The Evolution of the Large-scale ISM: Bubbles, Superbubbles and Non-Equilibrium Ionization
***Volume Title**ASP Conference Series, Vol. **Volume Number****Author** c (cid:13) **Copyright Year** Astronomical Society of the Pacific The Evolution of the Large-scale ISM: Bubbles, Superbubbles andNon-Equilibrium Ionization
Miguel A. de Avillez , Dieter Breitschwerdt Department of Mathematics, University of ´Evora, R. Rom˜ao Ramalho 59,7000 ´Evora, Portugal Zentrum f¨ur Astronomie und Astrophysik, Technische Universit¨at Berlin,Hardenbergstr. 36, D-10623 Berlin, Germany
Abstract.
The ISM, powered by SNe, is turbulent and permeated by a magneticfield (with a mean and a turbulent component). It constitutes a frothy medium that ismostly out of equilibrium and is ram pressure dominated on most of the temperatureranges, except for T <
200 K and T > K, where magnetic and thermal pressuresdominate, respectively. Such lack of equilibrium is also imposed by the feedback of theradiative processes into the ISM flow. Many models of the ISM or isolated phenomena,such as bubbles, superbubbles, clouds evolution, etc., take for granted that the flowis in the so-called collisional ionization equilibrium (CIE). However, recombinationtime scales of most of the ions below 10 K are longer than the cooling time scale.This implies that the recombination lags behind and the plasma is overionized whileit cools. As a consequence cooling deviates from CIE. This has severe implicationson the evolution of the ISM flow and its ionization structure. Here, besides reviewingseveral models of the ISM, including bubbles and superbubbles, the validity of the CIEapproximation is discussed, and a presentation of recent developments in modeling theISM by taking into account the time-dependent ionization structure of the flow in afull-blown numerical 3D high resolution simulation is presented.
1. Introduction
In the last decade due to the substantial increase of computing power, sophisticatedmodels of the interstellar medium (ISM), including the disk-halo interaction, bubbleand superbubble evolution, molecular clouds evolution and fragmentation, formationof shock compressed layers, etc., in a turbulent supernova-driven medium, have beendeveloped. In general these models included cooling and heating, which determine thephysical state of the gas. Interstellar cooling can be the result of line and continuumplasma emission processes, as well as of adiabatic expansion of over-pressured gas.The importance of the former depends on the amount of atoms and ions present in theflow, whereas the latter is related to thermodynamical processes. For optically thin in-terstellar plasmas, frequently the assumption of collisional ionization equilibrium (CIE)is used, according to which the collisional excitation of the gas is followed by photonemission, with the number of ionizations being equal to the number of (dielectronic orradiative) recombinations. However, CIE violates detailed balancing , since collisionalexcitation involves three particles, an atom or ion, an electron to collide with, and asecond electron which is ejected, whereas in radiative recombination, the third particle1 a r X i v : . [ a s t r o - ph . GA ] O c t M. Avillez & D. Breitschwerdt is a photon, leaving the system. Thus, strictly speaking, CIE can never be maintainedin an evolving plasma, although it might be a fair approximation, especially in hot(T > K) environments. For lower temperatures recombinations are not synchro-nized with the cooling and therefore, deviations from CIE inevitably occur (see e.g.,Kafatos 1973; Shapiro, & Moore 1976; Schmutzler & Tscharnuter 1993).The CIE assumption in all ranges of temperatures, or at least in part of it, in themodels discussed below implies the use of a specific cooling function, for given abun-dances, in the computational domain and at each time step. Obviously, the history ofthe ionization structure, which depends on the thermodynamic path of the plasma, willbe lost, in contrast to a full non-equilibrium ionization (NEI) structure giving rise to a time-dependent cooling function, which is quite di ff erent than that obtained under CIEconditions.The structure of this paper is the following: In Section 2 a review on ISM mod-elling including superbubbles and disk-halo interaction, is presented. Sections 3 and 4deal with the collisional ionization conditions adopted in the models, and compare CIEwith NEI results, respectively. As cooling is a process that depends on the history of theplasma, we discuss in Section 5 the cooling functions and emission spectra of gas in thelatest simulations of the ISM. The paper is closed with a final remarks and conclusionssection.
2. From the 3-Phase Model to Present day ISM and Superbubbles Models
Theoretical studies during the last three decades have culminated in the supernova reg-ulated Interstellar medium models of Cox & Smith (1974) and in the widely accepted“standard-model” (McKee & Ostriker 1977), in which the gas is distributed into threephases in global pressure equilibrium, a cold and warm neutral phase (CNM and WNM,respectively), a warm ionized (WIM) and a hot intercloud (HIM) medium. There isglobal mass balance by evaporation, ionization and condensation, and energy balancebetween supernova (SN) energy injection and radiative cooling. Most of the Galacticvolume (up to 70-80%) is filled with the hot ( > K) low-density ( ∼ − cm − )ionized gas, interspersed by cold neutral and relatively dense clouds. Observationally itwas di ffi cult to determine reliable volume filling factors of the hot phase in our Galaxydue to the observational vantage point. However, it became evident that the small sur-face coverage of H i holes in external galaxies (e.g., Brinks & Bajaja 1986) argues for amuch lower volume filling factor of the hot phase there.Furthermore, Population I stars typically born in OB associations (see, e.g., Mc-Cray & Snow 1979; McCray & Kafatos 1987). Since more massive stars evolve morerapidly than low mass stars, the associations still exist when the first SNe occur. Hence,SNe are not randomly distributed over the entire galaxy. As a result of their motions,up to 40% of the stars explode in the field (see review by Ferri`ere 2001). Therefore,the amount of hot gas will mostly be concentrated in isolated pools (forming superbub-bles), which may burst through the thick disk (composed of H i (Lockman 1984) and H ii (Reynolds 1985) layers) into the halo like chimney funnels (Norman & Ikeuchi 1989).The superbubble evolution in a static density stratified environment was modelled hy-drodynamically in two dimensions by, e.g., Tomisaka & Ikeuchi (1986), Mac Low et al.(1989), and Tenorio-Tagle et al. (1990). Tomisaka (1998) and Stil et al. (2009) devel-oped three-dimensional simulations of a superbubble evolving in a static magnetized ubbles, Superbubbles and Non-Equilibrium Ionization α , radio continuum and soft X-rays werefound (Dettmar 1992), arguing for local outflows as it had been suggested in the Galac-tic fountain (Bregman 1980; Kahn 1981), chimney (Norman & Ikeuchi 1989) and theGalactic wind model (Breitschwerdt et al. 1991; Breitschwerdt & Schmutzler 1994).These models capture some of the structure but not all of the essential physics.Taking into account that the ISM is a turbulent and compressible system (von Weizs¨acker1951), in which cooling and heating determine the physical state of the gas, more com-plex and sophisticated galactic disk (two-dimensional: Chiang & Prendergast 1985;Chiang & Bregman 1988; Rosen et al. 1993) and disk-halo interaction two- (Rosen& Bregman 1995) and three-dimensional (Korpi et al. 1999a; Avillez 2000; Avillez& Breitschwerdt 2004, 2005; Joung & Mac Low 2006; Melioli et al. 2009) modelswere developed. In turn, some of these models have been used to follow the evolutionof superbubbles within a realistic supernova-driven turbulent magnetized medium (incontrast to previous simulations that used a static medium) by Korpi et al. (1999b) andAvillez & Breitschwerdt (2005) (a field composed of a random and mean componentswith a total strength of 4.5 µ G was used) finding that blow-out is much more likely thanpreviously thought, mainly because bubbles evolve in an inhomogeneous backgroundmedium. However, Korpi et al.’s simulations are limited by the usage of a small gridextending only up to 1 kpc in the direction perpendicular to the disk in both sides ofthe midplane. Hence, the disk-halo-disk cycle could not be established nor followed.The simulations of Melioli et al. (2009) calculate the time evolution of H i , H ii , C ii -C iv ,and O i -O iii ions at T ≤ K and determine their contributions to the cooling function.For T > K they use a CIE cooling curve. Such setup has severe implications in thehistory and cooling of the plasma as will be discussed below.The evolution of superbubbles can be much improved by, instead of injecting en-ergy in a continuous way into a single point, identifying the missing stars in an associa-tion and follow in space and time all the stars during their main sequence life time untilthey explode. This methodology has been used in the disk-halo simulations, includ-ing those related to the evolution of the Local and Loop I superbubbles in a turbulentmedium (Breitschwerdt & Avillez 2006; Avillez & Breitschwerdt 2009). In this wayone can perform a detailed simulation of the properties of the bubbles and their spectro-scopic observables, allowing a direct comparison with observations. These simulations
M. Avillez & D. Breitschwerdt have been successful in reproducing not only the spatial structure of the bubbles, butalso the observed column densities of Li-like ions C iv , N v and O vi and their ratios.
3. Plasma Emission Modelling
A further improvement in modelling the ISM comprises the full-blown non-equilibriumionization structure (resulting from the ten most abundant elements), where the ioniza-tion, thermal and dynamical history of the plasma are fully nonlinearly coupled andtracked simultaneously both in space and time at high resolution. In order to achievethis, we developed a plasma emission code (hereafter EPEC - Eborae Plasma EmissionCode) which can be coupled to any MHD software through the proper interfacing calls.EPEC is written in Fortran 2003 in an object-oriented way making large use of proce-dure pointers. It is prepared to run both on multi-core CPUs (using OpenMP) as wellas on NVIDIA GPUs (graphics cards processor units) by means of CUDA Fortran.
EPEC includes the ten most abundant elements in nature (H, He, C, N, O, Ne, Mg, Si,S and Fe) and the default solar abundances are those recommended by Asplund et al.(2009, AGSS2009): log A ( X / H ) (cid:12) = -1.07 (He), -3.57 (C), -4.17 (N), -3.31 (O), -4.07(Ne), -4.40 (Mg), -4.49 (Si), -4.88 (S), and -4.50 (Fe). Other abundances (for com-parison studies with previously published results) are also available, e.g., Allen (1973),Anders & Grevesse (1989, AG1989) and Grevesse et al. (2007, GAS2007). The latterare used by Gnat & Sternberg (2007), but with the Ne overabundance (log A(Ne / H) (cid:12) = − .
71) of Drake, & Testa (2005). GAS2007 and AGSS2009 propose C, N, O and Neabundances smaller than those recommended by AG1989, but AGSS2009 increasesslightly those values from GAS2007. This variation in the abundances results fromthe improvement on three-dimensional hydrodynamical solar model atmospheres, thatinclude a relaxation assumption on the local thermodynamic equilibrium and improve-ments in the atomic and molecular data (see discussion in, e.g., AGSS2009).
The adopted physical processes in this work are the electron impact ionization, excitation-autoionization, radiative and dielectronic recombination, charge-exchange recombina-tion and ionization reactions, continuum and line emissions. Electron impact ionizationrates fits are taken from Mattioli et al. (2007, MAT2007) for all H, He, C, N, O, Neions, Mg i -Mg iii , Si i -Si viii , S i -S v , and Fe i -Fe xi ; The experimental data of Fogle et al.(2008) is used to fit the rates for C iii , N iv , and O v . Data for the remaining ions is takenfrom Mazzotta et al. (1998, MAZ1998). Excitation-autoionization rates are taken fromMAT2007 for C iv , N v , O vi , Ne viii , Si iii -Si iv , S iii , S v and Fe xi . For the remaining ionswhere EA is important we follow Arnaud & Rothenflug (1985, AR85).Radiative recombination rates are fitted following Verner & Ferland (1996) andGu (2003), for low charge ions. The fits parameters for bare through Na-like ions aretaken from Badnell (2006) and for other ions we follow Dere et al. (2009). Dielectronicrecombination rates fits coe ffi cients for H-like through Mg-like ions are taken fromBadnell (2006), Zatsarinny et al. (2003, 2004, 2006, and references therein), Colgan etal. (2003, 2004), Altun et al. (2004, 2006, 2007), Mitnik & Badnell (2004) and Bautista& Badnell (2007) with updates for S vi (Orban et al. 2009), Ne vii (Orban et al. 2008), ubbles, Superbubbles and Non-Equilibrium Ionization viii -Fe ix (Schmidt et al. 2008), Fe x -Fe xi (Lestinsky et al. 2009), Fe xiv (Schmidt etal. 2006), Fe xv (Luk´ıc et al. 2005), Fe xxiii (Savin et al. 2006). For the remaining ionsMAZ1998 data is used.Charge-exchange recombination (CER) with H i rates for He ii -He iii , N ii -N v , O iii ,O v , Ne iii -Ne v , Mg iii -Mg v , Si v , S iii -S v and Fe iii -Fe v are taken from Kingdon & Ferland(1996), C ii -C vii (Suno & Kato 2006), O ii (Spirko et al. 2003), O iv (Wang et al. 2003),Si iii (Clarke et al. 1998), and Si iv (Bruhns et al. 2008). Fits to the rates of CER withHe i for N iii -N v , O iii , O v , Ne iv -Ne v , C iv -C v , Mg iv -Mg v , Si iv -Si v , S iv and Fe iv -Fe v aretaken from Astrophysics Charge-Transfer Database (Wang et al. 2002a, and referencestherein), O ii (Zhao et al. 2005), O iv (Wu et al. 2009), Ne iii (Zhao et al. 2006), S iii (Zhao et al. 2005), S v (Wang et al. 2002b), and Fe vi -Fe xiv ( ˘Cade˘z et al. 2003). Charge-exchange ionization (CEI) with H ii rates for Mg ii , Si i -Si ii are taken from AR1985, C i ,N i , Mg i , S i and Fe i -Fe ii are taken from Kingdon & Ferland (1996) and O i from Spirkoet al. (2003). CEI with He ii comprised data for O i (Zhao et al. 2004) and Si ii (Wang etal. 2002b), C ii , N ii , Si iii and S ii -S iii (AR1985).Cooling rates include free-free emission with the averaged Gaunt factor by Karzas& Latter (1961), radiative and dielectronic recombination (Cox & Tucker 1969), lineemission in the range 1 Å -610 µ (Penston 1970; Jura & Dalgarno 1972; Dalgarno, &McCray 1972; Kato 1976; Stern et al. 1978; Gaetz & Salpeter 1983; Mewe et al. 1985),and two-photon emission. Spectra calculations include line and continuum emissions.The latter comprises free-free, free-bound to the ground and excited states, and two-photon - using 1s-2s transitions in H and He-like ions (Tucker & Gould 1966; Gronen-schild & Mewe 1978; Mewe et al. 1986). The time evolution of the ions fractions, where ionization and recombinations of ionsof nuclear charge Z occur between neighbouring ionization stages z − z and z +
1, isgiven by dn Z , z dt = I Z , z − n Z , z − n e − ( I Z , z + R Z , z ) n Z , z n e + R Z , z + n Z , z + n e , (1)where R Z , z and I Z , z are the rates of recombination and ionization from state ( Z , z ) to( Z , z −
1) and ( Z , z + n Z , z and n e are the ion density of element Z withe ff ective charge z and electron density, respectively. This constitutes a tridiagonal ma-trix if the charge exchange reactions are not included. However, if charge exchangereactions are included (as done in the present paper) new o ff -diagonals terms are intro-duced, becoming R Z , z = α rZ , z + α dZ , z + n e (cid:88) α ce ˜ n ˜ Z , ˜ z , (2)where the uppers indices stand for radiative, dielectronic and charge exchange pro-cesses, respectively, and I Z , z = C eiiZ , z + C eaZ , z + n e (cid:88) C ce ˜ n ˜ Z , ˜ z (3)with eii and ea standing for electron impact and excitation-autoionization processes, re-spectively, and ˜ n ˜ Z , ˜ z is the particle density of other ions involved in the charge exchange M. Avillez & D. Breitschwerdt reactions. In the EPEC version referred to here, we do neither consider photoioniza-tion nor ionization due to suprathermal electrons (see, e.g., Schmutzler & Tscharnuter1993) - this is the subject of a forthcoming paper. For the 10 elements considered in theEPEC, the number of ordinary di ff erential equations including the neutrals amounts to112. Conservation of species (atoms and ions) implies that n Z = Z (cid:88) z = n Z , z . (4)In addition the system of equations must account for the mass n tot = (cid:88) Z n Z + n e (5)and charge conservations n e = (cid:88) Z Z (cid:88) z = n Z , z z (6)The system of equations is closed by the energy balance equation dUdt − Pn dndt = − n e n H Λ (7)where Λ is the cooling function, i.e., it represents the radiative losses per unit emissionmeasure resulting from bremsstrahlung, radiative and dielectronic recombination, col-lisional ionization, line emission due to excitation, two-photon emission, and charge-exchange reactions. In these equations n H is the hydrogen density and U is the internalenergy density of the system. The internal energy comprises the contributions fromthermal motions of the particles, represented by U th , and the potential energy associ-ated with the ionization stages, that is the energy stored in or delivered from the highionization stages of chemical elements (Schmutzler & Tscharnuter 1993). Hence, theinternal energy density is given by U = U th + (cid:88) Z Z (cid:88) z = n Z , z z − (cid:88) z (cid:48) = I Z , z (cid:48) , (8)where I Z , z (cid:48) is the ionization potential of an ion with nuclear charge Z and e ff ectivecharge z (cid:48) . The thermal part of the internal energy is linked to the pressure of the systemthrough the equation of state P = ( γ − U th .As initial conditions for static plasma calculations we assume a fully ionized gas at10 K. As the temperature decreases, recombination and ionization rates are calculated,following the simultaneous implicit calculation of the ionization fractions (includingneutrals) and charge equation – implying the inversion of a 113 ×
113 matrix. Next theradiative losses, emission spectra and internal energy are calculated.
4. Collisional ionization Equilibrium vs. Non-Equilibrium ionization
Figure 1 shows the normalized cooling function of a static plasma (that is, with nodynamics included) that cooled from 10 to 10 K under CIE and NEI (isochorically) ubbles, Superbubbles and Non-Equilibrium Ionization . K are observed between the two e ffi ciencies with the CIE coolingdominating over the NEI case between 10 . K and 10 K (bottom panel of Figure 1).These variations are a consequence of the cooling e ffi ciency due to the di ff erent emis-sion processes (bremsstrahlung, radiative and dielectronic recombination, collisionalionization, line excitation and two-photon emission) being larger under CIE than NEIconditions for all elements taken into account. Figure 2 compares the contributions ofthese processes to the cooling per element (e.g, C, Ne and Fe) under CIE (top row) andNEI (bottom row) conditions.For T < . K the cooling e ffi ciency at the same temperature under NEI (iso-choric) conditions is larger than in the CIE case as a result of the delayed recombinationof the plasma. As recombination lags behind, single and double ionized species existat lower temperatures (right column in Figure 3), something that does not occur un-der CIE, because ionization and recombination is synchronized, and therefore neutralsform at temperatures near 10 K (left column in Figure 3).While in CIE the ionization fractions (left panel Figure 3) depend only on thetemperature and are sharply peaked, in NEI these same fractions (right panel Figure 3)depend on the dynamical and thermal history of the plasma. The higher ionizationstages recombine to lower ones and eventually (when T ∼ . K) only the loweststages are abundant. However, the qualitative behaviour of all ionic stages is not thesame. The highest ionic stages decrease continuously, that is, they always recombineto the next lowest stages, while the lowest stages increase continuously, that is thenext highest stage recombines to them; the intermediate stages have two peaks result-ing from the recombination of the next highest stage, but dielectronic recombination
Figure 1.
Top panel : Normalized CIE (dashed line) and NEI (solid line) cool-ing functions as function of temperature and calculated with AGSS2009 solar abun-dances.
Bottom panel : CIE and NEI cooling functions ratio.
M. Avillez & D. Breitschwerdt
Figure 2. Contributions to the CIE (top row) and NEI (bottom row) cooling due tobremsstrahlung (black dashed line), radiative and dielectronic recombination (blackand green solid lines, respectively), collisional ionization (blue line), line excitation(red line) and two-photon emission (brown line). rapidly depletes it, leading to the formation of the next lower ionization stage. Whendielectronic recombination is no longer e ff ective, recombination from the next higheststage increases the ion amount. As soon as the highest stage is depleted, the next stagerecombines to the next lowest stage.These di ff erences between CIE and NEI become quite noticeable in the emissionspectra of the plasma at di ff erent temperatures (Figure 4). The spectra include lineemission (cyan lines) and continuum (free-free (dashed black line), free-bound (greenline) and two-photon (red line) emissions). With the decrease in temperature from 10 to 10 . the CIE and NEI spectra become quite di ff erent as result of the free-boundemission dominating the spectra up to 500 Å at low temperatures. At high tempera-tures, above 10 K the di ff erences between the ionization structure under CIE and NEIconditions are small, and therefore the spectra in these two cases are similar. They ubbles, Superbubbles and Non-Equilibrium Ionization Figure 3. Temperature variation of the ionization structure of C (top) and Ne (Bot-tom) under CIE (left column) and NEI (right column) conditions for a gas coolingfrom 10 K. di ff er appreciably when the recombination lags behind, typically around 10 K, withthe continuum at low wavelengths (i.e., λ < (cid:28) − erg cm − s − Å − ) emission withincreasing range of wavelengths and decrease in temperature, e.g, at 10 K: λ < . K: λ < . K: λ <
5. Signature of the Initial Conditions in the Turbulent ISM - NEI Modelling
In a turbulent supernova-driven ISM the state of the plasma, and therefore its ionizationstructure, is determined by the heating and cooling as well as by the flow dynamics.Hence, it is expected that the ionization structure of the plasma varies from place toplace leading to a multitude of cooling functions in the computational box.We carried out three-dimensional hydrodynamical disk-halo interaction simula-tions (in a patch of the Galaxy located at the solar radius with an area of 1 kpc parallelto the Galactic midplane, and extending to ±
10 kpc perpendicular to it, similar to thosedescribed in Avillez & Breitschwerdt (2007) using a resolution of 0.5 pc (the highestso far used for large scale ISM evolution) corresponding to an e ff ective grid with 2000 cells per kpc boxes) and including (i) local self-gravity, (ii) heat conduction and (iii)time-dependent evolution of the ionization structure (of H, He, C, N, O, Ne, Mg, Si,S, and Fe) at each cell of the grid using EPEC described above; (iv) the revised solar0 M. Avillez & D. Breitschwerdt
Figure 4. Spectra of a plasma that cooled from 10 K under CIE (left column) andNEI (right column) conditions at 10 . K (top panel) and 10 K (bottom panel). Thetotal continuum (black solid line) results from free-free (black dashed line), free-bound (green line) and two-photon (red line) emissions. Line emission is shown incyan for the di ff erent wavelengths. Note the striking di ff erences between CIE andNEI emission spectra. abundances by Asplund et al. (2009) are used; (v) Periodic boundary conditions areused along the vertical faces, while outflow boundary conditions are set at the top andbottom of the grid.The left panel of Figure 5 displays the density distribution in the Galactic midplaneat evolution time 400 Myr, while the right panel shows the regions with temperaturesbetween 10 . K and 10 . K. The displayed time is long enough for (i) the signatureof the initial plasma conditions at t = (cid:39)
20% for the Galacticsupernova rate. Dark blue regions have temperatures ≥ K resulting from recentsupernova activity, whereas darkest red regions are molecular clouds with an excessdensity of > − and temperature T <
100 K. Cold gas (red regions) is formed asa result of shock compressed layers and cooling instabilities in the flow. The details ofthese simulations due to the high resolution allow us to identify turbulent motions andtheir e ff ects at small scales. Superbubbles and bubbles have turbulent flows of material ubbles, Superbubbles and Non-Equilibrium Ionization Figure 5.
Left panel:
Non-equilibrium ionization density distribution in theGalactic midplane at evolution time 400 Myr. The color scale refers to the loga-rithm of the number density. Cold (high density) gas is represented by red while hot(low density) gas is shown in blue.
Right panel:
Midplane gas temperature between10 . and 10 . K at 400 Myr of evolution. The labels refer to a selection of siteshaving temperatures of 10 K (labels A through E), 10 . K (labels F through J) and10 K (labels K through O). as can be seen in the cavities, which are crossed by sheet like structures with variablegeometries. These turbulent flows are responsible for the redistribution of energy insideand outside of the cavities.Because the plasma keeps a record of its history, and therefore, of its initial condi-tion (temperature, total pressure and density - including mass fluxes from neighbouringlocations), the ionization structure of the plasma varies from place to place leading to amultitude of cooling functions for the same initial temperature as can be seen in the leftpanel of Figure 6, which displays the cooling paths for gas having an initial tempera-ture of 10 K and located at sites K through O, respectively (shown in the right panel ofFigure 5). The cooling e ffi ciency fails to match that calculated under NEI (isochoric)conditions (black dashed line) all the way down to 10 K (left panel of Figure 6), be-cause the latter has less ”potential energy” stored in high ionization stages.An important consequence of this variability seen in the ionization structure evo-lution and cooling paths is the occurrence of X-ray emission, through free-bound tran-sitions, at low temperatures, becoming larger than the corresponding NEI emission ina static plasma. The NEI spectra were calculated for a gas cooling in a time-dependentfashion from 10 K. The right panel of Figure 6 shows that the free-bound emissionfrom the K through O sites (red, green, blue, brown and magenta lines in the left panel)dominates the NEI (solid black line) and CIE (dashed black line) static plasma emis-sion with decreasing temperature. This is a clear indication that recombination fromthe continuum is not following the cooling of the gas.2
M. Avillez & D. Breitschwerdt
6. Discussion and Final Remarks
In this paper we emphasize the importance in ISM simulations to follow the ionizationstructure of a plasma in a time-dependent fashion, coupled self-consistently to the dy-namics. In fact, the circulation of gas between the disk and halo is a dynamic process,which involves a time scale, that can be much shorter than any of the microphysicaltime scales due to ionization and recombination. The gas escaping into the halo has aninitial temperature well in excess of 10 K, where the assumption of collisional ioniza-tion equilibrium (CIE) is approximately valid. As the hot plasma expands away fromthe disk it will cool adiabatically thereby reducing its temperature and density. Therecombination of highly ionized species lags behind and occurs mainly at considerableheights from the disk.New state of the art simulations of the ISM, focusing on the detailed descriptionof the plasma ionization structure in a supernova driven ISM show that: (i) in a dy-namic ISM, the ionization structure and, therefore, the cooling function, varies withtime and from place to place, depending on the initial conditions and its history (a re-sult in accordance to previous discussions by Kafatos (1973), Shapiro, & Moore (1976)and Sutherland & Dopita (1993) regarding static plasmas, i.e., with no dynamics in-cluded), (ii) the cooling path can be quite di ff erent for gas even with the same initialtemperature, but having di ff erent densities and pressures, (iii) this path may not followthe one predicted by the pure plasma emission calculations, that is, without the dynam-ics included, and (iv) as a consequence, X-ray emission occurs at temperatures < K. This is a consequence of the important emission contribution of delayed recombi-
Figure 6.
Left panel:
Normalized cooling functions at sites K through O shownin the right panel of Figure 5 having an initial temperature of 10 K. Right panels:
Free-bound emission (color curves) from gas having an initial temperature of 10 K,located at sites K-O and having the cooling curves displayed in the left panel. Solidand dashed black lines represent the emission expected from NEI and CIE static (i.e.,no dynamics) plasma at the temperatures shown in each panel. ubbles, Superbubbles and Non-Equilibrium Ionization nation , arising from a severe mismatch of recombination and dynamical time scales ofthe plasma. Hence, as T decreases, the emissivity becomes much larger, by more thanan order of magnitude, than that predicted by CIE at the same temperature.A fundamental consequence of the previous discussion, is that the cooling at anypoint in the ISM depends clearly on the history and dynamics of the plasma, that is,the ionization structure keeps a record of its initial conditions and the thermodynamicpath it has taken. As the ionization structure varies from place to place there existsa multitude of di ff erent cooling functions in the ISM. Furthermore, with delayed re-combination having an important role in the cooling of overionized gas, i.e. gas whichonce had a high temperature during its history, X-ray emission at low temperatures isexpected. Consequently, the mismatch of observed plasmas, e.g. by DXS (Sanders etal. 2001), XQC (McCammon et al. 2002), EUVE (Jelinsky et al. 1995), with standardCIE emission models (even for multi-temperature fits) may eventually result from notcorrectly describing the NEI structure of the plasmas.In addition, the amount of singly ionized ions which are important for molecularcloud chemistry, will also be a ff ected by the timescales for recombination and coolingpaths. This implies that a careful study of the ionization structure at higher temperaturesis needed when one is dealing with molecular chemistry in the ISM. Acknowledgments.
M.A. would like to thank the Portuguese-American Founda-tion for Development (FLAD) for the financial support, under project F-V-162 / / CTE-AST / / ff use Extraplanar Gas Layers in Spiral Galaxies”). References
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