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Many papers on star formation histories begin by setting up a “straw-man target” that the quenching of star formation is mysterious. In contrast, it strikes me that the literature shows encouraging convergence on a picture at least at z < 1 in which well defined processes convert “blue cloud” star-forming galaxies to “red sequence” red and dead galaxies. This section rephrases Section 6.2 to describe this picture.

The essential observation that has driven progress on this subject is summarized in Figure 9. The left panel shows the Allen et al. (2011) version of the Behroozi et al. (2013) result that led to Equations (6) and (7) in Section 6.1. I use it because the abscissa is in the same units as in the right panel. It shows that the ratio of stellar mass to total mass reaches a maximum at Vcirc ∼ 300 km s−1 or, in Behroozi et al. (2013), at MDM ∼ 1012 M. This maximum is ∼1/5 of the cosmological baryon fraction, so most baryons in the universe have not yet made stars. Lower-mass halos have smaller stellar fractions (left panel) and smaller baryon fractions (right panel) because – we believe – the baryons have increasingly been ejected from DM halos by star-formation and supernova feedback or never accreted after cosmological reionization. But the focus here is on higher DM masses. They, too, have smaller stellar mass fractions than at the “sweet spot” halo mass of 1012 M. But Figure 9 (right) shows that these baryons are not “missing” at MDM ≫ 1012 M. On the contrary, the total baryon fraction converges to essentially the cosmological value in the highest-mass halos, which are halos of rich clusters of galaxies. This is the by-now well known result that, as MDM grows above 1012 M and Vcirc grows above 300 km s−1, an increasingly large fraction of the baryons are indeed present but have not made stars. Rather, they are suspended in hot, X-ray-emitting gas, until in rich clusters of galaxies, that hot gas outmasses the stellar galaxies in the cluster by 1.0 ± 0.3 dex (Kravtsov & Borgani 2012). This has led to the essential idea of “Mcrit quenching” of star formation by X-ray-emitting gas, which can happen provided that the DM mass is larger than the critical mass, MDMMcrit ≃ 1012 M, that is required to support the formation and retention of hot gas halos (e.g., Birnboim & Dekel 2003; Kereš et al. 2005; Cattaneo et al. 2006, 2008, 2009; Dekel & Birnboim 2006, 2008; Faber et al. 2007; KFCB; Peng et al. 2010, 2012; KH13, Knobel et al. 2015, and Gabor & Davé 2015).

Figure 9

Figure 9. Stellar mass fraction M* / (Mbaryon + MDM) (left) and total baryon mass fraction Mbaryon / (Mbaryon + MDM) (right) versus a circular-orbit rotation velocity Vcirc ∼ √G MDM / r (Dai et al. 2010>) that approximately characterizes the total mass distribution. Here M* is the stellar mass, MDM is the DM halo mass, r is the radius of the halo, and G is the gravitational constant. The cosmological baryon fraction has been adjusted very slightly to 0.16 ± 0.01, i.e., the mean of the WMAP and Planck measurements (Hinshaw et al. 2013 and Planck Collaboration 2014, respectively). Both figures originally come from Dai et al. (2010).

The transition mass between galaxies that should contain X-ray gas and those that should not is consistently derived by a variety of theoretical arguments and is consistent checked via a variety of observational tests. It should occur at the DM mass at which the hot gas cooling time is comparable to the infall time (Rees & Ostriker 1977). Birnboim & Dekel (2003) and Dekel & Birnboim (2006, 2008) argue from theory and Kereš et al. (2005) find from SPH simulations that gas that is accreted during hierarchical clustering falls gently into shallow potential wells and makes star-forming disks, whereas gas crashes violently onto giant galaxies and is shock-heated to the virial temperature. It is this hot gas that quenches star formation. Calculated hot-gas cooling times are short; this led to the well known “cooling flow problem” (Fabian 1994). But X-ray measurements of temperature profiles now show that they are much shallower than cooling-time calculations predict in the absence of heating (McNamara & Nulsen 2007; Kravtsov & Borgani 2012; Fabian 2012). Debate continues about how the gas is kept hot; Dekel & Birnboim (2006, 2008) suggest that the required heating is caused by continued accretion; AGN feedback is another candidate (e.g., Best et al. 2006; Best 2006, 2007a, b; Fabian 2012; Heckman & Best 2014), and dying stars return gas to the intergalactic medium at just the right kinetic temperature (Ostriker 2006). The engineering details need to be sorted out. It is likely that all processes are important. But from the point of view of this paper, the engineering is secondary. The important point is that the galaxies and clusters tell us that they know how to keep the gas hot.

Many observed properties of galaxies can be understood in the context of Mcrit quenching. E.g., it allows semianalytic models of galaxy formation to reproduce the color bimodality of galaxies (“red sequence” versus “blue cloud”; Blanton & Moustakas 2009) as a function of redshift (Cattaneo et al. 2006, 2008, 2009).

Faber et al. (2007) and KFCB emphasize the connection of the above results to this paper: Mcrit star-formation quenching is believed to explain the difference between the two kinds of ellipticals discussed in Section 4.1.1. I noted there that classical bulges and coreless-disky-rotating ellipticals generally do not contain X-ray-emitting gas, whereas core-boxy-nonrotating ellipticals contain more X-ray gas as their luminosities increase more above Lcrit = 1010.2 LB⊙ (Figure 3). Now, Lcrit corresponds to MV ≃ −20.9; i.e., 0.6 mag fainter than the divide between coreless-disky-rotating and core-boxy-nonrotating ellipticals. This is a factor of almost 2. If the most recent event that made an elliptical was an equal-mass merger, then the divide betweeen coreless-disky-rotating and core-boxy-nonrotating ellipticals happens at a luminosity below which neither of the merger progenitor galaxies should have contained X-ray gas and above which one or both progenitor galaxies should have contained X-ray gas. Thus KFCB point out that the E – E dichotomy occurs at the correct luminosity so that coreless-disky-rotating ellipticals formed in wet mergers whereas core-boxy-nonrotating ellipticals formed in dry mergers.

Specifically, MV ≃ −20.7 for merger progenitors corresponds (using M / LV ∼ 6) to a stellar mass of M* ≃ 1 × 1011 M or, using a baryon-to-total mass ratio of 1/6 (Komatsu et al. 2009), to MDM ≃ 6 × 1011 M. And the divide between coreless-disky-rotating Es and core-boxy-nonrotating Es happens at MDM ≃ 1012 M. So the agreement with the above picture of Mcrit star-formation quenching is good.

Thus our picture of the formation of classical bulges and elliptical galaxies by wet and (at MDM > 1012 M) dry major mergers (Section 4 of this paper) is a tidy addition to our developing paradigm of star-formation quenching. Many details of the structure of classical bulges and ellipticals (e.g., the list in Section 4.1.1) fit into and support this paradigm. But the paradigm is more general than just an explanation of the E – E dichotomy. I turn to these more general aspects next:

In a seminal paper, Peng et al. (2010) use a few robust observations to derive very general conclusions about how quenching must work. They do this completely operationally, without any need to identify the physical mechanism(s) of quenching. At redshift z ∼ 0 (Sloan Digital Sky Survey) and out to z ∼ 1 (zCOSMOS survey: Lilly et al. 2007) the most essential observations used are (1) that the specific star formation rate is almost independent of galaxy mass (there is a “main sequence” of star formation) but with rapidly decaying specific star formation rate as z → 0, and (2) that star-forming galaxies satisfy a Schechter (1976) mass function whose characteristic mass is almost independent of z. From a discussion of how star formation operates to reproduce the above and other observations, they deduce that quenching is driven by galaxy mass and by galaxy environment and that these two modes (not identified physically) are separable and independent. Plus there must be an additional quenching mode that is associated with bulge formation via mergers. Figure 10 connects their picture with the quenching paradigm that we review here.

Figure 10

Figure 10. Powerpoint slide connecting the star-formation quenching picture of Peng et al. (2010: central figure and its caption) with the picture that is summarized in this paper (surrounding text).

Peng et al. (2010) emphasize that their analysis is operational: it identifies the conditions in which quenching must operate, but it does not identify quenching mechanisms. However, with this section's background on Mcrit quenching and with results from KH13 on BH–host-galaxy coevolution (or not), we can identify aspects of our developing physical picture of star-formation quenching with the conclusions of Peng et al. (2010). This is illustrated in Figure 10.

The masses used in Peng et al. (2010) are estimated by integrating star formation rates and by fitting spectral energy distributions; in essence, they are stellar masses. Figure 10 suggests that mass quenching tends to happen at masses ∼ 1010.5 M. In Figure 7 of Peng et al. (2010), the fraction of quenched galaxies (independent of environment) reaches 50% at ∼ 1010.6 M and 80% at ∼ 1011.25 M. These correspond to MDM ∼ 1011.4 to 1012 M. The good agreement with Mcrit suggests that Peng's “mass quenching” is precisely our “Mcrit quenching” by hot gas.

Peng et al. (2010) conclude further that some low-mass galaxies are quenched by their environments. That is, these galaxies are quenched because they are satellites of higher-mass objects – ones (either individual galaxies or clusters of galaxies) that can have masses MDMMcrit. I suggest that Peng's “environmental quenching” is the same physical process as mass quenching, but in Peng's mass quenching, the X-ray gas that does the work belongs to the galaxy that is being quenched, whereas in environmental quenching, the X-ray gas that does the work belongs to somebody else; i.e., to the quenched galaxy's parent giant galaxy or galaxy cluster. This idea is verified by Peng et al. (2012), Knobel et al. (2015), and Gabor & Davé (2015).

The suggested connection with KH13 then is this: Both mass and environment quenching are aspects of point 3 in Section 6.2 – they are effects of hot gas that is kept hot by a combination of maintenance-mode AGN feedback and other processes such as continued infall of gas from the cosmological hierarchy and the injection of the kinetic energy of gas that is shed by dying stars.

But the above quenching processes are not sufficient. It is easy to explain why– to give an example that mass quenching and environment quenching cannot explain. What quenches field S0 galaxies with masses M ≪ Mcrit? Kormendy & Ho (2013) suggest that they are quenched in the context of wet galaxy mergers that include starbursts, with energy feedback from the starburst beginning the job of quenching and AGN feedback (Section 6.2, point 2) finishing the job. It seems natural to suggest that this is the Peng's “merger quenching”. Observations of gas outflows in high-z, star-forming galaxies such as submillimeter galaxies–at least some of which are mergers–are reviewed in KH13. Of course, bulge-formation and Mcrit quenching can be mutually supportive (e.g., Woo et al. 2015).

Once star formation is quenched at M > Mcrit, then dry mergers preserve both the quenched state and the M–host correlations (Section 6.2, point 4 and modes “mass quenched then merged”, “environment quenched then merged”, and “merger quenched then merged” in Figure 10).

The biggest remaining question in our z < 1 picture is this: In merger-quenched galaxies that have M ≪ Mcrit, i.e., in objects in which X-ray gas is not available even after the merger is finished, what preserves the quenched, red and dead state? We do not know, but episodic, low-level AGN feedback may be the answer.

The biggest overall uncertainty is that quenching may operate differently at z ≳ 2. Dekel and Birnboim argue (1) that Mcrit is higher at high z, when gas fractions in galaxies and gas accretion rates onto galaxies are both higher and (2) that cold streams can penetrate hot gas at high z and contribute to the growth of disks at masses that are unattainable at z ∼ 0 (Dekel et al. 2009). Another difference involves the observation that most star-forming galaxies define a main sequence of star formation with few outliers, implying that duty cycles are long and hence that star formation is not driven primarily by short-duration events such as mergers (Section 4.1.5). When strong gas outflows are seen in star-forming galaxies at z ∼ 2, the inference is that some combination of star formation and AGN feedback is responsible but that these are not primarily driven by major mergers (e.g., Förster Schreiber et al. 2014; Genzel et al. 2014). Because these processes are also associated with bulge growth in disk galaxies (Lang et al. 2014), the most consistent interpretation that also includes the M correlation results is that the bulge growth in these objects is by clump cluster sinking (Section 3 here). Genzel (private communication) suggests that Peng's mass quenching may be this outflow process associated with more-or-less steady-state star formation, AGN feedback, and classical bulge growth. On the “plus side”, there is clearly a danger that our tidy z < 1 picture is basically correct but not a description of what happens at z ≫ 1. On the other hand, we already know that many details of galaxy structure are well explained by the z ∼ 0 picture. Particularly important is the natural explanation of cores in dry-merger remnants and central extra light in wet-merger remnants (see KFCB). Alternative suggestions for quenching mechanisms at high z have not addressed and solved the problem of also explaining these aspects of z ∼ 0 galaxy structure. This is not a proof that the suggested high-z processes are wrong.

It seems reasonable to conclude that our z < 1 picture of star formation quenching is robust. Mostly, it needs clarification of engineering details. In marked contrast, star formation quenching at z ≳ 2 is less well understood, although progress is rapid.

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