Cold versus Warm Dark Matter Simulations of a Galaxy Group

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Cold versus Warm Dark Matter simulations of a galaxy group

Noam I. LibeskindA,†, Arianna Di CintioA.B,C, Alexander KnebeB, GustavoYepesB, Stefan GottloberA, Matthias SteinmetzA, Yehuda HoffmanD, Luis A.Martinez-VaqueroE

A Leibniz-Institut fur Astrophysik, Potsdam, An der Sternwarte 16, 14482 Potsdam, GermanyB Departamento de Fısica Teorica, Grupo de Astrofısica, Universidad Autonoma de Madrid, Madrid

E-28049, SpainC Physics Department ”G. Marconi”, Universita’ di Roma ”Sapienza”, Ple Aldo Moro 2, 00185 Rome,

ItalyD Racah Institute of Physics, Hebrew University, Jerusalem 91904, IsraelE Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matematicas, Universidad

Carlos III de Madrid, Leganes, Madrid, Spain† Email: [email protected]

Abstract:The differences between cold (CDM) and warm (WDM) dark matter in the formation of a group ofgalaxies is examined by running two identical simulations where in the WDM case the initial powerspectrum has been altered to mimic a 1keV dark matter particle. The CDM initial conditions wereconstrained to reproduce atz = 0 the correct local environment within which a “Local Group”(LG) ofgalaxies may form. Two significant differences between the two simulations are found. While in theCDM case a group of galaxies that resembles the real LG forms,the WDM run fails to reproduce a viableLG, instead forming a diffuse group which is still expanding atz = 0. This is surprising since, due tothe suppression of small scale power in its power spectrum, WDM is naively expected to only affect thecollapse of small haloes and not necessarily the dynamics ona scale of a group of galaxies. Furthermorethe concentration of baryons in halo center’s is greater in CDM than in WDM and the properties of thedisks differ.

Keywords: galaxies: Local Group – cosmology: dark matter – methods: N-body simulations

1 Introduction

The current paradigm of galaxy formation, known asCold Dark Matter (CDM), holds that structures in theuniverse grow in a bottom-up hierarchical fashion (e.g.White and Rees 1978). The universe’s initial condi-tions are conceived as a smooth roughly homogenousexpanse of gas and dark matter (DM). In CDM, smallperturbations imprinted on the primordial density fieldgrow via gravitational instabilities, and then merge witheach other to create the complex structures (such asclusters, groups of galaxies, galactic haloes, filaments,sheets and voids) we observed today.

Warm DM (WDM), an alternative to CDM, sug-gests that initial perturbations below a certain mass can-not collapse and as such the smallest structures to formout of gravitational instability are fairly large (e.g.∼1010h−1M⊙ Bode et al. 2001; Zavala et al. 2009). This

is because the temperature of the DM particle at de-coupling (specifically, whether it was relativistic or not)can cause the DM particle to escape from and erase theunderlying density fluctuation. This process, known as“free streaming”, inhibits the formation of small struc-tures by gravitational collapse.

The initial power spectrum of fluctuations, whichcan be measured directly from the CMB, describes thedegree of “contrast” in the density field and can be com-pared with the large scale clustering of galaxies ob-served in sky surveys (such as the SDSS or 2DF). Thesemeasurements probe the power spectrum on scales muchgreater than those scales where the nature of the darkmatter can be probed.

A number of suggestions as to the mass of DM par-ticles have recently been proposed (e.g. Boyarsky et al.2009b,a) which corresponds to the lack of DM haloesless than∼ 106M⊙ – roughly the mass of the small-

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Figure 1: A density map containing the three halos that make up the simulated group atz = 0 in CDM(left) and WDM (right). The CDM group is more compact and collapsing while the WDM is more diffuseand still expanding. Each plot is projection of a 2h−1Mpc cube.

est DM - dominated dwarf galaxy. Indeed invoking awarmer flavor of DM (such as a 2 keV sterile neutrino,see Lovell et al. 2011) may solve a number of issuesrelated to dwarf satellite galaxies including the “Miss-ing satellite problem” (Moore et al. 1999; Klypin et al.1999) as well as the “Massive failure problem” (Boylan-Kolchin et al.2011, 2012). Despite the many successes of CDM,there is thus more than just a hint that WDM may solvesome of the fundamental problems in galaxy formation.

Regardless of the nature of the DM, the gravita-tional collapse of structures in the Universe is a highlynon-linear process and can only be modeled by usingnumerical methods, such asN-body simulations (Springel et al.2005) of the cosmic density field. Numerical simu-lations have successfully probed a myriad of scales:from the largest conceivable simulations of the universe(e.g. the Horizon, Millenium-XXL and MultiDark runsKim et al. 2011; Angulo et al. 2012; Riebe et al. 2011),through clusters (e.g. the Phoenix project Gao et al.2012), to Milky Way (MW) type galaxies filled withsmall substructures (Springel et al. 2008; Stadel et al.2009).

Within the CLUES project1 we have used constrainedsimulations to shown that the specific environment ofthe Local Group is an important ingredient in the for-mation of the Milky Way and Andromeda galaxies (e.g.Libeskind et al. 2005; Knebe et al. 2010; Libeskind et al.2011b,a; Knebe et al. 2011b). Indeed the often used

1http://www.clues-project.org

term “MW-type galaxy” which lumps all galaxies inhaloes of∼ 1012M⊙ together, may be considered a stereo-type given the wide differences in merger history, mor-phology, and other properties among these galaxies (e.g.de Rossi et al. 2009; Busha et al. 2011; Forero-Romero et al.2011). Since the simulations can be directly comparedwith observations constrained simulations are extremelyuseful to study the formation of the Local Group galax-ies (e.g. Knebe et al. 2011a; Di Cintio et al. 2011, 2012a,b;Dayal and Libeskind 2012).

Constrained simulations have also been used to studythe velocity function of dic galaxies in the Local Vol-ume by Zavala et al. (2009). By using a simple modelto populate halos with disk galaxies, Zavala et al. (2009)showed that the velocity functions in the two regionsexplored by the ALFALFA survey agree quite well bothCDM and WDM cosmologies, as long as one considersmassive galaxies with circular velocities in the range inthe range between 80kms1 and 300kms1. However, forgalaxies with circular velocities below 80kms−1 onlythe predictions of a 1keV WDM particle, agrees withobservations. On the other hand, at a circular veloc-ity of ≈ 35kms−1 the CDM scenario predicts about 10times more sources than observed.

Using the same set of simulations as Zavala et al.(2009), Tikhonov et al. (2009) found that the observedspectrum of mini-voids in the local volume is in goodagreement with the WDM model but can hardly be ex-plained within the CDM scenario.

Given the importance of the Local Group on the

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formation of the MW, in this paper we examine theeffect of the type of DM assumed, on forming such agroup. We use the same model as Zavala et al. (2009)but run gasdynamical simulations with much higher res-olution as described in Section 2.In Section 3 we studythe cosmography of the simulated groups and in Sec-tion 4 the internal halo properties. In Section 4 we sum-marize and discuss our results.

2 Simulations

In this section we describe briefly the numerical meth-ods used to run our simulations as well as the meth-ods to identify halos in the simulation. We refer thereader to Libeskind et al. (2010) for details. As men-tioned before the original CDM simulation was con-strained by present day observations of our local uni-verse (Willick et al. 1997; Tonry et al. 2001; Karachentsev et al.2004; Reiprich and Bohringer 2002). Initial conditionsare then produced following the method described by(Hoffman and Ribak 1991). The zoomed DM initialconditions for a 2h−1 Mpc sphere were generated fol-lowing the prescription set out in Klypin et al. (2001).The reader should note that the constraints we have ap-plied to the initial conditions are on linear scales atz= 0 and are identical in the two cosmologies. The un-constrained phases, namely the power responsible forthe internal dynamics of the groups embedded in theconstrained realizations are effectively random. “Ef-fectively” because they have been selected in the CDMcase (by trial and error) to produce a group which re-sembles the LG in terms of number, mass, geometryand kinematics of three galaxies. Therefore, an uncon-strained random realization which produced a LG look-ing candidate with CDM initial conditions would haveequally sufficed for the purposes of our study.

Gas particles are included in the high resolution re-gions of both the WDM and CDM initial conditionswith a mass ofmGAS = 4.4 × 104h−1M⊙: during theevolution of the simulation they may spawn star parti-cles (see below), whose mass ismSTAR = 0.5mGAS =

2.2 × 104h−1M⊙. Star, gas and high resolution DMparticles are all softened on the same length scale of150h−1pc. Star formation rules are described in detailin Libeskind et al. (2010). The Springel and Hernquist(2003) method is used to model gas in the interstel-lar medium. A uniform but evolving ultra-violet back-ground is switched on atz= 6 (Haardt and Madau 1996).Only atomic cooling is assumed. Cold gas cloud forma-tion by thermal instability, star formation, the evapora-tion of gas clouds, and the heating of ambient gas bysupernova driven winds all occur at the same instant.Each star formation event injects energy and metals intothe ISM instantaneously. Feedback from SN explosionsis modeled kinetically using the stochastic approach de-

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Figure 2: The power spectrum used in this work.In black we show the CDM power spectrum, inred, the WDM power spectrum. The verticaldashed lines indicate thek interval used to gen-erate the initial conditions, from the fundamentalmode (k ∼ 2π/Lbox ≈ 0.1) to the Nyquist fre-quency (k ∼ 200).

veloped by Springel and Hernquist (2003).The PMTree-SPH MPI code Gadget2 (Springel 2005)

is used in both runs to to simulate the evolution of aperiodic cosmological box with side length ofLbox =

64h−1Mpc. Using the same sub-grid physics we mod-ified only the initial power spectrum of fluctuations tosimulate a WDM model. Since the phases of the con-strained initial conditions in both cases are identical,any differences in galaxy or halo properties is directlydue to the effect of changing the DM power spectrum.Both runs employ cosmologies that assume WMAP3parameters (Spergel et al. 2007), i.e.Ωm = 0.24,Ωb =

0.042,ΩΛ = 0.76. The rms mass fluctuation in spheresof 8 Mpc isσ8 = 0.73 andn = 0.95 is the slope of thepower spectrum.

When simulating WDM we suppress the power spec-trum below scales representative of a 1keV WDM par-ticle (see Fig. 2). The initial conditions are generatedby rescaling the CDM power spectrum and fitting itwith an approximation to the transfer function repre-sentative of the free streaming effect of WDM parti-cles (Viel et al. 2005). The the free-streaming length ofsuch a WDM particle is 350h−1kpc, which correspondsto a filtering mass of∼ 1.1x1010h−1M⊙ (Bode et al. 2001):the WDM power spectrum, shown in Fig. 2 thus con-tains a sharp cut-off at this free-streaming length.

In order to identify halos and subhaloes in our sim-ulation we have run the MPI+OpenMP hybrid halo finder

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Figure 3: Upper Panels:CDM; Lower Panels:WDM. Left Panels (a,c):The physical (thin line) andco-moving (thick line) distance as a function of look back time between the three pairs of LG haloes. Weshow the distances between the A and B in blue, the B and C in redand A and C in green. Each curveis normalized to itsz = 0 value which can be found in Table 1.Right Panels (b,d):The mass growth forhalo A (red), B (blue), and C (green) as a function of look-back time. The solid dots denote the time atwhich half thez= 0 mass was assembled.

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Figure 4: Internal properties of the three main haloes simulated as function of radius. Properties for haloA (red, left panel), B, (blue, center panel) and C (cyan, right panel) are shown for WDM (dashed) andCDM (solid). Top row: Density profile.Middle row: Baryon fraction.Bottom row:Gas fraction.

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AHF2. We refer the reader to the code description papers(Gill et al. 2004; Knollmann and Knebe 2009) for de-tails. AHF locates local over-densities in an adaptivelysmoothed density field as prospective halo centers. Thepotential minimum of each density peak is then calcu-lated; bound particles are then associated to possiblehaloes.

In the WDM simulation, discreteness effects whichcan cause haloes below a specific limit mass (Mlim) toarise from the unphysical numerical fragmentation offilaments, is an issue. In order to protect our analy-sis against these artificially formed haloes we use thevalue of Mlim provided by Wang and White (2007) asthe minimum trusted mass for a halo in the WDM sim-ulation. Their expression, originally based upon HotDark Matter models, readsMlim = 10.1ρd/k2

peak, whereρ is the mean density,d is the mean interparticle sep-aration, andkpeak is the wavenumber at which∆2(k) =k3P(k) reaches its maximum. In our WDM run, wherethe power spectrum has been modified to correspondto a 1keV particle, the values of this limiting mass isMlim ∼ 2.6x107M⊙/h, which corresponds roughly toa 100 particle limit. In practice in both the CDM orWDM simulation, only objects whose mass is greaterthan 500 particles are used. We note that since the sim-ulations have identical baryonic physics, particle massand spatial resolutions any of the differences reportedhere are due entirely to the nature of the DM model.

3 CosmographyWe begin with a cosmographic description of the twosimulated groups. Our simulations produce three dom-inant objects which we name galaxy A, B and C in de-creasing mass. In the CDM case these closely resemblethe Milky Way (MW), Andromeda (M31) and Triangu-lum (M33). An image of the two groups can be seenin Fig. 1. Two salient aspects of WDM are immedi-ately apparent from this figure: (1) there are far fewersmall substructures and (2) the two groups differ sub-stantially, cosmographically speaking.

In Figure 3(a,c) we show the co-moving and phys-ical distance between the three pairs of group mem-bers as a function of look back time, normalized tothe z = 0 value. In the CDM simulation, the physi-cal separation of each pair of galaxies reaches a max-imum “turn-around” (at a look back time of around 6Gyrs for galaxy B-A and galaxy B - C pair and arounda few Gyrs later for galaxy A - C). In the WDM sim-ulation this is not the case: the physical distance be-tween each pair of haloes at every redshift is smallerthan the corresponding distance at redshift zero, indi-cating that the Hubble expansion is the dominant forceat every epoch and that all three pairs of galaxies have

2Publicly available arhttp://popia.ft.uam.es/AHF

yet to begin approaching each other. Accordingly, thegroup is more compact in CDM than in WDM. Usingthese specific initial conditions, over densities that turnaround and are on a collision course at a given epoch incosmic time in CDM, have yet to approach each otherin WDM: where CDM produces an attracting, collaps-ing group of galaxies, WDM produces a still expandingversion. This is our first result:Using initial conditions,whose only difference is a suppression of small scalepower, the defining dynamics of the a group of galax-ies are completely different in CDM and WDM, withthe former predicting an attracting group that resem-bles the LG, while the later predicting a still expandingone.

The co-moving distances (shown as the thick linesin Fig. 3a,c) show monotonic attractions. In the WDMcase the simulated haloes are closer to each other (rel-ative to theirz = 0 distances) at early times than theCDM halos. In the CDM case, byz= 0 the haloes havebeen brought closer. Note that the small kinks in the A-C system (CDM) and B - C system (WDM case) ap-pear due to false identification of the main progenitorin the merger tree construction at a given snapshot.

We now examine the evolution of the three indi-vidual group members by examining the mass accre-tion history shown in Fig. 3(b,d). In both the CDM andWDM run, the two most massive galactic haloes (A andB) show jumps in the mass accretion history character-istic of merger activity occurring more or less contin-uously. Often, these haloes appear to lose mass aftera violent major merger. This is because of the uniquemerger history of these objects - violent mergers maybring material into the virial radius that is bound at oneredshift, but which may become unbound and flung outat a later time. The smallest halo (C) on the other handshows little evidence of major mergers in its past.

Although the mass growth histories look similar,in fact they differ slightly. The time at which half ofthe z = 0 mass has been assembled is shown in eachplot as a filled circle. In the WDM simulation, eachhalo assembles 50% of its mass later with respect tothe CDM model. Specifically, in the WDM run haloA, B and C accrete half-mass at a look-back time of∼ 4, ∼ 6, and∼ 9.5Gyrs, respectively. In the CDMcase this occurs at∼ 7, ∼ 7 and∼ 10Gyrs: that is∼ 3,∼ 1,∼ 0.5 Gyrs earlier. Since B and C are smaller masshaloes, their half mass times are considerably earlierand the delay is considerably smaller than for halo A.

A characteristic feature of the WDM model emergeshere: the finite primordial phase-space density due tothe large thermal velocities of the particles causes mostof the mass to undergo gravitational collapse at laterredshift (z< 5), resulting in the suppression of halo for-mation at higher redshift (Bode et al. 2001). Halo col-lapse is thus delayed with respect to the CDM model.Although not a new result, this finding directly informs

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Property CDM Group WDM Group

MA 7.49× 1011M⊙ 5.75× 1011M⊙MB 5.48× 1011M⊙ 4.15× 1011M⊙MC 2.78× 1011M⊙ 2.42× 1011M⊙dA−B 1.22 Mpc 2.26 MpcdA−C 1.37 Mpc 2.34 MpcdB−C 0.79 Mpc 1.22 MpcVA,B -110 kms−1 29 kms−1

VA,C -85 kms−1 35 kms−1

VB,C -4 kms−1 42 kms−1

Table 1: Thez = 0 properties of a simulated group in CDM and WDM. Note that theWDM group haslittle resemblance to the CDM one (which closely matched thereal LG, see Libeskind et al. (2010). Weshow the following properties: the mass of halo A, B and C (MA , MB and MC), the distance betweenhalos A, B and C (dA,B, dA−C anddB−C), and the relative line of sight velocity for each pair (VA,B, VA,C,andVAB,C

the main differences we find between CDM and WDM.

4 Internal Halo Properties

How do the different cosmographies and histories changethe internal structure of each of our three LG objects?In Fig. 4(a)-(c) we show the density profile of the threeLG members in both WDM (dashed) and CDM (solid)simulations. All density profiles are standard NFW fits,and in all three cases the WDM is nearly indistinguish-able from the CDM. That said, owing to the lower massof the WDM haloes, their density profiles are system-atically shifted to slightly lower densities.

In Fig 4(d)-(f) we show the cumulative baryon frac-tion as a function of radius. Again, WDM and CDMshow broad similarities in shape and value of the baryonfraction. In the inner parts, WDM shows a systemati-cally lower baryon fraction. At around∼ 0.03rvir , thetotal fraction of internal mass in baryons is roughly thesame in both cosmologies. Towards the outer parts ofthe halo, the baryon fraction of both cosmologies drops,reaching the cosmic mean of∼ 0.1 at the virial radius.That CDM haloes have more concentrated baryons islikely due to a number of combining factors: their ear-lier formation time, their greater mass and thus theirdeeper potential. This is our second main result:WDMhaloes have lower baryon fractions in their inner partswhere baryons dominate, than CDM haloes.

The baryonic properties of the three Local Groupmembers are summarized in Table 2.

The fraction of mass in a gaseous component ispresented in Fig.??(g)-(i). Although each halo showsdifferent specific behavior, some interesting similaritiesexist. Firstly, the fraction of mass in gas is almost al-

ways greater in WDM than in CDM. This is true forall radii in halo A, and for radii greater than 0.03rvir

for halo B and C (although in halo B, there is moregas in CDM forr < 0.2rvir). The higher gas fractions inWDM may inhibit infalling substructures from deposit-ing their material in the center of the halo thereby sup-pressing the baryon fraction in the inner parts of WDMhalos, as seen in Fig. 4(d)-(f).

Both gas and stars form well defined discs, a con-sequence of the star formation rules we have used. Thiscan be quantified by performing a dynamical bulge-discdecomposition. There are a number of ways this is donein the literature (e.g Abadi et al. 2003; Scannapieco et al.2010; Sales et al. 2012). In this work we dynamicallydecompose star and gas particles within the inner 10 kpcinto disc-like and bulge-like components using two meth-ods, one for each component (as in Knebe et al. 2013).For both methods a “disc-axis”, taken to be the total an-gular momentum of all baryonic particles within 10kpc,must be assumed.

For gas particles we follow Scannapieco et al. (2010);the component of each particle’s angular momentum inthis direction (Jz) is computed and compared with theangular momentum a particle would have at that radiusif it were on a circular orbit. The ratioJz/Jcirc is com-puted where:

Jcirc = r × vcirc (1)

= r ×

√

GM(r)r

(2)

Here M(r) is the total mass (including DM) within aradiusr. Note that in this formulation, particles withJz/Jcirc ≈ 1 are on circular orbits and thus compose adisc. Note thatJz > Jcirc and thus the ratio ranges from(0,∞).

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Galaxy Property CDM WDMTOTAL GAS STARS TOTAL GAS STARS

Nvir (106) 4.2 1.3 0.65 2.9 0.66 0.43A Mvir (1011M⊙) 5.5 0.52 0.14 4.2 0.27 0.094

fb,vir 0.12 0.09Nvir (106) 2.9 0.53 0.55 2.2 0.56 0.30

B Mvir (1011M⊙) 4.0 0.21 0.12 3.0 0.23 0.066fb,vir 0.08 0.09Nvir (106) 1.5 0.40 0.29 1.3 0.36 0.19

C Mvir (1011M⊙) 2.0 0.17 0.064 1.8 0.15 0.040fb,vir 0.11 0.11

Table 2: Properties of the three main galaxies in the CDM and WDM simulation. For each halo we showthe number (Nvir) and mass (Mvir) of stars, gas and all particles within the virial radius. Wepresent thebaryon fraction within the virial radius (fb,vir).

For star particles we follow Abadi et al. (2003) andcompare the component of the angular momentum inthe z-direction with the angular momentum of a cir-cular orbit of the same energy,Jc(E). First, the total(kinetic plus potential) energy of each particle is com-puted. Since circular orbits maximize angular momen-tum, the maximum value ofJz for all particles with agiven energy is taken asJc(E). In this case the ratioJz/Jc(E) is confined to the interval [-1,1], where neg-ative values imply counter-rotation with respect to to-tal angular momentum of all baryonic particles within10kpc.

Two different methods for gas and star particles areused because of the nature of the the methods them-selves. The Abadi et al. method is more appropriatefor N-body particles where the energy is simply kineticplus potential. Gas particles have an extra component(internal energy) which informs their dynamics. In thiscase its better to use the Scannapieco approach.

In Fig. 5 we present histograms ofJz/Jc(E) (leftcolumn, star particles) andJz/Jcirc (right column gasparticles) for the CDM (bottom row) and WDM (toprow) simulations. In the CDM simulation, gas in boththe B and C clearly define a very thin disc, while A’s gasis less ordered. Star particles on the other hand show awell defined disc in C’s case, a “fat” disc in B’s caseand no disc in A’s case

In the WDM run, the gas particles of halo C appearto define a clear disc while halos A and B have poorergaseous discs. With respect to the stars we see a similarsituation to the CDM case. Halo C has a disc compo-nent, B has a thicker disc and A has no real disc.

Due to the fact that halo A has a significative stel-lar bulge, the corresponding star particle histogram hasbeen rescaled by a factor of four with respect to the stel-lar particle histogram of the other two galaxies, for both

the CDM and WDM runs (the peak of the star compo-nent of halo A was 20 in both runs).

It is interesting to note that the discs of B and C aresmaller in the WDM case than in the CDM case. Thismay again be a result of the delayed formation timeof WDM haloes and the consequent lower mass. It isinteresting that the bulge component (namely the peakat Jz/Jc(E) = 0) seems to be roughly of the same sizein both A and B.

Note that the dip atJz/Jcirc ≈ 1 in the gas distribu-tion of A in the CDM simulation is due to a warping ofthe disc.

C is the only galaxy that, owing to its quiet mergerhistory, forms a clearly identifiable stellar disc, decom-posed in Fig. 5 into bulge and disc components (seedashed lines). The total mass in each component issimilar: In CDM, 44% and 56% of halo C’s galaxy isattributed to a bulge and disc, respectively. These frac-tions are nearly perfectly inverted in WDM: 45% and55% of halo C’s stellar component are disc and bulge,respectively.

Although our sample size is small, we note thatone of the more unanticipated consequences of haloesforming later in WDM, is their smaller and thicker disc.Indeed this may simply be a reflection of the differ-ent dynamical environments of the two groups. Morework on the relationship of disc thickness to DM parti-cle mass is encouraged to see if one can constrain theother.

Since the dynamical decomposition indicates thatthe galaxies within each halo differ substantially, it isperhaps no surprise that so too do their star formationhistories. Although not shown here, the SFR (being areflection of the merger history) is quantitatively verydifferent in the two cosmologies.

As expected (and seen elsewhere) our WDM sim-

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Figure 5: The fraction of stellar (gas) particles within 10kpc atz = 0 with a given ratio ofJz/Jc(E)(Jz/Jcirc) for the galaxies in halo A (red), B (blue) and C (green). Particles with Jz/Jcirc ≈ 1 are oncircular orbits and thus compose a disc. Note that the gas particles nearly all constitute a disc, while starparticles populate both disc and bulge components. The dip at Jz/Jcirc ≈ 1 of the gas component of galaxyA is due to warping of the disc. The dotted green line indicates a decomposition into bulge and disc starparticles for galaxy C.

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ulation has far fewer satellites than our CDM simu-lation. WDM produces roughly the same number (∼20) of subhaloes as satellites observed to be in orbitabout the Milky Way. However it is unclear if, owing tofeedback and other star formation suppression mecha-nisms, WDM subhaloes are luminous enough to matchthe MW’s satellite luminosity function.

5 Summary and Discussion

Since the temperature of the DM particle at decouplingdetermines its ability to “free-stream” out of potentialwells, it also sets the scale at which structures are ablecollapse. In principle this characteristic can be used toconstrain DM to be either “cold”, “warm”, or “hot”.Hot DM, such as Neutrinos which travel at relativis-tic speeds, were at first hailed as the solution to theDM problem but have now been effectively ruled out(Bertone et al. 2005) since they can escape most po-tential wells and prevent structures from formation viagravitational instability. Cold DM (CDM), on the otherhand moves non-relativistically and as such is able tocollapse into objects as small as an Earth mass (Ishiyama et al.2010). The prediction of small substructures embed-ded in larger objects is a generic feature of the CDMmodel and, since such objects are unobserved in theMilky Way, this has lead to the famed “Missing satelliteproblem” (Moore et al. 1999; Klypin et al. 1999), oftendubbed a crisis for CDM. Astrophysical process (suchas photo-evaporation of star forming gas due to UV ra-diation, see Benson et al. 2003) are invoked to inhibitthe gas cooling into small subhaloes. These processdo not erase substructures, they simply ensure that theyremain non-luminous. A large population of dark sub-haloes detectable via gamma ray emission from DMannihilation (Stoehr et al. 2003) or via strong gravita-tional lensing of background sources (Xu et al. 2009),is thus predicted albeit unobserved, in the Milky Wayhalo.

As a result of the apparent failures of CDM in overproducing and HDM in underproducing the number ofdwarf satellites around the Milky Way, warm DM (WDM),has recently been suggested and studied (by e.g. Bode et al.2001; Avila-Reese et al. 2001; Knebe et al. 2002, 2008;Maccio and Fontanot 2010; Lovell et al. 2011; Maccio et al.2013, among others). In this paper, we have used a setof initial conditions that constrain scales unaffected bythe nature of the DM to test the effect of the type of DMon a group of galaxies (i.e.∼ 1Mpc). Within the scalesthat are still linear atz = 0 (the “local environment”)a group of galaxies that in CDM resembles the localgroup (LG) is resimulated at high resolution, with gas-dynamics. In the CDM run, this local group includesthree galaxies that have the same mass, geometry andkinematics as the MW, M31 and M33. Thus our sim-

ulation allows us to study in detail the merger historyand internal structure of these galaxies as well as theirbaryonic properties. Since the local environment hasbeen kept identical, we can directly measure the effectthe type of DM has on our CDM LG.

The main difference between our CDM and WDMsimulations is that structure formation is delayed in WDM.This is a direct result of the suppression of small scalepower which, owing to the lack of mergers below thefiltering mass, means that it takes longer for haloes togrow to a given mass. The greatest effect this has isto inhibit the collapse of a group of galaxies in WDM.All our results regarding the differences in the galaxiesthemselves, follow directly from this main difference.

• A group of galaxies which atz = 0 closely re-sembles the LG in CDM, is dynamically verydifferent in WDM. Whereas in CDM the groupis collapsing and is compact, in WDM it is stillexpanding and is much more diffuse.

• Delayed halo collapse, implies that atz = 0WDM haloes are smaller than their CDM coun-terparts.

• Baryons are more centrally concentrated in CDMversus WDM haloes.

• In one of the galaxies we simulated, a clearlyidentifiable disc is found. This is fatter and smallerin WDM, a consequence of it being younger andhaving more recent merger activity.

Our conclusions are all consequences of the de-layed formation and collapse of haloes in WDM cos-mologies with respect to CDM. This simple attribute,a direct result of the lack of small scale power due tofree streaming of DM at early times, informs a myr-iad of physical properties, from star formation rates tobulge/disc ratios to colors. One of the more intriguingfindings in this work is the thickening of the one disc weformed (in halo C) in our WDM run. It remains to beseen if this is simply due to the unique dynamical his-tory of this particular realization or if WDM genericallyand systematically produces thicker discs than CDM.

AcknowledgmentsNIL is supported through a grant from the DeustcheForschungs Gemeinschaft (DFG). ADC acknowledgesthe AIP - Leibniz-Institut fur Astrophysik, where thiswork has been partially carried on. AK is supported bytheSpanish Ministerio de Ciencia e Innovacion(MICINN)in Spain through the Ramon y Cajal programme as wellas the grants AYA 2009-13875-C03-02, AYA2009-12792-C03-03, CSD2009-00064, and CAM S2009/ESP-1496and theMinisterio de Economıa y Competitividad(MINECO)through grant AYA2012-31101. GY also acknowledges

www.publish.csiro.au/journals/pasa 11

support from MINECO through research projects CSD2007-0050, AYA 2009-13875-C03-02 and AYA 2012-31101,and from Comunidad de Madrid through ASTROMADRIDproject (CAM S2009/ESP-1496). YH has been par-tially supported by ISF 1013/12. The simulations wereperformed and analyzed at the Leibniz RechenzentrumMunich (LRZ) and at the Barcelona SupercomputingCenter (BSC).

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