Star Formation Isochrone Surfaces: Clues on Star Formation Quenching in Dense Environments
aa r X i v : . [ a s t r o - ph . GA ] D ec Mon. Not. R. Astron. Soc. , 1– ?? (2002) Printed 13 July 2018 (MN L A TEX style file v2.2)
Star Formation Isochrone Surfaces: Clues on StarFormation Quenching in Dense Environments
M.A. Aragon-Calvo , ⋆ , Mark C. Neyrinck, , Joseph Silk , Department of Physics and Astronomy. University of California, Riverside, CA, USA. Department of Physics and Astronomy. Johns Hopkins University. Baltimore, MD 21218, USA. Institut d Astrophysique de Paris. Univ. Paris VI, 98 bis boulevard Arago, 75014 Paris, France
13 July 2018
ABSTRACT
The star formation history of galaxies is a complex process usually consideredto be stochastic in nature, for which we can only give average descriptions such asthe color-density relation. In this work we follow star-forming gas particles in a hy-drodynamical N-body simulation back in time in order to study their initial spatialconfiguration. By keeping record of the time when a gas particle started forming starswe can produce gas-star isochrone surfaces delineating the surfaces of accreting gasthat begin producing stars at different times. These accretion surfaces are closelypacked inside dense regions, intersecting each other, and as a result galaxies insideproto-clusters stop accreting gas early, naturally explaining the color dependence ondensity. The process described here has a purely gravitational / geometrical origin,arguably operating at a more fundamental level than complex processes such as AGNand supernovae, and providing a conceptual origin for the color-density relation.
Key words:
Cosmology: large-scale structure of Universe; galaxies: kinematics anddynamics, Local Group; methods: data analysis, N-body simulations
The observed properties of galaxies are the combined re-sult of complex internal mechanisms (secular evolution)such as supernovae, AGN feedback, etc. (Powell et al.2011; Larson et al. 1980), and ii) external environmen-tal mechanisms such as galaxy interactions and mergers,harassment, etc. (Gunn & Gott 1972; Moore et al. 1996;Kawata & Mulchaey 2008). The role of cosmic environ-ment on star formation is evident in processes such asthe morphology-density relation (Dressler 1980) and therelated color-density relation, which encode the effect ofenvironment (density) on star formation history (color)(Blanton et al. 2005; Bell et al. 2004; Baldry et al. 2004;Thomas et al. 2005; Dekel et al. 2009). While environmentalprocesses leave their imprint on all galaxies, they are moreclearly seen in dense environments such as massive galaxyclusters where star formation is mostly quenched. On theother hand, low-density environments contain the majorityof star-forming galaxies. Several mechanisms are assumedto contribute to the observed bimodality in the color dis-tribution and the decreasing fraction of blue galaxies withincreasing density, such as galaxy mergers and harassment. ⋆ E-mail:[email protected] (Gunn & Gott 1972; Larson et al. 1980; Moore et al. 1996).These mechanisms however, do not offer a direct link be-tween star formation and environment. Even galaxy merg-ers, which seemed to explain the relation via the apparentlyrelated morphology-density relation, have been shown toplay a minor role in color evolution (Blanton et al. 2005;Skibba et al. 2009).Galaxies accrete cold gas via narrow filamen-tary streams that penetrate deep into the galaxy(Kereˇs et al. 2005; Dekel & Birnboim 2006; Dekel et al.2009; van de Voort et al. 2011b), fueling star formationshortly after accretion (Bauermeister et al. 2010). The grav-itational collapse of matter into the galaxy sets a naturalorder in the accretion of gas, i.e. nearby gas is accreted firstwhile gas in distant reservoirs is accreted later. If star for-mation closely follows gas accretion, we should then expecta simple relation between star formation time and the orig-inal distance between the gas cloud that formed the starsand the galaxy, at least approximately. This may providea link between the stellar populations of galaxies, encodedin their color, and the initial spatial configuration of theproto-galaxy. In this Letter, we explore this idea by track-ing star-forming gas particles back to their initial positionin two extreme cases, one isolated “Milky Way” galaxy andone central galaxy inside a large cluster. c (cid:13) Aragon-Calvo M.A. et al.
Figure 1.
Gas → star conversion times ( t ∗ , z ∗ ) in an isolated “Milky Way” (MW) galaxy with a mass of ∼ × h − M ⊙ . We onlyshow star-forming gas particles. Colors indicate the gas → star conversion time using a color table that intuitively mimics the observedpresent-time stellar population colors. Left panel: four gas-star conversion isochrone surfaces at early times ( z = 19), corresponding to(from dark-blue to red) t ∗ = 10 . , . , . . The results presented in this work are based on two fullhydrodynamic zoom resimulations: i) an isolated “MilkyWay” galaxy with a present-time mass of 2 × h − M ⊙ located inside a cosmological wall identified with the MMF-2 method (Aragon-Calvo & Yang 2014) from a 32 h − Mpcbox and ii) a “galaxy cluster” with a present-time mass of3 × h − M ⊙ ( z =0) . selected from a 64 h − Mpc box. Bothhaloes were resimulated at high resolution by first select-ing particles inside a sphere of 3 h − Mpc radius centeredon the target halo identified at z = 0. From the selectedparticles’ initial positions we created a binary mask whichwas then filled with high-resolution particles and the rest ofthe box with layers of decreasing resolution particles. Themass resolution (corresponding to 1024 particles) for the“Milky Way” and “galaxy cluster” are 1 . × h − M ⊙ and2 . × h − M ⊙ respectively. The Gadget-3 code used torun the resimulations implements simple recipes for hydro-dynamics and chemical enrichment including stochastic starformation (for gas with a hydrogen number density > n h =0 . − ), SN feedback and winds (Springel & Hernquist2003). Additionally we ran a simulation on a 32 h − Mpcbox including gas and star formation used to compute meanstar formation time distributions (Fig. 3). While more de-tailed star formation recipes are possible, in the present worktheir are not critical, as the main constraint on star forma-tion we discuss here is geometric in nature.
In order to investigate the connection between primordialenvironment, gas accretion and star formation history, weidentified and followed star-forming gas particles, i.e. gasparticles that at some point during the simulation’s historyproduced stars, from the present time back to the initialconditions. The question we are trying to answer is: wheredid the gas that produced different star populations inside agiven galaxy come from? For each gas particle we also storedthe time when it started producing stars, here referred to asthe gas → star conversion time, t ∗ . When convenient, we willuse the equivalent gas → star conversion redshift z ∗ and scalefactor a ∗ . In cases where several star particles were spawnedfrom the progenitor gas particle or when the gas particle wascompletely converted to star particles we assigned t ∗ to thefirst time the gas particle produced a star. By doing so, wewere able not only to follow stars after they are formed, butto trace their “progenitor” gas particles back to their ini-tial comoving positions (Lagrangian coordinates) and studytheir initial spatial arrangement.We converted the discrete gas particle positions toa continuous scalar field containing the interpolated val-ues of t ∗ at each gas particle’s position. We usedthe Delaunay-based interpolation scheme described inBernardeau & van de Weygaert (1996) in which a scalarvalue ( t ∗ ) defined at each sampling point (gas particles) islinearly interpolated inside the tetrahedra defined by thepoint distribution. The tessellation was computed from the c (cid:13) , 1– ?? tar Formation Isochrone Surfaces Figure 2.
Gas-star conversion times in a galaxy cluster with mass of ∼ × h − M ⊙ . (see Fig. 1). Star-forming gas is accreted fromincreasingly distant isochrone surfaces, centered in the progenitors of massive galaxies (red blobs). Proto-cluster galaxies, being closelypacked, are surrounded by a layer of galaxies and are effectively isolated from late star-forming gas (light blue isochrone surfaces). Thewhite circle in the top panel shows the central proto-galaxy in a window carved through the gas cloud. For comparison, we show theMilky Way galaxy from Fig. 1 (small white square) on the left panel. particle positions at z = 19 instead of the true Lagrangianpositions in order to alleviate the degenerate cases arisingfrom computing the Delaunay tessellation on a regular gridof particles. The t ∗ field was interpolated into a regulargrid. From the t ∗ -field we computed iso-surfaces at a set ofgas → star conversion times. These gas → star isochrone sur-faces , S t ∗ define regions of gas that, after being accreted intogalaxies, started forming stars at the same time. We begin discussing the case of the relatively simple “MilkyWay” galaxy and then proceed to the more complex galaxycluster. Figure 1 shows the star-forming evolution of a galaxyin isolation. The left panel shows several gas → star isochronesurfaces color-coded with time. This technique allows us tosee the full time evolution and spatial arrangement of star-forming gas particles in one single frame. The earliest starforming gas is the closest to the proto-galaxy and the firstto be accreted (red surfaces). Subsequent layers of gas areaccreted and form stars at later times. The simple accretionhistory of this galaxy is reflected in its also simple isochronesurfaces. There is one single large proto-galaxy and radialsemi-spherical shell extending in Lagrangian space. Sincethere is no impediment for this galaxy to accrete star-forming gas, it can continue forming stars until the presenttime as indicated by the existence of the outer isochronesurface corresponding to z = 0 (dark blue). The subse-quent evolution of the particle distribution is shown in the right panels. Note that while the isochrone surfaces are semi-spherical shells in Lagrangian space they correspond to fil-aments in configuration (Eulerian) space. This techniqueallows us to directly see that star-forming gas is accretedmainly through narrow filamentary streams as first reportedby Dekel et al. (2009).Figure 2 shows the star formation isochrone surfaces fora galaxy cluster. The central proto-galaxy is the prominentstructure near the center of the proto-cluster. For conve-nience in what follows, we will call this the central galaxyand the rest the satellite galaxies. The isochrone surfacesare remarkably regular and there is a clear relation betweengas-star conversion time and radial distance from centers ofproto-galaxies even for this complex cluster (a triple majormerger and several substructures, see right panels in Fig. 2).As in the case of the isolated galaxy, early star-forming gas isaccreted first and so S z ∗ =9 (red surfaces) mark the centers ofgalaxies. The S z ∗ =9 surfaces enclose a volume of gas roughly8 times larger than the same isochrone for the Milky Waygalaxy, indicating a star formation rate 8 times larger forthe central galaxy compared to the Milky Way. The S z ∗ =3 surfaces (yellow) surrounding satellite galaxies are relativelyisolated compared to the S z ∗ =3 surfaces around the centralgalaxy where surfaces from adjacent galaxies are intersect-ing. The central galaxy, being surrounded by a compact shellof adjacent satellite galaxies is geometrically constrained toaccrete star-forming gas beyond the S z ∗ =3 surface. This canbe seen in the almost total lack of S z ∗ =1 surfaces (light blue)around the central galaxy. Satellite galaxies on the other c (cid:13) , 1– ?? Aragon-Calvo M.A. et al.
Figure 3.
Distribution of Gas-star conversion times (in units ofthe scale factor) as function of initial distance from centers ofproto-galaxies identified at z = 4 for three halo mass ranges. Byextrapolating the intersection between the dotted lines (shown forcomparison purposes) and the scale factor a = 1 we can infer themaximum radius that a galaxy would carve at the present timeunder no geometric or other constraints. hand are still able to accrete gas at this time although thereis no noticeable accretion of star-forming gas after z ∼ closely packed sys-tem of S z ∗ spheres where adjacent galaxies compete for theavailable gas as they “carve” the proto-cluster’s volume.The intersection of isochrone surfaces from adjacent galaxiesmarks the time where no more gas is available for accretionand star formation. This occurs roughly at half the meaninter-galaxy separation, imposing a fundamental geometriclimit to gas accretion in dense environments. On the otherhand, galaxies in the outskirts of proto-clusters can havean extended star formation history due to their access togas in the vicinity of the proto-cluster (Papadopoulos et al.2001; Riechers et al. 2010; Wolfe et al. 2013) as observed inthe different quenching times between central and satellitegalaxies in groups(Tal et al. 2014). → star conversion times Figure 3 shows the distribution of t ∗ vs. initial comoving dis-tance r from the center of proto-galaxies. Since star forma-tion closely follows gas accretion (Bauermeister et al. 2010)it should not be surprising that t ∗ is a monotonically in-creasing function of r . In the simplest case of a free-fallinggas particle, t ∗ depends on the Lagrangian distance fromthe gas particle to the center of the proto-galaxy and themass of the galaxy M , as t ∗ ∝ p r /M . In reality gas accre-tion is far more complex, involving both gravitational andhydrodynamical processes. We approximate the distributionin Fig. 3 by the empirical fit:log ( a ∗ ) = − . − .
04 log M + 3 . r − . r log M, (1) where a ∗ is the time of gas → star conversion in units of theexpansion factor, and M is the mass of the galaxy, here iden-tified at z = 4, when the r − a ∗ relation is still clearly de-fined. For galaxies identified at later times, the relation stillholds, but non-linear interactions increase the dispersion.The fit provides an approximate model for star formationtimes that depends only on the mass and initial distancefrom the proto-galaxy’s center, while ignoring feedback pro-cesses that further regulate star formation. In an isolatedgalaxy the accretion of star-forming gas is limited (in oursimple model) only by the background cosmology and sur-rounding gravitational field. The extrapolated values of r at a ∗ = 1 are close to the radius containing the total mass ofthe halo in the mass range. The competition for gas by adjacent proto-galaxies is simi-lar to other physical processes that result in a Voronoi seg-mentation (Okabe 2000). Using equation 1, we can modelthe isochrone surfaces as a system of random closely-packedspheres . Assuming accretion through spherical Lagrangianshells centered at the proto-galaxy’s position, we partitionthe space between proto-galaxies (identified at z = 4 withmasses > h − M ⊙ ) using a weighted Voronoi tessella-tion in which the volume inside Voronoi cells define regionsof gas accretion. The weight w is given by the isochroneradius extrapolated to the present time (from equation 1): w = r a ∗ =1 = 0 . . M . − . M (2)We then generate a continuous t ∗ time field by evaluatingequation 1 inside the Voronoi cell of each galaxy. Figure4 shows a side-by-side comparison between the measuredisochrones and the ones obtained from the Voronoi model.The correspondence between the hydrodynamic simulationand the Voronoi model is remarkable. It may seem surpris-ing that such a simple model based on geometric constraintsagrees at all with the result of complex gravitational andhydrodynamical processes but in a sense it is also expectedsince at cluster-size scales, gas in the early universe basi-cally follows dark matter. Early star formation has a strongdeterministic component given by geometric constraints. The most straightforward consequence of “galaxy closepacking” is that the massive galaxies which are the pro-genitors of present-time groups and clusters, being sur-rounded by gas-competing galaxies, become cut off fromtheir gas supply, becoming “quenched” already at earlytimes (Best et al. 1997; Thomas et al. 2005). Massive clus-ter galaxies are located in environments where the numberdensity of galaxies is several times the average (Daddi et al.2000). At z = 4, the mean separation between M > h − M ⊙ ( z =4) galaxies inside proto-clusters is d m ≃ . z = 4 haloes of mass be-tween 10 − h − M ⊙ ( z =4) and 10 − h − M ⊙ ( z =4) accretestar-forming gas from isochrone surfaces of ∼ . h − Mpc c (cid:13) , 1– ?? tar Formation Isochrone Surfaces A B z=19
Figure 4.
Gas-star conversion isochrones from the full N-body hydro simulation (left) and a Voronoi model (right) in a region of 12 h − Mpc of side (horizontal axis). For clarity we show two-dimensional slices through the isochrones inside the white circles at upper left. and ∼ . h − Mpc radius respectively. As early as z = 4,the radius of the corresponding isochrone surface for thosegalaxies is already of the same order as their mean separa-tion, indicating the time of quenching for the central galaxy.The mechanism described here offers a conceptual ori-gin for the observed color-density relation by limiting gas ac-cretion and star formation in dense environments. Galaxiesin low-density regions, on the other hand, are not geomet-rically constrained and can, in principle, freely continue toaccrete gas. However, the dominant role of the backgroundcosmology, tidal fields from nearby structures and super-Hubble dynamics in low-density environments, can reduceand even halt gas accretion. In addition to this, other pro-cesses such as AGN and SN feedback play an importantrole. Finally, the model presented here may also shed somelight on the observed cosmic star formation rate history.The peak in the t ∗ distributions in Fig. 3 lie in the range z = 4 −
3, close to the time when isochrone surfaces of mas-sive galaxies (which produce most of the stars at that time)begin to intersect, as discussed above. It also corresponds tothe observed peak in the cosmic star formation rate history(Heavens et al. 2004). This peak, and subsequent drop inthe star formation rate, can be interpreted as the result ofthe change in the main gas accretion mode from being gasaccretion-driven (before isochrone intersection) to a less ef-fective mode driven by galaxy mergers (van de Voort et al.2011a; Feldmann & Mayer 2014).
This research was funded by a Big Data UC Riversideseed grant, the Betty and Gordon Moore foundation and aNew Frontiers of Astronomy and Cosmology grant from theTempleton Foundation. Miguel Aragon would like to thankBernard Jones for valuable comments and Volker Springelfor the Gadget3 N-body code.
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