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The evolution of the Q total Toomre parameter in run 16 (i.e. low resolution) on the left and run 22 (i.e. high resolution) on the right. At t 0 the adiabatic relaxation phase ends and, in the case with high resolution, the profile is more stable and smoother than in the case with low resolution. For run 16 the time steps 0.2, 0.5. and 0.8 Gyr correspond to the beginning of the clump formation phase, the middle of the clumpy phase and the end of it, respectively. Horizontal dashed line marks the threshold 1.5 for the stability of a disc. Note that for run 16 at t = 0.2 Gyr the sudden drop around 3.5 kpc corresponds to the radius at which clumps form.  

The evolution of the Q total Toomre parameter in run 16 (i.e. low resolution) on the left and run 22 (i.e. high resolution) on the right. At t 0 the adiabatic relaxation phase ends and, in the case with high resolution, the profile is more stable and smoother than in the case with low resolution. For run 16 the time steps 0.2, 0.5. and 0.8 Gyr correspond to the beginning of the clump formation phase, the middle of the clumpy phase and the end of it, respectively. Horizontal dashed line marks the threshold 1.5 for the stability of a disc. Note that for run 16 at t = 0.2 Gyr the sudden drop around 3.5 kpc corresponds to the radius at which clumps form.  

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... The in situ formation of giant clumps is commonly attributed to Toomre instability (Toomre 1964;Dekel et al. 2009), where small fluctuations collapse to clumps as their self-gravity (Σ) overcomes turbulent pressure ( ) and rotational support ( ), namely once ∝ /Σ < 1. Fragmentation into massive ( c > ∼ 10 8 M ⊙ ) long lived clumps is commonly seen in simulations of isolated galaxy discs, especially when the gas fraction is greater than ∼ 50% (Fensch & Bournaud 2021), though Toomre-like instabilities manifest on multiple scales even when the gas fraction is as low as ∼ 20% (Renaud et al. 2021). Other studies of idealized isolated galaxies suggest that while linear Toomre instability (or a related spiral arm instability, Inoue & Yoshida 2018 is responsible for the initial fragmentation, this occurs on scales smaller than the observed giant clumps which are themselves agglomerations of many small sub-clumps, either physically bound or in projection (e.g Romeo & Agertz 2014;Agertz et al. 2015;Behrendt et al. 2015;Tamburello et al. 2015;Benincasa et al. 2019). However, the Toomre parameter is a linear concept applicable to axisymmetric systems, while the violently unstable discs at high redshift are far from being either linear or axisymmetric. ...
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... Efficient coupling of feedback energy to gas destroys clumps (Elmegreen et al. 2008;Hopkins et al. 2012) and many simulations that employ high feedback prescriptions have failed to find significant clumps or have found ones that do not contribute much to bulges (e.g. Tamburello et al. 2015). The short-lived clumps in the FIRE simulations do not manage to migrate to the bulge (Oklopčić et al. 2017), and may not even have been bound. ...
Preprint
Full-text available
In Paper I we showed that clumps in high-redshift galaxies, having a high star formation rate density (\Sigma_SFR), produce disks with two tracks in the [Fe/H]-[\alpha/Fe] chemical space, similar to that of the Milky Way's (MW's) thin + thick disks. Here we investigate the effect of clumps on the bulge's chemistry. The chemistry of the MW's bulge is comprised of a single track with two density peaks separated by a trough. We show that the bulge chemistry of an N-body + smoothed particle hydrodynamics clumpy simulation also has a single track. Star formation within the bulge is itself in the high-\Sigma_SFR clumpy mode, which ensures that the bulge's chemical track follows that of the thick disk at low [Fe/H] and then extends to high [Fe/H], where it peaks. The peak at low metallicity instead is comprised of a mixture of in-situ stars and stars accreted via clumps. As a result, the trough between the peaks occurs at the end of the thick disk track. We find that the high-metallicity peak dominates near the mid-plane and declines in relative importance with height, as in the MW. The bulge is already rapidly rotating by the end of the clump epoch, with higher rotation at low [\alpha/Fe]. Thus clumpy star formation is able to simultaneously explain the chemodynamic trends of the MW's bulge, thin + thick disks and the Splash.
... The giant star-forming clumps do not necessarily require mergers and, in simulations, can be produced as a result of secular processes such as cold stream accretion ) with subsequent clump mergers (Tamburello et al. 2015). All of these processes can be in play in J1652, but in addition, its tidal tail indicates a possibility of a recent major merger. ...
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Full-text available
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