Besides a self-consistent treatment of the gravitational and hydrodynamical forces,
Gadget offers implementations for a number of other physical processes, which are relevant to galaxy evolution. Here, we will give a short summary of the particular models we have used in this work. For a more complete overview we refer the reader to the cited literature of any specific model.
FollowingKatz et al.(1996), radiative cooling and heating is computed for an opti- cally thin plasma out of primordial hydrogen and helium, assuming collisional equilib- rium. As a source of heating, a local spatially uniform time-independent photo-ionizing UV background is taken into account, which is assumed to arise from quasi-stellar ob- jects (QSOs) and star-forming galaxies (Haardt & Madau 1996).
Star formation, together with associated supernova feedback is assumed to effec- tively heat and pressurize the surrounding ISM. It is modeled following the sub-grid multiphase prescription proposed by Springel & Hernquist (2002). In this model, the star-forming ISM is treated as an effective two-phase fluid, where cool dense clouds are embedded in a hot ambient medium assuming pressure equilibrium between the phases. This approach attempts to mimic some of the key aspects of the theoretical picture of a multi-phase ISM (McKee & Ostriker 1977), where hot gas is assumed to develop a run-away cooling instability if it exceeds a certain density threshold, ρ > ρcrit. Stars
are subsequently formed from cold clouds satisfying the above condition on a char- acteristic star formation timescale t⋆ and instantaneously return mass and supernova energy from massive short-lived stars (M⋆ >8 M⊙) to the surrounding ISM. Adopting a Salpeter initial mass function (IMF;Salpeter 1955), the fraction of massive stars has a value of approximatelyβ = 0.1, and the energy released to heat the ambient medium per supernova explosion is chosen to take a canonical value of 1051erg. The SFR then
simply reads dρ⋆ dt = ρc t⋆ −β ρc t⋆ = (1−β) ρc t⋆, (3.24)
where ρc and ρ⋆ are the densities of stars and cold gas, respectively, and the thresh- old density is determined self-consistently in our simulations by requiring the effective equation of state to be continuous at the onset of star formation. Adopting a charac- teristic star formation timescale oft⋆ = 2.1 Gyr·(ρ/ρ⋆)−1/2, the above relation is tuned such as to recover the observed Kennicutt-Schmidt “law” (Kennicutt 1998, seeSpringel & Hernquist 2003, Figure 2).
The mass and energy transfer between the hot and cold phases establishes a tightly self-regulated star formation prescription, where cloud condensation by cooling and subsequent star formation are efficiently balanced by the heating of the diffuse ISM and the evaporation of cold clouds through the thermal energy injected in supernovae explosions. The basic bookkeeping for the evolution of the densities in the cold and hot
3.1 The Numerical Code 31
phases, respectively, is given by the respective rate equations (Springel & Hernquist 2002) dρc dt = − ρc t⋆ −Aβ ρc t⋆ + 1−f uh −ucΛnet(ρh, ρc), and (3.25) dρh dt = β ρc t⋆ +Aβ ρc t⋆ − 1−f uh−ucΛnet(ρh, ρc), (3.26)
where ρh is the density of the hot component, and A ∝ A0ρ−4/5 governs the cloud
evaporation. The thermal energy per unit mass of the hot and cold component are given by uc and uh and Λnet(ρh, ρc) is the net cooling function in the presence of an external UV background (Katz et al. 1996). The latter terms in Equations (3.25) and (3.26) treat the growth of cold clouds via the thermal instability occurring at densities above the density thresholdρcrit, wheref = 0is set, andf = 1otherwise. On the other
hand, the first terms in Equations (3.25) and (3.26) describe the net mass transfer due to star formation and the instantaneous stellar feedback.
The thermal energy per unit volumeǫth =ρcuc+ρhuh of the gas phase then evolves
according to
d
dt(ρcuc +ρhuh) = −Λnet(ρh, ρc) +β ρc
t⋆uSN−(1−β) ρc
t⋆uc, (3.27)
whereuSNrepresents the amount of supernova energy feedback to the surrounding ISM.
As a result of the thermal feedback, the star-forming, dense part of the ISM is as- sumed to develop a two-phase medium which may be described by an effective equation of state of the form
Peff = (γ−1)ρ ueff, (3.28)
with ueff = ((1−x)uh+x uc) and x being the mass fraction in cold, star-forming
clouds. This effective equation of state is quite “stiff”, providing a high, steeply rising pressure support with increasing density. This effectively leads to a self-regulated for- mulation of the star formation and the associated stellar feedback. However, one is free to control the efficiency of the thermal feedback via a further dimensionless parameter
qEQS that interpolates the star formation model between the full “stiff” feedback model
(qEQS = 1.0) and a “soft” isothermal equation of state with T = 104 K (qEQS = 0, see Springel et al. 2005).
In this Thesis, we generally set the parameters governing the multi-phase SF model such as to ensure a SFR of ∼ 1 M⊙yr−1 for an isolated Milky-way like galaxy in the simulations (see also Chapters 5 - 7). For that we choose parameters for the star formation timescale t0
⋆ = 8.4 Gyr, the cloud evaporation A0 = 4000, and a supernova
“temperature” of TSN = 108 K, respectively. Cold dense gas is assumed to reside in
clouds with temperature Tcold = 1000 K. Given this parameter choice and requiring
that the equation of state is continuous at the onset of star formation, the critical hydrogen number density is set to ncrit= 0.128 cm−3.