Simulations of galaxies formed in warm dark matter halos of masses at the filtering scale
Pedro Colin, Vladimir Avila-Reese, Alejandro Gonzalez-Samaniego, Hector Velazquez
aa r X i v : . [ a s t r o - ph . GA ] F e b Draft version August 17, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
SIMULATIONS OF GALAXIES FORMED IN WARM DARK MATTER HALOS OF MASSES AT THEFILTERING SCALE
P. Col´ın , V. Avila-Reese , A. Gonz´alez-Samaniego , H. Vel´azquez Draft version August 17, 2018
ABSTRACTWe present zoom-in N-body + Hydrodynamic simulations of dwarf central galaxies formed in WarmDark Matter (WDM) halos with masses at present-day of 2 − × M ⊙ . Two different cases areconsidered, the first one when halo masses are close to the corresponding half-mode filtering scale, M f ( m WDM =1.2 keV) and the second when they are 20 to 30 times the corresponding M f ( m WDM = 3.0keV). The WDM simulations are compared with the respective Cold Dark Matter (CDM) simulations.The dwarfs formed in halos of masses (20 − M f have roughly similar properties and evolutionthan their CDM counterparts; on the contrary, those formed in halos of masses around M f , aresystematically different from their CDM counterparts. As compared to the CDM dwarfs, they assemblethe dark and stellar masses later, having mass-weighted stellar ages 1.4–4.8 Gyr younger; their circularvelocity profiles are shallower, with maximal velocities 20–60% lower; their stellar distributions aremuch less centrally concentrated and with larger effective radii, by factors 1.3–3. The WDM dwarfs atthe filtering scale ( m WDM =1.2 keV) have disk-like structures, and end in most cases with higher gasfractions and lower stellar-to-total mass ratios than their CDM counterparts. The late halo assembly,low halo concentrations, and the absence of satellites of the former with respect to the latter, are atthe basis of the differences.
Subject headings: cosmology:dark matter — galaxies:dwarfs — galaxies:formation — methods:N-bodysimulations — methods: Hydrodynamics INTRODUCTIONThe Λ cold dark matter (ΛCDM) cosmology providesthe most accepted background for studying the process ofcosmic structure formation in the Universe. The predic-tions of the ΛCDM-based scenario of structure formationare fully consistent with observations of the large-scalestructure of the present and past Universe, including theanisotropies in the cosmic microwave background radia-tion (see Frenk & White 2012, for a review). However,doubts have been cast on whether observations of mat-ter distribution at small –dwarf galactic and subgalactic–scales are consistent with the predictions of the ΛCDMscenario (see for recent reviews e.g., Weinberg et al. 2013;Del Popolo et al. 2014). Currently, it is matter of greatdebate whether the potential problems are real or conse-quence of observational biases and/or still poorly under-stood astrophysical processes at small scales. If they areconfirmed, introducing variations to the ΛCDM cosmol-ogy will appear as a feasible solution.From the point of view of initial conditions for the cos-mic structure formation, ΛCDM is the simplest model.For the ΛCDM model: (1) the cut-off scale in the lin-ear mass power spectrum of perturbations due to freestreaming, λ fs , is many orders of magnitude smaller thanthe resolution reached by current numerical cosmologicalsimulations of galactic halos so that in practice λ fs = 0and hierarchical cosmic structure formation proceeds atall scales; (2) the relic thermal velocities of the CDM par- Centro de Radioastronom´ıa y Astrof´ısica, Universidad Na-cional Aut´onoma de M´exico, A.P. 72-3 (Xangari), Morelia, Mi-choac´an 58089, M´exico Instituto de Astronom´ıa, Universidad Nacional Aut´onomade M´exico, A.P. 70-264, 04510, M´exico, D.F., M´exico Instituto de Astronom´ıa, Universidad Nacional Aut´onomade M´exico, Apdo. Postal 877, Ensenada, BC, CP 22830, M´exico ticles, v th , are very small, so in practice v th =0 is assumed;(3) since CDM particles are non-baryonic, they do notinteract electromagnetically, and are assumed to have anegligible self-interaction cross section, σ SI = 0, consti-tuting the CDM in practice a pure collisionless fluid; and(4) the statistical distribution of the primordial overden-sity perturbations is assumed to be Gaussian. Therefore,the relaxation of any of the above listed assumptions im-plies necessarily the introduction of free parameters inthe initial conditions of cosmic structure formation aswould be λ fs , v th , σ SI , or the skewness and kurtosis inthe primordial density perturbations distribution.More than a decade ago, high-resolution N-body cos-mological simulations were performed to explore howsubstructure, inner density profiles and shapes of ha-los were affected when one or several of the ΛCDMassumptions listed above were relaxed. Specifically,in these simulations were introduced: (a) a cut-off inthe power spectrum and/or non-negligible thermal ve-locities in the dark particles (in concordance with theΛ warm dark matter, ΛWDM, cosmology; Col´ın et al.2000; Avila-Reese et al. 2001; see also, Bode et al. 2001,Knebe et al. 2002); (b) a non-negligible self-interactionwith constant and velocity-dependent particle cross sec-tions (Yoshida et al. 2000; Col´ın et al. 2002, see alsoSpergel & Steinhardt 2000; Firmani et al. 2000); (c) andnon-Gaussian initial perturbations, positively or nega-tively skewed (Avila-Reese et al. 2003).Among alternative cosmologies, the most popular isthe ΛWDM one with a power spectrum filtered atscales corresponding to dwarf galaxies. As N-body sim-ulations show, in this case the amount of substruc-ture in Milky Way-sized halos is considerably reduced(e.g., Col´ın et al. 2000; Bode et al. 2001; Knebe et al.2002; Macci`o & Fontanot 2010; Kennedy et al. 2014), Colin et al.the abundance of low-circular velocity halos host-ing dwarf galaxies is lowered (e.g., Zavala et al.2009; Papastergis et al. 2011), and, although the ha-los/subhalos do not present shallow cores at thescales of astrophysical interest, they are less concen-trated and with lower maximum circular velocitiesthan their CDM counterparts (Avila-Reese et al. 2001;Col´ın et al. 2008; Lovell et al. 2012; Schneider et al.2012; Anderhalden et al. 2013). These and other effectsmake the ΛWDM model an appealing alternative for al-leviating the potential problems of the ΛCDM modelat small scales, while conserving its successes at largerscales.The main constraint to the ΛWDM scenario comesfrom the comparison of the results of WDM hydro-dynamic simulations in the quasi-linear regime withthe Ly- α flux power spectrum of high-redshift quasars(Narayanan et al. 2000; Viel et al. 2005), though thesecomparisons are not free of uncertainties and limitations(see e.g., de Vega et al. 2014). Depending on the natureof the WDM particle, thermal, sterile neutrino, etc., alower limit to its mass, m WDM , can be established fromthe Ly- α forest analysis, which implies an upper limit tothe damping scale in the mass power spectrum. Severalupdated estimates were presented recently in the liter-ature (e.g., Viel et al. 2013). Based on the constrainsof the latter authors (for a thermal relic particle, m WDM should be & . σ level), Schneider et al.(2014) conclude that the upper limit in the damping isat so small scales that the allowed ΛWDM models wouldnot be already able to solve the potential problems ofΛCDM.So far, most studies on galaxy properties in theΛWDM scenario were based on dark-matter-only sim-ulations or a combination of these kind of simula-tions with semi-analytic models (for the latter see e.g.,Macci`o & Fontanot 2010; Menci et al. 2012; Kang et al.2013). However, by their own nature, these approachescan not take into account the effects of the non-linearbaryonic physics on the evolution and dynamics of thehalos, which can be important. Thus, inferences based onthe analysis of dark-matter-only simulations (and, per-haps, semi-analytic models) are necessarily limited whencomparing with observations (see e.g. Kang et al. 2013).It is then important to go beyond those techniques andperform full N-body + Hydrodynamics simulations. Aninteresting question than one can ask is how much differthe evolution and properties of galaxies formed in theΛWDM scenario from those formed in the ΛCDM one.At this point, it is important to recognize that the dark-matter structure evolution is expected to be very similarin both scenarios at scales much larger than the filter-ing one, with differences appearing gradually at scalesapproaching this scale.The so-called half-mode wavelength or its correspond-ing mass, M f , is commonly chosen as the relevant filter-ing scale at which WDM halo abundance and propertiesstart to significantly deviate from the CDM case (see forthe exact definition and references Section 2). In thispaper, we present a set of zoom-in N-body + Hydrody-namics simulations of (dwarf) galaxies formed in WDMscenario in halos with masses . M f and 20 − M f , andcompare them with their CDM counterparts. Recently,Herpich et al. (2014, see also Libeskind et al. 2013) re- ported WDM simulations of this kind but for three halosof masses significantly larger than the filtering massescorresponding to their WDM particle masses ( m WDM =1, 2, and 5 keV). This is very likely the reason why theevolution of their WDM galaxies did not differ signifi-cantly from the CDM counterparts. After completionof our study, it appeared a preprint by Governato et al.(2014), where the authors present a simulation of one dwarf galaxy formed in a ∼ M ⊙ halo, both inWDM and CDM cosmologies. For the WDM cosmol-ogy, m WDM =2 keV was used, which implies that theirsystem is ∼ halos of masses similarto the filtering mass M f that corresponds to a thermalWDM particle mass of 1.2 keV. These are expected tobe among the most abundant halos in this WDM sce-nario; below ∼ . M f , the halo mass function stronglydecreases, and the structures, rather than virialized ha-los, are isolated 3D enhancements not assembled hierar-chically (Angulo et al. 2013). The evolution and proper-ties of the galaxy-halo systems around the filtering mass might in several aspects be generic regardless of the valueof this mass ; though, astrophysical processes such as stel-lar feedback and reionization could make the extrapola-tion of our results to other filtering or thermal WDMparticle masses inadequate.In Section 2, the cosmological background and the usedWDM models are presented. The details of the code andsimulations performed here are given in Section 3. Theproperties and evolution of the simulated WDM dwarfgalaxies and their corresponding CDM ones are presentedin Section 4. A summary of the results and further dis-cussion are presented in Section 5. THE COSMOLOGICAL MODELSThe cosmological background used in our numericalsimulations is a flat, low-density model with Ω m = 0 . b = 0 . Λ = 0 .
7, and h = 0 .
7. For the CDM initialpower spectrum, P ( k ) CDM , we adopt the approximationby Klypin & Holtzman (1997), which was obtained as adirect fit of the power spectrum calculated using a Boltz-mann code. For the scales studied in this paper, and evenlarger ones, this approximation is very accurate. In thecase of WDM, the power spectrum at large scales is essen-tially that of the CDM, but at small scales the power issystematically reduced due to the free-streaming damp-ing. The transfer function T W DM ( k ) describes such adeviation from the CDM power spectrum, P W DM ( k ) = T W DM ( k ) P CDM ( k ) . (1)The CDM or WDM power spectra are normalized to σ = 0 .
8, a value close to that estimated from the
Planck mission (Planck Collaboration et al. 2014); σ is the rmsof z = 0 mass perturbations estimated with the top-hatwindow of radius 8 h − Mpc.The free-streaming of collisionless particles erase darkmatter perturbations below a scale given by the proper-ties of the dark matter particle. Here, we will refer tothe case of fully thermalized particles at decoupling as thermal relics . A simple analysis gives an estimate of thecomoving length at which thermal particles diffuse outalaxies formed in WDM halos at the filtering scale 3(e.g., Kolb & Turner 1994; Schneider et al. 2012): λ fs ≃ . (cid:16) m WDM keV (cid:17) − / (cid:18) Ω W DM h . (cid:19) / [ h − M ⊙ ] . (2)However, in order to calculate the whole processed powerspectrum, the coupled Boltzmann relativistic system ofequations for the various species of matter and radiationshould be numerically solved. Here, we adopt the WDMtransfer function given in Viel et al. (2005): T W DM ( k ) = (cid:2) αk ) . ν (cid:3) − . /ν , (3)where ν = 1 .
12 and the parameter α is related to m WDM ,Ω W DM , and h through α = a (cid:16) m WDM (cid:17) b (cid:18) Ω W DM . (cid:19) c (cid:18) h . (cid:19) d h − Mpc , (4)with a = 0 . b = − . c = 0 . d = 1 .
22. Ineq. (3), α is a characteristic scale length that can berelated to an effective free-streaming scale, λ efffs ≡ α (e.g.,Schneider et al. 2012). The corresponding effective free-streaming mass is then: M fs = 4 π ρ (cid:18) λ efffs (cid:19) , (5)where ¯ ρ is the present-day background density. The pri-mordial density perturbations below M fs are expected tobe completely erased, while perturbations with massesup to thousand times M fs can be significantly affectedby the damping process. It is common, on the otherhand, to define a characteristic scale below which the lin-ear WDM power spectrum start to deviate significantlyfrom the CDM one (Sommer-Larsen & Dolgov 2001;Avila-Reese et al. 2001). Following Avila-Reese et al.(2001), we define the half-mode wavenumber, k hm , forwhich T W DM ( k ) = 0 .
5; i.e., where the value of the powerspectrum of the WDM model is half that of the corre-sponding CDM one. The associated half-mode filtering mass is given by: M f = 4 π ρ (cid:18) λ hm (cid:19) , (6)where λ hm = 2 π/k hm is the comoving half-mode length. This filtering mass scale, which is much larger than M fs , is where one expects the abundance and proper-ties of the halos to start to significantly deviate from theCDM case (Col´ın et al. 2008; Smith & Markovic 2011;Menci et al. 2012; Schneider et al. 2012; Benson et al.2013; Angulo et al. 2013). At masses around M f , theabundance of halos already falls below, by a factor of ∼
2, that of the corresponding CDM one, reaching its rel-atively shallow peak at ∼ . M f . Thus, the most abun-dant halos in the WDM cosmogony are those of massesaround to M f .Structures of masses close to M f can be unambigu-ously defined as approximately spherical virialized ob-jects that resemble those seen in CDM simulations, albeit Note that some authors define the half-mode wavenumber as T WDM ( k ) = 0 . M f than in our case. Herpich+Governato+
Fig. 1.—
The free-streaming and half-mode (filtering) mass scalesas a function of the thermal relic particle mass, m WDM (for asterile neutrino particle, see eq. 7). The squares show where oursimulations lie at z = 0 (red) and at z = 2 (blue; only for the1.2 keV case). Even at z = 2 our simulations are far from theartificial fragmentation scale for a filtering corresponding to 1.2keV (downwards arrow). The starred symbols and the open circlecorrespond to the simulations presented in Herpich et al. (2014)and Governato et al. (2014) at z = 0. with some differences; for instance, they are less con-centrated (e.g., Avila-Reese et al. 2001; Angulo et al.2013). Moreover, halos of masses ≫ M f are expectedto assemble hierarchically, sharing the same propertiesas their CDM counterparts. Systems of masses severaltimes smaller than M f but larger than M fs can be definedas ”protohalos”, that is halos that are not fully formed,but show clear isolated 3D enhancements (Angulo et al.2013). At masses close to M fs , these authors report struc-tures that appear as clear failures of their halo finder al-gorithm, these include outer caustics of large halos anddense sheets and filaments, where the collapse of a fur-ther axis has just started.Following Schneider et al. (2014), in Fig. 1, we showthe dependence of M f and M fs on the thermal WDMparticle mass m WDM . For a given m WDM and atany epoch, objects located well above the solid line( M = M f ) are halos assembled hierarchically, as inthe CDM cosmogony. Objects of masses close to M f ,on the other hand, can be considered “normal” halos.However, their early assembly is already affected bythe filtering at small scales; for example, they formlater than their CDM counterparts. The objects thatAngulo et al. (2013) define as “protohalos” start toapear as the mass decreases below M f and dominatethe population when M ≪ M f . In these “protoha-los”, the hierarchical assembly fails notoriously (e.g., Colin et al.Schneider et al. 2012). Finally, below the dot-dashedline ( M = M fs ), no structure formation is expected.However, in N-body simulations it is possible to findstructures smaller than M fs but they are actuallyartificial (see e.g., Avila-Reese et al. 2001; Bode et al.2001; G¨otz & Sommer-Larsen 2003; Knebe et al.2003; Wang & White 2007; Schneider et al. 2013;Angulo et al. 2013).In Fig. 1 we plot our eight simulated systems (pre-sented below) with red squares as well as those simulatedby Herpich et al. (2014) and Governato et al. (2014),starred and open circle symbols (their M masses weremultiplied by 1.24 so as to take into account our differ-ent definition of virial mass). These masses are at z = 0;we also plot the virial masses of our simulated systems at z = 2 (blue squares). The downwards arrow indicates themass scale where spurious structures would form in oursimulations with m WDM =1.2 keV (for m WDM =3 keV, itis at a smaller mass) due to numerical fragmentation, ac-cording to the criterion given by Wang & White (2007).This criterion depends on the filtering scale and the res-olution of the numerical simulation. As can be seen, ourhalos lie above the downwards arrow even at z = 2. Yet,it might be that numerical artifacts are present at thehighest redshifts, when the progenitor masses are verysmall.The relations show in Fig. 1 are for thermal relicparticles. Popular candidates for WDM are also thesterile and right-handed neutrinos, particles proposed tonever been in thermal equilibrium (Dodelson & Widrow1994; Shi & Fuller 1999; Abazajian et al. 2001; seeBoyarsky et al. 2009 for a review). Viel et al. (2005)provided a relation between the non-resonantly producedsterile neutrino mass and the mass of the thermal relicparticle such that the transfer function for this kind ofsterile neutrino can be calculated according to eq. (3).The relation is given by m ν s = 4 .
43 keV( m WDM / / (Ω W DM h ) − / . (7)Thus, for a given cosmological background, we can useFig. 1 also for the case of the non-resonantly producedsterile neutrino, after going from m WDM to m ν s . An-other particle candidate for WDM is the gravitino (e.g.,Pagels & Primack 1982; Ellis et al. 1984; Moroi et al.1993). Weakly interacting massive particles (WIMPs,the most favored candidates for CDM), if produced innon-thermal processes, can also have large free-streaminglengths and emulate the power spectrum of WDM (e.g.,Lin et al. 2001; He & Lin 2013).Finally, thermal WDM particles are expected to havea relic velocity dispersion, which could affect the innerstructure of halos due to the Liouville theorem limitfor the phase density (Hogan & Dalcanton 2000). How-ever, this velocity dispersion is very small for reason-able mass candidates ( ∼ . m WDM ∼ v th =0, in our simulations. THE CODE AND THE SIMULATIONS We have carried out a set of N-body + Hydrody-namics simulations of low-mass halos using the zoom-in technique in both the ΛWDM cosmology and itscounterpart the ΛCDM one. The simulations wererun using the Adaptive Refinement Tree (ART) N-body/hydrodynamic code (Kravtsov et al. 1997, 2003).The code includes gas cooling, star formation (SF), stel-lar feedback, advection of metals, and a UV heatingbackground source. The cooling and heating rates incor-porate Compton heating/cooling, atomic and molecularcooling, UV heating from a cosmological background ra-diation (Haardt & Madau 1996), and are tabulated fora temperature range of 10 < T < K and a grid ofdensities, metallicities, and redshifts using the CLOUDYcode (Ferland et al. 1998, version 96b4).The SF and feedback processes (subgrid physics)are implemented in the code as discussed in detail inColin et al. (2010) and Avila-Reese et al. (2011). Forcompleteness, they are briefly summarized below. TheSF takes place in those cells for which
T < T SF and ρ g > ρ SF , where T and ρ g are the temperature anddensity of the gas, respectively, and T SF and ρ SF arethe temperature and density threshold, respectively.Here, we use the same values of the T SF and n SF pa-rameters as in Avila-Reese et al. (2011); namely, 9000K and 6 cm − , respectively, where n SF is the den-sity threshold in hydrogen atoms per cubic centime-ter; see Avila-Reese et al. (2011), as well as Colin et al.(2010) and Gonz´alez-Samaniego et al. (2014) (hereafterG+2014), for a discussion on the choice of these values,in particular n SF . A stellar particle of mass m ∗ = ǫ SF m g is placed in a grid cell every time the above conditionsare simultaneously satisfied, where m g is the gas massin the cell and ǫ SF is a parameter that measures the lo-cal efficiency by which gas is converted into stars. As inAvila-Reese et al. (2011), we set ǫ SF = 0 . ⊙ injects instantaneously into the cell, where the particleis located, E SN+Wind = 2 × erg of thermal energy;half of this energy is assumed to come from the type-IISN and half from the shocked stellar winds. This en-ergy provided by the stellar feedback raises the temper-ature of the cell to values > ∼ K; the precise valuedepends on the assumed initial mass function (IMF), theamount of energy assumed to be dumped by each mas-sive star, and the value of the ǫ SF parameter. On theother hand, each 8M ⊙ ejects 1 . ⊙ of metals. For theassumed Miller & Scalo (1979) IMF, a stellar particle of10 M ⊙ produces 749 type-II SNe.In our previous works, we have delayed the radiativecooling for some time (typically between 10 and 40 Myr)in those cells where young stellar particles are, in or-der to avoid overcooling due to, for instance, resolutionlimitations. However, at the current resolution reachedby our simulations and for the typical densities found inthe SF cells ( ∼
10 cm − ), which in turn depend on n SF ,the cooling time is actually much larger than the cross-ing time (Dalla Vecchia & Schaye 2012). Thus, for thesimulations used in this study, switching-off the coolingtemporarily is expected to have only a minor effect on theproperties of the simulated galaxies. We have carried outsome tests and verified that this is the case. However, wealaxies formed in WDM halos at the filtering scale 5decided to keep in the code this cooling delay when run-ning the ΛWDM simulations because some of the corre-sponding CDM galaxies, to be compared with the WDMones, were run with this prescription (G+2014).3.1. The zoom-in simulations
The aim of this paper is to explore the evolution ofgalaxies formed in WDM halos of masses around the half-mode (filtering) scale M f . As discussed in Section 2, M f is a characteristic scale, where the properties and abun-dance of the WDM halos start to depart significantlyfrom those of their CDM counterparts.Here, we will study one particular value of M f , corre-sponding to dwarf-galaxy scales. At a qualitative level,the results might apply to other values of M f .According to eqs. (6) and (3), a half-mode mass of2 × h − M ⊙ is associated to a thermal relic parti-cle of m WDM = 1 . m WDM = 1 . . hereafter). We alsocarry out simulations of the same systems for a WDMpower spectrum corresponding to m WDM = 3 keV (caseWDM . hereafter), in order to explore whether the prop-erties of simulated galaxies in halos much more massivethan M f tend to be similar to those of galaxies formedin CDM halos. For this case, M f = 9 . × h − M ⊙ andthus, the simulated systems are about 20-30 times M f .The ΛWDM simulations performed here have the samerandom seed and box size as the ΛCDM simulations inG+2014. Therefore, all the target WDM halos/galaxieshere have their CDM counterpart simulations. The boxused in G+2014 has L box = 10 h − Mpc per side anda root grid of 128 cells. We first set the multiple-mass species initial conditions with the code PMstartM(Klypin et al. 2001) and then run a low–mass resolutionsimulation with the N-body ART code (Kravtsov et al.1997). A spherical region of radius three times the virialradius R v of the selected halo is chosen. The virial ra-dius is defined as the radius that encloses a mean densityequal to ∆ vir times the mean density of the universe,where ∆ vir is obtained from the spherical top-hat col-lapse model. The Lagrangian region corresponding to the z = 0 spherical volume is identified at z = 50 and resam-pled with additional small-scale waves (Klypin et al.2001). The new zoom-in simulation is then run withthe hydrodynamic/N-body version of ART. The numberof DM particles in the high-resolution zone changes fromhalo to halo but it is between 500 thousand and one mil-lion. The mass per particle m p in the highest resolutionregion is 6 . × h − M ⊙ and increases for the DM N-body only runs to 7 . × h − M ⊙ .In ART, the grid is refined recursively as the matter distribution evolves. The runs use a DM or gas den-sity criteria to refine. In the CDM runs presented inG+2014, the cell is refined when its mass in DM exceeds1 . m p or the mass in gas is higher than 1.4 F U m p , where F U ≡ Ω b / Ω m is the universal baryon fraction. For theWDM runs, we have decided to use a less aggressive re-finement (it acts as a softening of very small structures)in an attempt to eliminate artificial fragments , whichare known to arise due to the finite number of particlesand the resolved cut-off of the power spectrum (see abovefor references). Thus, we refine cells only until they reacha mass eight times the previous value of 1 . m p in DM or1.4 F U m p in gas. To make sure that the less aggressiverefinement does not introduce significant differences inthe simulations, we resimulated some of the CDM runswith the less aggressive refinement setting. A compari-son between the CDM halos/galaxies obtained with theaggressive and soft refinements was done for some of thedwarfs and roughly the same evolution and propertieswere obtained. In the Appendix, we show and discussthe case for run Dw3.As in G+2014, in the hydrodynamic simulations pre-sented in this paper, the root grid of 128 cubic cells isimmediately refined unconditionally to the third level,corresponding to an effective grid size of 1024 . Al-though we formally set the maximum refinement levelto 11, which implies a minimum cell size of 55 comov-ing pc, this is not reached in practice in the WDM runswith m WDM = 1 . R v depends on the mass of the halo/galaxy, cos-mology, and on the kind of refinement that was used, butit is roughly about one million and reduces by a factorof eight or so for the less aggressive refinement.As mentioned above, our study is focused on dwarfsformed in WDM halos that at z = 0 have masses closeto M f and much larger than M f , and on comparingthem with their CDM counterparts. From G+2014 wehave selected the CDM systems named there as Dw3,Dw4, Dw5 and Dw7, each one with a different haloMAH but with about the same present-day virial masses, M v = 1 . − × h − M ⊙ . Unfortunately, the halofinder could not identify the halos corresponding todwarfs Dw4 and Dw7 in the WDM simulation with m WDM = 1 . m WDM = 1 . m WDM = 3 keV, inwhich case the corresponding M f is much smaller thanthe masses of the simulated objects. In order to havemore WDM systems of masses around M f , we have iden-tified in the 1.2 keV WDM box two more distinct halos,around these masses, and performed the correspondingzoom-in hydrodynamical simulations (dwarfs Dwn1 andDwn2). The CDM simulations for these systems withthe aggressive refinement were also run for comparison. Although our target halos/galaxies have masses at z ∼ We use a variant of the bound density maxima (BDM) halofinder algorithm of Klypin et al. (1999), kindly provided by A.Kravtsov, and run it on the dark matter particles in order to iden-tify the dark matter halos or subhalos. The central galaxy is thencentered at the position of the corresponding most massive halo.
Colin et al.
TABLE 1Physical properties of WDM runs at z = 0
Name log( M v ) log( M s ) a log( M g ) V max R e b R v f g c M g,cold /M g d D/T e z f,h f T g (M ⊙ ) (M ⊙ ) (M ⊙ ) (km s − ) (kpc) (kpc) (Gyr) m p = 0 . m p = 1 . . )Dw3 10.43 8.74 8.92 47.87 2.03 75.24 0.60 0.86 0.43 1.85 4.89Dw5 10.29 7.80 8.28 37.57 1.51 68.86 0.76 0.56 0.46 1.86 6.42Dwn1 10.47 8.43 8.29 43.23 3.61 78.79 0.42 0.42 0.65 1.85 5.48Dwn2 10.45 8.41 9.00 49.34 3.85 76.60 0.80 0.80 0.73 1.50 6.26 m p = 3 . . )Dw3 10.36 8.67 6.27 50.83 0.86 72.54 0.004 0.00 0.00 2.60 9.69Dw4 10.35 8.21 7.75 48.07 0.80 72.50 0.26 0.20 0.14 2.10 10.09Dw5 10.44 8.47 9.07 58.23 1.44 76.23 0.80 0.87 0.55 2.10 7.95Dw7 10.38 7.99 8.73 42.80 3.08 73.23 0.85 0.60 0.78 1.60 5.69 a Mass within 0.1 R v (the same applies for M g ); b Radius that encloses half of the stellar mass within 0.1 R v ; c f g ≡ M g / ( M g + M s ); d The amount of cold gas inside the galaxy in units of M g e Ratio of the mass contained in the high-angular momentum disk stars with respect to the total stellar mass; f Redshift at which the given halo acquired one third of its present-day mass. g Stellar mass-weighted average age.
WDM
Stars Gass
CDM ars
Fig. 2.—
Stellar (two leftmost panels) and gas (two rightmost panels) projected distributions at z = 0 for the dwarf Dw3 in the WDM . (top) and CDM (bottom) runs within a sphere of radius 0.15 R v . The first and third (second and fourth) columns are projections inthe face-on (edge-on) planes of the galaxy. The WDM . run clearly show a more extended gaseous and stellar structure than its CDMcounterpart. alaxies formed in WDM halos at the filtering scale 7In Table 1, we present all the runs studied in this pa-per and summarize their main present-day properties.The WDM runs are shown in Fig. 1. As far as weare aware of, our simulations are the only ones, per-form within the full N-body + hydrodynamical scheme,that focus on halo/galaxy masses that at present-dayare close to the filtering scale M f (corresponding specif-ically to m WDM =1.2 keV). The galaxy properties ( M s ,stellar galaxy half-mass radius R e , SFR, etc.) are com-puted within a sphere of 0 . R v radius. We notice thatthe R e values reported in Table 1 of G+2014 were erro-neously boosted by a factor 1/ h ; the values presented inTable 1 here are the correct ones. This radius 0.1 R v contains essentially all the stars and cold gas of the sim-ulated central galaxy. The contamination of satellites orother substructures at this radius is negligible. On theother hand, because the outer stellar mass density pro-files decrease strongly with radius in most of the runs,the galaxy stellar mass would not differ significantly hadwe measure it at “aperture” radii slightly smaller than0.1 R v by, for example, 20-50%. The disk-to-total ratio(D/T) is found using a kinematic decomposition of thestellar galaxy into an spheroid and a disk. The massof the spheroid, M sph , is defined as two times the massof the stellar particles inside 0.1 R v that have negativespin values (counter-rotate), it implicitly assumes thatthe spin distribution of the spheroid is symmetric aroundzero. The D/T is then defined as ( M s − M sph ) /M s . RESULTS4.1.
General properties
All of our zoom-in simulations are for distinct halosthat at the present epoch end up with virial massesof ≈ . − × h − M ⊙ ; the dwarf galaxies insidethese halos are therefore centrals . Those halos of massesaround M f (runs WDM . ) are devoid of substructuresand have mass distributions less concentrated than theirCDM and WDM . counterparts. In Fig. 2, we plotthe 2D stellar and gaseous distributions at z = 0 fordwarf Dw3 in the WDM . (top) and CDM (bottom)runs. Projections in the face-on (first and third columns)and edge-on (second and fourth columns) planes of thegalaxy are shown. The FITS images of these projectionswere obtained with TIPSY . In these images, the galaxydisk lies on the plane perpendicular to the angular mo-mentum vector of the gas cells that are within a sphereof radius 0.15 R v , centered on the center of mass of thestellar particles. We use then the DS9 visualization pro-gram to create the images by color coding the density ofthe respective components within a fixed range of valuesfor a fair comparison between the panels.From a visual inspection of Fig. 2, we see that theWDM . dwarf galaxy has a more extended and less cen-trally concentrated stellar mass distribution than in theCDM case. Indeed, the R e of the former is 2 times largerthan the one of the latter (see Table 1). Moreover, theformer has a more disk-like structure than the latter. In-deed, we measure a disk-to-total mass ratio, D/T, of 0.43vs 0.01 (Table 1). A more pronounced disk-like structurefor the former than for the latter is also seen in the gas http://ds9.si.edu/site/Home.html distribution. The WDM . dwarf at the half-mode massis gas rich ( f g =0.60) and it has an extended and a low-surface density gaseous disk, unlike the CDM case, wherethe dwarf is gas poor ( f g =0.18) and has a compact gasdistribution. The spatial temperature distribution of thegas is also quite different: in the CDM case the gas inthe galaxy is colder than the one in the dwarf at the half-mode mass scale, while the gas in the corona is hotter.According to Table 1, the present-day dwarfs Dw3,Dw5, Dwn1 and Dwn2, formed in halos of masses around M f , are systematically more extended (larger R e ), have alower stellar mass and maximum circular velocities, V max ,and, in most of cases, end up with a higher gas frac-tions than their CDM counterparts. These differencesare likely a consequence of the later assembly, lower con-centrations and absence of mergers of the halos at the fil-tering mass . However, due to the complex and non-linearsubgrid physics, small variations in the non-linear evolu-tionary processes can also produce large differences andshifts in the galaxy properties at any given epoch. This iswhy we have simulated several systems to verify that thedifferences between the WDM . dwarfs and their CDMcounterparts are systematical and not due to small vari-ations in a particular case. Moreover, although the sys-tems with masses much larger than M f (runs WDM . )show some differences with respect to their CDM coun-terparts, these are already small and do not follow a sys-tematical trend as in the case of the WDM . runs. Forexample, in some WDM . runs f g , R e or D/T are largerin the WDM . runs than in their CDM counterparts,while in others they are smaller. This very likely meansthat the differences are due to small variations in thenon-linear evolution rather than due to the (small) dif-ferences in the initial power spectrum. Yet, V max is sys-tematically lower in all WDM . runs, but not by muchas seen in the case of the WDM . ones. The depth ofthe gravitational potential of the systems seems to be themain property systematically affected by the filtering inthe power spectrum of fluctuations.
Radial distributions
In this subsection, we explore in more detail thepresent-day inner structure and dynamics of the simu-lated dwarfs. Solid lines in Fig. 3 show the total cir-cular velocity profiles, V c ( r ), and their decompositionsinto DM, stars and gas (gray, blue and cyan lines, re-spectively) for the systems of mass around M f (runsWDM . , upper panels) and of mass (20 − × M f (runs WDM . , lower panels). The corresponding CDMdwarfs are also shown with dashed lines using the samecolor coding. The total circular velocity profiles (ma-genta lines) for dwarfs formed in halos at the filteringscale are shallower in the center than the CDM counter-parts with lower values of V max by . cosmogony, though they are small, showing that systemsformed in halos much larger than M f tend to be similarto those formed in the CDM scenario.The stellar V c ( r ) components (blue lines) of theWDM . runs are significantly lower and less peaked thanthe CDM cases. In all simulations, the halo componentdominates, at least from radii larger than ∼ . − . R e .The circular velocities of the gaseous component (cyanlines) tend also to be less peaked in the WDM . runs Colin et al. R [kpc] R [kpc] R [kpc] R [kpc]
Fig. 3.—
Circular velocity profiles and their decomposition for the WDM runs (solid lines) and their CDM counterparts (dashed lines) at z = 0. In the upper panels are plotted the profiles for the systems of masses around the filtering scale M f and in the lower panels for thosesystems of masses 20 to 30 times M f . We denote with magenta, gray, blue, and cyan lines the total, halo, stellar, and gaseous circularvelocities, respectively. than in the CDM ones. However, while in the CDM casetheir inner contributions to the total circular velocity liebelow that of the stellar component, except for dwarfDw7, in the case of the WDM . runs, the V c ( r ) of thegaseous component is similar or dominates at all radiiover the stellar one, except in the inner region of dwarfDw3 (WDM . dwarfs are more gaseous than the analo-gous CDM dwarfs, see Table 1). In any case, the bary-onic (stellar + gaseous) contribution to the total V c ( r )is more important and more centrally concentrated in allCDM runs than in the WDM . ones. Therefore, the cir-cular velocities of the WDM systems of masses around M f are shallower than the CDM ones mainly because less centrally concentrated baryonic galaxies form in theformer simulations (see also Fig. 4 below).On the other hand, V max is significantly lower in theWDM . runs than in the CDM ones mainly becausethe corresponding pure DM halos are already less con-centrated in the WDM case than in the CDM one (e.g,Avila-Reese et al. 2001; Lovell et al. 2012). However, theastrophysical processes in both cases are also expectedto produce different effects on the inner dynamics of thegalaxy-halo systems, which could increase/reduce the dif-ferences in V max , as well as in the innermost dynamicsof the galaxy-halo systems (for instance, the formationor not of shallow cores). We will study in detail thisquestion elsewhere.In Fig. 4, the stellar (blue) and cold gas (cyan) sur-face density (SD) profiles of the WDM . and WDM . runs (solid lines) are compared to those of their CDMcounterparts (dashed lines). The most noticeable differ-ence in the stellar SD profiles between the WDM . runsand the corresponding CDM ones (upper panels) is that the inner regions of the former are significantly lower .While the CDM dwarfs have a central peaked stellar den-sity, reminiscent of a bulge-like structure, in the WDM . ones a flattened SD is seen, except in run Dw3; though,even in this case, the CDM dwarf has a more peakedSD (see also Fig. 3). Regarding the gas SD profiles, forthe CDM dwarfs, they tend to be more extended thanthe stellar ones and of lower SDs in the center, while forthe WDM . dwarfs, the gas SD profiles roughly followthe stellar ones, except for run Dw3. The CDM dwarfshave higher baryonic (stars+gas) SDs in the center thanthe dwarfs formed in halos at the filtering scale. In thecase of the WDM . dwarfs (lower panels), their stellarand gas SD profiles tend to be similar to those of theirCDM counterparts; though, for Dw4 and Dw7 the gasSD profiles show significant differences.The systematical differences in the stellar SD profilesbetween the WDM . and CDM runs, specially in theinner regions, could be the result of many effects. Oneof them might be the angular momentum of the halos inwhich galaxies form. We have measured the halo (darkmatter particles only) spin parameter λ for all the runs The spin parameter is defined as λ = J | E | / GM / , where J , M alaxies formed in WDM halos at the filtering scale 9 Fig. 4.—
Stellar (blue lines) and gas (cyan lines) surface density profiles of the WDM dwarfs (solid lines), compared to their CDMcounterparts (dashed lines). The upper and lower panels are for the WDM . and WDM . runs, respectively. at z = 0 with the following results: runs Dw3 and Dw5have a lower spin parameter in the CDM runs than inthe WDM . ones (0.015 and 0.007 vs. 0.033 and 0.012,respectively) but for runs Dwn1 and Dwn2 we found thecontrary, CDM runs have a higher spin parameter (0.072and 0.083 versus 0.032 and 0.037, respectively). The lasttwo runs, specially Dwn2, have a relatively late mergerin the CDM simulations that could affect the spin pa-rameter, although these mergers happened more than ∼ λ introduced inBullock et al. (2001). Although the values of λ are dif-ferent, the trend is the same: runs Dwn1 and Dwn2 havelarger values in the CDM simulations, and Dw3 and Dw5have smaller values. In summary, it is not clear that thehalo spin parameter is the reason why the stellar distri-bution is less concentrated in the WDM runs than in theCDM ones. We plan to study in detail elsewhere (Avila-Reese et al in prep) the question of the spin parameter inWDM and CDM, both in DM-only and hydrodynamicalsimulations.The mechanism responsible for the stellar-SD profiledifferences between the WDM . and CDM dwarfs canbe traced probably to the merging history of the cen-tral galaxies (Herpich et al. 2014). The satellite inter-actions/mergers in the case of CDM simulations drivegas to the center, where SF proceeds efficiently, pro-ducing a cuspy stellar structure. The stellar specific and E are the total angular mometum, mass, and energy, respec-tively. This latter quantity is computed, assuming that the halo isvirialized, as - K , where K is the kinetic energy. angular momentum is also more likely to decrease inthe galaxies that suffered mergers since the angular mo-mentum of these merging galaxies can cancel each other(Cloet-Osselaer et al. 2014). These processes do not hap-pen in the WDM . dwarfs because they are practi-cally devoid of satellites. Besides, the galaxy assemblystarts later than in the CDM halos, being the disks moregaseous and less susceptible to secular evolutionary pro-cesses.In summary, dwarfs formed in halos of masses around M f in our WDM . simulations have a quite differentdynamical history and structural inner properties whencompared to their CDM counterparts, whereas dwarfsformed in a WDM cosmology but in halos with a massmuch larger than M f , tend to be similar to the corre-sponding CDM dwarfs. The latter is in agreement withthe simulation results of Herpich et al. (2014).4.2. Mass assembly histories
In Fig. 5 we plot the virial MAHs of the WDM . (upper panels) and WDM . (lower panels) runs alongwith their corresponding CDM counterparts (black solidand dashed lines, respectively). As can be seen, the ha-los around the filtering mass M f start to assemble laterand end up with masses slightly smaller than the cor-responding CDM ones. However, afterwards the formergrow faster, specially the runs Dw3 and Dw5. Thus,the epoch at which half or one-third of the present-dayvirial mass is acquired is not very different between bothcosmologies (see Table 1). The WDM halos of scales(20 − × M f assemble their masses practically in the0 Colin et al. Fig. 5.—
Mass assembly histories for the simulated dwarf galaxies. In the upper panels we show the MAHs for the WDM . runs, whilein the lower panels are the MAHs of the WDM . runs (solid lines). In each case, the MAHs of the corresponding CDM runs are alsoplotted (dashed lines). We denote with black lines the total (virial) MAHs and with blue lines the galaxy stellar MAHs. The MAHs of thedwarfs formed in halos around M f (WDM . runs) differ significantly from their CDM counterparts. same way as they do in the CDM scenario.The blue solid and dashed lines in Fig. 5 show the stel-lar MAHs of the WDM and CDM simulated dwarf galax-ies, respectively. In G+2014, it was shown that the stel-lar MAHs of dwarfs follow roughly their halo MAHs inthe CDM simulations; i.e., the M s -to- M v ratio is roughlyconstant, at least up to z ∼ . − . . dwarfs we find that from z & ∼ M s -to- M v ratio significantly increases;from z ∼ . baryonic galaxiesare in their active growth phase. Thus, the stellar massassembly of the dwarfs at the filtering scale shows a de-coupling from the assembly of their halos, unlike whathappens with the dwarfs in the CDM case. At z = 0, the M s -to- M v ratios of all WDM . galaxies are 2 − . runs;at z = 0, the maximum difference, which amounts a fac-tor of 1.6, is found for the dwarf Dw7. In general, the M s -to- M v ratio remains close to the CDM one at all red-shifts. Thus, as the halo mass gets closer to the filteringmass, the galaxies formed inside them end up with lower M s -to- M v ratios. This result strictly holds for the scalesand neutrino masses (1.2 and 3.0 keV) studied here.Our WDM . dwarf galaxies assemble their stellarmasses with a significant delay with respect to their CDMcounterparts. For example, the assembly of half of thepresent-day M s for dwarf Dw5 happens 1.3 Gyr later in the WDM . cosmology. For the dwarfs formed in halosmuch larger than M f (runs WDM . ), the stellar MAHsare close to those of the CDM counterparts, with mini-mum differences in the half-mass assembly epochs.The galaxy baryon (stars + gas) MAHs, M b ( z ), ofthe simulated galaxies follow moderately the halo MAHs,with some intermittence, both in the WDM and CDMsimulations. However, the WDM . runs show more in-termittent histories than the CDM ones, due to moreextended periods of gas infall/outflow onto/from the ha-los. This is likely because the WDM . halos accretebaryons in a more regular way than the CDM halos andbecause they blowout the gas more efficiently due theirlower concentrations and V max . The baryon-to-halo massratios, M b -to- M v , of the former are slightly lower thanthose of the latter at all epochs, except for run Dw3 at z . . z = 0, the M b -to- M v ratios ofthe WDM . galaxies are 1 . − . Gas fraction and star formation histories
In Fig. 6, we plot the change with redshift of the galaxy gas fractions ( f g = M g / M b , solid lines) for the WDM . and WDM . runs, upper and lower panels, respectively.The dashed lines show the change with redshift of thefraction of gas outside the galaxy but within the halo ,the“halo” gas fraction F g,h . This is defined as the ratioof the gas mass contained in the spherical shell of radiibetween 0.1 R v and R v to the gas mass in the whole halo.As in the case of the CDM simulations (see Fig. 6 inG+2014), the two gas fractions oscillate, and in periodsalaxies formed in WDM halos at the filtering scale 11 F r a c t i o n Dw3, WDM
Dw5, WDM
Dwn1, WDM
Dwn2, WDM f g F g,h F r a c t i o n Dw3, WDM
Dw5, WDM
Dw4, WDM
Dw7, WDM f g -CDMF g,h -CDM Fig. 6.—
Evolution of the galaxy gas mass fraction, f g , for the different WDM runs (blue solid lines). The black dashed line refers to F g,h , the ratio between the gas mass in the halo (the gas in the spherical shell of radii 0.1 R v and 1 R v ) and the total gas mass within R v .With blue and black dotted lines, f g and F g,h , respectively, we show the corresponding quantities for the CDM case. The WDM . runs,plotted in the upper panels, present evolutions of f g and F g,h that differ significantly from those of their CDM counterparts, while, on therother hand, for the WDM . runs, plotted in the lower panels, the differences are less notorious. where f g decreases (increases) typically F g,h increases(decreases). This is mainly due to the interplay amonggas accretion onto the galaxy, SF and SN-driven outflowsfrom the galaxy. It seems that this interplay is strongerin the CDM simulations than in the systems with massaround M f (WDM . ). The WDM . runs show a be-havior roughly close to their CDM counterparts.The galaxy gas fractions in the WDM . runs are, at allepochs, higher than those found in their CDM runs coun-terparts, probably as a consequence of the later galaxyassembly of the former runs. The values of f g at z = 0are shown in column eighth of Table 1. We see that the f g values of the WDM dwarfs formed in halos of scalesaround M f are relatively high.In Fig. 7 we plot the ”archeological” SF histories of ourWDM runs (solid lines) compared to their CDM coun-terparts (blue dashed lines). For illustration purposes,since the SF histories are strongly intermittent, theywere smoothed with a top-hat filter of 500 Myr width.The original histories were built with 0.1 Gyr bins. Thisis computed, for any given time t [Gyr], identifying allgalaxy stellar particles at z = 0 born within the time in-terval [ t − . , t] Gyr; the SFR at this time is then simplythe mass of these particles divided by 0.1 Gyr.As expected from the later halo assembly, the SF inthe WDM . systems of masses around M f starts laterthan in the CDM counterparts. Besides, the formerpresent more sustained SF histories at later epochs thanthe CDM dwarfs , for which the SFR tends to fall in the last Gyrs. This implies that the specific SFRs (SFR/ M s )of the WDM galaxies of scales around M f tend to behigher at late epochs than those of the CDM counter-parts. The fact that the WDM . galaxies assemble laterand have lower central gas surface densities than theCDM ones likely explains their less efficient but moresustained SF histories. As in the CDM runs (see a dis-cussion in G+2014), the SF histories in the WDM runsare also episodic. For those systems around the filteringmass M f , the SF is sometimes even more bursty thantheir CDM counterparts.To highlight the differences in the stellar populationsbetween the dwarfs in the WDM . runs and their CDMcounterparts, in Fig. 8 we plot the cumulative (archae-ological) SF histories. Solid lines are for the WDM . and WDM . dwarfs, left and right panel, respectively,while dashed lines in both panels are for the CDM coun-terparts. One clearly sees that the stellar populationsof present-day WDM . dwarfs are formed on averagesignificantly later than those of the CDM dwarfs, with20% of their stars being formed in the last ∼ ∼ . ∼ . . with CDM, and Dwn1 is theone that shows the most similar history (blue lines). In-terestingly, it is the galaxy Dw3 the one that differs lesswhen compared WDM . with CDM. In general, the dif-2 Colin et al. Fig. 7.—
Archaeological SF rate histories for the WDM . (upper panels) and WDM . (lower panels) runs presented in this paper(black solid lines). In each panel, the corresponding CDM SF histories are also shown (dashed blue lines). In the x-axis runs the cosmictime. The histories were smoothed with a top-hat filter of 500 Myr width; see text for details about how the SF histories were calculated. ferences between the WDM . and CDM galaxies (rightpanel), as expected, are lower than those found when theWDM . and CDM dwarfs are compared.We have calculated also the mass-weighted “archeolog-ical” ages of all runs and report them in the last columnof Table 1. This age is the result of multiplying the ageof each galaxy stellar particle at z = 0 by its mass frac-tion contribution (the particle mass divided by M s ), andsumming these terms for all the particles. The dwarfsof scales around M f are between ∼ . and 4.8 Gyrsyounger than their CDM counterparts. The largest dif-ference is for the dwarf Dw3 and the smallest for Dwn1(see above). The mass-weighted ages of the WDM . dwarfs are similar or slightly smaller (by ∼ central dwarf galax-ies in the WDM scenario are expected to have youngerstellar populations on average than their CDM counter-parts, the younger the closer their halo masses are to thefiltering scale. SUMMARY AND DISCUSSIONWe have presented the first N-body + Hydrodynam-ics (zoom-in) simulations of galaxies formed in distinctWDM halos with masses at present-day close to the half-mode filtered mass M f corresponding to a thermal WDMparticle mass of m WDM =1.2 keV. Halo masses are around3 × M ⊙ . Galaxies formed in WDM halos 20–30times more massive than M f were also simulated (runs WDM . , for which m WDM =3.0 keV). In a WDM cos-mology, the halos of masses around M f are close to thepeak of the halo mass function; at masses a factor of ∼ − ∼ M f at z = 0already do not appear to be virialized spherical overden-sities (halos) and they did not assemble hierarchically.Our results show that the WDM . galaxies have disk-like structures and circular velocity profiles that gentlyincrease and then flattens. These dwarfs are quite dif-ferent in several aspects from their CDM counterparts,which assembled hierarchically. The galaxies formed inhalos 20 −
30 times M f (runs WDM . ), instead, are verysimilar in properties and evolution to their CDM coun-terparts, in agreement with the results of Herpich et al.(2014). Therefore, the properties and evolution of WDMgalaxies differ more from those of the CDM galaxies asthe mass get closer to the filtering scale. In summary,our WDM . dwarf galaxies that formed in halos with amass around M f differ from their CDM counterparts inthat:1. they assemble their stellar masses later (Fig.5), with archaeological SF histories shifted toyounger stellar populations (Fig. 8; on average,the WDM dwarfs have mass-weighted ages 1.4–alaxies formed in WDM halos at the filtering scale 13 Dw3Dw5Dwn1Dwn2time(Gyr)0 2 4 6 8 10 1200.20.40.60.81 Dw3Dw5Dw4Dw7time(Gyr)0 2 4 6 8 10 12
Fig. 8.—
Cumulative SF histories of the WDM . and WDM . runs (solid lines), left and right panel, respectively, along withtheir CDM counterparts (dashed lines in both panels ). The dif-ferent dwarfs are identified with different colors. The WDM . runs clearly form most of their present-day stars much later thantheir CDM counterparts. As expected, the differences between theWDM . and CDM runs (right panel) are lower than those foundin the left panel, although there are runs and periods in whichthese differences are significant. V max values are 20–60% lower;3. they have significantly lower central stellar SDs andlarger R e values, by factors of 1.3–3 (Fig. 4);4. their V c ( r ) profiles are shallower, being this mainlybecause the baryonic (stars + gas) components areshallower (Fig. 3);5. on average, they have higher gas fractions andlower stellar masses (and thus lower M s -to- M v ra-tios).As stated above, the reported differences were foundin galaxies formed in halos with the particular value forthe filtering scale of M f = 2 × h − M ⊙ ( m WDM =1 . M s -to- M v ratios, etc., are systematically due to the lowerconcentrations and delay in the formation of the WDMhalos. Nevertheless, in general, the results of our hydro-dynamic simulations should not be rescaled with respectto the filtering mass because the astrophysical processessuch as cooling, feedback, etc., affect significantly theevolution of the galaxy-halo systems, specially in smallhalos (higher WDM particle masses).5.1. WDM galaxy formation
If the Ly- α power spectrum constrains WDM mod-els to be made of relic particles with masses above ≈ z = 0 should be . . × M ⊙ . Inthe CDM cosmology, the distinct halos of 1 . × M ⊙ have V max values of ∼
20 km/s and their stel-lar masses are expected to be . − M ⊙ ( M s -to- M v ratios . − . × − ), depending on the usedsubgrid physics (e.g., Sawala et al. 2010; Munshi et al.2013; Cloet-Osselaer et al. 2014; Sawala et al. 2014a,b;Governato et al. 2014).If we now extend our results found in this work; thatis, the differences found between the WDM . and CDMsimulations, to the hypothetical dwarfs formed in halosat the filtering scale of 1 . × M ⊙ ( m WDM =3 keV),then the corresponding V max and M s /M v ratio wouldbe around 12 km/s and 0 . ∼ M ⊙ areso limited that they can not be used to distinguish be-tween the CDM and the WDM with m WDM ≈ V max val-ues for a given M s smaller than those inferred or sim-ulated in the CDM scenario (e.g, Ferrero et al. 2012;Rodr´ıguez-Puebla et al. 2013), thus favoring the WDMscenario. However, as several authors have shown, thesepotential disagreements in the CDM scenario, in particu-lar those related to the too-high V max and M s / M v values,could be solved also by plausible changes/improvementsin the subgrid physics; for example, by introducinga metallicity-dependent H molecule formation process(Kuhlen et al. 2012; Christensen et al. 2012) or by in-troducing preventive/early mechanisms of feedback be-sides of increasing the strength of the ejective SN-driven feedback (Hopkins et al. 2012, 2014; Munshi et al.2013; Trujillo-Gomez et al. 2013; Stinson et al. 2013;Agertz et al. 2013).Along this venue, Governato et al. (2014, see also arecent review by Brooks 2014)) argue that the effectsof the SF-driven feedback overcome those of the initialpower spectrum regarding the inner dark matter andstellar mass distributions. This conclusion is based ononly one zoom-in simulated dwarf in both CDM andWDM cosmologies. For the latter, the filtering corre-sponds to a relic particle of mass 2 keV, which meansthat M f = 5 . × M ⊙ (see Fig. 1). The present-dayvirial mass of their dwarf is ≈ . × M ⊙ (after cor-recting by a factor of 1.23 as one goes from M to M v );that is, this system is ≈ V c ( r ) profiles are actually not too differentfrom each other (see their Fig. 8).At the level of dark-matter only simulations, the fourWDM . halos (to be presented elsewhere, Avila-Reeseet al. in preparation) show different V max values and4 Colin et al. V c ( r ) profiles as compared with the corresponding CDMhalos. There are also significant differences regarding theassembly histories. Thus, the effects of the damping ofthe power spectrum seem to have significant effects onthe structures close to M f already in pure N-body simu-lations. WDM halos at the cutoff of the power spectrumare certainly different than the CDM ones and, whenbaryons are included in the simulations, the initial con-ditions could leave an imprint in the respective galaxies.Note that the astrophysical effects also affect the darkmatter halo properties so that predictions based on dark-matter only results that are then compared to observa-tions should be taken with care (for example, when com-paring the WDM halo velocity function to the observedgalaxy velocity function Zavala et al. 2009; Klypin et al.2014; Papastergis et al. 2014)Future observational studies of central (field) dwarfgalaxies will be crucial for constraining the nature of darkmatter. In addition to the inner dynamics, we have alsofound important differences between CDM and WDMdwarfs in their SF histories, stellar SD profiles (speciallyin the central regions), and gas fractions.It should be said that resolution issues are likely affect-ing our results regarding the earliest stages ( z >
3) of theWDM galaxy assembly, where virial masses get closer tothe scale of artificial fragmentation of filaments and tothe free-streaming scale. Very high-resolution simula-tions, including baryons, suggest that structures aroundthe free-streaming scale are smooth and dense filamentsable to capture gas that can cool efficiently and form stars(Gao & Theuns 2007; Gao et al. 2014). Thus, the small-est (earliest) baryonic structures in a WDM cosmologyare expected to be filament-like; certainly, the formationof stars (the first ones) in this environment is differentfrom that in a virialized halo (see Gao & Theuns 2007).SF may efficiently proceed in these filaments before theydisappear into the more familiar halo-like structures, sothat a non-negligible fraction of stars in the z = 0 galaxymay have formed early in these filaments. Hence, ourresult that the fraction of stars formed during the first2–4 Gyr in the WDM . runs is negligible (Fig. 8) couldbe an underestimation due to our inability to adequatelyresolve and follow the physics of the gas in the first small-est filaments (their masses should be of the order of thecorresponding free-streaming mass, ∼ × h − M ⊙ ).We end the discussion by asking whether our simulateddwarfs with m WDM =1.2 keV are in agreement with ob-servations. In Avila-Reese et al. (2011) and in G+2014we studied the properties and evolution of CDM low-mass galaxies, some of which (Dw3, Dw4, Dw5 y Dw7)were also studied here. These CDM galaxies with totalmasses around 1 − × h − M ⊙ are relatively realis-tic in structural and dynamical properties; however, theyhave lower specific SF rates, too high M s -to- M v ratiosand lower gas fractions than the observed ones, showingthat they form most of their stars too early. The WDM . dwarfs simulated here with the same subgrid physics havedelayed SF histories, form less stars, and have more gasthan their CDM counterparts. However, when comparedto observed galaxies of similar stellar masses, they are tooextended. In any case, a WDM model with m WDM =1.2keV seems to be in conflict with the last Ly- α forest con-straints (Viel et al. 2013). Fig. 9.—
A comparison of the CDM and WDM . runs, blueand black lines, respectively, of dwarf Dw3 with aggressive (dottedlines) and soft (solid lines) refinements is presented. In the upperpanel we show the comparison regarding the cumulative SF historywhile in the lower panel the comparison is with respect to thecircular velocity (see discussion in the appendix). ACKNOWLEDGEMENTSWe are grateful to the Referee for his/her constructivecomments. VA and AG acknowledge CONACyT grant(Ciencia B´asica) 167332. AG acknowledges a PhD fel-lowship provided by DGEP-UNAMAPPENDIXAs mentioned in Section 3.1, the CDM dwarfs wererun with the same refinement setting used in G+2014.However, to try to reduce the probable appearance andgrowth of spurious fragments, a less aggressive refine-ment was used in the WDM runs. This means thatWDM dwarfs are slightly less resolved than their CDMcounterparts; that is, the halo/galaxy ends up with lessresolution elements. To show that no significant differ-ences appear when this setting (resolution) is used, werun some of our CDM simulations with this soft refine-ment. In Fig. 9, we compare the cumulative SFH (upperpanel) and circular velocity (lower panel) of the CDMrun of Dw3 using the aggressive refinement (blue dottedlines) with the corresponding quantities of the less ag-gressive setting (blue solid lines). The difference betweenthe two runs in V max amounts only to ∼ ∼ M s in the less resolved run is only 17%higher than the corresponding one with the aggressiverefinement setting.In Fig. 9, we also plot the WDM . runs for the sameDw3 galaxy. The use of an aggressive refinement (blackdotted lines), produces older stellar populations thanin the less aggressive refinement employed in the paper(black solid lines). The refinement setting clearly affectsmore the WDM . run than the CDM one. 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