DESI Survey Validation Spectra Reveal an Increasing Fraction of Recently Quenched Galaxies at z ∼ 1

In order to characterize the growth of the population of quiescent galaxies at intermediate redshifts, this work relies on the large program of deep spectra that were taken as a part of the DESI SV LRG sample (Zhou et al. 2020, 2023; DESI Collaboration et al. 2023, in preparation). The primary objective of DESI is to determine the nature of dark energy with precise cosmological measurements (Levi et al. 2013), but the wealth of spectroscopy provides an excellent sample for studies of galaxy evolution. The data volume of DESI requires multiple supporting software pipelines and products used in this work. Target selection and photometry, which included forward modeling of the differential effect of the point-spread function across bands, was performed on imaging from the DESI Legacy Surveys (Zou et al. 2017; Dey et al. 2019; D. Schlegel et al. 2023, in preparation). Fiber assignments, tiling, and target selection were performed with the algorithms outlined in A. Raichoor et al. (2023, in preparation), E. Schlafly et al. (2023, in preparation), and A. Myers et al. (2023, in preparation), respectively. All redshifts were determined with the Redrock pipeline (S. Bailey et al. 2023, in preparation). All spectroscopy was reduced using the "Fuji" internal spectroscopic data release, which will be identical to the DESI Early Data Release (Guy et al. 2023; tentatively expected in early 2023).

There are two primary reasons for the choice to utilize the SV sample. First, the SV selection is more inclusive than subsequent SV samples and the main DESI sample (see Appendix A in Zhou et al. 2023). While this was intended as a test of the redshift recovery so that targeting could be refined from the main survey, these expanded color cuts mitigate potential bias against observing young, recently quenched LRGs. Second, the SV observations were an order of magnitude deeper than the observations for the main survey, with ∼2.5 hr of integration per spectrum, resulting in the high signal-to-noise ratio measurements of the continuum. While the SV sample included fainter targets, we restrict this study to the brightest SV LRGs with an observed fiber z magnitude z_fiber < 21.6 cut similar to the one that is used in the full LRG sample.

We select all tiles that were observed under the dark time observing conditions in SV. We then select all galaxies that meet the LRG SV cuts outlined in Zhou et al. (2023) with an additional z_fiber < 21.6 mag constraint, a cut at z > 0.4 (above which the SV LRG sample begins to be mass complete), and a cut at z < 1.3 (at which point the age-sensitive H_δ absorption feature is no longer covered by DESI spectroscopy). We remove galaxies with poor redshift measurements by applying a cut of ZWARN == 0 to the DESI catalog. We then remove the 580/17,797 galaxies that did not reach the target depth (exposure time ${t}_{\exp }\gt 1$ hr). The median exposure time of this final sample is 2.4 hr, with 16th and 84th percentile exposure times of 1.5 and 4.1 hr, respectively. This selection results in a total sample of 17,217 galaxies.

We model the DESI spectra and photometry using nonparametric star formation histories with the SED fitting code Prospector (Johnson & Leja 2017; Leja et al. 2017; Johnson et al. 2021) to infer the detailed stellar populations of the sample. Nonparametric star formation histories are particularly useful for fitting post-starburst galaxies because they do not impose an analytic form on the shape of the star formation history, which allows for multiple rises and falls over the course of a galaxy's lifetime. We adopt a flexible bin model that is optimized to model recently quenching galaxies (Suess et al. 2022b). The model utilizes three fixed time bins at early times (t_look-back > 2 Gyr), five flexible bins that each form the same amount of total stellar mass (allowing for greater resolution near periods of intense star formation), and a final flexible bin that allows a galaxy to remain quenched after star formation is finished. This scheme was extensively tested and is well designed to recover quenching timescales and burst mass fractions (Suess et al. 2022a, 2022b).

We use the dynesty dynamic nested sampling package (Speagle 2020), the Flexible Stellar Population Synthesis stellar population synthesis models (Conroy et al. 2009; Conroy & Gunn 2010), the MILES spectral library (Sánchez-Blázquez et al. 2006; Falcón-Barroso et al. 2011), and the MIST isochrones (Choi et al. 2016; Dotter 2016). We assume a Chabrier (2003) initial mass function and fix the model redshift to the spectroscopic redshift. In contrast with the Suess et al. (2022a) prescription for fitting post-starburst galaxies, we elect to fit nebular emission nonphysically by marginalizing over Gaussian lines at the locations of emission features in the spectrum. The massive LRG sample likely hosts many active galactic nuclei (AGN), which can contribute strongly to a galaxy's emission line strength (especially the recently quenched galaxies; e.g., Greene et al. 2020). Additionally, the LRG selection allows for the targeting of a small fraction of dusty star-forming galaxies with strong emission lines; we want to be completely agnostic to the source of emission when fitting star formation histories to these galaxies. This procedure subtracts out the emission from the spectrum at each step in the fitting before calculating the likelihood, which allows the fits to utilize continuum information (e.g., Hβ absorption) despite the existence of emission that our models do not generate using information about the current star formation rate (SFR).

We use the mass–metallicity prior described in Leja et al. (2019). We utilize the PolySpecModel procedure, which accounts for deviations between the shape of the photometry and the spectrum by dividing out a polynomial from the observed and model spectra during fitting using a Prospecter-default 12th-order Chebyshev polynomial. We assume the Kriek & Conroy (2013) dust law with a free A_v and dust index. Additionally, following Wild et al. (2020), we assume that the attenuation is doubled around young (<10⁷ yr) stars. We fix the shape of the IR SED following the Draine et al. (2007) dust emission templates, with U_min = 1.0, γ_e = 0.01, and q_PAH = 2.0. Finally, we include both a spectroscopic jitter term to account for the possibility of underestimated noise and the Prospector pixel outlier model. We center priors on the star formation history such that they follow the predicted star formation history of a massive quiescent galaxy from the UNIVERSEMACHINE catalog (Behroozi et al. 2019); this weakly prefers solutions with early-time star formation in the star formation histories we fit to ensure that outshining of a young stellar population is treated conservatively. The fidelity of this star formation history at recovering mock parameters is illustrated in Suess et al. (2022b). Of principal importance to this work, the burst fraction is well recovered when <50% of a galaxy's stellar mass is formed in a burst. For greater burst fractions, outshining by the young stellar population becomes so dominant that the relative strength of the oldest stellar population cannot be constrained by the existing data, and as such, our conservative prior drives the fits to a higher burst fraction solution than the inputs. Thus, burst fractions measured in this work to be ≳50% can be thought of as strong lower limits.

We fit all 17,217 galaxies in the DESI SV LRG sample (z_fiber < 21.6) with this procedure, providing the Milky Way extinction-corrected g/r/z/W1/W2 photometry (using the extinction maps from Schlegel et al. 1998) and the galaxy spectrum. The scaling of the SED being fit is set by the photometry that captures all galaxy light, rather than just the light in the fiber. We expect the total fraction of galaxy light contained in the fiber to vary as a function of redshift but to always be ≳50% of the total light, as the fiber size is 075 in radius (4 kpc at z = 0.4, 6.5 kpc at z = 1.3). Our fits are constrained by the SED shape of the photometry, and the polynomial correction to the spectrum will account for any color gradients, though we expect those to be minimal given that the spectrum should be representative of the majority of the galaxy light for most of the sample. Because the signal in the redshift range of interest is concentrated at the red end of the spectrograph, we elect to only fit the spectra from the R and Z arms of the spectrograph (5800 Å < λ_obs < 9824 Å) to save on computation time and avoid any issues with the flux calibration at the fainter end of the spectra. In this wavelength range, the resolution R (λ/Δλ) ranges from ∼3200 to 5100. While the 15 (∼8 kpc at z = 0.4, ∼13 kpc at z = 1.3) diameter aperture of the DESI fiber is large enough to capture the majority of galaxy light at the highest-redshift end of our sample, we do note that our modeling approach assumes a lack of color gradients in the galaxies and that the light represented in the spectrum is identical to that of the photometry, which models all galaxy light. Fits failed to converge for 52/17,217 galaxies (0.3% of the total sample). Visual inspection of the spectra of these failed fits suggests that they broadly fall into four categories: extremely low signal-to-noise ratio galaxies, spectra with large masked regions, galaxies with incorrect redshift assignments, and broad-line AGN/QSOs (which our models are not equipped to characterize). As such, we omit the unmodeled galaxies and perform all analysis on the 17,703 successfully fit galaxies.

Example fits to quiescent (top; red) and recently quenched (bottom; green) galaxies are shown in Figure 1. The quiescent galaxy that is representative of the majority of the DESI LRG sample is fit entirely with early star formation, consistent with a very old stellar population, and as such, all of the mass was formed in the three fixed-width early-time bins. In contrast, the recently quenched galaxy is clearly fit with a post-starburst SED shape with strong Balmer absorption features and a characteristic lack of emission line infill. This indicates that the post-starburst galaxy has quenched after a period of intense star formation, and the star formation history reflects this. We infer that the galaxy began rapidly forming stars ∼500 Myr before observation and quenched ∼150 Myr ago.

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From the posteriors on the star formation histories, we derive a number of model parameters, many of which we directly use to select and characterize the properties of recently quenched galaxies. Stellar masses are calculated accounting for mass loss and have typical 1σ uncertainties of 0.025 dex, and rest absolute magnitudes are calculated directly from the spectra generated from the posterior. We measure the SFR in all galaxies as the SFR in the closest bin to the epoch of observation in the nonparametric star formation history. Above ∼1 M_⊙ yr⁻¹, these SFRs have been shown to reliably recover the instantaneous SFR of mock galaxies, and our measurements have typical uncertainties of ∼15%. Below this, they are effectively upper limits (Suess et al. 2022b). Additionally, we quantify the offset from the star-forming sequence, ΔSFR, as

$$\begin{eqnarray}&&{\rm{\Delta }}\mathrm{SFR}=\mathrm{log}(\mathrm{SFR})-\mathrm{log}({\mathrm{SFR}}_{\mathrm{SFS}}(z)),\end{eqnarray} \tag{ 1 }$$

where SFR_SFS(z) is the inferred SFR from the star-forming sequence at the observed redshift of the galaxy defined in Leja et al. (2022), which is also measured using Prospector SED fits. We set a fiducial threshold for quiescence at ΔSFR = −0.6, ∼2σ below the main sequence at a given redshift. Near the fiducial value, the typical uncertainty in ΔSFR is ∼0.1 dex. As with the SFR, this value is significantly more uncertain for measured values. Finally, we measure the fraction of the total stellar mass formed in the gigayear before observation, f_{1 Gyr}. Galaxies with small f_{1 Gyr} are very well constrained to be small, and for galaxies that formed 10%–70% of their stellar mass in the past gigayear, typical uncertainties are 15%–30%. A sample of constraints on the parameters is shown in Table 1.

Table 1. Selected Fit Quantities and Errors

z	$\mathrm{log}({M}_{\star }/{M}_{\odot })$	SFR (M⊙ yr−1)	ΔSFR	f1 Gyr
0.5568	${11.23}_{-0.01}^{+0.01}$	${2.31}_{-0.35}^{+0.47}$	−1.16${}_{-0.07}^{+0.08}$	${0.11}_{-0.01}^{+0.01}$
0.6701	${11.22}_{-0.01}^{+0.01}$	${1.17}_{-0.14}^{+0.14}$	−1.52${}_{-0.06}^{+0.05}$	${0.0}_{-0.0}^{+0.0}$
0.8976	${11.23}_{-0.1}^{+0.02}$	${0.92}_{-0.31}^{+0.84}$	−1.76${}_{-0.18}^{+0.39}$	${0.0}_{-0.0}^{+0.07}$
0.5396	${11.36}_{-0.01}^{+0.01}$	${2.98}_{-0.34}^{+0.4}$	−1.16${}_{-0.06}^{+0.06}$	${0.05}_{-0.02}^{+0.01}$
0.4364	${11.12}_{-0.01}^{+0.01}$	${2.85}_{-0.24}^{+0.27}$	−0.9${}_{-0.04}^{+0.05}$	${0.01}_{-0.0}^{+0.0}$
0.8807	${11.34}_{-0.03}^{+0.03}$	${0.08}_{-0.08}^{+0.28}$	−2.86${}_{-1.51}^{+0.62}$	${0.0}_{-0.0}^{+0.0}$
0.6999	${10.8}_{-0.04}^{+0.03}$	${19.39}_{-2.4}^{+2.56}$	${0.08}_{-0.09}^{+0.07}$	${0.22}_{-0.04}^{+0.05}$
0.5415	${11.11}_{-0.03}^{+0.04}$	${0.09}_{-0.04}^{+0.05}$	−2.45${}_{-0.28}^{+0.19}$	${0.01}_{-0.0}^{+0.01}$
0.5166	${11.2}_{-0.03}^{+0.02}$	${21.25}_{-3.02}^{+2.17}$	−0.15${}_{-0.08}^{+0.06}$	${0.1}_{-0.02}^{+0.02}$
1.0623	${11.04}_{-0.03}^{+0.03}$	${4.67}_{-1.63}^{+3.76}$	−0.94${}_{-0.18}^{+0.26}$	${0.45}_{-0.06}^{+0.07}$

Note. Selected median and 68% confidence values of relevant parameters derived from the posteriors of the Prospector fits to DESI SV LRGs for a random sample of galaxies.

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We show some of the observed and derived characteristics of the full LRG sample as red contours in Figure 2. In the left panel, we show the stellar mass versus the rest-frame absolute magnitude, M_z , illustrating the tight correlation between the two parameters. We additionally show lines that correspond to the cuts we make in the two parameters to construct the volume-limited samples described in Section 2.3. In the middle panel, we show the SFR versus the stellar mass along with the "star-forming sequence" at z = 0.7 with 0.3 dex scatter from Leja et al. (2022) to illustrate that the sample is largely quiescent. Finally, we show the sample in the recently quenched selection plane of f_{1 Gyr} versus ΔSFR discussed in Section 3.1 with our fiducial cuts to select recently quenched galaxies. In all three panels, we show the fiducial sample of recently quenched galaxies as green points.

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Because the choices made in spectroscopic targeting significantly impact the observed sample, it is necessary to select a volume-limited sample to fairly compare galaxies across redshift bins. This is especially true because the z_fiber < 21.6 cut in observed magnitude would observe a faint galaxy at low redshift but not high redshift. We use the fits to the spectrophotometric data to select samples that we can use to infer number densities. Throughout this letter, we utilize three relevant samples—the full LRG sample, the rest absolute Z-magnitude-selected "magnitude-limited" sample, and the "mass-complete" sample—to select recently quenched galaxies.

2.3.1. The Magnitude-limited Sample

2.3.2. The Mass-complete Sample

There are a number of ways of selecting recently quenched/post-starburst galaxies, all of which share the common goal of selecting galaxies that recently quenched after a period of significant star formation (French 2021). Historically, these galaxies have been selected using a combination of emission line cuts (to select against current star formation) and Balmer absorption depth (to select for a stellar population dominated by A-type stars; Dressler & Gunn 1983; Zabludoff et al. 1996; Balogh et al. 1999). Here we leverage the tightly constrained star formation histories to select a physically motivated sample of recently quenched galaxies. First, we focus on selecting a pure quiescent sample. In Figures 2(b) and (c), it is clear that some galaxies that are dusty and star-forming have been selected due to their red colors and exist in the LRG parent sample. To remove these, we perform a conservative cut in ΔSFR, classifying galaxies as quiescent only if their median ΔSFR is ∼2σ (0.6 dex) below the star-forming sequence at their redshift from Leja et al. (2022). This selection, which is highlighted in Figure 2(c), removes 2622 galaxies (∼15% of the total sample). All qualitative results in this work are insensitive to the exact definition of quiescence that we adopt, though exact sample sizes and number densities will, by definition, differ slightly.

Second, we are interested in physically separating the quiescent galaxy population into recent additions to the red sequence and older galaxies. In this work, our definition of recently quenched does not require a burst, as we are interested in classifying all galaxies that rapidly formed a significant amount of stellar mass before quenching as recently quenched galaxies. To select such a sample, we leverage the inferred star formation histories to measure the fraction of the stellar mass formed within the last gigayear (f_{1 Gyr}) for all galaxies (see also Webb et al. 2020). In combination with the cut for quiescence, selecting galaxies with high f_{1 Gyr} identifies a sample that must have rapidly truncated its star formation in order to have formed a large amount of its stellar mass while also reaching quiescence within 1 Gyr. We adopt f_{1 Gyr} > 0.1 (also shown in Figure 2(c)) for our fiducial recently quenched selection and explore the impact of different thresholds in Section 4. The fiducial selection identifies 1089 recently quenched galaxies from the 15,012 quiescent LRGs using the fiducial f_{1 Gyr} > 0.1 selection.

This sample of recently quenched galaxies is unparalleled in size beyond z ≳ 1. In Figure 3, we show the redshift distributions of this sample compared to other large spectroscopic samples of post-starburst galaxies at intermediate redshift. Our sample of hundreds of recently quenched galaxies at z < 0.8 is smaller than other samples that select galaxies from the full SDSS (Pattarakijwanich et al. 2016; Suess et al. 2022a) or VIPERS Survey (Rowlands et al. 2018). However, at z > 1 (shown in the inset), we find that this sample dramatically increases the number of spectroscopically confirmed recently quenched galaxies at the tail end of cosmic noon.

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While our selection of recently quenched galaxies relies on our inferred star formation histories, there are many other selections that use empirical measures of spectroscopic features to select post-starburst galaxies (French 2021). We choose a few common post-starburst identification methods and compare the resulting number densities with our fiducial model (see Section 3.2). For all literature comparisons, we use the same ΔSFR≤ −0.6 criterion for quiescence rather than relying on common empirical metrics like EW H_α , which falls out of our spectral window for most of the sample, or EW [O ii], which is an uncertain tracer of SFR due to potential contributions from AGN/LINERs. We note that while exact definitions of H_δ spectral indices vary in the literature (e.g., Alatalo et al. 2016 used H_δ , French et al. 2015 used H_δ,A , and Baron et al. 2022 used H_δ,F ), these differences are subtle. We adopt H_δ,A as our preferred definition, as it is optimized for features from A-type stars (Worthey & Ottaviani 1997). The three selections we compare to our fiducial selection (f_{1 Gyr} > 0.1 and ΔSFR < −0.6) are as follows (all numbers quoted are the raw number of galaxies in the full sample, not in a volume-limited sample).

• 1.  
  H_δ,A > 4 Å. After applying the quiescence criteria, we select 1727 galaxies with H_δ,A > 4 Å following, e.g., French et al. (2015, 2018), Wu et al. (2018), and Yesuf (2022).
• 2.  
  H_δ,A > 5 Å. We impose a more stringent cut, H_δ,A > 5 Å, following, e.g., Alatalo et al. (2016) and Baron et al. (2022), selecting 1035 post-starburst galaxies.
• 3.  
  $\mathrm{SQuIGG}\vec{L}{\rm{E}}$ selection. Finally, after applying the quiescence criteria, we use medium-band synthetic rest-frame UBV filters to identify post-starburst galaxies with U − B > 0.975 and −0.25 < B − V < 0.45 following the procedure for selecting galaxies with SEDs dominated by A-type stellar populations (Suess et al. 2022a). We apply these cuts to the median best-fit models because the spectral coverage is not red enough to consistently overlap with the synthetic V filter. This selection finds only 324 post-starburst galaxies.

The DESI SV LRG selection is designed to have a uniform comoving number density of galaxies at 0.4 < z < 0.8, which enables robust determination of the number densities of subsets of the spectroscopic sample (Zhou et al. 2023). For this selection, we use the target density of 1439 deg⁻² to calculate the number density in bins of Δz = 0.1 in redshift from z = 0.4 to 1.3 by measuring the density of targets for a given selection criterion and dividing by the volume of the bin. We measure the number densities only for the magnitude-limited or mass-complete samples. We utilize jackknife resampling of the 31 SV pointings to calculate the errors on the measured number densities. The errors do not account for catastrophic redshift errors, but those should be very rare (≤0.5%; see Zhou et al. 2023) and subdominant relative to cosmic variance and Poisson errors.

The comoving number density of each recently quenched subsample of the magnitude-limited sample as a function of redshift is shown in Figure 4. The raw number density of the DESI LRG SV sample (z_fiber < 21.6) is shown in gray. We show the number density of the rest-frame magnitude-limited (M_z < −23.2) sample with the fiducial quiescence cut (ΔSFR < −0.6) in red. We then apply the post-starburst selections outlined in Section 3.1 to the magnitude-limited sample. The number densities are shown for H_δ,A > 4 Å (light blue), H_δ,A > 5 Å (dark blue), $\mathrm{SQuIGG}\vec{L}{\rm{E}}$-like (light green), and our fiducial f_{1 Gyr} > 0.1 selection (dark green). In all cases, the number density of post-starburst galaxies rises as a function of redshift in the range of redshifts where the parent LRG sample is complete (z < 0.8). Above this, we illustrate that our measurements are lower limits.

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In the right panel of Figure 4, we compare our fiducial sample of recently quenched galaxies to several measurements from the literature. We find qualitative agreement with previous studies that observe the number density of recently quenched galaxies increasing with redshift (Wild et al. 2016; Rowlands et al. 2018; Belli et al. 2019). Additionally, the number density of the recently quenched galaxies that we measure is very similar to that of compact star-forming galaxies at z = 0.5, adding credence to the argument that such galaxies may be progenitors to local post-starburst galaxies (Tremonti et al. 2007; Diamond-Stanic et al. 2021; Whalen et al. 2022). However, in detail, this comparison is limited by systematic effects; our sample is systematically more massive than other post-starburst samples and is selected using a magnitude (not mass) limit. Additionally, as shown in the left panel of Figure 4, differing identification techniques can significantly impact the measured number density of post-starburst galaxies. Still, a clear consensus emerges from this comparison that recently quenched galaxies were increasingly common at greater look-back times.

In the previous section, we studied the number density of a magnitude-limited sample of recently quenched galaxies to maximize our sample size. Here we attempt to explicitly quantify the fraction of massive galaxies that have recently quenched and joined the red sequence as a function of cosmic time. To do so, we utilize the mass-complete ($\mathrm{log}({M}_{\star }/{M}_{\odot })$ > 11.2; see Section 2.3.2) subset of the LRG sample, which we show in the left panel of Figure 5 (red) along with the corresponding stellar mass function from Leja et al. (2020). This measurement overpredicts the stellar mass function by ∼0.2 dex at z ∼ 0.4 while matching well at z ∼ 0.7. This may be due to systematic differences in the stellar mass estimates (e.g., differences in modeled star formation histories, unmodeled contributions from AGN, or spectrophotometric modeling in our fits versus broadband multiwavelength SEDs), and the mismatch in redshift evolution may be a result of the targeting incompleteness. As such, we adopt the number densities from the stellar mass function as the total abundance of massive ($\mathrm{log}({M}_{\star }/{M}_{\odot })$ < 11.2) galaxies and note that the fractions we measure may be systematically lower than reported by ∼0.2 dex. Above z = 0.8, where LRG targeting is known to be incomplete, we inflate the upper error bar on the measured lower limits by assuming that every galaxy we have not targeted meets the selection criteria (quantified by the deviation between the measured number density and the stellar mass function) to capture the possibility that every galaxy we did not measure is a recently quenched galaxy. Since this is unlikely due to the lower M_⋆/L ratio of recently quenched galaxies, this conservative estimates captures the full range of possibilities in the number density of galaxies in a given selection at z > 0.8.

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We show the number densities of four different selections of recently quenched galaxies: f_{1 Gyr} > 0.05 (light green), >0.1 (medium green), >0.2 (dark green), and >0.5 (black). Points that do not appear indicate that the redshift bin contained zero galaxies that met the selection criteria. All four sets of recently quenched galaxies show increasing number densities with redshift. However, even at z ∼ 0.8, galaxies that formed a large fraction of their stellar mass in the past gigayear are very rare. For example, at z = 0.8, galaxies that formed >20% of their stellar mass in the past gigayear were significantly (>1 dex) rarer than those that formed 5% of their stellar mass. We find that the number density of the f_{1 Gyr} > 20% population cannot be decreasing with look-back time; in fact, at z ∼ 1.2, the lower-limit number density of this population is higher than the number density at z = 0.8. The rarity of such objects at intermediate z is extremely consistent with the rarity of "late bloomers," galaxies that formed the majority of their stellar mass in the 2 Gyr before quenching (Dressler et al. 2018). Additionally, we identify a very small population of galaxies that rapidly formed ≥50% of their stellar mass in the gigayear before observation at z = 1.1–1.3, with lower limits that indicate a number density of at least ${\mathrm{log}}_{10}(n)\gt -6.5\ {\mathrm{Mpc}}^{-3}$. Similar extreme post-starburst galaxies have been found in photometric samples with comparably low number densities and could represent analogs to the formation of massive quiescent galaxies at high z (Park et al. 2022).

In the right panel of Figure 5, we show the same recently quenched samples as fractions of the total massive galaxy population (shown with filled symbols using the stellar mass function from Leja et al. 2020 as the denominator and open symbols using our own measurements of the LRG number density). We find that galaxies that formed >20% of their stellar mass represent ∼0.5% of the total galaxy population at z = 0.8, but by z ∼ 1.2, they must be at least 1%, with an upper limit that extends to them being ∼50% of the quiescent population. Similarly, the most extreme burst-dominated systems (f_{1 Gyr} > 50%) must be at least ∼0.5% of the total galaxy population at z = 1.2, but this fraction could be as high as 20%. In contrast, galaxies with f_{1 Gyr} > 5% and >10% are significant even at z = 0.4, representing ∼1.5% and 0.5% of the massive galaxy population, and by z = 0.8, they are ∼10% and 3% of the total population. Studies of massive quiescent and post-starburst galaxies at similar redshifts have measured similar burst fractions of ∼5% in the bulk of their samples, indicating that at the massive end, the vast majority of "post-starburst" galaxies are the evolutionary products of a recent dusting of star formation, rather than the truncation of their primary epoch of star formation (Patel et al. 2011; French et al. 2018).

The general rarity of extreme massive post-starburst galaxies in this sample is consistent with findings that the formation redshift of $\mathrm{log}({M}_{\star }/{M}_{\odot })$ = 11.2 galaxies is z_form ∼ 2–3 (Gallazzi et al. 2014; Fumagalli et al. 2016; Pacifici et al. 2016; Carnall et al. 2019; Estrada-Carpenter et al. 2019; Díaz-García et al. 2019; Khullar et al. 2022; Webb et al. 2020). At the epochs we are probing, the average massive quiescent galaxy quenched long in the past. However, we find that a significant number of massive galaxies are still quenching with very high f_{1 Gyr} well after cosmic noon (z ∼ 2), and we expect that with a more complete sample at higher redshift, the population dominated by recent star formation would become the norm. The sharp observed decline in rapid quenching after cosmic noon suggests a fundamental shift in the evolutionary histories of massive galaxies. By combining this preliminary analysis with similar stellar population synthesis modeling of larger, mass-complete samples and ancillary data sets (e.g., by analyzing galaxy structural evolution and morphological transformation), we hope to illuminate the physical mechanism(s) that are responsible for halting star formation and sustaining the quiescence of massive galaxies since z ∼ 1.