The haloes of bright satellite galaxies in a warm dark matter universe

0.74 MB·English

by  Mark Lovell

Mon.Not.R.Astron.Soc.000,??–8(2011) Printed19January2013 (MNLATEXstylefilev2.2)
The haloes of bright satellite galaxies in a warm dark
matter universe
Mark R. Lovell1⋆, Vincent Eke1, Carlos S. Frenk1, Liang Gao2,1, Adrian Jenkins1,
Tom Theuns1,3, Jie Wang1, Simon D. M. White4, Alexey Boyarsky5,6,
2 and Oleg Ruchayskiy7
1
0 1Institute for Computational Cosmology, Durham University,South Road, Durham, UK, DH1 3LE
2 2National Astronomical Observatories, Chinese Academy of Science, Beijing, 100012, China
3Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
n
4Max-Planck-Institut fu¨r Astrophysik, Karl-Schwarzschild-Straße 1, 85740 Garching bei Mu¨nchen, Germany
a 5E´cole Polytechnique F´ed´erale de Lausanne, FSB/ITP/LPPC, BSP 720, CH-1015,Lausanne, Switzerland
J
6Bogolyubov Institute of Theoretical Physics, Kiev 03680, Ukraine
6 7 CERN Physics Department, Theory Division, CH-1211 Geneva23, Switzerland
1

]
O Accepted 2011November 13.Received2011October21;inoriginalform2011April15
C
. ABSTRACT
h
p High resolution N-body simulations of galactic cold dark matter haloes indicate that
- we should expect to find a few satellite galaxies around the Milky Way whose haloes
o have a maximum circular velocity in excess of 40 kms−1. Yet, with the exception
r
t of the Magellanic Clouds and the Sagittarius dwarf, which likely reside in subhaloes
s
with significantly larger velocities than this, the bright satellites of the Milky Way
a
[ all appear to reside in subhaloes with maximum circular velocities below 40 kms−1.
As recently highlighted by Boylan-Kolchin et al., this discrepancy implies that the
2
majority of the most massive subhaloes within a cold dark matter galactic halo are
v
too concentrated to be consistent with the kinematic data for the bright Milky Way
9
satellites. Here we show that no such discrepancy exists if haloes are made of warm,
2
rather than cold dark matter because these haloes are less concentrated on account
9
of their typically later formation epochs. Warm dark matter is one of severalpossible
2
. explanations for the observed kinematics of the satellites.
4
0 Key words: cosmology:dark matter – galaxies: dwarf
1
1
:
v
Xi 1 INTRODUCTION particles, free streaming in the early universe would have
erased primordial fluctuations below a scale that depends
r Measurementsoftemperatureanisotropiesinthemicrowave
a on the mass of the dark matter particle but could be of or-
background radiation (e.g. Komatsu et al. 2011), of galaxy der 109−1010M⊙. These mass scales correspond to dwarf
clustering on large scales (e.g. Cole et al. 2005), and of
galaxies and so, in principle, the abundance and properties
the currently accelerated expansion of the Universe (e.g
ofdwarfgalaxiescouldencodeinformationaboutthenature
Clocchiatti et al.2006;Guy et al.2010)haveconfirmedthe
of thedark matter.
“Lambda cold dark matter” (ΛCDM) model, first explored
theoretically 25 years ago (Daviset al. 1985), as the stan- The validity of the ΛCDM model on galactic and
dardmodelof cosmogony.Theseobservations probealarge subgalactic scales has been a subject of debate for many
rangeofscales,from∼1Gpcto∼10Mpc.Onsmallerscales, years.Initially Klypin et al. (1999) and Moore et al. (1999)
where the distribution of dark matter is strongly non lin- pointedoutalargediscrepancybetweenthenumberofdark
ear, observational tests of the model are more complicated matter substructures, or subhaloes, that survive inside a
because of the complexity added by galaxy formation pro- galactic haloand thenumberofsatellites that areobserved
cesses.However,itispreciselyonthesescalesthatthenature around the Milky Way. This so-called ‘satellite problem’ is
ofthedarkmattermaybemostclearlymanifest.Forexam- ofteninterpretedasindicatingthatthemodelrequiresmost
ple, if the dark matter is made of warm, rather than cold of the subhaloes to contain no visible satellite. This aspect
of the problem, however, is readily solved by invoking the
knownphysicsofgalaxyformation,particularlyearlyreion-
⋆ E-mail:[email protected] ization of the intergalactic medium and supernovae feed-
(cid:13)c 2011RAS
2 M. R. Lovell et al
back, which inevitably inhibit the formation of stars in
Name mp [M⊙] r200 [kpc] M200 [M⊙] Ns
small mass haloes. Detailed models that reconcile theory
and observations in this way date back to the early 2000s Aq-A2 1.370×104 245.88 1.842×1012 30177
(Bullock et al. 2000; Benson et al. 2002; Somerville 2002). Aq-A3 4.911×104 245.64 1.836×1012 9489
The paucity of observed bright satellites, however, is Aq-AW2 1.370×104 242.87 1.775×1012 689
only one aspect of the satellite problem. As already em- Aq-AW3 4.911×104 242.98 1.778×1012 338
phasized by Klypin et al. (1999) and Moore et al. (1999), Aq-AW4 3.929×105 242.90 1.776×1012 126
there is a problem not only with the abundance of satel-
lites, but also with their distribution of circular velocities. Table1.Basicparametersofthesimulationsanalysedinthispa-
InahalolikethatoftheMilkyWay,theΛCDMmodelpre- per.ThetoptwosimulationsaretakenfromtheAquariussample
dicts the existence of several subhaloes with maximum cir- of CDM dark matter haloes published in Springeletal. (2008).
cular velocities, Vmax1, in excess of ∼ 40kms−1. Using the The simulations are of a single halo, Aq-A, at different numeri-
high-resolution simulations of galactic haloes of the Aquar- calresolutions. Thebottom threeareWDM counterparts tothe
iusproject (Springel et al.2008),Strigari et al.(2010)have CDM simulations, as described in the main text. The second to
recently demonstrated that it is possible to find ΛCDM fifthcolumnsgivetheparticlemass(mp),theradiusofthesphere
subhaloes that accurately match the observed stellar kine- of density 200 times the critical density (r200), the halo mass
withinr200 (M200)andthenumberofsubhaloeswithinthemain
mThaetibcsesotffitths,ehfiovweevweerl,l-instvuadriiaedblysahtaevlleitVesmaoxf∼<t4h0ekMmislk−y1.W[Tahye. htaailno2(0Nsp)a.rTtichleess.mallestsubhaloes, determined by subfind,con-
Strigari et al. sample excludes the Large and Small Magel-
lanicClouds(LMCandSMC)whichresideinmoremassive
haloes, and Sagittarius which is currently being disrupted.] relativistic at a redshift of ∼ 106, have a mass of ∼ 2keV,
The discrepancy between the predicted and inferred and behave as warm dark matter (WDM). This model is
distributions of Vmax values has recently been highlighted consistent with astrophysical and particle physics data, in-
by Boylan-Kolchin et al. (2011). Using also the Aquarius cluding constraints on neutrino masses from the Lyman-α
haloes, as well as the Via Lactea simulations (Madau et al. forest (Boyarsky et al. 2009b).
2008), they show explicitly that the simulated haloes typ- To investigate this WDM model we have resimulated
ically contain a few subhaloes which are too massive and one of the Aquarius N-body haloes (Aq-A) with the power
toodense(asindicatedbytheirvalueofVmax/rmax)tohost spectrum suppressed at small scales, as expected in the
any of theobserved satellites. If such objects existed in the WDM case. N-body simulations of galactic and cluster
Milky Way, they would have to be empty of stars despite WDM haloes were first carried out in the early 2000s
their mass. This seems very unlikely so, unless the Milky (Col´ın, Avila-Reese, & Valenzuela 2000; Bode et al. 2001;
Way is atypical, there is an apparent discrepancy between Knebeet al. 2002). These studies found that fewer sub-
model and observations. haloes form than in the CDM case and that these tend to
ThattheMilkyWayisnottypicalofisolatedgalaxiesof be less concentrated than their CDM counterparts. Quali-
similar luminosity and colour has recently been established tatively,we findsimilar results but theconclusions of these
from SDSSdata.Liu et al.(2011)haveshownthatonly3.5 early simulations are difficult to interpret because, as we
per cent of such galaxies have 2 satellites as bright as the shallseelater,thesharpcutoffin thepowerspectrum gives
MagellanicClouds,whileGuo et al.(2011)haveshownthat rise to the formation of a large number of artificial haloes
the luminosity function of the bright (MV < −14) Milky that are purely numerical in origin (Wang& White 2007).
Way satellites has about twice the amplitude of the mean More recently, Maccio` & Fontanot (2010) carried out new
for similar galaxies (see also Lares et al. 2011). Whilethese simulations of WDMmodels and found thattheluminosity
measurements show that the Milky Way is not an average functionofsatellitescanbereproducedinthesemodelsjust
galaxy, it is not at present possible to compare the distri- as well as it can in the CDM case.
bution of Vmax of its satellites with that of similar galaxies Our simulations have orders of magnitude higher res-
directly.However,an indirect probeof thisdistributioncan olution than previous ones, enough to investigate reliably
beconstructedbycombiningN-bodysimulationswithasub- the inner structure of the galactic subhaloes that are po-
halo abundancematching procedure (Busha et al. 2011). tential hosts of the dwarf satellites. Furthermore, we carry
Inthispaperweexplorewhetheranalternativehypoth- out convergence tests of our results and develop a method
esis for the nature of the dark matter, a warm rather than for distinguishing genuine WDM haloes from the spurious
a cold particle, can provide a better match to the inferred objects thatinevitably form in simulations of thiskind.We
distribution of satellite circular velocities ormasses. Specif- describe oursimulations in Section 2,present ourresults in
ically, we test a model in which the dark matter is one Section 3, and conclude in Section 4.
of the particles predicted by the ‘neutrino minimal stan-
dard model (νMSM)’ of Asaka & Shaposhnikov (2005) and
Boyarsky et al. (2009a). In this model there is a triplet of
2 THE SIMULATIONS
sterile neutrinos, the lightest of which could become non-
Tocompare theproperties of subhaloes in Milky Waymass
haloes in CDM and WDM universes, we have assembled a
1 ThecircularvelocityisgivenbyV =(GM(<r)/r)1/2,where sample of five high resolution simulations of galactic mass
M is the mass enclosed within radius r and G is the universal haloes.Allthesimulationshavethesamebasiccosmological
gravitational constant; the value of r at which the maximum of parameters: in units of the critical density, a total matter
thisfunction,Vmax,occursisdenoted byrmax density,Ωm =0.25andacosmological constant,ΩΛ =0.75.
(cid:13)c 2011RAS,MNRAS000,??–8
Satellite Galaxies in WDM 3
Thelinearpowerspectrumhasaspectralindexn =1andis
s
normalisedtogiveσ8 =0.9,withH0 =100hkms−1Mpc−1 = 2
73kms−1Mpc−1 (Springelet al. 2008). 2 Cold
0 Warm
We have taken two simulations from the Aquarius M2L25
projectdescribedinSpringel et al.(2008),bothofthesame −2
halo,Aq-A,butofdifferentresolution,correspondingtolev-
els 2 and 3 in the notation of Springel et al. (2008). The k)) −4
hdirgehdermriellsioolnutpioanr,tilcelveselw2i,thsiimnurla20t0io,nthheasramdoiures tohfaan asphhuenre- 3g(kP(10 −6
about the halo centre, encompassing a mean density of 200 lo −8
times the critical density. The level 3 simulation has 3.6
times fewer particles. In both cases, the mass of the halo −10
within r200 isabout 1.8×1012M⊙,which is consistent with
the estimated mass of the Milky Way (Li & White 2008; −12
Xueet al.2008;Gnedin et al.2010).Thebasicpropertiesof
−4 −2 0 2
these haloes are given at the top of Table 1. Substructures log (k/h Mpc−1)
wereidentifiedusingthesubfindalgorithm (Springel et al. 10
2001) to findgravitationally boundsubhaloes within them. Figure 1. The solid lines show the linear power spectra (from
We created three WDM counterparts to the CDM cmbfast; Seljak&Zaldarriaga 1996) used for the two simula-
haloes by running new simulations using the same code tions. Black is the original, CDM Aq-A spectrum, and red is
that of Aq-AW. The vertical dashed line marks the peak of the
andnumericalparametersasSpringel et al.(2008)butwith
WDMspectrumpeak.ThearrowmarkstheNyquistfrequencyof
WDM initial conditions. The WDM initial conditions were
thelevel2simulations.Thedashedredcurvecorrespondstothe
createdkeepingthesamephasesandthesameunperturbed
M2L25modelof(Boyarskyetal.2009b)whichisalmostidentical
particle positions as in the CDM case, but using a WDM tothesolidredcurveforscalesbelowk∼10hMpc−1.
matter power spectrum instead to scale the amplitudes of
thefluctuations.Thelinearmatterpowerspectrumforboth
theCDMandWDMsimulationsisshowninFig.1withsolid comoving position of a particle and is determined solely by
lines adopting an arbitrary normalisation at large scales. thematter fluctuations.
TheWDMpowerspectrumhasastrongcutoffathigh The WDM matter power spectrum we assume has a
wavenumbers due to the free streaming of the WDM par- shape characteristic of a ‘thermal relic’ (Bode et al. 2001).
ticles. In an unperturbed universe at the present day the However our WDM matter power spectrum is also an ex-
typical velocities of WDM particles are only a few tens of cellent fit for scales below k ∼ 10 hMpc−1, to the mat-
ms−1.This implies that theparticles ceased to berelativis- ter power spectrum of the M2L25 model of Boyarsky et al.
tic after a redshift of z ∼ 107, well before the end of the (2009b), which is shown as a dashed line in Fig. 1. At
radiation-dominated era, as suggested by the word ‘warm’. k = 10 h‘mathrmMpc−1 the power in both WDM curves
Fig. 2 illustrates the free streaming of a typical WDM par- is a factor three below that of CDM and falls away very
ticle over cosmic time. The area under the curve is the rapidlybeyondhereinbothmodels.TheM2L25modelcor-
comoving distance traveled. It is evident that the WDM responds to a resonantly produced 2keV sterile neutrino
particle travels the greatest comoving distance during the with a highly non-equilibrium spectrum of primordial ve-
radiation-dominated era after it has become nonrelativistic locities. The model is only just consistent with astrophys-
(Bode et al. 2001). Over the duration of the N-body simu- ical constraints (Boyarsky et al. 2009b) and so maximizes
lation,whichstartsatz=127, aparticletypicallytravelsa the differences between the substructures in the CDM and
distance of around 14 kpc, which is small compared to the WDM haloes, both in their internal structure and in their
total distance from early times of 400 kpc. For comparison, abundance.
themeaninterparticleseparation forthehighresolution re- Forwavenumbersbelowthepeakat4.5hMpc−1 thelin-
gion in our highest resolution simulation is 7.4 kpc, similar earWDMpowerspectrumiswellapproximatedbytheprod-
tothefree-streamingdistancetraveledbytheparticlesafter uct of the linear CDM power spectrum times the square of
z=127.Thismeansthattheeffectsofstreamingduringthe the Fourier transform of a spherical top-hat filter of unit
simulation are small, and only affect scales that are barely amplitudeandradius 320 kpc,orequivalently,containing a
resolved in our simulations. For this reason we chose to set mass of 5×109M⊙ at the mean density.
theparticle velocities in thesame way as in theCDM case, Images of the CDM and WDM haloes are shown in
where theparticle velocity is a function of theunperturbed Fig. 3. As shown in Table 1, the mass of the main halo in
the WDM simulation is very similar to that of the CDM
halo, just a few per cent lighter. However, the number of
2 Although this set of parameters is discrepant at about the substructuresintheWDMcaseismuchlower,reflectingthe
3σ level with the latest constraints from microwave background
factthatthesmallscalepowerinthesesimulationsisgreatly
andlarge-scalestructuredata(Komatsuetal.2011),particularly
reduced. Some of the largest subhaloes can be matched by
with the values of σ8 and ns, the differences are not important eyein theimages of thetwo simulations.
forourpurposes.Forexample,Boylan-Kolchinetal.(2011)show
Springel et al.(2008)showedthatitispossibletomake
thatthestructureofAquariussubhaloesisstatisticallysimilarto
that of subhaloes in the Via Lactea simulations which assume a precise matches between substructures at different resolu-
valueofσ8=0.74,lowerthanthatofKomatsuetal.(2011),and tionsfortheAq-Ahalo,allowingthenumericalconvergence
aspectralindexof0.95. of properties of substructures to be checked for individual
(cid:13)c 2011RAS,MNRAS000,??–8
4 M. R. Lovell et al
ferentresolution,andselectasgenuineonlythosesubhaloes
with strong matches between all three resolutions. We find
thatthesecriteriaidentifyasampleoffifteenrelativelymas-
sive subhaloes with mass at infall greater than 2×109M⊙,
together with a few more subhaloes with infall mass below
109M⊙. This sample of fifteen subhaloes includes all of the
subhaloes with infall masses greater 109M⊙.
We have also found that the shapes of the Lagrangian
regionsofspurioushaloesinourWDMsimulationsaretyp-
ically very aspherical. We have therefore devised a second
measurebasedonsphericityasanindependentwaytoreject
spurious haloes. All fifteen of the massive subhaloes identi-
fiedbythefirstcriterionpassourshapetest,butallbutone
subhalowithan infall massbelow 109M⊙ areexcluded.For
thepurposesofthispaperweneedonlythe12mostmassive
subhaloesatinfalltomakecomparisonswiththeMilkyWay
satellites.
For both our WDM and CDM catalogues, we select a
sample made up of the 12 most massive subhaloes at in-
fall found today within 300 kpc of the main halo centre. In
the Aq-AW2 simulation these subhaloes are resolved with
between about 2 and 0.23 million particles at their maxi-
Figure2.Thefreestreamingcomovingdistancetraveledperlog
mum mass. We use the particle nearest the centre of the
interval of 1+z, where z is redshift, for a WDM particle with
gravitational potential to define the centre of each subhalo
a fiducial velocity of 24 m s−1 at the present day. The dashed
verticallinemarkstheredshiftofmatter-radiationequality. The andhencedeterminethevaluesofVmax andrmax definedin
Section 1.
dottedverticallineindicatesthestartredshiftoftheWDMsim-
ulations.
3 RESULTS
substructures. For this paper, we have found matches be-
tween subhaloes in the Aq-AW2, Aq-AW3, and Aq-AW4 In this section, we study the central masses of the sub-
simulations. We make these matches at the epoch when structures found within 300 kpc of the centres of the CDM
thesubhaloes first havea mass which is more than half the and WDM Milky Way like haloes. These results are com-
mass they have at the time when they first infall into the pared with the masses within the half-light radii, inferred
main halo (which is very close to the maximum mass they by Walker et al. (2009, 2010) and Wolf et al. (2010) from
everattain).Atthisepochit isrelatively easytomatchthe kinematic measurements, for the 9 bright (LV > 105L⊙)
largestsubstructuresinthesethreesimulationsasthecorre- Milky Way dwarf spheroidal galaxies.
sponding objects have very similar positions, velocities and FollowingthestudybyBoylan-Kolchin et al.(2011),in
masses. Fig. 4 we plot the correlation between Vmax and rmax for
Thenumberofsubhaloesthatcanbematchedbetween thesubhaloesinAq-AW2andAq-A2thatliewithin300kpc
the two WDM simulations is much smaller than that be- of thecentreof themain halo. Onlythose WDMsubhaloes
tween the corresponding CDM simulations, and is also a selected using our matching scheme are included, whereas
muchsmallerfractionofthetotalnumberofsubhaloesiden- all Aq-A2 subhaloes are shown. The CDM subhaloes are
tified by subfind. The majority of substructures identified a subset of those shown in fig. 2 of Boylan-Kolchin et al.
intheWDMsimulationsformthroughfragmentationofthe (2011), and show Vmax values that are typically ∼ 50 per
sharply delineated filaments characteristic of WDM simu- cent larger than those of WDM haloes with a similar rmax.
lations and do not have counterparts in the simulations of Byassumingthatthemassdensityinthesubhaloescontain-
different resolution. The same phenomenon is seen in hot ing the observed dwarf spheroidals follows an NFW profile
dark matter simulations and is numerical in origin, occur- (Navarroet al. 1996b, 1997), Boylan-Kolchin et al. (2011)
ringalongthefilamentsonascalematchingtheinterparticle found the locus of possible (rmax,Vmax) pairs that are con-
separation(Wang & White2007).Thisartificialfragmenta- sistent with the observed half-light radii and their enclosed
tion is apparent in Fig. 3. masses. This is represented by the shaded region in Fig. 4.
Wewillpresentadetaileddescriptionofsubhalomatch- As Boylan-Kolchin et al. (2011) observed with their larger
ing in a subsequent paper but, in essence, we have found sample, several of the largest CDM subhaloes have higher
that matching subhaloes works best when comparing the maximumcircularvelocitiesthanappearstobethecasefor
Lagrangian regions of the initial conditions from which the the Milky Way bright dwarf spheroidals. By contrast, the
subhaloes form, rather than the subhaloes themselves. We largest WDM subhaloes are consistent with theMilky Way
use a sample of the particles present in a subhalo at the data.
epoch when it had half of the mass at infall to define the Rather than assuming a functional form for the mass
Lagrangian region from which it formed. We have devised density profile in the observed subhaloes, a more direct ap-
a quantitative measure of how well the Lagrangian regions proach is to compare the observed masses within the half-
of thesubstructuresoverlap between thesimulations of dif- light radii of the dwarf spheroidals with the masses within
(cid:13)c 2011RAS,MNRAS000,??–8
Satellite Galaxies in WDM 5
Figure 3. Images of the CDM (left) and WDM (right) level 2 haloes at z = 0. Intensity indicates the line-of-sight projected square
of the density, and hue the projected density-weighted velocity dispersion, ranging from blue (low velocity dispersion) to yellow (high
velocity dispersion). Each box is 1.5Mpc on a side. Note the sharp caustics visibleat large radii inthe WDM image, several of which
arealsopresent,althoughlesswelldefined,intheCDMcase.
2200..00 associate final satellite luminosity with the maximum pro-
genitor mass for each surviving subhalo. This is essentially
1100..00 the mass of the object as it falls into the main halo. The
77..00 smallest subhalo in each of our samples has an infall mass
55..00 of 3.2×109M⊙ in the WDM case, and 6.0×109M⊙ in the
CDM case.
pc]pc] 33..00 The LMC, SMC and the Sagittarius dwarf are all
[k [kmaxmax 22..00 more luminous than the 9 dwarf spheroidals considered by
rr Boylan-Kolchin et al.(2011)andbyus.Asnotedabove,the
11..00 Milky Way is exceptional in hosting galaxies as bright as
theMagellanicClouds,whileSagittariusisintheprocessof
Cold
00..55 Warm being disrupted so its current mass is difficult to estimate.
Cold (Top 12) Boylan-Kolchin et al. hypothesize that these three galaxies
Warm (Top 12)
allhavevaluesofVmax>60kms−1 atinfallandexcludesim-
ulated subhaloes that have these values at infall as well as
1100 2200 3300 4400 5500 6600 7700 8800
VVmmaaxx [[kkmmss−−11]] Vmax > 40kms−1 at the present day from their analysis. In
what follows, we retain all subhaloes but, where appropri-
Figure 4. The correlation between subhalo maximum circular ate, we highlight those that might host large satellites akin
velocity and the radius at which this maximum occurs. Sub- to theMagellanic Clouds and Sagittarius.
haloes lying within 300kpc of the main halo centre are in-
The circular velocity curves at z = 0 for the 12 sub-
cluded. The 12 CDM and WDM subhaloes with the most mas-
haloes which had themost massiveprogenitors at infall are
sive progenitors are shown as blue and red filled circles respec-
shown in Fig. 5 for both WDM and CDM. The circular
tively; the remainingsubhaloes are shown as empty circles. The
shadedarearepresentsthe2σconfidenceregionforpossiblehosts velocitieswithinthehalf-lightradiusofthe9satellitesmea-
of the 9 bright Milky Way dwarf spheroidals determined by suredbyWolf et al.(2010)arealsoplottedassymbols.Leo-
Boylan-Kolchinetal.(2011). II has the smallest half-light radius, ∼ 200pc. To compare
the satellite data with the simulations we must first check
the convergence of the simulated subhalo masses within at
thesameradiiinthesimulated subhaloes.Toprovideafair leastthisradius.Wefindthatthemedianoftheratioofthe
comparison we must choose the simulated subhaloes that masswithin200pcintheAq-W2andAq-W3simulations is
aremostlikelytocorrespondtothosethathostthe9bright W2/W3 ∼ 1.22, i.e., the mass within 200pc in the Aq-W2
dwarf spheroidals in the Milky Way. As stripping of sub- simulation has converged to betterthan ∼22%.
haloes preferentially removes dark matter relative to the As can be inferred from Fig. 5, the WDM subhaloes
morecentrallyconcentratedstellarcomponent,wechooseto have similar central masses to the observed satellite galax-
(cid:13)c 2011RAS,MNRAS000,??–8
6 M. R. Lovell et al
1.8
Cold Canes Venatici I Warm
Ursa Minor
Sextans Cold
Sculptor Warm
1.6 Leo II 8.6
Leo I
FDorarncaox ]MO •
−1V / kms ]circ1.4 Carina 1kpc) / infall 8.4
og[101.2 M(< 8.2
l g[10
o
l 8.0
1.0
7.8
0.8
0.1 1.0 10.0 0.1 1.0 10.0 12 10 8 6 4 2
r [kpc] r [kpc] z
form
Figure 5. Circular velocity curves for the 12 CDM (left) and Figure6.Thecorrelationbetweensubhalocentralmassatinfall
WDM (right) subhaloes that had the most massive progenitors. and the redshift of formation, zform, defined as the redshift at
The3redcurvesrepresentsubhaloeswiththemostmassivepro- which the total mass of each proto subhalo first exceeded this
genitors,whichcouldcorrespondtothosecurrentlyhostingcoun- value.Centralmassisdefinedwithin1kpc,andCDMandWDM
terpartsoftheLMC,SMCandtheSagittariusdwarf.The9black resultsareshownwithblueandredsymbolsrespectively.
curves might more fairly be compared with the data for the 9
brightdwarfspheroidalgalaxiesoftheMilkyWayconsideredby
Wolfetal. (2010). Deprojected half-light radii and their corre- tantin theouterregions of thesubhaloes, themass profiles
sponding half-light masses, as determined by Wolfetal. (2010) in Fig. 5 show that the inner regions of some of the sub-
from line-of-sight velocity measurements, are used to derive the haloes have also endured significant depletion since infall.
half-lightcircularvelocitiesofeachdwarfspheroidal.Theseveloc- Fig. 7 shows, for both WDM and CDM subhaloes, the ra-
itiesandradiiareshownascolouredpoints.Thelegendindicates tio, Mz=0(< r)/Minfall, of the present day mass contained
thecolourcodingofthedifferentgalaxies.
within r = 0.5, 1 and 2 kpc to the mass at infall, as a
function of the central mass at infall at the chosen radius.
On average, the median mass at infall for WDM is lower
ies, while the CDM subhaloes are almost all too massive at by ∼ 0.15 dex than the corresponding mass for CDM. One
the corresponding radii. The CDM subhaloes have central subhalo gains mass between infall and z =0 because it ac-
masses that are typically 2-3 times larger than the Milky cretesanothersubhalo.Whilethereisalargescatteramong
Waysatellites. ThereisoneCDMsubhalothatliesatlower the different subhaloes, with some having lost the majority
massesthanall9dwarfspheroidals, butthishadoneofthe of their central mass since infall, no significant systematic
three most massive progenitors and has been almost com- difference between WDM and CDM subhaloes is apparent.
pletely destroyed bytidal forces. This implies that the reason why the WDM subhaloes pro-
Fig. 4 and 5 show that the WDM subhaloes are less videabetterfittothehalf-light massesofthe9MilkyWay
centrallyconcentratedthanthoseinthecorrespondingCDM dwarfspheroidalsstudiedbyWolf et al.(2010)isnotexcess
halo.Concentrationstypicallyreflecttheepochatwhichthe strippingbutthelaterformation time,andcorrespondingly
halo formed (Navarroet al. 1996b, 1997; Ekeet al. 2001). typical lower concentration, of the WDM proto subhaloes
Toinvestigatesystematicdifferencesintheformationepoch compared to theirCDM counterparts.
of the WDM and CDM subhaloes in our sample, we must
choose a suitable definition of formation time. Since we are
considering only the central mass, and we do not wish to 4 DISCUSSION AND CONCLUSIONS
introducescatterinanycorrelation byusingsubhaloesthat
may have been stripped, we define the formation time as The properties of the satellite galaxies of the Milky Way
thefirsttimeatwhichthetotalprogenitormassexceedsthe haveposedalongstandingpuzzleforCDMtheoriesofgalaxy
mass within 1 kpc at infall. The correlation of this redshift formation. Two aspects of this puzzle have reportedly been
withthemasswithin1kpcatinfallisshowninFig.6forthe separately and independently solved. One is the luminos-
12mostmassiveWDMandCDMprogenitorsthatsurviveto ity function of the satellites. The basic idea - the suppres-
z =0 as distinct subhaloes. Evidently, the proto subhaloes sion of galaxy formation in small haloes by a combination
that form later, which are generally WDM not CDM ones, of feedback effects produced by the reionization of gas at
havethelowestcentralmasses.Themeandifferencebetween high redshift and supernova heating - was suggested by
the top 12 WDM and CDM proto-subhalo masses within 1 Kauffmann,White, & Guiderdoni(1993)andexploredthor-
kpcis approximately a factor 2. oughlyintheearly2000s(Bullock et al.2000;Benson et al.
Because of their later formation time, the infalling 2002; Somerville 2002) and has been revisited many times
WDM subhaloes already have lower central masses than since then (see Font et al. 2011, and references therein for
those falling into the corresponding CDM haloes. As their the most recent discussion). The other aspect concerns the
massislesscentrallyconcentrated,theWDMsubhaloesare dynamical state of the satellites. Strigari et al. (2010) have
more susceptible to stripping. While this is most impor- shownthatthereexistsubhaloesintheAquariusCDMsim-
(cid:13)c 2011RAS,MNRAS000,??–8
Satellite Galaxies in WDM 7
(Strigari et al. 2007). Also, it must be borne in mind that
1.4 r < 500pc trehcetlyvamlueeassuorfedVmbauxt ifnofrerMreidlkbyyWmaaykinsgataesllsiutemspatiroensnoatboduit-
r < 1kpc
1.2 r < 2kpc their dynamical state. If some of these assumptions are un-
realistic, this could lead to an underestimate of the val-
<r) 1.0 ues of Vmax (e.g. Stoehr et al. 2002). Another possibil-
M(infall 0.8 intoytitsypthicaatl othfethseataevlleirtaegepotpouwlahtiiochn tohfetmheodMelilpkyredWicatyioniss
<r)/ apply. It has recently been shown by Liu et al. (2011),
M(z=0 0.6 Guo et al. (2011) and Lares et al. (2011) that the bright
endof theMilky Waysatellite luminosity function is differ-
0.4
ent from the average. Finally, we cannot exclude the pos-
0.2 sibility that baryonic processes occurring during the for-
mation of satellite galaxies in the CDM cosmogony might
0.0
have lowered the concentration of haloes, for example, in
7.0 7.5 8.0 8.5 9.0
log [M (<r) / M ] the manner suggested by Navarroet al. (1996a). Recent
10 infall O •
simulations(Read & Gilmore2005;Mashchenko et al.2008;
Figure 7.Thevariationwithsubhalomassatinfalloftheratio Governato et al.2010)suggestthattheseprocessescouldbe
ofthepresentdaymasstotheinfallmasscontainedwithin500pc, importantalthoughitremainstobeseeniftheyareenough
1kpcand2kpc.Dataareshownforthe12subhaloesidentifiedat toreconciletheCDMmodelwiththedynamicsoftheMilky
z=0whichhadthemostmassiveprogenitors,withCDMinblue
Way satellites.
and WDM in red. The symbol type denotes the radius interior
to which the central mass is being measured and large symbols
showthemediansofthecorrespondingdistributions.Wefindno
systematicdifferencesbetweentheCDMandWDMsubhalomass
ACKNOWLEDGEMENTS
ratios.
We thank Qi Guo and Louis Strigari for useful discussions.
MLacknowledgesanSTFCstudentship.CSFacknowledges
ulations that fit the stellar spectroscopic data for the well-
aRoyalSocietyWolfsonResearchMeritAwardandanERC
studied satellites extremely well.
Advanced Investigator grant. The simulations used in this
There is a third aspect to the puzzle, however, that
paperwerecarried outon theSupercomputerCenterof the
has not yet been fully addressed and this is whether the
Chinese Academy of Science and the Cosmology Machine
CDMmodels thataccount for thesatellite luminosity func-
supercomputer at the Institute for Computational Cosmol-
tion also account for the satellites’ internal dynamics. In
ogy,Durham.LGacknowledges supportfrom theOnehun-
other words, do the models assign the correct luminosities
dred talents Program of the Chinese Academy of Science
to subhaloes with the correct dynamics? At face value, the
(CAS),theNationalBasicResearchProgramofChina(pro-
answerseemstobe‘no’.Thisisalreadyevidentintheanal-
gram 973, undergrant No. 2009CB24901), NSFC grant No.
ysis of Strigari et al. (2010) in which the best fit dynami-
10973018,andanSTFCAdvancedFellowship.TheCosmol-
cal models imply velocity dispersions (or equivalently Vmax ogy Machine is part of the DiRAC Facility jointly funded
values) for the brightest dwarf spheroidals that are smaller
by STFC, the Large Facilities Capital Fund of BIS, and
than the velocity dispersions of the largest subhaloes. It
Durham University. This work was supported in part by
is this discrepancy that has recently been highlighted by
an STFC rolling grant to the ICC.
Boylan-Kolchin et al. (2011).
In this paper, we have compared a high resolution N-
bodysimulation ofoneoftheAquariusgalactic haloeswith
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