We study the evolutionary trend of the total density profile of early-type galaxies (ETGs) in IllustrisTNG. To this end, we trace ETGs from $z=0$ to $z=4$ and measure the power-law slope $gamma^{prime}$ of the total density profile for their main pro
genitors. We find that their $gamma^{prime}$ steepen on average during $zsim4-2$, then becoming shallower until $z=1$, after which they remain almost constant, aside from a residual trend of becoming shallower towards $z=0$. We also compare to a statistical sample of ETGs at different redshifts, selected based on their luminosity profiles and stellar masses. Due to different selection effects, the average slopes of the statistical samples follow a modified evolutionary trend. They monotonically decrease since $z=3$, and after $zapprox 1$, they remain nearly invariant with a mild increase towards $z=0$. These evolutionary trends are mass-dependent for both samples, with low-mass galaxies having in general steeper slopes than their more massive counterparts. Galaxies that transitioned to ETGs more recently have steeper mean slopes as they tend to be smaller and more compact at any given redshift. By analyzing the impact of mergers and AGN feedback on the progenitors evolution, we conjecture a multi-phase path leading to isothermality in ETGs: dissipation associated with rapid wet mergers tends to steepen $gamma^{prime}$ from $z=4$ to $z=2$, whereas subsequent AGN feedback (especially in the kinetic mode) makes $gamma^{prime}$ shallower again from $z=2$ to $z=1$. Afterwards, passive evolution from $z=1$ to $z=0$, mainly through gas-poor mergers, mildly decreases $gamma^{prime}$ and maintains the overall mass distribution close to isothermal.
We explore the isothermal total density profiles of early-type galaxies (ETGs) in the IllustrisTNG simulation. For the selected 559 ETGs at $z = 0$ with stellar mass $10^{10.7}mathrm{M}_{odot} leqslant M_{ast} leqslant 10^{11.9}mathrm{M}_{odot}$, the
total power-law slope has a mean of $langlegamma^{prime}rangle = 2.011 pm 0.007$ and a scatter of $sigma_{gamma^{prime}} = 0.171$ over the radial range 0.4 to 4 times the stellar half mass radius. Several correlations between $gamma^{prime}$ and galactic properties including stellar mass, effective radius, stellar surface density, central velocity dispersion, central dark matter fraction and in-situ-formed stellar mass ratio are compared to observations and other simulations, revealing that IllustrisTNG reproduces many correlation trends, and in particular, $gamma^{prime}$ is almost constant with redshift below $z = 2$. Through analyzing IllustrisTNG model variations we show that black hole kinetic winds are crucial to lowering $gamma^{prime}$ and matching observed galaxy correlations. The effects of stellar winds on $gamma^{prime}$ are subdominant compared to AGN feedback, and differ due to the presence of AGN feedback from previous works. The density profiles of the ETG dark matter halos are well-described by steeper-than-NFW profiles, and they are steeper in the full physics (FP) run than their counterparts in the dark matter only (DMO) run. Their inner density slopes anti-correlates (remain constant) with the halo mass in the FP (DMO) run, and anti-correlates with the halo concentration parameter $c_{200}$ in both types of runs. The dark matter halos of low-mass ETGs are contracted whereas high-mass ETGs are expanded, suggesting that variations in the total density profile occur through the different halo responses to baryons.
