Collisional Ionization Equilibrium Plasmas

From an historial perspetive, the rst type of model proposed to explain the

available EUV and soft x-ray data, was a model in whih the ionization ours

by ollisional proesses and in equilibrium. This type of models are ontrolled by

ollisional ionization equilibrium (CIE) physis. They are also known as oronal

plasmas. Adetaileddisussionofthesemattersisfarbeyondthesopesofthiswork.

However, averyshortdesriptionofthephysialonditions,inwhihtheCIEplasma

holds, is given. For a more detailed physial desription of these models, and for

someof their appliationssee the artilesby Böhringer [121℄,Mewe [122℄, Kallman

and Palmeri [123℄ and Kaastra[124℄, respetively.

Collisionalionizationours,whenaneletronollideswithanionwitharelative

kineti energy greater than the ionization potential of that ion. As a result of

this physial proess, an amount of energy equal to the ionization potential of the

ion is removed from the eletron plasma and transfered as kineti energy to the

removed eletron. Therefore resulting in a net ooling of the eletron plasma. In

the oronal approximation it is assumed, that the eletrons and ions have reahed

thethermalisationstate, meaningthat they havereahed the sametemperature. It

istherefore assumed that a Maxwellian distribution desribestheir energies.

The ollisionalionizationproess is then balaned by areverse proess of equal

magnitude, the reombination of an eletron with an ion. This proess leads to a

radiativeproesswithtwomainhannels. Theradiativeproess ours,beausethe

eletrons are mostly aptured inan exited state of the ion. The eletron then

de-exitesvia a asade through permittedradiativetransitions intothe groundstate.

Itishoweverpossible,that theaptured eletron exites aninnershell eletron. As

onsequene, the exited ion will deay via a two-step proess, alled di-eletroni

reombination. Oneofthevaleneeletronsradiativelyde-exitesinduingaasade

ofphotons similartoradiativereombination. Athigh enoughtemperatures the

di-eletronireombinationdominates overthe radiative reombination. Sinethe hot

gas is a tenuous one, the photons produed in these reombination proesses will

havealowprobabilitytointeratwiththeplasma. Therefore, theyleavetheplasma

withoutany futher interation.

Several models, e.g. from Hayakawa [125℄ and Sanders et al. [103℄, using the

assumption of CIE were developed to explain the LB UV and x-ray emission. The

rstseriousattempttoexplaintheavailableEUVandsoftx-raydatawiththemodel

from Cox and Anderson [120℄. In their model a very large supernova blast wave,

propagatingintothe hot low-density omponent of the interstellar (ISM) medium,

was invoked to explain the soft x-ray observations with typial parameters of the

gas: a temperature of

∼ 10 ⁶

^{K, a}

p/k B ∼ 10 ⁴

^m

^{− 3}

^{K and an extent ranging from}

one toseveral hundred p. In this modelthe bubblehad anage of

∼ 10 ⁵

^years.

Innes and Hartquist [126℄ built a model in whih the H i avity was arved

by very old supernova remnants and superbubbles. On their model a superbubble

reated roughly

4 × 10 ⁶

^{yr ago was} responsible for injeting

∼ 10 ⁵²

^{erg into the}

interstellarmediumsurroundingtheSolarsystem,whihouldproduetheobserved

softx-ray and extreme ultravioletradiation bakground.

A deade later Edgar and Cox [127℄ investigated the possibility,that the Loal

Bubble had been reated either by a single supernova or by a series of supernovae.

In this way, they have tried tond the physial parameters that ould parametrize

hot bubbleswith atypialradiusof 100 p and with the average ount rates inthe

B and Cbands mathing the observed ones. Withthe right modelthen they ould

proeed inexploringthe featuresof thismodel,suhasthe x-ray and EUVspetra,

the emissivity and O vi olumn densities. In the models developed by Innes and

Hartquist[126℄ andEdgar and Cox[127℄ the age ofthe superbubble ismuh larger.

However, later it was realized by Breitshwerdt [128℄, that these CIE models

produe a high pressurean order of magnitude higherwhih is in onit with

thepresene ofloallouds,whihrequire muhlowerpressure inordertosurvive 5

.

Anotherdiultyofthiskindofmodelresidesonitsveryfoundations,see

Breitshw-erdt [130℄. The assumption, that athree body proess ours in a tenuous and hot

optially thin plasma is not likely to happen in real hot and rareed astrophysial

plasmas. Moreover, the assumption, that the ionization rate by inelasti ollisions

isexatlybalaned by reombinationproesses, requiresathirdbody. Therefore, in

this proess the temperature of the plasma inreases. The other diulty of these

models resides in the assumption, that reombination proesses dominate in CIE

plasmas. Sine radiative reombination is a ooling proess, the plasma will

even-tuallydepartfrom equilibriumand enter in anon-equilibriumionizationphase, see

Kafatos [131℄,Shapiro and Moore [132℄, Shmutzler and Tsharnuter [133℄.

There are two importanttime saleswhihontrolthe evolution of the thermal

plasmatheooling time (

t cool

^{)and the} reombinationtime (

t rec

^).

t cool

^{is the time}

that a plasma needs to onvert all its internal energy into radiative energy. The

typial ooling time for a thermal plasma an be estimated by using the following

equation:

t cool = 3 2

nk B T

L = 3 2

(n e + n p )k B T n e n p Λ = 3

2 n p n e

n p + 1 k B T n e n p Λ =

= 6.57 × 10 ⁴

n e

n p + 1 T ₆ n e Λ 22

yr

^(2.1)

where

L

^{is the} interstellarooling funtion,

Λ 22 = Λ/10 ⁻²²

^{denotes the ooling rate}

inunits of

10 ^{− 22}

^{erg m}

^{− 3}

^s

^{− 1}

^{, and T}

6

^isthe temperaturein units of T

/10 ⁶

^K.

The reombinationtime, dened by

t rec = 1/(n e α ^total _rec )

^(2.2)

5

There are several louds in the solar neighbourhood. One of the best studied loud is the

loalinterstellarloud(LIC). ForareentreviewontheLoalInterstellarMediumseetheartile

fromRedeld[129℄. ThederivedtemperatureanddensityfortheLICare6300K,and0.33m

− 3

,

respetively. These values imply a

p/k ^B ∼ 3200

^{K m}

^{− 3}

^{for the LIC. The pressure imbalane}

betweentheLB(

p/k ^B ∼ 10 ⁴

^Km

^{− 3}

^{)and theLICwouldmaketheexisteneofthese loudsnot}

is the time required for a given ion to reombine with a free eletron plasma, in a

plasma with eletron density

n e

^{and where}

α ^total _rec

^{is total} reombination rate for a given ion ata given temperature. After

t rec

^{the ion should not be present anymore}

inthe plasma, orit shouldhave a redued ionizationstage.

Thesetwotimesalesan beeasilyalulated. UsingthevaluesfortheLB from

Snowdenetal.[116℄,assuminga

Λ = 1.081 × 10 ⁻²²

^{erg m}

⁻³

^s

⁻¹

^and

n e ≃ n p

^,a

t cool

of 31.6 Myr is obtained. Comparing this value with the time required for the, e.g.,

Ovii toreombine, wenda

t rec

^{of4.8Myr,withthe}

α ^total _rec

^of

1.47 × 10 ^{− 12}

^m

³

^s

^{− 1}

^,

a oeient taken from Nahar [134℄. Doing the same exerise for the C vi ion

one nds a

t rec

^{of 7.2 Myr, using the} reombination rates oeients of Nahar and Pradhan[135℄.

The ooling time establishes howlong a hot plasmaan exist inCIE atagiven

temperature and eletron density. The time sale required for a plasma to ahieve

aCIE state is given by the followingexpression:

τ

^ie

= 1

( α coll + α rec ) n e

(2.3)

where

α coll

^and

α rec

^{are the ollisional ionization and} reombination rates. This equation gives an estimate of the time sale neessary for a given ion speies to

ahieve a CIE state. It is normally assumed that the CIE ondition for a thermal

plasmais ahieved, when

τ

^{ie is muh smallerthan the}

t cool

^:

τ

^ie

<< t cool

^(2.4)

There areurrentlyalarge numberofnumerialodes,that alulatethe

emer-gent spetrum of hot plasmas in CIE and whih are used to t x-ray spetra from

interstellarplasmas. Mostited in the literature are the odes fromRaymond and

Smith[111℄, Mewe etal. [136℄and Kaastraand Mewe [137℄.

The so-alledRaymond-Smithollisionalionizedplasma have been widely used

totlowresolution spetra obtained duringmissionslikeROSAT and others. This

plasmaodehasevolvedtotheAstrophysialPlasmaEmissionCode(APEC),whih

ombines a sophistiated ode along with the APED database, omposed by more

thanone milliontransitionemission lines [138℄.

2.2.2 Non-Equilibrium Ionization Plasmas

A ompletely dierent approah to model the EUV and the soft x-ray bakground

emission was proposed by Breitshwerdt and Shmutzler [92℄. The authors have

inorporated the atomi physis ode developed by Shmutzler and Tsharnuter

[133℄intoanalgorithmwherethe atomiphysisevolvesaording tothedynamis

of the astrophysialsystem in whih the atomi proesses take plae.

The alulationsbyKafatos[131℄andtheShapiroandMoore [132℄havealready

shown, that even bystarting fromanequilibriumondition, non-equilibriumeets

our, leadingtoa dierent ooling funtionfor ahot plasma. In theiralulations

thenon-equilibriumeetshappeninthetemperaturerangefrom3

× 10 ⁵

^to5

× 10 ⁵

^K.

i

ii iii

iv

v vi vii

-4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

CarboninCIECarboninCIE

log(IonFration)log(IonFration)

i ii iii iv v vi vii

viii ix

OxygeninCIEOxygeninCIE

i ii iii iv

v vi vii

-4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

4.0 4.5 5.0 5.5 6.0 6.5

log(T)[K℄

log(T)[K℄

log(IonFration)log(IonFration) CarboninNIECarboninNIE

i ii iii iv v vi vii

viii

ix

4.0 4.5 5.0 5.5 6.0 6.5

log(T)[K℄

log(T)[K℄

OxygeninNIEOxygeninNIE

Figure 2.3: Ionization frations of arbon and oxygen. The left top plot shows the

arbon ionization frations assuming a plasma in CIE. The left bottom plot shows the

arbon ionization frations assuming a plasma in a NEI state. Onthe right top plot the

ionization frations ofoxygen inCIEstate are shown. The ionization frations of oxygen

inaNEIonditionareshownonthebottomrightplot. Thesealulationswereperformed

by Shmutzler and Tsharnuter [133 ℄. The NEI ondition allows the presene of an ion

overa large rangeoftemperatures.

In this regime, more highly ionized speies are found, ontributing then with more

strongemission lines.

The rst real attempttosimultaneously alulatethe emissionof an

astrophys-ial optially thin plasma and to take into onsideration the time-dependent

ion-izationstagesdue totheir thermodynamialhistory path, wasdone by Shmutzler

andTsharnuter [133℄with the purpose ofinvestigatingthe emissionlineregions in

Ative GalatiNulei.

isshownthe ionizedarbonand theionized oxygen alulatedin CIEand NEI,

taken fromShmutzlerand Tsharnuter [133℄. Asitan beseen, thesetwodierent

physial onditions result in two distint ionizationstrutures. The top plots show

the alulationsassuming the ondition of CIE, and the bottom ones the ondition

of NEI.

Shmutzler and Tsharnuter [133℄ had alreadyargued that the CIEassumption

for the Galati halo and hot ISM plasmas with temperatures of 10

5

K [139℄ and

10

6

K [140℄, respetively, had a serious aw. No global astrophysial mehanism,

apableof permanently maintainingthis wide temperaturerange is known.

There-fore,itwassuggested,that wewereobservingthesegasesinapointoftheirthermal

history wherethe gas isout of the CIE ondition.

In the Breitshwerdt and Shmutzler [92℄ elegant model, the dynamialhistory

of the physial system is taken into onsideration. This model assumes, that

sev-eral supernovae explosions ourred inthe past, reatinga superbubble, in adense

environment.

The most important onept of this model is the assumption, that during a

phase of fast adiabati expansion, the temperature of the plasma dereases very

fast, leaving all high ionization stages frozen into the plasma. This happens,

be-ause the reombination time is muh longer than the ooling time of the plasma.

Therefore,alargefrationoftheinternalenergyoftheplasmaisstoredinthehighly

ionizedspeies,whihansubsequentlybereleasedbyreombinationradiation. The

dynamis of the plasma also hanges the density of the plasma and the ionization

struture, whih hanges the ooling funtion, and therefore the dynamis of the

plasma itself. With this new lass of model, Breitshwerdt and Shmutzler [92℄

derived a muh lower temperature T

≈ 4.2 × 10 ⁴

^{K for the LB. From this model}

they alsoinferred an emissionmeasure EM

≈ 5.8 × 10 ⁻²

^m

⁻⁶

^{p, to whih}

orre-sponds an eletron density n

e ≈ 2.4 × 10 ⁻²

^m

⁻³

^{along a line of sight of 100 p.}

From the two physial parameters, temperature and eletron density, a pressure of

p/k

B

^{= 2nT}

≈ 2000

^{K m}

⁻³

^{isthen obtained, whih is four times less than the one}

derivedfromCIEmodels. ThisthenmakestheveryexisteneofloudsinsidetheLB

mediumpossible. Theestimatedageofthe LBforthismodelisabout

4 × 10 ⁶

^years.

Theirmodel also predits the loss of some of the hot ISM into agalati wind.

The emerging spetrum of a LB in a NEI state is haraterized by an unusual

largeontributionfromthe reombinationlines, insuhaway that thehigh energy

part of the spetrum is ompletely dominated by reombination photons. Due to

this highenergy reombinationtail,aNEI plasma witha temperature of

4 × 10 ⁴

^K

an mimi the spetrum of

∼ 10 ⁶

^{K CIE plasma in shape and in hardness, see}

gure2afromBreitshwerdt and Shmutzler [92℄. Also,this delayed reombination

emission lines leave a strong singnature in the plasma spetrum with a saw-tooth

prolein the upper energy part of the spetrum.

In this type of model the existene of ion speies like O vi, N v and C iv

intheinterstellarmediuman beeasilyaommodatedwithinthe lowtemperature

plasmas. Beauseofthehighlyionizedspeiesandbeausetheydidnothaveenough

timetoreombine,they are abletoexistwithinalargerangeof temperatures. This

regimes.

Im Dokument The Soft X-Ray Background Towards Ophiuchus (Seite 55-60)