Dark Matter 2016 UCLA's 12th Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe
ΛCDM cosmology: successes, challenges, and opportunities for progress Joel Primack, UC Santa Cruz
Successes: CMB, Expansion History, Large Scale Structure Challenges: Cusp-Core, Too Big To Fail, Satellite Galaxies Opportunities for Progress Now: Halo Substructure by GalaxiesGravitational Lensing and Stellar Motions, Early GalaxiesGalaxies, Reionization, Galaxies in the Cosmic Web This series of conferences started in 1992 In my talk at the February 1992 conference at UCLA, I reported on research with my former PhD student Jon Holtzman (now chair of the NMSU Astronomy Department). Holtzman used and improved the code that George Blumenthal and I had written to calculate the linear power spectrum for CDM for our Blumenthal, Faber, Primack, & Rees 1984 Nature paper, “Formation of Galaxies and Large Scale Structure with Cold Dark Matter.” In his 1989 dissertation, Holtzman calculated 96 variants of CDM, and then he and I compared the predictions with all the available large scale data such as galaxy distributions and velocities and galaxy cluster abundance. In February 1992, I reported that the available data favored two models in particular,
Cold + Hot DM (with ΩCDM = 0.8 and Ων = 0.2) and ΛCDM (with ΩCDM = 0.3 and ΩΛ = 0.7, the current values).
At Aspen in summer 1992, UCLA professor Ned Wright told me that he had practically fallen off his chair when I said that, since he had used Holtzman’s thesis results to analyze the COBE DMR data, released April 29, 1992, and he had found that the same two CDM variants were favored. 1992ApJ...396L..13W 1992ApJ...396L..13W
one of two CDM models in our 1984 Nature paper (the other had ΩCDM = 0.2) The other two favored CDM variants were
Cold + Hot DM (with ΩCDM = 0.8 and Ων = 0.2) ΛCDM (with ΩCDM = 0.3 and ΩΛ = 0.7, the current values). ΛCDM won with the 1998 discovery of accelerated expansion and high-z galaxies. Matter and Energy Content of the Universe
Imagine that the entire universe is an ocean of dark energy. On that ocean sail billions of ghostly ships made of dark matter... Matter and Energy Content of the Dark Universe Matter Ships
on a ΛCDM
Dark Double Energy Dark Ocean Imagine that the entire universe is an ocean of dark Theory energy. On that ocean sail billions of ghostly ships made of dark matter... Planck Collaboration: Cosmological parameters
PlanckPlanck Collaboration: Collaboration: The ThePlanckPlanckmissionmission Planck Collaboration: The Planck mission 6000 6000 Angular scale 5000 90 500018 1 0.2 0.1 0.07 Planck Collaboration: The Planck mission
European 6000 ] 4000 2
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D 2000 2000Theory
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] 4000 2 Cosmic 0 0 PLANCK 600 Variance600 60
µ K 60
[ 3000 300300 30 TT 30 TT 0 0 Satellite D 0 0 D D Fig. 7. Maximum posterior CMB intensity map at 50 resolution derived from the joint baseline-30 analysis of Planck, WMAP, and
-300 -300 408 MHz observations. A small strip of the Galactic plane, 1.6 % of the sky, is filled in by-30 a constrained realization that has the same statistical properties as the rest of the sky. 2000 -600 -60-60 Data -600 Temperature-Temperature 22 1010 3030 500500 10001000 15001500 20002000 25002500 Released 1000The Planck 2015 temperature power spectrum. At multipoles ` 30 we show the maximum likelihood frequency averaged Fig.Fig.Fig. 9. 9. 10.ThePlanckPlanck TT2015power temperature spectrum. power The points spectrum. in the At upper multipoles panel show` 30 the we maximum-likelihood show the maximum estimateslikelihood of frequency the primary averaged CMB temperature spectrum computed from the Plik cross-half-mission likelihood with foreground and other nuisance parameters deter- temperaturespectrum computed spectrum{ as computed described from in the the textPlik forcross-half-mission the best-fit foreground likelihood and nuisance with foreground parameters and of other the Planck nuisance+WP parameters+highL fit deter- listed February 9, mined from the MCMC analysis of the base ⇤CDM cosmology. In the multipole range 2 ` 29, we plot the power spectrum minedin Table from5. The the red MCMC line shows analysis the of best-fit the base base⇤⇤CDMCDM cosmology. spectrum. The In the lower multipole panel shows range the 2 residuals` 29, with we plot respect the powerto the theoretical spectrum 2015 estimatesestimates from the Commander component-separationcomponent-separation algorithm algorithm computed computed over over 94 94 % % of of the the sky. sky. The The best-fit best-fit base base⇤CDM⇤CDM theoretical theoretical spectrummodel. The fitted0 error to barsthe Planck are computedTT+lowP from likelihood the full covariance is plotted in matrix, the upper appropriately panel. Residuals weighted with across respect each to band this (see model Eqs. are36a shownand in spectrum fitted to the Planck TT+lowP likelihood is plotted in the upperFig. 8. Maximum panel. posterior Residuals amplitude Stokes Q ( withleft) and U ( respectright) maps derived to from thisPlanck observations model between are 30 and shown 353 GHz. in 36b), and include2 beam uncertainties10 and50 uncertainties500 in the foregroundThese1000 model mapS have been parameters. highpass-filtered with1500 a cosine-apodized filter between ` = 202000 and 40, and the a 17 % region of the Galactic2500 thethe lower lower panel. The error error bars bars show show 11 uncertainties.uncertainties. From FromPlanckPlanck Collaborationplane Collaboration has been replaced with a XIII constrained XIII( Gaussian2015(2015 realization). ). (Planck Collaboration IX 2015). From Planck Collaboration X ±± Multipole moment,(2015). viewed as work in progress. Nonetheless, we find a high level of 8.2.2. Number of modes consistency in results between the TT and the full TT+TE+EE likelihoods. Furthermore, the cosmological parameters (which One way of assessing the constraining power contained in a par- 100 ticular measurement of CMB anisotropies is to determine the 140 do not depend strongly on ⌧) derived from the TE spectra have comparable errors to the TT-derived parameters, and they are e↵ective number of a`m modes that have been measured. This
The temperature angular power spectrum of the primary CMB from Planck] , showing a precise measurement of seven acoustic peaks,/ that Fig. 19. consistent to within typically 0.5 or better. Polarization-is equivalent to estimatingPolarization 2 times the square of the total S N
Temperature-Polarization 2 are well fit by a simple six-parameter ⇤CDM theoretical model (the model plotted80 is the one labelled [Planck+WPin the power+highL] spectra, a measure in Planck that contains all Collaborationthe available ] 70 2 XVI (2013)). The shaded area around the best-fit curve represents cosmic variance,µ K 16 including the sky cut used. The error bars on individual points 60
also include cosmic variance. The horizontal axis is logarithmic up to ` = 50, 5 and linear beyond. The vertical scale is `(` + 1)Cl/2⇡. The measured [ µ K 0
spectrum shown here is exactly the same as the one shown in Fig. 1 of Planck[10 Collaboration40 XVI (2013), but it has been rebinned to show better TE the low-` ` region. D EE -70 ` 20 Double Dark Theory C 0 Double Dark Theory -140 Angular scale tected by Planck over the entire sky, and which therefore con- 9010 18 1 0.2 0.1 tains both4 Galactic and extragalactic objects. No polarization in- EE `
6000TE ` 0 formation0 is provided for the sources at this time. The PCCS C 5000 D -10 di↵ers-4 from the ERCSC in its extraction philosophy: more e↵ort has been made on the completeness of the catalogue, without re- 30 500 1000 1500 2000 30 500 1000 1500 2000
] 4000 ducing notably the reliability of the detected sources, whereas 2 ` the ERCSC was built in the spirit of` releasing a reliable catalog µ K
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Fig. 10. Frequency-averaged TE (left) and EE (right) spectra (withoutsuitable fitting for quick for T– follow-upP leakage). (in The particular theoretical withTE theand short-livedEE spectra Fig.Fig. 10. 11.Frequency-averagedPlanck T E (left) andTEEE(leftspectra) and (right)EE (right computed) spectra as (withoutdescribed fitting in the for text.T– TheP leakage). red lines The show theoretical the polarizationTE and spectraEE spectra from plottedD in the upper panel of each plot are computed from the best-fitHerschel modeltelescope). of Fig. 9. Residuals The greater with amount respect of to data, this theoretical di↵erent selec- model plottedthe2000 base in⇤ theCDM upperPlanck panel+ ofWP each+highL plot aremodel, computedwhich from is fitted the to best-fit the TT model data only of Fig.. 9. Residuals with respect to this theoretical model areare shown shown in the lower panel panel in in each each plot. plot. The The error error bars bars show show 1tion 1 errors. processerrors. The The and green thegreen improvementslines lines in inthe the lower lower in thepanels panels calibration show show the and the best-fit map-best-fit temperature-to-polarization leakage model, fitted separately to the±± TE and EE spectra. From Planck Collaboration XIII (2015). temperature-to-polarization1000 leakage model, fitted separately to the makingTE and EE processingspectra. (references)From Planck help Collaboration the PCCS XIII to( improve2015). the performance (in depth and numbers) with respect to the previ- 0 2 10 50 500 1000 1500 2000 ous ERCSC. 4 cosmologicalcosmological informationMultipole if if we we assume assumemoment, that that the the anisotropies anisotropies are are andandThe 96 96 000 sources 000 modes, modes, were respectively. respectively. extracted4 fromFromFrom the this 2013 this perspective perspectivePlanck thefrequency the2015 2015 purelypurely Gaussian Gaussian (and hence hence ignore ignore all all non-Gaussian non-Gaussian informa- informa- mapsPlanckPlanck (Sect.datadata 6), constrain constrain which approximatelyinclude approximately data acquired 55 %55 more % over more modes more modes than than intwo in Fig.tiontion 20. coming comingThe temperature from lensing, angular the the power CIB, CIB, cross-correlations cross-correlationsspectrum of the CMB, with with other esti- other skythethe coverages.2013 2013 release. release. This Of Of implies course course this that this is the not is flux not the thedensities whole whole story, of story, most since since of matedprobes,probes, from etc.). etc.). the SMICA CarryingPlanck out outmap. this this procedure The procedure model for plotted for the the isPlanckPlanck the one20132013 la- somesome pieces pieces of of information information are are more more valuable valuable than than others, others, and and TT power spectrum data provided in Planck Collaboration XV thein sources fact Planck are anis able average to place of three considerably or more tighter di↵erent constraints observa- on belledTT [Planckpower+ spectrumWP+highL] data in provided Planck Collaboration in Planck Collaboration XVI (2013). The XV tionsin fact overPlanck a periodis able of to 15.5 place months. considerably The tighterMexican constraints Hat Wavelet on shaded((20142014 area)) and and aroundPlanck the Collaboration best-fit curve XVI represents XVI((20142014 cosmic),), yields yields variance, the the number number in- particularparticular parameters parameters (e.g., (e.g., reionization reionization optical optical depth depth or certain or certain 24 algorithm (Lopez-Caniego´ et al. 2006) has been selected as the cluding826826 000 000 the sky (which (which cut used. includes The error the the e ebars↵↵ectsects on of ofindividual instrumental instrumental points noise, do noise, not cos- in- cos- mic variance and masking). The 2015 TT data have increased baseline4 method for the production of the PCCS. However, one cludemic cosmic variance variance. and masking). The horizontal The axis 2015 is logarithmicTT data have up to increased` = 50, 4HereHere we we have have used used the the basic basic (and (and conservative) conservative) likelihood; likelihood; more more this value to 1 114 000, with TE and EE adding a further 60 000 additional methods, MTXF (Gonzalez-Nuevo´ et al. 2006) was andthis linear value beyond. to 1 114 The 000, vertical with scaleTE and is `EE(` +adding1)Cl/2 a⇡ further. The binning 60 000 modesmodes are are e↵ eectively↵ectively probed probed by byPlanckPlanckif oneif one includes includes larger larger sky skyfrac- frac- scheme is the same as in Fig. 19. implementedtions.tions. in order to support the validation and characteriza- tion of the PCCS.
8.1.1. Main catalogue The source selection for the PCCS is made on the basis17 of17 Signal-to-Noise Ratio (SNR). However, the properties of the The Planck Catalogue of Compact Sources (PCCS, Planck background in the Planck maps vary substantially depending on Collaboration XXVIII (2013)) is a list of compact sources de- frequency and part of the sky. Up to 217 GHz, the CMB is the
27 Planck 2015 XIII Cosmology Conclusions The six-parameter base ΛCDM model continues to provide a very good match to the more extensive 2015 Planck data, including polarization. This is the most important conclusion of this paper. The Planck TT, TE, and EE spectra are accurately described with a purely adiabatic spectrum of fluctuations with a spectral tilt ns = 0.968 ± 0.006, consistent with the predictions of single-field inflationary models. Combining the Planck and BICEP2/Keck/ Planck likelihoods, we find a tight constraint on tensor modes r0.002 < 0.09, strongly disfavouring inflationary models with V(φ) ~ φ2. The Planck best-fit base ΛCDM cosmology is in good agreement with results from BAO surveys, with the recent JLA sample of Type Ia SNe, and with the recent analysis of redshift-space distortions of the BOSS CMASS-DR11.
The Hubble constant in this cosmology is H0 = (67.8 ± 0.9) km s−1Mpc−1. Dark energy is constrained to w = −1.006 ± 0.045 and is therefore compatible with a cosmological constant, as assumed in the base ΛCDM cosmology.
Combining Planck TT+lowP+lensing with BAO we find Neff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value Neff = 3.046 of the standard model. The sum of neutrino masses is constrained to ∑mν < 0.23 eV. The standard theory of big bang nucleosynthesis is in excellent agreement with Planck data and observations of primordial light element abundances. The analysis of 2015 Planck data reported in Planck Collaboration XVII (2015) sets unprecedentedly tight limits on primordial non-Gaussianity. If there is new physics beyond base ΛCDM, then the corresponding observational signatures in the CMB are weak and difficult to detect. This is the legacy of the Planck mission for cosmology. Aquarius Simulation Volker Springel
Milky Way 100,000 Light Years
Milky Way Dark Matter Halo 1,500,000 Light Years 8
Bolshoi Cosmological Simulation Anatoly Klypin & Joel Primack NASA Ames Research Center 8.6x109 particles 1 kpc resolution
1 Billion Light Years Bolshoi-Planck Cosmological Simulation Anatoly Klypin & Joel Primack NASA Ames Research Center 8.6x109 particles 1 kpc resolution Halo Demographics with Planck Parameters 9 Halo and Subhalo Demographics with Planck Cosmological Parameters: Bolshoi-PlanckHalo Demographics and MultiDark-Planck with Planck Parameters Simulations9 Aldo Rodrıguez-Puebla, Peter Behroozi, Joel Primack, Anatoly Klypin, Christoph Lee, Doug Hellinger HaloHalo Demographics Demographics with with Planck Planck Parameters Parameters15 15 2 Halo Demographics with Planck Parameters 9 on arXiv today deed, techniques such as subhalo abundance matching and halo occupation distribution models require as inputs the Cosmological Simulations2 Halo Mass Function Mean Cumulative
iue1. Figure ae ovle sue ncosmological in assumed values to pared h bevtospotdaea olw:WMAP5+BAO+SN follows: as are plotted observations The Hnhwe l 09,WMAP7+BAO+ 2009), al. et (Hinshaw 01,WMAP9+eCMB+BAO+ 2011), lnk3W+ih+A Pac olbrto ta.2014) al. et Collaboration (Planck Planck13+WP+highL+BAO n lnk5T,EE+oPlniget(lnkCollabo (Planck Planck15+TT,TE,EE+lowP+lensing+ext and aine l 2015a). al. et ration ie Wto ta.21) akk Sila ta.21) Q 2014), al. et (Skillman DarkSky 2013), al. et (Watson bilee otnu Himn ta.2015), al. et (Heitmann Continuum 05,adBlhiPac n utDr-lnk(Klypin MultiDark-Planck and Bolshoi-Planck and 2015), ta.21)smltos iue1sosteWMAP5/7/9 the shows 1 Figure simulations. 2014) al. et Hnhwe l 03)adPac 03(lnkCollabo- (Planck 2013 Planck and 2013b) al. et (Hinshaw aine l 04 n lnk21 Pac Collaboration (Planck 2015 Planck and 2014) al. et ration ta.21a omlgclparameters cosmological 2015a) al. et halo/subhalo number densities. Furthermore, simplified pre- omlgclprmtr dpe o hs iuain.Th simulations. these for adopted parameters cosmological ilnimsmltosue h rtya WA1 pa- (WMAP1) first-year the used simulations Millennium aees(pre ta.20) h oso,QContinuum, Q Bolshoi, the 2003); al. et (Spergel rameters n uie iuain sdteWA57cosmological WMAP5/7 the used simulations Jubilee and aaees hl the while parameters; sdtePac 03prmtr,adteDrSysimula- DarkSky the and parameters, 2013 Planck the used in sdprmtr ewe MP n lnk2013. Planck and WMAP9 between parameters used tions
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nti ae euethe use we paper this In properties of halos and the galaxies that they host.
nti ae efcso h cln eain fsev- of relations scaling the on focus we paper this In Here we analyze all dark matter halos and subhalos found by Rockstar,anddonotjustfocusonthosethatsat- isfy some criteria for being “relaxed” or otherwise “good,” in contrast to some earlier studies of dark matter halo prop- bevtoa osrit on constraints Observational erties (e.g., Bett et al. 2007; Macci`oet al. 2007; Ludlow et al. 2014). The reason is that all sufficiently massive halos 14 are expected to host galaxies or, for the more massive ones, groups or clusters of galaxies. This paper is an introduction to a series of papers presenting additional analyses of the Bolshoi-Planck and
ν Figure 1. Figure 7. Left Panel:ObservationalThe halo constraints mass function on σ from8 andz =0toΩM com-z =9.RightMultiDark-Planck Panel: Cumulative simulations. halo mass The function. statistics The and various physica solidl
2 Number Density of Halos: Planck / WMAP7 pared to values assumed in cosmological N−body simulations. Figure 18. Mean cumulative number of subhalos of maximum circular velocity V for host halos with maximum velocities Vmax = CadBlhiPac simulations Bolshoi-Planck and GC lines show the fits to the simulations, Equation (25). meaning of halo concentration are discussed in detail in sub Figure 7. Left Panel: The halo massThe observations function plotted from arez as=0to follows:z WMAP5+BAO+SN=9.Right Panel: Cumulative halo massFigure function. 18. Mean The cumulative various solid number of subhalos of maximum circular velocity Vsub for host halos with maximum velocities Vmax = Figure 7. Left Panel: The halo mass function from z =0toz =9.KlypinRight et Panel: al. (2014),Cumulative which is also an200 halo overview, 500 mass, 1000 of the function. and Bolshoi 1580- The kmThere /s various as are a function many solid ofmoreVsub /Vmax for (left panel) Vsub = Vacc,and(right panel) Vsub = Vpeak.Thedotted (Hinshaw et al. 2009), WMAP7+BAO+H (Jarosik et al. 200, 500, 1000 and 1580 km /s as a function of Vsub/Vmax for (left panel) Vsub = Vacc,and(right panel) Vsub = Vpeak.Thedotted lines show the fits to the simulations, Equation (25). 0 Planck and MultiDark-Planck simulations,curve is the including fitting Big-functionhalos Equation with (48). the Planck lines show the fits2011), to the WMAP9+eCMB+BAO+ simulations, EquationH0 (Hinshaw (25). et al. 2013a), −1 curve3 is the fitting function Equation (48). Planck13+WP+highL+BAO (Planck Collaboration et al. 2014), MultiDark simulations in (2.5h Gpc) volumes that we cosmology, especially H and Planck15+TT,TE,EE+lowP+lensing+ext (Planck Collabo- do not discuss here since they are mainly useful for statis- at high masses and 0 ration et al. 2015a). tics of galaxy clusters. The Stellar Halo Accretion Rate Co- evolution (SHARC) assumption—i.e., that the star forma- redshifts.
Hnhwe l 2013a), al. et (Hinshaw
Rockstar tion rate of central galaxies on the main sequence of star
ν We are now releasing bilee (Watson et al. 2013), DarkSky (Skillman et al. 2014), Q formation is proportional to their host halo’s mass accretion 2 2 the halo catalogs and
σ
N C(siaae al. et (Ishiyama GC Continuum (Heitmann et al. 2015), ν GC (Ishiyama et al. rate—was explored in Rodr´ıguez-Puebla et al. (2016), which
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− 2015), and Bolshoi-Planck and MultiDark-Planck (Klypin used abundance matching based on the Bolshoi-Planck sim-
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8 oysimulations. body et al. 2014) simulations. Figure 1 shows the WMAP5/7/9 ulation. That paper showed that SHARC is remarkably con- our new cosmological (Hinshaw et al. 2013b) and Planck 2013 (Planck Collabo- sistent with the observed galaxy star formation rate out to simulations. The paper
Jrske al. et (Jarosik and ration et al. 2014) and Planck 2015 (Planck Collaboration z 4andthatthe 0.3dexdispersioninthehalomass includes Appendices
Ω ∼ ∼ et al. 2015a) cosmological parameters σ8 and ΩM ,andthe accretion rate is consistent with the observed small disper-
aofinder halo with instructions for M cosmological parameters adopted for these simulations. The sion of the star formation rate about the main sequence. The
Ω reading these files. ,andthe Millennium simulations used the first-year (WMAP1) pa- clustering properties of halos and subhalos is the subject of M Rodriguez-Puebla et al. 2016b (in prep.). How properties of ff rameters (Spergel et al. 2003); the Bolshoi, Q Continuum,
csof ects and Jubilee simulations used the WMAP5/7 cosmological dark matter halos vary with the density of their environment com- 2 −1 sas ns parameters; while the ν GC and Bolshoi-Planck simulations on length scales from 0.5 to 16 h Mpc is discussed in Lee used the Planck 2013 parameters, and the DarkSky simula- Figureet al. (2016a, 9. Characteristic in prep.), halo which mass showsMC amongas a function other things of redshift. that
- e , The red solid line shows the numerical solution to Equation (31). rt Figuretions used 15. parameters between WMAP9 and Planck 2013. halos in low-density regions experience lower tidal forces r The ratio of the distinct halo number densites between the Bolshoi-Planck nBP and the Bolshoi nB simulations as a function In this paper we use the Rockstar halo finder Theand dashed have lowerblack line spin shows parameters, our numerical and that fit a to largeMC fractiongiven by Figureof V 8. Amplitudeat z =0, of1, linear2, 4, 6and perturbations,z =8. σ(Mvir), as a func- max Consistent Trees Equationof lower-mass (29). halos in high-density regions are “stripped,” tion of(Behroozi,Mvir.Theredsolidlineshowsthenumericalsolutionto Wechsler & Wu 2013) and Equation(Behroozi (26). The et dashed al. 2013) black to line analyze shows the results fit to the for ampli the- re- i.e. their mass at z =0islessthanthatoftheirprogeni-
ed ehiussc ssbaoaudnemthn and matching abundance subhalo as such techniques deed, aoocpto itiuinmdl eur sipt the inputs as require models distribution occupation halo aosbaonme este.Frhroe ipie pr simplified Furthermore, densities. number halo/subhalo citosfrteeouino akmte aoproperties halo matter dark of evolution the for scriptions r da ol o epeitrse nudrtnigaver understanding in interested people for tools ideal are rpriso ao n h aaista hyhost. they that galaxies the and halos of properties
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§
∼ ∼ − .)adms rwh( growth mass and 3.2) based on the 2013 Planck cosmological parameters (Planck Baldry,of such Glazebrook stripped halos. & Driver Further 2008; papers Baldry comparing et al. 2012) with mean- ob-
eew analyze we Here hsppri nitouto oasre fpapers of series a to introduction an is paper This ingservations that, for someare also reason, in preparation, the star formation along with effi mockciency galaxy in low 4andthatthe Collaboration et al. 2014) and compatible with the Planck hsppri raie sfollows: as organized is paper This halo mass function using the best fit parameters from table Figure 9. Characteristic halo mass MC as a function of redshift. 2015 parameters (Planck Collaboration et al. 2015a). The masscatalogs halos based has been on Bolshoi-Planck. suppressed (e.g. Behroozi, Wechsler & 3. The red solid line shows theFigure numerical 19. Halo solution concentration to Equation as a ( function31). of Mvir at z =0, 1, 2, 4, and 6. The left panel in the figure shows halo concentrations BolshoiP, SMDPL and MDPL simulations are not the ConroyThis 2013b; paper Moster, is organized Naab as & follows: White 2013).2 discusses Nevertheless, the sim- FigureRockstar 10 shows the ratio of the number densities nBP calculatedFigure§ by 19. findingHalo theconcentration scale radius, asR as functionassuming of aM NFWat profilez =0, 1 in, 2 the, 4, and simulation. 6. The Instead, left panel the in right the figure panel shows shows halo Klypin concentrations halo largest of the new high-resolution simulations, but they do measurementsulationsThe dashed and how of blackthe we baryonicdefine line the shows mass halo mass. have our found numerical3describesthe slopes fit as to MC given by vir
V
§ Figure 8. Amplitudeand nB between of linear the perturbations, Bolshoi-Planck andσ(M thevir), Bolshoi as aFigure func- sim- 9. Characteristic halo massconcentrationsMcalculated§as a function fromby finding determining of the redshift. scale the scale radius, radius,Rs assumingRs using the a NFWVmax profileand Mvir inrelationship the simulation. from Instead, the NFW the formulae right p (seeanel text). shows Klypin halo
.)nme este,adtenme fsubha- of number the and densities, number 4.2) max have the advantage that they have been analyzed in great steepkeyEquation as scalingα 1 relations. (29).9(Baldry,Glazebrook&Driver2008). for distinct halos (i.e.,C those that are tion of M .Theredsolidlineshowsthenumericalsolutiontoulations as a function of Mvir from z =0toz =8.The vir detail, and all of these analyses are being madeThe publicly red solidnot subhalos) line∼ shows and gives the figures numerical and fittingconcentrations solution formulas for to max- from Equation determining (31). the scale radius, Rs using the Vmax and Mvir relationship from the NFW formulae (see text). Equation (26).di Thefferentavailable. dashed cosmological In black addition, parameters line in shows this paper imply the we fit that show to at the thez =0,on ampli effects- of imum halo circular velocity ( 3.1), halo mass accretion rates average, there are 12% more Milky-Way mass halos inThe the dashed black line shows§ our numerical fit to4ρMs given by n h tla aso h eta galaxies central the of mass stellar the and tude of perturbationsthe change given from by Equation the WMAP5/7 (29). to the Planck 2013 cosmo- 4.2( 3.2) Subhalo and mass mass growth function ( 3.3). 4discusseshalo(4.1) and C concentrations calculated by determining the scale radius, Figure 8. Amplitude of linear perturbations,∼σ(Mvir), as a func- § § § ρNFW(r)= § 2 . (51) Bolshoi-Plancklogical parameters. than in the Bolshoi simulation. This fractiEquationon (29).subhalohave found ( 4.2) number slopes densities, between andα the number1.4 (r/R1 of.6(Blantonetal.2005; subha-s)(1 + r/R4ρs s) 13 ρ (r)= . (51) Rs usingconcentrations the Vmax and calculatedMvir relationship by determining from the the NFW scale for- radius, z tion of M .Theredsolidlineshowsthenumericalsolutiontoincreases to higher masses, 25% for Mvir 3 10 M⊙. Subhalos can§ lose a significant fraction∼NFW of their− mass due vir ,aIn n dd on this o tj u s tfpaper o c u so nt h we o s et focus h a ts a t - on the scaling relations of sev- los as a function of their host halo mass ( 4.3). 5presents 2 ∼ ∼ × Baldry, Glazebrook & Driver 2008;§ Baldry§ (r/R ets)(1 al. + 2012)r/Rs) mean- mulae,Rs seeusing Klypin, the Vmax Trujillo-Gomezand Mvir relationship & Primack from (2011) the and NFW for-
§ The scale radius R is the radius where the logarithmic slope ∼ This fraction also increases with redshift, and we find that to tidal striping. Since tidal stripping affects the dark mats - =0i sl e s st h a nt h a to ft h e i rp r o g e n i - Equation (26). The dashed black lineeral shows basic halo the properties, fit to updating the ampli their- scaling relations as the halo and subhalo velocity functions. 4and 5alsocom-
7d i s c u s s e st h ee v o l u t i o no ft h eT u l l y - all ing that, for some reason, the§ star formation§ efficiency in low Klypinmulae, et al. see (2014); Klypin, see Trujillo-Gomez also Behroozi, & Wechsler Primack & (2011) Wu and at z afunctionofredshiftforthePlanckcosmologicalparame-=2, 4and6thereare 25, 40 and 60% more Milky- terpare more the than Planck the cosmology stars of halo the centralmassof andtheThe galaxy velocity density scale deep functions radius profile insideR iss is -2. the The radius NFW where profile the is logarithmic completely slope
0 halo mass function using the best fit∼ parameters from table tude of perturbations given by EquationWayters mass as halos well (29). as in the the redshift Bolshoi-Planck evolution of than halo/subhalo in the Bolshoi number thewith halo, those this from means the WMAP5/7 that the correlation cosmological between parameters. galaxy6 (2013).Klypin For the et NFWal. (2014); profile, see the also radius Behroozi, at which Wechsler the cir- & Wu . mass halos has been suppressedcharacterizedof the (e.g. density by Behroozi, two profile parameters, is Wechsler -2. The for NFW & example profileρs isand completelyRs, 3d e xd i s p e r s i o ni nt h eh a l om a s s have found slopes between α 1.4 1.6(Blantonetal.2005;§ 3. simulation.densities. subhalos and halos matter Atdark Forz the=8,thereareabout3timesasmany majority of these halo properties we report stellardiscusses mass the and dependence present subhalo of halo mass concentration is not trivial. and spin There- on cular(2013). velocity For is maximized the NFW profile, is Rmax the=2 radius.1626R ats which(Klypin the cir- § or more usefully the halo mass, M ,anditsconcentration 11 Conroy 2013b; Moster,∼ Naab−characterized & White 2013). by two Nevertheless, parameters,vir for example ρs and Rs, 3.3). M fitting=10 functionsM⊙ halos that in Bolshoi-Planck can be very useful as notin Bolshoi. only to gain in- foremass in andapproaches redshift. for7discussestheevolutionoftheTully- connecting galaxies to dark matter Figure 10 showsvir the ratio of the number densitiesBaldry,nBP Glazebrook & Driver 2008;parameter, Baldryc et.Theconcentrationparameterisdefinedas al. 2012) mean- et al.cular 2001; velocity Behroozi, is Wechsler maximized & Wu is R 2013),max =2 and.1626 it canRs be(Klypin measurements§ of the baryonicor more mass usefullyvir have the found halo slopes mass, M asvir,anditsconcentration . Insight the about cold dark the halo/subhalo matter cosmology population it is predicted but also for that the (sub)halos,Fisher and such Faber-Jackson as the abundance relations matching between halotechnique, circular it §
⃝ shown that 5 et al. 2001; Behroozi, Wechsler & Wu 2013), and it can be c and nB between the Bolshoi-Planck and the Bolshoi sim- the ratio between the virial radius R and the scale radius .) aoms crto rates accretion mass halo 3.1), ing that, for some reason, the star formationparameter, cvir effi.Theconcentrationparameterisdefinedasciency in lowvir h the numbergalaxy-halo density connection of dark matter and thus halos for is galaxy a strong evolution. function In- hasvelocitysteep been shownasVmaxαand that1 the.9(Baldry,Glazebrook&Driver2008). the stellar mass mass the of subhalo the central had galaxies when it h halo mass function using the best fit parameters from table−1.8 cvirshown thatRvir 2.1626 − Rs: 2 06RS MNRAS RAS, 2016 ulations as a function of Mvir from z =0toz =8.The § of halo mass at low masses dnh/dMvir M .Incontrast, was still a distinct∼ halo correlates betterthe withratio the between stellar the virial radius Rvir and the scale radius − vir mass halos has been suppressed (e.g. Behroozi, Wechsler & = Vmax (53)
4discusseshalo( 1 ∝ ⃝c 2016 RAS, MNRAS 000,1–?? f(cvir) GMvir f(2.1626) 1 3. different cosmologicalthe observed parameters galaxy stellar mass imply function, that as at wellz =0,on as the lu- mass of the galaxy it hosts. This comesR from: the fact that cvir 2 Rvir 2.1626 Gpc) s Rvir minosity function, has a slope that is flatter. Recent analysConroyis when 2013b; assuming Moster, identical Naab stellar-to-halo &cvir White= mass relations2013).. fo Nevertheless,r (52) = Vmax (53) p sdsusdi Lee in discussed is Mpc Figure 10 showsaverage, theffi thereratio are of the12% number more Milky-Way densities massnBP halos in the R wheref(cvir) GMvir f(2.1626) ∼ 4.2 Subhalo mass function s Rvir inl asv halos massive ciently measurements of the baryonic mass have found slopes as Bolshoi-Planck than in the Bolshoi simulation. This fraction cvir = . (52) x and nB between the Bolshoi-Planck⃝c 2016 RAS, and MNRAS the000,1– Bolshoi?? sim- Rs where
3 § Figure 19 shows halo concentrations, c ,asafunction 13steep as α 1.9(Baldry,Glazebrook&Driver2008). vir f(x) ln(1 + x) . (54) icse h sim- the discusses 2 1+x § ⊙ ≡ − increases to higher masses, 25% for Mvir 3 10 M . Subhalos can lose a significantof Mvir for fraction redshifts ofz their=0, 1 mass, 2, 4, and due 6. The left panel of x oue htwe that volumes ulations as a function of M from z =0toz =8.The 4and vir ∼ ∼ × ∼ Figure 19 shows halo concentrations, cvir,asafunction f(x) ln(1 + x) . (54) § This fraction also increases with redshift, and we find that to tidal striping. Since tidalthe figure stripping shows aff haloects concentrations the dark mat calculated- by finding The Klypin≡ concentration− 1+cvirx ,K can be found be solving
4.3). § different cosmological parameters imply that at z =0,on of Mvir for redshifts z =0, 1, 2, 4, and 6. The left panel of
3describesthe at z =2, 4and6thereare 25, 40 and 60% more Milky- ter more than the starsthe of best the scalecentral radius, galaxyRs assuming deep inside a NFW profile for each Equation (53) numerically. It is more robust than deter- average, there are 12% more Milky-Way∼ mass halos in the the figure shows halo concentrations calculated by finding The Klypin concentration cvir,K can be found be solving Way mass halos in the Bolshoi-Planck than in the Bolshoi4.2 Subhalothe halo, mass this function means thathalo the in the correlation simulation. between Instead, galaxy the right panel shows halo mining Rs by fitting the NFW profile, especially for halos § ∼ the best scale radius, Rs assuming a NFW profile for each Equation (53) numerically. It is more robust than deter-
5alsocom- § Bolshoi-Planck thansimulation. in the Bolshoi At z =8,thereareabout3timesasmany simulation. This fraction stellar mass and present subhalohalo in mass the simulation. is not trivial. Instead, There- the right panel shows halo mining R by fitting the NFW profile, especially for halos 5presents s
§ 13 ⃝c 2016 RAS, MNRAS 000,1–?? 000,1– 11
.)and 4.1) increases to higherM masses,=10 M⊙25%halos for inM Bolshoi-Planckvir 3 10 asM in⊙ Bolshoi.. Subhalosfore can in lose approaches a significant for connecting fraction galaxies of their to mass dark matterdue vir ∼ ∼ × This fraction also increasesIn the cold with dark redshift, matter and cosmology we find it isthat predictedto that tidal striping.(sub)halos, Since such tidal as the stripping abundance⃝c 2016 aff RAS,ects matching MNRAS the dark technique,000,1– mat?? - it the number densityFigure of 16. darkRedshift matterage evolution halos of is the a strong subhalo function maximum circularhas beenFigure shown 17. Redshift that the evolution mass of the the subhalo subhalo circular had when velocity it e- on at z =2, 4and6thereare 25, 40 and 60% more Milky- ter more than the stars of the central galaxy deep inside velocity function, with circular velocity−1.8 Vacc measured at accre- function, as a function of the subhalo’s peak circular velocity h
re § - ?? l
” - ∼ f of halo mass at low masses dnh/dMvir M .Incontrast, was still a distinct halo correlates better with the stellar s 6 Way mass halos in the Bolshoi-Plancktion. than in the∝ Bolshoivir the halo, this meansVpeak. that the correlation between galaxy the observed galaxy stellar mass function, as well as the lu- mass of the galaxy it hosts. This comes from the fact that simulation. At z =8,thereareabout3timesasmany stellar mass and present subhalo mass is not trivial. There- minosity function, has a slope that is flatter. Recent analysis when assuming identical stellar-to-halo mass relations for 11 6HALOCONCENTRATIONANDSPIN Mvir =10 M⊙ halos in Bolshoi-PlanckUsing this definition as in Bolshoi. we can thus derive thefore maximum in approaches cir- for connecting galaxies to dark matter In the cold dark⃝c 2016 matter RAS, cosmology MNRAScular velocity000,1– it function is?? predicted as: that (sub)halos, such6.1 as Halo the abundanceconcentrations matching technique, it the number density of dark matterdnsub halos is a strong functiondnh has been shownHigh that resolution the massN body the simulations subhalo have had shown when that it the = Φ−sub1.8(Vsub Vmax) d log Vmax. (50) − of halo mass at low masses dnh/dMd log Vvirsub M .Incontrast,| d log Vmax was still a distinctdensity halo profile correlates of dark matter better halos can with be well the described stellar by ∝ ! vir the observed galaxy stellar mass function, as well as the lu- mass of the galaxythe Navarro, it hosts. Frenk This & White comes (1996, from NFW) the profile, fact that ⃝c 2016 RAS, MNRAS 000,1–?? minosity function, has a slope that is flatter. Recent analysis when assuming identical stellar-to-halo mass relations for
⃝c 2016 RAS, MNRAS 000,1–?? 18
Table 8. Best fit parameters to Schechter-like distribution functionforP (log λ)d log λ.
Simulation αP βP log λ0,P αB βB log λ0,B
BolshoiP 4.126 0.610 -2.919Mon. 3.488 Not. R. Astron. 0.6042 Soc. 000 -2.878,1–?? (2016) Printed 12 February 2016 (MN LATEXstylefilev2.2)
SMDPL 4.090 0.612 -2.917 4.121 0.611 -2.916 MDPL 4.047 0.612 -2.914Halo 3.468 and 0.591 Subhalo -2.907 Demographics with Planck Cosmological Parameters: Bolshoi-Planck and MultiDark-Planck of λ and Rvir.SpecificallytherelationisgivenbyRd Simulations Halo Demographics with Planck Parameters 19 1/3 ∝ λ Rvir λ M .Asbefore,ifweassumeforsimplicity × ∝ × vir that the Mb/Mvir ratio is constant, the relation between sler & Conroy (2013b), and we use the fits for the Tully- 1⋆ 2,3 4 5 Fisher and Faber-Jackson relations reported in Dutton et al. agalaxy’sradiusanditsbaryonicmassisgivenbyRd Aldo Rodr´ıguez-Puebla , Peter Behroozi , Joel Primack ,AnatolyKlypin, 1/3 ∝ 4 4 (2011). The fraction of quiescent galaxies fQ has been taken λ Mb .Notethatthescatterofthesize–massrelationis Christoph Lee , Doug Hellinger from Behroozi, Wechsler & Conroy (2013b). We assume for × 1 just the resulting scatter of the λ Mvir relation. Indeed, Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA simplicity that the maximum circular velocity of dark matter − 2Astronomy and Physics Departments and Theoretical Astrophysics Center, University of California, Berkeley, BerkeleyCA94720,USA the dispersion of the spin parameter, either λ or λ ,is halos, Vmax, corresponds to the maximum circular velocity of P B 3Hubble Fellow galaxies, Vmax,g,i.e.,Vmax = Vmax,g.Inthisway,wecanthen very similar to the observed dispersion of disk galaxy scale 4Physics Department, University of California, Santa Cruz, CA 95064, USA solve Equation (61), log Vmax,g = log Vmax,g (log M∗), for 5Department of Astronomy, New Mexico State University, Las Cruces, NM 88001, USA ⟨ ⟩ ⟨ ⟩ lengths at least at low redshifts where reliable measurements M∗ and thus transform velocities into stellar mass. can be obtained (see e.g., Mosleh, Williams & Franx 2013). The black solid line in Figure 23 shows the predicted Note that the different redshift evolution of the λP cosmic stellar mass density for galaxies with stellar mass 8.5 11.25 − M∗ =10 10 M⊙ since z =9assumingthat Mvir and λB Mvir relations leads to different predictions Released 2016 Xxxxx XX − − log Vmax,g (log M∗)isindependentofredshift,andthered of the Rd Mb relation and its evolution. In particular, ⟨ ⟩ − and blue curves are the same for wider ranges of stellar models of galaxy formation calculating galaxy sizes based masses. For comparison, we plot a recent compilation from ABSTRACT Madau & Dickinson (2014) of the evolution of the observed on the spin parameter λB will result in more extend galaxies We report and provide fitting functions for the abundance of dark matter halos and (and potentially in larger numbers of low surface brightness stellar mass density. Our simple model represented by the subhalos as a function of mass, circular velocity, and redshift from the new Bolshoi- black curve seems to be roughly consistent with the obser- galaxies) at high redshifts compared to those models using Planck and MultiDark-PlanckFigureΛCDM 23. cosmologicalCosmic stellar masssimulations, density since basedz ∼ 9. on Filledthe circles Planck The cumulative number of halos > Vmax is pretty Tully-Fisher and Faber-Jackson M* ~ V4 scaling vational evidence of the weak evolution of the maximum cir- Figure 22. Evolution of thecosmological velocity function parameters.Vmax Weforshow also fixed the report observations the halo compiled mass in accretion Madau & r Dickinsonates, which (2014). may λP.Isalsopossiblethatgalaxystarformationratescould constant out to redshift z ~ 4 for galaxy-mass cular velocity since z 1. In contrast, at high redshifts the Vmax =100, 190 and 450 km /s for the BolshoiP, SMDPL,The and solidrelations curves for show spiral the and predicted elliptical cosmic galaxies stellar mass must den- ∼ be affected since more extended galaxies presumably have be connected with galaxy star formation rates. We show that the higher cosmological model produces far too many stars. We thus conclude that MDPLhalos. simulations. But these Thehalos solid arematter linessmaller are density and the denser, fits of the to Equation Planck parameterssity (42 usingchange). fits compared by to thez ~ Tully-Fisher1, withor they the would and WMAP Faber-Jackson predict parameters far veloci too leads ty-high lower gas surface densities than more compact disks, and and they cannot host high-M* galaxies at high to-stellar-massstellar mass relations density as described at z > in1. the text, assuming that astrongevolutionoftheTully-FisherandFaber-Jacksonre- For low velocities the velocity functionto higher is abundance practically of con massivestant after halos at high redshifts. We find that the median halo lations is required to higher redshifts in order to reconcile redshifts. ′ these relations−1 are independent of redshift and that the Vmax of thus lower SFRs according to the Kennicutt-Schmidt law. redshift z ∼ 4, while for highspin velocity parameter halos itλ is= nearlyJ(2M constantvirRvirVvir) is nearly independent of redshift, leading dark matter halos is the same as the Vmax,g of galaxies. The solid the predicted cosmic stellar mass density with observations. Two recent papers have discussed the evolution of after redshift z ∼ 1. to predicted evolution of galaxyblack sizes line thatshows is the consistent predicted cosmic with observstellar massations, density while for the a Based only on theoretical arguments, is it possible λ J E −1/2G−1M −5/2 galaxy sizes out to redshift z 8usingHubbleSpaceTele- significant decrease with redshiftrange in of stellar median masses= log(M| ∗/M| ⊙)=8.5−11.25. Comparingpredicts more the to derive a simple model for the redshift evolution for ∼ decrease in galaxy sizes thanred is observed. curve, for log( UsingM∗/M the⊙)=7 Tully-Fisher− 11.25, to the and blackFaber-Jackson curve shows log Vmax,g (log M∗)? In Section 3.1, we found that the evo- scope images, mainly from the CANDELS survey. Shibuya, ⟨ ⟩ relations between galaxy velocitythat and including mass, lower we show stellar that masses a simple increases modρ∗ moreel of at how high galaxy red- lution of the maximum circular velocity of dark matter halos Ouchi & Harikane (2015) finds that the median effective ra- shifts; comparing the blue curve, for log(M∗/M⊙)=7−12, to the α the Tully-Fisher relation forvelocity spiral is galaxies related to and halo the maximum Faber- circular velocity leads to increasing overprediction is well described by Vmax [MvirE(z)] .Inotherwords, −1.3 black and red curves shows that including higher stellar masses ∝ dius re evolves with redshift as re (1 + z) ,withno Jackson relation for ellipticals—haveof cosmic stellar found mass only density a weak as evo redshift- increases beyond redshifts z ∼ 1, implying the zero point of the maximum circular velocity evolves with ∝ that such velocity-mass relationsincreases mustρ change∗ more at at low redshifts redshifts.z > Clearly,1. By all making of these a realistic predic- α evolution in the slope, the median S´ersic index (n 1.5), or lution from z 0.85 to 0 (Conselice et al. 2005). This result ∼ > E(z) .Ifweadoptthesamereasoning,wecanassumethat ∼ model of how observed galaxytions velocities are inconsistent are related with to observations halo circular at z ∼ velocity,1—they produce we show the standard deviation of the log-normal distribution. They ∼ too much stellar mass density at early redshifts, and the wider the zero point of the Tully-Fisher and Faber-Jackson rela- has been further supported and generalized in Kassin et al. αTF αFJ that recent optical and radiostellar observations mass range of represented the abundance by the blue of g curvealaxies exceeds are the in goodob- tions evolve with redshift as E(z) and E(z) respec- find that the ratio of the effective radius to the virial radius (2007) from z 1to0,basedonfairlylargesamplesofagreement with our ΛCDM simulations. Our halo demographics are based on updated ∼ served stellar mass density even at z =0.Sincethestellarmass tively, where αTF =0.259 and αFJ =0.37 are their corre- of the halos is nearly constant at re/Rvir =0.01 0.035. versions of the Rockstar and Consistent Trees codes, and this paper includes sponding slopes at z =0.ThedottedlineinFigure23shows − galaxies from AEGIS and DEEP2 and adopting thefunction indi- is evolving, velocity-mass relations like Tully-Fisher must This is just what one would expect from the lack of red- 2 2 2appendices explaining all of theiralso outputs.evolve. The This dotted paper lines is show an the introduct predictionsion when to a seriesusinga of the predicted cosmic star formation rate density based on cator S0.5 =0.5Vmax + σg which accounts for disordered related papers presenting othermodel analyses in which of the the maximum Bolshoi-Planck circular velocity-to-stellar and MultiDark-Planck mass re- this simple evolutionary model. Despite the simplicity of this shift evolution in λB,whilethefactorof 2declineinλP motions (Weiner et al. 2006; Covington et al. 2010). On the ∼ simulations. lation evolves with redshift as described in the text. model, the predictions are much more consistent with obser- from z =0to8wouldpredictacorrespondingdeclinein < other hand, observations indicate that at z 1.5thenumber vations at high redshifts than the non-evolving model that Key words: Cosmology:∼ Large Scale Structure - Dark Matter - Galaxies: Halos - the ratio re/Rvir.Theotherrecentpaper,Curtis-Lakeetal. density of star forming galaxies at a fixed velocity evolvesdence between the maximum circular velocity of halos and led to the solid black line in the figure. Nevertheless, the Methods: Numerical above models are very simple and they ignore the fact that (2014), finds a slower decline of effective radius with red- very little, while the number density of quiescent galaxiesgalaxies, i.e., Vmax = Vmax,g.Todoso,ourfirststepisto shift, and in fact cannot reject the possibility that there is evolves more rapidly (e.g., Bezanson, van Dokkum &convert Franx the Tully-Fisher and Faber-Jackson relations into the Vmax of dark matter halos is not the Vmax,g of galaxies, as we discuss in the next section. no size evolution. This is possibly consistent with the mod- 2012). circular velocities. Arguments based on the Jeans equation est increase with redshift of λ for lower mass halos, and in virialized systems result in the relation Vc = Kσ,where B 1INTRODUCTIONFigure 22 shows that the comoving number densitytypicale.g. Kuhlen,of values Vogelsbergerfor K are √2 &√ Angulo3(Binney&Tremaine2008). 2012), although many inconsistent with the expected decrease in re/Rvir from the cover large volumes but with− resolution too low to identify lowIn the circularΛCDM standard velocity modern halos theory is nearly of structure constant forma- since zWhile4 there is an extensive discussion in the literature of 8OBSERVEDVELOCITYFUNCTIONOF whatall∼ dark is the matter right halos value that for K host,followingDuttonetal.(2011) most galaxies. The mass res- decline in λP.Theradiiofthesehigh-redshiftgalaxiesare buttion inhigh the mass/velocity universe, galaxies halos populate have dark more matter evolution. halos Halos of < 8 −1 NEARBY GALAXIES olution required to do this is 10 h M⊙,andtheforce and subhalos. The demographics of these halos as a func- here we assume that K =1− .54 which is a value halfway being measured in rest-frame UV, which is typically rather agivencircularvelocityathighredshiftarelowerinmassresolution should be < 1h 1 kpc.∼ High-resolution cosmolog- tion of redshift are thus an important input to the predic- between different groups. The next step is to derive an av- Previous studies have considered that the observed distri- clumpy (Shibuya et al. 2015; Curtis-Lake et al. 2014). It but denser than halos of the same circular velocity atical lower dark matter simulations∼ that are particularly useful for tion of the properties and distribution of galaxies. A num- erage maximum circular velocity-to-stellar mass relation for bution of galaxy velocities is a strong test for galaxy for- will be very interesting to see what sort of galaxy size evolu- redshift. To what extent is the nearly constant comovingallstudying galaxies: galaxylog Vmax hosts,g = includelog Vmax the,g Millennium(log M∗). The simulations method mation models and cosmology (Cole & Kaiser 1989; Shi- ber of large cosmological simulations have now been run (see ⟨ ⟩ ⟨ ⟩ tion with higher redshifts is revealed by James Webb Space number density of halos as a function of their circularis(Springel to ve- use the et average al. 2005; Tully-Fisher Boylan-Kolchin and Faber-Jackson et al. 2009; Angulo rela- masaku 1993; Klypin et al. 1999b). The reason is simply et al. 2012), Bolshoi (Klypin, Trujillo-Gomez & Primack Telescope at rest-frame optical wavelengths. locity consistent with the weak evolution of the Tully-Fishtionser for local galaxies and take into account the observed because the comparison, at a first order, between the the- fraction2011), MultiDark of disk and (Prada elliptical et galaxies. al. 2012; For Riebe simplicity, et al. 2013), weas- Ju- oretical halo+subhalo velocity function and the observed relation?⋆ [email protected] This is particularly interesting if the galaxy stsumeellar that all disk galaxies are star-forming systems while velocity function of galaxies is more direct than the stel- mass function evolves with redshift, as was first pointedellipticals out correspond to quiescent galaxies. Then the aver- lar mass/luminosity and halo+subhalo mass functions. In in⃝c 2016 Bullock RAS et al. (2001b). age maximum circular velocity is given by this section, we compare the local volume galaxy velocity 7 ON THE EVOLUTION OF Vmax M∗ function derived from optical galaxy observations in Klypin − In this section we investigate the above question assum-log Vmax,g = fSF log Vmax,TF + fQ log Vmax,FJ . (61) ⟨ ⟩ ⟨ ⟩ ⟨ ⟩ et al. (2015) and the HI radio galaxy velocity function based Early determinations of the evolution in the maximum cir- ing that the Tully-Fisher and Faber-Jackson relations dowhere not log Vmax,FJ = log(1.54σ) and fSF =1 fQ.Note on the ALFALFA survey from Papastergis et al. (2015) to ⟨ ⟩ ⟨ ⟩ − cular velocity and the stellar mass/luminosity relations— evolve with redshift and that there is a one-to-one correspothatn- the above equation depends on stellar mass. We take compare with the theoretical halo+subhalo velocity function the fraction of quiescent galaxies fQ from Behroozi, Wech- from ΛCDM with the Planck cosmological parameters. ⃝c 2016 RAS, MNRAS 000,1–?? ⃝c 2016 RAS, MNRAS 000,1–?? The Astrophysical Journal,795:104(20pp),2014November10 Whitaker et al. 4 BEHROOZI, WECHSLER & CONROY (a) (b) The AstrophysicalRelationship Journal,795:104(20pp),2014November10 Between Galaxy Star-forming Galaxies LieWhitaker et al. z TheStellar Astrophysical Mass Journal,795:104(20pp),2014November10 and Halo Mass 8on42 a “Main 1 Sequence”0.5Whitaker 0.2 et al. 0 0.1 (a) (b) (a) (b) ] 3 0.1 0.01 / yr Mpc • O
0.001 z=0.1 0.01 z=1.0 z=2.0 Observations
Stellar Mass / Halo z=3.0 Full Star Formation History Best-Fit Model 0.0001 z=4.0 Cosmic SFR [M Time-Independent SFE Time-Independent SFE Mass and Time-Independent SFE 10 11 12 13 14 15 0.001 10 10 10 10 10 10 1 2 4 6 8 10 12 13.8 Halo Mass [M ] Time Since Big Bang [Gyr] O•
The stellar mass to halo mass ratio at multiple FredshiftsIG.3.—Left as panel:derived the from stellar observations mass to halo mass compared ratio at multiple to a redshifts as derived from observations (Behroozi et al. 2012) compared to a model which hasFigure a time-independent 1. Star formation rate star as aformation function of efficiency stellar mass (SFE). for star-forming Error bars galaxies. show Open 1 circlesuncertainties indicate the (Behroozi UV+IR SFRs et from al. 2012). a stacking A time-independent analysis, with a second-order SFE predicts a roughly Figure 1. Star formationFigure ratepolynomialmodel 1. asStar a function formationwhich fit above ofhas the rate stellar mass a as time-independent a completeness function mass for of star-formingstellar limits (solid mass star verticalfor galaxies. star-formingformation lines). Open Open galaxies. squares circles Open signify- indicate circlesJust measurements indicate theas UV+IRthe the below properties UV+IR SFRs the mass-completeness SFRs from of from hydrogen-burning a stacking a stacking limits. analysis, analysis, Therunningmedians with withstars a a seco second-ordernd-order polynomialtime-independent fit above the stellar mass mass completeness to halo mass limits relationship. (solid vertical Right: lines). Openthe cosmic squares star signify formation measurements rate for below a compilation the mass-completeness of observations limits. (Behroozi Therunningmedians et al. 2012) compared polynomial fit above the massforefficiency individually completeness detected(SFE). limits objects Error (solid in bars MIPS vertical show 24 µm imaging lines).1σ uncertainties. withOpen S/N squares> 3(shownasagray-scaledensityplotinthePanel(a),left)areindicatedwithfilledcirclesinthe A signify measurementsare controlled below theby their mass-completeness mass, the galaxy limits. star Th erunningmedians for individually detectedforto objects individuallyright the panel best-fit in and MIPS detected model are color-coded 24 objects fromµm aimaging in star by MIPS redshift. formation with24 Theµm S numberimaging history/N > of3(shownasagray-scaledensityplotinthePanel(a),left)areindicatedwithfilledcirclesinthe reconstruction with star-forming S/N > 3(shownasagray-scaledensityplotinthePanel(a),left)areindicatedwithfilledcirclesinthe galaxies technique with S (Behroozi/N > 3 detections et al. 2012) in the 24 asµ wellm imaging as the and time-independent those with S/N < SFE3areindicated model. The latter model rightin paneltime-independent the bottom and are right color-coded of each SFE panel. by redshift. predicts The star The formation a number roughly sequence of star-forming time- for star-forming galaxies galaxies with S/ isN curved,formation> 3 detections with a rate constant in the(SFR) slope 24 µ m ofis imaging unityapproximately at log( andM those⋆/M with )proportional< S10/N (solid< 3areindicated black right panel and are color-codedworks surprisingly by redshift. well The up number to redshifts of star-forming of z 4. However, galaxies awith model S/N which> 3 has detections a constant in the efficiency 24 µm (with imaging mass and and those time) with also⊙ S reproduces/N < 3areindicated the decline in star in thelineindependent bottom in Panel right (b) is of linear), each stellar panel. whereas mass The the star slope to formation athalo the⇠ massive mass sequence end flattens for star-forming with α 0. galaxies3–0.6from istoz curved,the0 .5stellar to withz a 2mass,. constant5. We show with slope the the ofSDSS unity proportionality curve at log( (grayM dotted⋆/M line) < in10 Panel (solid black in the bottom right of eachformation(b)) panel. from Brinchmann well The since star formation etz al.2. (2004) as sequence it is one of for the star-forming few measurements galaxies that goes= is to curved, very low mass, with= but a constant it is= based on slope another of SFR unity indicator. at log(M⋆/M ⊙) < 10 (solid black line inrelationship Panel (b) is linear),. (Behroozi, whereas⇠ the slopeWechsler, at the massive Conroy, end flattensApJL with α 0.3–0.6fromconstantz 0. 5 increasing to z 2.5. We with show redshift the SDSS up curve to (grayabout⊙ dotted z = line in Panel line in Panel (b) is linear),(b))(A from whereas color Brinchmann version the slope of this et al. figureat ( the2004 is massive) available as it is one in end the of flattens online the few journal.) withmeasurementsα 0.3–0 that.6from goes= to veryz low0.5 mass, to=z but2 it.5. is= basedWe show on another the SDSS SFR indicator. curve (gray dotted line in Panel 2013) = =2.5. (Whitaker= et al. ApJ 2014) (b)) from Brinchmann(A et color al. (2004 version) as of it this is figureone of is the available few measurements in the online journal.) that goes to very low mass, but it is based on another SFR indicator. (A color version of this figureWuyts is available et al. 2007 in;Williamsetal. the online journal.)z 2009; Bundy et al. 2010; 24 µmdetections,totaling9015star-forminggalaxiesoverthez Cardamone8 42 et al. 2010; Whitaker 1 et0.5 al. 2011; Brammer 0.2 et 0 al. full redshift8 range.42 Mass completeness 1 limits are0.5 indicated 0.2 by 0 Wuyts14 et al. 2007;Williamsetal.2009; Bundy et al. 2010; 24 µmdetections,totaling9015star-forminggalaxiesoverthe12 Cardamone10 2011;Pateletal. et al. 20102012;); Whitaker quiescent galaxies et al. 2011 have; strongBrammer Balmer et/ al. verticalfull10 redshift lines. The range. GOODS-N Mass completenessand GOODS-S limitsfields have are deeper indicated by Wuyts et al. 2007;Williamsetal.4000 Å breaks, characterized2009; Bundy by red et rest-frame al. 2010U–;V colors24 µmdetections,totaling9015star-forminggalaxiesovertheMIPS imaging (3σ limit of 10 µJy) and HST/WFC3 JF 125W 2011;Pateletal.2012); quiescent galaxies have strong Balmer/ vertical lines. The GOODS-N∼ and GOODS-S fields have deeper Cardamone et al. 2010and; relatively Whitaker blue et rest-frame al. 2011V;–J Brammercolors. Following et al. the two-full redshiftand HF 160 range.W imaging Mass (5σ completeness26.9 mag), whereas limits the are other indicated three by 400013 Å breaks, characterized by red rest-frame U–V colors MIPS11 imaging (3σ limit∼ of 10 µJy) and HST/WFC3 JF 125W 2011;Pateletal.201210 color); quiescent separations galaxies defined in have Whitaker strong et al. Balmer (2012a),/ we select fields have10 shallower MIPS imaging∼ (3σ limits of 20 µJy) and and relatively blue rest-frame V–J colors. Following the two-verticaland lines.HF 160 TheW imaging GOODS-N (5σ and26. GOODS-S9 mag), whereas∼ fields the have other deeper three 58,973 star-forming galaxies at 0.5 • 12 10 O ∼ ∼ and relatively blue58,97310 rest-frameabove star-forming the mass-completenessV–J galaxiescolors. atFollowing limits 0.5 the shallower HST/WFC3 imaging. 10 detections (amongst10 whichdensities 9,015 in Section have4.2 S. /N > 3) and 35,916 are(SFR*ND) the CANDELSof the SFR10 are/wide indicated fields. with Although solid circles the when mass the data completeness are detections in the following analysis, we estimate15 the contribution10 First, we look at the measurements for individual galaxies. undetected in MIPS 24 µm photometry (S/N < 1). The full in thecomplete deeper both GOODS-N in stellar mass and and GOODS-S SFR (above fields the shallower will extendlog to of active galactic nuclei (AGNs) to the median 24 µ-4.0mflux The running median of the individual UV+IR measurements-4.0 8 3. THE STAR FORMATION SEQUENCElog data 3σ MIPS6 24 µm detection limit).16 We consider all MIPS sample of star-formingdensities10 galaxies in Section are4.2 considered. in the stacking lower stellarof the10 masses, SFR are indicated we adopt with the solid more circles conservative when the limits data are for analysis. Although we have1 2 not removed 4 6 sources 8 with 10 X-ray 12 13.8 photometry in1 the/ 2 median 4 for the 6 individual 8 UV+IR 10 SFRs 12 13.8 Figure 1 shows the star formation sequence, log Ψ asthe a shallowermeasurementscompleteHST both (filledWFC3 in circles),stellar imaging. mass even thoseand SFR galaxies (above intrinsically the shallower Time Since Big Bang [Gyr] Time Since Big16 Bang [Gyr] detections in the followingfunction analysis,3. of THE log STARM⋆ we,infourredshiftsbinsfrom estimate FORMATION the contribution SEQUENCEz 0.5to First,faintdata we in 3 the lookσ MIPS IR. at Only 24 the 1%µm measurements of detection the star-forming limit). for galaxiesWe individual consider above the all galaxies. MIPS z 2.5. We use a single SFR indicator, the UV+IR= SFRs photometry in the median for the individual UV+IR SFRs of active galactic nuclei= (AGNs) to the median 24 µmflux The running20 µJy limit median in each of redshift the bin individual have 24 µm UV+IR photometry measurements with Figuredescribed1 shows in Section the2.4 star,probingovertwodecadesinstellar formation sequence, log Ψ as a S/measurementsN < 1. (filled circles), even those galaxies intrinsically densities in Section 4.2FIG..4.—Left panel: Star formation rate as a function of halo massof and the cosmic SFR time, are weighted indicated by the number with density solid of circles dark matter when halos the at that data time. are Contours functionmass. The of log grayM scale⋆,infourredshiftsbinsfrom represents the density of pointsz for0 star-.5to faintTo leverage in the IR. the Only additional 1% of thedecade star-forming lower in galaxies stellar mass above the show where 50 and 90% of all stars were formed; dashed line= shows the median halo mass for star formation as a function of time. panel: Star formation z forming2.5. We galaxies use a selected single in SFR Section indicator,2.5 with the S/ UV+IRN > 3MIPS SFRscompletethat the both CANDELS in stellarHST mass/WFC3 and imaging SFR enables (above usRight to the probe shallower rate= as a function of galaxy stellar mass and time, weighted by the number density20 µJy of limit galaxies in each at that redshift time. Contours bin have and16 24 dashedµm photometry line are as in top-left with panel; 3. THEdescribed STAR FORMATION in Section 2.4,probingovertwodecadesinstellar SEQUENCE data 3σSMIPS/N < 1. 24 µm detection limit). We consider all MIPS dotted14 line shows current minimum stellar masses reached by observations. 16 mass.Essentially The gray identical scale to represents the publicly released the density catalogs of available points through for star-photometryInTo the case leveragein of the the 1.0 median the ∗ ! " EquationDownloaded from (4) implies stellar-halo accretion rate coevolution, 1/2 formation rates and cosmic star formation rates from z =0 The dynamical time of the halo is t (z) [G" (z)ρ ]− , which (2007) group catalog presented in Yang et al. (2012).dyn = Thevir m the spherical overdensity criterion of Bryan & Norman (1998). We is 20 per cent of the Hubble time. Simulations (e.g. Dekel et al.SHARC. The left panel of Figure 4 shows the resulting also assume a Chabrier (2003) IMF. Finally, Table 1 lists all the 2009∼ ) suggest that most star formation results from cold gas flowing to z =8combinedwiththegrowthhalosobtainedfromN- correspondingacronyms used in this SHMR paper. is shown as theinward black at about the curvevirial velocity in– i.e. roughly Fig- a dynamical time ∗ Figure 7. Upper Panel: Cosmic mass density as a function of stellar-to-halobody mass simulations, ratio, f ,derivedforSDSScentralgalax-? show that the M∗–Mvir relation evolves after the gas enters. As instantaneous accretion rates for distinct z z ure 3, and the SHMR for all galaxieshaloes from near clusters Behroozi, can also be negative Wech- (Behroozi et al. 2014), http://mnras.oxfordjournals.org/ .Cosmicstar-formationrateasafunctionof . 2STELLARHALOACCRETIONRATE ies (see Section 2.2). Consistent with previous studies, we using time-averaged accretion rates allows galaxies in these haloes slowly with redshift. Moreover, ? showed that12 when assum- COEVOLUTION (SHARC) sler & Conroy (2013a) is shown as theto continue red forming curve. stars. The dif- find that f∗ has a maximum of ∼ 0.03 at Mvir ∼ 10 M⊙, Fig. 1 shows the instantaneous and the dynamical-time-averaged ing that the ratio of galaxies specific star formation rates 2.1 The simulation ference between the two curves for halohalo MARs masses as a function of lower halo mass and than redshift, and Fig. 2 shows 12 and it decreases(sSFR) at to both their higher host and halos lower specific halo masses. mass accretion The rates We generate our mock galaxy catalogues based on the N-body their respective scatters. Even before converting halo accretion rates rates averaged over a dynamical time instead. Additionally, Mvir ∼ 10 M⊙ reflects the fact that the SHMR of cen- Bolshoi–Planck simulation (Klypin et al. 2014). The Bolshoi– into SFRs (Section 2.3), it is evident that both the slope and disper-product f∗(sMAR),× ϵ = dM star∗/dM formationvir will effi beciency shownϵ,isindependentofred- as the black Planck simulation is based on the !CDM cosmology with param- sion in halo MARs are already very similar to that of galaxy SFRs we show that a redshift-independent M∗–Mvir model ex- trals andeters consistent satellite with the latest galaxies results from the are Planck slightlyCollabora- on di theff mainerent sequence. as mentioned Is Main Sequence12 SFR Controlledcurves in Figurebyshift Halo simply 5 below. explainsMass theAccretion? cosmic star formation rate since tion (Planck Collaboration XIII 2015) and run using the ART code vir at University of California, Santa Cruz on December 10, 2015 plains the observed scatter of the SFR−M∗ in main sequence above.(Kravtsov, At Klypin halo & Khokhlov masses1997;Gottloeber&Klypin higher than2008). M ∼ 10 M⊙ ,this In the more general case M∗ = M∗(Mvir(t),z), equation by Aldo Rodríguez-Puebla,1 3 2.2 Connecting galaxies toJoel haloes Primack, Peter Behroozi,z =4. Sandra Faber MNRAS 2016 The Bolshoi–Planck simulation has a volume of (250 h− Mpc) and galaxies. differencecontains 2048 is3 particles primarily of mass 1.9 10 due8 M .Haloes/subhaloes to the diThefferences abundance matching between technique is a simple the and powerful statis- × (4) generalizesIn to this paper we use theseGalaxy-evolution results by5 assuming that GSMFsand their used merger trees to were deriveHalo calculated with mass these the⊙ phase-space SHMRs, accretion tempo- tical Behroozi approach rates to connecting etz=0 galaxies al. toto 2013 haloes. 3 In its most simple the M∗–Mvir is independent of redshift. We use the relation dM∗ ∂M∗(Mvir(t),z) dMvir ∂M∗(Mvir(t),z) dz used (Moustakas et al. 2013). When comparing both GSMFs = obtained in Section 2.3+ for local galaxies., Specifically,(5) we dt ∂Mvir dt ∂z dt we find that the high mass-end from Rodr´ıguez-Puebla et al. infer galaxy star formation rates from halo mass accretion 3RESULTS (2015) is significantly different to the one derive in (Mous- where the first term is the contribution to the SFR from but if the M∗–Mratesvir relation as follow. is independent Let M∗ = M of∗( Mredshiftvir(t),t then)thestellarmassof the Figures: SFR vs M∗;sSFRvsM∗;SFRDvszandcosmic takas et al. 2013). In contrast, when comparing Rodr´ıguez- stellarhalo mass MAR ofacentralgalaxyformedinahaloofmass and a central the second galaxy term formed is the in changea halo of in mass theMvir SHMR (t)attimet.If Puebla et al. (2015) GSMF with Bernardi et al. (2010) we with redshift. Although in this paper we assume a constant mass density vs z. Mvir(t) is M∗ =M M∗∗–(MMvirvir(t)).is independent From this relation of redshift star thenformationM∗ = M∗(Mvir(t)). find an excellent agreement, for a more general discussion ratesSHMR, are given theFrom formalism simply this by relation that we star describe formation below rates applies are given to this simply by; see Rodr´ıguez-Puebla et al. (2015). In less degree, we also more general case. dM∗ d log M∗ dMvir find that the different values employed for the scatter of the The relation= betweenf∗ stellar mass, growth and observed (3) 4DISCUSSION dt d log Mvir dt SHMR explain these differences. star formation rate is given by where f∗ = M∗/Mvir.Moreover,fromtheaboveequation Discuss about the star formation efficiency. For which galax- where f∗ = M∗/Mvir. We call this Stellar-Halo Accretion Rate ⃝c 0000 RAS, MNRAS 000,000–000 we can deduce that the star formation efficiency, ϵ,isjust, ies ϵ =1.Doweneedafigureofϵ vs Mvir? Coevolution (SHARC) if true halo-by-halo. sSFR d log M∗ = ϵ = . (4) Figure 1. Halo MARs from z 0 to 3, from the Bolshoi–Planck simulation. The instantaneous rate is shown in black, and the dynamically time averaged rate Stellar halo accretion rate coevolution 2595 = ˙ ˙ sMAR d log Mvir in red. The grey band is the 1σ (68 per cent) range of the instantaneous MARs. All the slopes are approximately the same 1.1 both for Mvir and Mvir,dyn. Figure 5. sSFRs using Eq. 4. 4.1 Implications for the bathtub model Scatter of halo mass accretion∼ rates Implied scatter of star formation rates While in the above analysis the term dMvir/dt refers to MNRAS 455, 2592–2606 (2016) Equation 3 is essentially the bathtub model. Differences be- the instantaneous mass accretion rates we also infer SFRs tween the observed SFRs and our models will give con- by using dMvir/dt averaged over a dynamical time scale as straints on the regime where the bathtub model is valid. measured from the simulations. As we will show below, we confirm the previous claim • For z>5ourSFRsareaboveobservations.Thismeans in ? that this model reproduces the observed evolution of that at early epochs galaxies did not convert gas in stars as the SFR−M∗ and cosmic star formation rate. Moreover, we fast as they receive it. This is a phase of gas accumulation show that this is also true when using halo mass accretion where the bathtub is being fill with gas. ⃝c 20?? RAS, MNRAS 000,1–?? Downloaded from Figure 2. Scatter of halo MARs from z 0 to 3 from the Bolshoi–Planck Figure 6. Scatter of the SFRs using Eq. 3. = simulation. As in Fig. 1, scatter for the instantaneous rate is shown in black, ⃝c 20?? RAS, MNRAS 000,1–?? and that for the dynamically time averaged rate in red. http://mnras.oxfordjournals.org/ form, the cumulative halo and subhalo mass function1 and the cu- mulative GSMF are matched in order to determine the mass relation between haloes and galaxies. In order to assign galaxies to haloes in the Bolshoi–Planck simulation, in this paper we use a more gen- eral procedure for abundance matching. Recent studies have shown that the mean SHMRs of central and satellite galaxies are slightly different, especially at lower masses where satellites tend to have more stellar mass compared to centrals of the same halo mass (for a more general discussion see Rodr´ıguez-Puebla et al. 2012, 2013; at University of California, Santa Cruz on December 10, 2015 Reddick et al. 2013;Watson&Conroy2013;Wetzeletal.2013). Since we are interested in studying the connection between halo mass accretion and star formation in central galaxies, for our anal- ysis we derive the SHMR for central galaxies only. We model the GSMF of central galaxies by defining P (M Mvir) as the probability distribution function that a distinct halo of∗| mass Mvir hosts a central galaxy of stellar mass M . Then the GSMF for central galaxies as a function of stellar mass∗ is given by Figure 3. Upper panel: SHMR for SDSS galaxies. The red curve is for all ∞ SDSS galaxies, from Behroozi et al. (2013d) abundance matching using the φ ,cen(M ) P (M Mvir)φh(Mvir)dMvir. (2) ∗ ∗ = 0 ∗| Bolshoi simulation. The black curve is for SDSS central galaxies, using the ! abundance matching method of Rodr´ıguez-Puebla, Avila-Reese & Drory Here, φh(Mvir) is the halo mass function and P (M Mvir) is a log- (2013)appliedtotheBolshoi–Plancksimulation.Thelatteriswhatwe normal distribution assumed to have a scatter of ∗σ| 0.15 dex c = use in this paper, where we restrict attention to central galaxies. Bottom independent of halo mass. Such a value is supported by the anal- Panel: halo-to-stellar mass relations. The dotted vertical line and the blue ysis of large group catalogues (Yang, Mo & van den Bosch 2009; arrow indicate that galaxies below M 1010.5 M are considered as main ∗ = Reddick et al. 2013), studies of the kinematics of satellite galaxies sequence galaxies, while some higher mass galaxies⊙ are not on the main (More et al. 2011), as well as clustering analysis of large samples sequence. of galaxies (Shankar et al. 2014;Rodr´ıguez-Puebla et al. 2015). 12 Note that this scatter, σ c, consists of an intrinsic component and a to 10 M based on the NYU-VAGC (Blanton et al. 2005)and measurement error component. At z 0, most of the scatter ap- using the⊙ 1/V estimator. The membership (central/satellite) for = max pears to be intrinsic, but that becomes less and less true at higher each galaxy was obtained from an updated version of the Yang redshifts (see e.g. Behroozi, Conroy & Wechsler 2010;Leauthaud et al. (2007) group catalogue presented in Yang et al. (2012). The et al. 2012; Behroozi et al. 2013d; Tinker et al. 2013). Here, we corresponding SHMR is shown as the black curve in Fig. 3,and do not deconvolve to remove measurement error, as most of the the SHMR for all galaxies from Behroozi et al. (2013a) is shown observations that we will compare to include these errors in their as the red curve. The difference between the two curves for halo 12 measurements. masses lower than Mvir 10 M reflects the fact that the SHMR As regards the GSMF of central galaxies, we here use the results of centrals and satellite∼ galaxies are⊙ slightly different as mentioned 12 reported in Rodr´ıguez-Puebla et al. (2015). In a recent analysis of above. At halo masses higher than Mvir 10 M , this difference the SDSS DR7, Rodr´ıguez-Puebla et al. (2015) derived the total, is primarily due to the differences between∼ the GSMFs⊙ used to derive central, and satellite GSMF for stellar masses from M 109 M these SHMRs, Behroozi et al. (2013c) used Moustakas et al. (2013). ∗ = ⊙ When comparing both GSMFs, we find that the high-mass end from Rodr´ıguez-Puebla et al. (2015) is significantly different to the one 1 Typically defined at the time of subhalo accretion. derive in Moustakas et al. (2013). In contrast, when comparing MNRAS 455, 2592–2606 (2016) Is Main Sequence SFR Controlled by Halo Mass Accretion? by Aldo Rodríguez-Puebla, JoelStellar-Halo Primack, AccretionPeter Behroozi, Rate Coevolution Sandra Faber11 MNRAS 2016 SHARC correctly predicts star formation rates to z ~ 4 SHARC predicts “Age Matching” (blue galaxies in accreting halos) and “Galaxy Conformity” at low z Open Questions: Extend SHARC to higher-mass galaxies Check predicted correlations vs. observations at high z Can SHARC be used to measure growth rate of halos from the star Stellar-Halo Accretion Rate Coevolution 9 formation rate, as a dark energy vs. Stellar-Halo Accretion Rate Coevolution 9 gravity test? 9 9.5 10 10.5 Figure 8. Specific star formation rates as a function of redshift z for stellar masses M∗ =10, 10 , 10 and 10 M⊙ from time- independent SHMR model. The red and black curves are the sSFRs, from both dynamically-time-averaged and instantaneous mass accretion rates, respectively, with the gray band representing the dispersion in the latter. Both are corrected for mergers. The orange curve is the Speagle et al. (2014) summary of observed sSFRs onthemainsequence.ObservationsfromWhitakeretal.(2014Put SHARC in ), Ilbert et al. (2015) and Schreiber et al. (2015) are also included. “bathtub” equilibrium esting to discuss these differences in the light of the constant models of galaxy SHMR model. formation & predict First, the observed sSFRs of galaxies at z>4aresys- tematically lower than the time independent SHMR model mass loading and predictions. These differences increase at z =6.Thedis- metallicity evolution agreement between the constant SHMR predicted SFRs and the observations implies that the changing SHMR must be used, as in equation (5), at least at high redshift. Net mass loading factor η from an Figure 6. Left Panel: Net mass loading factor, η = ηw,ISM − ηr,ISM as a function of halo mass at z =0, 1, 4, and 6, obtained assuming equilibrium bathtub model (E+SHARC) z Between z =4andz =3theobservedstar-forming preventive feedback described by Eeff = Eh × Eq.Thecalculateddispersionisshownat =0and6.Right Panel: Net mass loading sequence is consistent with the SHARC predictions. Between factor and its dispersion as a function of galaxy stellar mass. z =2andz =0.5, the observed sSFRs are slightly above Figure 6. Left Panel: Net mass loading factor, η = ηw,ISM − ηr,ISM as a function of halo mass at z =0, 1, 4, and 6, obtained assuming the SHARC predictions. This departure occurs at the time preventive feedback12 described by Ee = Eh × Eq.Thecalculateddispersionisshownatz =0and6.Right Panel: Net mass loading than f∗ × ϵ in Mvir ∼ 10 M⊙ halos. Then theff mass loading In this Section we presented a simple framework that of the peak value of the cosmic star formation rate. factorfactor should and increase its dispersion at high redshift. as a function of galaxy stellarclarifies mass. how the net mass loading factor is connected to After the compilation carried out by Speagle et al. Halo mass quenching is more relevant for high mass preventive feedback in the context of the equilibrium time- (2014), new determinations of the sSFR have been pub- halos. This imposes the constraint that any functional form independent SHMR model. As long as the SFR is driven lished, particularly for redshifts z<2.5. In Figures 7 and 8, proposed for Eq should reproduce the12 fall off at higher masses by MAR these assumptions can be generalized in the same Figure 9. Scatter of the sSFR for main-sequencethan galaxiesf∗ × ϵ in pre-Mvir ∼ 10 M⊙ halos. Then the mass loading In this Section we presented a simple framework that of the term f∗ϵ.Giventheuncertainredshiftdependenceof framework, as we mention briefly in the discussion section. we reproduce new data published in Whitaker et al. (2014); dicted in our model. factor should increase at high redshift. clarifies how the net mass loading factor is connected to Ilbert et al. (2015) and Schreiber et al. (2015). This new Eq,wewillassumeforsimplicitythatitisindependentof set of data agrees better with our model between z =2 redshift. TheHalo functional mass quenching form Eq that is describes more therelevant fall-off for high mass preventive feedback in the context of the equilibrium time- and z =0.5, implying that the time-independent SHMR of f∗ϵ at z =0isgivenby 4.2 Scatter of the sSFR Main Sequencehalos. This imposes the constraint that any functional form independent SHMR model. As long as the SFR is driven (SHARC assumption) may be nearly valid across the wide 4SPECIFICSTARFORMATIONRATES proposed for Eq should reproduce−0.5 the fall off at higher masses by MAR these assumptions can be generalized in the same redshift range from z ∼ 4toz ∼ 0, a remarkable result. We now turn our discussion to the scatter of the star-forming Mvir FROM SHARC Eq(Mvir)=min(1, 0∗.85 12 ) . (16) However, it is not clear whether this is valid since the newer main sequence, displayed in Figure 9. Whenof using the termM˙ vir,thef ϵ.Giventheuncertainredshiftdependenceof„ 10 M⊙ « framework, as we mention briefly in the discussion section. 4.1 SHARC Compared with Observations observations have not been recalibrated as in Speagle et al. scatter is nearly independent of redshift andEq,wewillassumeforsimplicitythatitisindependentof it increases 12 (2014). very slowly with mass for z<2. TheNote valueredshift. that of at thez = The 0 scat- for functional halos more massive form E thanq that∼ 10 describesM⊙, theWe have fall-o nowff collected together all the tools needed to fol- Eeff ∼ ϵ × f∗/fb.Suchafall-off is thus necessary in or- low several aspects of galaxy evolution while galaxy stel- of f∗ϵ at z =0isgivenby ⃝c 000 der to make SHMR+equilibrium assumptions work, in other 9 10.5 0000 RAS, MNRAS ,000–000 lar masses are in the4SPECIFICSTARFORMATIONRATES range M∗ =10M⊙ to 10 M⊙. words, equation (12). The green long dashed-dotted−0. lines5 in We start by showing the evolution in the slope and zero- vir Figure 5 show Eq.AthigherredshiftsEeMff > ϵ×f∗/fb imply- point of the star-formingFROM main sequence SHARC inferred by the Eq(Mvir)=min(1, 0.85 12 ) . (16) ing that the mass-loading factor becomes„ 10 moreM⊙ important« at time-independent SHMR (SHARC model) in Figure 7. Re- high redshifts in high mass galaxies. call that when assuming4.1 a time-independentSHARC Compared SHMR, stellar with Observations Next, in equation (13) we use the functional forms de- mass12 growth can be inferred directly from halo mass accre- Note that at z = 0 for halos more massive than ∼ 10 M⊙, scribed in equations (15) and (16) to deduce a relation for tion rates via M˙ ∗ =Wef∗ × haveϵ × M now˙ vir,withthecorresponding collected together all the tools needed to fol- e ∗ b the netE ff mass∼ loadingϵ × f factor:/f .Suchafall-off is thus necessarySFR in = M or-˙ ∗/(1 − Rlow). Black several solid aspects lines show of results galaxy using evolution while galaxy stel- 9 10.5 der to make SHMR+equilibrium assumptions work,instantaneous in other mass accretion rates, M˙ vir,inequation(4). fb Eeff (Mvir,z) lar masses are in the range M∗ =10M⊙ to 10 M⊙. η = − 1 (1 − R). (17) Red solid lines show the SFRs when using mass accretion »words,f∗(Mvir equation) ϵ(Mvir) (12).– The green long dashed-dotted lines in We start by showing the evolution in the slope and zero- rates smoothed over a dynamical time scale, M˙ vir,dyn,in- Figure 5 show Eq.AthigherredshiftsEeff > ϵ×f∗/fb imply- The left hand panel of Figure 6 shows the net mass loading stead. The gray bandpoint indicates of the the intrinsic star-forming scatter around main sequence inferred by the factor,ingη = thatηw,ISM the− mass-loadingηr,ISM,asafunctionofhalomassat factor becomes morez = importantthe star-forming at maintime-independent sequence when using SHMRM˙ vir.Notethat (SHARC model) in Figure 7. Re- 0, 1, 4and6.Notethatthegenericredshiftevolutionofhigh redshifts in high mass galaxies. η is our model sSFRs werecall corrected that when in order assuming to take a into time-independent ac- SHMR, stellar governed byNext, the evolution in equation of Eeff .Forhaloslessmassivethan (13) we use the functionalcount forms the de- contribution of mergers to stellar mass growth, 11.5 mass growth can be inferred directly from halo mass accre- ∼ 10scribedM⊙,Figure6showsthatthemassloadingfactor in equations (15) and (16) to deduce a relationas explained for in §2.5. We show the resulting˙ sSFRs without˙ approximately scales as a power law with a power that is this merger correctiontion with rates the blackvia M and∗ = redf∗ dashed× ϵ × linesMvir,withthecorresponding −2.13 ˙ roughlythe independent net mass loading of redshift, factor:η ∝ Mvir .Equivalently, when using M˙ vir andSFRM˙ vir =,dynMrespectively.∗/(1 − R). Note Black that solid the lines show results using 9.7 we find that for galaxies with stellar mass below ∼ 10 M⊙ contribution from mergersinstantaneous becomes more mass important accretion for red- rates, M˙ vir,inequation(4). fb Eeff (Mvir,z) −1.07 the massη = loading factor scales as η ∝ M−∗ 1 (1.Massloading− R). shifts z<(17)0.5. Hereafter,Red solid we will lines focus show our discussion the SFRs on when using mass accretion factors are» predictedf∗(Mvir to) beϵ very(Mvir small) for halos– more massive the merger-corrected results, also shown as the solid lines in 12 ˙ vir dyn than ∼ 10 M⊙,especiallyatlowredshifts. Figure 8. rates smoothed over a dynamical time scale, M , ,in- The left hand panel of Figure 6 shows the net mass loading stead. The gray band indicates the intrinsic scatter around ⃝c 0000factor, RAS,η MNRAS= ηw,000ISM,000–000−ηr,ISM,asafunctionofhalomassatz = the star-forming main sequence when using M˙ vir.Notethat 0, 1, 4and6.Notethatthegenericredshiftevolutionofη is our model sSFRs were corrected in order to take into ac- governed by the evolution of Eeff .Forhaloslessmassivethan count the contribution of mergers to stellar mass growth, 11.5 ∼ 10 M⊙,Figure6showsthatthemassloadingfactor as explained in §2.5. We show the resulting sSFRs without approximately scales as a power law with a power that is this merger correction with the black and red dashed lines −2.13 roughly independent of redshift, η ∝ Mvir .Equivalently, when using M˙ vir and M˙ vir,dyn respectively. Note that the 9.7 we find that for galaxies with stellar mass below ∼ 10 M⊙ contribution from mergers becomes more important for red- −1.07 the mass loading factor scales as η ∝ M∗ .Massloading shifts z<0.5. Hereafter, we will focus our discussion on factors are predicted to be very small for halos more massive the merger-corrected results, also shown as the solid lines in 12 than ∼ 10 M⊙,especiallyatlowredshifts. Figure 8. ⃝c 0000 RAS, MNRAS 000,000–000 Velocity function 1807 Velocity function 1807 Is there a “Too Big To Fail” problem in the field? Velocity function 1807 Not down to Bolshoi-Planck simulation Vmax > 50 km/s Increasing discrepancy for extrapolated Vmax < 50 km/s Downloaded from Downloaded from Downloaded from http://mnras.oxfordjournals.org/ http://mnras.oxfordjournals.org/ http://mnras.oxfordjournals.org/ Figure 12. Relation between 3D circular velocity dN/dlog V and line-width Figure 13. Comparison of the observed and theoretical estimates of the Figure 12. Relation betweenComparison 3D circular of the velocity Local Volume dN/dlog 3DV andvelocity line-width function dN/d logFigure V 13.ObservedComparison and theoretical of the observed estimates and of the theoretical 3D velocity estimates function of the dN/dlog V functions for observations (short-dashed and solid curves) and circular VF of galaxies. The shaded area shows the region of the observed from losthe SMDPL simulation with the observed Local Volume of galaxies. The LCDM-Planck model overpredicts dwarf dN/dlog Vlos functionsfor for the observations!CDM-Planck (short-dashedmodel (dot–dashed and and solid long-dashed curves) and curves). ThecircularVF VF – a of strip galaxies. of 20 The per cent shaded around area the shows reconstructed the region VF in of the the Local observed optical velocity function of galaxies within 10 Mpc (Figure 12 of galaxy abundance± with V < 60 km/s. The WDM model predicts for the !CDM-Planckshort-dashedmodel (dot–dashed curve shows our and estimate long-dashed of the circular curves).∼ VF The in the LocalVF –Volume a strip as of given20 by per equation cent (12). around The solid the curves reconstructed show the !CDM VF in model the Local Klypin, Karachentsev et al. 2015) and the HI radio velocity a wrong± shape for the VF; it fails by a factor of 2–3 at small short-dashed curve showsVolume. our It produces estimate the ofdistribution the circular of line VF widths in that the accurately Local fits theVolumepredictions. as given The by dashedequation curve (12). shows The the solid best prediction curves show for the the WDM!CDM model model function from the ALFALFA survey (Papastergis et al. 2015). velocities while still overpredicting the abundance of 30 km/s Volume. It producesobservations. the distribution The disagreement of line widths between that the ! accuratelyCDM model fits and the observationspredictions.with thermal The dashed neutrino curve mass of showsmdwm the1.35 best keV. prediction Both theoretical for the WDMmodels model Figure 12. Relation between 3D circular velocity dN/dlog V and line-width Figure 13. Comparison= of the observed and theoretical at University of California, Santa Cruz on February 6, 2016 estimates of the becomesThe slightlygrey band worse is for the the 1σ 3D spread circular around velocities mock as compared Milky Way with thecenters havegalaxies. severe problems. (Klypin, The Karachentsev, WDM model predicts et al. a2015; wrong see shape also for the VF; dN/dlog Vobservations.los functions The for disagreement observationsline-of-sightof 10 Mpc betweenline Local width. (short-dashed the Volume.!CDM (Rodriguez-Puebla model and and solid observations curves) et al. 2016 and) with thermalcircularit failsPapastergis by neutrino a VF factor of& of mass Shankar 2–3galaxies. at of smallm 2015)dwm velocities The1.35 shaded while keV. still Botharea overpredicting theoretical shows the the models region of the observed 1 = at University of California, Santa Cruz on February 6, 2016 becomes slightly worse for the 3D circular velocities as compared with the have severeabundance problems. of 30 km The s− WDMgalaxies. model The !CDM- predictsPlanck a wrongmodel shapeoverpredicts for the VF; for the !CDM-Planck model (dot–dashed and long-dashed curves). The VF – a strip of 20 per cent around1 the reconstructed VF in the Local line-of-sight line width.for dN/dlog Vlos by assuming a random orientation of disc galaxiesit failsthe by abundance a factor of of dwarf 2–3 galaxies at± small with velocitiesV ! 60 km while s− . still overpredicting the short-dashed curve shows our estimate of the circular VF in the Local Volume as given1 by equation (12). The solid curves show the !CDM model and by taking the observed fraction of early-type galaxies. We thenabundance of 30 km s− galaxies. The !CDM-Planck model overpredicts Volume. It produces the distributionchange the free of parameters line widths until we that get an accurately acceptable fit fits to the the data. predictions. The dashed curve shows the1 best prediction for the WDM model for dN/dlog Vlos by assuming a random orientation of disc galaxies the abundance of dwarf galaxies with V ! 60 km s− . The best fit to observed circular VF of galaxies is 6DISCUSSION observations.and by The taking disagreement the observed between fraction the of! early-typeCDM model galaxies. and observations We then with thermal neutrino mass of mdwm 1.35 keV. Both theoretical models 1 Estimates of the abundance of galaxies with a= given line width at University of California, Santa Cruz on February 6, 2016 becomes slightlychange the worse free parameters for thedN 3D until circular we get velocitiesV an acceptable− as compared fit to the data.with the have severe problems. The WDM model predicts a wrong shape for the VF; 0.18 1 Vlos presented in Fig. 10 for different observational samples show line-of-sightThe line best width. fit to observedd log10 circularV = VF100 of km galaxies s− is 6DISCUSSIONit fails by a factor of 2–3 at small velocities while still overpredicting the ! " that results mostly agree for intermediate-size galaxies with Vlos 3 1 1 abundance(25–150) km of s− 30. The km Local s Volumegalaxies. results The are! systematicallyCDM-Planck model overpredicts 1 V 3 3 Estimates of the abundance− of galaxies with a given line width dN V exp− h Mpc− . (12) ≈ 1 0.18 × − 250 km s 1 theabove abundance the HIPASS (Zwaan of dwarf et al. galaxies2010) and ALFALFAwith V (Papastergis60 km s . for dN/dlog Vlos by assuming a random1 # orientation! − " $ of disc galaxies Vlos presented in Fig. 10 for different observational! samples− show d log10 V = 100 km s− et al. 2011) estimates, but this is mostly due to the fact that H I and by taking the observed! Note fraction that the" slope of early-type of the circular VF galaxies. dN/dlog V Weis close then to, butthat resultsmeasurements mostly do agree not cover for early-type intermediate-size galaxies, which galaxies are present with Vlos 3 1 slightly smallerV than, the slope of the related line-width function (25–150)in the Local km s Volume.− . The The Local agreement Volume between results the ALFALFA are systematically (Pa- change the free parameters until we get an acceptable3 3 fit to the data. ≈ expdN/dlog Vlos.Onecanshowanalyticallythatapurepowerlaw1 h Mpc− . (12) abovepastergis the HIPASS et al. 2011 (Zwaan)andLocalVolumeresultsisparticulargood et al. 2010) and ALFALFA (Papastergis × #− 250 km s− $ 6DISCUSSION The best fit to observedd circularN/dlog! V gives VF a ofpower-law galaxies" line-width is function dN/dlog Vlos withet al. once2011 ALFALFA) estimates, results but are this corrected is mostly by the duefraction to of the early-type fact that H I exactly the same slope. The small change in the slope between galaxies in the Local Volume as presented in Fig. 4. This is very en- Note that the slope of the circular1 VF dN/dlog V is close to, but measurementsEstimates do not of cover the abundance early-type galaxies, of galaxies which are with present a given line width dN dVN/dlog V and− dN/dlog Vlos seen in Fig. 12 is, thus, due to the couraging because it indicates that we finally have an accurate mea- slightly0. smaller18 than,bending the of slope dN/dlog ofV theat large relatedV. line-width function in theVsurement Localpresented Volume. of the abundance The in Fig.agreement of galaxies10 for in between a broad different range the of ALFALFA observational velocities (Pa- samples show 1 los 1 d log10 VdN=/dlog Vlos.Onecanshowanalyticallythatapurepowerlaw100 kmComparison s− of the observed and theoretical circular VF presentedpastergis(10–200) et al. km2011 s− . )andLocalVolumeresultsisparticulargood ! " that results mostly agree for intermediate-size galaxies with Vlos dN/dlog V gives a power-lawin Fig. 12 leads line-width to the same function conclusion, dN which/dlog weV foundlos with comparingonce ALFALFAFig. 13 compares results observational are corrected estimates by the for fraction the circular of early-type VF 3 1 exactly the same slope.the line-width The small functions change in Fig. 11 in: the the! slopeCDM model between gives a goodgalaxiesof galaxies in(25–150) the Local with theoretical km Volume s− predictions. as The presented Local for the in Fig.! VolumeCDM4. This and WDMresults is very en- are systematically V 3 3 1 exp fit for massive galaxies withhVlosMpc> 70 km. s− , but it has(12) problems ≈models. As one may have expected, the !CDM model dramatically dN/dlog V and dN/dlog Vlos seen1 in Fig. 12 is, thus,− due to the couragingabove because the HIPASS it indicates (Zwaan that we finally et al. have2010 an) andaccurate ALFALFA mea- (Papastergis × #−explaining250 km the s abundance− $ of galaxies with small velocities. How- overpredicts the abundance of dwarf galaxies. The WDM is not bending of dN/dlogever,!V at the large disagreementV. " is slightly worse for dN/dlog V functions assurementetbetter. al. of It the was2011 abundance designed) estimates, to fix of the galaxies small-scale but in this problemsa broad is mostly range of the ! ofCDM. velocities due to the fact that H I 1 1 Comparison of thecompared observed with and dN/ theoreticaldlog Vlos. For circular example, VF at V presentedlos 40 km s− the(10–200)As far km as the s abundance. of dwarfs is concerned, the WDM still fails. Note that the slope of the circular VF dN/dlog V is close= to, but measurements− do not cover early-type galaxies, which are present in Fig. 12 leads to thedisagreement same conclusion, with the ! whichCDM-Planck we foundmodel comparing was a factor of 3.5 Fig. 13As Fig.compares13 shows, observational the WDM model estimates with mwdm for the1.25 circular keV VF = 1 slightly smaller than, thefor theslope line-width of the functions. related It is line-width factor of 6 for the function circular ve- inpredicts the a Local factor of Volume.2–3 too few The dwarfs agreement with V (10–15) between km s− the ALFALFA (Pa- the line-width functions in Fig. 11: the !CDM model gives a good of galaxies with theoretical∼ predictions for1 the=!CDM and WDM locities. Qualitatively, it is clear why the disagreement is worse in and a factor of 2 too many at V 25 km s− . As plots in Fig. 11 dN/dlogfitVlos for.Onecanshowanalyticallythatapurepowerlaw massive galaxies with V > 70 km s 1, but it has problems models.pastergis As one may et al. have2011 expected,)andLocalVolumeresultsisparticulargood≈ the !CDM model dramatically V-space: somelos fraction of galaxies− with given Vlos are intrinsically indicate, decreasing neutrino mass to mwdm 1.0 keV fixes the 1 = dN/dlogexplainingV gives a the power-law abundancelarger galaxies line-width of galaxies with large withfunctionV, for small which d velocities. theN/!dlogCDMV predicts How-los with correctoverpredictsonceproblem ALFALFA with theV abundance25 km s results− , of but dwarf it also are ruins galaxies. corrected the small-scale The by WDM tail the by fraction is not of early-type ≈ 1 ever, the disagreementabundance. is slightly worse for dN/dlog V functions as better.reducing It was designed the abundance to fix of theV small-scale(10–15) km s problems− dwarfs by of another the !CDM. exactly the same slope. The small change in the slope between galaxies in the Local= Volume as presented in Fig. 4. This is very en- 1 compared with dN/dlog Vlos. For example, at Vlos 40 km s− the As far as the abundance of dwarfs is concerned, the WDM still fails. dN/dlog V and dN/dlog Vlos seen in Fig. 12 is,= thus, due to the couraging because it indicates that we finally have an accurate mea- disagreement with the !CDM-Planck model was a factor of 3.5 As Fig. 13 shows, the WDMMNRAS model454, with1798–1810mwdm (2015)1.25 keV bending of dN/dlog V at large V. surement of the abundance of galaxies in= a broad range1 of velocities for the line-width functions. It is factor of 6 for the circular ve- predicts a factor of 2–3 too few dwarfs with V (10–15) km s− ∼ 1 1 = Comparisonlocities. of Qualitatively, the observed it is and clear theoretical why the disagreement circular VF is worse presented in and a(10–200) factor of 2 km too s many− . at V 25 km s− . As plots in Fig. 11 ≈ in Fig. 12V-space:leads to some the fraction same conclusion, of galaxies with which given weVlos foundare intrinsically comparing indicate,Fig. decreasing13 compares neutrino mass observational to mwdm 1.0 estimates keV fixes for the the circular VF 1 = the line-widthlarger galaxies functions with in large Fig.V,11 for: which the ! theCDM!CDM model predicts gives correct a good problemof withgalaxiesV 25 with km s− theoretical, but it also ruins predictions the small-scale for the tail! byCDM and WDM ≈ 1 abundance. 1 reducing the abundance of V (10–15) km s− dwarfs by another fit for massive galaxies with Vlos > 70 km s− , but it has problems models. As one may= have expected, the !CDM model dramatically explaining the abundance of galaxies with small velocities. How- overpredicts the abundance of dwarf galaxies. The WDM is not ever, the disagreement is slightly worse for dN/dlog V functions as better. It was designed toMNRAS fix the454, small-scale1798–1810 problems (2015) of the !CDM. 1 compared with dN/dlog V . For example, at V 40 km s− the As far as the abundance of dwarfs is concerned, the WDM still fails. los los = disagreement with the !CDM-Planck model was a factor of 3.5 As Fig. 13 shows, the WDM model with mwdm 1.25 keV = 1 for the line-width functions. It is factor of 6 for the circular ve- predicts a factor of 2–3 too few dwarfs with V (10–15) km s− ∼ 1 = locities. Qualitatively, it is clear why the disagreement is worse in and a factor of 2 too many at V 25 km s− . As plots in Fig. 11 ≈ V-space: some fraction of galaxies with given Vlos are intrinsically indicate, decreasing neutrino mass to mwdm 1.0 keV fixes the 1 = larger galaxies with large V, for which the !CDM predicts correct problem with V 25 km s− , but it also ruins the small-scale tail by ≈ 1 abundance. reducing the abundance of V (10–15) km s− dwarfs by another = MNRAS 454, 1798–1810 (2015) REVIEW RESEARCH BOX 2 0.5 Observations Challenges: Cusp-Core, Too Big to Fail, Satellite Galaxies REVIEW RESEARCH How to generate outflows Simulations Flores & Primack94 and Moore94 first pointed out that dark matter simulations have Outflows are probably generated by young starsdensity inside ρ(r) galaxies. ~ rα at small r with α ≈ −1 (“cusp”)NFW/ref. while observed 111 small spiral galaxies Computer simulations of the formation of galaxiesand clusters would therefore appeared to have α ≈0.0 0 (“core”). BOX 2 0.5 Observations α ideally resolve cosmological large-scale structure (over tens of Adams, Simon+14 find ρ( r) ~ r , α ≈ 0.5 Governato+10,13 and the Nature review by REVIEW RESEARCH megaparsecs) downHow to the to scale generate of individual stars outflows (at least 1014 times for dwarf spirals,Simulations in agreement with recent Pontzen & Governato14 show that in high- high-resolution simulations with baryons. smaller). This is, and seems certain to remain, unfeasible. The line Outflows are probably generatedresolution by young galaxy stars simulations, inside galaxies. baryonic NFW/ref. 111 of attack is instead to mimic the effects ofBOX stars 2 without actually Observations Computer simulations of thephysics formation softens of galaxies the central would therefore DM cusp–0.5 to a 0.5 0.0 resolving themideally individually. resolve Because cosmological starHow formation larcorege-scale to as generate is long the structure conclusion as enough outflows (over stars tens ofform, M* ≥ Simulations Outflows are probably generated by young stars inside14 galaxies. NFW/ref. 111 of runaway gasmegaparsecs) cooling and colla downpse, to a the typical scale10 computational7 of M individual⦿. This happens stars (at because least 10 of timesrepeated Cored Computer simulations of the formation of galaxies would therefore 0.0 approach is tosmaller). form stars This when is, andgas satisfies seemsideally certain certainepisodes resolve cosmological to averaged remain,when lar thege-scale unfeasible. baryons structure cool (over The tensand line of slowly 14 conditions, andof in attack particular is instead when to it reaches mimicmegaparsecs) thefall a threshold effectsinto down the to of thegalaxy density. stars scale of center, without individual As starsand actually (at are least then 10−1.0times –0.5 smaller). This is, and seems certain to remain, unfeasible. The line expelled rapidly (in less than a dynamical (at 500 parsecs) resolution slowlyresolving improves them in simulations, individually.of attacksmaller Because is instead regions star to mimic formation and the effects larger of is stars the without conclusion actually –0.5 time) by energy released by stars and densities can beof self-consistently runaway gas cooling resolved andresolving89 colla.Untilthemid-2000s,a thempse, individually. a typical Because computational star formation is the conclusion Cusped Cored of runaway gas cooling and collapse, a typical computational Cored approach is to form stars when2supernovae.3 gas satisfies certain averaged typical threshold density was set at 0.1mHapproachcm ,where is to form starsmH whenis the gas mass satisfies certain averaged conditions, and in particularconditions, whenObservers and it in reaches particular (e.g., when a Walker threshold it reaches & aPeñarrubia11, threshold density. density.−1.5 As As −1.0−1.0 of a hydrogen atom. This corresponds to the mean density of galactic (at 500 parsecs) resolution slowly improves in simulations, smaller regions and larger (at 500 parsecs) NFW resolution slowly improves inAmorisco simulations, & Evans12) smaller regions had89 agreed and largerthat the neutral atomic gas, so stars form throughoutdensities the can disk be self-consistently of a simulated resolved .Untilthemid-2000s,a Cusped 89 23 densities can be self-consistentlytypicallarger threshold resolved dwarf density wasspheroidal.Untilthemid-2000s,a set at 0.1mH cmMilky,where WaymH satelliteis the mass Cusped galaxy. Energy output from stars in the diffuseof a hydrogen medium atom. This results correspon23 inds a to the mean density of7 galactic −1.5 typical threshold density was setgalaxies at 0.1 msuchH cm as Fornax,where (Lm H≈ is1.7x10 the mass L⦿) have gentle heating of the entire galaxy, slowingneutral the atomic process gas, so of stars further form throughout star the disk of a simulated −1.5Insuffcient Core creation of a hydrogen atom. Thisgalaxy. corresponcores, Energy output dsbut to recent from the stars mean papers in the densitydiffuse (e.g., medium of Breddels galactic results−2.0 in a& formation. However, if one can achieve sufficient resolution (and energy permitted gentleHelmi13,14, heating of the entire Jardel galaxy, slowing& Gebhardt13, the process of furtherRichardson star Insuffcient Core creation neutral atomic gas, so stars form throughout the disk of a simulated −2.0 implement the more complicated coolingformation. physics& Fairbairn14) However, required if one can16,38,110 have achieve questioned)to sufficient resolution this. (and energy permitted galaxy. Energy output from stars in the diffuse medium results in16,38,110 a 23 23 implement the more complicated cooling physics required )to 104 105 106 107 108 109 1010 1011 push to 10mH cm or 100mH cm ,thenaqualitativelydifferent(Reviewed23 in Kormendy23 & Freeman16.) Thus 104 105 106 107 108 109 1010 1011 gentle heating of the entirepush galaxy, to 10mH cm slowingor 100 themH cm process,thenaqualitativelydifferent of further star Insuffcient Core creation behaviourthe results. cusp-core This is the densityquestion that corresponds is now to molecular −2.0 M /M behaviour results.formation. This is the However, density if that one corresponds can achieve tosufficient molecular resolution (and M /M* energyPontzen permitted & Governato14 cloudobservational formation in our Galaxy, and known theoretical. to be the precursor of star * cloud formationimplement in our Galaxy, the more known complicated toformation. be the precursor Instead cooling of forming ofphysics starstars in a required diffuse way through16,38,110 the)to entire Figure 3 | Dark matter cores are only generated in sufficiently bright formation. Instead of forming stars23 in a diffusedisk, now way stars2 formthrough3 efficiently the in small, entire isolated regionsFigure23,44,whichis 3 | Dark mattergalaxies. Here cores we have are10 plotted4 only the generated10 power-law5 10 index in6 a sufficientlyof the10 dark7 matter10 bright8 109 1010 1011 push to 10mH cm or 100considerablymH cm more,thenaqualitativelydifferent realistic. When energy from the resulting stellar density (as in Fig. 2, but here measured at radius 500 parsecs) against the mass 23,44 disk, now starsbehaviour form efficiently results. in small, This is isolatedpopulations the density regions is dumped that into corresponds,whichis the gas, the cloud to heats moleculargalaxies. to much higherHere weof stars have formed, plottedM* (updated the power-law from ref. 90). The index expecteda slopesof the fromM dark/ pureM dark matter temperatures than diffuse star formation achieves. It is likely that matter calculations are approximated by the solid line (using the scaling* considerably morecloud realistic. formation When in our energy Galaxy, from known the resulting to be the stellar precursor ofdensity star (as in Fig.relations 2, but from here ref. 111),measured whereas hydrodynamic at radius 500 simulations parsecs) at high against mass have the mass intense radiation pressure is also a significant factor34.Inanycase,the of stars formed, Mshallower* (updated slopes, indicated from ref. by the 90). crosses. The Large expected crosses show slopes halos resolved from pure dark populations is dumpedformation. into Instead the gas, of forming the cloudgas is overpressurized stars heats in to a diffuse much by a factor higher way of at least through a hundred the compared entire to its withFigure more than 3 | 500,000Dark simulated matter dark cores matter are particles. only Smaller generated crosses have in sufficiently bright surroundings and expands rapidly. The combination23,44matter of high initial calculations are approximated by the solid line (using the6.5 scaling temperatures thandisk, diffuse now stars star form formation efficiently achieves. in small, It is likely isolated that regions ,whichis fewergalaxies. particles, butHere always we more have than 50,000. plotted When the less than power-law about 10 M index[ of a of the dark matter density and explosive decompression is suitable for launching gas has formed into stars, there is insufficient energy available to flatten the 34 relations from ref. 111), whereas hydrodynamic simulations at high mass have intense radiationconsiderably pressure is alsomore a realistic.significantgalactic-scale When factor outflows; energy.Inanycase,the it is from also what the allows resulting an efficient stellar coupling of the cuspdensity93. The box (as symbols in Fig. show 2, data but from here the measuredTHINGS survey at50 of radius field dwarf 500 parsecs) against the mass available energy to dark matter (Box 1). shallower slopes,galaxies.of indicated stars Additional formed, by observationaltheM crosses.(updated data Large at stellar from crosses masses ref. lower 90). show than The 10 halos6M expected resolved slopes from pure dark gas is overpressurizedpopulations by a factor is dumped of at least into a the hundred gas, the compared cloud heats to its to much higher * [ with more than 500,000wouldmatter be highly calculationssimulated valuable. This dark are figure matter approximated is updated particles. from figure by Smaller 1 of the ref. solid90. crosses line have(using the scaling surroundings andtemperatures expands rapidly. than diffuse The combination star formation of high achieves. initial It is likely that 6.5 matter halo through sufficiently rapid galactic fountainsfewer or particles, outflows90, butrelations always more from than ref. 111), 50,000. whereas When hydrodynamic less than about simulations 10 M[ of at high mass have intense radiation pressure is also a significant factor34.Inanycase,the 98 density and explosive decompression isbut suitable few simulations for launching of luminous galaxies reach the resolutiongas has necessary formed into(such stars, as a sterile there neutrino), is insufficient suppressing the formation energy of available small-scale structure to flatten the andshallower delaying the slopes, collapse indicated of dwarf-sized by halos the and crosses. their associated Large star crosses show halos resolved gas is overpressurized byto a study factor the formation of at least of cores. a hundred Some high-resolution compared simulations93 to its of 50 galactic-scale outflows; it is also what allows an efficient coupling of the 99 Milky Way analogues have been reported to form darkcusp matter. The cores box on symbolsformationwith more to show slightly than data later 500,000 fromepochs the. simulated However, THINGS these dark models survey matter do notof pro- particles. field dwarf Smaller crosses have surroundings and expands rapidly. The combination of high initial 100 6 6.5 available energy to dark matter (Box 1).scales of a kiloparsec or larger94,95. On the othergalaxies. hand it has Additional been ducefewer observational cores particles, on observationally but data always relevant at stellar more scales masses thanand are 50,000. currently lower than When strongly 10 lessM than about 10 M[ of 101 [ density and explosive decompressionreported that cores shrink is suitable with respect for to the launching halo scale radius96 for total constrainedgas has formed by the clustering into stars, of the neutral there gas is in insufficient the cosmic web energy. available to flatten the 11 would be highly valuable.Another major This class, figure self-interacting is updated dark from matter figure (SIDM) 1102 of, refers ref. 90. masses exceeding 10 M[ (the mass of the Milky Way is about 93 50 galactic-scale outflows; it is12 also what allows an efficient coupling of the cusp . The box symbols show data from the THINGS survey of field dwarf 10 M ). These statements may be reconcilable;furtherhigher-resolution to particle physics scenarios with significant ‘dark sector’ interactions. [ 90 6 matter halo throughavailable sufficiently energy rapid to dark galacticwork matter is required fountains (Box for 1). progress or in outflows our understanding., As masses continue SIDMgalaxies. behaves Additional more like a collisional observational fluid, preventing data the at central stellar high- masses lower than 10 M[ to increase to the cluster scale (see the ‘High-mass(such galaxies’ as a section sterile neutrino),densitywould cusp be from suppressing highly forming valuable. andthe making formation This the central figure of regions small-scaleis updated more spher- fromstructure figure98 1 of ref. 90. but few simulations of luminous galaxiesabove), reach further the processes resolution become necessary interesting. For instance, numerical ical103. Unlike in the WDM case, the number density of dark matter and delaying thehalos collapse remains relatively of dwarf-sized unchanged even halos at the and smallest their scales associated104. The star to study the formation of cores. Somework high-resolution has shown that accretion simulations onto the central of black hole, if proceeding90 matter halo through sufficiently rapid galactic fountains or outflows , diversity of theoretical models,99 however, gives significant freedom in the in repeated, highly energetic bursts, replicates the effectformation of supernovae to on slightly later epochs . However, these models do not pro- 98 Milky Way analogues have been reported to form97 dark matter cores on choice(such of as the a cross-section sterile neutrino), and its possible suppressing dependence onthe particle formation velo- of small-scale structure but few simulations of luminousdwarf galaxies galaxies. reach the resolution necessary 100 scales of a kiloparsec or larger94,95. On the other hand it has been duce cores on observationallycityand105. This delaying makes it difficult relevant the collapse to establish scales a of single dwarf-sizedand baseline are SIDM currently scenario. halos strongly and their associated star to study the formation of cores. Some high-resolution simulations of 101 Modifying dark matter 96 constrained by theThe clustering majority of work of the on non-minimal neutral gas dark in matter99 the cosmic falls into the web . reported that coresMilky shrink Way with analogues respect have toWe the been have halo established reported scale that radius there to form arefor many dark total processes matter that can cores modify on the WDMformation or SIDM categories.to slightly However, later modifications epochs to. However, the dark matter these models do not pro- 11 100102 dark matter94,95 distribution in the centre of galaxies, even ifAnother the dark matter majorprofileduce class, can cores also self-interacting be on achieved observationally through other dark processes. relevant matter For instance,(SIDM) scales par-and, refers are currently strongly masses exceedingscales 10 ofM a[ kiloparsec(the mass or of larger the Milky. On Way the other is about hand it has been 106 is cold and collisionless (that is, interacts only through gravity)—a ‘min- ticle–particle annihilations can reduce central densities directly, pro- 101 12 to96 particle physics scenarios with significant ‘dark sector’ interactions. 10 M[). Thesereported statements that may cores be shrink reconcilable;furtherhigher-resolutionimal’ with scenario respect motivated to the by supersymmetric halo scale weakly radius interactingfor totalmassive videdconstrained the physics is by tuned the to clustering prevent rapid of annihilation the neutral in the early gas in the cosmic web . 11 particles. However, the observational controversiesSIDM detailed behaves in the moreuniverse.Another like Alternatively, a collisional major if dark class, matter fluid, self-interacting decays preventing over long timescales the dark central to matter high- (SIDM)102, refers work is requiredmasses for progress exceeding in our 10 understanding.M[ (the mass As masses of the continue Milky Way is about 12 ‘Evidence for a cusp–core discrepancy’ section above have prompted slightly lighter daughter particles, the lost mass provides a source of density cusp fromto formingparticle physics and making scenarios the central with significantregions107 more ‘dark spher- sector’ interactions. to increase to10 theM cluster[). These scale statements (see theconsiderable may ‘High-mass be interest reconcilable;furtherhigher-resolution in galaxies’ non-minimal section dark matter models. By changing kinetic energy for expanding the centre of dark matter halos .Another above), furtherwork processes is required become for interesting. progressthe properties in our For of understanding. instance,the dark matter numerical candidate As particle, massesical the predictions103 continue. Unlike for inrelevantSIDM the possibility WDM behaves is case, that more the the dark like number matter a collisional is not density formed from fluid, of particles dark preventing matter the central high- the distribution within halos are altered; potentially, therefore, galaxies at all. In the case of an ultralight scalar field, for instance, the Compton 104 work has shownto that increase accretion to the onto cluster the centraland scale galaxy black clusters (see hole, thebecome ‘High-mass if an proceeding important probe galaxies’ of particlehalos physics.section remains relativelywavelengthdensity becomes cusp unchanged from larger than forming even the supposed at and the interparticle making smallest separation; the scales central. The regions more spher- 103 in repeated, highlyabove), energetic further bursts, processes replicates becomeFor instance, the effect interesting. the warm of darksupernovae matter For models instance, on (WDM)diversity invoke numerical a candidate of theoreticalaccordinglyical . models, Unlikethe field behaves however, in the as a Bose–Einstein WDM gives significantcase, condensate the108 numberrather freedom than density in the of dark matter particle with non-negligible residual streaming motions after decoupling as individual particles, preventing the central cusps from forming. 104 dwarf galaxies97work. has shown that accretion onto the central black hole, ifchoice proceeding of the cross-sectionhalos remains and relativelyits possible unchanged dependence even on particle at the smallest velo- scales . The in repeated, highly energetic bursts, replicates the effect of supernovae105 on diversity of13 theoretical FEBRUARY 2014 models, | VOL however, 506 | NATURE gives | 175 significant freedom in the ©2014 Macmillancity .Publishers This makes Limited. itAll difficultrights reserved to establish a single baseline SIDM scenario. 97 Modifying darkdwarf matter galaxies . The majoritychoice of work of the on cross-section non-minimal and dark its matter possible falls dependence into the on particle velo- city105. This makes it difficult to establish a single baseline SIDM scenario. We have established that there are many processes that can modify the WDM or SIDM categories. However, modifications to the dark matter Modifying dark matter The majority of work on non-minimal dark matter falls into the dark matter distribution in the centre of galaxies, even if the dark matter profile can also be achieved through other processes. For instance, par- We have established that there are many processes that can modify the WDM or SIDM106 categories. However, modifications to the dark matter is cold and collisionless (that is, interacts only through gravity)—a ‘min- ticle–particle annihilations can reduce central densities directly, pro- dark matter distribution in the centre of galaxies, even if the dark matter profile can also be achieved through other processes. For instance, par- imal’ scenario motivated by supersymmetric weakly interacting massive vided the physics is tuned to prevent rapid106 annihilation in the early is cold and collisionless (that is, interacts only through gravity)—a ‘min- ticle–particle annihilations can reduce central densities directly, pro- universe. Alternatively, if dark matter decays over long timescales to particles. However,imal’ scenario the observational motivated by controversies supersymmetric detailed weakly in interacting the massive vided the physics is tuned to prevent rapid annihilation in the early ‘Evidence for a cusp–core discrepancy’ section above have prompted slightly lighter daughteruniverse. particles, Alternatively, the lost if dark mass matter provides decays a source over of long timescales to particles. However, the observational controversies detailed in the 107 considerable interest‘Evidence in non-minimal for a cusp–core dark discrepancy’ matter models. section By changing above havekinetic prompted energy forslightly expanding lighter the daughter centre of particles, dark matter the halos lost mass.Another provides a source of the propertiesconsiderable of the dark matter interest candidate in non-minimal particle, the dark predictions matter models. for Byrelevant changing possibilitykinetic is that energy the dark for expanding matter is notthe centre formed of from dark particles matter halos107.Another the distributionthe within properties halos of are the altered; dark matter potentially, candidate therefore, particle, galaxies the predictionsat all. In the for caserelevant of an ultralight possibility scalar is that field, the for dark instance, matter the is Compton not formed from particles and galaxy clustersthe distribution become an within important halos probe are altered; of particle potentially, physics. therefore,wavelength galaxies becomesat all. larger In the than case the of an supposed ultralight interparticle scalar field, separation; for instance, the Compton For instance,and the galaxy warm dark clusters matter become models an (WDM) important invoke probe a candidate of particleaccordingly physics. the fieldwavelength behaves becomes as a Bose–Einstein larger than condensate the supposed108 rather interparticle than separation; particle with non-negligibleFor instance, residual the warm streaming dark matter motions models after (WDM) decoupling invokeas a individual candidate particles,accordingly preventing the field the behaves central cusps as a Bose–Einstein from forming. condensate108 rather than particle with non-negligible residual streaming motions after decoupling as individual particles, preventing the central cusps from forming. 13 FEBRUARY 2014 | VOL 506 | NATURE | 175 ©2014 Macmillan Publishers Limited. All rights reserved 13 FEBRUARY 2014 | VOL 506 | NATURE | 175 ©2014 Macmillan Publishers Limited. All rights reserved “Too Big To Fail” MWy Satellite Problem !CDM subhalos vs. Milky Way satellites “Missing satellites”: Klypin et al. 1999, Moore et al. 1999 Aquarius Simulation dwarf satellites around the Milky Way Diameter of visible Milky Way 30 kpc = 100,000 light years 250 kpc sphere Diameter of Milky Way Dark Matter Halo 1.5 million light years 5 5 >10 identified subhalos 12 bright satellites (LV > 10 L ) V. Springel / Virgo Consortium S. Okamoto Of the ~10 biggest subhalos, ~8 cannot host any known bright MW satellite ??? ??? ??? Possible Solutions ??? to “Too Big to Fail” The Milky Way is anomalous? ??? The Milky Way has a low ??? mass dark matter halo? ??? Galaxy formation is ??? stochastic at low masses? Observed Milky Way Satellites Image credits: V. Springel / Virgo Consortium; A. Riess / HST; SDSS; M. Schirmer LMC Dark matter is not just SMC “massive failures”: CDM -- maybe WDM (e.g., highest resolution Lovell+12,13,14)? LCDM simulations predict ~10 subhalos in this range in the MW, Or even self-interacting DM but we don’t see any No indication that more (Rocha+13, Peter+13, Zavala such galaxies [except massive halos host more Sagittarius (?)] luminous galaxies +14, Vogelsberger+14)? But maybe just including All of the bright MW dSphs are c.f. Strigari et al. 2008 baryons properly will do the consistent with trick. Vmax . 25 km/s (see also Strigari, Frenk, Or maybe high-resolution & White 2010) Boylan-Kolchin,CDM Bullock, simulations Kaplinghat 2011, are 2012being MBK, Bullock, & Kaplinghat (2012) misinterpreted? Maybe Feedback & the Dark Matter Distribution Mvir =3E9M at z =0 Mvir =1E10M at z =0 Challenges: Cusp-Core, Too Big to Fail, Satellite Galaxies In addition to the Governato group’s papers on this (including Zolotov+12, Brooks+13) there are several other recent papers (e.g., Teyssier+13,No core Arraki+14, Trujillo-Gome+14,Core DelPololo&Pace15, Simpson+15) arguing that baryonic effects convert the DM cusp to a core. The highest- resolutionFeedback simulation & the yet Darkof a dwarf Matter spiral was Distribution presented in Onorbe, Boylan-Kolchin, Bullock,Star Formation et al. 2015. Rate: The Dwarf continuous Irregular central star formation converted the central cusp to a core, reducing the rotation velocity, and thus resolving the TBTF challenge. 4 6 Mvir =3E9M at z =0 M =2Mvir10=1ME10M at z =0 M =4 10 M Bursty Star Formation ⇤ ⇥ ⇤ ⇥ re = 338pc re = 1068pc SF regulated by feedback:Fe/H]= 3.3 [Fe/H]= 1.9[ Bursty on small Feedback & the Dark Matter Distribution timescales No core Flatter in time Core Jose O˜norbe The Role of Stellar Feedback in Dwarf Galaxy Formation 9 Mvir =3E9M at z =0 Mvir =1E10M at z =0 4 6 Jose O˜norbe M The=2 Role of Stellar10 FeedbackM in Dwarf Galaxy Formation M 7 =4 10 M ⇤ ⇥ ⇤ ⇥ Repeated episodes when baryons cool r = 338pc r = 1068pc e ande slowly fall into the galaxy center, No core Core Fe/H]= 3.3 dominate[Fe/H]= the 1mass,.9[ and then are expelled rapidly (in less than tdyn) by radiation pressure and supernovae, soften the central DM cusp to a core . Jose O˜norbe The Role of Stellar Feedback in Dwarf Galaxy Formation 9 Onorbe, Hopkins+14 FIRE (Feedback in Realistic Environments) simulations M =2 104M M =4 106M ⇤ ⇥ ⇤ ⇥ re = 338pc re = 1068pc Fe/H]= 3.3 [Fe/H]= 1.9[ Jose O˜norbe The Role of Stellar Feedback in Dwarf Galaxy Formation 9 Challenges: Cusp-Core, Too Big to Fail, Satellite Galaxies Some papers (e.g., Garrison-Kimmel,Rocha,Boylan-Kolchin,Bullock+13) claimed that feedback can’t solve the TBTF problem. But Onorbe,Boylan-Kolchin,Bullock+15 (including some of the same authors) showed that a better treatment of feedback can do so, as have Maxwell,Wadsley,Couchman15 and Nipoti&Binney15. Despite the growing consensus among galaxy simulators that including baryons appears to convert the DM cusp to a core and can resolve the Too Big To Fail and Satellites challenges, papers continue to explore alternative solutions such as WDM and SIDM. Recent Warm Dark Matter (WDM) papers WDM doesn’t resolve small scale problems: Schneider,Anderhalden,Maccio,Diemand14 WDM constraints from lensing: Li,Frenk+1512.06507 WDM constraints from reionization - strong: Schultz,Onorbe+14 - weak: Lapi&Danese15 - but this conflicts with Behroozi&Silk15 Non-thermal (Shi&Fuller99) WDM for 3.5 keV line MWy mass > 1.2x1012 M⦿: Lovell,Bose+1511.04078 Barely produces enough satellites w/o baryons: Horiuchi+16 Excluded at 2σ by Lyα Forest: Schneider1601.07553 Self-Interacting Dark Matter (SIDM) Cluster shapes: σ/m < 1 cm2/g : Peter+12 Merging clusters: σ/m < 1.5 cm2/g : Kalhoefer+15 Strongly affected by baryons: Elbert+15 Velocity-dependence allows bigger σ/m for dwarf galaxies, makes them rounder But forming galaxies are not round, they are elongated (prolate, sausage-shaped) Satellite Galaxies in WDM 5 CDM WDM FigureAquarius 3. Images simulation. of the CDM (left) Springel and WDM (right)et al. level2008 2 haloes at z =0.Intensityindicatestheline-of-sightprojectedsquarLovell, Eke, Frenk, et al. 2012 e of the density, and hue the projected density-weighted velocity dispersion, ranging from blue (low velocity dispersion) to yellow (high velocity dispersion). Each box is 1.5 Mpc on a side. Note the sharp caustics visible at large radii in the WDM image, severalofwhich are alsoWDM present, although simulation less well defined, at inright the CDM has case. no “too big to fail” subhalos, but it doesn’t lead to the right systematics to fit dwarf galaxy properties as 20.0 associate final satellite luminosity with the maximum pro- Kuzio de Naray+10 showed. It alsogenitor won’t mass have for each the surviving subhalos subhalo. Thisneeded is essentiall y 10.0 the mass of the object as it falls into the main halo. The 7.0to explain grav lensing flux anomaliessmallest and subhalo gaps in in each stellar of our samples streams. has an infall mass 9 9 5.0 of 3.2 × 10 M⊙ in the WDM case, and 6.0 × 10 M⊙ in the CDM case. 3.0 The LMC, SMC and the Sagittarius dwarf are all [kpc] 2.0 more luminous than the 9 dwarf spheroidals considered by max r Boylan-Kolchin et al. (2011) and by us. As noted above, the 1.0 Milky Way is exceptional in hosting galaxies as bright as Cold the Magellanic Clouds, while Sagittarius is in the process of 0.5 Warm being disrupted so its current mass is difficult to estimate. Cold (Top 12) Boylan-Kolchin et al. hypothesize that these three galaxies Warm (Top 12) −1 all have values of Vmax > 60kms at infall and exclude sim- 10 20 30 40 50 60 70 80 ulated subhaloes that have these values at infall as well as −1 −1 Vmax [kms ] Vmax > 40kms at the present day from their analysis. In what follows, we retain all subhaloes but, where appropri- Figure 4. The correlation between subhalo maximum circular ate, we highlight those that might host large satellites akin velocity and the radius at which this maximum occurs. Sub- to the Magellanic Clouds and Sagittarius. haloes lying within 300kpc of the main halo centre are in- The circular velocity curves at z =0forthe12sub- cluded. The 12 CDM and WDM subhaloes with the most mas- sive progenitors are shown as blue and red filled circles respec- haloes which had the most massive progenitors at infall are tively; the remaining subhaloes are shown as empty circles. The shown in Fig. 5 for both WDM and CDM. The circular shaded area represents the 2σ confidence region for possible hosts velocities within the half-light radius of the 9 satellites mea- of the 9 bright Milky Way dwarf spheroidals determined by sured by Wolf et al. (2010) are also plotted as symbols. Leo- Boylan-Kolchin et al. (2011). II has the smallest half-light radius, ∼ 200pc. To compare the satellite data with the simulations we must first check the convergence of the simulated subhalo masses within at the same radii in the simulated subhaloes. To provide a fair least this radius. We find that the median of the ratio of the comparison we must choose the simulated subhaloes that mass within 200pc in the Aq-W2 and Aq-W3 simulations is are most likely to correspond to those that host the 9 bright W 2/W 3 ∼ 1.22, i.e., the mass within 200pc in the Aq-W2 dwarf spheroidals in the Milky Way. As stripping of sub- simulation has converged to better than ∼ 22%. haloes preferentially removes dark matter relative to the As can be inferred from Fig. 5, the WDM subhaloes more centrally concentrated stellar component, we choose to have similar central masses to the observed satellite galax- ⃝c 2011 RAS, MNRAS 000, ??–8 The High-z Universe Confronts Warm Dark Matter: Galaxy Counts, Reionization and the Nature of Dark Matter 5 CDM WDM WDM simulation at right has no “too big to fail” subhalos, but it is inconsistent at Figure 3. Simulation snapshots from CDM (left) and 0.8 keV WDM (right) overlaid with circles to indicate identified dark matter halos that are more massive 8 1 >10σ with Ultra Deep Field galaxy counts. It also won’t have the subhalos needed than 3.4 10 h M . The size of the circle is proportional to the virial radius of each halo. The CDM slice is filled with collapsed structure at z=6, while the ⇥ thermal sterile WDM slice is largely devoidto reionize of collapsed the halos universe that are unless massive enoughmν for hydrogen≳ 2.6 keV cooling. (or Note mν that artificial ≳ 15 haloeskeV) wouldassuming show upan as regularly separated haloes in the filaments,optimistic suggesting that ionizing contamination radiation by artificial escape haloes fraction is likely (Schultz, negligible here. Onorbe, Abazajian, Bullock14). thermal ShiFuller Faint z=2 galaxies exclude mν ≲ 1.8 keV and mν ≲ 4 keV (Menci+16). thermal matching techniqueAnd we took the into Ly- accountα forest(Viel+13) the merger history excludes of each mν in the ≲ 1.32 keV keV model.at 4σ, Detections≲ 3.3 keV at at these 2σ epochs. should be robust in halo and used its maximal mass obtained over its lifetime Mpeak in- the future with JWST. However, even current detections offer an in- stead of Mh. In any case, this correction turned to be small due to teresting test: the point with error bar (2 ) corresponds to the lower the lack of substructure at high redshifts. We used a requirement of limit on the cumulative abundance of galaxies at those redshifts, as at least 40 simulation particles to constitute a halo, setting a halo set by the faintest galaxies observed in the HUDF (Bouwens et al. 8 1 mass completeness limit of Mh =3.4 10 h M . 2007; McLure et al. 2012; Oesch et al. 2013). Its horizontal po- ⇥ Compared to the density maps shown in Figure 2, the differ- sition (corresponding halo mass) is based on the luminosity limit ences between WDM and CDM become even more apparent when and our adopted Mh-L relation presented in the next section. Im- we compare halo counts. Figure 3 shows two of the same density portantly, the total abundance of galaxies at each redshift must be slices overlaid with white circles to indicate identified dark matter above the data point shown (regardless of its horizontal positioning 8 1 halos more massive than our Mh =3.4 10 h M complete- on the plot). One can see without any further analysis that the 0.8 ⇥ ness limit. Circle sizes are proportional to the virial radius of each keV WDM model will have trouble producing enough galaxies to identified halo. The difference in collapsed structures is striking be- match current observations at z>8; there are simply not enough tween these two simulations. For example, the void in the upper left collapsed objects of any mass to account for the known galaxies at corner is completely empty of any haloes in the 0.8 keV WDM run. this epoch. Figure 4 provides a more quantitative demonstration of the In order to provide a more precise connection with observa- differences in halo abundances from model to model, where each tions we will need a mapping between halo mass and galaxy lumi- panel shows the cumulative dark halo mass function at redshifts nosity. This is a primary subject of the next section. z =6, 7, 8, and 13. The CDM result (dotted line with shading) is in all cases above the WDM models (solid lines with shading, as labeled). Angulo et al. (2013) found a suppression of the halo mass 3 PREDICTING OBSERVABLES function of the form1 ↵ 3.1 Observed Luminosity Functions n 1 M M WDM (M)= 1+ 1 1+erf log . (5) nCDM 2 M M2 We will normalize our predictions using observed high-z galaxy ✓ ◆ ✓ ◆ counts. In doing so, we follow the literature and assume that high-z We have verified this expression provides a good fit to the luminosity function is well characterized by a Schechter function WDM/CDM abundance ratio for z . 10, with decreasing accu- racy with increasing redshift. In our simulations, at 109M , the L ↵ L dL (L) dL = exp . (6) 0.8 keV model is suppressed by more than an order of magnitude ⇤ L L L at all redshifts relative to CDM. ✓ ⇤ ◆ ✓ ⇤ ◆ ⇤ Robust observations of luminosity functions with measures of , As can be seen in the z =13panel of Figure 4, no haloes at all ⇤ L , and ↵ exist out to z 8 (Bouwens et al. 2011; McLure et al. exist in 0.8 keV WDM model. Indeed we find that no haloes have ⇤ ⇠ formed before z =12for 0.8 keV WDM and none before z =15 2012; Schenker et al. 2013) and current observations can provide constraints on the normalization (with other parameters fixed) out to z 10 (Oesch et al. 2013). ⇠ 1 Strictly speaking Angulo et al. (2013) has ↵ =1fixed, however they also We parameterize the evolution of the luminosity function with redshift by fitting quoted observational results for log ,L and ↵ correct for artificial haloes. We find that keeping ↵ as a free fitting parameter ⇤ ⇤ is necessary to provide reasonable fits, probably owing to a strong evolution and fitting them linearly as a function of z from z =4 8. Fig- with redshift. ure 5 shows the fit used in this work in comparison with fits from c 0000 RAS, MNRAS 000, 000–000 Challenges: Cusp-Core, Too Big to Fail, Satellite Galaxies Some papers (e.g., Garrison-Kimmel,Rocha,Boylan-Kolchin,Bullock+13) claimed that feedback can’t solve the TBTF problem. But Onorbe,Boylan-Kolchin,Bullock+15 (including some of the same authors) showed that a better treatment of feedback can do so, as have Maxwell,Wadsley,Couchman15 and Nipoti&Binney15. Despite the growing consensus among galaxy simulators that including baryons appears to convert the DM cusp to a core and can resolve the Too Big To Fail and Satellites challenges, papers continue to explore alternative solutions. Recent Warm Dark Matter (WDM) papers WDM doesn’t resolve small scale problems: Schneider,Anderhalden,Maccio,Diemand14 WDM constraints from lensing: Li,Frenk+1512.06507 WDM constraints from reionization - strong: Schultz,Onorbe+14 - weak: Lapi&Danese15 - but this conflicts with Behroozi&Silk15 Non-thermal (Shi&Fuller99) WDM for 3.5 keV line MWy mass > 1.2x1012 M⦿: Lovell,Bose+1511.04078 Barely produces enough satellites w/o baryons: Horiuchi+16 Excluded at 2σ by Lyα Forest: Schneider1601.07553 Self-Interacting Dark Matter (SIDM) Cluster shapes: σ/m < 1 cm2/g : Peter+12 Merging clusters: σ/m < 1.5 cm2/g : Kalhoefer+15 Velocity-dependent SIDM simulations: Vogelsberger+12, Zavela+13 σ/m = 2 cm2/g SIDM w baryons just like CDM, need V-dependence: Fry,Governato+15 SIDM with V-4 dependence can arise from Rutherford-like scattering: Feng+09, Tulin+13 σ/m = 50 cm2/g for dwarf galaxies OK with V-dependence, makes them rounder: Elbert+15 But forming galaxies are not round, they are elongated (prolate, sausage-shaped) The Astrophysical Journal Letters,792:L6(6pp),2014September1 van der Wel et al. 1 0.75 0.5 0.25 0 1 Low-mass Forming Galaxies are Elongated (Prolate) 0.75 van der Wel+ApJ 2014 0.5 Prolate 0.25 Spheroidal Oblate 0 Figure 3. Reconstructed intrinsic shape distributions of star-forming galaxies in our 3D-HST/CANDELS sample in four stellar mass bins and five redshift bins. The model ellipticity and triaxiality distributions are assumed to be Gaussian, with the mean indicated by the filled squares, and the standard deviation indicated by the open vertical bars. The 1σ uncertainties on the mean and scatter are indicated by the error bars. Essentially all present-day galaxies have large ellipticities, and small triaxialities—they are almost all fairly thin disks. Toward higher redshifts low-mass galaxies become progressively more triaxial. High-mass galaxies always have rather low triaxialities, but they become thicker at z 2. ∼ (A color version of this figure is available in the online journal.) Figure 4. Color bars indicate the fraction of the different types of shape defined in Figure 2 as a function of redshift and stellar mass. The negative redshift bins represent the SDSS results for z<0.1; the other bins are from 3D-HST/CANDELS. See also WHEN DID ROUND DISK GALAXIES FORM? T. M. Takeuchi et. al ApJ 2015 (A color version of this figure is available in the online journal.) Letter allows us to generalize this conclusion to include earlier Despite this universal dominance of disks, the elongatedness epochs. of many low-mass galaxies at z ! 1impliesthattheshapeof At least since z 2moststarformationisaccountedforby agalaxygenerallydiffersfromthatofadiskatearlystages 10 ∼ !10 M galaxies (e.g., Karim et al. 2011). Figures 3 and 4 in its evolution. According to our results, an elongated, low- show that⊙ such galaxies have disk-like geometries over the same mass galaxy at z 1.5 will evolve into a disk at later times, or, redshift range. Given that 90% of stars in the universe formed reversing the argument,∼ disk galaxies in the present-day universe over that time span, it follows that the majority of all stars in the do not initially start out disks.13 universe formed in disk galaxies. Combined with the evidence As can be seen in Figure 3, the transition from elongated that star formation is spatially extended, and not, for example, to disky is gradual for the population. This is not necessarily concentrated in galaxy centers (e.g., Nelson et al. 2012;Wuyts et al. 2012)thisimpliesthatthevastmajorityofstarsformedin 13 This evolutionary path is potentially interrupted by the removal of gas and disks. cessation of star formation. 4 FormationIn hydro sims,of elongated dark-matter galaxies dominated with low massesgalaxies at arehigh prolate redshift High-resolution (~20 pc) cosmological zoom-in hydro simulations Ceverino, Primack, Dekel MNRAS 453, 408 (2015) Stars 10 M* <10 M☉ at z=2 Dark matter See also Tomassetti, Dekel+arXiv151206268 20 kpc Gaps in Cold Stellar Streams Probe DM Halo Substructures Direct Detection of Cold Dark Matter Substructure Yoon, Johnston, Hogg ApJ (2011) Density fluctuations in cold stellar streams will reflect DM substructure. Fluctuations in the Pal5 stream suggest the existence of missing satellites in numbers predicted by ΛCDM. Dark Matter Sub-Halo Counts via Star Stream Crossings R. G. Carlberg ApJ (2012), Carlberg,Grillmair, Hetherington ApJ (2012), Carlberg & Grillmair ApJ (2013) Comparison of the CDM based prediction of the gap rate-width relation with published data for four streams shows generally good agreement within the fairly large measurement errors. The result is a statistical argument that the vast predicted population of sub-halos is indeed present in the halos of galaxies like M31 and the Milky Way. Feeling the pull, a study of natural Galactic accelerometers - I. Stellar Stream of Palomar 5 R. Ibata, G. Lewis, N. Martin arXiv:1512.03054 Our deep CFHT data do not support the presence of significant gaps along the stream. The origin of the difference between our results and those of Carlberg et al. (2012) is likely that it is due to variations in homogeneity of the SDSS as one approaches the limiting magnitude of that survey. Detecting dark matter substructures around the Milky Way with Gaia R. Feldmann, D. Spolyar MNRAS (2015) Gaia should detect the kinematic signatures of a few starless substructures Properties of dark subhaloes from gaps in tidal streams D. Erdal, V. Belokurov MNRAS (2015) SDSS, DES, Gaia, and LSST can measure the complete set of properties (including the phase-space 7 coordinates during the flyby) of dark perturbers with M > 10 M⊙ Reviewed in Tidal Streams in the Local Group and Beyond (Springer, 2016) More evidence for substructure in DM halos: lensing flux anomalies Direct Detection of Cold Dark Matter Substructure Neal Dalal & Christopher S. Kochanek ApJ 572, 25 (2002) We devise a method to measure the abundance of satellite halos in gravitational lens galaxies and apply our method to a sample of seven lens systems. After using Monte Carlo simulations to verify the method, we find that substructure comprises fsat=0.02 (median, 0.006 Effects of Line-of-Sight Structures on Lensing Flux-ratio Anomalies in a ΛCDM Universe D. D. Xu, Shude Mao, Andrew Cooper, Liang Gao, Carlos S. Frenk, Raul Angulo, John Helly MNRAS (2012) We conclude that line-of-sight structures can be as important as intrinsic substructures in causing flux-ratio anomalies. ... This alleviates the discrepancy between models and current data, but a larger observational sample is required for a stronger test of the theory. Constraints on Small-Scale Structures of Dark Matter from Flux Anomalies in Quasar Gravitational Lenses R. Benton Metcalf, Adam Amara MNRAS 419, 3414 (2012) We investigate the statistics of flux anomalies in gravitationally lensed QSOs as a function of dark matter halo properties such as substructure content and halo ellipticity. ... The constraints that we are able to measure here with current data are roughly consistent with ΛCDM N-body simulations. Constraints on WDM from weak lensing in anomalous quadruple lenses K. T. Inoue, R. Takahashi, T. Takahashi, T. Ishiyama MNRAS (2015) Observed four quadruple lenses that show anomalies in the flux ratios, we obtain constraints on the mass of thermal WDM, mWDM ≥ 1.3 keV (95 per cent CL). More evidence for substructure in DM halos: lensing flux anomalies How well can CDM substructures account for the observed radio flux-ratio anomalies D. D. Xu, Dominique Sluse, Liang Gao, Jie Wang, C. Frenk, Shude Mao, P. Schneider, V. Springel MNRAS (2015) We find that CDM substructures are unlikely to be the whole reason for radio flux anomalies. How well can CDM substructures account for the observed radio flux-ratio anomalies J.-W. Hsueh, C. Fassnacht, S. Vigetti, J. McKean, C. Singola, M. Auger, L. Koopmans, D. Lagattuta arXiv:1601.01671 Keck~II adaptive optics imaging and HS T data reveal the lensing galaxy to have a clear edge-on disc component that crosses directly over the pair of images that exhibit the flux-ratio anomaly. CDM Substructures in Early-Type Galaxy Halos Davide Fiacconi, Piero Madau, Doug Potter, Joachim Stadel arXiv:1602.03526 13 Very high-resolution DM simulations of ~10 M⦿ halos show more substructure than previous simulations. Baryonic contraction increases the number of massive subhalos in the inner regions of the main host. The host density profiles and projected subhalo mass fractions appear to be broadly consistent with observations of gravitational lenses. Gravitational detection of a low-mass dark satellite galaxy at cosmological distance, Simona Vigetti+ 2012 Nature This group uses galaxy-galaxy lensing to look for the effects of substructure. Our results are consistent with the predictions from cold dark matter simulations at the 95 per cent confidence level, and therefore agree with the view that galaxies formed hierarchically in a Universe composed of cold dark matter. Inference of the cold dark matter substructure mass function at z = 0.2 using strong gravitational lenses S. Vegetti, L. V. E. Koopmans, M. W. Auger, T. Treu and A. S. Bolton MNRAS (2015) No detection of substructure in 11 lens galaxies from the SDSS ACS survey. With earlier detections, the inferred fraction is consistent with the expectations from CDM simulations and with inference from flux ratio anomalies at 68% C.L. New ways of observing dark matter halo substructure Optical lensing of quasar narrow line regions Detection of a substructure with adaptive optics integral field spectroscopy of the gravitational lens B1422+231 A. M. Nierenberg, T. Treu, S. A. Wright, C. D. Fassnacht, M. W. Auger MNRAS (2014) In this paper we demonstrate for the first time that subhalos can be detected using strongly lensed narrow-line quasar emission, as originally proposed by Moustakas & Metcalf (2003). Many quasars have detectable narrow line emission, so this technique can really measure substructure. ALMA spectral detection of lensing of dusty galaxies Dark Matter Substructure Detection Using Spatially Resolved Spectroscopy of Lensed Dusty Galaxies Yashar Hezaveh, Neal Dalal, G. Holder, M. Kuhlen, D. Marrone, N. Murray, J. Vieira ApJ (2013) We find that in typical DSFG lenses, there Lensed is a ∼55% probability of detecting a SubMM 8 σ Galaxies substructure with M > 10 M⊙ with >5 significance in each lens, if the abundance of substructure is consistent with previous lensing results. Detection of Lensing Substructure in SDP.81 Yashar Hezaveh, Neal Dalal+ 1601.01388 We find evidence for the presence of a 8.96±0.12 M = 10 M⊙ subhalo with 6.9σ significance. Rotating Planes of Galaxies About the Milky Way14 andM.LETTER L. McCallRESEARCH Andromeda 14 M. L. McCall A7 IC10 C2 185 147 A26 A vast, thin plane of corotating dwarf A5 A25 A24 A18 A27 All the northern red A10 A17 A21 galaxies orbiting the Andromeda galaxy A9 205 satellites are coming M32 A28 A23 Ibata et al. Nature 2013 A15 A1 towards us and all the Galactic latitude A3 A20 A19 A12 A11 A2 southern ones are A13 Intriguingly, the plane we identify is approximately A16 A29 M33 A14 moving away Downloaded from Downloaded from aligned with the pole of the Milky Way’s disk. A22 LGS3 IC1613 A6 14 M. L. McCall Galactic longitude Figure 1 | Map of the Andromeda satellite system. The homogeneous sample, discovered in various surveys with non-uniform spatial coverage, and PAndAS survey (irregular polygon) provides the source catalogue for the their distances are not measured in the same homogeneous way. A reliable http://mnras.oxfordjournals.org/ 20 detection and distance measurements of the 27 satellite galaxies (filled circles) spatial analysis requires a data set with homogeneous selection criteria, so we do http://mnras.oxfordjournals.org/ used in this study. Near M 31 (blue ellipse), the high background hampers the not include these objects in the sample either. The analysis shows that the detection of new satellites and precludes reliable distance measurements for satellites marked red are confined to a highly planar structure. We note that this M 32 and NGC 205 (labelled black open circles); we therefore exclude the structure is approximately perpendicular to lines of constant Galactic latitude, A Council of Giants region inside 2.5u (dashed circle) from the analysis. The seven satellites known so it is therefore aligned approximately perpendicular to the Milky Way’s disk outside the PandAS area (green circles and arrows) constitute a heterogeneous (the grid squares are 4u3 4u). Marshall McCall MNRAS 2014 600 A21 A26 A18 by guest on March 12, 2014 500 by guest on March 12, 2014 A25 A ‘Council of Giants’ with a radius of 3.75 Mpc and 147 A27 A30A17 400 A20 185 A19 M 31-centric galactic latitude A24 A5 300 MW A9 M 31-centric galactic longitude A10 A12 thickness of 0.2 Mpc defines the Local Sheet, which is A3 A16 200 A15 A1 A11 A2 A14 A13 100 perpendicular to the Milky Way disk. [The planes of A22 A23 Planes of satellites and the cosmic web 1055 M33 0 Downloaded from Figure 2 | Satellite galaxy positions as viewed from Andromeda. The Aitoff– plane of lowest root mean square from a subsample of 15 (the colour scale on Hammer projection shows the sample of 27 satellites20 (filled circles from Fig. 1) the right shows the relative probability of the poles, and is dimensionless). A as they would be seen from the centre of the Andromeda galaxy. In these clear narrow peak at (lM315 100.9u 6 0.9u, bM315238.2u 6 1.4u) satellite galaxies about Andromeda and the Milky Waycoordinates the disk of Andromeda lies along the equator. ‘M 31-centric highlights the small uncertainty in the best-fit plane. The solid red line, galactic latitude’ means what a fictitous observer in the M31 galaxy would which passes within less than 1u of the position of the Milky Way call ‘galactic latitude’. The background image represents the probability (yellow circle labelled ‘MW’), represents the plane corresponding to this best density function of the poles derived from 105 iterations of resampling the 27 pole location. Planes ofhttp://mnras.oxfordjournals.org/ satellites and the cosmic web 1055 lie in the Local Sheet.] satellites from their distance probability density functions, and finding the 3JANUARY2013|VOL493|NATURE|63 ©2013 Macmillan Publishers Limited. All rights reserved Figure 3. The spatial distribution of sample galaxies within 6.25 Mpc of the centre of the CouncilFigure of Giants. 3. The Shown spatial are top distribution and side ofviews sample in a galaxies coordinate within 6.25 Mpc of the centre of the Council of Giants. Shown are top and side views in a coordinate system with an x–y plane coincident with the mid-plane of the Local Sheet, which is displayed as a dashedsystem grey with line an inx– they plane lower coincident panel. To with optimize the mid-plane clarity, the of the Local Sheet, which is displayed as a dashed grey line in the lower panel. To optimize clarity, the x-axis of Sheet coordinates has been rotated 107 clockwise around the z-axis from the direction of the line of intersection with the supergalactic plane. In both x-axis of Sheet coordinates has been rotated 107◦ clockwise around the z-axis from the direction of the line of intersection with the supergalactic plane.◦ In both panels, all sample galaxies within the spherical volume delineated by the large grey circles are displayed.panels, Galaxies all sample are marked galaxies by within circlets the whose spherical diameters volume are delineated by the large grey circles are displayed. Galaxies are marked by circlets whose diameters are proportional to the cube root of the stellar mass. Giants are highlighted in pink, and a bold cross marksproportional the centre to of the the cube Council root of of the Giants. stellar In mass. the top Giants view, are highlighted in pink, and a bold cross marks the centre of the Council of Giants. In the top view, Planes of satellite galaxies and the cosmicblack bars superimposed web upon the galaxy markers convey the uncertainties in distance. The luminosity-weightedblack bars superimposed centroid of upon the Local the galaxy Group markers is noted convey with the uncertainties in distance. The luminosity-weighted centroid of the Local Group is noted with a small black disc, and the trajectory of the Local Group with respect to Council giants is conveyeda by small the black attached disc, arrow. and the The trajectory solid pink of circle the Local is the Group fit to with respect by guest on March 12, 2014 to Council giants is conveyed by the attached arrow. The solid pink circle is the fit to the Council of Giants. The inner dashed pink circle marks the edge of the cylindrical realm of influencethe Council of the Local of Giants. Group The defined inner by dashed density pink matching. circle marks The the edge of the cylindrical realm of influence of the Local Group defined by density matching. The outer dashed pink circle correspondingly marks the outer edge of the density-matched volume of theouter Council. dashed Curves pink in circle blue correspondingly are the loci of potential marks the ma outerxima edge of the density-matched volume of the Council. Curves in blue are the loci of potential maxima Libeskind, Hoffman, Tully et al. MNRAS 2015as viewed today from the centroid of the Local Group in directions parallel to the plane of the Sheet.as viewed Dashed today grey lines from mark the centroid the intersections of the Local of the Group Sheet in directions parallel to the plane of the Sheet. Dashed grey lines mark the intersectionsDownloaded from of the Sheet The Local Group and Centaurus A reside in a filamentwith the Galactic and supergalactic planes. with the Galactic and supergalactic planes. stretched by the Virgo cluster and compressed by the http://mnras.oxfordjournals.org/ expansion of the Local Void. The alignment of satellite systems in the local Universe with the ambient Downloaded from shear field is thus in general agreement with predictions of ΛCDM. Figure 3. The spatial distribution of sample galaxies within 6.25 Mpc of the centre of the Council of Giants. Shown are top and side views in a coordinate system with an x–y plane coincident with the mid-plane of the Local Sheet, which is displayed as a dashed grey line in the lower panel. To optimize clarity, the http://mnras.oxfordjournals.org/ at University of California, Santa Cruz on February 12, 2016 x-axis of Sheet coordinates has been rotated 107◦ clockwise around the z-axis from the direction of the line of intersection with the supergalactic plane. In both panels, all sample galaxies within the spherical volume delineated by the large grey circles are displayed. Galaxies are marked by circlets whose diameters are proportional to the cube root of the stellar mass. Giants are highlighted in pink, and a bold cross marks the centre of the Council of Giants. In the top view, black bars superimposed upon the galaxy markers convey the uncertainties in distance. The luminosity-weighted centroid of the Local Group is noted with Planes of satellite galaxies: when exceptionsa small black disc, and the trajectory ofare the Local Group withthe respect to Council rule giants is conveyed by the attached arrow. The solid pink circle is the fit to the Council of Giants. The inner dashed pink circle marks the edge of the cylindrical realm of influence of the Local Group defined by density matching. The outer dashed pink circle correspondingly marks the outer edge of the density-matched volume of the Council. Curves in blue are the loci of potential maxima as viewed today from the centroid of the Local Group in directions parallel to the plane of the Sheet. Dashed grey lines mark the intersections of the Sheet Catun, Bose, Frenk, Qi Guo, Han, Hellwing,with Sawala, the Galactic and supergalactic planes. Wang MNRAS 2015 ~10% of simulated Local Groups have satellite planes even more prominent than observed. at University of California, Santa Cruz on February 12, 2016 Figure 1. The cosmic peculiar velocity and related overdensity field in the local Universe, reconstructed from the CF2 survey, by means of the WF methodology. In both plots stream-lines are coloured according to the local speed, shown by the colour bar at right. In the top plot (a), the overdensity field is coloured from the highest density regions (the Virgo Cluster in red) to underdense ones (voids, in blue). In the bottom plot (b) all galaxies from the V8k survey (Tullyetal. 2009)inthis20 20 3Mpch 1 slab are plotted as black dots. The flow towards the Virgo Cluster, as well as the ‘local filament’ that bridges the Local × × − Group with the Virgo Cluster, exhibits clear features in both the density and velocity fields. Cen A is located on the edge of this filament. The Local Void, which sits above the slab in the positive SGZ direction, pushes down on to the local filament. The shear eigenframe centred on the LG is indicated by the three eigenvectors. The (e2–e3) plane is shown as the grey disc in (b). The e1 eigenvector points mostly out of the slab. Note how the local filament and flow towards Virgo are aligned closely with e3. In both figures, labels for some well-known objects are also included. and λ λ )andthestabilityofeacheigenvector(eWF eCR). The 3.2 The case for the MW misalignment 2 − 3 i · i filamentary nature of the local environment is thus confirmed at As shown in Fig. 2, the MW satellite plane is not as well aligned around the 3σ level. The table further shows the mean and standard with the shear field as these other four systems. The normal to this deviation of the alignment of each eigenvector of the CRs with plane appears to have been rotated (around e2)byabout38deg.This the corresponding eigenvector of the WF field. The stability in the offset may not be a surprise if MW is less massive than its partner Figure 1. directionThe cosmic of each peculiar eigenvector velocity is statisticallyand related veryoverdensity significant. field Note in the local Universe, reconstructed from the CF2 survey, by means of the WF methodology. In both plots stream-lines are coloured according to the local speed, shown byM31 the as colour suggested bar at by right. a number In the of top studies plot (Smith(a), the et overdensity al. 2007;Xue field is coloured from that the direction of the filament, given by e3, is statistically the et al. 2008;Kafleetal.2014;Penarrubia˜ et al. 2014; Piffl et al. the highestmost density robust regions eigenvector. (the Virgo Cluster in red) to underdense ones (voids, in blue). In the bottom plot (b) all galaxies from the V8k survey (Tullyetal. 2009)inthis20 20 3Mpch 1 slab are plotted as black dots. The flow towards the Virgo Cluster, as well as the ‘local filament’ that bridges the Local × × − Group with the Virgo Cluster, exhibits clear features in both the density and velocity fields. Cen A is located on the edge of this filament. The Local Void, which sits above the slab in the positive SGZ direction, pushes down on to the local filament. The shear eigenframeMNRAS centred452, 1052–1059 on the LG (2015) is indicated by the three eigenvectors. The (e2–e3) plane is shown as the grey disc in (b). The e1 eigenvector points mostly out of the slab. Note how the local filament and flow towards Virgo are aligned closely with e3. In both figures, labels for some well-known objects are also included. and λ λ )andthestabilityofeacheigenvector(eWF eCR). The 3.2 The case for the MW misalignment 2 − 3 i · i filamentary nature of the local environment is thus confirmed at As shown in Fig. 2, the MW satellite plane is not as well aligned around the 3σ level. The table further shows the mean and standard with the shear field as these other four systems. The normal to this deviation of the alignment of each eigenvector of the CRs with plane appears to have been rotated (around e2)byabout38deg.This the corresponding eigenvector of the WF field. The stability in the offset may not be a surprise if MW is less massive than its partner direction of each eigenvector is statistically very significant. Note M31 as suggested by a number of studies (Smith et al. 2007;Xue that the direction of the filament, given by e3, is statistically the et al. 2008;Kafleetal.2014;Penarrubia˜ et al. 2014; Piffl et al. most robust eigenvector. MNRAS 452, 1052–1059 (2015) Dark Matter 2016 UCLA's 12th Symposium on Sources and Detection of Dark Matter and Dark Energy in the Universe ΛCDM cosmology: remaining challenges and opportunities for progress Challenges: Too Big To Fail in the Field, Distribution of DM in GalaxGalaxies like the MWy, Diversity of Galaxy Rotation Curves, GalaxAbundance of Bulgeless Galaxies, Galaxies in the Web Observational Opportunities: Measuring Halo Substructure Galaxby Gravitational Lensing and Stellar Motions, Reionization, GalaxStructure of dwarf Galaxies, Galaxies in the Cosmic Web