THE DRIVING MECHANISM OF STARBURSTS IN GALAXY MERGERS

We use the AMR code RAMSES to evolve the dark matter and the stellar component using a particle-mesh solver, and the gas component using a second-order Godunov scheme (Teyssier 2002). Throughout our study, we model SF with a Schmidt law: the local SF rate is $\dot{\rho }_* = \epsilon _* \rho _{\rm gas}/t_{\rm ff}$, where $t_{\rm ff} = \sqrt{3\pi / 32G\rho _{\rm gas}}$ is the free-fall time computed at the gas density ρ_gas. The efficiency of SF is controlled by the parameter _* ≃ 1%. SF occurs only in dense enough regions (molecular clouds), defined by the gas density n_H being greater than some threshold value n_*. These two main parameters are usually calibrated using observations of nearby galaxies and the so-called Kennicutt–Schmidt (KS) law. The real efficiency is high with a high threshold, but models with a limited resolution have to use a low threshold combined with a low efficiency (Wada & Norman 2007), which globally reproduces the same KS law (Elmegreen 2002).

The global SFR in our model (like most others) can be computed directly by integrating the Schmidt law over the gas density probability distribution function (PDF) above the threshold n_*. The problem therefore boils down to predicting the PDF evolution during the merger process. As shown by several authors (Elmegreen 2002; Elmegreen & Scalo 2004; Wada & Norman 2007), the multiphase structure of the ISM is built up from complicated processes involving radiative losses (ultraviolet and infrared line cooling, molecular and dust cooling) as well as various heating mechanisms (cosmic rays and UV heating, supernovae and stellar feedback) and of course self-gravity. Surprisingly, numerical experiments have shown universal properties for the gas density PDF in isolated galaxies, with log-normal or power-law distribution shapes. This was explained as a fundamental property of isothermal (or dissipative) self-gravitating turbulence. In this Letter, our goal is to resolve this supersonic turbulence to compute self-consistently the density PDF and the resulting SFR in the course of a galaxy collision.

We use for that purpose a simple thermodynamical model mimicking gas cooling due to a detailed balance between atomic and fine structure cooling and UV radiation heating from a standard cosmic radiation background (Haardt & Madau 1996). Assuming solar metallicity, we have computed the equilibrium temperature as a function of gas density to define our polytropic equation of state (EOS) T = T_eq(n_H). For densities between n_H = 10⁻³ H cm⁻³ and n_H = 0.3 H cm⁻³, our model has T_eq ≃ 10⁴ K, while above n_H = 0.3 H cm⁻³, we have T_eq ≃ 10⁴ × (n_H/0.3)^−1/2 K. In this derivation, we neglected self-shielding of the radiation by the gas: gas cooling at very high density may have been underestimated, but we have also neglected the effect of local radiation sources such as OB stars as additional heating sources. Although our thermal model appears rather uncertain, it provides a reasonable route of gas dissipation, maintaining the gas temperature to a realistic average value at a given density. This EOS-based model produced a log-normal gas density PDF in isolated galaxies similar to the results of complete cooling/heating calculations (see Section 3) and a realistic density power spectrum of ISM substructures (Bournaud et al. 2010).

Another important ingredient is the thermal support added at small scales to avoid artificial fragmentation (Truelove et al. 1997). To ensure that the Jeans length is always sampled by at least four cells, we add an artificial pressure defined as P_Jeans = 16Δx²Gρ²_gas/γπ. This technique, introduced in a different context by Machacek et al. (2001), efficiently prevents the formation of spuriously fragmenting clumps in galaxy formation simulations (Robertson & Kravtsov 2008; Agertz et al. 2009b). From our EOS, we can compute the typical density at which this pressure floor dominates, namely, n_Jeans ≃ 6 × (Δx/100 pc)^−4/3 H cm⁻³ and the equivalent gas temperature as T_Jeans ≃ 2500 × (Δx/100 pc)^2/3 K. This density corresponds to our minimum thermal Jeans mass, which defines our mass resolution m_res = M_Jeans.

We use a quasi-Lagrangian refinement strategy: each cell for which the mass exceeds m_res is subdivided into eight children cells, down to the maximum level of refinement. In order to study the convergence properties of our system and identify qualitative changes, we performed a low-resolution model with Δx = 96 pc, m_res = 10⁶ M_☉ and a high-resolution one with Δx = 12 pc, m_res = 4 × 10⁴ M_☉. Note that in the low-resolution run, the gas cannot cool significantly below 10⁴ K, while in the high-resolution case, it can reach a minimum temperature of T_Jeans ≃ 500 K at the Jeans density.

We have fixed the SF efficiency parameter to _* = 0.01, adjusting the SF density threshold to n_* = 0.1 H cm⁻³ (n_* = 8 H cm⁻³) for the low- (high) resolution run. This ensures that both simulations initially have the same initial SFR of ∼1 M_☉ yr⁻¹ per galaxy in isolated disks, in agreement with the KS law of local spirals. Since in both cases, n_* is significantly below n_Jeans, the star forming part of the PDF is well sampled.

We model a pair of galaxies in a box of size 200 kpc, with isolated and outflow boundary conditions. Each galaxy is embedded in a live halo with a Hernquist (1993) density profile with masses M_h,1 = M_h,2 = 1.8 × 10¹¹ M_☉ and scale lengths equal to the truncation radii r_h,1 = r_h,2 = 30.8 kpc. The pre-existing stars are described as two exponential disks of masses M_*,1 = M_*,2 = 3.6 × 10¹⁰ M_☉, scale lengths r_d,1 = r_d,2 = 4.4 kpc, and truncation radii r_max,1 = 22 kpc, r_max,2 = 13.2 kpc, respectively. The disks' scale heights are h_d = 0.2r_d. A central bulge with B/D = 1 is added, with a Hernquist (1990) profile with a = 4.4 kpc. The gas distribution follows the stellar disk profile with a total gas fraction of 10% in each galaxy. The total number of dark matter particles was set to N_dm = 8 × 10⁵ and the initial number of stars to N_old,* = 6 × 10⁵ for both the low- and high-resolution simulations. We use the hyperbolic orbit proposed by Renaud et al. (2008) to reproduce the Antennae system (see Figure 1). Our AMR grid has a coarse level of ℓ_min = 7 (i.e., 128³ cells) and a maximum level of refinement of ℓ_max = 11 (resp. ℓ_max = 14) for the low- (resp. high) resolution simulation.

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Although merger-induced SF in our model is not primarily driven by an inflow of gas and less concentrated than in earlier models, it remains relatively concentrated near the center of the merging systems (Figure 3): there is still a tidally induced inflow, and the central regions are denser and more prone to star-forming instabilities. This is consistent with SF in ultra-luminous infrared galaxies (ULIRGs) being in general centrally concentrated (assuming ULIRGs are mergers). Nevertheless, our model also explains that the interaction-induced SF can also be, for a part, radially extended (see Figure 3). This can explain why a number of interacting galaxies actually show extended SF with SSCs forming at several kpc from their center, such as Arp 140 (Cullen et al. 2006) and the Antennae (Wang et al. 2004).

As for the Antennae, the orbit of which is matched by our simulation, there is a general consensus that we are witnessing the merger close to the second pericenter passage, when the two disks are still well separated (Renaud et al. 2008). This corresponds to an epoch close to 450 Myr in our simulation (Figure 1). Our low-resolution models reaches SFRs around 10 M_☉ yr⁻¹ just after the second pericenter passage and during only 50 Myr: these properties are in broad agreement with recent SPH simulations by Karl et al. (2010) and with the observed SFR (Zhang et al. 2001). Karl et al. (2010) then proposed that this high SFR and the extended SF in the Antennae result from the system being observed just at the particular instant of overlap between the two disks. Our high-resolution model, however, shows that high SFR around 20 M_☉ yr⁻¹ and relatively extended SF can be produced during a longer period (300 Myr) and does not require the system to be observed at a particular and brief instant.

Observations suggest a dual law for SF, where the integrated gas consumption timescale (Σ_SFR/Σ_gas) is relatively low for quiescent star-forming disks and higher for starbursting ULIRGs and sub-millimeter galaxies (likely major mergers), as pointed out independently by Daddi et al. (2010a) and Genzel et al. (2010). To compare our models with these observations, we retrieved integrated properties such as half-light radii, the total gas mass, and the total SFR at several instants. The low-resolution model, where the starburst is driven only by the central gas inflow, does not show the observed change in Σ_SFR/Σ_gas: the SFR increases during the merger, but only in proportion corresponding to the increase in the global gas density Σ_gas, and this model remains close to the standard relation for isolated disks (Figure 5). The high-resolution model has its starburst driven mostly by increased gas turbulence and fragmentation. The gas density increases mostly on small scales in dense clumps throughout the system: this process does not affect the total effective size of the gas component, so the observable global density Σ_gas has only a modest increase. At the same time, the starburst is even stronger than in the low-resolution model. This process brings our model in agreement with the "starburst versus quiescent KS law" pointed out by observations, throughout the duration of the merging process. Clustered SF in high-resolution merger models can also affect the final structure of the resulting early-type galaxies (Bois et al. 2010).

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We thus propose that these recent observations unveiled a "starburst regime," where the efficiency of SF on small scales and at high densities is unchanged, but exacerbated gas turbulence and fragmentation into massive clouds result in faster gas consumption and higher integrated SF efficiency. The adopted SF law inside the clouds is not the key ingredient in the interpretation, the main effect being the rapid evolution of the density PDF. Different SF models can indeed lead to different quantitative predictions, but the main qualitative change comes from resolving the high-density tail of the PDF (Governato et al. 2010). Previous models of galaxy mergers did not resolve ISM turbulence and clouds, and could not unveil the physical processes driving this starburst mode. The actual process of SF in starbursting mergers cannot be captured with sub-grid models on scales larger than 100 pc and requires clustered SF in a multiphase ISM to be directly resolved.