Cosmic Reionization On Computers II. Reionization History and Its Back Reaction on Early Galaxies
DD raft version M ay
6, 2019
Preprint typeset using L A TEX style emulateapj v. 5 / / COSMIC REIONIZATION ON COMPUTERS II. REIONIZATION HISTORY AND ITS BACK REACTION ON EARLYGALAXIES N ickolay Y. G nedin and A lexander A. K aurov Draft version May 6, 2019
ABSTRACTWe compare the results from several sets of cosmological simulations of cosmic reionization, produced underCosmic Reionization On Computers (CROC) project, with existing observational data on the high-redshift Ly α forest and the abundance of Ly α emitters. We find good consistency with the observational measurements andthe previous simulation work. By virtue of having several independent realizations for each set of numericalparameters, we are able to explore the e ff ect of cosmic variance on observable quantities. One unexpectedconclusion we are forced into is that cosmic variance is unusually large at z >
6, with both our simulationsand, most likely, observational measurements are still not fully converged for even such basic quantities as theaverage Gunn-Peterson optical depth or the volume-weighted neutral fraction. We also find that reionization haslittle e ff ect on the early galaxies or on global cosmic star formation history, because galaxies whose gas contentis a ff ected by photoionization contain no molecular (i.e. star-forming) gas in the first place. In particular,measurements of the faint end of the galaxy luminosity function by JWST are unlikely to provide a usefulconstraint on reionization. Subject headings: cosmology: theory – cosmology: large-scale structure of universe – galaxies: formation –galaxies: intergalactic medium – methods: numerical INTRODUCTION
If cosmic reionization can be called the current frontier ofextragalactic astronomy, then, in historic terms, we live in themiddle of XIX century. I.e., the frontier is being settled...Ultra Deep Field campaigns with the Hubble Space Tele-scope pushed the search for the most likely reionizationsources - young star-forming galaxies - to double digit valuesof cosmic redshift (Bouwens et al. 2007, 2011; Oesch et al.2012; Bradley et al. 2012; Schenker et al. 2013; Willott et al.2013; Oesch et al. 2013a; Bowler et al. 2013; Oesch et al.2013b). Observations of Ly α emitters at z ∼ α absorp-tion spectroscopy of high redshift quasars new advances areexpected in the nearest future, as new discoveries of z > Particle Astrophysics Center, Fermi National Accelerator Laboratory,Batavia, IL 60510, USA; [email protected] Department of Astronomy & Astrophysics, The University ofChicago, Chicago, IL 60637 USA; [email protected] Kavli Institute for Cosmological Physics, The University of Chicago,Chicago, IL 60637 USA approaches for modeling reionization (Furlanetto & Oh 2005;Furlanetto et al. 2006; Mesinger & Furlanetto 2007; Alvarez& Abel 2007; Zahn et al. 2011; Mesinger et al. 2011; Al-varez & Abel 2012; Zhou et al. 2013; Battaglia et al. 2013;Kaurov & Gnedin 2013; Sobacchi & Mesinger 2014), andmore traditional models were pursued as well (Choudhury &Ferrara 2005, 2006; Shull & Venkatesan 2008; Mitra et al.2011; Venkatesan & Benson 2011; Mitra et al. 2012; Kuhlen& Faucher-Gigu`ere 2012; Robertson et al. 2013). Unfortu-nately, on the numerical simulation front the progress was lessdramatic, although important advances in the simulation tech-nology did take place (e.g. Iliev et al. 2006; Zahn et al. 2007;McQuinn et al. 2007; Trac et al. 2008; Shin et al. 2008; Croft& Altay 2008; Lee et al. 2008; Iliev et al. 2009; Aubert &Teyssier 2010; Friedrich et al. 2011; Ahn et al. 2012; Shapiroet al. 2012, for a complete review see Trac & Gnedin (2009)).However, the primary brake on the simulation progress - in-su ffi cient computing power - is finally being released, thanksto Moore’s Law.Modern High Performance Computing platforms havecrossed an important threshold of “sustained peta-scale” per-formance. This level of performance, currently available onabout a dozen or so (non-classified) supercomputers acrossthe globe, o ff ers a unique opportunity for reionization theo-rists to make a substantial breakthrough in our ability to modelcosmic reionization with high physical fidelity, and some ofthe most recent simulation work already took advantage ofthat opportunity (Iliev et al. 2014; So et al. 2013; Normanet al. 2013; Hutter et al. 2014).Cosmic Reionization On Computers (CROC) project is an-other e ff ort in producing peta-scale simulations of reioniza-tion in su ffi ciently large volumes (above 100 Mpc in comov-ing units), with spatial resolution reaching down to 100 pc,and including most (if not all) of the relevant physical pro-cesses, from star formation and feedback to radiative transfer.In the first paper in the series (Gnedin 2014, hereafter Pa-per I) we described in complete detail the simulation design a r X i v : . [ a s t r o - ph . C O ] A ug and the calibration of numerical parameters. In this paper weexplore the overall process of cosmic reionization as capturedby CROC simulations, and compare our theoretical predic-tions to several observational constraints.We deliberately limit the scope of this paper to relativelyeasily computable quantities, which give only a global, broad-brush view of reionization, due to the limited human e ff ortavailable for the analysis of the rich, but complex simulationdata. We intend to continue this paper series as more detailed,labor-intensive analysis gets completed. CROC SIMULATIONS
All CROC simulations are performed with the Adaptive Re-finement Tree (ART) code (Kravtsov 1999; Kravtsov et al.2002; Rudd et al. 2008). The ART code is capable of mod-eling a diverse set of physical processes, from the dynamicsof dark matter and gas to star formation, stellar feedback, andradiative transfer. A detailed description of all physical pro-cesses followed in the CROC simulations is presented in Pa-per I.CROC simulations performed in volumes with 20 h − Mpcand 40 h − Mpc on a side, and 80 h − Mpc boxes will beadded to the full data set as the project progresses. Allsimulations but one have the same mass resolution of 7 × M (cid:12) (20 h − Mpc boxes use 512 dark matter particles,40 h − Mpc use 1024 particles, etc). One of 20 h − Mpc boxes(B20HR.uv2) has been run with 1024 particles, achieving the8 times higher mass resolution of 9 × M (cid:12) ; we use that sim-ulation for testing numerical convergence and for some of thescientific results where high mass resolution is required. Us-ing the full Adaptive Mesh Refinement (AMR) functionalityof ART, we reach formal spatial resolution (smallest simula-tion cell size) of 125 pc at z =
6, and even higher resolution atearlier times, as our resolution remains constant in comovingunits. The real resolution of the simulations is a factor of 2-3worse.Paper I describes numerical parameters of CROC simula-tions, and how we calibrate their values. The only parameterthat we vary in this paper is the “escape fraction of ionizingradiation up to the simulation resolution” (cid:15) UV . In a numericalsimulation with finite spatial resolution not all absorptions ofionizing photons can be accounted for, because some of thephotons will be lost in structures that are not resolved in thesimulation (like a parent molecular cloud). Hence, to accountfor those absorptions, we assign each stellar particle ionizingluminosity L ion = (cid:15) UV L origion , where L origion is unattenuated luminosity of a single-age stel-lar population and the parameter (cid:15) UV accounts for unresolvedphoton losses.Since the ionizing output of our model galaxies is propor-tional to (cid:15) UV , that parameter critically controls the whole pro-cess of reionization in the intergalactic medium (IGM).For each value of simulation parameters (box size, (cid:15) UV , etc)we perform a set of simulations that start from independentrealizations of initial conditions and properly account for thefluctuations outside the box using the so-called “DC mode”(Gnedin et al. 2011). Hence, we can use a given simulationset to quantify the e ff ect of cosmic variance on our results.Table 1 lists simulation sets that we use in this paper. Starformation and stellar feedback parameters in these simula-tions are calibrated so that the observed galaxy UV luminosityfunctions are matched to the observations at all redshifts from
105 6 7 8 9 12 14 z -5 -4 -3 -2 -1 › X fi B ,† UV =0 . B ,† UV =0 . B ,† UV =0 . › HI fi V › HI fi M › HII fi V › HII fi M F ig . 1.— Evolution of mass- and volume-weighted hydrogen fractions withredshift in the best-fit 20 h − Mpc simulation set B20.uv2 and both 40 h − Mpcsets. Data points are from Fan et al. (2006). z = z =
10. Hence, for all simulation sets used in thispaper stellar sources of cosmic reionization are followed ac-curately (at least for z ≤ RESULTS
Reionization History
In Paper I it was showed that the value of (cid:15) UV between 0.1and 0.2 provides the best match to the observed evolution ofthe Ly α forest at z < h − Mpc set (B20.uv2) and both 40 h − Mpc sets(in all cases we average over all independent realizations).Shapes of various curves in the Figure are highly expected,and are consistent between almost all previous simulations ofreionization. Ionized fractions grow steadily with time, asionized bubbles expand in the neutral IGM. Neutral fractionsdecrease in response until the moment of overlap, when the
TABLE 1S imulation S ets Set Id (cid:15) UV Stopping Number ofredshift realizations20 h − Mpc boxes, 512 particlesB20.uv1 0.1 5 6 [A-F]B20.uv2 0.2 5 6 [A-F]B20.uv4 0.4 5 3 [D-F]20 h − Mpc boxes, 1024 particlesB20HR.uv2 0.2 5.7 1 [B]40 h − Mpc boxes, 1024 particlesB40.uv1 0.1 5 3 [A-C]B40.uv2 0.2 5.5 3 [A-C] z › τ G P fi ∆ z = . AverageMedian (1 − − − F ig . 2.— Probability Density Function (PDF) of the average Gunn-Petersonoptical depth (cid:104) τ GP (cid:105) ∆ z = . in redshifts intervals ∆ z = .
15 along individuallines of sight as a function of redshift for the B20.uv2 simulation set. PDFis shown with 3 progressively more opaque bands that mark progressivelynarrower percentile ranges around the median (the dashed line). A solid lineshows the average, that at z > . τ GP and the gasproperties. Data points are from Fan et al. (2006). volume-weighted neutral hydrogen fraction decreases rapidly(Gnedin 2000). In the post-overlap stage the IGM is highlyionized, and the evolution of neutral fractions is governed bythe mean free path of ionizing photons and the level of cos-mic ionizing background (see also Trac & Gnedin 2009, for ageneral overview of reionization process).Lack of numerical convergence that we discussed in PaperI is also visible in Figure 1 - in the set B40.uv1 the overlapof ionized bubbles (indicated by the rapid drop in the aver-age volume-weighted HI fraction just before z =
6) occurs atabout the same time as in the smaller box set B20.uv2, butthe post-reionization Ly α forest is better matched by the setB40.uv2, which has a significantly earlier overlap.As we discussed in Paper I, that lack of convergence iscaused by cosmic variance - having multiple independent re-alizations allows to explore it well. Our (still unconverged)simulations sample a much larger number of independentsightlines than is available observationally, hence the lack ofagreement between the simulations and observations at z > z < ff erent:simulations with the same value of the (cid:15) UV parameter do con-verge, the cosmic variance is small (since the radiation field isdominated by the cosmic background - this is apparent fromFigure 4 of Paper I), and the correct simulations should matchthe observational data. The mismatch between the simula-tions and the observations at z (cid:46) . z = z ≈ .
3, most likely becauseour spatial resolution, being kept fixed in comoving units, de-grades too much by z ≈ Under the term “cosmic variance” we understand the di ff erence betweenseparate regions of the universe; such di ff erence is caused both by the varia-tion of densities and by variation in the distribution of ionized bubbles, andthe latter almost always dominates. › τ GP fi ∆ z =0 . -3 -2 P ( > › τ G P fi ∆ z = . ) .
Time evolution of the distribution of ionized bubbles is oneof the most important characteristics of the reionization pro-cess. Unfortunately, in a realistic cosmological simulation theconcept of an “ionized bubble” is not well defined mathemat-ically, especially at late times, as can be easily seen from Fig-ure 4. Hence, in order to have a working definition that canalso be compared with other studies, we closely follow theprocedure from Zahn et al. (2007) to compute the probabilitythat a given point in the simulation is located inside an ion-ized bubble of size R . The scale R is defined as the largestradius of a sphere in which the volume-weighted average ion-ized fraction is higher than the threshold value, which is cho-sen to be 90%. The only di ff erence with Zahn et al. (2007)is normalization: we normalize the bubble size distribution tothe total volume (an integral over the distribution is equal tothe volume-weighted average ionized fraction), whereas Zahn F ig . 4.— Slices through the computational domain for the first realizationof B40.uv1 set (run B40.uv1.A in the notation of Paper I) at z = z = z = z = et al. (2007) normalize their distributions to the total ionizedvolume (an integral over the distribution is equal to unity).Distributions of sizes of ionized and neutral bubbles (shownas a di ff erential volume function) are presented in Figure5 for several values of redshift for both 20 h − Mpc and40 h − Mpc simulation sets. Somewhat unexpectedly, we findgood convergence in the bubble size distribution even for the20 h − Mpc box size all the way to z ∼
7. At lower redshiftsthe convergence does break down, simply because some ofthe smaller boxes are going to be completely ionized beforelarger boxes (and the same applies to neutral “bubbles” at highredshifts). The volume fraction in such boxes is shown withhorizontal arrows on both panels, and it also is reasonablyconsistent between the 20 h − Mpc and 40 h − Mpc simulationsets.At face value, this result is inconsistent with the recent sim-ulations of Iliev et al. (2014), who found incomplete con-vergence in simulation volumes as large as 114 h − Mpc atall redshifts. Without detailed comparison, it is di ffi cult toisolate the source of the discrepancy. We notice, however,that the spatial resolution of the radiative transfer solver inIliev et al. (2014) simulations is only about 200 h − kpc in co- R [ h − Mpc] -4 -3 -2 d f V / d l n R z =6 . z =7 . z =8 z =9 R [ h − Mpc] -4 -3 -2 d f V / d l n R z =6 . z =7 . z =8 F ig . 5.— Di ff erential volume function of ionized (top) and neutral (bottom)bubbles in our simulations at several values of redshift. Solid lines with semi-transparent bands show the average and the rms for our fiducial 40 h − Mpcset B40.uv1; dashed lines show averages for the 20 h − Mpc set B20.uv2.Horizontal errors show the volume fraction in individual boxes that are morethan 90% ionized (top panel) or more than 90% neutral (bottom panel) ata given redshift. We find good convergence of sizes of ionized bubbles inboxes as small as 20 h − Mpc at z >
7, and at z < moving units, which is inadequate for resolving absorptionsin galactic halos and Lyman Limit systems, while our spatialresolution (0 . h − comoving kpc) is better suited for properlyaccounting for all absorptions of ionizing radiation. Damping Wing of Ly α Absorption
Before the universe is completely reionized, patches of thestill neutral IGM can significantly absorb Ly α emission fromhigh-redshift galaxies, as the damping wing of Ly α absorptionextends far redward of the galaxy systemic velocity (Miralda-Escude 1998). In order to model that e ff ect, we also generatesynthetic Ly α spectra that originate at galaxy locations. The“sky” of each galaxy is sampled uniformly with 12 directions,corresponding to 12 zero level cells of the HEALPix tessel-lation of a sphere (G´orski et al. 2005). In order to excludethe local absorption from the galactic ISM, we start the lineof sight 10 kpc away from the center of the galaxy. http://healpix.sourceforge.net z D E W ( k m / s ) (1 − − B ,† UV =0 . B ,† UV =0 . B ,† UV =0 . M UV ∈ [ − . , − . M UV ∈ [ − . , − . › X HII fi V D E W ( k m / s ) B ,† UV =0 . B ,† UV =0 . B ,† UV =0 . − − F ig . 6.— Equivalent width of Ly α absorption D EW as a function of redshift(top) or volume-weighted neutral hydrogen fraction (bottom). Colored linesshow averages over all realizations of simulation sets B20.uv4 (red), B20.uv2(green), and B20.uv1 (blue) for all galaxies with UV magnitudes between -22and -18. Green semi-transparent bands give the distribution of D EW aroundthe mean (as 1-99 and 10-90 percentiles). Green dashed and dotted lines show D EW for the subsets of galaxies with magnitudes in bins [-21.72,-20.25] and[-20.25,-18.75] respectively. An exact calculation of the e ff ect of the damping wing onthe Ly α emission line of a galaxy requires complex Ly α radia-tive transfer in the galactic ISM and surrounding IGM. Sucha calculation is a separate research project in itself, and in anycase our simulations do not have enough spatial resolution toperform such a calculation with su ffi cient accuracy. Instead,we approximate the e ff ect of the damping wing by computingthe absorption equivalent width of the red part of the syntheticspectrum, D EW = (cid:90) ∞ λ e − τ λ d λ, where λ is the wavelength of Ly α at the systemic velocity ofeach model galaxy. Hence, we compute 12 values of D EW foreach galaxy, achieving dense sampling of the full distributionfunction for D EW .From comparison between Figures 1 and 6 it is clear thatbeginning of the overlap of ionized bubbles corresponds to arapid decrease in the equivalent width of the damping wing -in our fiducial B20.uv2 run D EW drops by an order of magni-tude between z = z = .
5. Such behavior is consistent M vir [M fl ] f ga s / f un i Fiducial, z =5 High Res, z =6 High Res, z =7 High Res, z =8 F ig . 7.— Average gas fractions (in units of the universal) for the high res-olution run B20HR.uv2 at z =
6, 7, and 8 (solid lines) and for the fiducialB20.uv2 run at z = z = z (cid:46)
6) almost perfectly. with the observed sharp decline in the fraction of Ly α emit-ters between z = z = α emitters in the simulations.We also notice that in our simulations there is little depen-dence of the damping wing equivalent width D EW on galaxyluminosity - dotted and dashed lines in Figure 6 show the evo-lution of D EW for two luminosity bins, but both lines tracesimilar behavior. The luminosity dependence of the fractionof Ly α emitters has been seen in some observational stud-ies (c.f. Schenker et al. 2012) but not in others (c.f. Penter-icci et al. 2011). If such dependence is confirmed by furtherobservations, it would imply that brighter galaxies have in-trinsically higher probability of becoming a Ly α emitter thanfainter ones.The observed measurements of the fraction of galaxies thatremain strong Ly α emitters have been also used to constraintthe mean volume-weighted neutral fraction. The bottom panelof Figure 6 replaces the redshift axis with the (monotonicallydecreasing with time) volume-weighted HI fraction. The sen-sitivity of D EW ( (cid:104) X HI (cid:105) V ) to the (cid:15) UV parameter is much lessthan when D EW is treated as a function of z , confirming thevalidity of the assumption that the decrease in the observedfraction of Ly α emitter at higher redshifts indicates a changeof the volume-weighted average neutral fraction. In fact, itappears that a condition D EW < / s corresponds to (cid:104) X HI (cid:105) V (cid:46) .
2, while a condition D EW <
500 km / s correspondsto (cid:104) X HI (cid:105) V (cid:46) .
1. This conclusion is in good agreement withother recent simulation studies (c.f. Taylor & Lidz 2014; Hut-ter et al. 2014).
Back Reaction of Reionization on Early Galaxies
The most immediate e ff ect of reionization on the earlygalaxies - or, rather, galactic halos - is to expel photoionizedgas from su ffi ciently low mass halos. This process, some-times inaccurately called “photoevaporation”, has been a fo-cus of a large number of studies, reviewing which is beyondthe scope of this paper. So far, the highest mass resolution (upto 3 × M (cid:12) - a critical numerical parameter for this ques-tion) has been achieved by Okamoto et al. (2008, they also
105 6 7 8 9 12 14 z ˙ ρ ∗ ( + z ) [ M fl / y r / ( h − M p c ) ] † UV =0 . † UV =0 . † UV =0 . High Res, † UV =0 . F ig . 8.— Cosmic star formation histories for the three fiducial simulationsets with varied ionizing intensity and the high resolution run B20HR.uv2.Thin vertical lines mark reionization redshifts for each simulation set (definedas times when the volume weighted neutral fraction falls below 10 − , seeGnedin (2000)). Black points with error-bars are the data from Bouwenset al. (2014). Reionization does not introduce any noticeable feature in theglobal star formation history. review the previous works), who provided accurate fits for theaverage gas fraction as a function of halo mass and redshift.In Figure 7 we compare the gas fractions in our simulationswith the fits from Okamoto et al. (2008). Our fiducial sim-ulation sets barely have enough mass resolution to properlycapture the characteristic mass below which halos start losinggas due to photoionization. A high resolution run B20HR.uv2captures that e ff ect well, and our results post-reionization (at z (cid:46)
6) agree with Okamoto et al. (2008) fits extremely well.At earlier redshifts the di ff erence is expected, as Okamotoet al. (2008) assumed an instantaneous reionization at z = ff ect of reion-ization on the gas fractions to be fully established (Iliev et al.2005) - for example, our B20HR.uv2 run reionizes at z ≈ . z =
6, only 210 Myr later.A secondary e ff ect of reionization is on the actual star for-mation rates in early galaxies. That e ff ect can be large or nil,depending on the fraction of star formation in halos that area ff ected by photoionization. The simplest manifestation ofsuch back reaction is a change in the global cosmic star for-mation history. Studies of the response of the global star for-mation history to reionization were pioneered by Barkana &Loeb (2000), who found a large suppression in the global starformation history at reionization. This “Barkana & Loeb” ef-fect has been revisited repeatedly in the previous studies (Tas-sis et al. 2003; Wyithe & Loeb 2006; Barkana & Loeb 2006;Dav´e et al. 2006; Wyithe & Cen 2007; Pieri & Martel 2007;Yoshida et al. 2007; Mu˜noz & Loeb 2011; Du ff y et al. 2014),with di ff erent groups disagreeing significantly in its strength.Global star formation histories of our three fiducial simulationsets as well as the high resolution run are B20HR.uv2 shownin Figure 10. No e ff ect of reionization is noticeable in thefigure, in contradiction with some of the previous studies.In order to elucidate that disagreement, we show in Fig-ure 9 the cumulative fraction of molecular gas in halos abovea given mass at several redshifts. There is always at least a M vir [M fl ] f H ( > M v i r ) , f ga s / f un i z =6 z =7 z =8 z =9 z =10 F ig . 9.— Average gas fractions (dotted lines - the same as shown in Fig. 7)and cumulative molecular gas fractions in halos above a certain mass (solidlines) for the high resolution run B20HR.uv2 at several redshifts. Notice thathalos a ff ected by reionization contain little molecular gas and, hence, formno stars. decade in mass di ff erence between the halos that are a ff ectedby reionization and halos that contain substantial amount ofmolecular gas. Since our model for star formation is cruciallybased on the (observationally motivated) paradigm that starsform primarily in the molecular gas, the negligible back re-action on the star formation in early galaxies is naturally ex-plained by the large di ff erence in the two mass scales.As a side note, we recall that our fiducial runs and the highresolution run B20HR.uv2 both reproduce observed galaxyUV luminosity functions at all redshifts z (cid:38) ff erat z ≈
10 (Fig. 8) by more than the claimed observational er-rorbars from Bouwens et al. (2014). Hence, we conclude thatthe observational determination of the global star formationhistory is based on the assumptions that do not always hold,and, hence, the systematic errors of such determinations aresubstantially larger than the formal statistical errors at z > ff ecting the global star formation history in anysignificant way, reionization may still leave more subtle sig-natures in the properties of early galaxies. For example, thesensitivity of the faint end slope of the galaxy luminosity func-tion to the reionization history has been proposed as an impor-tant science goal for JWST (Gardner et al. 2006a). To explorethe feasibility of such a test, we show in Figure 10 galaxy lu-minosity functions for the three fiducial simulation sets withvarying ionizing emissivity. In this case the e ff ect of reion-ization is detectable, although it is not large. As the bottompanel of Fig. 10 shows, a factor of two variation in the ioniz-ing emissivity (which corresponds to about ∆ z ≈ . (cid:15) UV = . M (cid:38) −
17, although at brighter magnitudes the di ff erencerapidly disappears. This variation is likely to be too small tobe usable as a constraint on the reionization history. CONCLUSIONS
We present reionization history and global characteristicsof the reionization process from a suite of recent numericalsimulations performed as part of the Cosmic Reionization OnComputers (CROC) project. CROC simulations reproduce theobserved evolution of the galaxy UV luminosity function be- -9 -8 -7 -6 -5 -4 -3 -2 -1 − z φ ( M ) [ M p c − m ag − ] z ≈ z ≈ z ≈ z ≈ z ≈ z ≈ † UV =0 . † UV =0 . † UV =0 .
22 20 18 16 14 12 M φ / φ R E F F ig . 10.— Top: ultraviolet galaxy luminosity functions for the three simu-lation sets with varied ionizing intensity at 6 di ff erent redshifts (as shown inthe legend). Circles with error-bars are a compilation of recent observationalmeasurements (Bouwens et al. 2007, 2011; Oesch et al. 2012; Bradley et al.2012; Schenker et al. 2013; Willott et al. 2013; Oesch et al. 2013a; Bowleret al. 2013; Oesch et al. 2013b). Di ff erent redshifts are shifted vertically by 1dex for clarity. Bottom: di ff erences between simulation sets with (cid:15) UV = . (cid:15) UV = . (cid:15) UV = .
2. Black dashed lines show the variation in the faint-end slope by ± . tween z =
10 and z = α forest at 5 < z <
6, we need toset the ionizing emissivity parameter (cid:15) UV (that measures theescape fraction up to the resolution limit of our simulations)to just under (cid:15) UV = .
2. However, as we also emphasized inPaper I, cosmic variance increases sharply with redshift, andat z > ∆ z ≈ .
15 is extraordinary wide at z >
6, but even at z < τ GP distribution retains a relatively long tail towards highvalues.The distributions of ionized and neutral bubbles duringmost of cosmic reionization is approximately flat, meaningthat it is roughly equally likely for a random place of the uni-verse to be in a large or a small bubble. We find good numeri-cal convergence in bubble sizes down to z ∼
7, at which pointthe finite sizes of our simulation boxes start biasing the dis-tribution of ionized bubbles. That result illustrates the impor-tance of achieving consistent numerical resolution betweenthe gas dynamic solver and the radiative transfer solver - themismatch between the two resolution likely results in erro-neous over-propagation of ionizing radiation beyond the fewmean free path lengths. We show that the equivalent width of the damping wingof Ly α absorption increases rapidly from mellow values of D EW ∼
100 km / s at z = D EW ∼ / s by z =
7. While D EW serves only as a rough proxy for the sup-pression of galaxy Ly α emission line by the neutral IGM infront of it, this result is generally consistent with the observedsharp decline in the fraction of Ly α emitting galaxies at z = z =
6. We also confirm conclusions from theprevious simulation and analytical work that such suppressioncorresponds to substantial, but not dominant volume weightedneutral fraction of about 0.2.While our results on the reionization history are in goodagreement with most of prior studies, we find little back re-action of reionization on the properties of early galaxies. Be-cause galaxies that are a ff ected by photoionization contain lit-tle molecular gas (and, hence, star formation), we find thatthe global star formation history is insensitive to the reioniza-tion history, i.e. the “Barkana & Loeb” e ff ect does not exist. Amore subtle e ff ect of reionization is in modifying the faint endslope of the galaxy UV luminosity function, but such a mod-ification is rather small (change in the slope of about 0.1 fora unit shift in the redshift of reionization). Since predictingthe faint end slope to such precision theoretically would beextremely challenging, we conclude that, unfortunately, mea-suring the faint end slope by JWST will not be a useful con-straint on reionization, contrary to expectations (Gardner et al.2006b).One observational constraint that we have ignored so far isthe optical depth to Thompson scattering from the CMB ob-servations by the WMAP mission. While the history of
WMAP measurements of the Thompson optical depth is rocky, thelatest value from the 9-year
WMAP data is 0 . ± .
014 (or0 . ± .
012 if other data are included in a joint fit, Bennettet al. 2013; Hinshaw et al. 2013). The value we get for fidu-cial sets B20.uv2 and B40.uv1 is 0 . ± . . ± . σ level) consistent with the WMAP values.A large portion, if not all, of this discrepancy is due to in-complete numerical convergence of our simulations. In PaperI we compared our fiducial runs (an equivalent of 512 parti-cles in a 20 h − Mpc box) with a single higher mass resolutionrun B20HR.uv2 that we were able to complete (an equivalentof 1024 particles in a 20 h − Mpc box). While numerical con-verge tests indicate that our fiducial runs account for 55% ofall ionizing photons, the higher reslution B20HR.uv2 run ac-counts for 80% of them. As the result, the Thompson opticaldepth raises to 0.067 in that run. Simple linear extrapolationto the limit of 100% of ionizing radiation gives a value of 0.08for the Thompson optical depth, fully consistent with the cur-rent observational measurements.Whether incomplete numerical convergence is, indeed, afull story will have to wait for more powerful computers,however, as at present we are unable to run the whole en-semble of higher mass resolution simulations - for example, ahigher mass resolution equivalent of our planned 80 h − Mpcrun would have 4096 particles and will require of order of200 million CPU hours, the amount not currently feasible toobtain for this kind of work.We are grateful to George Becker for valuable commentson the early draft of this paper.Simulations used in this work have been performed onthe Joint Fermilab - KICP cluster “Fulla” at Fermilab, onthe University of Chicago Research Computing Center clus-ter “Midway”, and on National Energy Research Supercom- puting Center (NERSC) supercomputers “Hopper” and “Edi-son”. REFERENCESAhn, K., Iliev, I. T., Shapiro, P. R., Mellema, G., Koda, J., & Mao, Y. 2012,ApJ, 756, L16Alvarez, M. A. & Abel, T. 2007, MNRAS, 380, L30—. 2012, ApJ, 747, 126Aubert, D. & Teyssier, R. 2010, ApJ, 724, 244Ba˜nados, E., Venemans, B. P., Morganson, E., Decarli, R., Walter, F.,Chambers, K. C., Rix, H., Farina, E. P., Fan, X., Jiang, L., McGreer, I., DeRosa, G., Simcoe, R., Weiß, A., Price, P. A., Morgan, J. S., Burgett, W. S.,Greiner, J., Kaiser, N., Kudritzki, R.-P., Magnier, E. A., Metcalfe, N.,Stubbs, C. W., Sweeney, W., Tonry, J. L., Wainscoat, R. J., & Waters, C.2014, ArXiv e-printsBarkana, R. & Loeb, A. 2000, ApJ, 539, 20—. 2006, MNRAS, 371, 395Battaglia, N., Trac, H., Cen, R., & Loeb, A. 2013, ApJ, 776, 81Bennett, C. L., Larson, D., Weiland, J. L., Jarosik, N., Hinshaw, G.,Odegard, N., Smith, K. M., Hill, R. S., Gold, B., Halpern, M., Komatsu,E., Nolta, M. R., Page, L., Spergel, D. N., Wollack, E., Dunkley, J.,Kogut, A., Limon, M., Meyer, S. S., Tucker, G. S., & Wright, E. L. 2013,ApJS, 208, 20Bouwens, R. J., Illingworth, G. D., Franx, M., & Ford, H. 2007, ApJ, 670,928Bouwens, R. J., Illingworth, G. D., Oesch, P. A., Labb´e, I., Trenti, M., vanDokkum, P., Franx, M., Stiavelli, M., Carollo, C. M., Magee, D., &Gonzalez, V. 2011, ApJ, 737, 90Bouwens, R. J., Illingworth, G. D., Oesch, P. A., Trenti, M., Labbe’, I.,Bradley, L., Carollo, M., van Dokkum, P. G., Gonzalez, V., Holwerda, B.,Franx, M., Spitler, L., Smit, R., & Magee, D. 2014, ArXiv e-printsBowler, R. A. A., Dunlop, J. S., McLure, R. J., Rogers, A. B., McCracken,H. J., Milvang-Jensen, B., Furusawa, H., Fynbo, J. P. U., Taniguchi, Y.,Afonso, J., Bremer, M. N., & Le Fevre, O. 2013, ArXiv e-printsBradley, L. D., Trenti, M., Oesch, P. A., Stiavelli, M., Treu, T., Bouwens,R. J., Shull, J. M., Holwerda, B. W., & Pirzkal, N. 2012, ApJ, 760, 108Caruana, J., Bunker, A. J., Wilkins, S. M., Stanway, E. R., Lacy, M., Jarvis,M. J., Lorenzoni, S., & Hickey, S. 2012, MNRAS, 427, 3055Caruana, J., Bunker, A. J., Wilkins, S. M., Stanway, E. R., Lorenzoni, S.,Jarvis, M. J., & Elbert, H. 2013, ArXiv e-printsChoudhury, T. R. & Ferrara, A. 2005, MNRAS, 361, 577—. 2006, MNRAS, 371, L55Croft, R. A. C. & Altay, G. 2008, MNRAS, 388, 1501Dav´e, R., Finlator, K., & Oppenheimer, B. D. 2006, MNRAS, 370, 273Dillon, J. S., Liu, A., Williams, C. L., Hewitt, J. N., Tegmark, M., Morgan,E. H., Levine, A. M., Morales, M. F., Tingay, S. J., Bernardi, G.,Bowman, J. D., Briggs, F. H., Emrich, D., Mitchell, D. A., Oberoi, D.,Prabu, T., Wayth, R., & Webster, R. L. 2013, ArXiv e-printsDu ff y, A. R., Wyithe, J. S. B., Mutch, S. J., & Poole, G. B. 2014, ArXive-printsFan, X., Strauss, M. A., Becker, R. H., White, R. L., Gunn, J. E., Knapp,G. R., Richards, G. T., Schneider, D. P., Brinkmann, J., & Fukugita, M.2006, AJ, 132, 117Friedrich, M. M., Mellema, G., Alvarez, M. A., Shapiro, P. R., & Iliev, I. T.2011, MNRAS, 413, 1353Furlanetto, S. R., Hernquist, L., & Zaldarriaga, M. 2004, MNRAS, 354, 695Furlanetto, S. R., McQuinn, M., & Hernquist, L. 2006, MNRAS, 365, 115Furlanetto, S. R. & Oh, S. P. 2005, MNRAS, 363, 1031Gardner, J. P., Mather, J. C., Clampin, M., Doyon, R., Greenhouse, M. A.,Hammel, H. B., Hutchings, J. B., Jakobsen, P., Lilly, S. J., Long, K. S.,Lunine, J. I., McCaughrean, M. J., Mountain, M., Nella, J., Rieke, G. H.,Rieke, M. J., Rix, H.-W., Smith, E. P., Sonneborn, G., Stiavelli, M.,Stockman, H. S., Windhorst, R. A., & Wright, G. S. 2006a,Space Sci. Rev., 123, 485—. 2006b, Space Sci. Rev., 123, 485Gnedin, N. Y. 2000, ApJ, 535, 530—. 2014, submittedGnedin, N. Y., Kravtsov, A. V., & Rudd, D. H. 2011, ApJS, 194, 46G´orski, K. M., Hivon, E., Banday, A. J., Wandelt, B. D., Hansen, F. K.,Reinecke, M., & Bartelmann, M. 2005, ApJ, 622, 759 Hinshaw, G., Larson, D., Komatsu, E., Spergel, D. N., Bennett, C. L.,Dunkley, J., Nolta, M. R., Halpern, M., Hill, R. S., Odegard, N., Page, L.,Smith, K. M., Weiland, J. L., Gold, B., Jarosik, N., Kogut, A., Limon, M.,Meyer, S. S., Tucker, G. S., Wollack, E., & Wright, E. L. 2013, ApJS,208, 19Hu, E. M., Cowie, L. L., Barger, A. J., Capak, P., Kakazu, Y., & Trouille, L.2010, ApJ, 725, 394Hutter, A., Dayal, P., Partl, A. M., & M¨uller, V. 2014, ArXiv e-printsIliev, I. T., Mellema, G., Ahn, K., Shapiro, P. R., Mao, Y., & Pen, U.-L.2014, MNRASIliev, I. T., Mellema, G., Pen, U.-L., Merz, H., Shapiro, P. R., & Alvarez,M. A. 2006, MNRAS, 369, 1625Iliev, I. T., Pen, U.-L., McDonald, P., Shapiro, P. R., Mellema, G., &Alvarez, M. A. 2009, Ap&SS, 320, 39Iliev, I. T., Shapiro, P. R., & Raga, A. C. 2005, MNRAS, 361, 405Kashikawa, N., Shimasaku, K., Matsuda, Y., Egami, E., Jiang, L., Nagao, T.,Ouchi, M., Malkan, M. A., Hattori, T., Ota, K., Taniguchi, Y., Okamura,S., Ly, C., Iye, M., Furusawa, H., Shioya, Y., Shibuya, T., Ishizaki, Y., &Toshikawa, J. 2011, ApJ, 734, 119Kaurov, A. A. & Gnedin, N. Y. 2013, ApJ, 771, 35Kravtsov, A. V. 1999, PhD thesis, New Mexico State UniversityKravtsov, A. V., Klypin, A., & Ho ff man, Y. 2002, ApJ, 571, 563Kuhlen, M. & Faucher-Gigu`ere, C.-A. 2012, MNRAS, 423, 862Lee, K.-G., Cen, R., Gott, III, J. R., & Trac, H. 2008, ApJ, 675, 8McQuinn, M., Lidz, A., Zahn, O., Dutta, S., Hernquist, L., & Zaldarriaga,M. 2007, MNRAS, 377, 1043Mesinger, A. & Furlanetto, S. 2007, ApJ, 669, 663Mesinger, A., Furlanetto, S., & Cen, R. 2011, MNRAS, 411, 955Miralda-Escude, J. 1998, ApJ, 501, 15Mitra, S., Choudhury, T. R., & Ferrara, A. 2011, MNRAS, 413, 1569—. 2012, MNRAS, 419, 1480Mu˜noz, J. A. & Loeb, A. 2011, ApJ, 729, 99Norman, M. L., Reynolds, D. R., So, G. C., & Harkness, R. P. 2013, ArXive-printsOesch, P. A., Bouwens, R. J., Illingworth, G. D., Gonzalez, V., Trenti, M.,van Dokkum, P. G., Franx, M., Labb´e, I., Carollo, C. M., & Magee, D.2012, ApJ, 759, 135Oesch, P. A., Bouwens, R. J., Illingworth, G. D., Labb´e, I., Franx, M., vanDokkum, P. G., Trenti, M., Stiavelli, M., Gonzalez, V., & Magee, D.2013a, ApJ, 773, 75Oesch, P. A., Bouwens, R. J., Illingworth, G. D., Labbe, I., Smit, R., vanDokkum, P. G., Momcheva, I., Ashby, M. L. N., Fazio, G. G., Huang, J.,Willner, S. P., Gonzalez, V., Magee, D., Trenti, M., Brammer, G. B.,Skelton, R. E., & Spitler, L. R. 2013b, ArXiv e-printsOkamoto, T., Gao, L., & Theuns, T. 2008, MNRAS, 390, 920Ono, Y., Ouchi, M., Mobasher, B., Dickinson, M., Penner, K., Shimasaku,K., Weiner, B. J., Kartaltepe, J. S., Nakajima, K., Nayyeri, H., Stern, D.,Kashikawa, N., & Spinrad, H. 2012, ApJ, 744, 83Ouchi, M., Shimasaku, K., Furusawa, H., Saito, T., Yoshida, M., Akiyama,M., Ono, Y., Yamada, T., Ota, K., Kashikawa, N., Iye, M., Kodama, T.,Okamura, S., Simpson, C., & Yoshida, M. 2010, ApJ, 723, 869Parsons, A. R., Liu, A., Aguirre, J. E., Ali, Z. S., Bradley, R. F., Carilli,C. L., DeBoer, D. R., Dexter, M. R., Gugliucci, N. E., Jacobs, D. C.,Klima, P., MacMahon, D. H. E., Manley, J. R., Moore, D. F., Pober, J. C.,Stefan, I. I., & Walbrugh, W. P. 2013, ArXiv e-printsPentericci, L., Fontana, A., Vanzella, E., Castellano, M., Grazian, A.,Dijkstra, M., Boutsia, K., Cristiani, S., Dickinson, M., Giallongo, E.,Giavalisco, M., Maiolino, R., Moorwood, A., Paris, D., & Santini, P.2011, ApJ, 743, 132Pieri, M. M. & Martel, H. 2007, ApJ, 662, L7Robertson, B. E., Furlanetto, S. R., Schneider, E., Charlot, S., Ellis, R. S.,Stark, D. P., McLure, R. J., Dunlop, J. S., Koekemoer, A., Schenker,M. A., Ouchi, M., Ono, Y., Curtis-Lake, E., Rogers, A. B., Bowler,R. A. A., & Cirasuolo, M. 2013, ApJ, 768, 71Rudd, D. H., Zentner, A. R., & Kravtsov, A. V. 2008, ApJ, 672, 19Schenker, M. A., Robertson, B. E., Ellis, R. S., Ono, Y., McLure, R. J.,Dunlop, J. S., Koekemoer, A., Bowler, R. A. A., Ouchi, M., Curtis-Lake,E., Rogers, A. B., Schneider, E., Charlot, S., Stark, D. P., Furlanetto,S. R., & Cirasuolo, M. 2013, ApJ, 768, 196man, Y. 2002, ApJ, 571, 563Kuhlen, M. & Faucher-Gigu`ere, C.-A. 2012, MNRAS, 423, 862Lee, K.-G., Cen, R., Gott, III, J. R., & Trac, H. 2008, ApJ, 675, 8McQuinn, M., Lidz, A., Zahn, O., Dutta, S., Hernquist, L., & Zaldarriaga,M. 2007, MNRAS, 377, 1043Mesinger, A. & Furlanetto, S. 2007, ApJ, 669, 663Mesinger, A., Furlanetto, S., & Cen, R. 2011, MNRAS, 411, 955Miralda-Escude, J. 1998, ApJ, 501, 15Mitra, S., Choudhury, T. R., & Ferrara, A. 2011, MNRAS, 413, 1569—. 2012, MNRAS, 419, 1480Mu˜noz, J. A. & Loeb, A. 2011, ApJ, 729, 99Norman, M. L., Reynolds, D. R., So, G. C., & Harkness, R. P. 2013, ArXive-printsOesch, P. A., Bouwens, R. J., Illingworth, G. D., Gonzalez, V., Trenti, M.,van Dokkum, P. G., Franx, M., Labb´e, I., Carollo, C. M., & Magee, D.2012, ApJ, 759, 135Oesch, P. A., Bouwens, R. J., Illingworth, G. D., Labb´e, I., Franx, M., vanDokkum, P. G., Trenti, M., Stiavelli, M., Gonzalez, V., & Magee, D.2013a, ApJ, 773, 75Oesch, P. A., Bouwens, R. J., Illingworth, G. D., Labbe, I., Smit, R., vanDokkum, P. G., Momcheva, I., Ashby, M. L. N., Fazio, G. G., Huang, J.,Willner, S. P., Gonzalez, V., Magee, D., Trenti, M., Brammer, G. B.,Skelton, R. E., & Spitler, L. R. 2013b, ArXiv e-printsOkamoto, T., Gao, L., & Theuns, T. 2008, MNRAS, 390, 920Ono, Y., Ouchi, M., Mobasher, B., Dickinson, M., Penner, K., Shimasaku,K., Weiner, B. J., Kartaltepe, J. S., Nakajima, K., Nayyeri, H., Stern, D.,Kashikawa, N., & Spinrad, H. 2012, ApJ, 744, 83Ouchi, M., Shimasaku, K., Furusawa, H., Saito, T., Yoshida, M., Akiyama,M., Ono, Y., Yamada, T., Ota, K., Kashikawa, N., Iye, M., Kodama, T.,Okamura, S., Simpson, C., & Yoshida, M. 2010, ApJ, 723, 869Parsons, A. R., Liu, A., Aguirre, J. E., Ali, Z. S., Bradley, R. F., Carilli,C. L., DeBoer, D. R., Dexter, M. R., Gugliucci, N. E., Jacobs, D. C.,Klima, P., MacMahon, D. H. E., Manley, J. R., Moore, D. F., Pober, J. C.,Stefan, I. I., & Walbrugh, W. P. 2013, ArXiv e-printsPentericci, L., Fontana, A., Vanzella, E., Castellano, M., Grazian, A.,Dijkstra, M., Boutsia, K., Cristiani, S., Dickinson, M., Giallongo, E.,Giavalisco, M., Maiolino, R., Moorwood, A., Paris, D., & Santini, P.2011, ApJ, 743, 132Pieri, M. M. & Martel, H. 2007, ApJ, 662, L7Robertson, B. E., Furlanetto, S. R., Schneider, E., Charlot, S., Ellis, R. S.,Stark, D. P., McLure, R. J., Dunlop, J. S., Koekemoer, A., Schenker,M. A., Ouchi, M., Ono, Y., Curtis-Lake, E., Rogers, A. B., Bowler,R. A. A., & Cirasuolo, M. 2013, ApJ, 768, 71Rudd, D. H., Zentner, A. R., & Kravtsov, A. V. 2008, ApJ, 672, 19Schenker, M. A., Robertson, B. E., Ellis, R. S., Ono, Y., McLure, R. J.,Dunlop, J. S., Koekemoer, A., Bowler, R. A. A., Ouchi, M., Curtis-Lake,E., Rogers, A. B., Schneider, E., Charlot, S., Stark, D. P., Furlanetto,S. R., & Cirasuolo, M. 2013, ApJ, 768, 196