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Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed18January2010 (MNLATEXstylefilev2.2) Photoionized gas in hydrostatic equilibrium: the role of gravity 0 Y. Ascasibar⋆ and A. I. D´ıaz 1 0 Departamento de F´ısica Teórica, Universidad Autońoma de Madrid, 28049 Madrid, Spain 2 n a Draftversion2.0(18January2010) J 8 1 ABSTRACT We present a method to include the effects of gravity in the plasma physics code ] Cloudy. More precisely, a term is added to the desired gas pressure in order to M enforcehydrostaticequilibrium,accountingforboththeself-gravityofthegasandthe presenceofanoptionalexternalpotential.Asatestcase,aplane-parallelmodelofthe I . vertical structure of the Milky Way disk near the solar neighbourhood is considered. h It is shown that the gravitational force determines the scale height of the disk, and p - it plays a critical role in setting its overall chemical composition. However, other o variables, such as the shape of incident continuum and the intensity of the Galactic r magnetic field, strongly affect the predicted structure. t s a Key words: ISM:structure – methods:numerical – gravitation – radiative transfer [ 1 v 5 3 1 INTRODUCTION whereP0 is thecentralpressure.There aremanysituations 0 Many astrophysical objects, from the scale of individual ofastrophysicalinterestwhere∆Pgrav(x)≪P0,andthehy- drostaticequilibriumconditionresultsinanalmost isobaric 3 stars to the hot plasma of the intracluster medium, can be . atmosphere. However,dependingon thetotal mass and the 1 approximatelydescribedasbeinginhydrostaticequilibrium characteristictemperatureofthegas,thegravitationalfield 0 withtheunderlyinggravitationalpotential.Thedensityand may be strong enough to have a significant effect on the 0 temperature of the gas are related to the enclosed mass by structureof the system. 1 the condition that the net acceleration vanishes. Thus, the One example of a photoionized gas where the gravi- : hydrostatic equilibrium equation reads v tational acceleration is not negligible is the Galactic inter- i 1 dP(x) stellarmedium(ISM).Althoughinterstellarmatteronlyac- X =g(x) (1) ρ(x) dx countsfor a relatively small fraction of the total disk mass, r a it playsa crucialrole on theformation andevolution of the whereP denotesthetotal(gas,magnetic,turbulent,cosmic- Galaxy.Newstarsareformedfromthecoldmolecularphase ray, and radiation) pressure, and x is the relevant spatial of the ISM, and the energy input from the stellar popula- coordinate. In spherical coordinates, x r, and the gravi- ≡ tion influences the structure and composition of the inter- tational acceleration stellargas.Thecomplexinterplaybetweengas,stars,cosmic g(r)= GM(r) = 4πG rx2ρ(x) dx (2) rays,andmagneticfieldsisresponsiblefortherichstructure, − r2 − r2 Z dynamics, and observational phenomenology of our Galaxy 0 (see e.g. Ferrière 2001). is determined by the total mass M(r) contained within ra- Thepresentworkdescribestheimplementationofgrav- diusr.Forasymmetricplane-parallelatmosphere,therele- itationalhydrostaticequilibriumintheplasmaphysicscode vantcoordinate isthedistancetothemid plane,z,andthe Cloudy,last described byFerland et al.(1998).Numerical gravitational acceleration is details are given in Section 2 and Appendix A. Section 3 z discusses the results obtained for the vertical structure of g(z)= 2πGΣ(z)= 4πG ρ(x)dx (3) − − Z theMilkyWaydiskin thesolar neighbourhood,andabrief 0 summary is given in Section 4. In either case, thesolution to equation (1) is x P(x)=P0+∆Pgrav(x) P0+ ρ(u) g(u) du (4) ≡ Z0 2 NUMERICAL IMPLEMENTATION The Cloudy photoionization code computes the ionization ⋆ E-mail:[email protected] structure, level populations, electron temperature, and ob- 2 Y. Ascasibar and A. D´ıaz servable spectrum of a gas, given its chemical composition andthespectrumofanionizingsource.Theprogramallows the user to set the gas density at the illuminated face and tochoose from several prescriptionstospecify howit varies with distance. Oneoftheseprescriptionsisconstant pressure,which may refer to thegas or thetotal pressure P(x)=Pgas+Pram+Pturb+Pmag+Plines+∆Prad (5) where Pgas = nkT is the thermal pressure, Pram = ρvw2ind and P = ρv2 /2 arise from uniform and turbulent turb turb 2 motion, respectively, Pmag = B8π is the magnetic pressure, P is the radiation pressure of trapped emission lines lines (Ferland & Elitzur 1984; Elitzur & Ferland 1986) and ∆P ρa dx compensates for the acceleration a rad rad rad ≡ duetotheRabsorptionoftheincidentradiation.Thistermis analogous to ∆Pgrav and, to some extent, one could argue that the command should already be named “hydrostatic” ratherthan“constantpressure”evenifitdidnotaccountfor the effect of gravity. Since a is positive (the momentum rad of the absorbed photons points outwards), ∆P induces rad a positive pressure gradient (see Figure 3), whereas gravity must be balanced bya negative gradient. We have modified the constant pressure option in version 08.00 of Cloudy to account for the gravitational term ∆Pgrav. Source code is available upon request, and a brief user guide is provided in Appendix A. The required modificationsarerelativelyminor,andtheyarenotexpected to incur in any side effect on the functionality of the algo- rithm. They are currently being implemented in the devel- opmentversionofthecodeandwillbeavailableinthenext official release1. First, new variables are created to store the values of Figure 1. Molecular,neutral, and ionizedHydrogen densityas ∆Pgrav (initialized to 0 at the illuminated face), the sym- afunctionofheightzwithrespecttothediskmidplane(dotted, metry of the problem (spherical or plane-parallel) and the solid, and dashed lines, respectively) for different values of the mass (0 by default) of an additional component located at mid-planedensityn0. thecentre. As Cloudy moves away from the illuminated face, ∆Pgrav is updated according to 3 THE MILKY WAY DISK ∆Pi+1 =∆Pi+ρigihi (6) Inordertotesttheproposedimplementationofhydrostatic equilibrium, we consider a simple model of the ISM in the where∆Pi and∆Pi+1 denotetheoldandnewvalues,while solar neighbourhood, assuming a plane-parallel geometry ρ ,g ,andh arethedensity,gravitationalacceleration,and i i i that is symmetric with respect to the Galactic mid plane, thickness of the last zone, respectively. The gravitational z = 0. The gas chemical composition (Cowie & Songaila acceleration is computed according to expression (2) or (3) 1986;Savage & Sembach1996;Meyeret al.1998),including dependingon thegeometry. Cloudy keeps track of the cu- dust grains (Mathis et al. 1977), is set by the abundances mulativemassM(r)andthegascolumndensityΣ(z)ineach ISM command, while cosmic ray heating and ionization are case.Additionalmasscomponentsoranyexternal(gravita- treated following Ferland & Mushotzky (1984) with the in- tionalornot)potentialcanbetriviallyaccountedfor,simply struction cosmic ray background (see Hazy2, theCloudy addingtheappropriatecontributiontothelocalacceleration documentation, for details). g . i Given a mid-plane density n0, the vertical structure Finally,onehastomodifythepressureloopsothatthe of the disk is self-consistently computed by the program the term ∆Pgrav is added right after ∆Prad to balance the under the assumptions of ionization, thermal, and hydro- gravitational force. Then, the code proceeds exactly as in static equilibrium. An important limitation is that the gas theoriginalconstantpressurecase,tryingdifferentvaluesof is described by a single density and temperature that may thegasdensityuntilthedeviationfromthedesiredpressure varywithdistance,butthecoexistenceofdifferentphasesat is smaller than the requested tolerance. thesamepointisnotimplemented(seee.g.Boulares & Cox 1990; Silich & Tenorio-Tagle 1998; Ferrière2001;Cox 2005, 1 ThecurrentstableversionofCloudycanbedownloadedfrom http://wiki.nublado.org/wiki/Download 2 Availableathttp://www.nublado.org Self-gravitating photoionized gas 3 Figure 2. Gas temperature (top) and pressure (bottom) along the z-axisfor values of the mid-planedensity n0 =1.0, 0.5, 0.2, and0.1cm−3. Figure 3. DensityofthedifferentHydrogenphases (top), electron temperature (middle) and total pressure (bottom) in the forexamplesofmultiphasemodelsofgalaxydisksinhydro- standardconstant pressure case. static equilibrium). Another simplification is that the radiation field is assumed to strike the system from one side (in our case, the mid plane), whereas in reality the stars ular and atomic Hydrogen at high densities, and an outer are distributed across a scale height comparable to that of region of low-density gas where Hydrogen is predominantly thegaseouscomponent(e.g.Miller & Cox1993;Robin et al. neutral,becomingmoreandmoreionizedatlargedistances 2003). With these caveats in mind, it is not surprising that as density decreases. Gas temperature and pressure as a our simple model does not provide a perfect match to the function of z are shown in Figure 2. The temperature of available observational data. It should be able, though, to the cold dense phase is of the order of 10 100 K, while give a rough estimate of the volume-averaged densities and − the diffuse gas ranges from 5000 to 10000 K. Gas pressure scaleheightsofthedifferentISMphases.Moreimportantly, is roughly constant up to the ionization front, but it de- this kind of models offers some quantitative insight on the creases rapidly through themolecular layer dueto thehigh role played by the different physical mechanisms that may gasdensities(above100cm−3).Thepressurestabilizesagain beatstake.Althoughthepresentstudyismostlyconcerned in the outer region, although the gravitational acceleration with gravity, we will also explore the influence of the spec- imposes a negative pressure (and density) gradient. The ef- tral energy distribution of theincident radiation, as well as fect increases with distance; at some point, the cumulative thepresence of an external potential and a magnetic field. gas mass and therefore the gravitational force are so high that both density and pressure decay extremely fast. Gas temperature, on the other hand, increases steadily towards 3.1 The role of gravity theGalactic halo. To illustrate the effect of gravitational acceleration on the This structure does not provide a realistic description equilibrium structure of a generic photoionized region, we of thelocal ISM. On theone hand, the approximation that ran a first model where the incident continuum consists of all the radiation comes from an infinitely thin disk at the the cosmic microwave background and the interstellar ra- mid plane creates a photoionized region at low z. Although diation field, interpolated from the measurements of Black thereis indeed a thin layer of ionized gas near theGalactic (1987) by means of thetable ISM command. plane,composedofbothdiscreteHiiregionsanddiffusegas Resultsfordifferentvaluesofthecentraldensityn0 are (see e.g. Paladini et al. 2005), its contribution near the so- plotted in Figure 1. In all cases, there is an inner region lar neighbourhood is negligible (e.g. Taylor & Cordes 1993; where the gas is almost fully ionized, a thin layer of molec- Cordes & Lazio 2002). On the other hand, neither the po- 4 Y. Ascasibar and A. D´ıaz Figure4. Incidentcontinuumgivenbythetable ISMcommand (dashed line), absorption of ionizing photons by the extinguish command with a Hydrogen column density of 1021 cm−2 (solid line),andpropagation throughauniformgasslabwithconstant densityof1cm−3andthesameHydrogencolumndensity(dotted line). sition nor the thickness of the neutral phases agree with observations of the Milky Way ISM (Boulares & Cox 1990; Ferrière2001;Nakanishi& Sofue2003,2006).Nevertheless, a central ionized region may be present in several astro- physicalscenarios3,andthereforeitisinterestingtotestthe influenceof gravity in this particular example. Theroleofgravitycanbeassessed bycomparison with the standard constant pressure solution, depicted in Fig- ure 3 for a mid-plane density n0 = 0.5 cm−3. The vertical Figure5. Effectsoftheincidentcontinuumontheverticalstruc- structure of the disk is basically the same (i.e. gravity does notplayasignificantrole)uptotheionizationfront.There, tureofamodelwithn0=1cm−3.Thetable ISMcaseisdepicted inFigures1and2.Thetwotoppanelsshowthemolecular,neutral the temperature decreases sharply, and the density has to and ionized Hydrogen densities for the incident radiation fields riseaccordinglytocompensate.Inthestandardimplementa- obtained by applying the extinguish command and the trans- tion,pressureincreasesinordertobalancetheradiativeac- missionthroughauniformslab.Thethirdandfourthpanelsshow celeration(∆Prad >0).Theeffectisverysignificantnearthe thegastemperatureandthetotalpressureineachcase. ionization front,butitrapidlydecreasesasphotonsbecome absorbed.Althoughthepressurekeepsincreasingmonoton- ically with z, the slope is quite shallow, and the physical absorbed by the neutral Hydrogen in the ISM so that few state of the gas in the outer region (density, chemical com- such photons exist, at least in the Galactic plane. In order position,andtemperature)remainsapproximatelyconstant. to describe the actual radiation field incident on a typical Thus, the main effect of gravity on a plane-parallel atmo- regionintheGalacticplane,theuseoftheextinguishcom- sphereistosettheextentofthemolecularlayerandtheto- mand is recommended. However, it is also stated that this tal scale height of the system. Without gravity, the neutral command should not be used except as a quick test, and a (mostlymolecular) layerwouldsimplyextendtoinfinity,as more physical extinction of the continuum may be accom- can bereadily seen in Figure 3. plishedbytransmittingitthroughamodeloftheabsorbing slab. Forthesakeofsimplicity,weassumeauniformdensity 3.2 The incident radiation field of 1 cm−3 and a total column density of 1021 cm−2, appro- priate for the Milky Way disk (Dickey& Lockman 1990). As discussed in the documentation of the table ISM com- The main difference between the resulting continua, shown mand,ionizingradiationbetween1and4Rydbergisheavily inFigure4,isthattheextinguishcommanddoesnotaffect theenergybandbetween0.1and1Rydberg,responsiblefor molecular Hydrogen photodissociation. When the incident 3 Note that such an equilibrium configuration is, in any case, radiationfieldispropagatedthroughtheISM,manyofthese Rayleigh-Taylor unstable. Cold gas blobs and filamentary struc- tures would slowly detach from the dense, neutral material and ultravioletphotonsbecomeabsorbedbythedustcomponent falltowardsthelow-density,ionizedregion,whereashotgasbub- and re-emitted in thefar infrared. bleswouldtendtorisebuoyantlythroughtheneutralphase. Thedetailsoftheinterstellarradiationfieldhaveadra- Self-gravitating photoionized gas 5 Figure 6. Total stellar mass density (solid line) and contribu- tions of individual populations withdifferent ages (dotted lines) according to Robinetal. (2003). The approximation given in equation(7)isshownasadashedline. matic impact on the vertical structure computed by the code. Figure 5 compares the results obtained for n0 = 1cm−3 usingtheextinguishcommandandthoseobtained bypropagatingthetable ISMfieldthroughtheuniformslab beforereachingtheGalacticmidplane.Themaindifference between either method and the unextinguished case repre- sentedonthetoppanelofFigure1istheabsenceoftheinner layerofionizedgas.Centraltemperaturesandpressuresare almosttwoordersofmagnitudelower,and,sincethereisno phasetransitionassociated toanyionization front,theden- sity of the cold neutral material is equal to n0, also orders Figure 7. DensitiesofthedifferentHydrogen phases(top pan- of magnitude lower than in themodel without attenuation. els),temperatures(thirdpanel)andpressures(bottompanel)for The absorption of the ultraviolet photodissociating ra- two models including a stellar mass component of the form (7). diationturnsouttobeveryimportantaswell.Thelocation In addition, one of them also includes a tangled magnetic field of the transition from the cold to the warm neutral phase withanintensityB0=5µGattheGalacticplane. may change by a large factor, but the most relevant issue is the predicted fraction of Hydrogen in molecular form. In particular,theextinguishcommandoverestimatesthepho- 2z z2 todissociation ratesomuchthatthereisvirtuallynomolec- ρ∗(z)=ρ0 (cid:20)1−0.9(cid:18)h∗ − h2∗(cid:19)(cid:21) (7) ular Hydrogen at all. Our results can only strengthen the advice given in Hazy of modelling the absorbing material whereρ0 =0.042 M⊙ pc−3 andh∗ =520 pc.Thisfunction, rather than using theextinguish command. plotted as a dashed line in Figure 6, provides a reasonable approximation for z < h∗, well beyond the half-width half- maximum of the distribution4. At larger distances, we take 3.3 Stellar mass and Galactic magnetic field ρ∗ 0. The adopted value of the central stellar density ρ0 i≈mplies thesame mass as1.7 cm−3 of pureHydrogen,or We have shown that photoionized regions must have a fi- 1.2cm−3inthecaseoftheISM,whereHydrogenaccounts nite extent because of self-gravity. The exact value of the ∼for 72 percentof thegas mass. Thecontribution ofstars characteristicscalelengthdepends,however,onmanyother tot∼helocaldensityneartheSunisthuscomparabletothat factors. For instance, the gas may represent only a small of thegaseous component. Thecumulative surface density fraction of the total mass of the system, and there can be a significant amount of non-thermal pressure support z2 z3 from turbulent motions, cosmic rays, and magnetic fields Σ∗(z)=2ρ0 (cid:20)z−0.9(cid:18)h∗ − 3h2∗(cid:19)(cid:21) (8) (Abel& Ferland 2006; Pellegrini et al. 2007, 2009). In the case of the Milky Way, the distribution of stel- increases up to ∼ 17.5 M⊙ pc−2 at z = h∗, about 3 times the observed surface density of Hydrogen (in all forms) at lar mass in the Galactic disk can be inferred by combining numbercountsofindividualstarsanddynamicalarguments. WeapproximatetheresultsobtainedbyRobin et al.(2003) with theexpression 4 Infact,ρ∗(h∗)=0.1ρ0 6 Y. Ascasibar and A. D´ıaz thesolarradius,and2timesthatoftheISMgas,addingup themass in Helium and heavier elements. When the contribution of the stellar component to the gravitational acceleration is taken into account, the pressure gradient required to maintain hydrostatic equilibrium increases, and the transition between the cold and the hot phase moves inwards by about a factor of 2 (top panel in Figure7).Ingeneralterms,thepresenceofanexternalgrav- itational potential will always push the gas distribution inwards, leading to a reduction of the relevant scale lengths and the total gas mass obtained for the system. On the other hand, magnetic fields tend to counter- act the action of gravity. Dueto theeffect of line dragging, theintensityof atangled field increases with gas densityas B n2/3 (observationally, B nκ, with 0.5 < κ < 1, see ∝ ∝ e.g. Crutcher 1999; Henneyet al. 2005), and theassociated magnetic pressure varies as Pmag B2 n4/3. This equa- ∝ ∝ tionofstateisstifferthanthatofanidealgas,andtherefore amuchmilderchangeingasdensityisnecessaryinorderto achieve hydrostaticequilibrium. ThesecondpanelofFigure7showshowtheinclusionof atangledmagneticfieldwithmid-planeintensityB0 =5µG (Beck 2001; Heiles & Crutcher 2005) changes the structure ofourISMmodel.Ascanbeinferredfromthebottompan- els, the magnetic field provides most of the pressure support against gravity.The extentof thecold phase increases by roughly an order of magnitude, reaching now hundreds of pc. In the outer, hot layer, pressure is dominated by the thermalcomponent,andthemagneticfield(forouradopted valueof B0) does not play a significant role. Figure 8. Comparison between the model predictions and the observed densities of molecular (top), atomic (middle) and ion- 3.4 Comparison with observations ized(bottom) Hydrogen.Theobservationaldataarerepresented Oursingle-phasemodelcanonlydescribetheaverageprop- asdashedlines,withthegreyareasdelimitedbydottedlinescor- responding to 20 per cent error bands. Black solid lines display ertiesoftheISM.Moreprecisely,itshouldbeabletopredict thedensityofmolecular,atomic,andionizedHydrogenasa the results of the model with n0 = 1 cm−3, B0 = 5 µG, and stellar density (7). A model with n0 = 0.75 cm−3, B0 = 4 µG, functionofthedistancez fromthemidplaneoftheGalaxy, κ=0.5,andN(H)=1022 cm−2 isplottedinsolidblue(seetext averaged over some scale larger than the typical size of the fordetails). inhomogeneities. Muchobservationalworkhasbeendevotedtothedeter- minationoftheaverageverticalstructureoftheMilkyWay isrepresentedbyshadedareasenclosedbydottedlines.This ISM near the solar neighbourhood. For the ionized compo- estimateroughly correspondstotheactualerrors quotedin nent, we will adopt the distribution derived by Reynolds Reynolds(1991),anditissubstantiallysmallerthanthosein (1991) Nakanishi& Sofue(2006).Noinformation about theobser- nHII(z) =0.015 exp z +0.0025 exp z (9) vationalerrorsisprovidedinNakanishi & Sofue(2003),but, cm−3 (cid:18)−70 pc(cid:19) (cid:18)−900 pc(cid:19) giventhelargedispersionintheHydrogencolumndensities along different lines of sight (Dickey & Lockman 1990), as from pulsar dispersion measures, where the first term rep- wellastheamplitudeofthefluctuationsintheazimuthally- resents the contribution from discrete Hii regions near the averaged surface density profiles, 20 per cent is arguably a Galactic plane,andthesecond termcorresponds tothedif- realistic estimate. fuse ionized gas. For the neutral Hydrogen, we use the for- The results of a model with central density n0 = mula 1 cm−3, central magnetic field B0 = 5 µG, and a stellar z distribution given by equation (7) are also shown in Fig- nHI,H2(z)=n0sech2(cid:20)z ln(1+√2)(cid:21) (10) ure 8 as black solid lines. Although the model gives a rea- 1/2 sonableorder-of-magnitudeestimate(inagreementwiththe with n0 = 0.6 cm−3 and z1/2 = 125 pc for the observedvalueswithinafactoroftwo)ofthescaleheightof atomiccomponent(Nakanishi& Sofue2003),whereasn0 = theGalacticdisk,aswellasthedensitiesandtotalmassesof 0.09 cm−3 and z = 93 pc describe the molecular gas bothatomicandmolecularHydrogen,therearesomeimpor- 1/2 (Nakanishi& Sofue2006).Thecorrespondingdensitydistri- tantdiscrepancies:first,themolecularfractionnearthemid butionsareshowninFigure8bydashedlines,andtheeffect planeisseverelyunderestimated;second,thecentraldensity of 20 percenterrors in each normalization and scale length is almost a factor of 2 above the observed one; and third, Self-gravitating photoionized gas 7 the amount of diffuse ionized gas is extremely low over the turbulent motions, cosmic rays, dust grains, or variations whole radial range, especially in theinnerregions. in theatomic rate coefficients (see e.g. Abelet al. 2008), as The first two problems are closely related. One could well as the external pressure of the intergalactic medium easilyspecifyalowermidplanedensity,butthentheamount (Silich & Tenorio-Tagle 2001) may also play an important of molecular Hydrogen would decrease to unacceptably low role. To summarize, the present results show that gravity levels. It seems that,even after transmission through a col- (in particular, theself-gravity of thegas) should not be ne- umn density of 1021 cm−2, the intensity of the photodis- glected in studies of thestructure of theatomic and molec- sociating continuum is still too high for molecules to form ular layers of a photoionized region, especially when one is at the observed rate. The third problem is also related to interested in their total extent. thesimpleprescriptionadoptedfortheincidentcontinuum, Concerningthespecificproblemoftheverticalstructure sincealmostalltheionizingradiationbecomesabsorbedbe- oftheMilkyWayISM,themodelsdiscussedhereareableto forereachingtheilluminatedface.Inreality,youngstarsare reproducetheobserveddistributionofatomicandmolecular spread around the Galactic plane. Adding any thin source Hydrogenwithanaccuracyofaboutafactoroftwo,butthe of ionizing photons at the mid plane results in an Hii re- amount of diffuse ionized gas is severely underestimated at gion qualitatively similar to the one observed in Figure 1; allheights.Muchmorerealisticresultscouldbeobtainedby in order to reproduce the observed ionization fraction, one providing support for distributed radiation sources, as well would need to specify a distributed radiation source, but asatreatment forthecoexistenceof differentgas phasesat such feature is unfortunately not currently implemented in thesame point. Cloudy. The values of the model parameters can be tuned to better match the observed total density profiles and the molecular Hydrogen fraction. Blue solid lines in Figure 8 ACKNOWLEDGMENTS showstheresultsofamodelwherethemid-planedensityis set to n0 = 0.75 cm−3, the intensity of the magnetic field fWoredweovuellodpliinkge,tmoatihnatanikniGng.,FaenrldanmdaaknindgtthheeCsolfotwudaryetpeuabm- is B0 = 4 µG at the centre and varies with gas density as licly available. It is also a pleasure to acknowledge useful (B/B0) = (n/n0)0.5, and the incident continuum has been propagatedthroughacolumndensityofN(H)=1022cm−2. comments from G. Tenorio-Tagle and E. Pérez on a pre- liminary version of this manuscript. Implementation in the Nevertheless, we strongly advise caution when interpreting developmentversionofCloudywouldnotbepossiblewith- these results. Although the fair agreement obtained for the out the help from G. Ferland, R. Williams, R. Porter, and atomicandmoleculardataprovidesencouragingsupportfor P. van Hoof. We also thank the referee, W. Henney,for his the validity of our implementation of gravity, a more real- insightful comments and suggestions, leading to major im- istic model of the ISM is clearly required in order to derive provementsin our Milky Way model. Financial support for robust quantitative constraints on its physical properties. this work has been provided by the Spanish Ministerio de Basedonourcrudemodel,wewouldsimplyarguethatrea- Educación y Ciencia through project AYA2007-67965-C03- sonablevaluesoftheinputparameters(inparticular,central 03. gasdensityandmagneticfield)yieldreasonablescaleheights for thedisk.Atomicand molecular Hydrogendensities typ- ically agree with observations within a factor of two, but a prescription for distributed sources is necessary in order to REFERENCES model the ionized component. Abel N.P., Ferland G. 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M., 1993, ApJ, 411, 674 gravity plane-parallel gravity external Sigma = 43.680, z0 = 520, a = 1 gravity external Sigma =-39.312, z0 = 520, a = 2 gravity external Sigma = 13.104, z0 = 520, a = 3 APPENDIX A: USER GUIDE c ----------------------------------------------- In order to specify a hydrostatic equilibrium configuration, c Non-thermal components the constant pressure command must be included in the c ----------------------------------------------- Cloudyinputscript.Inaddition,agravitycommandwith cosmic ray background syntax magnetic field -5.3 c ----------------------------------------------- gravity <symmetry> [<factor> [_log]] c Stopping conditions hasbeenimplemented.Thecompulsoryargumentsymmetry c ----------------------------------------------- mustbeeitherspherical orplane-parallel inordertotellthe stop temperature off codewhethertouseequation(2)or(3)tocomputethegrav- stop thickness 1e4 linear parsec itationalacceleration5.Anoptionalfactorcanbeintroduced stop eden -4.5 that multiplies the gas mass, mimicking the presence of an iterate to convergence externalcomponentwithidenticaldistribution.Amoreflex- c ----------------------------------------------- ible way to specify an external potential is provided by the c Output files command c ----------------------------------------------- punch overview "overview.txt" last gravity external <mass> [<extent> <index>] [_log] punch pressure "pressure.txt" last thatmodelsadistributionofmassaroundthecentreofsym- # punch transmitted continuum "trans.txt" last metry of thesystem. Inthespherical case, thefirst number # punch hydrogen conditions "Hydrogen.txt" last represents the mass (in solar masses) of a pointlike object c ----------------------------------------------- located at r = 0; in the plane-parallel case, it corresponds c ... Paranoy@ Rulz! ;^D to thetotal surface density (in M⊙ pc−2) of a uniform thin c ----------------------------------------------- sheet at the mid plane z =0. In both cases, the total mass The first blocks set a label to identify the run, the in- pmo0weisr laaswsuwmietdh itondbeex dαi,sti.reib.umte(dx)o=vemr 0a(nx/exx0t)eαn.tAxll0nausma- tchideegnatsrachdeiamtiiocnalficeolmd,ptohseiticoenn.trCaolmHmydarnodgsenreldaetnedsittyonh0ydarnod- bers are interpreted as linear, unless the keyword log is static equilibrium come next. Note, in particular, how sev- specified. eral gravity external commands have been combined in ordertospecifythestellarmassdistributiongivenbyexpres- 5 Actually,thecommandparserlooksforthecharactersequences sion(8).Theintegrationcontinuesuntiloneofthestopping “sphe” and “plan”, so expressions like “sphere” or “planar” are conditionsismet (thediskthicknessreaching10 kpcorthe alsovalid. electron density falling below 3 10−5 cm−3), and it is ∼ × Self-gravitating photoionized gas 9 iterateduntiltheopticaldepthsconverge.Finally,themain physical properties of the gas (e.g. densities, temperatures) as a function of distance, as well as the different contribu- tionstothetotalpressure,areprintedtooutputfilesonthe disk.