1. Atomic Processes 2. Ionization Equilibrium 3. Radiation ... · Interpretation of X-ray Spectra...

H. Böhringer MPE Seminar 24.11.2005 1

Interpretation of X-ray Spectra from Hot Thermal Plamsa

1. Atomic Processes

2. Ionization Equilibrium

3. Radiation Processes

4. Equilibrium Spectra

5. Non-Equilibrium Spectra

6. Hot gas in Clusters of Galaxies


Hot Thermal Plasma in Astrophysics

Corona of the sun (~1 Mill. K)

Hot interstellar Medium and winds of galaxies

Supernova remnants (Kepler, Vela) ~ few Mill. K

Hot intra-cluster plasma of galaxy clusters


Radiation Processes that Contribute to the Radiation of the Hot Plasma

1. Line radiation: excited by electron collisions

dominant at T < 106 K

2. Free-free radiation (Bremsstrahlung) dominant above 107 K

3. Recombination radiation „free-bound emission“ e- + I+ I0 + γ

4. Two-photon radiation: only possibility to radiatively depopulate the 2S level in H-like ions (longer lifetimes, comparable to forbidden transitions)

• All these processes have at their base the collision of an electron with an ion !

continu um rad ia ti on


Atomic Processes (in a thin plasma)

1) Thin pasma concerning radtation transport


Free-Free Radiation Iformulae

1Hz

3cm

1serg

22138

22121

233

6

),(108.6

),(32

332

−−−−−

−

−−

⋅≈

⎟⎟⎠

⎞⎜⎜⎝

⎛=

ieiffTk

h

ieiffTk

h

Be

ff

NNZTgTe

NNZTgTekmc

e

B

B

ν

νππε

ν

ν

νGaunt factor

• The temperature dependence comes from the v-1 dependence

• The Boltzmann factor creates a sharp high frequency cut-off

• The Gaunt factor is near unity and has a weak temperature and frequency dependence (approximations given by Karzas & Latter 1961, Gronenschild & Mewe 1978)

Produced by the acceleration of an electron when it passes an ion close enough (inside the shielding radius). The observed radiation is an integral over all possible impact parameters and over the thermal distribution of the electrons. A rough results can be derived classically and analytically (see e.g. Jackson „Electrodynamics“). But quatum effects play an essential role for close impact. The quantum mechanical „corrections“ are summed into the „Gaunt factors“.


Free-Free Radiation IIGaunt factor

Frequency and temperature dependence of the Gaunt factor :

Typical Bremsstrahlungs spectrum :

Iν

ν

From Rybicki & Lightman

u = 4.8 1011 ν/T

γ2 = 1.58 105 Z2/T


Free-Free Emission IIIcooling coefficient

peff

Biff

Bieepe

ff

NNTdtdVdE

TgZTT

TgZchm

emkT

NNdVdtdET

⋅Λ=

⋅=Λ

⎟⎟⎠

⎞⎜⎜⎝

⎛==Λ

−−

)(

)(104.1)(

)(32

321)(

3cm

1serg

22127

23

6521ππ

The cooling rate increases with T1/2 and the cooling time also increases with T1/2 . At high temperature when most of the ions are completely ionized and free-free emission dominates, the total cooling coeficient also has this temperature dependence.


Recombination Radiation

Most of the recombination radiation comes from recombination into the ground state (for systems with not too many electrons) and about 5 – 15% contribution is from recombination into higher levels.

Considering only the ground state contribution we have the following frequency and temperature dependence:

ikT

fbkTh

fb heTgTei

χννεχν

≥∝ −−for

21 ),(χi = ionization potential

Typical spectrum:

hiχν =0

ν

Iν


Recombination Continuumof C at 106 K


Two-Photon Radiation

1S

2S 2P

allowed

allowed as for the simultaneous emission of two photons

functionGreensteinSpitzer)(strengthoscillator

)(),(

.

2.1

2

−=Φ=

Φ⋅∝−−

nf

Tgfe

osc

osckTh

νννε γ

ν

γ

The Spitzer-Greenstein function determines how the energy is distributed between the two photons. The function has a maximum for equal share of the energy:

νν0

Φ(ν)


Continnuum Radiation at 104 and 105 K

Dotted line: bremsstrahlung rad., dashed-dotted line:recombination rad., thin solid line: two-photon radiation

Bremsstrahlung Recombination

2-Photon


Continnuum Radiation at 106 and 107 K

Dotted line: bremsstrahlung rad., dashed-dotted line: recombination rad., thin solid line: two-photon radiation


Line Radiation I

For the line contribution to the spectrum we have to take care of:

• the excitation of higher levels by electron collisions (in the thin plasma approximation all excitations lead to radiation of a (or more) photons)

• the braching ratio of radiative transitions into different lower lewels

• all the transitions allowed by the selection rules have to be considered (inspection of Grotrian diagrams)

• Astrophysical X-ray spectra are dominated by allowed transitions contrary to what is observed in the optical band.

αβ


Grotrain Diagram for C0


Ionization Equilibrium Iprocesses

All radiation processe depend on Ne Ni.. Thus we need to now all Ni = Nx x fi (the chemical abundance of the species and the fractional ionization).

Thus we have to calculate the ionization structure (determined at this hot temperatures mostly by collisional ionization) either for a thermal equilibriukm situation or much more complicatedly by a time dependend model.

In thermal equilibrium we have:

I+n I+(n+1)

Ionization A

Recombination B

with A = B

Charge exchange Or if necessary with charge exchange rates included


Ionization Equilibrium IIprocesses

Ionization processes:

1. Direct ionization e- + O+ O++ + 2e-

2. Autoionization e- + O O* + e-

O* O+ + e-

Recombination processes :

1. Direct (radiative) recombination e- + O+ O + hν

2. Dielectronic recombination: e- + O+ O*

O* O + hν

Charge exchange:

e.g. O2+ + H O+ + H+


Ionization Equilibrium IIIionization rates (for C-ions)

without charge exchange


Inonization Ratesfor Fe-ions


Ionization Equilibrium IVrecombination rates (for Fe-ions)


Radiation Codesscheme of the calculations


Radiation Codes II

5) New: APEC


Thermal Spectra 105 and 106 K

Line radiation is very important, show here for solar metallicity


Thermal Spectra 107 and 108 K

With increasing temperature bremsstrahlung becomes more and more dominant (most species are almost fully ionized).


Equilibrium Ionization Cooling

Böhringer & Hensler 1989


X-ray Observations of Hot Plasma in Galaxy Clusters Leads to a Revision of Atomic Data


Revision of Atomic Data II


Non-Equlibrium Ionization


Elektron – Ion non-equilibration behind a shock

SN 1006

O VIII O VII

Electron temperature from spectral fit ~ 1.5keV

Ion temperature from line width ~ 530 keV




LTE versus non-LTE Cooling


green =

cie-model


Observation of O VI in the LTE Case


Observation of O VI in the non-LTE case


Results From the XMM Newton Observatory


Reflection Gratting Spectrometer (RGS) Spectrumof Abell 1835


XMM Observations of the X-ray Halo of M87

Böhringer et al. 2001


Isothermality of the ICM in the Halo of M87

Deprojected spectrum of the inner 2 arcmin radius region compared to isothermal and cooling flow models(Matsushita et al. 2001)

Deprojected Spectrum from the radial region 2-4 arcmin fit with isothermal (and two-temperature) models

Si

S


The Fe-L-Shell-Line Complex as a Thermometer

0.5 keV

1.0

1.5

2.0

2.5

3.0

TemperatureTX = 0.4 keV



0.5 keV

1.0

1.5

2.0

2.5

3.0




0.5 keV

1.0

1.5

2.0

2.5

3.0




0.5 keV

1.0

1.5

2.0

2.5

3.0




0.5 keV

1.0

1.5

2.0

2.5

3.0




0.5 keV

1.0

1.5

2.0

2.5

3.0




0.5 keV

1.0

1.5

2.0

2.5

3.0




0.5 keV

1.0

1.5

2.0

2.5

3.0




0.5 keV

1.0

1.5

2.0

2.5

3.0




0.5 keV

1.0

1.5

2.0

2.5

3.0




0.5 keV

1.0

1.5

2.0

2.5

3.0




The iron L-shell line blend as a function of temperature


Spectral Model for Cooling Flows

Reservoir

Thot

T1

T2

T3

T4

Steady State

• Spectrum of one temperature phase:

dTMmk

TdTdTdTL

dTTenthalpybolemissivity

demissivitydTdTL

p

B

bol

dtd

&μ

νν

ννν

νν

ν

25

)()()(

)()(

)()( )(

ΛΛ

=

=

• Full cooling flow spectrum :

TdTdTM

mkdL

hot

cutoff

T

T bolp

B ′′Λ

′Λ= ∫ )(

)(25 νμ

ν νν

&


Near Local Isothermality of the Cooling Core ICM

NH = 1.8 1020cm-2 (fix)

Thigh = 2.0 keV (fix)

Tlow = 1.44 keV (free)

M = < 2.4 Msun/yr[Böhringer et al. 2001, 2002; Matsushita 2002]

NH = 1.8 1020cm-2 (fix)


Tlow = 0.01 keV (fix)

M = ~ 10 Msun/yr

Almost isothermal plasma

Classical „cooling flow“

XMM-PN spectrum from the radial zone 1´-2´ (outside the inner radio lobes)


Cooling Core Spectrum in the M87 Halo

XMM-PN spectrum from the radial zone 1´-2´ (outside the inner radio lobes) NH = 1.8 1020cm-2 (fix)



M = 1.9 Msun/yr

• Adopting a slightly too wide temperature range :


Cooling Flow Spectra in the M87 Halo

XMM-PN spectrum from the radial zone 1´-2´ (outside the inner radio lobes)

NH = 3.3 1021cm-2(free)



M = 2.2 Msun/yr

Energy range : >0.6 keV

• Using a higher interstellar column density (than allowed) :


Test for ICM Intrinsic Absorption Using the M87 Nucleus and Jet

nucleus jet

Both spectra can be well fitted by a power law spectrum with the galactic absorption value of NH ~ 2-4 1020 cm-2.

Upper limits for ΔNH ~ 3 1020 cm-2 for the nucleus and jet respectively.

MOS image


Constraints on the Absorption for the Nucleus and Jet in M87 (from XMM-PN)

from nucleus from the jet

The constraints for NH are close to the galactic value with ΔNH < 3 1020 cm-2 as compared to 3.8 1021 cm-2 required by the Allen et al. (2001) cooling flow model


Tests for intrinsic Absorption in the Perseus Cooling Flow by Means of the Nucleus of NGC

1275Spectral fits to the nuclear emission of NGC 1275 from CHANDRA observations

NH = 0.6 1020 cm-2 (free), Γ ~ 0.7 NH = 3.3 1021cm-2 (fix), Γ=1.2


XMM Observations of the X-ray Halo of M87



Metal Abundances in M87

1´ - 3´

8´ - 16´

Radial Zones :Normalized to solar abundances


Finoguenov, Matsushita, Böhringer, Arnaud 2002


Decomposition of the Metal Abundances into Contributions from SN Ia and SN II

SN Ia SN II

Fe/H (SN II) ~ 0.11Fe/H (SN II) ~ 0.11--0.15 Fe/H (SN Ia) ~ 0.4 0.15 Fe/H (SN Ia) ~ 0.4 –– 0.80.8

Woosley & Weaver 1995

Finoguenov, Matsushita, Böhringer et al. 2002 A&A 381, 21

Different deflagration models by Nomoto,Thielemann et al. 1997

Nomoto et al. 1997

H. Böhringer MPE Seminar 24.11.2005 61Finoguenov et al. 2000Finoguenov et al. 2000

In the outer regions the In the outer regions the mass of Fe in the ICM is mass of Fe in the ICM is dominated by the dominated by the contribution from SN II ! contribution from SN II !

SN Ia

SN II

[Si/Fe]

Radial Abundance Variations of Fe and Si


Ergebnisse

• Plasma temperatures• Element abundances• Thermal equilibrium conditions


O & Si Abundance Profiles in M87

The O profile is almost flat (consistent with a flat profile within +- 10 %)

The O/Si ratio increases from about 0.4 to 0.7 (from r = 2 – 50 kpc)

- (using MEKAL models)

Si

1-temp

O Si

Matsushita, Finoguenov, Böhringer 2003

2-temp


Origin of the Central Abundance Peak

Result from M87 (Matsushita et al. 2003) Gas mass inside r < 10 kpc

~ 2.9 109 Msun

Stellar mass loss ~2.5 10-11 LB Msun

~ 0.63 108 Msun / Gyr

Replenishment time ~ 3 Gyr

Cooling time ~ 1 Gyr (at 10 kpc)

• Central Fe peak (r < 2‘ ,10 kpc) ~ 7 106 Msun Fe (excess ~ 6 106 Msun Fe)

• SN Ia rate ~ SNU *10-12 * LB ~ 0.12 * 10-12 * 2.5 1010 ~ 0.003

• ΔM(Fe) ~ R(SN Ia) * 109 yr * 0.7 Msun(Fe) ~ 2.1 106 M(Fe)

Enrichment time ~ 3 Gyr Turatto et al. rate

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