tokens: left-hand panel of Fig. 3 ). Despite such significant perturbations, the presence of a DM filament potential well coupled to the relatively high density of the gas ensures that the cooling time within the filament remains short. As a result, the filament is still visible as a cold stream cutting through the hot superbubble in the middle right-hand panel of Fig. 3 . Due to these consequent perturbations induced by the stellar feedback, we cannot use either the temperature or vorticity to define the gas filament truncation radii in the feedback run. It should also be noted that our assumption of isothermality of the filaments becomes less valid than in the no stellar feedback case as stronger temperature gradients develop between core and outer envelope. To be more specific, in the no feedback case, the temperature varies between core and truncation radius by about a factor of 2, but in the feedback case in can reach an order of magnitude. However, most of this gradient is localized in the outer parts of the filament, so that the central region retains a significantly large isothermal core. This can be understood by performing the following simple calculation. Neglecting the presence of the wall, we may integrate both the gas and DM density profiles (from equation 4 ) to obtain the filament mass per unit length, μ , and its half-mass radius The fact that the (small) core radius contains half of the mass makes the filamentary material relatively impervious to the stellar feedback/filament interaction: provided the core is shielded from it, there can only be a minor change in the amount of gas mass that the filament carries. It has been suggested in the literature that Kelvin–Helmholtz instabilities could be triggered at the interface between cold filament gas and the feedback powered, hot, galactic wind (e.g. Mandelker et al. 2016 and subsequent work). These will depend non-trivially on redshift and the distance of a filament segment to the central galaxy, so it is quite difficult to define a unique characteristic time-scale, t KH . Nevertheless, writing , where v w is the relative velocity between the wind and the gas filament and ρ w the density of the wind, we can see that given the steepness of the filament density profile that we measure, t KH becomes larger as the perturbation progresses deeper in the filament. This means that the time-scale is ultimately set by t KH ( r 0 ). Plugging in typical numbers for our feedback run at z = 4, i.e. r 0 ∼ 5 kpc, ρ ( r 0 ) ∼ 3 × 10 −27 g cm −3 , v w ∼ 100 km s –1 , and ρ w ∼ 3 × 10 −28 g cm −3 , we, thus, get t KH ∼ 20 Myr which is about an order of magnitude shorter than the infall time from the virial radius of the embedded halo. The conclusion is, thus, that our gas filaments should not survive the interaction. Notwithstanding that this does not happen in our simulations, which might admittedly be of too low a resolution to capture the instability properly, the calculation ignores both the
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