© The Authors 2024

1. Introduction

The structure and star formation activity of a galaxy are closely linked to its kinematic properties. It has been proposed that disc galaxies are formed from gas accretion and acquire angular momentum from tidal torques (see e.g., Fall & Efstathiou 1980; Barnes & Efstathiou 1987; Mo et al. 1998; Bullock et al. 2001; Kereš et al. 2005). On the other hand, elliptical galaxies have a factor of five less angular momentum than disc galaxies of similar masses (e.g., Fall 1983; Romanowsky & Fall 2012; Fall & Romanowsky 2013).

Thanks to large-scale integral field spectroscopy (IFS) surveys, galaxies can be further classified by their dynamical features rather than by simple morphology or colour (Driver et al. 2007). The SAURON project (Bacon et al. 2001), which is based on the IFS, complements the traditional classification of early-type galaxies (ETGs) by including information about galaxy kinematics. The ETGs are divided into fast and slow rotators in the anisotropy diagram between the ratio of ordered and random motion (V/σ) and ellipticity (ε) (see e.g., Cappellari et al. 2007; Emsellem et al. 2007). van de Sande et al. (2018) further found a strong correlation between the stellar population age and the location in the (V/σ, ε) diagram, where fast rotators are younger and slow rotators are relatively old. This suggests that the star formation history is correlated with galaxy stellar kinematics.

The circumgalactic medium (CGM) is believed to be a source of fuel for star formation and is thus expected to be linked to star formation activity. Using the IllustrisTNG hydrodynamical simulation (hereafter TNG; Pillepich et al. 2018; Nelson et al. 2019b), Lu et al. (2022) found that quenched early-type galaxies typically have higher specific angular momenta than their star-forming disc counterparts with similar stellar masses. This high angular momentum of the CGM could impede the efficient radial gas inflow that is necessary to maintain star formation in the centre and is thus seen as an additional factor in keeping galaxies quenched, a process known as angular momentum quenching (Peng & Renzini 2020). The high angular momenta of quenched galaxies in TNG are probably related to the more frequent prograde merger events (relative to the spin of the galaxy itself, as the angular momentum of the CGM gas is inherited from the large-scale halo environment (Lu et al. 2022; Wang et al. 2022b).

However, the angular momentum and gas distributions of galaxies in hydrodynamical simulations can be easily altered by the baryon physics employed. Negative feedback from the active galactic nucleus (AGN) is one of the most effective ways to quench galaxies in these simulations. Ma et al. (2022) compared the hydrodynamical simulations of TNG and SIMBA (Davé et al. 2019) and found that the kinetic AGN feedback in TNG only moves cold gas from the inner discs to the outer regions, thus reducing the star formation activities in the inner regions. This leads to TNG overestimating the overall cold-gas reservoir in quenched galaxies compared to observations. Therefore, angular momentum quenching is necessary in TNG to prevent the CGM gas of these quenched galaxies from falling into the centre. On the other hand, the bipolar injection of kinetic AGN feedback in SIMBA only slightly reduces the cold gas densities in the inner regions, but significantly heats the CGM gas, which brings SIMBA into better agreement with the observed cold-gas masses for quenched galaxies. Without a consistent supply of cold gas in the CGM, quenched galaxies will remain with low star formation rates, so it does not seem necessary to have the additional input of angular momentum quenching.

It is perplexing to consider the impact of angular momentum on star formation in galaxies when comparing the two simulations. To gain a better understanding of the effect of angular momentum in different hydrodynamical simulations, this paper will explore the relationship between star formation rate (SFR) and CGM angular momentum in TNG and SIMBA. In addition, we will examine the influence of various morphologies on the angular momentum distribution. The paper is organised as follows. Section 2 provides an overview of the galaxy samples in the two simulations. The main findings are summarised in Section 3. Conclusions and discussions are described in Section 4.

2. Simulation and data

2.1. The IllustrisTNG simulation

The IllustrisTNG project consists of a set of magnetohydrodynamical simulations of different cosmological volumes (Marinacci et al. 2018; Naiman et al. 2018; Nelson et al. 2018, 2019b; Pillepich et al. 2018; Springel et al. 2018), run with the Arepo code (Springel 2010). In this paper, we focus on the TNG100-1 simulation with a box size of 75 h⁻¹Mpc on a side, and the cosmological parameters are Ω_m = 0.3089, Ω_λ = 0.6911, Ω_b = 0.0486, and h = 0.6774. The dark matter mass resolution is m_DM = 7.5 × 10⁶ M_⊙ and the average gas cell mass is around m_gas = 1.4 × 10⁶ M_⊙.

The Illustris simulation (Vogelsberger et al. 2014) has been improved by the TNG model with the introduction of two AGN feedback modes: thermal and kinetic. These two modes are exclusive and are determined by comparing the Eddington ratio, λ_Edd, with the critical value, χ, which is calculated using equation χ = min[0.002(M_BH/10⁸ M_⊙)²,0.1]. When the Eddington ratio is greater than or equal to the critical value, the thermal mode is activated, which injects energy isotropically into the environment and heats the surrounding gas. On the other hand, when the Eddington ratio is less than the critical value, the AGN feedback switches to the kinetic mode, which produces black hole-driven winds and transfers energy to the neighbouring gas in the form of random momentum (Weinberger et al. 2017). This kinetic mode has enabled the stellar mass fraction in massive haloes to be more in line with observations, without the overheating of gas as in Illustris.

2.2. The SIMBA simulation

SIMBA simulations (Davé et al. 2019) are carried out using the GIZMO code (Hopkins 2015), which is a solver for cosmological gravity and hydrodynamics. This paper adopts the flagship run of SIMBA (m100n1024), which has a box size of 100 h⁻¹Mpc on a side and cosmological parameters that are consistent with TNG, including Ω_m = 0.3, Ω_λ = 0.7, Ω_b = 0.048, and h = 0.68. The resulting dark matter and gas cell mass resolutions are 9.6 × 10⁷ M_⊙ and 1.82 × 10⁷ M_⊙, respectively. Galaxies in SIMBA are identified by a 6D friends-of-friends (FOF) finder with a linking length of 0.0056 times the mean inter-particle distance, while haloes are identified using a 3D FoF finder with a linking length parameter of 0.2.

SIMBA assumes the H₂-based star formation law (Schmidt 1959), where the H₂ fraction is determined by local metallicity and gas column density (Krumholz & Gnedin 2011). The star formation rate (SFR) is then calculated using the equation: SFR = ε_*ρ_H2/t_dyn, where ε_* = 0.02 (Kennicutt 1998) and the dynamical time $t_{\mathrm{dyn}}=1/\sqrt{G\rho }$. The H I gas fraction is calculated based on the prescription of Rahmati et al. (2013). The total neutral gas can then be calculated on the fly. Each gas cell in haloes is assigned to the galaxy with the highest value of M_baryon/R², where M_baryon is the total baryonic mass of the galaxy and R is the distance from the gas cell to the centre of the galaxy. SIMBA incorporates the star formation-driven feedback from MUFASA and a torque-limited accretion model (Hopkins & Quataert 2011; Anglés-Alcázar et al. 2017) to accrete cold gas (T < 10⁵ K), which does not require self-regulation for black hole growth (Anglés-Alcázar et al. 2015). For hot gas (T > 10⁵ K), Bondi accretion is used (Bondi 1952), which is the same as in TNG.

In SIMBA, two main kinetic feedback models are present, along with an X-ray feedback model. When the Eddington ratio is high (λ_Edd > 0.2), a radiative or wind mode is activated, which propels the gas away from the black hole at speeds of up to 1000 km s⁻¹. When the Eddington ratio is low (λ_Edd < 0.2) and the black hole mass is greater than 10^7.5 M_⊙, a jet mode is triggered, which can reach velocities of up to 8000 km s⁻¹ when λ_Edd < 0.02. Both the jet and wind modes are bipolar and purely kinetic, and a small fraction of the energy of the jet mode will increase the virial temperature of the halo. When the full jet condition (λ_Edd < 0.02) and f_H2 < 0.2 is met, the X-ray heating mode is activated. This mode has the least effect on galaxies (Davé et al. 2019), and is usually insignificant.

The SIMBA project has a set of simulations with a box size of 50 h⁻¹Mpc on a side (simulation name m50n512), containing 2 × 512³ particles (i.e. the same resolution and input physics as the flagship run m100n1024), but with a volume eight times smaller. In addition to the full m50n512 run, there are catalogues that have different AGN feedback mechanisms turned off: ‘No-Xray’, ‘No-jet’, and ‘No-AGN’, which correspond to X-ray feedback off, both X-ray and jet models off, and all AGN feedback models off, respectively. We use both m100n1024 and m50n512 runs to investigate the effect of CGM angular momentum with different feedback conditions.

2.3. Sample selection

In this paper, we focus exclusively on the central galaxies in both TNG and SIMBA. The SFR in TNG is determined from the value of ‘SubhaloSFR’, that is, the total SFR of all gas cells in a given subhalo. In SIMBA, the SFR is defined as the total SFR in gas particles belonging to each galaxy. Figure 1 displays the central galaxy distributions in the SFR–M_* plane, with the colour indicating the number density of central galaxies. We use the definitions of the star formation main sequence (SFMS) SFR_MS(M_*) in SIMBA (left panel) and TNG (right panel) from Ma et al. (2022), which are shown as the crosses and the dot-dashed line, respectively. Since the SFMS of SIMBA is curved for M_* > 10^9.5 M_⊙, we only consider galaxies with stellar masses ranging from 10^9.5 M_⊙ to 10^11.2 M_⊙ in both simulations at z = 0 to ensure that the galaxies in our sample are fully resolved.

Fig. 1. Distribution of central galaxies at z = 0 as a function of SFR and M*, for SIMBA and TNG in 100 Mpc/h, from left to right, respectively. The coloured background is the logarithmic number of central galaxies. The black dot-dashed line is the SFMS of TNG100, following the definition in Ma et al. (2022): log(SFR/yr−1 M⊙) = 0.83log M* − 8.32, and black cross represents SFMS of star-forming central galaxies in SIMBA100, where star-forming galaxies are simply selected with log(sSFR/Gyr−1 M⊙)≥ − 1.8. Magenta lines separate the star-forming and quenched galaxies in both panels.

Finally, we select a total of 6925 and 14479 central galaxies in the mass range of 9.5 ≤ log(M_*/M_⊙)≤11.2 from SIMBA and TNG, respectively. For a fair comparison between the two simulations, we focus on the SFR offsets from the SFMS, ΔlogSFR, defined as,

$$\begin{array}{c}\hfill \mathrm{\Delta }log\mathrm{SFR}=log\mathrm{SFR}-log{\mathrm{SFR}}_{\mathrm{MS}}.\end{array}$$(1)

Following Ma et al. (2022), we separate the star-forming and quenched galaxies with the cutoff SFR of ΔlogSFR = −1, that is, 1 dex below the SFMS.

2.4. Kinematic properties

According to Lu et al. (2022), we consider the region beyond twice the half stellar mass radius of the galaxy (2R_hsm) and within 100 kpc to be the CGM domain. Beyond this scale, the connection between CGM cold gas and inner star formation is weak. We focus on the cold phase of the CGM gas, which has a temperature range of 10⁴ K < T < 2 × 10⁴ K. In Wang et al. (2022b), it was found that the cold-phase CGM gas has a higher angular momentum and more tangential motion than its hot-phase (T > 10⁵ K) counterparts.

In both TNG and SIMBA simulations, we calculate the specific angular momentum of the cold-phase CGM gas (10⁴ K < T < 2 × 10⁴ K), j_CGM, as follows,

$$\begin{array}{c}\hfill {\mathbf{j}}_{\mathrm{CGM}}=\frac{{\sum }_i{m}_{\mathrm{gas},i}{\mathbf{r}}_{\mathrm{gas},i}\times {\mathbf{v}}_{\mathrm{gas},i}}{{\sum }_i{m}_{\mathrm{gas},i}},\end{array}$$(2)

where m_gas, i is the mass of a given gas cell i, r_gas, i is the relative distance from the galaxy centre, and v_gas, i is the velocity. The summation is performed in all cold gas cells with 2R_hsm < r_gas, i < 100kpc. The dimensionless spin of CGM (λ_CGM) can be measured as follows (Lu et al. 2022),

$$\begin{array}{c}\hfill {\lambda }_{\mathrm{CGM}}=\frac{{\mathrm{\Sigma }}_i{m}_{\mathrm{gas},i}{v}_{t,\mathrm{g}as,i}^2{r}_{\mathrm{gas},i}/GM(\le r_{\mathrm{gas},i})}{{\mathrm{\Sigma }}_i{m}_{\mathrm{gas},i}}\end{array}$$(3)

where v_t,gas,i is the tangential velocity of the i-th gas cell and M(≤r_gas, i) is the total mass (including all types of particles) within r_gas, i.

Different from Lu et al. (2022), we calculate the environmental angular momentum of each central galaxy, j_env, by summing the contribution from all particles (including dark matter, star, and gas particles) as,

$$\begin{array}{c}\hfill {\mathbf{j}}_{\mathrm{env}}=\frac{{\mathrm{\Sigma }}_i{M}_{\mathrm{par},i}{\mathbf{r}}_i\times {\mathbf{v}}_i}{{\mathrm{\Sigma }}_i{M}_{\mathrm{par},i}},\end{array}$$(4)

where M_par, i is the mass of an individual particle i, r_i is the relative distance from i to the central galaxy, and v_i is the relative velocity. The summation is performed on all particles with 2R_hsm < r_i < 100 kpc, where dark matter will dominate the contribution of angular momentum. This will ensure a better quantification of the environmental angular momentum than just using the satellite galaxies as in Lu et al. (2022).

3. Results

3.1. Trend with SFR

In Figure 2, we show the distribution of galaxies in the λ_CGM–ΔlogSFR plane for SIMBA (top panel) and TNG (bottom panel). The colour coding indicates the logarithmic number of galaxies. The solid line in each panel indicates the median values with errors estimated from the 16^th–84^th percentile ranges. The two simulations show different correlations between λ_CGM and ΔlogSFR. In TNG, galaxies with a low ΔlogSFR have much higher λ_CGM than their star-forming counterparts. This is in agreement with the findings of Lu et al. (2022), which suggest that the CGM gas of the quenched galaxies still has a strong rotational motion. It is likely related to the surplus of cold gas in the CGM caused by the relatively weak kinetic AGN feedback in the TNG (Ma et al. 2022).

Fig. 2. Distribution of λCGM as a function of ΔlogSFR in SIMBA (top panel) and TNG (bottom panel). The background is the logarithmic number of galaxies, with colours ranging from light (blue) to dark (red) indicating an increasing number of galaxies. From top to bottom panels, the blue and red lines show the median values and errors estimated from the 16th − 84th percentile ranges for SIMBA and TNG, respectively.

On the other hand, λ_CGM gradually increases with ΔlogSFR in SIMBA and most quenched galaxies only have a small λ_CGM (< 0.2), indicating that the CGM gas in quenched galaxies is more likely to have random motion rather than rotational motion. This is also in line with their low cold gas reservoir, as reported in Appleby et al. (2021) and Ma et al. (2022). The majority of galaxies with high-λ_CGM are the disc galaxies in the SFMS.

We note that the comparisons in Figure 2 do not include galaxies without SFR measurements (i.e. SFR = 0) in both simulations. The fraction of galaxies with SFR = 0 is 3.5% and 9% for SIMBA and TNG, respectively. These galaxies are caused by the stochastic star formation algorithms and the limited simulation resolution. So they can be effectively considered as fully quenched. To be comprehensive, Figure 3 displays the probability distributions of λ_CGM for all quenched galaxies (including galaxies with SFR = 0) and star-forming galaxies in SIMBA (orange) and TNG (blue). Both the star-forming and quenched galaxies show very different distributions in λ_CGM between SIMBA and TNG. Star-forming galaxies in SIMBA have significantly lower λ_CGM compared to TNG. It is evident that the λ_CGM distributions for all quenched galaxies still follow the trend for quenched galaxies shown in Figure 2, whether in TNG or SIMBA. Although galaxies with SFR = 0 in TNG have slightly lower λ_CGM values (with an average of around 0.72) than the median values (∼0.8) shown in Figure 2, they are still comparable to the λ_CGM values of star-forming galaxies (with an average of 0.76), as illustrated in Figure 3. The situation is similar in SIMBA. Those with SFR = 0 in SIMBA have an average λ_CGM of 0.11, while those star-forming galaxies have an average value of 0.28.

Fig. 3. Histograms of λCGM for SIMBA and TNG, with the top and bottom panels representing star-forming and quenched galaxies, respectively, where quenched galaxies include those with SFR = 0, and the Y-axis is normalised by the total number of central galaxies in each simulations. Blue and orange bins represent normalised probability of TNG and SIMBA, respectively, and the brown is cross area.

Figure 4 presents examples of cold gas distributions in star-forming and quenched galaxies in TNG (two left panels) and SIMBA (two right panels). The top and bottom panels display face-on and edge-on projections, respectively. The colour scales indicate the SFRs of the gas cells, as labelled. The total specific SFR of each galaxy (sSFR = SFR/M_*) is also shown in the panel. Notably, both the star-forming and quenched galaxies in TNG have large cold-gas discs in the CGM, which is in agreement with their high angular momenta, as seen in Figure 2. However, the quenched galaxies have an obvious cavity of cold gas in the central region (roughly the size of the stellar disc). As demonstrated in Ma et al. (2022), galaxies in TNG are quenched by the ejection of cold gas from inner discs to the outer regions, which is caused by the kinetic AGN feedback mode. This naturally creates a hole in the gas distribution and halts star formation in the central stellar disc.

Fig. 4. Spatial distribution of cold gas in four examples of TNG and SIMBA, respectively. Stellar masses of all four galaxies are in the range of 1010.2 − 1010.8 M⊙. Top panels are shown in face-on projection, along with the direction of galaxy gas angular momentum, and bottom is in edge-on projection. The gas distribution is colour-coded by its star-formation rate, and λCGM and log sSFR (M⊙/Gyr) are labelled in each panel.

In contrast to star-forming galaxies, quenched galaxies in SIMBA have very few cold gas cells, and their distribution is more spherical than disc-like. Additionally, there is no visible cavity of cold gas in the core. The cold gas density in the central parts of star-forming and quenched galaxies in SIMBA are quite similar (see Fig. 5 of Ma et al. 2022). However, the quenched galaxies have much less cold gas in the CGM, which reduces the amount of cold gas that can reach the core, and, as a result, the overall SFR decreases.

It is evident from the comparisons that galaxies in TNG and SIMBA, despite having similar stellar masses and star formation rates, have distinct CGM gas kinematics that are linked to the total cold gas supply and their AGN feedback processes.

3.2. Cold gas reservoir

To be clear, we compute the cold gas mass in the CGM, M_gas, by summing the cold gas cells within the range of 2R_hsm to 100 kpc. Additionally, we define f_cold ≡ M_gas/M_* as the ratio of M_gas to the total stellar mass of galaxies (M_*). The relationship between f_cold and ΔlogSFR is analysed in Figure 5, with SIMBA displayed in the two left panels and TNG in the two right panels. The colour scales, as indicated by the colour bar on the right, represent the normalised galaxy number density in each simulation. We categorise the galaxy distributions into subsamples of λ_CGM < 0.5 and λ_CGM > 0.5, as labelled in each panel. It is apparent that in SIMBA, angular momentum scarcely affects the correlation between SFR and the CGM gas mass. In most quenched galaxies, the CGM shows low f_cold and low angular momentum. In TNG, the decline in ΔlogSFR with decreasing f_cold reflects the trend seen in SIMBA. For quenched galaxies, the association between ΔlogSFR and f_cold is considerably weaker because the cold gas in CGM is not actively involved in star formation. However, there are very few quenched galaxies with λ_CGM < 0.5, which is in stark contrast to the results in SIMBA. The physical mechanisms behind these differences will be examined in Sect. 3.4.

Fig. 5. Relations between log fcold and ΔlogSFR, for TNG and SIMBA, from left to right, respectively. The coloured background is the probability density distribution, as described in Figure 2. The solid red line is plotted by median values with errors estimated from the 16th − 84th percentile ranges, and is simply distinguished by high and low spin.

3.3. Environmental effect

According to classical galaxy formation theory, galaxies gain angular momentum by accreting gas from their host halos as they evolve, influenced by the torque field (Peebles 1969; Mo et al. 1998), consistent with findings in Lu et al. (2022). Figure 6 illustrates the relationship between the angular momentum of the CGM (j_CGM) and that of the environment (j_Env) within the range of 2R_hsm–100 kpc for galaxies of log(M_*/M_⊙) > 9.5. The top and bottom panels reveal the results for SIMBA and TNG simulations, respectively, distinguishing star-forming galaxies (SFGs, shown by blue points) from quenched galaxies (QGs, depicted by orange circles). The median values of j_CGM for the two populations in different j_Env bins are shown with solid lines. It is apparent that the CGM angular momentum, j_CGM, is influenced by the environmental angular momentum, j_Env, for both SFGs and QGs in both simulations. This indicates that the galaxy’s angular momentum is largely inherited from its surrounding environment. But the correlation between j_CGM and j_Env decreases at lower values of j_Env.

Fig. 6. Relations between jCGM and jEnv within 2Rhsm to 100 kpc, for SIMBA and TNG, from top to bottom, respectively. The black line is the relation of SFGs and red line is the relation of QGs in each panel. To show the trend more clearly, we present 1:1 baselines, indicated by the magenta dotted lines. For SFGs and QGs, each sample is plotted with a blue dot and an orange circle, respectively. Each line shows the median values, with errors estimated from the 16th − 84th percentile ranges.

Interestingly, the SFGs in two different simulations demonstrate a similar relationship between j_CGM and j_Env. The angular momentum of the CGM is influenced by both the inner stellar disc and the outer halo environment. When j_Env is large, the environment primarily contributes to j_CGM. Consequently, the SFGs and QGs in both simulations converge for log(j_Env/kpc km s⁻¹) > 3.5, with a slope of j_CGM/j_Env near unity. Conversely, at low j_Env values, the inner disc’s influence becomes significant, making the j_CGM/j_Env slope approach zero. This accounts for the behaviour of the SFGs in the simulations, which are likely to be significantly influenced by powerful AGN feedback. We note that j_CGM and j_Env cover the same range of CGM (2R_hsm–100 kpc) and, in principle, are closely connected. It would be intriguing to compare the relation between j_CGM and j_gal, where j_gal is the angular momentum calculated using all particles within 2R_hsm of each galaxy. We find that j_Env and j_gal are closely correlated with each other, and the relations between j_CGM and j_gal still largely follow the trends between j_CGM and j_Env.

The primary difference between the two simulations is that QGs in the TNG simulation consistently exhibit higher j_CGM compared to their star-forming counterparts at a specific j_Env, a trend also observed in Lu et al. (2022). However, the median values of j_CGM for QGs in the SIMBA simulation are roughly the same as those of SFGs. The distribution of j_CGM for QGs is significantly broader. This distinct behaviour of QGs in the two simulations is most likely caused by the predominant impact of the AGN feedback mechanisms.

3.4. Effect of AGN feedback

The SIMBA simulation set comprises three variations of the implementation of the AGN feedback model by disabling different AGN feedback modes, as described in Sect. 2.2. To examine the influence of AGN feedback on the CGM angular momentum, we compare the fiducial model with the different variations. Figure 7 illustrates the relationship between j_CGM and j_Env for these model variations. The models displayed from left to right are the fiducial model, ‘No-Xray’, ‘No-jet’, and ‘No-AGN’ runs. These simulations use a smaller volume of 50³ h⁻³Mpc³, resulting in fewer galaxies compared to the fiducial run in Figure 6. We show the median values of j_CGM in different j_Env bins for SFGs and QGs as the black and red dashed lines, respectively. For fair comparisons, we also replicate in each panel the median values of j_CGM from SIMBA100 in Figure 6 as solid lines. The median j_CGM for SFGs in the SIMBA50 variation models closely follows the fiducial one in SIMBA100, as expected. But there are slightly larger differences for QGs. The scatters of j_CGM in QGs are significantly increased when more AGN feedback mechanisms are included, confirming the results shown in Figure 6.

Fig. 7. Same as Fig. 6, but for the fiducial SIMBA50 run, No-Xray run, No-jet run, and No-AGN run, respectively. The black and red dashed lines show the relations of SFGs and QGs in SIMBA50, respectively. To clearly illustrate the effect of feedback, we replicate in each panel the medians for SFGs and QGs in SIMBA100 with black and red solid lines, respectively.

AGN feedback serves as the principal mechanism to quench galaxies in SIMBA. The ‘No-AGN’ run, which disables all AGN feedback modes, shows only a small number of QGs. It is clear that the j_CGM distribution for QGs matches that of SFGs when jet-mode feedback is disabled in both the ‘No-jet’ and ‘No-AGN’ runs. Kinetic jet feedback leads to a notable increase in the scatter of j_CGM for QGs. As outlined in Davé et al. (2019) (and further discussed in Ma et al. 2022), the bipolar kinetic feedback in the low-accretion mode ejects gas particles from within the black hole accretion kernel at an outflow velocity of up to 8000 km s⁻¹. The collimated nature of the outflow restricts its extent to approximately 1 kpc. As a result, the cold gas distribution in the centres of the galaxies is not severely affected by the jet-mode feedback, as also shown in Fig. 5 of Ma et al. (2022). However, jet energy is effectively distributed spherically within the CGM gas due to hydrodynamic interactions between the outflow and the CGM gas, thus modifying the distribution j_CGM and significantly reducing the cold gas content in the CGM.

TNG has significantly different AGN feedback mechanisms. During its low-accretion kinetic feedback phase, gas cells around a black hole are expelled with momentum in random directions. However, the mean momentum is preserved over numerous energy injection events. Despite the isotropic nature of kinetic energy release in TNG, bipolar gas outflows are still present. As discussed in Nelson et al. (2019a), the collimated outflow in TNG is largely caused by a ‘path of least resistance’ effect. Kinetic feedback-driven outflows encounter enhanced resistance on the planes of galactic discs and are reshaped into high-velocity collimated outflows perpendicular to the discs. Meanwhile, outflows along the plane of a disc will expel gas from the centre of the galaxy, which explains the void observed in the CGM gas distribution in Figure 4, as well as the extensive cold gas disc in the QG.

The influence of kinetic feedback on the CGM gas distribution depends on both the feedback mechanism and the strength of the released energy. Due to the mild energy release, the outflow velocity in TNG can only reach a maximum value around 3000 km s⁻¹ in very massive galaxies (Nelson et al. 2019a), which is significantly smaller than the typical outflow velocity (with a maximum value of 8000 km s⁻¹) in SIMBA (Davé et al. 2019). As reported in Ma et al. (2022), kinetic AGN feedback causes the cold gas in TNG to migrate from the inner discs to the outer regions while maintaining the overall cold gas mass. When the cold gas is redistributed in the outer region, due to momentum conservation, the angular momentum of the CGM will increase accordingly, as shown in the right panel of Figure 6.

To gain a deeper understanding of how CGM angular momentum and AGN feedback influence the gas distribution, Figure 8 displays the galaxy distributions within the log f_cold–ΔlogSFR plane for the various AGN feedback models of SIMBA50. The distributions for galaxies with λ_CGM ≥ 0.5 and λ_CGM < 0.5 are illustrated in the top and bottom panels, respectively. We used the same galaxy mass range and colour scales as in Figure 5. The dashed magenta line in each panel represents the median values of f_cold in different ΔlogSFR bins.

Fig. 8. Relations between ΔlogSFR and fcold, for central galaxies with λCGM < 0.5 and λCGM ≥ 0.5 in SIMBA50. Here we show relations of fiducial SIMBA50 run, No-Xray run, No-jet run, and No-AGN run, from left to right, respectively. The background is a probability density distribution of central galaxies, as described in Figure 2. Magenta lines show the change of medians of fcold with the change of ΔlogSFR.

When comparing the upper and lower panels within identical AGN feedback models, it is evident that the CGM angular momentum does not notably influence the relationship between the gas reservoir and the SFR in SIMBA, in agreement with the result depicted in Figure 5. There is a subtle trend indicating that QGs with higher spins have a slightly stronger dependency of f_cold on ΔlogSFR. However, due to the significant scatter, the results for low and high spins are consistent with each other, similarly shown in Figure 5, and this holds even when AGN feedback is disabled.

In summary, the AGN feedback mechanisms will considerably influence the distribution of the CGM angular momentum, as well as the cold gas in the CGM (as illustrated in Figure 4). Nonetheless, the correlation between f_cold and ΔlogSFR is not strongly altered by AGN feedback or CGM angular momentum.

4. Conclusions and discussions

In this research, we explore the impact of CGM angular momentum on star formation processes within galaxies. Employing advanced hydrodynamical simulations from TNG and SIMBA, we have quantified the effects of CGM angular momentum across various AGN feedback scenarios. The key findings of our study are summarised as follows.

(i) The distributions of galaxies in the λ_CGM–ΔlogSFR plane differ significantly between TNG and SIMBA. The most noteworthy distinction between these simulations is that most QGs in TNG exhibit high CGM angular momentum, whereas in SIMBA the opposite is observed. Both simulations show similar distributions of λ_CGM for SFGs. Additionally, in TNG, QGs generally possess a large cold gas disc in the CGM, and the central cavity in the gas distribution is due to kinetic AGN feedback. However, QGs in SIMBA have minimal cold gas in the CGM and typically lack prominent cold gas discs, in line with their low CGM spin.

(ii) The angular momentum of the CGM is influenced by both the angular momentum of the environment and the feedback from inner stellar discs (notably the AGN feedback). The SFGs in both TNG and SIMBA exhibit similar strong correlations between j_CGM and j_Env, with a slope near unity for high j_Env values. At lower j_Env, j_CGM is more impacted by inner stellar discs and shows a weaker dependence on j_Env. On the other hand, TNG and SIMBA’s QGs show markedly different distributions in the j_CGM–j_Env space. In TNG, QGs have consistently higher j_CGM than SFGs with the same j_Env, resulting from randomised momentum injection events in the kinetic AGN feedback mode. Meanwhile, QGs in SIMBA have median j_CGM values similar to SFGs, but the scatter is significantly larger due to collimated jet-mode feedback.

(iii) While the AGN feedback and CGM angular momentum affect the cold gas distribution within the CGM, the relationship between f_cold and ΔlogSFR remains largely consistent across various AGN feedback models in SIMBA50. This indicates that the star formation process steadily relies on the availability of cold gas in the CGM.

Angular momentum quenching has previously been suggested as another mechanism to quench galaxies (Peng & Renzini 2020). According to Lu et al. (2022), the high angular momentum of CGM in the QGs of the TNG might be instrumental in preserving their quenched state. Our findings indicate that the CGM angular momentum distribution in SFGs and QGs is heavily influenced by the AGN feedback mechanisms implemented in various simulations. In SIMBA, the jet-mode AGN feedback primarily depletes the cold gas in the CGM of QGs, resulting in these QGs typically having low CGM spins. This indicates that a high CGM angular momentum is not always essential for QGs. Finally, in Appendix A, we show that our results are not affected by the simulation resolutions.

Observationally, galaxies that possess relatively large H I discs (i.e. H I-rich) in comparison to typical galaxies with identical stellar masses have also been found (see e.g., Lemonias et al. 2014; Lutz et al. 2018). These galaxies exhibit high CGM angular momenta that contribute to the stabilisation of cold-gas discs and the reduction in star formation efficiency (Obreschkow et al. 2016; Lutz et al. 2018). However, these galaxies remain predominantly SFGs, with high CGM angular momentum supporting the large H I discs, unlike the QGs in TNG.

The red spiral galaxies appear analogous to the QGs in TNG in reality, characterised by their red central regions and higher H I gas fractions when compared to elliptical galaxies of comparable mass (Hao et al. 2019; Guo et al. 2020; Zhou et al. 2021). Nevertheless, as shown in Wang et al. (2022a), these red spiral galaxies with higher H I masses often exhibit bluer outer discs, suggesting that optically selected red spirals are not completely quenched. Using the H I observations from ALFALFA (Haynes et al. 2018), Guo et al. (2021) demonstrated that the optical morphology of a galaxy does not influence the relationship between total H I mass and SFR. Therefore, the primary characteristic of the cold gas discs in the CGM of QGs in TNG is largely due to its unique AGN feedback mechanism (Guo et al. 2022; Ma et al. 2022). Future studies of CGM gas and more sophisticated simulation models will offer a deeper understanding of the impact of CGM angular momentum on star formation activities.

Acknowledgments

We thank the reviewer for the constructive report that significantly improves the presentation of this paper. This work is supported by the National SKA Program of China (grant No. 2020SKA0110100), the CAS Project for Young Scientists in Basic Research (No. YSBR-092), the National Natural Science Foundation of China (No. 12433003), and the science research grants from the China Manned Space Project with NOs. CMS-CSST-2021-A02. W.C. is supported by the STFC AGP Grant ST/V000594/1, the Atracción de Talento Contract no. 2020-T1/TIC-19882 was granted by the Comunidad de Madrid in Spain, and the science research grants were from the China Manned Space Project. W.C. thanks the Ministerio de Ciencia e Innovación (Spain) for financial support under Project grant PID2021-122603NB-C21 and HORIZON EUROPE Marie Sklodowska-Curie Actions for supporting the LACEGAL-III project with grant number 101086388. We acknowledge the use of the High Performance Computing Resource in the Core Facility for Advanced Research Computing at the Shanghai Astronomical Observatory.

References

Appendix A: Resolution effect

In order to check whether our main results will be affected by the resolutions of the specific TNG and SIMBA simulations used in this paper, we investigate the two primary results in TNG100-2 and TNG50. We show the distribution of λ_CGM as a function of ΔlogSFR and the relations between j_CGM and j_Env, as illustrated in Figure A.1. We repeat the results of TNG100 and SIMBA for better comparisons. TNG100-2 has the same box size as TNG100, with mass resolutions lower than TNG100, but very similar to those of SIMBA. The dark matter mass resolution is m_DM = 6.0 × 10⁷ M_⊙, and the average gas mass is around 1.1 × 10⁷ M_⊙ in TNG100-2. TNG50 simulation has a box size of 35 h⁻¹Mpc on a side, with a dark matter mass resolution of m_DM = 4.5 × 10⁵ M_⊙ and an average gas mass around 8.5 × 10⁴ M_⊙, which are significantly higher than those of TNG100 and TNG100-2. Here, we confirm that, even though the exact values of λ_CGM and j_CGM will be affected by the simulation resolution, our results remain unchanged in simulations of different resolutions.

Fig. A.1. Same to Figs. 2 and 6, but also including the results for TNG100-2 and TNG50. Overall, the trends in TNG100-2 and TNG50 are very similar to that in TNG100, with weak dependence on resolution. The quenched galaxies in TNG100-2 and TNG50 still show a higher λCGM than their star-forming counterparts.

All Figures

Fig. 1. Distribution of central galaxies at z = 0 as a function of SFR and M*, for SIMBA and TNG in 100 Mpc/h, from left to right, respectively. The coloured background is the logarithmic number of central galaxies. The black dot-dashed line is the SFMS of TNG100, following the definition in Ma et al. (2022): log(SFR/yr−1 M⊙) = 0.83log M* − 8.32, and black cross represents SFMS of star-forming central galaxies in SIMBA100, where star-forming galaxies are simply selected with log(sSFR/Gyr−1 M⊙)≥ − 1.8. Magenta lines separate the star-forming and quenched galaxies in both panels.

In the text

Fig. 2. Distribution of λCGM as a function of ΔlogSFR in SIMBA (top panel) and TNG (bottom panel). The background is the logarithmic number of galaxies, with colours ranging from light (blue) to dark (red) indicating an increasing number of galaxies. From top to bottom panels, the blue and red lines show the median values and errors estimated from the 16th − 84th percentile ranges for SIMBA and TNG, respectively.

In the text

	Fig. 3. Histograms of λCGM for SIMBA and TNG, with the top and bottom panels representing star-forming and quenched galaxies, respectively, where quenched galaxies include those with SFR = 0, and the Y-axis is normalised by the total number of central galaxies in each simulations. Blue and orange bins represent normalised probability of TNG and SIMBA, respectively, and the brown is cross area.
In the text

Fig. 4. Spatial distribution of cold gas in four examples of TNG and SIMBA, respectively. Stellar masses of all four galaxies are in the range of 1010.2 − 1010.8 M⊙. Top panels are shown in face-on projection, along with the direction of galaxy gas angular momentum, and bottom is in edge-on projection. The gas distribution is colour-coded by its star-formation rate, and λCGM and log sSFR (M⊙/Gyr) are labelled in each panel.

In the text

	Fig. 5. Relations between log fcold and ΔlogSFR, for TNG and SIMBA, from left to right, respectively. The coloured background is the probability density distribution, as described in Figure 2. The solid red line is plotted by median values with errors estimated from the 16th − 84th percentile ranges, and is simply distinguished by high and low spin.
In the text

Fig. 6. Relations between jCGM and jEnv within 2Rhsm to 100 kpc, for SIMBA and TNG, from top to bottom, respectively. The black line is the relation of SFGs and red line is the relation of QGs in each panel. To show the trend more clearly, we present 1:1 baselines, indicated by the magenta dotted lines. For SFGs and QGs, each sample is plotted with a blue dot and an orange circle, respectively. Each line shows the median values, with errors estimated from the 16th − 84th percentile ranges.

In the text

	Fig. 7. Same as Fig. 6, but for the fiducial SIMBA50 run, No-Xray run, No-jet run, and No-AGN run, respectively. The black and red dashed lines show the relations of SFGs and QGs in SIMBA50, respectively. To clearly illustrate the effect of feedback, we replicate in each panel the medians for SFGs and QGs in SIMBA100 with black and red solid lines, respectively.
In the text

Fig. 8. Relations between ΔlogSFR and fcold, for central galaxies with λCGM < 0.5 and λCGM ≥ 0.5 in SIMBA50. Here we show relations of fiducial SIMBA50 run, No-Xray run, No-jet run, and No-AGN run, from left to right, respectively. The background is a probability density distribution of central galaxies, as described in Figure 2. Magenta lines show the change of medians of fcold with the change of ΔlogSFR.

In the text

	Fig. A.1. Same to Figs. 2 and 6, but also including the results for TNG100-2 and TNG50. Overall, the trends in TNG100-2 and TNG50 are very similar to that in TNG100, with weak dependence on resolution. The quenched galaxies in TNG100-2 and TNG50 still show a higher λCGM than their star-forming counterparts.
In the text