn & RGS, Fe blend
Δr/r<1
D
RGS O VIII
Long-term pn
E
pn, Fe blend
Δr/r<1
56
Results: where is the outflow?
(Kaastra et al. 2012, paper VIII)
57
Abundances outflow
(Steenbrugge et al. 2011, paper VII)
• Relative metal
abundances close
to Solar
• Absolute
abundances await
new COS data with
hydrogen Lyman
series
• Only doable after
carefull
photoionisation
modelling
58
Challenge: NGC 5548 in an obscured state
Surprise: very low soft X-ray flux
Strong absorption but normal high-E flux
Appearance of lowly ionised gas
UV broad absorption lines
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=1027 m-2, fcov=0.3 (Xray) 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
What is going on?
1
0.8
0.6
0.4
0.2
0
Transmission
WA 2002
WA 2013
Obscurer nr. 1 2013
Obscurer nr. 2 2013
Total obscurer 2013
Total obscurer + WA 2013
1
2
5
10
Restframe wavelength (Å)
20
Shielding
Importance for feedback
(Murray et al. 1995)