Quenching Timescales in the IllustrisTNG Simulation

Observations of local galaxy properties have shown that galaxies are bimodal in many properties, such as colour (e.g. Strateva et al., 2001; Blanton et al., 2003; Baldry et al., 2004), stellar age (e.g. Kauffmann et al., 2003; Gallazzi et al., 2008; Peng et al., 2015), and morphology (e.g. Fisher & Drory, 2011; Bottrell et al., 2019; Luo et al., 2020), but most importantly, star formation rate (SFR) (e.g. McGee et al., 2011; Wetzel et al., 2012). Galaxies can be broadly classified into two categories: star forming (SF) and quiescent (or passive/quenched, Q). Between SF and Q galaxies lie Green Valley (GV) galaxies (Wyder et al., 2007), although growing evidence against a true bimodality in SFR suggests that GV and Q galaxies may form a single extended population (e.g. Feldmann, 2017; Terrazas et al., 2017; Eales et al., 2018a, b). Galaxies form and grow along an SF main sequence (SFMS), with more massive SF galaxies having higher SFR (Noeske et al., 2007). This evolution is stochastic, typically including multiple movements on and off the SFMS (e.g., Tacchella et al., 2016a; Orr et al., 2017). Regardless, galaxies generally seem to evolve along the SFMS, until at some point they are forced off the SFMS, rarely to return (the “grow & quench” framework, e.g. Tacchella et al., 2021). The process of transitioning off the SFMS is known as quenching, and it is a central focus in the study of galaxy evolution.

The causes of quenching are still poorly understood. Different populations of galaxies exhibit different correlations between various galaxy properties and quiescence, which are thought to point to different quenching mechanisms (Baldry et al., 2004; Bamford et al., 2009; Woo et al., 2015; Bluck et al., 2016). In particular, galaxies are often divided into centrals (those that are isolated, or lie at the centre of a group or cluster’s potential) and satellites (those that orbit centrals). Satellite galaxies are thought to quench via a variety of environmental processes which probably do not affect centrals, such as ram pressure stripping (e.g. Abadi et al., 1999), strangulation (e.g. Van Den Bosch et al., 2008), or harassment (e.g. Moore et al., 1996).

In this paper we focus on the quenching of central galaxies for which several possible mechanisms have been proposed. Most mechanisms focus on depleting a galaxy’s supply of gas, either by preventing gas inflow or by ejecting it. In the most massive galaxies, accreting gas can become shock heated, preventing cooling and collapse (e.g. Dekel & Birnboim, 2006). Feedback from star formation and supernovae can expel gas in low-mass galaxies (e.g. Dekel & Silk, 1986; Dekel & Woo, 2003), but is likely not strong enough alone to induce galaxy-wide quenching in massive galaxies (e.g. Su et al., 2019). Feedback from accreting supermassive black holes (BHs), known as active galactic nuclei (AGN), can eject gas from a galaxy’s core while also heating it and preventing infall (e.g. Croton et al., 2006; Zinger et al., 2020), although the strongest effects may be limited to the central few kpc (Ellison et al., 2021). Morphological quenching is another possibility, whereby a dense galaxy core creates a steep potential, which in turn smooths the density of gaseous discs (Martig et al., 2009). This prevents the clumping of the gas necessary for star formation to occur. Galaxy mergers/interactions may play a role by triggering bursts of star formation or AGN activity (e.g. Ellison et al., 2011; Knapen et al., 2015; Ellison et al., 2019; Hani et al., 2020), although Quai et al. (2021) found that mergers in TNG do not lead to significant populations of quenched galaxies. Another newly proposed quenching mechanism is angular momentum quenching (Peng & Renzini, 2020; Renzini, 2020). In this scenario, based on established scaling relations, gas accreting to high mass galaxies (particularly later in the universe) is prevented from cooling and clumping due to excessive angular momentum. It is safe to say, out of the many proposed quenching mechanisms, AGN feedback remains the most popular, with many simulations relying on some form of AGN feedback in order to reproduce the observed quiescent population (e.g. Weinberger et al., 2018; Schaye et al., 2015). Yet it has become increasingly accepted that several mechanisms may play a role (e.g. Woo et al., 2015; Trussler et al., 2020; Tacchella et al., 2021).

The timeline of the quenching process can offer clues to the physical mechanisms at play. For example, purely ejective mechanisms should act on shorter timescales comparable to the dynamical time, whereas preventative feedback should lead to longer timescales comparable to the depletion timescale (e.g., Schawinski et al., 2014a; Hahn et al., 2017). Both the duration of quenching and its dependence on epoch remain largely unconstrained. Since we cannot directly observe the evolution of galaxies, determining quenching timescales accurately is inherently difficult.

It has been argued, based on the dearth of galaxies in the GV, that quenching might be a fast process (relative to the age of the universe) (e.g. Hahn et al., 2017). However other interpretations of the apparent GV are possible. For example, Eales et al. (2018a, b) argue that the apparent dearth of observed low-z GV galaxies (in terms of colour) is due to an overabundance of red galaxies, since galaxies in a wide range of low specific SFR (sSFR) all map to red colours. They show that the sSFR distribution is smooth rather than bimodal, weakening the argument that galaxies must pass quickly through the GV. They further argue that many red galaxies in fact continue to form stars at low rates. Likewise, Terrazas et al. (2017) found that low-z galaxies show a smooth distribution in $M_{BH}/M_{*}$, and proposed that the GV is populated with both transitioning and steady-state galaxies. In a similar vein, McDonald et al. (2016) examined a sample of brightest cluster galaxies (BCGs), which harbour the most massive BHs (McConnell & Ma, 2013). McDonald et al. (2016) found that BCGs in the local universe continue to form stars at low rates (below the widely used sSFR cutoff of $10^{-11}$ yr^-1 for SF galaxies) and their sSFRs have been gradually decreasing over very long timescales ($\sim$9 Gyr). Schawinski et al. (2014b) studied the morphologies of local galaxies, and argued through a study of their SEDs that quiescent galaxies with different morphologies must transition through the optical GV on very different timescales. Indeed, the appearance of a shallow GV is partly due to the common practice of combining SFR measurements with SFR upper limits in the same histograms. Feldmann (2017) showed that the sSFR distribution in low- and high-z observations, as well as simulations, can be better fit by zero-inflated negative binomial distributions, rather than the commonly used overlapping log-normal distributions.

The duration of quenching is expected to depend on both epoch and mass, but determining the direction of these correlations is not at all trivial. For example, if we consider quiescent galaxies at all redshifts and ask how long it took these galaxies to quench, we will find that the quenching timescale is shorter for quiescent galaxies observed at earlier times simply due to the limit of the age of the universe at the time of observation. Observations of stellar populations of quiescent galaxies (Gonçalves et al., 2012; Tacchella et al., 2021) and post-starburst galaxies (Wild et al., 2016; Suess et al., 2021) seem to corroborate this idea. If however we take quiescent galaxies at $z=0$ and measure quenching timescales as a function of when they began to quench, those that began to quench earlier might on average have longer quenching timescales simply because they have more time to quench than a galaxy that began to quench recently. Therefore the epoch-dependence of quenching timescales depends on whether the “epoch” refers to the beginning or end of quenching. To our knowledge, this subtlety has not been sufficiently appreciated in studies of quenching timescales.

Related to the question of quenching timescale as a function of epoch is the question of mass dependence. It has been established that more massive galaxies appear to finish quenching earlier since the red sequence seems to be built from the top down (Cowie et al., 1996; Bell et al., 2004; Faber et al., 2007; Tacchella et al., 2021), a phenomenon called “downsizing”. Given that more massive galaxies quench earlier, and that earlier (completed) quenching is more rapid, one might naively expect that more massive galaxies quench more rapidly. However the mass-dependence of the quenching timescale is not at all straightforward. Some simulation studies find that more massive galaxies quench more quickly (Nelson et al., 2018a; Wright et al., 2019; Davé et al., 2019), while some observational studies seem to indicate the opposite (Peng et al., 2015; Trussler et al., 2020). Still others find little to no mass correlation at all (Tacchella et al., 2021).

As we show in this study, at least some of the discrepancies are likely due to differing definitions of quenching timescales. For example, Nelson et al. (2018a) defined quenching in the IllustrisTNG simulation using $g-r$ colour instead of sSFR, the latter of which is more directly related to quenching. As we show here, it turns out that measuring timescales by sSFR as opposed to by colour actually reverses the direction of mass-dependent quenching, particularly with respect to the dependence of quenching duration on $M_{\rm*}$.

In this paper, we study quenching timescales in the IllustrisTNG simulations (hereafter TNG) (Nelson et al., 2018b; Pillepich et al., 2017; Springel et al., 2018; Naiman et al., 2018; Marinacci et al., 2018; Nelson et al., 2019a) as a function of epoch, mass and other galaxy properties. TNG is a set of magneto-hydrodynamical simulations covering large cosmological volumes with sub-kpc resolution. By tracking individual galaxy evolution in TNG, we aim to quantify quenching duration timescales and quenching rates over cosmic time. Our main goal is to determine the galaxy properties that predict quenching duration, and the evolution of these properties over time. To complement our simulation study, we also use measurements of stellar age gradients (Woo & Ellison, 2019) from the Mapping Nearby Galaxies at the Apache Point Observatory (MaNGA) survey (Bundy et al., 2015) of local quiescent galaxies to validate our TNG results.

This paper is structured as follows. In Section 2 we discuss our methods. In Section 3, we present the overall distribution of quenching durations in TNG. In Section 4 we investigate the evolution of quenching rates over cosmic time. We then examine the relationship between quenching duration and the properties of simulated galaxies immediately prior to leaving the SFMS in Section 5. Next, in Section 6 we explore galaxy properties at $z=0$ based on quenching duration. Finally, we discuss the implications of our results, compare our results with observations, and address tensions with other studies in Section 7. We conclude in Section 8.

We begin by presenting the overall distributions of $\tau_{q}$ (the quenching duration for galaxies that have fully quenched at least once) and $\tau_{t}$ (the time in transition for galaxies that have left the SFMS, never fully quenched, and are still in the GV by $z=0$) in TNG. The red line in Fig. 3 shows $\tau_{q}$ for our sample. Many subhaloes ($\sim 40\%$) quench quickly ($<$ 1 Gyr), but a significant tail of subhaloes with longer quenching times (up to $\sim$ 10 Gyr) exists, in agreement with the TNG results of Nelson et al. (2018a). 38% of quiescent central galaxies took more than 2 Gyr to quench (16% with a narrower 1-dex GV). The median $\tau_{q}$ is 1.3 Gyr (0.7 Gyr with a 1-dex GV). This is broadly consistent with the recent observational results of Tacchella et al. (2021) at $z>0.8$, who found $\tau_{q}\approx$ 0-5 Gyr with a median of 1.0 Gyr, although they use a different definition of $\tau_{q}$. We caution that exact $\tau_{q}$ values less than 1 Gyr are unreliable due to the snapshot spacing of TNG, however we can confidently state that these subhaloes quenched in $<$ 1 Gyr.

The green histogram in Fig. 3 shows the transition time, $\tau_{t}$, for all centrals that are in the GV at $z=0$ and never fully quenched. The majority of subhaloes that have been in the GV for $\lesssim$ 1-2 Gyr are likely in the process of transitioning to quiescence. However, 29% of transitioning galaxies left the SFMS more than 2 Gyr ago, never fully quenched but are still showing non-negligible SFR at $z=0$. A few galaxies (8 total, $\sim$ 1%) have been in the GV for over 10 Gyr. Galaxies in TNG can therefore clearly inhabit the GV for a very extended period of time, contrary to the idea of a quick transition from the SFMS to the passive regime.

The long-lived nature of GV galaxies is even more stark when we trace subhalo histories forward in time. Of those in transition at $z=2$ ($\sim$ 10 Gyr ago), 49% remain in the GV at $z=0$ and do not fully quench. If we define a narrower GV width of 1.0 dex, the number is smaller (25%) but still significant.

The exact percentages and timescales are of course dependent on the width of the transition range of sSFR. Nevertheless, we qualitatively conclude that in TNG the GV is populated both with subhaloes in a true transition to quiescence as well as with subhaloes ‘residing’ in the GV. These findings support the proposal of Terrazas et al. (2017) that many galaxies may live in a “quasi-stable” state of “partial quiescence.” In summary TNG produces a broad range of quenching times, whereas many quench in under a Gyr the slowest quenchers never fully cease to form stars within the age of the universe.

Next, we investigate the dependence of quenching duration on cosmic epoch. It is important to emphasize that here we refer to the epoch at which the galaxies begin to quench. As argued in the Introduction, the maximum possible $\tau_{q}$ will decrease with the redshift of quenching ($z_{q}$) if $z_{q}$ refers to the time at which the galaxy completes its quenching, simply because of the smaller age of the universe at high $z_{q}$ (see for instance Fig. 13 of Tacchella et al., 2021 which shows the upper physical bound to $\tau_{q}$ given their definition of $z_{q}$). If instead the epoch $z_{q}$ refers to the time at which a galaxy leaves the SFMS, median $\tau_{q}$ values might be expected to increase with $z_{q}$ simply because galaxies that begin to quench earlier will have had more time to quench by the time they reach $z=0$. We illustrate this idea in Fig. 4 which shows $\tau_{q}$ for quiescent galaxies as a function of $t_{\rm LSF}$ (left panel; the lookback time of leaving the SFMS) and as a function of $t_{Q}$ (right panel; the lookback time of becoming fully quenched). By definition, $\tau_{t}$ values for GV galaxies lie on the 1:1 diagonal line in the left panel. For the quiescent galaxies the average $\tau_{q}$ does indeed decrease slightly at late times (left panel) or early times (right panel) due to the limited values possible, but is otherwise is surprisingly close to constant for most of the history of the universe. In other words, $\tau_{q}$ in TNG only weakly depends on the epoch at which quenching begins or ends, with any dependence plausibly explained by the constraints discussed above.

In a similar vein, we next look at the rate at which certain types of quenchers leave the SFMS as a function of time. Fig. 5 shows the fractional rate of subhaloes leaving the SFMS (either to fully quench, or to enter the GV and not return) over time. We define the fractional rate as the number of subhaloes leaving the SFMS per unit time (over a sliding bin of $\pm$1 Gyr) divided by the median total number of subhaloes on the SFMS within the time bin above a mass of $10^{9}{\rm M}_{\odot}$. The width of the shaded area is the Poisson error in the bin. The dotted grey curve shows the whole galaxy population of central subhaloes with $M_{\rm*}>10^{9}{\rm M}_{\odot}$. In TNG, after $z\sim 2$, the total fractional quenching rate steadily increases (prior to $z\sim 2$, the small number of total galaxies with $M_{\rm*}>10^{9}{\rm M}_{\odot}$ drives the fractional rate up). We note that the number of subhaloes on the SFMS is roughly constant after this point, and indeed the absolute quenching rate also steadily increases (not shown). The bumps and plateaus are somewhat sensitive to our SFMS boundary, which itself evolves over time. However the steady increase of the rate at which galaxies leave the SFMS with time is a robust prediction of TNG, regardless of our choice of SFMS width.

The other three curves in Fig. 5 show components of the total, split by their fate: fast quenchers ($\tau_{q}<1$ Gyr - red solid), slow quenchers (1 Gyr $<\tau_{q}<$ 4 Gyr - orange dashed), and those still in the GV at $z=0$ (green dash dotted). We note that these curves do not add up to the total fractional rate due to the range limits on $\tau_{q}$ for each class. For example, subhaloes that will take 3 Gyr to quench will not have time to do so if they leave the SFMS 2 Gyr ago. Thus we omit the very long quenchers ($\tau_{q}>$ 4 Gyr) from the plot, which limits the orange curve to extend only to a lookback time of $>4$ Gyr.

At all epochs at $z<2$, slow quenching ($\tau_{q}>$ 1 Gyr) is more common than fast quenching ($\tau_{q}<$ 1 Gyr). From $z\sim 2$ to $z\sim 0.7$, Fig. 5 shows that slow quenchers leave the SFMS at about double the rate of fast quenchers. That is, slow quenchers are about twice as common as fast quenchers at intermediate redshifts. We also see the same trend if we use $t_{Q}$ instead of $t_{\rm LSF}$ (not shown). However the numbers of subhaloes quenching at these epochs are low. After $z\sim 0.5$, we do not know the fates of enough of the quenching subhaloes to make meaningful comparisons, at least for the slow quenchers. However the rate of galaxies leaving the SFMS between 4 and 1 Gyr ago that are still in the GV today is well above the rate of the fast quenchers leaving the SFMS, indicating that slow quenching continues to dominate at late times.

How does quenching epoch depend on galaxy mass? Fig. 6 shows the median epoch of leaving the SFMS as a function of stellar mass. This figure shows that the epoch at which galaxies leave the SFMS depends on mass such that more massive galaxies begin quenching earlier. In other words, not only do slower quenchers dominate at higher $z$, in TNG, more massive galaxies leave the SFMS earlier than less massive galaxies. We also find that more massive galaxies finish quenching earlier ($\sim$2 Gyr earlier on average, not shown for brevity), but the mass dependence is weaker. These results are qualitatively consistent with observational studies of number density statistics that more massive galaxies finish quenching at earlier times (Cowie et al., 1996; Bell et al., 2004; Faber et al., 2007; Tacchella et al., 2021). Note however that observational studies are not directly comparable to our results because they are based on observed quiescent galaxies at different redshifts, which are upper limits to the epoch of quenching completion, and do not include galaxies that are in transition to quenching.

Why do some TNG subhaloes quench quickly, some slowly, and some never fully quench at all? To answer this, we investigate which properties of the subhaloes prior to leaving the SFMS correlate with quenching duration.

We begin by examining the correlation of $\tau_{q}$ and $\tau_{t}$ with 12 subhalo properties taken at the last snapshot prior to leaving the SFMS (Fig. 7). Each panel shows two running medians: the green dash dotted curve shows $\tau_{t}$ for subhaloes in transition at $z=0$ which have never fully quenched, and the solid red curve shows $\tau_{q}$ for subhaloes that have fully quenched at least once. Binning details for the running medians are in the caption. Each panel is labelled with the Spearman correlation coefficient for each data set.

The first two panels (a and b) of Fig. 7 show the stellar mass and the halo mass prior to leaving the SFMS. They show that in TNG, more massive galaxies living in more massive halos tend to take longer to quench. Despite the large scatter, TNG predicts a clear positive correlation between quenching duration and stellar mass. This result at first seems to be in conflict with the observations that more massive galaxies quench earlier (Bell et al., 2004; Faber et al., 2007; Tacchella et al., 2021) and that earlier quenching is more rapid (Gonçalves et al., 2012; Suess et al., 2021). Furthermore, they are in conflict with the results of previous simulation work (Nelson et al., 2018a; Wright et al., 2019; Davé et al., 2019). However, we will show in Section 7 that our results do in fact agree with observations, and that the discrepancies depend crucially on definitions of quenching timescale.

Panel (c) of Fig. 7 shows BH mass. Virtually all quiescent and long-term GV galaxies have BH masses higher than $M_{\rm BH}\sim 10^{8.0}{\rm M}_{\odot}$. At this mass, BHs tend to switch to kinetic feedback, which is the primary cause of quenching in TNG (Terrazas et al., 2020). Galaxies with higher BH masses prior to quenching tend to take longer to quench, which is consistent with the relation between $M_{\rm*}$ and $\tau_{q}$. This is contrary to the common view (e.g. Nelson et al., 2018a) that the most massive BHs drive the fastest quenching.

These first three properties ($M_{\rm*}$, $M_{\rm halo}$, and $M_{\rm BH}$) show the strongest correlation with $\tau_{q}$ and $\tau_{t}$ (all have Spearman $\rho>$ 0.4). We note that all three of these properties are also well known to correlate with each other.

Panels (d) and (e) of Fig. 7 examine the gas accreting to the subhalo from a large radius. We take all gas particles with position and inward radial velocity such that they will cross $R_{\rm vir}/2$ in the next 100 Myr, summing their specific angular momentum (panel d) and mass (panel e). These panels show that the properties of the infalling gas are moderately correlated with $\tau_{q}$ and $\tau_{t}$ (Spearman $\rho>$ 0.2). Galaxies accreting less gas, or gas with lower specific angular momentum, tend to quench quickly.

Panel (f) of Fig. 7 shows subhalo half-mass radius prior to quenching. Larger galaxies tend to quench slowly compared to smaller galaxies. This is consistent with the the relation between $\tau_{q}$ and the specific angular momentum of their accreting gas. Gas with lower angular momentum will tend to funnel toward the centre of the galaxy before forming stars, decreasing the effective radius. Panels (d) and (f) show that such galaxies tend to be fast quenchers. When gas accretes with higher angular momentum, we expect that more star formation will occur in a galaxy’s outskirts, increasing $R_{e}$. This is broadly consistent with the results of Gupta et al. (2021), who found that, in TNG, massive extended galaxies selected at $z=2$ tend to quench later and more slowly (see their Figure 3, right hand panel). We also note the reversal of this trend at small $R_{e}$ for $\tau_{q}$ only. As we will show shortly in Fig. 8, this regime represents only a very small portion of our sample so we refrain from drawing inferences from this result.

The remainder of the properties show very little correlation with $\tau_{q}$ or $\tau_{t}$. To calculate the disc fraction, we first compute the total angular momentum vector of the subhalo. For each gas particle within $2R_{e}$, we then compute the component of the angular momentum parallel to the total subhalo angular momentum ($J_{z}$). Next we compute the angular momentum of the same gas particle assuming a circular orbit with the same energy ($J_{c}$). Particles are identified as part of the disc component when $J_{z}/J_{c}>0.7$. The disc fraction is then the mass of all disc component gas particles divided by the total gas mass. We also tried other common definitions for the disc fraction and found similar results. We note the moderate negative value of the Spearman coefficient for the gas fraction inside 1 kpc. This appears to be driven by a significant population of subhaloes with zero gas inside these radii, with a corresponding wide range of $\tau_{q}$ and $\tau_{t}$ values. Since the running medians themselves are fairly flat, we assess that this correlation is not significant.

To complement the above analysis of Fig. 7, we now split our sample of subhaloes into three groups. We define fast quenchers as those with $\tau_{q}<$ 1 Gyr (386 total in our sample), slow quenchers as those with $\tau_{q}>$ 1 Gyr (569 total), and long-term GV residents as those with $\tau_{t}>$ 3 Gyr (213 total). We note that our definitions exclude some subhaloes that have left the SFMS recently but have not yet quenched (those with $\tau_{t}<$ 3 Gyr), since their status as fast or slow quenchers is yet to be determined. Long-term GV residents may eventually become slow quenchers (but not fast quenchers). We classify them separately because their exact quenching duration is undetermined and $\tau_{t}$ is essentially a lower limit on their future $\tau_{q}$. We tried varying these definitions and found no significant change in our results.

Fig. 8 shows histograms of six properties, which showed significant correlation with $\tau_{q}$ and $\tau_{t}$ in Fig. 7 (Spearman $\rho>$ 0.2 or clear visual correlation in the case of $R_{e}$), separated into our three classes of quenching duration. The histograms more clearly illustrate the parameter space in which most galaxies begin quenching, and also show the relationship between long-term GV residents and quenched galaxies in a straightforward way. We note that there is a fair amount of overlap between the histograms, and likewise scatter in the continuous plots, in all cases. However in most properties (except the infalling gas mass in panel e), the distribution for slow quenchers lies between the fast quenchers and the long-term GV residents.

We also include in all panels of Fig. 8 the SF population at $z=2$ (grey outline) and $z=0$ (grey shaded) for reference. The three quenched populations lie roughly where we expect compared to SF galaxies: they have higher mass, higher mass BHs, and less gas infalling with more angular momentum. There is significant evolution of the SF $M_{\rm BH}$ distribution between $z=2$ and $z-0$, but at the same time there is very little evolution of the SF $M_{\rm*}$ distribution. While concerning, we will show that the same distributions for GV and Q galaxies do not evolve much. In other words, the TNG model may produce too aggressive evolution over cosmic time of the $M_{\rm BH}$-$M_{\rm*}$ relation at low mass, but closer to the quenching mass regime the results are reasonable. The infalling gas mass for SF galaxies decreases substantially over time, in agreement with the decline of the cosmic accretion rate over time (see, for example, Chen et al., 2020). $R_{e}$ increases modestly in agreement with the size evolution of galaxies (e.g., van der Wel et al., 2014).

The first two panels of Fig. 8 are histograms of the stellar mass and the halo mass for our three classes of quenching duration. Fig. 7 showed that less massive galaxies in less massive halos tend to quench more quickly; Fig. 8 shows the complementary relationship: fast quenchers tend to be less massive and live in less massive halos. The histograms also show that long-term GV residents tend to be the most massive galaxies.

Panel (c) of Fig. 8 shows histograms of BH mass. As noted earlier, virtually all quiescent and long-term GV galaxies have BH masses higher than $M_{\rm BH}\sim 10^{8.2}{\rm M}_{\odot}$ since BHs tend to switch to kinetic feedback at this mass. Slow quenchers tend to have slightly higher BH masses prior to quenching, which is consistent with their higher $M_{\rm*}$. We note that the histograms paint a slightly more nuanced picture than the same panel in Fig. 7. Although $\tau_{q}$ appears to be a continuous function of $M_{\rm BH}$ in Fig. 7, the histogram in Fig. 8 shows that (at least for fast quenchers), the majority of galaxies leave the SFMS at essentially the same $M_{\rm BH}$ as shown by the narrow peak in the histograms. Slow quenchers and long-term GV subahloes are able to build their $M_{\rm BH}$ modestly higher (but in most cases $<$ 0.5 dex) prior to leaving the SFMS.

Taking the first three panels of Figs. 7 and 8 together, it seems that in TNG, slower quenchers, which tend to be more massive, require more massive BHs in order to begin quenching. Their deeper potentials are able to hold on to their gas longer following the onset of kinetic BH feedback at $10^{8}{\rm M}_{\odot}$. We have confirmed that $\tau_{q}$ and $\tau_{t}$ do indeed increase with increasing escape velocity at $R_{e}$ (similar to the first two panels of Fig. 7, not shown for brevity). They are therefore able to continue to grow both their BHs and their stellar mass prior to, eventually, quenching.

Panels (d) and (e) of Fig. 8 show the complementary picture for accreting gas as shown in the same panels of Fig. 7. Fast quenchers tend to accrete less gas than slow quenchers, and that gas tends to have lower specific angular momentum. We also note with interest that there is a small population of fast quenchers with high infalling gas mass. We do not see this population at $z=0$. Since fast quenchers also tend to accrete gas with low specific angular momentum, this suggests that some fast quenching events may be preceded by wet minor mergers. However, these galaxies contribute insignificantly to the total population of fast quenchers.

Angular momentum is expected to naturally increase with mass (Peng & Renzini, 2020; Renzini, 2020), so it is not unexpected that slower quenchers, with higher mass, should have gas accreting with higher $j$. To check whether the angular momentum of accretion correlates with $\tau_{q}$ independently of $M_{\rm*}$, we calculated $\Delta j$, the difference between $j$ and the median $j$ for a given mass at a given redshift. We find that $\Delta j$ at $t_{\rm LSF}$ is weakly correlated with $\tau_{t}$ or $\tau_{q}$. However, by $z=0$, $j$ for all quenched galaxies is consistent with their expected distributions given their mass.

The last panel of Fig. 8 shows histograms of half-mass radius for our three classes of quenching duration. In Fig. 7 we see that larger galaxies tend to quench more slowly than smaller galaxies, while here we find the complementary relationship: slow quenchers tend to be larger than fast quenchers. Long-term GV residents tend to be the largest galaxies. Similar to our test for angular momentum, we also computed $\Delta R_{e}$ to check whether the variation in $R_{e}$ was due to the $R_{e}-M_{\rm*}$ scaling relation. In this case, we confirmed that fast quenchers were smaller than similar mass SF galaxies prior to quenching. We note with interest that $R_{e}$ (and $\Delta R_{e}$) are better predictors of $\tau_{q}$ than $j$ (and $\Delta j$).

In summary, we find that in TNG, prior to leaving the SFMS, fast quenching galaxies tend to have (compared to slow quenching galaxies): lower stellar mass, less massive halos, less massive BHs, less infalling gas (although a few have very high infalling gas mass), less specific angular momentum in their infalling gas, and smaller effective radii. Galaxies that have lived in the GV for very long times occupy the opposite end of this spectrum of properties.

We have seen that most galaxies in TNG take $\raise-2.15277pt\hbox{$\buildrel<\over{\sim}$}2$ Gyr to quench, but a significant number stay in the GV for much longer, some never fully quenching. The slow quenchers leave the SFMS with higher mass, higher BH mass, larger sizes and higher angular momentum accreting gas compared to the faster quenchers. Having established the properties of quenching galaxies prior to leaving the SFMS, do the properties of any of our groups evolve significantly by $z=0$? Put another way, are the $z=0$ properties of quenched galaxies indicative of their past quenching timescales?

Fig. 9 shows the same properties of the same subhaloes as Fig. 8, but at $z=0$. The first three properties are largely unchanged, suggesting TNG subhaloes evolve very little after quenching. The median values of $M_{\rm*}$, $M_{\rm halo}$, and $M_{\rm BH}$ for the populations (shown at the top of Figs. 8 and 9) evolve by less than 2%. Moreover, the change in $M_{\rm*}$ for individual galaxies between leaving the SFMS and either quenching or reaching $z=0$ was less than 1% for all quenched galaxies and long-term GVs with $\tau_{t}<3$ Gyr. There was a detectable increase in the mass of long-term GVs with $\tau_{t}>3$ Gyr, but the median increase was modest (only about 17%.).

Three properties did change, on average, between Figs. 8 and 9, indicating some redshift evolution. The first is the specific angular momentum of infalling gas (panel d). At $z=0$, all three groups show similar distributions that are weighted toward high specific angular momentum. Compared to Fig. 8 the red and orange histograms have moved up to coincide with the green histogram, and all lie higher than the SF population. In other words, the fast and slow quenchers, which were once accreting gas with lower specific angular momentum, are now accreting gas with higher specific angular momentum just as the long-term GV galaxies. Other simulation studies have shown that the angular momentum of infalling streams increases with time (Danovich et al., 2015; Stewart et al., 2017), and thus the long-term GV may have been accreting gas with unusually high angular momentum prior to quenching.

The second property that shows redshift dependence is the infalling gas mass. Prior to quenching, all three groups were located about 1 dex below the $z=2$ SF population. At $z=0$, they again sit about 1 dex below the corresponding SF population. So although we see a significant evolution in the infalling gas mass for the quiescent galaxies, this change mirrors the same decrease in infalling gas to the SF galaxies. Therefore this evolution is roughly consistent with the overall change in available gas over cosmic time.

The third property of quiescent galaxies that evolved over cosmic time is $R_{e}$. Again, the increase in median $R_{e}$ for our quenched groups is roughly consistent with the increase in $R_{e}$ of SF galaxies from $z=2$ to $z=0$, and with the observed size evolution of galaxies (e.g., van der Wel et al., 2014). As with our analysis prior to quenching, $R_{e}$ values at $z=0$ for faster quenchers are lower than typical SF galaxies at the same mass.

Regardless, TNG makes several directly testable predictions. At low redshift, fast quenchers in the TNG model end up with lower $M_{\rm*}$, lower $M_{\rm BH}$, and smaller $R_{e}$. We will return to these predictions in the next section.

There are three other properties that differ between our three groups at $z=0$ that did not differ (much) prior to quenching: sSFR, gas fraction, and gas disciness. First, we examine the sSFR of the two quenched groups (i.e. those that have fully quenched at least once) that still have some residual sSFR today. Fig. 10 shows the residual sSFR at $z=0$ for all subhaloes that have ever quenched, split into fast and slow quenchers. There is a distinct population of fast quenchers which have rejuvenated, having fairly high sSFR today (i.e. on the SFMS). Rejuvenation is more common in fast quenchers. About $13^{+4}_{-3}$% (Poisson errors) of fast quenchers will experience rejuvenation, compared with only $4^{+2}_{-2}$% of slow quenchers. We defer investigation of any link between $\tau_{q}$ and rejuvenation rate to future studies. We speculate that perhaps low mass BHs can be powerful enough to temporarily expel central star-forming gas from low-mass (i.e. shallow potential) galaxies, but for some reason are less effective at heating the CGM and preventing gas infall than more massive BHs. There is also the possibility that fast quenchers simply have more time to experience rejuvenation, since they spend less cosmic time in the quenching process. The rejuvenated galaxies push the median sSFR for fast quenchers slightly higher than the slow quenchers. However only 27% of fast quenchers have non-zero sSFR compared to 43% of slow quenchers. Furthermore, in all parameters shown in Figs. 8 and 9, the slow quenching population lies between the fast quenchers and the long-term GV residents, which by definition have higher residual sSFR. In other words, the long-term GV residents are essentially very slow quenchers. Therefore we conclude that in TNG, fast quenchers are more likely to quench completely compared to slow quenchers, although they are also more likely to rejuvenate.

We next examine the gas fraction of our GV/Q subhaloes at $z=0$. Fig. 11 shows the total bound (i.e. SUBFIND) gas fraction for our three groups at $z=0$. Slower quenchers tend to have more gas, which could contribute to their longer quenching times. On the other hand, it could be that slower quenchers have more gas simply because they are consuming it more slowly.

Our choice to use total bound gas fraction is important. We find that most of our subhaloes have negligible gas fractions inside 1-2 kpc or even inside 1-2 $R_{e}$. Indeed, visual examinations of our long-term GV residents show that any residual star formation usually occurs outside of 2$R_{e}$ (see Fig. 12 for an example, where the white circles indicate $R_{e}$ and $2R_{e}$). Such residual star formation may be difficult to detect, especially in galaxies at higher $z$, although it is not unexpected in GV galaxies (see e.g. Salim et al., 2012; Dekel et al., 2020).

Lastly, we examine the shape of our subhaloes in terms of disc fraction. Fig. 13 shows the disc fraction of the gas component for our three groups. The stellar components for all three groups are fairly similar (not shown). However, the disc fraction of the gas component within $2R_{e}$ for the long-term GV residents tends to be higher than in the quenched groups. Fast and slow quenchers have similar distributions of disc fractions.

In summary, the distributions of most properties for fast and slow quenchers and the long-term GV residents remain largely unchanged by $z=0$. The exception is the infalling gas angular momentum, which increases for fast and slow quenchers. By $z=0$, fast quenchers are more likely to have experienced a rejuvenation event, but generally have lower gas fractions. Long-term GV residents have higher disk gas fractions and are weakly star-forming in large extended disks.

We investigated the quenching timescales of central galaxies in the IllustrisTNG simulations. Our results are summarized as follows:

1. 1.

   Roughly 40% of the galaxies in TNG quench rapidly ($\tau_{q}<$ 1 Gyr). A significant tail of the $\tau_{q}$ distribution extends to longer times, up to $\sim$ 10 Gyr (Fig. 3, red line).

2. 2.

   TNG predicts another significant population of galaxies that leave the SFMS but do not completely quench within the age of the universe. These galaxies reside in the GV for very long times until $z=0$ (Fig. 3, green line).

3. 3.

   Quenching duration is slightly longer for galaxies that began to quench earlier, or that finished their quenching later, but overall the average quenching timescale depends only weakly on cosmic time (Fig. 4).

4. 4.

   The absolute and fractional rates of galaxies leaving the SFMS increase steadily over cosmic time. Slow quenchers are about twice as common as fast quenchers at intermediate redshifts ($z\sim 2$ to $z\sim 0.7$, Fig. 5).

5. 5.

   Prior to quenching, galaxies that will quench slowly tend to have: higher $M_{\rm*}$, higher $M_{halo}$, higher absolute $M_{\rm BH}$ and larger $R_{e}$ (Figs. 7 and 8). They accrete more gas, and with higher specific angular momentum.

6. 6.

   We find no significant correlation between $\tau_{q}$ and sSFR, instantaneous BH accretion rate, or gas fraction prior to quenching (Fig. 7).

7. 7.

   With the exception of the accreting gas angular momentum, the distributions of properties of quenched galaxies at $z=0$ are largely unchanged since leaving the SFMS, suggesting that quiescent galaxies in TNG evolve very little during and after quenching (Fig. 9).

8. 8.

   At $z=0$, fast quenchers, which were accreting gas at lower angular momentum prior to quenching, are now acreting gas with the same high angular momentum as slow quenchers.

9. 9.

   At $z=0$, galaxies that quenched slowly tend to have extended gas disks/rings with low star formation rates (Fig. 13).

10. 10.

    A comparison with observations of nearby quiescent galaxies, using IFU derived age gradients as a proxy for $\tau_{q}$, shows broad agreement with TNG’s predictions for $z=0$ $M_{\rm*}$, $\Sigma_{\rm*,2kpc}$, $R_{e}$, and residual sSFR (Figs. 15 and 16).

Our results imply that galaxies evolve as shown in the schematic diagram in Fig. 18. Prior to quenching, the angular momentum of accreting gas determines the evolutionary track of a galaxy in $M_{\rm BH}$-$M_{\rm*}$ plane. In turn, this determines where a galaxy will reach the quiescent region of the diagram. Galaxies with deeper potentials take longer to quench, requiring more massive BHs to expel gas and prevent its infall.

Our comparison with observations suggests that TNG’s model for AGN feedback and quenching is on the right track. We caution, however, that we have not yet performed the same analysis on other modern cosmological simulations. It is entirely possible that these results could be common to any model using AGN-driven gas ejection and infall prevention to quench galaxies.

Data from the IllustrisTNG simulations are publicly available at www.tng-project.org. Data specific to this paper are available on request from the corresponding author.

We sincerely thank the referee for the constructive feedback and excellent suggestions. We acknowledge the helpful and stimulating discussions with Salvatore Quai and Sandro Tacchella. SLE gratefully acknowledges the receipt of an NSERC Discovery Grant.

The simulations of the IllustrisTNG project used in this work were undertaken with compute time awarded by the Gauss Centre for Supercomputing (GCS) under GCS Large-Scale Projects GCS-ILLU and GCS-DWAR on the GCS share of the supercomputer Hazel Hen at the High Performance Computing Center Stuttgart (HLRS), as well as on the machines of the Max Planck Computing and Data Facility (MPCDF) in Garching, Germany.

This research made use of Astropy,¹¹1http://www.astropy.org a community-developed core Python package for Astronomy (Robitaille et al., 2013; Price-Whelan et al., 2018). This research also made use of the computation resources provided by Westgrid (www.westgrid.ca) and Compute Canada (www.computecanada.ca).

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org. SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatório Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.