Delayed metal recycling in galaxies: the inefficiency of cold gas enrichment in colliding supershell simulations
aa r X i v : . [ a s t r o - ph . GA ] N ov Delayed metal recycling in galaxies: the inefficiency of cold gasenrichment in colliding supershell simulations
Evangelia Ntormousi , and Andreas Burkert , , ABSTRACT
The fate of metals ejected by young OB associations into the Interstellar Medium (ISM) isinvestigated numerically. In particular, we study the enrichment of the cold gas phase, which isthe material that forms molecular clouds. Following previous work, the expansion and collision oftwo supershells in a diffuse ISM is simulated, in this case also introducing an advected quantitywhich represents the metals expelled by the young stars. We adopt the simplest possible approach,not differentiating between metals coming from stellar winds and those coming from supernovae.Even though the hot, diffuse phase of the ISM receives a significant amount of metals fromthe stars, the cold phase is efficiently shielded, with very little metal enrichment. Significantenrichment of the cold ISM will therefore be delayed by at least the cooling time of this hotphase. No variations in cloud metallicity with distance from the OB association or with directionare found, which means that the shell collision does little to enhance the metallicity of the coldclumps. We conclude that the stellar generation that forms out of molecular structures, triggeredby shell collisions cannot be significantly enriched.
Subject headings:
ISM: bubbles — ISM: clouds — ISM: general — ISM: kinematics and dynamics —ISM:structure — stars: formation
1. Introduction
Stellar feedback is a very powerful source ofthermal and turbulent energy in the Interstel-lar Medium (ISM). Young massive stars pro-duce ionizing photons, expel large amounts ofmass and momentum in winds and end theirlives in supernova explosions, all processes whichshape the matter around them in shells and cav-ities (Heiles 1979, 1984; Ehlerov´a & Palouˇs 2005;Churchwell et al. 2006). Young OB associations,typically containing between 10 and 100 stars,create giant shell-like shocks from the combinedfeedback of their member stars. These supershellsare among the largest structures in the Galaxy.Massive stars are also believed to be an impor- University Observatory Munich, Scheinerstr. 1, D-81679 Germany Max Planck Institute for Extraterrestrial Physics,Giessenbachstr. 85748 Garching Germany Excellence Cluster Universe, Boltzmannstr. 2 D-85748Garching Germany tant source of metals for the ISM. According toour standard picture of the chemical evolution ofgalaxies, material ejected by the stars in an OBassociation will take part in forming new stars.But, how long does it take before the metals re-leased by one generation of stars actually end upin molecular clouds?Molecular clouds collapse gravitationally togive stars very soon after they come into existence(Hartmann 2002), so any metals they contain aremost likely in place when they form. Simulationsof molecular cloud formation are then a natu-ral way of answering the question posed above.Usually, such simulations fall into two categories:Galactic scale simulations, which study the gravi-tational collapse of gas caused either by global diskinstabilities (Kim & Ostriker 2002, 2006) or by theself-gravity of large amounts of gas accumulatedby spiral density waves (Dobbs et al. 2011a,b),and local simulations of converging atomic flows,which show that atomic gas converts to molec-ular material under the combined effect of vari-1us fluid instabilities (Heitsch et al. 2005, 2006;Hennebelle et al. 2007; V´azquez-Semadeni et al.2007). These approaches could lead to differentanswers regarding the enrichment of molecularclouds.In Ntormousi et al. (2011), hereafter Paper I,we presented the results of superbubble collisionsin a uniform and in a turbulent diffuse environ-ment. The energetic feedback from young OB as-sociations, inserted as a time-dependent mass andenergy source in the numerical simulations, con-densed the gas in large spherical shocks.One indirect conclusion of that work was thatthe clumps which form from the fragmentation ofthe shells seemed to be largely composed by diffuseInterstellar Medium (ISM) material, swept-up andcondensed by the shocks. However, even in sucha case, some enrichment may still be possible asa result of the turbulence generated by the shellcollision. To resolve this issue, in this work we in-vestigate the possible metal enrichment of clumpsformed in such an environment in detail.There is little previous work studying thefate of the metals ejected by OB associations.Tenorio-Tagle (1996) considered all the possi-ble mechanisms for mixing between the differentphases in the dense shells of single supernova rem-nants and in supershells formed by combined ex-plosions. With dimensional arguments he showedthat the mixing should be most efficient in the hotphase of the gas. Spitoni et al. (2008) studied thefate of dense clouds formed by the condensationof supershells and expelled from the galactic diskin the form of an outflow. However, they focusedmore on the landing coordinates of these cloudswhen they fall back on the disk.In this work for the first time we study the ef-ficiency of the metal enrichment of the cold phaseformed at the edges of supershells numerically. Weadopt a very simple approach, in which the OB as-sociations inject a constant amount of metals withtime.Our methods is presented in Section 2, the re-sults are discussed in Section 3 and we commenton their implications in Section 4.
2. Numerical Method
A two-dimensional, high-resolution simulationvery similar to those in Paper I is performed with the hydrodynamical code RAMSES (Teyssier2002). The setup consists of two young OB asso-ciations, placed at a certain distance from eachother in a warm diffuse background. Their feed-back creates two expanding shells that sweep upthe surrounding gas. These cold and dense shellseventually collide in the middle of the computa-tional domain.The time-dependent wind and supernova feed-back from these stellar associations is implementedas a source of energy and mass in the code. AnOB association in this simulation comprises 20”average” stars. Each of these stars representsa fraction of an entire population. For simplic-ity, all stars are placed in a circular region of5 pc radius. The associations are assumed toform simultaneously and all stars within each ofthem are also assumed to have formed at thesame time. The wind and supernova data weretaken from population synthesis models createdby Voss et al. (2009). For more details on thewind implementation we refer the reader to Pa-per I. Cooling and heating processes appropri-ate for the ISM are also included, according toDalgarno & McCray (1972), Wolfire et al. (1995)and Sutherland & Dopita (1993). The simulationdoes not include gravity.An important increase in efficiency in compar-ison to previous simulations is achieved with theuse of Adaptive Mesh Refinement (AMR). Giventhe nature of the problem under study, the mostadequate refinement policy is to trigger the divi-sion of a cell when the difference in the gradients ofpressure and density exceeds a certain threshold.We have used a threshold equal to 1% of the gra-dient of the density and the pressure in this work,but experimenting with the value of the thresholdgave no significant differences in the grid struc-ture. Thresholds higher than 10%, however, failedto capture the shock structure properly.The supershells in this setup are expanding in auniform diffuse background, which means that anyperturbations that are expected to seed the fluidinstabilities must arise at the grid level. In orderto be able to compare this simulation, which usesAMR, to our simulations from Paper I, which weredone with a uniform grid, we must seed the pertur-bations at the smallest grid level and at the samephysical scale. For this reason, the simulation isinitiated with a nested grid configuration, where2he highest resolution region is located at the cen-ter of the simulation box. Once the first seeds ofthe perturbation start to grow, we switch to theadaptive refinement policy described above. Fig-ure 1 shows the grid structure for a nested and foran adaptive grid refinement policy. The top panelof the Figure shows the logarithm of the hydrogennumber density and the bottom panel shows thelevel of refinement in powers of two. For example,a level of refinement equal to 6 in this notationmeans that, if the entire domain were simulatedat this resolution, it would contain 2 cells.Comparison between simulations of this setupwith this AMR approach and uniform grid simu-lations have shown no difference in the amount ofcold gas formed in the simulation, the position ofthe shocks and the sizes or velocity dispersions ofthe formed clumps. Small differences in the shockmorphology are, of course, always present, due tothe very nonlinear nature of these phenomena.For this particular simulation we use a box of250 pc physical size, at an effective resolution of2048 (a maximum level of refinement equal to11 according to the notation described above).This allows us to resolve the Field length of thewarm ISM (Koyama & Inutsuka 2002), withoutactually implementing numerical thermal conduc-tion. Higher resolution simulations would requiresuch implementation (see also discussion in Pa-per I). The choice of a smaller box with respectto Paper I is both more physical, in terms of theaverage distance between OB associations in theGalaxy and it also yields a smaller computationalvolume for the same physical resolution, thus sig-nificantly reducing the computational cost of thesimulation.We stop the calculation when the turbulencein the collision area starts expanding towards theinflow boundaries. In this particular case this hap-pens 4.36 Mys after star formation in the OB as-sociations.The aim of this work is to follow the advectionof metals from the OB associations into the coldgas formed at the shock wake. This is done bymeans of a passive advected quantity, representingthe metals from the stars. A constant amount ofmetals, equal to 10 − metal particles/cm is addedat the wind region at each coarse timestep. Thisvalue is totally arbitrary, so it can be scaled torepresent different environments. The amount of metals introduced by the OBassociations is assumed here to have a negligi-ble effect on the amount of cold gas formed. Inprinciple, though, extra metals could affect ourresults due to their contribution to the cooling,which would also change the regime where thegas becomes thermally unstable. In our calcu-lations the most important coolant of the gas isline emission from carbon and oxygen. A decreasein the abundance of these elements would causethe area where we can have phase formation dueto the Thermal Instability to shrink, and an en-richment would enlarge the Thermal Instabilityregime (Wolfire et al. 1995).Support for the approximation we are makingcomes from Walch et al. (2011), who studied theeffect of metallicity on the formation of cold gasfrom Thermal Instability in simulations of tur-bulence. They found that, for driven turbulence(which is the case in our models), the total amountof cold gas in the simulation is not significantly af-fected by changes in the metallicity. This meansthat, as long as the metallicity of the gas we aresimulating is high enough to capture the ThermalInstability regime of the ISM, we are not makingsignificant errors in the total amount of cold gas inthe domain by ignoring the enrichment from theOB stars in the cooling function.
3. Delayed metal recycling
Figure 2 shows snapshots of the simulation be-fore and after the shell collision. The top panelsof this Figure are contours of the logarithm of thegas temperature and the bottom panels show thelogarithm of the ratio of newly ejected metals tohydrogen atoms in the cell.The general picture of the simulation is thesame as in Paper I. The spherical shocks createdby the stellar feedback are unstable to the Vish-niac instability (Vishniac 1983, 1994) as small-scale wind fluctuations create ripples on their sur-face. The result of the gas condensation at thepeaks of these ripples is to trigger the Thermal In-stability (Field 1965; Burkert & Lin 2000), whichcreates cold and dense clumps at the shock wake.The shear on the shell surface, also caused bythe Vishniac Instability, gives rise to characteristicKelvin-Helmholtz eddies, thus contributing to thedynamics of the newly-formed cold clumps (right3ig. 1.— Snapshots of two runs using different refinement techniques, taken at the same timestep, about 3Myrs after star formation. On the left, nested grid and on the right gradient-based refined grid. The plotson the top row show the logarithm of hydrogen number density and the plots on the bottom row show thecorresponding grid structure. The axes coordinates are in parsecs.4ig. 2.— Logarithm of temperature (top) and logarithm of relative metal content (bottom) for two snapshots.On the left, 1.22 Myrs and on the right, 4.46 Myrs after star formation took place in the OB associations.5anel of Figure 2).When the shells collide, the combination of thelarge-scale shear by the collision and the small-scale structure already carried by the shells givesrise to a turbulent region at the collision interfacewhich contains a mixture of warm and cold gas(right panel of Figure 2). Turbulence is a veryefficient mixing mechanism, so we expect an en-hancement in metallicity of the warm gas after theshell collision.In Figure 2, we can indeed see that the warmgas has enhanced metal content. The same can beshown more clearly by plotting the mass fractionof the gas in the computational domain in density-metallicity bins. In Figure 3, showing such plotsfor two snapshots of the simulation, we can seethat the dense gas dominates the mass of the gasin the computational domain. At the same timewe see that it never reaches relative enrichment ofmore than 10 − . For comparison, we note that,were the metals ejected by the stars to be instan-taneously and homogeneously mixed in the diffusegas phase, the relative enrichment would be 10 − and if all the metals from the stars ended up in thecold phase, the relative enrichment of that phasewould be of about 5 · − .Throughout the simulation practically all themetals injected by the OB associations stay in thehot wind, despite the fact that most of the massis in the cold gas component. At late times asmall fraction of the metals (1-5%) mixes into theslightly denser, warm gas ( n H ≃ − , T ≃ )due to the shell collision that causes turbulentmixing. A clump is identified as a collection of adjacentcells with densities above 50 cm − and tempera-tures lower than 100 K. By this definition, Figure3 already indicates that the clumps do not con-tain significant amounts of material from the OBassociations.To look at the clump metallicities in more de-tail, we plot their metallicity distributions in Fig-ure 4. The plots show distributions of the meanmetallicity over the mean hydrogen number den-sity of the clumps, on the left-hand side for a snap-shot at 1.22 Myrs and on the right-hand side forthe final snapshot, at 4.36 Myrs. Even though the numbers can be rescaledto mean different absolute metal content in theclumps, the important fact here is that the coldphase will always receive at least two orders ofmagnitude less metals than the diffuse warmphase.Even though the metal injection from the OBassociations does not stop during the simulationtime, the metal content of the clumps does notseem to increase significantly. The spread of thedistribution of the relative metal content of theclumps seems to increase with time. As the systemevolves, new clumps are formed at relatively lowermetallicities. The little metals they accumulateover time leads to the formation of a peak in thedistribution. However, the maximum value of thedistribution does not increase, meaning there is nosignificant enrichment.Figures 5 and 6 show the mean number den-sity of metals in a clump as a function of distancefrom its closest OB association and as a functionof the polar angle with respect to the horizontalline in the middle of the domain, respectively. Theamount of metals in a clump does not seem to de-pend on its position with respect to the OB asso-ciations, pointing to a very uniform distribution ofthe molecular cloud metallicities around the youngassociations.
4. Conclusions
We have presented results of a high-resolutionsimulation of colliding supershells created by thefeedback from young stars. The evolution of theseshells was followed with ideal hydrodynamics andno gravity for about 4.3 Myrs. In agreement withthe results of previous work we observe the for-mation of complex cold structure as these shellscondense, fragment and collide.In this simulation we have used an advectedquantity, inserted in the region of the domain rep-resenting the wind, to follow the metals ejected bythe winds and supernova explosions in these OBassociations. In this way, we were able to distin-guish between material originating from the starsand material originating from the diffuse ISM inthe composition of the cold clumps.We find that the metal enrichment of theclumps is very small throughout the simula-tion. The maximum relative metallicity reached6ig. 3.— Mass fractions in density-metallicity bins at two snapshots, 1.22 Myrs (left) and 4.36 Myrs (right)after star formation.Fig. 4.— Distributions of the metal content of the clumps over their hydrogen number density. The dataare from snapshots 1.22 Myrs (left) and 4.36 Myrs (right) after star formation.7ig. 5.— Dependence of the clump metal content on their distance from the closest association. The plotsare shown at 1.22 Myrs (left) and 4.36 Myrs (right) since the beginning of the simulation.Fig. 6.— Dependence of the clump metal content on their polar angle calculated with respect to thehorizontal line at the center of the computational domain. The plots are shown at 1.22 Myrs (left) and 4.36Myrs (right) since the beginning of the simulation. 8y the cold gas in the simulation is two or-ders of magnitude lower than that of the warm(25000 < T < K) diffuse medium and negli-gible compared to that of the hot (
T > K)medium. The fact that the hot gas receives asignificant fraction of the injected metals impliesthat, if molecular clouds were to form in this envi-ronment, enrichment would be delayed by at leastthe cooling time of this gas. This effect is evenmore relevant if we consider that the free-fall timefor each of these dense clumps is about 1 Myr,which means that many of them would be collaps-ing before the end of this simulation, had gravitybeen considered, leaving even less time for enrich-ment. We predict that the stars that are formed inmolecular clouds triggered by shell fragmentationshould not be significantly enriched, even takingshell collisions into account.A delay in the metal mixing before star forma-tion has important implications for the chemicalevolution of galaxies. The traditional approachfor studying the evolution of the metallicity in agalaxy is the closed-box model, (Searle & Sargent1972; Tinsley 1974), where mixing is assumed tobe instantaneous. However, it has been shownthat, at least for the solar neighborhood, betteragreement between the observed metallicities andthe models is obtained when this assumption isrelaxed. Thomas et al. (1998) showed that a de-lay of the order 10 years in the enrichment ofthe star-forming gas results in a better fit of themodel to local yields. Spitoni et al. (2009) cameto a similar conclusion, for stellar yields dependingon metallicity.In our simulations the delay in enrichment ofthe cold gas could be even longer than the 10 yrs quoted in Thomas et al. (1998). The windsfrom the OB association would keep the hot gasat temperatures of 10 K for at least 30 Myrs. Thecooling time for this gas, given its very low density( n ≃ − cm − ) is very long ( t cool ≃ nk B T / Λ ≃ − yrs). This provides further support for theassumptions of previous work regarding delayedmetal enrichment of the star-forming phase of theISM.The metal content of the clumps seems to be in-dependent of their position with respect to the OBassociation. This, in combination with the smallspread in cloud metallicities, means that the nextstellar generation, formed by the clumps created in such an environment, would be very uniform inits metal content.Of course, there are many effects that havenot been included in this work. For instance,we have assumed that the metal mass injectedby the OB associations is roughly constant withtime and that it is uniformly distributed in thewind region. Both these assumptions are question-able. We would, in principle, expect the metals tobe contained in small clumps, as part of clumpywinds or fast supernova ejecta, possibly makingmixing more efficient. In addition, the wind ma-terial should vary in composition from the super-nova material, although this would still mostly endup in the diffuse rather than the dense cold phase.These are all complications that should be takeninto account in future work.The numerical simulations were performed onthe local SGIAltix 3700 Bx2, which was partlyfunded by the Cluster of Excellence: Origin andStructure of the Universe. REFERENCES
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