Code tests: 26 Al feedback

5.2 Implementation of mass, momentum and energy feedback 95 JIM uses the settings for the SPH data provided by Jim Dale (ISM structures in the simulations presented inDale and Bonnell,2011). If it is not defined, the data format of the SPH data provided by Clare Dobbs (molecular clouds in the simulations presented inDobbs et al.,2011) is used.

Other patches

Additionally we have set default units inamr_commons.f90(Code ListingC.22). These defaults can be overwritten by different choices in the namelist. Since some of our simulations (namely the simulations with stellar feedback into the clouds of Clare Dobbs (Dobbs et al.,2011)) observe energy flowing out of the computational box, we monitored such energy losses with the new mod-ule inoutflow.f90(Code ListingC.23). Finally we often re-started our simulations and thus we patchedinit_amr.f90(Code ListingC.20) since R^AMSESdoes not allow to change the initially chosen output times, which is quite inconvenient for re-simulations when the initial simulation showed an interesting phase in the model’s evolution that should be analyzed in more detail. Our version ofgodunov_utils.f90(Code ListingC.21) removes outflows from almost empty cells.

It can also ignore almost empty cells when theCFL(sect3.3) is evaluated. For the HLLC solver, the preprocessor directive ALUSTOP only allows the radioactive tracers to flow into cells with temperatures above a temperature threshold.

To stabilize our simulations we also avoid negative internal energies in set_uold (Code List-ing C.24, godunov_fine.f90). We remove outflows from almost empty cells and reset the pressures in these cells in subroutine godfine1 (Code Listing C.24, godunov_fine.f90) and subroutinectoprim(Code ListingC.25,umuscl.f90). godunov_fine.f90can also be used to reset the cooling losses.

The Makefile in Code ListingC.26summarizes the newly definedpreprocessor directives.

1e-34 1e-33

0 1 2 3 4 5 6

26 Al[gcm−3 ]

Radius [pc]

Simulation with 9 processors, 0.6 Myr

5e+23 1e+24

0 1 2 3 4 5 6

26 Al[g/shell]

Radius [pc]

Simulation with 8 processors Hilbert

Planar Planar, 50 kyr Planar, 0.5 kyr Hilbert, no decay

Figure 5.1: This figure shows the convergence of different decay routines. The back arrow in-dicates the location of the border of the feedback region. The turquoise line shows a simulation without decay. A simulation in which the decay of²⁶Al is calculated every 50 kyr is shown in blue.

Obviously this line has to overestimate the decay since it assumes that all the²⁶Al in the cell has been there since the last calculation of the decay. The simulation with decay at every time step (green, typical time step ∼ 50yr) coincides with the simulation with 500 yr between decay cal-culations. Number precision problems are expected if the time steps become of the order of years or smaller. It is interesting to note that different parallelization methods or a different number of processors influenced the result (green line and red line). It has to be tested if this is just a problem of the boundary cells if domain decomposition happens inside the driver region or if this problem always occurs ifAMRis combined with MPI.

Simulations

The main questions addressed in the simulations described in this work are, how long massive star feedback takes to disrupt aGiant Molecular Cloud (GMC)(GMC) (→molecular cloud lifetimes), how much of thefeedback energycan be converted to kinetic and thermal energy of theGMCgas (→ feedback energy efficiency, energy reservoir for driving of turbulence) and which fraction of the cold GMCgas is heated (→ mass distribution ofISM phases). Another important aspect of these simulations was to check whether a scaledVoss et al.(2009) feedback model, which is based on the mean of 100 coeval stars between8and120M, is a suitable model for the feedback of an OB association with ∼10massive stars. This is of importance for modeling theOrion-Eridanus Superbubble (OES), because the feedback ofVoss et al.(2009) destroys homogeneousGMCsvery efficiently and produces bubbles significantly larger than observed. To assess if the Voss et al.

(2009) prescription is a realistic model for the feedback of a typical⁸OB association, we compared its influence ontoGMCs(1) to the influence of the feedback of individual Monte-Carlo realizations of an OB association with 10 stars between8and120Mand star formation with a dispersion (σ) of1Myr (as described inVoss et al.,2010) and (2) to feedback of individual massive stars.

For all simulations in this work we use a cooling-heating prescription describing a cold neutral medium (CNM) and not molecular clouds (T ∼ 10–30K and n ∼ 1000 particles cm⁻³). This prescription does not include ionization, cosmic ray heating, C⁺, CO, C or H2O cooling.

8We call an OB association “typical” if its stellar mass distribution has a high probability to be drawn from the assumedIMF.

Chapter 6

1D: Feedback efficiency in spherical symmetry

We start to investigate the amount of energy massive stars can convert to kinetic energy of the surroundingISM with one-dimensional spherically symmetric models. The big advantage of 1D simulations is that they make it feasible to search a large region of parameter space in a short time.

The obvious drawback is that non-radial motions (e.g. hydrodynamic instabilities in the bubble’s shell) cannot be taken into account. We will thus assume that the retained energy in the 1D models is just an upper limit and re-simulate the most interesting models in more dimensions. The 1D simulations were carried out with the patched P^LUTO code (Sect. 5.2.1) and contain a single, massive star with 60 M. As we have shown in Sect. 2.7.5, this is a valid first approximation for feedback in GMCs. The stellar feedback is calculated from the mass loss rate of the rotating models of Ekström et al. (2012) as described in Sect. 2.7.3. The implementation in the code is discussed in Sect.5.2.1.

With the 1D models it is possible to study thefeedback energy efficiency’s dependence on resolu-tion. Our simulations use a static mesh with up to250cells per parsec. We assume that the star is placed in an infinite, homogeneous cloud and start with a computational box of5pc. During the simulation, we monitor how many undisturbed cells of ambient medium are left and add another 5 pc of undisturbed medium to the computational box if the number of such cells drops below 100. The standard assumptions for the cloud material in this study are solar metallicity, a density of ρ0 = 2.2×10⁻²² g cm⁻³ and a pressure of p0 = 1.48×10⁻¹² erg cm⁻³ corresponding to a temperature of approximately37K. This phase of theISMis in cooling-heating equilibrium if we use the same cooling model asNtormousi et al.(2011) (see Fig.2.1for the cooling-heating equi-librium). The cooling-heating equilibrium temperatureTeq(n)depends on the cooling model. We added an artificially stable gas phase for theinitial conditions(n0, T0) if thisISMphase was not in cooling-heating equilibrium in the chosen cooling model. The number density (n) of∼100cm⁻³ resembles the average density of molecular cloud complexes as shown in Sect. 2.5. It is known that molecular clouds exhibit a fractal structure, which will be addressed in our future work with models taking more dimensions into account.

Our work extends the published stellarfeedback energy efficiencymodels in two important aspects:

1. In all simulations shown in this section, we follow the energy content of the simulations from star formation until several million years after theSN, when peak velocity in the bubble shell becomes smaller than the sound speed of the ambient medium. At this time the shell is not

infinitely thin and the highest velocity is found near the highest density. We argue that at latest at this point turbulent motions will lead to break-up of the shell and very efficient mixing (and energy deposition) in the ambient medium. Therefore, we follow the evolu-tion of the models substantially longer than it was done in the work ofTenorio-Tagle et al.

(Tenorio-Tagle et al.,1990,1991;Tenorio-Tagle,1996). Thornton et al.(1998) also stop the simulations after 13 time of maximal luminosity (t0)s (defined in Sect.6.1.1), which is in most models shortly after the transition to the momentum conserving phase (Sect.4.5.2).

2. We test how stellar winds and variations of the wind strength affect the feedback energy efficiency.

Observationally, the impact of the wind of theSN’s progenitor star is illustrated for example by the shell of the progenitor star aroundSN1987A reported byWampler et al.(1990), the wind shell of a 25M star seen in the SNremnant G296.1–0.5 (Castro et al., 2011) or the stellar-wind envelope seen inSN2006aj (Sonbas et al.,2008).

However, in the literature on feedback energy efficiencies stellar winds are either ignored (e.g.Thornton et al.,1998) or assumed to be constant (e.g.Tenorio-Tagle et al.,1990,1991;

Tenorio-Tagle, 1996). In our simulations, it turned out that ignoring winds is problematic:

Table 6.2 shows that the amount of mechanical luminosity¹ that can be converted to shell motions differs between models, which insert all energy in a blast (aSN) and models where stellar winds are energy sources over long periods of time. Similar effects were observed by: Tenorio-Tagle et al.(1990, 1991); Oey and Massey(1994);Oey(1996);Tenorio-Tagle (1996). The reason for the higherfeedback energy efficienciesof continuous energy injection processes is thatWR winds of the progenitor star create a bubble in the ISM. Blast waves of SN explosions in such cavities undergo an almost loss-less expansion until they hit the cavity walls. As a consequence, wind-blown bubbles delay the time of maximal luminosity (defined in Sect.6.1.1) and increase the amount of retained energy, since such cavities can act as pressure reservoirs. When the blast hits the cavity walls, so-called catastrophic cooling in the dense shell of swept-up ambient medium sets in (Tenorio-Tagle et al.,1990;Smith and Rosen,2003). This process (strong radiative cooling losses caused by aSNblast wave hitting a pre-existing shell) is a likely explanation for the X-ray emission in excess of an adiabatic model in X-ray brightsuperbubbles (Chu and Mac Low, 1990;Arthur and Henney, 1996;

Oey,1996).

In the first part of this chapter (Sect. 6.1) we will discuss wind-less reference models and proceed to time dependent winds in Sect.6.2.