All about baryons: revisiting SIDM predictions at small halo masses

1.5 MB·English

by  A. Bastidas Fry

Mon.Not.R.Astron.Soc.000,1–13(2012) Printed18June2015 (MNLATEXstylefilev2.2)
All about baryons: revisiting SIDM predictions at small halo masses
A.Bastidas Fry1, F.Governato1(cid:63), A.Pontzen2, T.Quinn1, M.Tremmel1, L.Anderson1,
H.Menon3, A.M.Brooks4 and J.Wadsley5
1AstronomyDepartment,UniversityofWashington,Box351580,Seattle,WA,98195-1580
2UCL,DepartmentofPhysics&Astronomy,GowerPlace,LondonWC1E6BT,UK
3DepartmentofComputerScience,UniversityofIllinoisatUrbana-Champaign,USA
5 4Dept.ofPhysics&AstronomyRutgersUniv.136FrelinghuysenRd,Piscataway,NJ08854
1 5Dept.ofPhysicsandAstronomy,McMasterUniv.,Hamilton,Ontario,L884M1,Canada
0
2
RevisedversionApril2015;InoriginalformDec2014
n
u
J
ABSTRACT
6
We use cosmological hydrodynamic simulations to consistently compare the assembly of
1
dwarf galaxies in both Λ dominated, Cold (CDM) and Self–Interacting (SIDM) dark mat-
] ter models. The SIDM model adopts a constant cross section of 2 cm2/g, a relatively large
O valuetomaximizeitseffects.ThesearethefirstSIDMsimulationsthatarecombinedwitha
C description of stellar feedback that naturally drives potential fluctuations able to create dark
matter cores. Remarkably, SIDM fails to significantly lower the central dark matter density
.
h withinthecentral500pcathalopeakvelocitiesV <30kms−1.Thisisduetothefactthat
max
p
thecentralregionsofverylow–massfieldhaloshaverelativelylowcentralvelocitydispersion
-
o and densities, leading to time scales for SIDM collisions greater than a Hubble time. CDM
r haloswithVmax<30kms−1haveinefficientstarformation,andhenceweaksupernovafeed-
st back. At a fixed 2 cm2/g SIDM cross section, the DM content of very low mass CDM and
a SIDMhalosdiffersbynomorethanafactoroftwowithin100-200pc.Atlargerhalomasses
[ (∼ 1010 M ), the introduction of baryonic processes creates field dwarf galaxies with dark
(cid:12)
2 matter cores and central DM+baryon distributions that are effectively indistinguishable be-
v tweenCDMandSIDM.BothmodelsareinbroadagreementwithobservedLocalGroupfield
7 galaxiesacrosstherangeofmassesexplored.TosignificantlydifferentiateSIDMfromCDM
9 atthescaleoffaintdwarfgalaxies,avelocitydependentcrosssectionthatrapidlyincreases
4 tovalueslargerthan2cm2/gforhaloswithV <25-30kms−1needstobeintroduced.
max
0
0 Keywords: Galaxies:formation–Cosmology–darkmatter,Galaxies:dwarf.
.
1
0
5
1 1 INTRODUCTION cosmictimescales.Thisprocesscreateslargecores,morespherical
:
v halos,andasignatureflatradialprofileoftheDMvelocitydisper-
InthispaperweusehighresolutionSPH+N-Bodycosmological
i sion (Spergel & Steinhardt 2000; Burkert 2000). A SIDM model
X simulationstofocusontwomainquestions:Canweidentifyaclear
with fixed cross section and elastic collisions represents the sim-
difference between Cold Dark Matter and Self–Interacting Dark
r plestmodelinalargeclassofplausible“darksector”DMmodels.
a Matter(CDMandSIDMrespectively)predictionsforthestructural
However,significantlymorecomplexinteractionsarepossible,in-
andobservablepropertiesofdwarfgalaxies?Howdotheproperties
cludingYukawapotentials(Fengetal.2009,2010;Loeb&Weiner
of CDM and SIDM halos differ at halo masses below 1010 M ,
(cid:12) 2011),andcoolingoratomicdarkmatter(Cyr-Racine&Sigurdson
wherestarformation(SF)becomesveryinefficientandtheeffect
2013;Schutz&Slatyer2015;Buckleyetal.2014).Thedynamics
oftheunderlyingDMcomponentshoulddominate?
of SIDMwas firstimplemented incosmological simulationsas a
SIDMwasoriginallyintroducedasasolutionforthesocalled
fluid(Mooreetal.2000)andthenaselasticcollisionsbetweenpar-
“core-cusp” problem, the excess of dark matter predicted by the
ticles(Spergel&Steinhardt2000;Burkert2000;Dave´etal.2001;
CDMmodelatthecenteroffieldandsatellitedwarfgalaxiescom-
Col´ınetal.2002;Strigarietal.2007;Martinezetal.2009;Koda&
paredtoobservations(Mooreetal.1999b;Ohetal.2008;Walker
Shapiro2011;Vogelsbergeretal.2012).
&Pen˜arrubia2011;Adamsetal.2014).IntheSIDMmodeldark
matterparticlecollisionsisotropizethecoresofgalaxiesandtrans-
Numerical studies combined with observations (the elliptic-
fermassoutwardfromthedensecentralregionsofDMhalosover
ityofgalaxyclusters,theabundanceofandthecoresizeoffield
dwarfgalaxies)haveconstrainedthecrosssectionofSIDMtobe
oftheorderof∼0.1–1cm2/g(Loeb&Weiner2011;Rochaetal.
(cid:63) E-mail:(FG);[email protected] 2013; Peter et al. 2013; Zavala et al. 2013). However, a variable
©2012RAS
2 Bastidas-Fryetal.
SIDM cross section (a decreasing function of the DM particles’ cialindeterminingthecollisionrate,boostingitinsmallhalos(that
relativevelocity)canpreservetheellipticityanddensityofgalaxy have intrinsic low σ). Our subset of DM-only simulations is also
clusterswhileproducingcoresindwarfgalaxies(Peteretal.2013, oneofthefirsttocompareverysmallfieldandsatellitegalaxiesat
butseeNewmanetal.(2013)forevidenceforDMcoresinclus- similarmassandspatialresolution.Thecentraldensityoffieldand
ters).Whileweakeningexistingconstraints,avariableSIDMcross satellitedwarfs(thatmovefastthroughadenseDMenvironment)
sectioniswellmotivatedby“hiddensector”particlephysicsmod- may then be significantly different, but it has not been properly
els(Tulin etal. 2013).Further crucialconstraints onlarge SIDM comparedyet.
crosssections(Elbertetal.2014)comefromthenecessityofform- In this work we adopt a constant velocity cross section of 2
ingcoresinveryfaintgalaxieswithoutevaporatingthesatellitesof cm2/gintheSIDMruns(arelativelylargevaluetomaximizeitsef-
MW-likehalosandgalaxysizedhalosinclustersastheyinteract fects)andacommondescriptionofSFandfeedbackinbothCDM
withadenseDMenvironment(Gnedin&Ostriker2001;Vogels- andSIDMmodels.TheSFandfeedbackprescriptionshavebeen
bergeretal.2012). showntoformCDMgalaxieswithSFefficiency,photometric,and
Unfortunately, a large fraction of the astrophysically driven kinematic properties close to those of real ones (Oh et al. 2011;
supportfornon-standardDMmodelshascomesofarfromsimpli- Munshi et al. 2013; Christensen et al. 2014a; Shen et al. 2014;
fiedsimulationsthatlackthecomplexitiesof“baryonphysics”and Brooks&Zolotov2014).Thesesimulationsarethefirsthighres-
followonlythetheassemblyoftheDMcomponent(seethereview olutionsimulationstocomparetheassemblyofdwarfgalaxiesin
by Brooks2014).ThenecessitytocoupleaDMmodelwithbaryon CDMvsSIDMcosmologiesincludingadescriptionofSFandsu-
physicscomesfromtheexistenceof“bulgelessgalaxies”,aprob- pernovafeedbackthatcreatesrealisticgalaxieswhilecreatingDM
lemthatrequirestheremovaloflowangularmomentumgasfrom cores through “DM dynamical heating.” Other recent numerical
galaxies(Binneyetal.2001;vandenBoschetal.2001;Governato work(Vogelsbergeretal.2014)focusedonsmallgalaxiesinSIDM
etal.2010)throughfeedbackprocesses(Brooketal.2011).Fur- andexploredtheroleplayedbyavariablecrosssection,however,
thermotivationforincludingbaryonphysicsincludesthenecessity the feedback recipe implemented in their work does not generate
toquenchSFingalaxysatellites(Klypinetal.1999;Mooreetal. DMcores.
1999a;D’Onghia&Burkert2003),especiallyiftheSIDMpower In§2wedescribethesimulationandthecodeused.In§3we
spectrum is similar to CDM at small scales and subhalos survive presenttheresults,whicharethendiscussedin§4.
evaporation(asfoundbyZavalaetal.2013).
Crucially, analytical and numerical work have shown that
feedback lowers the central DM density in galaxies, creating gas
outflows and repeated fluctuations in the gravitational potential
(Mashchenkoetal.2008;DelPopolo2009;Governatoetal.2010;
2 METHODOLOGY
Pontzen & Governato 2012; Di Cintio et al. 2014; Teyssier et al.
2013;Velliscigetal.2014).Thisresultsinirreversibleenergytrans- 2.1 ChaNGA,starformationandburstyfeedbackwith
fer to the DM (see also review by Pontzen & Governato 2014). outflows
Theseoutflows,generatedbyaburstySF,havestrongobservational
The simulations were run in a full cosmological context and to
support(vanderWeletal.2011;Martinetal.2012;Lundgrenetal.
a redshift of zero using the N-body Treecode + Smoothed Par-
2012;Dom´ınguezetal.2014;Geach2015).BurstySFHhavealso
beenrobustlyassociatedwiththebuildupofthestellarcontentof ticle Hydrodynamics (SPH) code CHANGA (Jetley et al. 2008;
galaxiesinthe108–1010M range(Tolstoyetal.2009;Kauffmann Quinnetal.2013;Menonetal.2014)2. CHANGA includesstan-
(cid:12)
2014).TheabilityoffeedbacktodynamicallyheattheDMcanpo- dardphysicsmodulespreviouslyusedinGASOLINE(Wadsleyetal.
2004, 2008; Stinson et al. 2012) including a treatment of metal
tentiallyremovetheneedforSIDMatgalacticscales.Asaresult
linecooling,selfshielding,cosmicUVbackground,starformation,
itisfundamentaltoidentifytheuniquedifferencesbetweenCDM
“blastwave”SNfeedbackandthermalfeedbackfromyoungstars
andSIDMwhenbothmodelsincludeanexplicittreatmentofthe
(Stinsonetal.2006,2012).TheSPHimplementationincludesther-
physicsofgalaxyformation.
maldiffusion(Shenetal.2010)andeliminatesartificialgassurface
ThisstudyisabletofollowtheevolutionoffieldSIDMhalos
atmassesbelow∼1010M (V 1<40kms−1).Thisisanim- tension through the use of a geometric mean density in the SPH
(cid:12) max
forceexpression(Ritchie&Thomas2001;Governatoetal.2015;
portantregimeas(1)observationaldataarebecomingrobust(e.g.,
Menon et al. 2014). This update better simulates shearing flows
Papastergis et al. 2015), and (2) feedback processes become less
withKelvin-Helmholtzinstabilities.Forconsistencywithourpre-
efficientwithdecliningV (Governatoetal.2012;Pen˜arrubia
max
viousworkcomparingCDMandWDMscenarios,weadoptedthe
et al. 2012; Di Cintio et al. 2014). The most recent simulations
samefeedbackandSFparametersasinGovernatoetal.(2015).A
(Madau et al. 2014; Governato et al. 2015; On˜orbe et al. 2015)
showcoreformationwhenonly105.7−6 M ofstarshaveformed. KroupaIMFisassumed(Kroupa2001)andthedensitythreshold
(cid:12) forSFissetat100amu/cm3.Limitingstarformationtodensegas
Also, itis often naively assumed thatSIDM will form DM cores
regions is a realistic approach and concentrates feedback energy
atalldwarfmasses.However,atthesesmallhalomassesthetrend
(Brook et al. 2012; Christensen et al. 2014b; Agertz & Kravtsov
oflaterassemblyepochofthefirstprogenitor(Lietal.2008),and
2014).100%ofSNenergyiscoupledtothesurroundinggas.
consequentially lower central densities (Avila-Reese et al. 2005),
willaffectthetimescaleandextentofSIDMcoreformationinfield
galaxiesbeyondsimplescalingcalculations.Furthermore,therela-
tivevelocityofahaloandthesurroundingDMbackgroundiscru-
2 CHANGAispartoftheAGORAgroup,aresearchcollaborationwith
thegoalofcomparetheimplementationofhydrodynamicsincosmolog-
1 whereVmaxisdefinedasthepeakoftherotationcurve,withVrot = ical codes (Kim et al. 2014). CHANGA is available here: http://www-
(GM/r)1/2. hpcc.astro.washington.edu/tools/changa.html
©2012RAS,MNRAS000,1–13
DwarfGalaxiesinSIDMvsCDM 3
Name Physics DM/gasparticlemassM(cid:12) ForceSoftening(pc) halomassrange(M(cid:12))
h516CDM SFandDM-only 1.6104/3.3103 86 109-5×1010
h516SIDM SFandDM-only 1.6104/3.3103 86 109-5×1010
h2003CDM SFandDM-only 0.67104/1.4103 64 4×108-1×1010
h2003SIDM SFandDM-only 0.67104/1.4103 64 4×108-1×1010
40Thieves-CDM DM-only 0.81104 64 4×108-2.7×1010
40Thieves-SIDM DM-only 0.81104 64 4×108-2.7×1010
40Thieves-SIDM.hr DM-only 0.24104 64 1.25×108-2.7×1010
h148CDM DM-only 1.93104 86 109-2×1012
h148SIDM DM-only 1.93104 86 109-2×1012
Table1.SIMULATIONSANDPHYSICSPARAMETERSEXPLOREDINOURSIMULATIONS.AllSIDMrunsadoptσSIDM = 2[cm2g−1].Themassrange
showshaloswithatleast50,000DMparticleswithintheirvirialradius.Themainhalosineachvolumearestudiedwithseveralmillionparticleseach.The
DM-onlysubsampleisoneofthefirsttosimulateasampleoffieldandsatellitehalosatsimilarmassandspatialresolution.Thisapproachallowedustostudy
theeffectoftheenvironmentontheDMdistributionofthehalosinthetwopopulations.
2.2 SIDMImplementationandAnalyticalExpectations ferenthaloscanbereadilyunderstoodsettingN = 1ineq.1and
(cid:112)
v = v (wherev = max GM(<r)/r)toobtainachar-
The SIDM implementation closely follows the standard Monte max max
acteristicmaximumtimescaleonwhichagivendensityisstable,
Carloapproachdescribedinpreviousworks(Dave´etal.2001;Vo-
1
gelsbergeretal.2012),andhereisonlybrieflysummarized,while τ = . (2)
testsarepresentedinAppendixA.SIDMinteractionsaremodeled SI ρvmaxσdm
undertheassumptionthateachsimulatedDMparticlerepresentsa After a collision, the change in momentum is usually enough to
patchofDMphase-spacedensityandthattheprobabilityofcolli- fullyejecttheparticle(Kahlhoeferetal.2014),sodarkmatterden-
sionsisderivedfromthecollisiontermintheBoltzmannequation. sitiesmustdropoverafewτ .
SI
Collisionsarethenelasticandexplicitlyconserveenergyandmo- Oneimportantconclusiontodrawfromeq.3isthatnotevery
mentum.Foradetaileddiscussionsee(Rochaetal.2013)andalso SIDMmodelwillnecessarilyformsignificantcoresinthesmallest
(Yoshidaetal.2000;D’Onghia&Burkert2003;Kaplinghatetal. halos.Lowhalopeakvelocitiesandlowcentraldensities(atafixed
2014). The number of interactions N that occur in a region with radius)mayresultinτ comparabletothelifetimeofahaloand
SI
localDMdensityρinatime∆tis therefore in the preservation of cusps. Another important conse-
quenceisthatinSIDMthecentraldensitiesofverysmallsatellite
haloscouldbedifferentiatedfromthoseoftheirfieldcounterparts
N =ρvσdm∆t (1) bytheinteractionwiththeDMhaloofamoremassivehostasthe
orbital velocity is much higher than the internal velocities of the
In practice to simulate interactions for discrete N-body DM
satellite. We test these analytical predictions in the next section,
particlesweuseequationoneastheimpliedprobabilityforapar-
where we present results of simulations that resolve the internal
ticletoscatter.Thisassumptionisvalidas∆tapproacheszeroor
structure of DM halos smaller than most previous SIDM studies.
numericallywhere∆tischosentobemuchsmallerthanneeded
Observational evidence of DM cores in small field halos where
toavoidmultiplecollisions.Ateachtimestepournumericalcode baryonicprocessesmaybeinefficient(V <20-30kms−1and
max
calculatestherelativevelocityanddensityρusingthesamefunc- in satellite galaxies (which move at 100-200 km s−1in a ∼ 200-
tionalSPHkernelasinhydrocalculationsofeachDMparticlein
1000×ρ DMfield)canthenprovideusefullowerlimitstothe
crit
relationtoits32nearestneighbors.Thesevaluesareusedtocal-
SIDMcrosssection.
culatetheprobabilitythattheDMparticleinteractswithoneofits
neighbors.SimilartoVogelsbergeretal.(2012),ascatteringevent
mayoccurateachtimestepbetweenparticlesiandjifauniform
3 CDMANDSIDMSIMULATIONS
randomvariableintheinterval(0,1)islessthanP /2(theprob-
ij
abilityisdividedbytwoinordertoaccountforthefactthateach In all simulations we assumed a Λ dominated cosmology (Ω =
0
setofparticlesarecomparedtoeachothertwice).Whileproducing 0.26Λ=0.76,σ =0.77,n=0.96)andusedthe“zoom-in”tech-
8
similarresults,thisapproachdiffersslightlyfromtheoneadopted niquetoachievehighresolutionintheregionsofinterest(Katz&
inRochaetal.(2013),wherecollisionsaredefinedbetweenDM White1993).Thegravitationalforcesplinesofteninglengthisin
particle pairs and the probability of interaction P(i|j) is explicitly therange64-86pc(Poweretal.2003)andthesmoothinglength
=P(j|i).Whenaparticlecollisionisdetectedweisotropicallyand forthegascomponentisallowedtoshrinkto0.1theforcesoften-
elasticallyscattertheparticlestorandomangles. ing.Simulationsstartatz =120−100.Thecombinationofsim-
TheinteractioncrosssectionσforallSIDMrunsinthiswork ulations(seeTable1)allowustocomparetheeffectsofSIDMand
was set to the relatively large value of 2 g/cm2, close to the up- baryonphysicsonarangecoveringalmostfourordersofmagni-
perlimitforconstantσ,inordertomaximizeitseffectscompared tudeinhalomassesandavarietyofenvironmentsfromthefieldto
to that of baryon physics. The way in which SIDM reshapes dif- thedenseregionwithinthevirialradiusofalargefielddiskgalaxy.
©2012RAS,MNRAS000,1–13
4 Bastidas-Fryetal.
40Thieves
h148
M M
-3pc108 CD SID Cencitrrcallesd are
k
M
/
c) τ
p SI=1
00 Gyr
5107
(
τ
SI=5
Gyr
1 2
10 10
V /km s-1
max
Figure 1. DM-ONLY SIMULATIONS: The DM density measured at 500
pcasafunctionofhalomaximumvelocityanddarkmattermodel.Blue Figure2.THERELATIVEDMCONTENTASAFUNCTIONOFRADIUSIN
crosses:CDM,redcrosses:SIDM.Circledsymbolscorrespondtoisolated DM-ONLYSIMULATIONS:TheratioofthecumulativeDMcontentmea-
halos,non-circledsymbolsshowthesatellitesoftheMW-sized,h148halo. suredforasetofsmallhalosoverthe0-1.5kpcradialrange(fromthe40-
At small halo masses the central densities of CDM and SIDM halos do Thievesrun).EachCDMhalowasmatchedwithits’twin’halointheSIDM
notdiffersubstantially,whileatlargervelocities/halomassesSIDM-only simulation.Thesplinekernelforceresolutionis64pc.Verticallinesmark
haloshavelowercentraldensitiesthantheirCDM-onlycounterparts.This 150and500pc(2.3and5softeninglengths).Withouradoptedcrosssec-
differencecanbeunderstoodintermsofthedottedlineswhichshowthe tionof2cm2/gsmallCDMandSIDMbecomeprogressivelydifficultto
maximumtimescaleτSIatwhichcollisionsaresignificantintheSIDMcase differentiate,withDMcontentatagivenradiusbeingwithinafactoroftwo
(seetextfordetails).Thisresultshowsthatfixedcrosssectionscommonly inthetwocosmologies.Detectingsuchadifferenceinfielddwarfscould
adoptedatthescaleoflargersystems(0.1-2cm2/g)wouldnotbesufficient requireanextgenerationtelescope(M.Walker,privatecommunication).A
toformkpcsizedcoresinthesmallestobservablefieldhaloswithVmax< SIDMwithavariablecrosssectioncouldshowamoresignificantdifference
30kms−1.IntheVmax30-60kms−1rangeSIDMsatelliteshavecentral comparedtoCDM.
densitieslowerbyafactortwocomparedtotheirfieldcounterparts,due
theaddedboosttoSIDMcollisionscomingfromsatellitesorbitingathigh
velocityinthedenseDMhaloofthehost.
at least 50,000 DM particles within the virial radius. To comple-
mentthisdataset,ahighresolutionsimulationofamassivehalos
anditssystemofsatelliteshasbeenincluded(h148).Thehalosin
Cosmological simulations of well resolved halos with mass
< 1010 M (corresponding to a halo peak velocity V < 30 thissimulationhavemassandspatialresolutionsimilartotheir‘40
(cid:12) max
kms−1)areparticularlyrelevantforSIDM,asbaryoniceffectsat Thieves’counterpartsandmassandspatialresolutionbetterbyfac-
tortwocomparedtorecentworkVogelsbergeretal.(2012);Zavala
thesescalesshouldbelimited(Governatoetal.2012;Pen˜arrubia
et al. (2013). In Appendix 1 we verified that our results and the
etal.2012).Basedonequation(2),theabilityofSIDMtolower
Monte Carlo implementation of SIDM collisions are not affected
thecentraldensityofhalosdependsontheDMρandthetypical
byresolutioneffects.
particlevelocity,whichislowerinlessmassivehalos.Interestingly,
InFigure1weshowthedensitymeasuredat500pc(aradius
previousCDMsimulationshavesuggestedthatthecentraldensity
atwhichtherotationcurvesofmanydwarfgalaxieshavebeenre-
of small mass field halos decreases with their halo mass (Avila-
solved,e.g.,Ohetal.2011)forallresolvedhalosinourh148(×)
Reeseetal.2005;Lietal.2008).InaSIDMscenario,extending
and “the 40 Thieves” (+) DM-only simulations as a function of
this trend to very small halos could prevent the formation of low
V . We then over plot lines of fixed τ for 1 Gyr and 5 Gyr.
densitycentralcoresbyincreasingthetimescaleofDM-DMcolli- max SI
SIDMandCDMshowidenticalcentralDMdensitiesifthetypical
sions.
scaleforDMinteractionsislongerthan5Gyr.Atlargerpeakve-
locities (and halo masses) with shorter timescales for interaction,
theSIDMdensitiesdecreasecomparedtotheirCDMcounterparts
3.1 DM-onlySimulations:Environmentaleffectsandcuspy
and fall in a valley between the 1 and 5 Gyr lines, matching re-
halosatV <30kms−1
max sultsfrompreviousworks(Rochaetal.2013;Vogelsbergeretal.
To study the structure of a significant sample of DM halos in a 2012).Inotherwords,SIDMinteractionsforcetheDMdensityto
rangeofenvironmentswesimulatedfourdifferentregionswiththe dropuntil,goingtosmallerandsmallerhalomasses,theinterac-
zoomed-inapproach(Katz&White1993).Thefirstthreeregions tiontimescalerisestoasignificantfractionoftheHubbletimeand
(Table1)arecenteredonfilamentarystructureswithadensityclose SIDM (with a σ = 2 cm2/g) is not effective anymore. Figure 2
toaveragemeasuredinsideasphereof5Mpcinradius.Thelargest showstheSIDMvsCDMratiooftheenclosedmassasafunction
one of them is nicknamed ‘The Forty Thieves’ and includes sev- ofradiusforpairedhalosfromthe‘40Thieves’run.Atradiicur-
eraltensofhaloswithV <30kms−1,equivalenttoamass rentlytestedbyobservations(100-500pc),butentirelyneglecting
max
range108-1010M ,wheretheminimummassreferstohaloswith baryonicphysics,thedifferencebetweenthetwomodelsdecreases
(cid:12)
©2012RAS,MNRAS000,1–13
DwarfGalaxiesinSIDMvsCDM 5
80
10­23
70
10­24
)
) 1 60
3 −
−
m10­25 h2003 SIDM+baryons  s
m
 c h2003 CDM+baryons k50
(g h2003 CDM  (
ρ 10­26 σv
h516 CDM
40
h516 SIDM+baryons
10­27 h516 CDM+baryons
2003 SIDM 30
h516 SIDM
10­2180­1 100 101 2100­1 100 101
R (kpc) R (kpc)
Figure3.RADIALPROFILES.Left:TheradialdensityprofileoftheDMcomponentforhalos/galaxiesh516andh2003.Right:ThevelocitydispersionofDM
componentinthesamehalos/galaxies.h516-CDM:blue.h516-SIDM:red.h2003-CDM:cyan.h2003-SIDM:magenta.Dashed:DM-onlyruns.Bothdensity
anddispersionprofilesbecomesimilarinCDMvsSIDMoncebaryonicprocessesareintroduced.
theDM-onlyhalosmatchthoserecentlypublishedin(Elbertetal.
2014),whichatV ∼35kms−1formsignificantcores(seealso
max
nextsectionwheretheeffectofbaryonsintheselargersystemsis
included).Thisresultconfirmsoursimpleanalyticalexpectations
and shows that even with a significant constant SIDM cross sec-
tion,DMcoresrapidlybecomesmallerthanourresolvedscale(∼
100-200pcortwicethesplinekernelsoftening)infieldhaloswith
virial mass < 1010 M and V < 30 km s−1. Confirming the
(cid:12) max
resultsfromLietal.(2008)andextendingthemtomuchsmaller
halo masses and higher resolution we verified that the increased
τ at small halo masses comes not only from a lower σ but
SI DM
alsofromlowercuspdensities,possiblyduethelaterepochofcol-
lapseofthecentralregionsofahalo.WeverifiedtheDMdensity
within the central 250 pc decreases by a factor of eight in CDM
haloswithmassfrom108 M comparedtohalosof1010 M .If
(cid:12) (cid:12)
welookattheaveragedensitiesasafunctionofV ,anotherdif-
max
ferenceemergesbetweentheSIDMfield(circledredcrosses)and
satellites(redcrosses),withsatellitehalosshowingcentraldensi-
tieslowerbyaboutfactoroftwocomparedtofieldhalosofsimilar
V .Thisimportantenvironmentaldifferencecouldbeduetothe
max
Figure4. STELLAR MASS/HALO MASS RELATION: TheStellarMass- satellitesformingtheircentralregionsearlier,ortothesignificant
HaloMassrelationforthesimulatedgalaxies.Dashedlinesandsolidlines boosttoρandvmaxineq.3duetotheirorbiting1)insidethedense
showtherelationobtainedfromLocalGroupdata(Brook&DiCintio2014; haloofamuchmoremassivehostand2)atamuchhigherspeed
Garrison-Kimmeletal.2014)Therelationsareextrapolatedbelow∼106.5 thantheirinternalvelocitydispersion.Oursimulationswereableto
M(cid:12)duetosampleincompleteness(dottedlines).Circlesshowtherawdata, highlightthisdifferenceasoursimulationsresolvefieldandsatel-
soliddotsshowthesimulationdatacorrectingforobservationalandsim- liteshaloswithsignificantlylowerpeakvelocities(10-20kms−1)
ulationbiases(Munshietal.2013)inmeasuringstellarandhalomasses.
thaninpreviousworks.
Overallthesimulationsproducetherightamountofstars.Themostmas-
sivehaloconvertsabout1%ofgasintostars.TherapiddropinSFefficiency ThemainresultfromthissectionisthatevidenceofDMcores
athalomassesbelow1010M(cid:12)isduetotheintroductionof’earlyfeedback’ inrealgalaxieswithVmax <30kms−1wouldconstraintheSIDM
(seetext). crosssectiontovaluesσ>>2cm2/gwhenthetypicalDMvelocity
dispersionislow.IfsignificantDMcoresarefoundinthesegalax-
ies, their existence would give support to models with a variable
rapidly. A factor of two in the DM content within 100-500pc of SIDMcrosssectionthatishigher(20cm2/g,seeeq.2)atsmallhalo
faintfielddwarfs,couldberevealedbylargespectroscopicsamples massesandthendeclinesrapidlyatthescaleofgroupsandgalaxy
oftheassociatedstellarpopulations(M.Walker,privatecommuni- clusters as constraints at scale support small cross sections σ <
cation).WealsoverifiedthatatlargerV thedensityprofilesof 1cm2/g.Weplantofurtherexploretherelativeeffectofstronger
max
©2012RAS,MNRAS000,1–13
6 Bastidas-Fryetal.
Run HaloMass Vmax StellarMass HImass
ID CDM/SIDM kms−1 CDM/SIDM CDM/SIDM
h516 4.1×1010 58.4 6.2/4.9×107 3.3/2.0×108M(cid:12)
h516b 1.1×1010 33.0 9.8/14.7×106 1.6/0.94×108M(cid:12)
h2003 1.1×1010 30.5 3.1/3.4×106 5.0/16.6×106M(cid:12)
Table2.THETOTALHALOMASS,STELLARANDHIMASSESANDVmax
(INKMS−1)forsomerepresentativehalosintheCDMrunswithSFand
theirSIDMcounterparts.z=0stellarmassesweremeasuredwithin2.5kpc.
h516bisthesecondmostmassivehalointheh516run.
108 h516
h2003
M b b
-3pc CD M + f M + f
k D D
C I
M S
/
)
c
p
0
0107
5
(
Figure6.THESLOPEαOFTHEDMDENSITYPROFILEINSIDMAND
CDM OVER DIFFERENT MASS RANGES: blueand cyan: CDM,red and
magenta:SIDM,solidlines:baryon+DMruns,dashedlines:DM-onlyruns.
Top:haloh516.TheDMslopeevolvesrapidlyandinasimilarwayinboth
101 102 CDMandSIDM,asdynamicalheatingisveryefficientatthisscale.Middle:
V /km s-1 haloh2003.(blue:CDM,red:SIDM).Bottom:acollectionoffieldhalos
max withtotalmass<109M(cid:12)fromoursimulations.SFefficiencyistoolow
andtheSIDMinteractionrateistoolowtocreatecores.
Figure5.EFFECTSOFBARYONSPHYSICS:ThecentraldensityofCDM-
onlyhalos(blue)vstheirSIDM(red)counterpartsrunwithbaryonphysics
andburstyfeedback.LinesconnecttheDM-onlyrunsofh516andh2003 Multi-wavelengthevidenceforoutflows,analysisofthestellarpop-
totheircounterpartswithbaryons.ForourchoiceoftheSIDMinteraction ulationsintheSDSSdwarfsandrealisticCMDs(Governatoetal.
crosssectionandforhaloswithVmax>50kms−1(correspondingtostel- 2015) give strong support to our implementation of SF. This ap-
larmasseslargerthan108M(cid:12))thecentralmassofCDMandSIDMhalos proachdiffersfromtheSIDMstudyofVogelsbergeretal.(2014)
issimilar,butsignificantlylowerthanthepredictionsofCDM-onlyruns.
wherelessburstyfeedbackstillremovesgasfromgalaxycenters,
DuetolowDMinteractionratesandlackofburstyoutflows,atlowerhalo
butdoesnotcreatesubstantialDMcores.Thebaryoniccontentof
massesbothcosmologiesgivesimilarpredictions:cuspycentralDMpro-
files.LargerSIDMcrosssectionswouldbeabletodifferentiatethevarious thegalaxiesinourstudyaresummarizedinTable2.
modelsinhaloswithVmax<20kms−1asDMcoreswouldthenformin Figure3(leftpanel)comparesthedensityprofilesoftheDM
galaxieswerebaryonphysicsdonotplayamajorrole. component of galaxies h516 and h2003. In DM-only simulations
halos with masses > 1010 M have cuspy profiles (halo h2003:
(cid:12)
cyan dashed, halo h516: blue dotted). Once baryon physics and
SIDM interactions on satellites compared to field halos in future
outflows are introduced, flatter DM profiles are created in both
work.
SIDM and CDM cosmologies. The blue dashed (CDM-only) vs
blue (CDM+SF) lines and the red (SIDM+SF) show results for
h516.Thecyandashed(CDM-only)vscyansolid(CDM+SF)lines
3.2 SimulationswithSF:SIDMsimilartoCDMwhen
and the magenta (SIDM+SF) lines show results for h2003, the
BaryonPhysicsarerelevant.
smallerhalo.InbothCDMandSIDMmodelsthecentralcuspypro-
Wefocusedourhydrodynamicalsimulationsonthelargestgalax- fileshavebeensignificantlyflattenedinside1kpc.h516,themost
iesformedinthefilamentaryregions‘h516’and‘h2003’.Theseare massive halo studied with the inclusion of SF, is the one where
twowellstudiedfields:h2003isthesamehalosimulatedinGov- the central DM density decreases the most. This result is consis-
ernatoetal.(2015)whileh516isthemainhaloofGovernatoetal. tentwithpreviousfindings(Governatoetal.2012;DiCintioetal.
(2010)andofthe“7dwarfs”galaxiessamplestudiedinShenetal. 2014),showingthattheefficiencyofcoreformationpeaksinhalos
(2014) and Madau et al. (2014). The SF parameters in our study withV ∼50kms−1.
max
wereidenticalforallCDMandSIDMsimulations.Theyalsocor- Figure3(rightpanel)comparesinsteadthevelocitydispersion
respondtothefiducial“g5”runsinGovernatoetal.(2015),where profilesoftheDMcomponentinhalosh516andh2003.Asforthe
weexploredtheeffectsofdifferentfeedbackandSFrecipesinthe densityprofiles,DM-onlyrunsofdifferentcosmologieshavedif-
context of comparing the formation of dwarfs in CDM vs Warm ferentlocalDMvelocitydistributionprofiles:CDMhalosshowa
scenarios.HereweemphasizethatourSFimplementationcreates decreasing dispersion closer the halo center while the SIDM ha-
repeatedstarburtsandgasoutflowswithsignificantloadingfactors losshowaratherflatprofile.Thisdifference,aresultoftheenergy
(gasmassejectedfromthecenterdividedbystarformationrate). transfertothecenterofthehaloduetocollisionalprocesses,had
©2012RAS,MNRAS000,1–13
DwarfGalaxiesinSIDMvsCDM 7
10 10 10 10
5 5 5 5
pc] 0 pc] 0 pc] 0 pc] 0
[k [k [k [k
5 5 5 5
10 CDM 10 10 kpc 10 10 10 kpc
10 5 0 5 10 10 5 0 5 10 10 5 0 5 10 10 5 0 5 10
10−4 10−3 10−2 10−6 10−5 10−4 10−3
Gas Surface Density [g cm−2] Stellar Surface Density [g cm−2]
10 10 10 10
5 5 5 5
pc] 0 pc] 0 pc] 0 pc] 0
[k [k [k [k
5 5 5 5
10 SIDM 10 10 10
10 5 0 5 10 10 5 0 5 10 10 5 0 5 10 10 5 0 5 10
Figure7.THEPROJECTEDCOLORDENSITYMAPOFTHEBARYONDISTRIBUTIONINGALAXYH516.Top:CDM.Bottom:SIDM.Leftpanels:projected
gasdensityatz=0seenedge-onandface-on.Rightpanels:Stellarprojecteddensityatz=0.Thestellardisksarerelativelythickerthaninearliersimulations
(Governatoetal.2010),aneffectoftheintroductionof‘earlyfeedback’fromyoungstars.Weverifiedthatinbothmodelsthestellardistributionisexponential,
withasimilardiscscalelengthandlackofacentraldensespheroid.
beenconsideredastrongsignatureofSIDM.Howeverthisdiffer- encebetweenSIDMandCDM(toppanel).IntheSIDM-onlyrun,
enceiserasedbytheintroductionofburstyfeedback,thatcreates theDMcoreformsmoreslowlythanwhentheeffectofbaryonsare
significantDMcoresintheCDMhalos.‘Dynamicalheating’also included.TheeffectofbaryonfeedbackontheDMprofileisclearly
causesthevelocitydispersionprofilesofallhalostoflattenout. detectableassoonasabout106M ofstarshavebeencreated(see
(cid:12)
Figure 4 shows the stellar mass/halo mass ratio of the halos alsoGovernatoetal.2015;Pen˜arrubiaetal.2012).Ingalaxieswith
we simulated with the inclusion of baryon physics, showing that presentdaystellarmassesbelow107−8M(cid:12),theeffectof‘dynam-
theyfollowthestellarmass/halomassrelationinferredusinglocal icalheating’inducedbyfeedbackisprogressivelyreduced(Gover-
data and the abundance matching technique (Brook & Di Cintio natoetal.2012,2015;DiCintioetal.2014).Attheradialscaleof
2014; Garrison-Kimmel et al. 2014). This is particularly relevant 500pctheCDMandSIDMhalosofh2003showDMprofilesthat
asproducingthecorrectamountstarsisnecessarytoestimatethe startcuspyandthenslowlydevelopaflatterprofile.InbothSIDM
minimum mass at which baryonic processes can originate cores. andCDMtheprocessismoregradualcomparedtomoremassive
Afterthispaperwassubmitted(On˜orbeetal.2015)publishedre- systems,duetoanumberoffactors(starformationratesarelower
sultsfromasimulatedCDMhaloofsimilartotalmass,whichalso and τSI is longer). However, the inclusion of baryonic processes
formedabut106M instars,leadingtoacoredDMprofile. againmakesthegalaxyevolvesimilarlyinCDMvsSIDM.Byred-
(cid:12)
shiftz<1thedifferenceinDMslopesisnotsignificantenoughto
Figure5showstheDMcentraldensitiesasafunctionofhalo
discriminate between SIDM and CDM. Halo h2003 was also re-
peakvelocityonceSFisincluded.ThecomparisonwithFigure1is
striking:whereatV >30kms−1CDMwasclearlydifferenti- centlyruninaWDMcosmology(Governatoetal.2015).Similar
max
totheCDMcasetheWDMcuspturnedintoacoreovertime,dueto
atedfromSIDM,nowthecentraldensityofCDMandSIDMhalos
isalmostidenticaloverthewhole10to50kms−1range.Thisresult burstyfeedback.Byz=0thecentralDMdistributionofhaloh2003
issimilarinCDM,WDM(Governatoetal.2015)andSIDM(this
clearlyillustrateshowpredictionsformDM-onlyrunscanbecom-
work).
pletely superseded by the addition of the complex baryon – DM
interactions. Atevensmallermasses,theevolutionoftheDMslopeαwith
In Figure 6 we investigate how the slope of the DM profile theinclusionofbaryonicprocesses(continuouslines)confirmsthe
(measuredat500pc)evolveswithtimeinasampleoffieldhalos results from the DM-only runs (dashed lines). SF at such small
witharangeofmasses.Asthemechanismsofcoreformationdif- scales is strongly inhibited by the cosmic UV field. Similarly, at
fer(potentialfluctuationslinkedtoSFvsSIDMcollisions)thetime such small masses the SIDM interaction timescale becomes long
evolutionoftheDMslopemayalsobesignificantlydifferent.We compared to the Hubble time and the survival time of the halo.
havefoundthattheevolutionofthesystemscanberoughlydivided HencethecentralDMslopemeasuredat500pcisnotsignificantly
inthreestellarmassranges.Presentdaysystemswithstellarmasses differentinSIDMvsCDMhalos,aspredictedbytheempiricalcal-
largerthan108 M (V >50kms−1asinclassicfielddwarfs) culationsintheprevioussection.ThefailureofSIDMtoformsub-
(cid:12) max
hadcoredDMprofilessinceredshift>4,withnosignificantdiffer- stantialDMcoresinveryfaintdwarfswithhosthaloswithmass
©2012RAS,MNRAS000,1–13
8 Bastidas-Fryetal.
Figure8.THESFRASAFUNCTIONOFCOSMICTIME.Leftpanel:haloh516inCDMandSIDMcosmologies.Bothgalaxieshaveextended,gasrichdisks
andnegligiblebulges.Rightpanel:theburstinessofmodelsh516andh2003inCDMandSIDM,measuredatdifferenttimescales(seetextforadefinition).
SFdoesnotdiffersignificantlyinCDMvsSIDM,andappearstobemostlyregulatedbyfeedbackandaccretionrates.
< 1010 M had not been explored in previous numerical works, extendedstellarsystemsandroughlyconsistentwithobservational
(cid:12)
where high resolution simulations mostly focused on halos more data.Thehalflightradiusforh516b(Table1)isforexample,2.0
massivethan1010M . kpcinSIDM,vs1.8kpcinCDM.Thisisadifferentoutcomecom-
(cid:12)
Overall,theinclusionofSFandbaryonicprocesseserasethe paredtotheresultsofalessburstySFscenarioastheonestudied
differencesseenintheDM-onlyruns.Atthescaleofdwarfgalax- in Vogelsberger et al. (2014), which followed galaxies in a simi-
ieswithV ∼30-50kms−1.energytransfertotheDMmakes larmassrangetoours.IntheirsimulationstheSIDMdistribution
peak
theDMdistributionatthecenterofgalaxiesflatterthananNFW islessconcentratedcomparedtotheCDMone,leading“todwarf
profile and almost identical in CDM vs SIDM . As a result cur- galaxieswithlargerstellarcoresandsmallerstellarcentraldensi-
rentconstraintsontheSIDMcrosssectionfromdwarfsizedfield ties.”InoursimulationsthedynamicalcouplingofbaryonstoDM,
comeoutconsiderablyweakenedandwillhavetobereconsidered. drivenbyfastandrepeatedoutflows,shapesthestellardistribution
Moreover,wepredict(seeFigure1)thataSIDMcrosssection> andleadstoasimilarbaryondistributionandcontent.
10cm2/gwouldnecessarytocreateDMcoresinsmallerhaloswith
V < 10 km s−1. As the shapes of galaxy clusters require a Furthermore,withtheadoptedSFprescription,thestarforma-
max
SIDM cross section smaller than 1 cm2/g (Peter et al. 2013). If tionhistories(SFH)ofthegalaxiesformedintheCDMmodellook
coresexistindwarfgalaxies,theseresultsargueinfavorofavari- verysimilartotheSIDMcounterparts.Thisismostlikelydueto
ableSIDMcrosssection(seealsoVogelsbergeretal.(2012)). twomainreasons:1)theassemblyrateofbothDMandbaryons,
being driven by the large scale structure remains unchanged in
SIDMand2)thereisnodifferenceinthecentralDMdistribution
betweenthetwomodelsasitisrespondsquicklytotheeffectsof
3.3 StarFormationHistoriesandAssemblyofthebaryonic
feedback.Asanexample,Figure8showstheSFHofhaloh516in
component
theCDMandSIDMmodels,whichshowaverysimilartimeevolu-
Inthissectionweanalyzethez = 0baryonicdistributionofthe tion,peaking5GyrsaftertheBigBang.Overall,SIDMandCDM
galaxiesthatformstarsinoursimulations,whilefocusingonthe halos have almost identical DM masses by z=0 and the SF effi-
twomainhalos:h2003andh516.WeverifiedthatinbothCDMand ciencyissimilar,within20%inthetwomodels.Thisresultdiffers
SIDMcosmologiesthestellarmassofgalaxyh516followsanex- from the CDM vs WDM comparison in Governato et al. (2015),
ponentialprofilewithnospheroidalcomponent.Theprojectedgas wheretheWDMversionofh2003formedonlyhalfthestarsdue
andstellardensitiesofgalaxyh516areshowninFigure7,show- to the delayed assembly of the halo (see also Col´ın et al. 2015).
ingasimilardistributioninCDMvsSIDM.Bothstellardiscsare However,changesonthetimescaleandintensityoftheindividual
thickanddynamicallyhot(Figure7)andmoreextendedthanthe SF events could be driven by subtle effects and still differentiate
CDMversionofh516describedinChristensenetal.(2014a),an betweenCDMandSIDM,forexampleashallowerdensityprofile
effectoftheintroductionofearlyfeedback(Trujillo-Gomezetal. coulddrivemoregasinstabilitiesthatleadtoradialinflowsandin-
2013;Rosˇkaretal.2014).Confirmingthevisualimpressionfrom creasetheburstinessofSF,or,ontheotherhand,lowerDMdensi-
Figure7,weverifiedthattheradialdistributionofstarsatz=0does tiescouldslowdownthecollapseofgasandreduceSFintheSIDM
notchangesignificantlyintheCDMgalaxiesvstheirSIDMcoun- scenario.WequantifiedtheburstinessofSFinSIDMvsCDMby
terparts, both following a trend for larger systems to have more measuring the dispersion in star formation rates (SFR) measured
©2012RAS,MNRAS000,1–13
DwarfGalaxiesinSIDMvsCDM 9
Figure9.THE ROTATION CURVES Vc ofhalosh516andh2003inCDM(blueandcyan)andSIDM(redandmagenta)comparedwiththeobservational
constraintsfromasampleofLocalGroupfielddwarfs(Wolfetal.2010;McConnachie2012;Weiszetal.2014).Theintroductionoffeedbackprocesses
lowersVcouttoatleast2kpc,wheremassdecompositionbasedonHIkinematicsarecrucial.(Vcisdefinedas=(GM/r)1/2).Softeningis64pcforh2003
and86pcforh516.
in ∆T intervals, where ∆T was varied from 106 to 109 uncertaintiesremainontheobservationalestimates).Atthesame
SFR SFR
years(forasimilarapproachbutdifferentdefinitionofburstiness, time,SIDM-onlyrunswitharangeofcrosssections(Elbertetal.
seeHopkinsetal.2014).Measuring∆T overhundredsofran- 2014)showabetteragreementwithobservationalestimatesasthe
SFR
domlysampledintervals,burstySFatagiventimescaleshowsasa centralDMdensitiesarelower.However,therightpanelofFigure
largedispersioniftheSFrateatatimeT+∆T differssubstan- 7showsthatoncebaryonphysicsareintroduced,thecentralmass
SFR
tiallyfromtheSFRataprevioustimeT.TherightpanelofFigure distribution(DM+baryons)ofCDMdwarfsmatchestheobserva-
8showsthattheburstinessmeasuredoverdifferenttimescaleswas tional data, equally well, without requiring SIDM. Recent works
similarforbothhaloh516andh2003inbothmodels.Bothh516 have compared dwarf galaxies in the Local Group (Brook & Di
andh2003showaSFratedominatedbysmalltimescalefluctua- Cintio2014;Sawalaetal.2015)andMWsatellitesZolotovetal.
tions,withasimilardependenceontimescaleandhalomass,with (2012); Arraki et al. (2014) with simulations. They have shown
thelessmassivehaloshavingaburstierSFatalltimescales(are- howtheintroductionoffeedback(andtidalprocessesforsatellites)
sultseenalsoinsimulationswithdifferentfeedbackmodels,e.g., generatesarealisticM –M relation,asgalaxiesatafixed
star halo
Hopkins et al. 2014). Observations of nearby stellar populations M are hosted by more massive halos than when a universal
star
andcomparisonswithsimulations(Tolstoyetal.2009;Kauffmann NFWprofileisassumedintheanalysis3.Thisresultshowshow
2014;Governatoetal.2015;Weiszetal.2014)stronglysupporta theperceiveddiscrepancybetweentheobservednumberdensityof
burstybuildupofthestellarcontentofdwarfgalaxies.Weverified fieldgalaxiesasafunctionofV andthatoftheunderlyinghalo
max
that our set of simulations qualitatively reproduce the fraction of populationisnaturallyaccountedforinaCDMcontextwherefeed-
starsformedinburstsasestimatedinKauffmann(2014)):20-50% backisintroducedandthecentraltotaldensityislowered.Ingood
with a larger fraction formed in the less massive system. Bursts agreementwithresultsfromoursimulations,therevisedabundance
weredefinedasperiodswithSF>2−4×<SFH >andduration matchingfromBrook&DiCintio(2014)predictthatfieldgalax-
of107-108 years.AburstierimplementationofourSFmodel(as iesarehostedinhaloswithmass>5×109 M ,withmostha-
(cid:12)
onethatneglectedHIselfshielding)wouldberuledoutbyexces- losbelowthatthresholdbeingdevoidofstars.Ourresultsprovide
sivestructureinthestellarCMD,asdiscussedinGovernatoetal. direct evidence that SIDM-only simulations mimic the effects of
(2015). feedback,butalsothatwhenburstyfeedbackisintroduced,SIDM
galaxies are essentially indistinguishable from their CDM coun-
Overall,Withinoursmallsampleofgalaxies,wedonotfind
terparts.BothSIDMandCDMmodelscreategalaxieswithmass
evidenceoflargedifferencesinthebaryoniccontentanddistribu-
distributionsandobservablepropertiesinbroadagreementwiththe
tioningalaxiesformedinaCDMvsSIDMmodel.
observedones.
Finally, Figure 9 show the rotation curves V (defined as
c
(cid:112)
GM(<r)/r)ofourgalaxiesh516andh2003comparedtoes-
timatesfromasampleoflocaldwarfs(emptysquares,fromWolf 3 inahalomodelwithacentralmassdensitylowerthanNFWtheVcirc
etal.2010;Weiszetal.2014).Theleftpanelshowsthewellknown measuredat∼1kpctranslatestothesameVpeakandhencehalomassof
resultthathalosformedinCDM-onlysimulationshavehighercen- anNFWhalo.Asaconsequence,anobservedVcirc translatestohigher
tralmassdensitiesthatmostobserveddwarfs(althoughsignificant halohostmassthanwhenamoreconcentratedNFWhaloisassumed.
©2012RAS,MNRAS000,1–13
10 Bastidas-Fryetal.
4 CONCLUSIONS observablepropertiesinbroadagreementwithobservationaldata.
Asaresult,whilecertainlynotexcluded,SIDMisnotnecessaryto
Westudiedasetofcosmologicalsimulationsoffielddwarfgalax-
solvetheproblemoftheexcessofDMatthecenterofsimulated
iesinCDMandSIDM.TheSIDMsimulationsincludeforthefirst
dwarf galaxies with V > 30 km s−1. Furthermore, because
timeadescriptionofburstySFandfeedbackthatcreatespotential max
the effect of SIDM becomes negligible at very small galaxy/halo
fluctuations able to lower the central DM density of halos where
massesevenwitharelativelylargeconstantvelocitycrosssection
atleast106 M ofstarshaveformed.Theforceresolutionofour
(cid:12) (2cm2/g),SIDMwithavelocitydependentcrosssectionwillbe-
simulations(64-86pcwithasplinekernelsoftening)allowsusto
come necessary if even very faint dwarf galaxies are observed to
resolvewithmanythousandsofparticlesthecentralregionsofha-
havedarkmattercores.Thisworkhighlightshowsimulationsthat
los(andmillionstothevirialradius)downtohalomasseswhere
a)includerealisticSFandfeedbackprocessesandb)studyalarge
theimpactofstarformationwillnotplayamajorroleandwhere
sample of faint dwarfs are necessary to take advantage of astro-
the effect of SIDM alone dominates. A relatively large value (2
physicalconstraintsonDMmodels.
cm2/gfortheSIDMcrosssectionwaschosentomaximizeitsdif-
ferencefromtheCDMmodel.WehavealsorunasetofDM-only
simulationsthatallowedustostudytheevolutionofauniformres-
olution set of DM halos down to masses of only few times 108
M (equivalent to V < 20 km s−1) both in the field and in ACKNOWLEDGMENTS
(cid:12) max
thedenseenvironmentofamoremassivehost.Ourresultscanbe
ABFwasfundedbyWashingtonNASASpaceGrantConsortium,
summarizedbythreemainfindings:
NASA Grant NNX10AK64H. FG and TQ were funded by NSF
grant AST-0908499. FG acknowledges support from NSF grant
• OnceSFandresultingfeedbackisintroduced,thecentralDM
AST-0607819 and NASA ATP NNX08AG84G. AP is supported
massdistributionandvelocitydispersionbecomessimilarforCDM
byaRoyalSocietyUniversityResearchFellowship.Someresults
andSIDMgalaxieswithstellarmassesinthe106–108 M range
(cid:12) wereobtainedusingtheanalysissoftwarepynbody,(Pontzenetal.
and circular velocity 25-50 km/sec (Fig.3). At the scale of 0.5–2
2013).ChaNGawasdevelopedwithsupportfromNationalScience
kpc the total matter content is in good agreement with observa-
FoundationITRgrantPHY-0205413totheUniversityofWashing-
tionalestimatesofLocalGroupdwarfs.Thisresultdiffersstarkly
ton,andNSFITRgrantNSF-0205611totheUniversityofIllinois.
fromthepredictionsofDM–onlysimulations,orsimulationswhere
WethankHaiboYu,SeanTulin,MattWalkerandLucioMayerfor
energyfeedbackdoesnotleadtocoreformation(Boylan-Kolchin
stimulatingdiscussionsandacarefulreadingofthemanuscript.We
etal.2011;Garrison-Kimmeletal.2014).
thanktherefereeforconstructivecomments.
• Analyticalexpectationsandsimulationsshowthatwithafixed
SIDMcrosssectionof2cm2/gtheDMcentraldensityandinternal
velocities of halos with mass below 109 M are too low to have
(cid:12)
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