Can Supernovae Quench Star Formation in High-z Galaxies?

To compute the evolution of the stellar population in the galaxy, we use starburst99 (Leitherer et al. 1999), adopting the Geneva stellar tracks and assuming a Salpeter initial mass function (IMF) in the range (1–100)M_⊙. Assuming a burst of constant SFR, the energy released by stellar winds and SNe can be expressed as a function of time (t) and stellar metallicity (Z_⋆). The energy rate evolution can be written as

$$\begin{eqnarray}&&{\dot{E}}^{+}=G(t,{Z}_{\star })\,\mathrm{SFR},\end{eqnarray} \tag{ 2 }$$

where the SFR is in units of M_⊙yr⁻¹ and G(t, Z_⋆) is the energy input rate in [erg s⁻¹/(M_⊙yr⁻¹)] for a continuous burst of SF with SFR = 1 M_⊙ yr⁻¹. The energy rate as a function of time for an SFR = 1 M_⊙ yr⁻¹ burst is shown on the left in Figure 1 for different stellar metallicities. We see that the energy input rates increase for increasing metallicity. In particular, during the first ≤5 Myr of evolution, the rates of energy injected by metal-rich stellar populations (Z_⋆ ≥ Z_⊙) exceed by more than an order of magnitude those of metal-poor ones, Z_⋆ ≤ 0.1Z_⊙, while at later times their differences are less pronounced.

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We assume a galaxy to be quenched when the energy input from SNe heats up all the gas available for SF above the virial temperature, T_vir, effectively counteracting cooling losses. This assumption ensures that the gas is maintained in a hot state at high temperature, ⁶ hence preventing SF, and it translates into expressing the cooling rate in Equation (1) as

$$\begin{eqnarray}&&{\dot{E}}^{-}=\displaystyle \frac{{M}_{g}}{\mu {{\rm{m}}}_{p}}{k}_{{\rm{B}}}{T}_{\mathrm{vir}}\displaystyle \frac{1}{{t}_{\mathrm{cool}}},\end{eqnarray} \tag{ 3 }$$

where M_g is the total gas mass of the galaxy, t_cool is the gas cooling time, and μ = 0.6 is the mean molecular weight for ionized gas.

Considering the baryonic mass fraction f_b ≡ (Ω_b /Ω_m ), we can express the gas mass as M_g = M_baryons − M_⋆ = (Ω_b /Ω_m )M_h − M_⋆. Equation (3) can be rewritten as

$$\begin{eqnarray}&&{\dot{E}}^{-}=\displaystyle \frac{3}{2}\displaystyle \frac{n{\rm{\Lambda }}({T}_{\mathrm{vir}},Z)}{\mu {{\rm{m}}}_{p}}[{f}_{b}{M}_{h}(z,{T}_{\mathrm{vir}})-\mathrm{SFR}\,{\rm{\Delta }}{t}_{b}],\end{eqnarray} \tag{ 4 }$$

where Λ(T_vir, Z) is the cooling rate and n (and Z) the gas number density (and metallicity). The gas density is ρ = μm_p n = 18π²Ω_b ρ_c (z), where ρ_c (z) is the critical density at redshift z. The cooling function is computed using KROME (Grassi et al. 2014), and it is shown in the right panel of Figure 1 as a function of T_vir for different metallicities. For virial temperatures T_vir ≥ 10^4.2 K, we see that the higher the gas metallicity, the higher the gas cooling rate. The differences are maximal at T_vir ≈ 10^5.5 K, where the cooling rate of metal-rich gas exceeds by almost 2 orders of magnitude the one of metal-poor gas, Z ≤ 0.01Z_⊙.

By substituting Equations (2) and (4), Equation (1) can be cast in the following form:

$$\begin{eqnarray}&&\mathrm{SFR}\geqslant \displaystyle \frac{{f}_{b}{M}_{h}(z,{T}_{\mathrm{vir}})}{\tau +{\rm{\Delta }}{t}_{b}}\equiv {\mathrm{SFR}}_{\min },\end{eqnarray} \tag{ 5a }$$

where

$$\begin{eqnarray}&&\tau =\displaystyle \frac{3}{2}\displaystyle \frac{\mu {{\rm{m}}}_{p}G({\rm{\Delta }}{t}_{b},{Z}_{\star })}{n{\rm{\Lambda }}({T}_{\mathrm{vir}},Z)}.\end{eqnarray} \tag{ 5b }$$

Equation (5a) describes the minimum SFR, ${\mathrm{SFR}}_{\min }$, needed for SNe to suppress SF after a burst lasting for a time Δt_b . We note that the relation depends on the halo properties of the galaxy through T_vir (or, equivalently, the halo mass M_h ). The metallicity also plays a key role, entering both in the gas cooling function and in the SNe energy input rate. Hereafter, for simplicity, we assume that Z = Z_⋆.

When interpreting observations, by approximating the SFH of a galaxy before the quenching with a top-hat function based on SED fitting results, one can infer the corresponding values of SFR and Δt_b . If Equation (5a) is satisfied, SN feedback is predicted to halt SF in the galaxy; on the contrary, other mechanisms must be invoked. Let us proceed with a more detailed analysis of this result by applying it to the two recently observed quiescent high-z galaxies, whose properties are reported in Table 1.

Table 1. The Two Observed Quiescent Galaxies JADES-GS-z7-01-QU and MACS0417-z5BBG

Parameter	JADES-GS-z7-01-QU	MACS0417-z5BBG
z	7.3	5.2
$\mathrm{log}{M}_{\star }/{M}_{\odot }$	8.6	7.6
Z⋆/Z⊙	0.01	1.0
$\mathrm{log}{M}_{h}/{M}_{\odot }$	11.0	10.5
SFR/M⊙ yr−1	17.0	1.0
Δtb /Myr	30.0	40.0
sSFR/Gyr−1	43.0	25.0
AV	0.1	0.19

Note. The table shows the following quantities: redshift z, stellar mass M_⋆, metallicity Z_⋆, halo mass M_h (derived from Behroozi et al. 2019), SFR, burst duration Δt_b , sSFR at the end of the burst sSFR, and dust extinction, A_V .

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JADES-GS-z7-01-QU (Looser et al. 2023) has a redshift of z = 7.3 and a stellar mass M_⋆ = 10^8.6 M_⊙. Based on these measurements, using the stellar-to-halo mass relation of Behroozi et al. (2019), we find M_h = 10¹¹ M_⊙. This implies a virial temperature at that redshift of T_vir = 10^5.9 K (see Table 1 for a summary of the galaxy's properties). Having fixed these parameters, we plot ${\mathrm{SFR}}_{\min }$ as a function of Δt_b (Equation (5a)) for JADES-GS-z7-01-QU in the left panel of Figure 2.

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The curves shown in Figure 2 represent the value of ${\mathrm{SFR}}_{\min }$ required for SNe to quench SF in the galaxy as a function of the burst duration, Δt_b . If a galaxy lies above the curve, after a timescale Δt_b the SF will be quenched by SNe. The gray region locates forbidden solutions for which M_⋆ > f_b M_h (z, T_vir). Also shown are curves for different metallicities. ⁷ The increasing trend of ${\mathrm{SFR}}_{\min }$ with metallicity indicates that low-Z systems are more fragile to SN-induced quenching, due to their inability to efficiently cool the shocked gas and make it available again to form stars. As metallicity is increased from Z = 0.01Z_⊙ to solar value, ${\mathrm{SFR}}_{\min }$ rises by ≳1 dex for a typical M_h = 10¹¹ M_⊙.

Let us now directly compare the model with the SFH of JADES-GS-z7-01-QU. The post-starburst galaxy has experienced a short and intense burst of SF followed by an abrupt SF drop. Its SFH, as inferred by Looser et al. (2023) using bagpipes (Carnall et al. 2018), can be approximated as a top hat with SFR ∼ 15 M_⊙ yr⁻¹ and Δt_b ∼ 30 Myr. The measured stellar metallicity is Z_⋆ ∼ 10⁻² Z_⊙. Therefore, to guide the eye, the curve to compare the data with is the corresponding green one. Despite the low metallicity, we see that the JADES-GS-z7-01-QU point lies below the ${\mathrm{SFR}}_{\min }$ curve by a factor of ∼3. This means that the SN energy production is not sufficient to quench the SF under our assumptions. Therefore, we conclude that the quiescence in JADES-GS-z7-01-QU must have been induced by a different physical process. This finding lends further support to the previous studies based on cosmological simulations and quenching timescales reaching the same conclusion. In fact, not only does the quenching appear to be too swift to be produced by SNe (Gelli et al. 2023; Dome et al. 2024), but our model also convincingly shows that the SFR level sustained in the observed burst cannot produce enough energy to suppress SF.

MACS0417-z5BBG is a z = 5.2 lensed galaxy observed by Strait et al. (2023); it has a low stellar mass, M_⋆ = 4.3 × 10⁷ M_⊙. Just like JADES-GS-z7-01-QU, it exhibits a recent sudden SF drop, likely leading to a quiescent phase. Considering the SED fitting from Strait et al. (2023), the SFR is equivalent to a top hat with SFR ∼ 1 M_⊙ yr⁻¹ and Δt_b ∼ 40 Myr. The estimated halo mass and virial temperature are M_h = 10^10.5 M_⊙ and T_vir = 10^5.5 K. Its stellar metallicity is rather high, Z = Z_⊙ (see Table 1). Thus, in this case, to guide the eye, we should compare the data with the corresponding violet curve in the right panel of Figure 2, where the resulting ${\mathrm{SFR}}_{\min }\mbox{-}{\rm{\Delta }}{t}_{b}$ relation is shown. We see that the galaxy falls by a factor of ∼50 below the critical ${\mathrm{SFR}}_{\min }$ line, implying that SN energy also cannot be responsible for the observed SF drop in this case. Stated differently, SF could be quenched by SNe in this galaxy only if it would experience a 50 M_⊙ yr⁻¹ burst of SF. As for the previous case, a process different from SN explosions must be invoked to explain the data.

To generalize our findings and enable their application to quiescent galaxies of different mass and redshift, we show the ${\mathrm{SFR}}_{\min }\mbox{-}{\rm{\Delta }}{t}_{b}$ relation for a variety of cases in Figure 3. The panels correspond to four different halo masses in the range M_h = 10^9–12 M_⊙ and two metallicities, Z = 0.01 − 1 Z_⊙. In order to also analyze the redshift dependence of SN quenching, the shaded areas in the figures cover, for each metallicity, the redshift range 5 < z < 15, with T_vir = T_vir(M_h , z), as indicated in each panel.

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At low halo masses, SN quenching is more likely to happen, as the conditions for SF suppression can be reached in short times and with low SFRs. For instance, for M_h = 10⁹ M_⊙ (upper left panel), the SNe produced in a burst of SFR > 1 M_⊙yr⁻¹ are expected to quench the SF after only ∼20 Myr at redshift z ∼ 5. In this case, there is a weak dependency on Z descending from the small sensitivity of the cooling function on this quantity for T_vir < 10^4.9 K (see Figure 1). The redshift dependence is instead more pronounced: for a ∼10 Myr burst, the SFR needed to quench SF increases from ∼2 M_⊙ yr⁻¹ at z = 5 to ∼20 M_⊙ yr⁻¹ at z ∼ 15.

At higher halo masses, meeting the quenching condition becomes more challenging (due to the increased gas mass that must be heated), and higher SFR values are required to suppress SF. The middle panels, displaying the M_h = 10^10–11 M_⊙ cases, illustrate the major role played by metallicity at intermediate virial temperatures, T_vir ∼ 10⁵–10⁶ K, with metal-poor galaxies being more likely to experience SN quenching following bursts of SF. The extreme case of M_h = 10¹² M_⊙ (bottom right panel) essentially highlights the impossibility for very massive galaxies to be quenched by stellar feedback alone.

We caution that our simple model approximating galaxy evolution as a single burst of SF is more likely realistic toward lower masses, where systems are expected to be more compact and less complex. However, our conclusions at higher masses can give us an estimate and show the extreme feedback that would be required to counteract SF in such galaxies.

We can further test our model by applying it to observed bursty star-forming galaxies and verifying that they do not satisfy the quenching condition. Let us consider the case of GN-z11, the most UV-luminous galaxy at z = 10.6 known to date (Oesch et al. 2016; Bunker et al. 2023). It has a stellar mass of M_⋆ = 5.4 × 10⁸ M_⊙, a halo mass of M_h ∼ 3 × 10¹⁰ M_⊙ (Scholtz et al. 2023), and gas metallicity of $\mathrm{log}(Z/{Z}_{\odot })\,=-0.92$. Its SFH can be approximated with an SFR ≈ 20M_⊙ yr⁻¹ burst lasting Δt_b ≈ 30 Myr. These values are below the ${\mathrm{SFR}}_{\min }$ threshold, confirming that SNe are not expected to quench the galaxy as expected.

The SN quenching condition illustrated by Equation (5a) depends on halo mass, metallicity, and redshift. While the latter two quantities can usually be directly obtained from current observations, it is more difficult to measure M_h at high z. In the frequent case of unavailable kinematics measurements in the halo, some assumptions must be made in order to fix M_h . This can be derived from the stellar mass by assuming a stellar-to-halo mass ratio defined as f_⋆ = M_⋆/M_h . In the above analysis, we have adopted the redshift-dependent stellar-to-halo mass ratio versus halo mass relation derived by Behroozi et al. (2019) through empirical modeling. However, this model is mostly based on constraints from galaxy observations at z < 8 and M_h > 10¹¹ M_⊙. Indeed, especially at lower masses, the uncertain nature of the bursty SFR of high-z galaxies makes it difficult to infer their stellar-to-halo mass relation from observations and, in general, simulations often predict higher SF efficiencies at high z (e.g., Xu et al. 2016; Rosdahl et al. 2018; Pallottini et al. 2022). We here want to assess the impact of the choice of f_⋆.

To this aim, we refer to the case study of JADES-GS-z7-01-QU. In Figure 4, we show the f_⋆–M_h relation by Behroozi et al. (2019) at redshift z = 7.3 (black line). The background colors show regions of constant stellar mass, with the green stripe locating the stellar mass of JADES-GS-z7-01-QU, M_⋆ = 10^8.6 M_⊙. The green star marks the intersection with the Behroozi et al. (2019) relation, thus identifying the values that we have been using for the observed galaxy: f_⋆ = 0.4%, M_h = 10¹¹ M_⊙, and T_vir = 10^5.9 K. Instead, assuming a higher value, e.g., f_⋆ = 1%, the halo mass for JADES-GS-z7-01-QU is decreased to M_h = 10^10.6 M_⊙ or T_vir = 10^5.7 K (orange star).

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Figure 5 illustrates the impact on the ${\mathrm{SFR}}_{\min }\mbox{-}{\rm{\Delta }}{t}_{b}$ relation of these two different assumptions for f_⋆. If f_⋆ is increased, the consequently lower massive halo requires a smaller SFR to quench SF. The point corresponding to JADES-GS-z7-01-QU now lies closer to the curve, but it is still below the SN quenching limit. This reinforces our findings, meaning that, even when assuming a higher stellar-to-halo mass ratio, it is unlikely that the JADES-GS-z7-01-QU galaxy has been quenched solely by SNe. The actions of SNe could be able to definitely provoke its quenching only if the ratio is as high as f_⋆ ≳ 2%, and thus M_h < 10^10.4 M_⊙.

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Another factor of uncertainty is brought by the adopted stellar IMF. If the IMF at high z is more top-heavy than the assumed Salpeter IMF, it would result in a larger energy deposition by SNe (Koutsouridou et al. 2023), hence facilitating galaxy quenching. Nonetheless, the metallicities in the two currently observed quiescent galaxies are sufficiently high (Z > 10⁻² Z_⊙) to rule out the presence of pristine stellar populations, typically associated with top-heavy IMFs.

From the analysis of the general trends of the SN quenching condition, we have concluded that SF can be suppressed by SNe in: (i) low-mass (M_h < 10⁹ M_⊙) galaxies; or (ii) highly star-forming galaxies, i.e., SFR ≳100 M_⊙ yr⁻¹ for M_h ∼ 10¹¹ M_⊙ at z ∼ 10.

Specifically, for the two currently observed quenched high-z galaxies JADES-GS-z7-01-QU and MACS0417-z5BBG, we find that the energy input from their SNe is not sufficient to produce quenching. As a consequence, additional physical processes need to be at play in these systems on top of SNe to provide the extra energy needed to suppress SF.

Environmental effects, such as ram pressure stripping and strangulation, can most likely be excluded as being responsible for high-z galaxy quenching, since they are believed to occur predominantly at lower redshifts, once large-scale structures have developed in the Universe (e.g., Peng et al. 2010). Moreover, simulations predict that at high z the evolution and quenching of galaxies is driven by their mass, rather than by the environment (Contini et al. 2020; Gelli et al. 2020). In the specific cases of JADES-GS-z7-01-QU and MACS0417-z5BBG, furthermore, no massive nearby galaxy that would be able to contribute to environmental quenching is observed. Finally, these external physical processes act on typically long timescales (≫100 Myr; e.g., Emerick et al. 2016) and cannot cause a swift stop of SF.

The additional energy needed to produce the witnessed quenching has to instead be associated with a fast physical mechanism, such as radiation-driven dusty outflows. The radiation pressure may be provided by young massive stars (e.g., Ferrara et al. 2023; Fiore et al. 2023; Ziparo et al. 2023) associated with the starburst. When the specific star formation rate (sSFR) exceeds a threshold, the galaxy becomes super-Eddington and develops powerful outflows clearing the galaxy and quenching the SF. The precise value of the sSFR threshold somewhat depends on the dust properties, but a reasonable range is sSFR^⋆ = 10–25 Gyr⁻¹ (Ferrara 2023; Fiore et al. 2023). When such a condition is satisfied, the outflows produced can efficiently contribute to heating and evacuating the gas available for SF and lead to the galaxy quenching. The sSFRs derived for the starbursts in JADES-GS-z7-01-QU and MACS0417-z5BBG are 43 Gyr⁻¹ and 25 Gyr⁻¹, respectively. Both galaxies exceed the sSFR threshold, implying that stellar radiation pressure may be a viable explanation for their quiescent state. This scenario is also supported by the low amount of dust (A_V ∼ 0.1 and ∼0.2, respectively), which should indeed be efficiently ejected during the starburst phase (Ferrara et al. 2023).

Alternatively, the radiation pressure needed to quench the galaxy may be provided by an AGN. Even if supermassive black holes are typically invoked to explain the suppression of SF in massive galaxies (M_⋆ > 10¹⁰ M_⊙), there is some evidence of their presence also in M_⋆ ≈ 10⁸ M_⊙ systems (e.g., Manzano-King et al. 2019) and at high z (e.g., Maiolino et al. 2023). However, in the cases of JADES-GS-z7-01-QU and MACS0417-z5BBG, no broad emission lines are observed, implying that the accretion stops as soon as the SF does, and the putative black hole must be dormant in these galaxies at the time of observation.