On the fragmentation of cosmic gas clouds. I - The formation of galaxies and the first generation of stars

“Finally, we note that the existence and importance of these two modes were the major insights of the original work of Silk (1977), Binney (1977) and Rees & Ostriker (1977) and have been built into all modern theories for galaxy formation.”

“Simple scaling arguments suggested that the observed break in the luminosity function at bright magnitudes would naturally arise from the long cooling time of gas in large haloes (Binney 1977; Rees & Ostriker 1977; Silk 1977; White & Rees 1978).”

“The standard paradigm of disc formation (Rees & Ostriker 1977; Silk 1977; White & Rees 1978; Blumenthal, Faber, Primack & Rees 1984; White & Frenk 1991; Mo, Mao & White 1998), which lies at the basis of all current models of galaxy formation, assumes that while a DM halo relaxes to a virial…”

“Omukai & Nishi (1999; see also Silk 1977) have argued that the photo-dissociation of H2 could be even more effective due to a small number of stars embedded within the gas clouds themselves.”

“…UV LF, i.e., heating from an AGN (Croton et al. 2005), the inefficiency of gas cooling for high-mass halos (e.g., Binney 1977; Rees & Ostriker 1977; Silk 1977), and the increasing importance of dust attenuation for the most luminous and likely most massive galaxies (Bouwens et al. 2009; Pannella…”

“The possible importance of distinguishing between gas flows occurring in the regime tcool < tff versus tcool > tff (where tff is the free-fall time) has been highlighted many times in the literature (Binney 1977; Rees & Ostriker 1977; Silk 1977; White & Frenk 1991).”

“The subject of the formation of the Ðrst stars has a long and venerable history (e.g., Yoneyama 1972 ; Hutchins 1976 ; Silk 1977, 1983 ; Carlberg 1981 ; Kashlinsky & Rees 1983 ; Palla, Salpeter, & Stahler 1983 ; Carr, Bond, & Arnett 1984 ; Couchman & Rees 1986 ; Haiman, Thoul, & Loeb 1996 ; Uehara…”

“By itself, the accretion of gas into dark matter halos and its subsequent cooling onto a centrally forming galaxy (Silk 1977; White & Rees 1978) leads to an excess of baryons across ?”

“Early models of structure formation have predicted the condensation of baryons via radiative cooling at the centres of a population of hierarchically growing DM haloes, forming galaxies (Silk 1977; Rees & Ostriker 1977; White & Rees 1978; Blumenthal et al. 1984).”

“Applying the familiar criterion (Rees & Ostriker 1977, Silk 1977) for the formation of galaxies that the cooling timescale has to be shorter than the dynamical timescale, tcool < tdyn, one can derive the minimum halo mass at a given redshift inside of which the gas is able to cool and eventually…”

“…to dissipate their kinetic energy and collapse more than the dark matter, to eventually become self-gravitating and form an interesting object like a galaxy, a V.M.O. or a black hole (see e.g. Binney 1977, Rees and Ostriker 1977; Silk 1977; White and Rees 1978; Araujo & Opher 1988, 1989, 1991).”

“This process, virial shock heating followed by radiative cooling, is the one highlighted in classic papers on galaxy formation theory (e.g. Rees & Ostriker 1977; Silk 1977; White & Rees 1978; White & Frenk 1991), and to differentiate it from the previous mode we call it hot mode accretion.”

“To match the observed properties of galaxies and galaxy clusters, purely gravitational processes on their own cannot account for cosmological structure formation, but gas cooling/dissipation processes must be considered (Binney 1977, Rees & Ostriker 1977, Silk 1977).”

“The second is the physics of gas cooling, which selects a characteristic mass scale for galaxy formation (Rees & Ostriker 1977; Silk 1977; White & Rees 1978).”

“…be much lower (<1012 M⊙) and therefore many of the physical mechanisms likely to be important for truncating the LFs at z ∼ 0 (e.g., transition to hot flows: Birnboim & Dekel 2003; Rees & Ostriker 1977; Binney 1977; Silk 1977 or AGN feedback: Croton et al. 2006) may not be as relevant at z & 8.”

“This idea was later developed by Rees & Ostriker (1977) and Silk (1977).”

“…a characteristic mass above which gas in a gravitationally contracting halo cannot cool in a Hubble time (tH) to form stars (Rees & Ostriker 1977; Silk 1977; White & Rees 1978), thereby providing a turnover in the theoretical GSMF, though in the absence of feedback the implied mass scale is…”

“Several authors have tackled this crucial issue through theoretical (Rees 1976; Rees & Ostriker 1977; Silk 1977, 1983; Haiman, Thoul & Loeb 1996; Uehara et al. 1996) and numerical approaches (Omukai & Nishi 1998; Nakamura & Umemura 1999, 2001; Abel, Bryan & Norman 2000; Bromm, Coppi & Larson…”

“Afterhalo collapse, 1 Their ideas were based on those of Binney (1977); R ees & O striker(1977)and Silk (1977)and wereapplied to CD M speci cally byBlum enthalet al.(1984) gas is assum ed to shock-heatto the halo tem perature,and to coolovera characteristic tim escale c ’ kbT ni (T) ; (1) which…”

“In the traditional scenario of galaxy formation (Rees & Ostriker 1977; Silk 1977; White & Rees 1978; Blumenthal et al. 1984; White & Frenk 1991), the infalling gas is shock-heated to the virial temperature of the dark halo near the virial radius.”

“…times on galaxy scales indeed seem to be at present shorter than a Hubble time, lending support to this picture & Ostriker Furthermore, dissipative(Silk 1977 ; Rees 1977). collapse within dark halos seems to be the only way to turn the meager angular momentum induced by tidal torques into the…”

“The efficiency can also be kept low by internal feedback mechanisms inside each halo, such as destruction of molecules by an internal UVH2source (Silk 1977 ; Omukai & Nishi 1999), or blow-out of the gas by supernovae (Mac Low & Ferrara 1999).”

“C O ] 2 8 Ja intergalactic medium gas shock-heats to the virial temperature of the halo and forms a hot pressure supported atmosphere in approximate equilibrium (Rees & Ostriker 1977; Silk 1977; White & Rees 1978).”

“Any subsequently accreted gas is also shocked to the virial temperature as it enters the virial radius (Rees & Ostriker 1977; Silk 1977; White & Rees 1978).”

“…criterion for the formation of galaxies that the cooling timescale has to be shorter than the dynamical timescale, tcool tdyn, one can derive the minimum halo mass at a given redshift inside of which the gas is able to cool and eventually form stars (Rees and Ostriker 1977, Silk 1977).”

“The requirement that the cooling time be less than the dynamical time sets a natural upper limit to the galaxy mass function (Binney 1977; Rees & Ostriker 1977; Silk 1977; White & Rees 1978).”

“This seemed natural in the case of a joint semi-spherical infall from outside the halo, and where the gas within the halo goes through a phase where it is pressure-supported after being heated to the virial temperature by a virial shock (Binney 1977; Rees & Ostriker 1977; Silk 1977).”

“Cooling is generally considered to be the key to understanding the luminous mass of a galaxy (Rees and Ostriker 1977; Silk 1977).”

“This is the regime in which galaxies are thought to form (Rees & Ostriker 1977; Silk 1977).”

“The result is that one finds a characteristic galactic halo mass, in terms of fundamental constants, to be of order 1012M (Silk, 1977).”

“While this bimodality is closely related to the classical ‘rapid cooling’ and ‘slow cooling’ regimes (Rees & Ostriker 1977; Silk 1977; White & Rees 1978; White & Frenk 1991), recent studies have shed new light on the properties of the flows and the transition between the two modes.”

“…molecules play in the collapse of primordial gas clouds to form metal-free stars has a long history of investigation (Hirasawa 1969; Hutchins 1976; Silk 1977; Hartquist & Cameron 1977; Shchekinov & Edelman 1978; Yoshii & Sabano 1979; Tohline 1980; Carlberg 1981; Lepp & Shull 1984; Yoshii & Saio…”

“The first is that if M is larger than about 1012M , the bound region will not form a single galaxy but fragment into a cluster of galaxies (Silk 1977).”

“Classically, this cut-off has been explained as a result of the inefficiency with which gas can cool in halos above 1012 M⊙ (e.g., Binney 1977; Rees & Ostriker 1977; Silk 1977) and settle out of hydrostatic equilibrium.”

“…by guest on 17 January 2020 as M < 1012–1013 M , the gas in the halo can cool in a dynamical time (shorter than the Hubble time) and contract to form stars (Rees & Ostriker 1977; Silk 1977; White & Rees 1978; Blumenthal et al. 1984, in the context of dark haloes).”

“For example, the cooling time in clusters today is much longer than the Hubble time, and this has been used to explain why not all of the gas in these environments has cooled (Binney 1977; Silk 1977; Rees & Ostriker 1977).”

“In the canonical theory of galaxy formation (e.g. Silk 1977; Rees & Ostriker 1977; White & Rees 1978), galaxies form stars when hot gas radiates away energy, cools and looses pressure support.”

“Theorists have long predicted that galaxy formation is most efficient near a mass of ∼ 1012M based on analyses of supernova feedback, cooling times, and galaxy number counts (Silk 1977; Rees & Ostriker 1977; Dekel & Silk 1986; White & Rees 1978; Blumenthal et al. 1984).”

“The main external process is halo mass quenching (Silk 1977; Rees & Ostriker 1977; Blumenthal et al. 1984; Birnboim & Dekel 2003; Kereš et al. 2005; Dekel & Birnboim 2006; Cattaneo et al. 2006); this posits that dark matter halos above a critical halo mass establish virial shocks that stop the flow…”

“Similar suggestions were made by Hutchins (1976), Silk (1977) and Tohline (1980) whose work indicated a minimum mass of150− 200M⊙.”

“In the classic sketch of galaxy formation (Rees & Ostriker 1977; Silk 1977; White & Rees 1978), gas falling into dark matter halos is shocked and heated to the virial temperature.”

“Heritage of the Topic All modern discussions of thermal instability in the context of galaxy formation are rooted in the classic work of Rees & Ostriker (1977), Binney (1977), and Silk (1977), which themselves owe a debt to Hoyle (1953).”

“In a cosmological context, gas that falls into a dark matter halo is able to lose energy and cool via dissipative processes to form a disc of cold gas at the bottom of the halo’s potential well (e.g. Silk 1977; White & Rees 1978; Fall & Efstathiou 1980; Katz & Gunn 1991).”

“In the classic theory (Rees & Ostriker 1977; Silk 1977; White & Rees 1978), galaxies collect their baryons via so-called hot mode accretion where diffuse gas symmetrically falls into dark matter (DM) halos and is shock-heated as it hits the gas residing in them.”

“…al. 2004; Croton et al. 2006; Bower et al. 2006), inefficiency of gas cooling in high- mass dark matter haloes (e.g., Binney 1977; Rees & Ostriker 1977; Silk 1977; Benson et al. 2003), and dust attenuation, which becomes substantial for the most luminous galaxies (e.g., Wang & Heckman 1996;…”

“During the expansion of the Universe, cosmological gas that falls into the potential well of a DM concentration eventually shocks when it meets other gas and stops or deflects in its path (Rees and Ostriker 1977; White and Rees 1978; Binney 1977; Silk 1977).”

“Following the classic work on the interplay between cooling and dynamical times in galaxy formation (Binney 1977; Rees & Ostriker 1977; Silk 1977; White & Rees 1978; Blumenthal et al. 1984), and earlier one-dimensional (1D) simulations (Thoul & Weinberg 1995; Forcada-Miro & White 1997; Ciotti &…”

“…halo mass marking a sharp transition in gas cooling rates has persisted since the early days of analytic galaxy formation models (Rees & Ostriker 1977; Silk 1977; Binney 1977), and been refined by modern cosmological hydrodynamical simulations (e.g. Kereš et al. 2005; Stinson et al. 2015;…”

“This is a refinement of the classical idea attributing galaxy formation to cooling on a dynamical time scale (Rees & Ostriker 1977; Binney 1977; Silk 1977; White & Rees 1978; Blumenthal et al. 1984).”

“…Croton et al. 2006), inefficiency of gas cooling in massive dark matter halos due to virial shock heating (e.g., Binney 1977; Rees & Ostriker 1977; Silk 1977; Benson et al. 2003), and dust obscuration that becomes substantial for the most luminous galaxies (e.g., Wang & Heckman 1996; Adelberger &…”

“The third component to the energy density in this scenario, the baryons, condenses via radiative cooling at the centres of a population of hierarchically merging DM haloes, forming galaxies (Rees & Ostriker 1977; Silk 1977; White & Rees 1978; Blumenthal et al. 1984).”

“…massive dark matter haloes continuing to grow over cosmic time by accretion of smaller haloes, the formation and growth of galaxies inside those halos proceeds differently (e.g., Silk 1977; Rees & Ostriker 1977; White & Rees 1978; Fall & Efstathiou 1980; Blumenthal et al. 1984; Cole & Lacey 1996) .”

“Simulations have provided predictions for emission from the WHIM as well as from the gaseous halos around larger groups and clusters (Kravtsov et al. 2002; Yoshikawa et al. 2003; Fang et al. 2005; Bertone et al. 2010) as expected from the theory of collapse (Silk 1977; White & Rees 1978).”

“…formation, it is envisioned that lower cooling efficiencies in massive galaxies would explain the exponential tail of the LF (Rees & Ostriker 1977; Silk 1977; White & Rees 1978), while supernova feedback is typically invoked to reduce the star formation efficiency in low-mass haloes (Larson 1974;…”

“This is quite different from the canonical picture where gas first obtains the halo virial temperature and spin before falling in to form an angular momentum supported disk (Silk 1977; White & Rees 1978; Barnes & Efstathiou 1987; White & Frenk 1991; Maller & Bullock 2004).”

“In-falling baryonic matter condenses through radiative cooling at the centres of growing dark matter halo groups, which leads to the formation of massive galaxies surrounded by a distribution of smaller subhalos (Silk 1977; White & Rees 1978; Moore et al. 1999).”

“The standard paradigm in galaxy formation (Rees & Ostriker 1977; Silk 1977; Binney 1977; Birnboim & Dekel 2003), which omitted feedback, identified a critical halo mass (∼ 1011.5 M⊙ relatively independent of z), above which the virial shock heated halo gas cools slowly and remains thermally…”

“Gas in our simulation is allowed to radiate energy by atomic collisions in an H/He primordial gas (Sutherland & Dopita 1993) so that it can collapse into dark matter (DM) potential wells to form galaxies (Silk 1977).”

“This cold-to-hot transition can be understood analytically in terms of the ratio of gas cooling time to the halo dynamical time (Binney 1977; Rees & Ostriker 1977; Silk 1977; White & Rees 1978; White & Frenk 1991; Birnboim & Dekel 2003; Dekel & Birnboim 2006).”

“Thus, the transition from a cold gas accretion mode to a hot gas accretion mode occurs at z ∼ 2–3, corresponding to halo masses of Mhalo = 5 × 1011 M –1012 M in good agreement with the predictions of Dekel & Birnboim (2006), see also Rees & Ostriker (1977) and Silk (1977).”

“This difference in the behaviour of quasi-static hot halo gas between more and less massive dark matter haloes is motivated largely from the classic, analytical argu- ments of Silk (1977), Rees & Ostriker (1977), and White & Rees (1978).”

“The physical processes accounted for here are thought to be the dominant processes in the formation of cosmological structures such as large galaxies & Ostriker & Rees(Rees 1977 ; Silk 1977 ; White 1978).”

“In standard galaxy formation models (Rees & Ostriker 1977; Silk 1977; White & Rees 1978; Blumenthal et al. 1984; White & Frenk 1991; Mo et al. 1998), gas shockheats to the virial temperature as it falls into DM halos.”

“…depends crucially on the ratio of the cooling timescale toqcool4 T /T0the gravitational collapse timescale (see,qgrav D (ovir G)~1@2e.g., & OstrikerBinney 1977 ; Rees 1977 ; Silk 1977 ; White & Rees If M and t are such that (the1978). qcoolZ qgravdark-shaded region in the cloud cannot promptlyFig.”

“…of Physics and Astronomy, McMaster University, Main Street West, Hamilton L85 4M1, Canada halo shock-heats to the virial temperature of the halo (Silk 1977; White & Rees 1978; Barnes & Efstathiou 1987; White & Frenk 1991; Maller & Bullock 2004), spending a considerable amount of time in the…”

“…could have been much smaller than at present (Palla, Salpeter, & Stahler 1983 ; Yoshii & Saio 1986), others that they could have been much larger (Silk 1977 ; Tohline 1980 ; Kashlinsky & Rees 1983), others that they may have collapsed directly to supermassive black holes (Gnedin & Ostriker 1992…”

“…ic.oup.com /m nras/article-abstract/370/2/902/969076 by guest on 16 M arch 2020 is allowed to radiatively cool and settles down into a rotationally supported gas disc at the centre of the halo, which we identify as the central galaxy (e.g. Silk 1977; White & Rees 1978; White & Frenk 1991).”

“In the absence of heavy elements and dust grains, the cooling mechanisms may indeed be less efficient and favor the formation of massive or very massive stars (e.g. Silk 1977, Bromm et al. 1999).”

“(Rees & Ostriker 1977; Binney 1977; Silk 1977; White & Rees 1978).”

“This paper concentrates on the impact of Ly photon trapping on the EOS, and the interested reader is referred to Rees & Ostriker (1977) and Silk (1977) for some of the fundamental thermodynamic and star formation considerations that come into play here.”

“…most efficient in galaxies with luminosities lower than L∗ (White & Frenk 1991; Birnboim & Dekel 2003; Kereš et al. 2005; Dekel & Birnboim 2006; Dekel et al. 2009; van de Voort et al. 2011; L’Huillier et al. 2012) owing to the short cooling times in these halos (Rees & Ostriker 1977; Silk 1977).”

“The existence of a characteristic mass for massive galaxies emerges from the the competition between the gravitational dynamical time and the radiative cooling time (Rees & Ostriker 1977; Binney 1977; Silk 1977; White & Rees 1978; Blumenthal et al. 1984).”

“Early theoretical works predicted the existence of the CGM as a by-product of the interactions between cooling and accretion during galaxy formation (Binney 1977; Rees & Ostriker 1977; Silk 1977).”

“White and Rees [17] presented one of the first models of galaxy formation in a cosmological context (see also [16,28]).”

“The basic physics of CGM virialization was originally discussed by Rees & Ostriker (1977), Silk (1977), and White & Rees (1978) and has since been corroborated by more detailed (but still idealized) calculations (Birnboim & Dekel 2003; Dekel & Birnboim 2006; Fielding et al. 2017).”