Table Of ContentMon.Not.R.Astron.Soc.000,000–000(0000) Printed14January2015 (MNLATEXstylefilev2.2)
Reionizing the Universe in Warm Dark Matter cosmologies
Pratika Dayal1,2(cid:63), Tirthankar Roy Choudhury3 , Volker Bromm4 & Fabio Pacucci5
1 SUPA†, Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh, EH9 3HJ, UK
2 Institute for Computational Cosmology, Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK
5
3 National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Pune 411007, India
1
4 Department of Astronomy and Texas Cosmology Centre, University of Texas, Austin, TX 78712, USA
0
5 Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
2
n
a
J
2
ABSTRACT
1
We compare model results from our semi-analytic merger tree based framework for
high-redshift (z (cid:39) 5−20) galaxy formation against reionization indicators including
]
O the Planck electron scattering optical depth (τ ) and the ionizing photon emissivity
es
(n˙ ) to constrain the particle mass of Warm Dark Matter (WDM). Our framework
C ion
traces the Dark Matter (DM) and baryonic assembly of galaxies in 4 DM cosmolo-
.
h gies: Cold Dark Matter (CDM) and WDM with a particle mass of m = 2.25,3 and
x
p 5 keV. It includes all the key processes of star formation, supernova feedback, the
- merger/accretion/ejection driven evolution of gas and stellar mass, and the effect of
o
the ultra-violet background (UVB) created during reionization in photo-evaporating
r
st the gas content of galaxies in halos with Mh ∼< 109M(cid:12). We show that current Planck
a τes values rule out mx ∼< 2.5 keV WDM, even in the physically unlikely scenario that
[ all ionizing photons produced by these galaxies escape and contribute to reionization
(i.e. f = 1). With the largest number of UVB-suppressed galaxies, CDM faces a
1 esc
v “stalling” of the reionization process with this effect decreasing with the disappear-
3 ance of small-scale structure with decreasing mx. Finally, we find the bulk of the
2 reionization photons come from galaxies with a halo mass Mh ∼< 109M(cid:12), stellar mass
8 M∗ ∼< 107M(cid:12) and UV magnitude −18∼< MUV ∼< −13 in CDM. The progressive sup-
2 pression of low-mass halos with decreasing m leads to a shift in the “reionization”
x
0 population to larger (halo and stellar) masses of Mh ∼> 109M(cid:12) and M∗ ∼> 107M(cid:12) for
1. mx ∼> 3 keV WDM, although the UV limits effectively remain unchanged.
0
Key words: Cosmology:dark matter-reionization-cosmological parameters-cosmic
5
1 microwave background; galaxies-intergalactic medium
:
v
i
X
r 1 INTRODUCTION 1971; Blumenthal et al. 1984; Bond & Szalay 1983; Cole
a
et al. 2005; Lange et al. 2001; Hinshaw et al. 2013; Planck
According to the standard Lambda Cold Dark Matter
Collaboration et al. 2014a; Slosar et al. 2013). However, as
(ΛCDM)cosmologicalmodel,galaxyformationproceedshi-
recently reviewed by Weinberg et al. (2013), CDM exhibits
erarchically through time, driven by a cold (dark) matter
a number of small scales problems: it produces halo pro-
ofunknowncomposition.Inthiseraofprecisioncosmology,
files that are cuspy as opposed to the observationally pre-
its energy density has been measured to have a value of
ferred constant density cores (Navarro et al. 1997; Subra-
Ω h2 = 0.133 with baryons comprising Ω h2 = 0.0196 of
m b manian et al. 2000), it over-predicts the number of satellite
thetotal(PlanckCollaborationetal.2014b).CDMclusters
andfieldgalaxiesascomparedtoobservations(the“missing
on all scales and has been remarkably successful in predict-
satellite problem”; Klypin et al. 1999; Moore et al. 1999),
ing the large scale structure of the Universe, the tempera-
predicts massive (Large Magellanic Cloud mass), concen-
tureanisotropiesmeasuredbytheCosmicMicrowaveBack-
tratedGalacticsubhalosinconsistentwithobservations(e.g.
ground (CMB) and Lyman-α forest statistics (e.g. Peebles
Boylan-Kolchinetal.2012)andfacesdifficultyinproducing
typical disks due to ongoing mergers down to z (cid:39)1 (Wyse
2001). The limited success of baryonic feedback in solving
(cid:63) [email protected]
† ScottishUniversitiesPhysicsAlliance these small scale problems (e.g. Boylan-Kolchin et al. 2012;
(cid:13)c 0000RAS
2
Teyssier et al. 2013) has prompted questions regarding the evolution with redshift, that should be detectable by the
validity of the CDM scenario. A popular solution to the James Webb Space Telescope (JWST) integrating down to
small scale problems in CDM cosmology involves invoking MUV (cid:39) −16.5 at z∼> 10 (see also Calura et al. 2014; Gov-
(∼ keV) Warm Dark Matter (WDM) particles that erase ernato et al. 2014).
small-scalepower(Blumenthaletal.1984;Bodeetal.2001, Since low-mass high-z galaxies are now believed to be
e.g)1.BeyonditsStandardModel,particlephysicsprovides the main sources of reionization photons in the early Uni-
compelling motivation for WDM candidates, which can be verse (e.g. Barkana & Loeb 2001; Ciardi & Ferrara 2005;
aslightas∼O(1)KeV,suchassterileneutrinos.Theseap- Choudhury & Ferrara 2007; Choudhury et al. 2008), their
pear in an extension of the Standard Model with 3 sterile delayed and accelerated assembly would naturally lead to a
neutrinos, out of which 2 could be as heavy as 1−10 GeV, correspondingdelayandaccelerationinthereionizationhis-
while the lightest one could be within O(1) keV (for a re- tory. Now that we have verified that our theoretical galaxy
view see Abazajian et al. 2012). There are some tantalising populationsareinagreementwithobservationsatz(cid:39)7−12
observational hints such as the 3.5keV monochromatic line for m =1.5,3and5keV,webuildreionizationhistoriesfor
x
observedbyXMM-NewtoncomingfromthePerseusgalaxy 4 DM models with m =2.25,3 and 5keV to see if we can
x
cluster.Thislinemightarisefromalightsterileneutrinoan- obtain tighter constraints on m by comparing to existing
x
nihilating into photons (Bulbul et al. 2014; Boyarsky et al. observations of the Planck CMB electron scattering optical
2014). depthandtheionizingphotonemissivity.Inadditiontoin-
Astrophysical constraints on the WDM particle mass ternal feedback from supernovae (see Sec. 2.3 Dayal et al.
range from m (cid:62)3.3keV using the Lyα forest power spec- 2014b) our model self-consistently includes the “external”
x
trum (Viel et al. 2013), m > 1.6−1.8keV using num- feedback effect from reionization in photo-evaporating gas
x
ber counts of high-z gamma ray bursts (de Souza et al. from DM halos (Sec. 2.2), and yields both the reionization
2013), mx ∼> 1.3keV using abundance matching of theo- history, and the ionizing photon contribution across differ-
retical and observed high-z galaxies (Schultz et al. 2014), ent halo mass, stellar mass and magnitude bins (Sec. 3), as
mx ∼> 1keV using dwarf spheroidal galaxy observations (de explained in what follows.
Vega & Sanchez 2010), simultaneously reproducing stellar The cosmological parameters used in this
massfunctionsandtheTully-Fisherrelationforz=0−3.5 work correspond to (Ω ,Ω ,Ω ,h,n ,σ ) =
m Λ b s 8
galaxies (Kang et al. 2013) and comparing the observed (0.2725,0.702,0.04,0.7,0.96,0.83), consistent with the
numberdensityofz≈10galaxiestothatexpectedfromthe latest results from the Planck collaboration (Planck Col-
halomassfunction(Pacuccietal.2013),and mx ∼> 0.5keV laboration et al. 2014b) and we quote all quantities in
inferred using the presence of supermassive black holes at comoving units unless stated otherwise.
z(cid:39)5.8 (Barkana et al. 2001),
A combination of ground and space-based observa-
tionshasallowedastatisticallysignificantdataavailablefor
z(cid:39)6−10LymanBreakgalaxies(LBGs;Oeschetal.2010; 2 THEORETICAL MODEL
Bouwens et al. 2010, 2011; Castellano et al. 2010; McLure
We now briefly summarise the theoretical model and inter-
et al. 2010; Bradley et al. 2012; Oesch et al. 2013; McLure
estedreadersarerefereedtoDayaletal.(2014a,b)forcom-
etal.2013;Bowleretal.2014b;Bouwensetal.2014;Bowler
plete details. We explore 4 DM models: CDM and WDM
et al. 2014a) enabling such constraints to be extended to
with m = 2.25,3 and 5keV. Although we cite m values
thehigh-z Universe.Indeed,inDayaletal.(2014b),wepre- x x
assuming thermally decoupled relativistic particles, these
sented a merger-tree based semi-analytic model that traces
numbers can also be converted into sterile neutrino masses
both the DM and baryonic assembly of high-z(z (cid:39)7−15)
(m ) using (Viel et al. 2005)
galaxies in 4 cosmologies: CDM and WDM with particle sterileν
masses mx = 1.5,3 and 5keV. While the halo mass func- (cid:32) m (cid:33)4/3(cid:32)0.1225(cid:33)
tdioownnistoinhdaislotinmgausisshesabalselofowr aCsDMM a(cid:39)nd10m8.5xM∼> 3,ksmeVallWmDaMss msterileν =4.43keV 1kexV Ωmh2 , (1)
h (cid:12)
(M (cid:39)109.5M )structuresaresuppressedmoreseverelyin
h (cid:12) yielding m = (13.1,18.6,36.8)keV corresponding to
the 1.5keV scenario. We showed that the ultraviolet lumi- sterileν
m =(2.25,3,5)keV respectively.
nosity functions (UV LFs), mass to light (M/L ratios) and x
stellarmassdensities(SMD)arethesameinallthe4models
for the massive, luminous (M (cid:54)−18) galaxies that have
UV
2.1 Merger trees and the baryonic
been observed so far. However, the delay in structure for-
implementation
mationinthe1.5keVWDMscenarioleadstoadelayedand
accelerated baryonic assembly resulting in a steeper SMD We start by constructing 400 merger trees starting at
z = 4 linearly distributed across the halo mass range
log(M /M ) = 9−13 for the 4 DM models considered.
h (cid:12)
1 However, some works caution that the extremely low mass The merger-trees use 320 equal redshift steps (∆z = 0.05)
WDM particles required to make constant density cores prevent between z = 20 and z = 4 with a mass resolution of
theveryformationofdwarfgalaxies(Macci`oetal.2012;Schnei- Mres = 108M(cid:12) using the modified binary merger tree al-
deretal.2014). gorithm with smooth accretion detailed in Parkinson et al.
(cid:13)c 0000RAS,MNRAS000,000–000
Reionization in CDM and WDM 3
(2008)andBensonetal.(2013).Wescaletherelativeabun- andpredictsthez-evolutionofthefaintendUVLFslopein
dances of the merger tree roots to match the z = 4 Sheth- in addition to reproducing observables including the SMD
Tormen halo mass function (HMFs; Sheth & Tormen 1999) and mass-to-light ratios using fiducial parameter values of
andhaveverifiedthattheseyieldHMFsingoodagreement f =0.038andf =0.1.Wemaintainthesefiducialparam-
∗ w
withtheSheth-Tormen(Sheth&Tormen1999)HMFatall eter values in all the calculations carried out in this work.
z. Further, we replace 1.5keV WDM with a heavier mass of
We implement the merger trees with baryonic physics 2.25keV togettighterconstraintson m ;wenotethatthe
x
including star formation, supernova (SN) feedback driven latter mass naturally fits all of the observed data sets pre-
ejection of gas, and the merger/accretion/ejection driven sented in Dayal et al. (2014a,b).
evolution of the gas and stellar masses. Our model is based
onthesimplepremisethatthemaximumstarformationef-
ficiency (feff) of any halo is limited by the SN binding en- 2.2 Modelling reionization
∗
ergyrequiredtounbind/ejecttherestofthegasandquench The quantity which plays a crucial role in modelling reion-
further star formation, up to a maximum threshold value ization is the rate of ionizing photons per unit comoving
of f∗ (see Dayal et al. 2014a). This model has two z and volume n˙ion (s−1Mpc−1) in the IGM, which is essentially
massindependentfreeparameterswhosevaluesareselected obtainedby(i)integratingthephotonproductionrateN˙
ion
tomatchtheevolvingUVLF:themaximumthresholdstar of individual galaxies over relevant halo mass ranges, and
formationefficiency(f∗)andthefractionofSNenergythat (ii)multiplyingbythefractionfesc ofionizingphotonsthat
goesintounbindinggas(fw).Whilefw affectsthefaint-end escape from halos into the IGM.
slopeof theUV LFwhere feedback is most effective, f∗ de- AlthoughreionizationisdrivenbytheH I ionizingpho-
terminesthenormalizationatthebright-endwheregalaxies tonsproducedbyearlygalaxies,theultra-violetbackground
can form stars with the maximum allowed efficiency. (UVB) built up during reionization suppresses the bary-
We implement this simple idea proceeding forward in onic content of galaxies by photo-heating/evaporating gas
time from the highest merger tree output redshift, z = 20. at their outskirts (Klypin et al. 1999; Moore et al. 1999;
At any z step, the initial gas mass, Mg,i(z), in a galaxy Somerville 2002) preventing efficient cooling and slowing
depends on its merger history: while galaxies that have no downitsprogress.Inordertoaccountfortheeffectofreion-
progenitors are assigned a value Mg,i(z)=(Ωb/Ωm)Mh(z), izationfeedbackonn˙ion,weassumetotalphoto-evaporation
the value is determined both by the gas mass brought in of gas from halos below M = 109M (at any z) within
min (cid:12)
by merging progenitors as well as that smoothly-accreted ionized regions. In other words, halos below M and can
min
fromtheintergalacticmedium(IGM)forgalaxiesthathave neitherformstarsnorcontributeanygasinmergersifthey
progenitors.Apart(f∗eff)ofthisgasformsnewstellarmass, areforminginsidetheregionswhichhavealreadybeenion-
M∗(z)withthefinalgasmassleftdependingontheratioof ized. Hence the globally averaged n˙ion is given by
the (instantaneous) energy provided by exploding SN and
the potential energy of the halo. We note that at any step, n˙ion(z)=fesc(z)[QII(z)n˙II(z)+[1−QII(z)]n˙I(z)], (4)
the total stellar mass in a galaxy is the sum of mass of the
where Q (z) is the volume filling fraction for ionized re-
II
newly-formed stars, and that brought in by its progenitors.
gions, and n˙ (n˙ ) is the photon production rate density
II I
For simplicity, we assume every new stellar population
within ionized (neutral) regions. Clearly n˙ contains con-
I
has a fixed metallicity of 0.05Z and an age t = 2Myr.
(cid:12) 0 tribution from all sources which can form stars and is un-
Using the population synthesis code STARBURST99 (Lei-
affected by the UVB, while n˙ represents the case where
thereretal.1999),itsinitialUVluminosity(atλ=1500˚A) II
sources below M do not contribute to ionizing photons.
canbecalculatedasL (0)=1033.077(M /M )ergs−1˚A−1 min
UV ∗ (cid:12) At the beginning of the reionization process the volume
andtheinitialoutputofionizingphotonscanbecalculated
filled by ionized hydrogen is very small (Q << 1) and
as N˙ (0) = 1046.6255(M /M )s−1. Further, the time evo- II
ion ∗ (cid:12) most galaxies are not affected by the UVB, thus giving
lution of these quantities can be expressed as
n˙ (z) ≈ n˙ (z). However, as Q increases and reaches a
ion I II
t value (cid:39) 1 (note reionization is said to be complete when
L (t)=L (0)−1.33log +0.462 (2)
UV UV t0 QII =1),allgalaxieslessmassivethanMmin arefeedback-
suppressed such that n˙ (z)≈n˙ (z).
t ion II
N˙ion(t)=N˙ion(0)−3.92logt +0.7 (3) The reionization history, expressed through the evolu-
0 tion of Q , can then be written as
II
For any galaxy along the merger tree, its UV luminosity
dQ dn Q dt
and ionizing photon output rate are the sum of the values II = ion − II , (5)
dz dz t dz
from the new starburst, and the contribution from older rec
populationsaccountingforthedropwithtime.Wetherefore where dt/dz =[H(z)(1+z)]−1. Here, the first term on the
have these quantities for 320 z steps between z = 20 and right hand side represents the ionizing photon production
z=4. which drives reionization, and the second term shows the
As shown in Dayal et al. (2014a,b), our model repro- decrease in the H II volume filling fraction due to recombi-
duces the observed UV LF for all DM models (CDM and nation of electrons and protons to form H I . Further, nH
WDM with m = 1.5,3 and 5keV) at z (cid:39) 5−10 over 2.5 is the comoving hydrogen number density, and t is the
x rec
orders of magnitude in luminosity (7 magnitudes in M ) recombination time that can be expressed as
UV
(cid:13)c 0000RAS,MNRAS000,000–000
4
Figure 1. The CMB electron scattering optical depth (τes) as a function of redshift for the 4 DM models considered in this paper, as
markedineachpanel.Ineachpanel,the4linesshowresultsusingfourdifferentvaluesoffesc=1.0(dot-dashedline),0.5(dashedline),
0.35(dottedline)andthefiducialz-dependentvaluemarked(solidline);weusethesamez-dependenceoffescforboththe3and2.25keV
cases.Thez-dependentfesc valuehasbeenobtainedbysimultaneouslyfittingtoτes andionizingphotonemissivityobservations.The
horizontal dashed line shows the central value for τes inferred by Planck with the shaded region showing the errors allowed (Planck
Collaboration et al. 2014b). As seen, while a z-dependent fesc gives reasonable results for CDM and mx∼>3keV WDM, the 2.25keV
modeliseffectivelyruledoutbycurrentCMBconstraints,evenusingthemaximumallowedvalueoffesc=1.
1
trec = χnH(1+z)3αBC (6) wfohredriefffe0reanntdDαMamreozd-einlsdaerpeenshdoewntnpianraTmabetleer1s.whosevalues
where α is the hydrogen case-B recombination coefficient,
B
χ=1.08 accounts for the excess free electrons arising from
3 RESULTS
singly ionized helium and C is the IGM clumping factor
which we assume to be evolving as (Pawlik et al. 2009; Now that the model has been described we start by dis-
Haardt & Madau 2012) cussing the model constraints on m using observed values
x
oftheCMBelectronscatteringopticaldepth(τ )andion-
es
<n2 > izing emissivity (n˙ ). We then present the inferred reion-
C = HII =1+43z−1.71. (7) ion
<n >2 ization history and sources for all the 4 DM models, as de-
HII
scribed in what follows.
As seen above, the photon production rate depends on
f and hence we need to know the value of the param-
esc
eter to calculate the reionization history. In this work we 3.1 Joint reionization constraints from the CMB
assumef tobeindependentofthehalomass,andtaketo optical depth and UVB emissivity
esc
beafunctionofonlyz.Oncethefunctionf (z)ischosen,
esc Combining Planck and WMAP low-l polarization data, the
thereionizationhistoryofthemodelcanbeworkedout.As current best estimate of τ = 0.089+0.012 (Planck Collab-
shown in Sec. 3.1 that follows, simultaneously fitting to ob- es −0.014
oration et al. 2014b). We calculate τ at any given z by
es
servationsoftheCMBelectronscatteringopticaldepth(τ )
es solving the equation:
andtheionizingemissivity(n˙ )requireaz-dependentf
ion esc (cid:90) z
that evolves as τ (z)=σ c dtn (1+z)3 (9)
es T e
0
(cid:32) (cid:33)α
1+z where n (z) = Q (z)n is the global average comoving
f =f , (8) e II H
esc 0 7 value of the electron number density and σ = 6.6524×
T
(cid:13)c 0000RAS,MNRAS000,000–000
Reionization in CDM and WDM 5
Figure 2.RedshiftevolutionoftheHIionizingphotonemissivity(foralltheoreticalgalaxies)forthe4DMmodelsconsideredinthis
paper, as marked in each panel. In each panel, the 4 lines show results using four different values of fesc = 1.0 (dot-dashed line), 0.5
(dashedline),0.35(dottedline)andthefiducialz-dependentvalue(solidline);weusethesamez-dependenceoffesc forboththe3and
2.25keV cases. As clearly seen, a constant fesc value severely over-predicts n˙ion compared to the observations (points) at z (cid:39) 5,6 in
allDMmodels.Theobservationalresults(andassociatederrorbars)havebeencalculatedfollowingtheapproachofKuhlen&Faucher-
Giguere(2012),i.e.,bycombiningtheobservationalconstraintsonΓHI fromWyithe&Bolton(2011)withλmfpfromSongaila&Cowie
(2010).Seetextfordetails.
izing photons in addition to n˙ (see, e.g., Choudhury &
Model f0×100 α Ferrara2005,2006).Inthisworikon,wefollowtheapproachof
CDM 1.65 5.4 Kuhlen & Faucher-Giguere (2012) and combine the obser-
mx=5keV (13.1keV) 1.25 6.8 vational constraints on ΓHI from Wyithe & Bolton (2011)
mx=3keV (18.6keV) 1.2 8.2 with λ from Songaila & Cowie (2010) to obtain the ob-
mfp
mx=2.25keV (36.8keV) 1.2 8.2 servationalestimateofn˙ .Wehaveusedthefiducialvalues
ion
fromKuhlen&Faucher-Giguere(2012):γ =1forthesource
Table1.Theparametervaluesforz-evolutionoftheescapefrac-
spectral index and β = 1.3 for the H I column density dis-
tionfesc fordifferentDMmodels;thenumbersinbracketsshow tribution.Varyingthesewithinallowedwouldonlyresultin
thesterileneutrinomasscorrespondingto mx.Thez-dependence larger error bars, hence leaving our results unchanged (see
offesc istakentobefesc(z)=f0[(1+z)/7]α.
Kuhlen & Faucher-Giguere 2012).
The most common approach adopted in calculating
the reionization history (and τ ) is to assume a redshift-
es
10−25cm2istheThomsonscatteringcross-section.Notethat independentconstantvalueoff (e.g.Schultzetal.2014).
esc
f governs the evolution of Q as shown in Eqns. 4 and We start by following this basic approach to calculate τ
esc II es
5. and n˙ for our 4DM models,to compare toobservations.
ion
A second observable that needs to be fit by any reion- As shown in Fig. 1, matching to the Planck optical depth
izationmodelistheemissivityofionizingphotonsatz(cid:46)6. constraints requires fesc ∼> 0.5 for CDM and mx ∼> 3keV
It is currently believed that reionization was completed in WDM models; a value of f = 0.2 does not result in
esc
a “photon-starved” manner, which is constrained mainly enough electrons to produce the measured optical depth at
by the observations of H I photoionization rate ΓHI from high-z. As shown in Dayal et al. (2014b, see Fig. 3), struc-
quasar absorption lines (Lyα forest) at 5 (cid:54) z (cid:54) 6 (Bolton tureformationisprogressivelydelayedwithdecreasing m ,
x
& Haehnelt 2007). In order to calculate ΓHI in reionization resulting in a lack of H I ionizing photons which naturally
models,oneneedstomodelthemeanfreepathλ ofion- leads to a low value of τ . Indeed, our model shows that
mfp es
(cid:13)c 0000RAS,MNRAS000,000–000
6
by an increase in f (or α) to obtain the required τ at
esc es
early epochs: the values of f and α which best fit the cen-
0
tral τ value, while being within n˙ bounds, for different
es ion
DMmodelsareshowninTable1.Giventhateventhemax-
imum allowed value of f = 1 is not enough to reach the
esc
measuredτ forthe2.25keVWDMscenario,wesimplyuse
es
the values as in the 3keV case.3
We show the redshift evolution of the best-fit f
esc
values for all the DM models in Fig. 3. As mentioned,
with the largest number of low mass halos available to
provide H I ionizing photons CDM requires a shallower z-
dependenceonf .Asuccessivedecreaseinthenumberof
esc
low mass halos from CDM to 5 to 3 keV requires a larger
f at early times, resulting in a steeper z-dependence. To
esc
quantify, we find f (cid:39) 1.4% at z (cid:39) 6 which rises to 50%
esc
atz(cid:39)12,11,10forCDM,5and3keVWDM,respectively.
3.2 Reionization histories and sources in different
DM models
As discussed in Secs. 2.2 and 3.1, given the source galaxy
Figure 3. The redshift evolution of the fiducial value of fesc = population, the reionization history (or the global z-
f0(1+7z)α usedinthiswork(seetextfordetails).Theresultsfor evolution of QII) is fixed once the z-evolution of fesc is
2.25and3keVarethesamesinceweusethesamez-dependence determined. We start by noting that CDM allows galaxy
forboth.Asseen,progressivelylighterWDMparticlesrequirea formationonthesmallestscales,withlowmassgalaxiesbe-
larger photon escape fraction at earlier times to compensate for
ing progressively suppressed as m decreases. It naturally
x
thelackoflowmasshalos.
followsthatlow-massgalaxiesintheCDMmodelwillbethe
mostaffectedbyUVBfeedback,drawingouttheprocessof
τ is lower than the Planck limits even in the case that reionizationwiththiseffectdecreasingwiththeWDMparti-
es
fesc = 1, where all the H I ionizing photons escape out of clemass.ThisisthebehaviourshowninFig.4:reionization
galaxiesandcontributetoreionizationrulingoutWDMwith starts earliest in the CDM model and is 50% complete by
mx ∼< 2.25keV.2 Although they match the observed τes, z- z (cid:39)13, initially driven by low mass halos (see also Bromm
independent constant values of f = 0.5(1) severely over- & Yoshida 2011). Suppression of star formation in the nu-
esc
predict the ionizing photon emissivity by about 1.6 (1.9) merous sources with Mh ∼< 109M(cid:12) leads to a “stalling” of
orders of magnitude at z (cid:39) 6 as shown in Fig. 2. A sce- thereionizationprocesswithonlya10%changeinQII over
nario wherein f is z-independent is therefore ruled out the 200 Myrs till z (cid:39)9. Thereafter reionization extends for
esc
by the emissivity constraints, irrespective of the DM model about 650 Myrs driven by more massive galaxies, with the
considered. entire volume being reionized by z(cid:39)5.
Reconciling these two data sets requires a z-dependent From the same figure we see that while reionization
fesc =f0[(1+z)/7]αwithα>0,whichprovidesenoughpho- starts off at a slower rate for mx = 5 and 3keV WDM,
tons at high-z to obtain the right optical depth τ , whilst it “catches up” fairly quickly due to the slower z-decline
es
yieldingreasonablylown˙ionvaluesatlatertimes;wechoose of fesc that results in a larger number of ionizing photons;
f andαforeachDMmodelsuchthatboththeconstraints indeed, the IGM is 50% by z (cid:39) 11.5−12.5 in these mod-
0
are satisfied simultaneously. The fact that one requires ion- els. As expected, the progressive lack of low-mass galaxies
izing sources with higher efficiency to match the two data means there is a slightly (almost no) stalling of the reion-
setshasbeennotedearlier(seee.g.,Mitraetal.2011,2012). ization process in the 5(3)keV WDM scenario resulting in
WithrespecttoCDM,thenumberdensityofthe(lowmass) aquickerendtoreionization:indeed,reionizationisoverby
galaxiesoccupyingthefaintendoftheUVLF(MUV ∼> −11) a z (cid:39) 6 (8.5) in the 5(3)keV WDM scenario, having taken
isincreasinglysuppressedwithredshiftastheWDMparticle
massdecreasesfrom5to3 keV.Thismustbecompensated
3 It is, however, possible to obtain a τes∼>0.062 for the mx =
2.25 keVcase,whileatthesametimematchthen˙ion constraints
2 Note, however, that the constraints on τes from atz=6,ifwechoosef0=1.2andα=8.2.Thesewouldthenbe
the recent (12/2014) Planck data seem to have been consistentwiththelatest(12/2014)Planckresults.Wealsofind
(tentatively) revised to τes = 0.079 ± 0.017, see that the mx = 1.5keV WDM gives τes ∼ 0.062 in the unlikely
http://www.cosmos.esa.int/web/planck/ferrara2014 for scenariothatconstantfesc=1,i.e.,thenewPlanckresultswould
details.Inthatcaseonemaybeabletoreconcilethe mx=2.25 possiblyweakenthelowerlimiton mx from2.25keV to1.5keV
keV case with CMB data by choosing fesc (cid:38) 0.3 which yields ifweassumedeveryionizingphotonproducedby1.5keVgalaxies
τes∼>0.062. tohavecontributedtoreionization.
(cid:13)c 0000RAS,MNRAS000,000–000
Reionization in CDM and WDM 7
videabout30%(65%)ofthetotalionizingphotonsinCDM
(2.25keV WDM). From the same panel, we see that the
UV suppression of low mass halos leads to a flattening in
their fractional contribution for CDM. However, the frac-
tionalcontributionoflowmasshalosrisesmuchmoresteeply
withdecreasing m sincehaloscollapseatscaleslargerthan
x
that affected by the UVB.
We now express the fractional contribution of galaxies
in terms of observables including the stellar mass, and UV
magnitude (panels b and c in Fig. 5). We find that galax-
ies with M∗ ∼> 107M(cid:12) contribute 20% to the total ionizing
photon emissivity in CDM. Given that forthcoming instru-
ments like the JWST will be able to detect galaxies with
M∗ ∼> 107.5M(cid:12) (Fig. 4; Dayal et al. 2014b; Pawlik et al.
2011), our results imply that the bulk (∼ 80%) of the stel-
larmassresponsibleforproducingreionizationphotonswill
likely not be directly detectable. As explained above, the
contribution to the total ionizing emissivity rises with de-
creasing mx,withM∗ ∼> 107M(cid:12)galaxiescontributingabout
∼ 65% to the total for the 2.25keV model. From the same
panel, we see that galaxies with M∗ ∼> 109M(cid:12) contribute a
negligible 2% to the total emissivity, with this value rising
Figure 4.Volumefillingfractionofionizedhydrogenasafunc- to ∼8% in the 2.25keV model.
tionofzforthe4DMmodelsconsideredusingthefiducialmodel. Finally,wefindthatgalaxiesbrighterthanM =−13
UV
As seen, reionization is progressively delayed (and its rate en-
provide∼63%ofthetotalionizingphotonsforCDMimply-
hanced)fordecreasing mx whencomparedtoCDMduetopro- ing that the rest 37% must come from even fainter galax-
gressive suppression of small scale structure. This naturally re-
ies. This value rises to about 80% for the 2.25keV model
sultsinreionizationbeingthemost“drawn-out”forCDMwhere
wherefewerlowermass/luminosityhaloscollapseintobound
theeffectsoftheUVBarefeltmoststrongly.
structures.Currentlydetectedgalaxies(MUV ∼< −18)only
contribute 6% of the total emissivity in CDM that rises to
roughly 780 (420) Myrs, as compared to CDM which re- 18%inthe2.25keVmodelwiththelattershowingasteeper
quiresabout1.02Gyrs.Adelayofaboutafewtenstoa100 z-evolution of the emissivity driven by the faster galaxy as-
Myrs in structure formation results in reionization starting sembly.
ataz(cid:39)16.5inthe2.25keVWDMscenario.Thelargerhalo Tosummarize,wefindthebulkofthereionizationpho-
masses result in this model being independent of the feed- tons come from galaxies with Mh ∼< 109M(cid:12), M∗ ∼< 107M(cid:12)
backeffectsofreionization,resultinginasmoothz-evolution and −18∼< MUV ∼< − 13 in CDM. The progressive sup-
of QII from completely neutral to ionized in the 520 Myrs pression of low-mass halos with decreasing mx leads to
between z (cid:39) 16.5 to 6.7. In principle, these different sce- a shift in the “reionization” population to larger (halo
narios could be distinguished with future 21cm cosmology and stellar) masses of Mh ∼> 109M(cid:12) and M∗ ∼> 107M(cid:12) for
surveys with next-generation facilities such as the Square mx ∼> 3keV WDM, although the UV limits effectively re-
Kilometre Array (SKA). main unchanged.
The next question that needs to be answered concerns
the main reionization sources in these 4 DM models, for
which we calculate the fractional contribution to the to-
4 CONCLUSIONS AND DISCUSSION
tal ionizing emissivity at z (cid:39) 5 from galaxies in varying
halomass,stellarmassandUVmagnitudebinsasshownin Although the Cold dark matter (CDM) paradigm has been
Fig. 5. Starting with the halo mass (panel a), we find that enormously successful in explaining the large scale struc-
CDMgalaxieswithMh ∼> 109M(cid:12)provideonlyabout35%of tureoftheUniverse,itshowsanumberofsmallscaleprob-
the total ionizing photons, with the dominant contribution lems that can be alleviated by invoking (keV) Warm Dark
coming from lower halo masses. As noted, small mass halos Matter (WDM) particles that erase small scale power, sup-
are increasingly suppressed with decreasing m in WDM pressing the formation of low-mass structures. Given that
x
models which leads to an increase in the fractional contri- the low-mass high-z galaxies are believed to be the main
bution of Mh ∼> 109M(cid:12) galaxies. Indeed, their contribution contributors to the process of cosmic reionization, our aim
increasesfrom50to63toa80%,as m decreasesfrom5to is to use reionization tracers including the Planck CMB
x
3to2.25keV.Asexpectedfromthedecreasingnumberden- electron-scatteringopticaldepth(τ )andthemeasuredion-
es
sitieswithincreasingMh,thecontributionofMh ∼> 1010M(cid:12) izingphotonemissivity(n˙ion)toputconstraintsonthemass
halosislower(∼4%forCDM)andshowsthesametrendof (m ) of WDM particles. We use a merger-tree based semi-
x
increasing with decreasing m , to ∼ 15% for the 2.25keV analyticmodelthattracestheDMandbaryonicassemblyof
x
model; this implies galaxies with M (cid:39) 109−10.5M pro- high-z (z(cid:39)5−20)galaxiesin4DMcosmologies:CDMand
h (cid:12)
(cid:13)c 0000RAS,MNRAS000,000–000
8
Figure 5.FractionalcontributiontothecumulativeHIionizingphotondensityatz=5bygalaxiesofdifferenthalomasses(Mh;left
panel), stellar masses (M∗; middle panel) and UV magnitude bins (MUV; right panel) for the fiducial DM models considered in this
paper, as marked. Left panel: the solid and dashed lines show the contribution from galaxies with x∼>109 and 1010.5M(cid:12), respectively.
Middle panel: the solid and dashed lines show the contribution from galaxies with x∼>107 and 109M(cid:12), respectively. Right panel: the
solidanddashedlinesshowthecontributionfromgalaxieswithx∼< −13and−18,respectively.
WDMwith m =2.25,3and5keV.Ourmodelincludesthe onciling these two data sets requires a z−dependent f =
x esc
key baryonic processes of star formation, SN feedback and f (1+z)α which provides enough photons at early times to
0 7
the merger/accretion/ejection driven evolution of gas and obtaintherightτ value,whilstyieldinglown˙ valuesat
es ion
stellar mass, and has been shown to fit observables over 7 later times. We find that simultaneously fitting to the two
magnitudes (including the UV LFs, M/L ratios and SMD) reionization data sets requires f = (1.65,1.25,1.2)% and
0
usingonlytwoz andmass-independentfreeparameterswith α = (5.4,6.8,8.2) for CDM and m = 5,3keV WDM, re-
x
fiducialvaluesof3.8%forthemaximumstarformationeffi- spectively.Weusethesamevaluesfor2.25keV asfor3keV
ciency and 10% of the SN energy going into unbinding gas sincetheformerneverreachestherequiredτ value.Quan-
es
(Dayaletal.2014a,b).Inthiswork,weusethestellarmass titatively,wefindf (cid:39)1.4%atz(cid:39)6forallmodels,rising
esc
assemblydrivenionizingphotonoutputfromthesetheoret- to 50% at z (cid:39) 12,11,10 for CDM, 5 and 3keV WDM, re-
ical galaxies to model the reionization history. We include spectively.
theeffectofexternalfeedback,i.e.,anevolvinghomogeneous Asaresultofthepresenceofthemostsmall-scalestruc-
UVB suppressing the baryonic content of galaxies below a ture, reionization starts earliest in CDM, and is 50% com-
thresholdmass(Mh (cid:39)109M(cid:12))toexploretheWDMmasses pletebyz(cid:39)13.Thereafter,therisingUVBsuppressesstar-
allowedbyreionizationconstraints.Theonlyadditionalpa- formation in the very halos that drive reionization drawing
rameterintroducedisthefractionofionizingphotons(fesc) out its end stages. Indeed, reionization is “photon-starved”
that escape out of galaxies and ionize the IGM. inCDMandtakesatotalofaboutaGyrtogofromacom-
Wefindthat mx ∼< 2.25keVWDMmodelsareruledout pletely neutral to ionized IGM. While the progressive lack
because they yield τes values lower than that measured by ofsmall-scalestructureleadstoadelayinthestartofreion-
Planck even in the (unlikely) case that all the H I ionizing ization with decreasing mx, it also transpires that existing
photonsproducedbyeverygalaxyescapeintotheIGM(i.e. galaxiesarelessaffectedbytheUVBleadingtoanenhanced
fesc = 1). Thus, using a model that incorporates the key rate in its progress. While the latter effect is dominant for
physicsdrivingthebaryoniccontentofhigh-z galaxies(star mx ∼> 3keV resulting in reionization lasting for about 780
formation/feedback/mergers) yields a limit of mx ∼> 3keV and 420 Myrs for mx = 5 and 3keV respectively, reioniza-
that is competitive with results of mx ∼> 3.3keV obtained tion lasts for about 580 Myrs in the 2.25keV model, given
using the Lyman-α forest (Viel et al. 2013).4 its lack of low-mass halos.
We also find that while constant values of fesc ∼> 0.5 Finally, we find that the bulk of H I ionizing photons
fit the observed τes for CDM and mx ∼> 3keV WDM, a come from galaxies with Mh ∼< 109M(cid:12), M∗ ∼< 107M(cid:12) and
constant fesc value severely over-predicts the emissivity by −18∼< MUV ∼< −13 in CDM. The progressive suppression
about1.6(1.9)ordersofmagnitudeforfesc =0.2(0.5).Rec- oflow-masshaloswithdecreasing mx leadstoashiftinthe
“reionization”populationtolarger(haloandstellar)masses
of Mh ∼> 109M(cid:12) and M∗ ∼> 107M(cid:12) for mx ∼> 3keV WDM,
4 Theconstraintsobtainedfromreionizationmodelscould,how- although the UV limits effectively remain unchanged.
ever, weaken to mx∼>1.5keV in case the bounds on τes are re- We end with a few caveats. Firstly, we have ignored
vised,e.g.,asinthelatest(12/2014)Planckresults. SN radiative losses that could significantly reduce the to-
(cid:13)c 0000RAS,MNRAS000,000–000
Reionization in CDM and WDM 9
tal energy available to drive winds. However, a decrease in Bowler R. A. A. et al., 2014a, ArXiv e-prints
this total energy could be countered by scaling up the frac- Bowler R. A. A. et al., 2014b, MNRAS, 440, 2810
tion of the total energy we put into driving winds from the Boyarsky A., Ruchayskiy O., Iakubovskyi D., Franse J.,
fiducial value of 10% used in this work. Secondly, Pawlik 2014, Phys.Rev.Lett., 113, 251301
et al. (2009) have shown that UVB photo-heating reduces Boylan-Kolchin M., Bullock J. S., Kaplinghat M., 2012,
theclumpingfactoroftheIGMsincetheadditionalpressure MNRAS, 422, 1203
supportfromreionizationsmoothesoutsmall-scalesdensity Bradley L. D. et al., 2012, ApJ, 760, 108
fluctuations. While we have used their results for an over- Bromm V., Yoshida N., 2011, ARA&A, 49, 373
density of 100, we have confirmed that our results do not BulbulE.,MarkevitchM.,FosterA.,SmithR.K.,Loewen-
change using threshold values of 50, or 200. Thirdly, while stein M., et al., 2014, Astrophys.J., 789, 13
we assume that all halos with mass Mh ∼< 109M(cid:12) are feed- CaluraF.,MenciN.,GallazziA.,2014,MNRAS,440,2066
back suppressed, we find our results are equally consistent Castellano M. et al., 2010, A&A, 524, A28
with observations (τes and n˙ion) using values ranging be- Choudhury T. R., Ferrara A., 2005, MNRAS, 361, 577
tween 108.5 −109.5M(cid:12). Finally, we have made the simpli- Choudhury T. R., Ferrara A., 2006, MNRAS, 371, L55
fying assumption of using a mass-independent fesc at all z. Choudhury T. R., Ferrara A., 2007, MNRAS, 380, L6
This is partly motivated by the uncertainty regarding the ChoudhuryT.R.,FerraraA.,GalleraniS.,2008,MNRAS,
mass-dependence of fesc: while some authors find fesc to 385, L58
decrease with an increase in the halo mass (Razoumov & Ciardi B., Ferrara A., 2005, Space Sci. Rev., 116, 625
Sommer-Larsen 2010; Yajima et al. 2011; Ferrara & Loeb Cole S. et al., 2005, MNRAS, 362, 505
2013), other works have found the opposite trend (Gnedin DayalP.,FerraraA.,DunlopJ.S.,PacucciF.,2014a,MN-
etal.2008;Wise&Cen2009).Althoughthereareanumber RAS, 445, 2545
ofcaveatsinvolved,ourmodelfitsobservedUVLFsatfaint DayalP.,MesingerA.,PacucciF.,2014b,ArXiv:1408.1102
endvalidatingthetheoreticalunderlyingstellarpopulation. deSouzaR.S.,MesingerA.,FerraraA.,HaimanZ.,Perna
Unless the results on LBG faint-end or τes evolve signifi- R., Yoshida N., 2013, MNRAS, 432, 3218
cantly, our results rule out mx ∼< 2.25keV WDM models. de Vega H. J., Sanchez N. G., 2010, MNRAS, 404, 885
Significant progress is expected to be made by comparing Ferrara A., Loeb A., 2013, MNRAS, 431, 2826
our model predictions with actual faint LBG data such as Gnedin N. Y., Kravtsov A. V., Chen H.-W., 2008, ApJ,
thatimminentlyexpectedfromtheFrontierFields,andfrom 672, 765
forthcoming observatories such as the JWST. Furthermore, Governato F. et al., 2014, ArXiv e-prints
if the claim of 3.5 KeV X-ray line holds to be true, it will Haardt F., Madau P., 2012, ApJ, 746, 125
usher in an exciting era for WDM dominated cosmology. Hinshaw G. et al., 2013, ApJS, 208, 19
Kang X., Maccio` A. V., Dutton A. A., 2013, ApJ, 767, 22
KlypinA.,KravtsovA.V.,ValenzuelaO.,PradaF.,1999,
ApJ, 522, 82
ACKNOWLEDGMENTS
Kuhlen M., Faucher-Giguere C.-A., 2012, MNRAS, 423,
PD acknowledges the support of the Addison Wheeler Fel- 862
lowship awarded by the Institute of Advanced Studies at Lange A. E. et al., 2001, Phys. Rev. D, 63, 042001
Durham University and of the European Research Council. Leitherer C. et al., 1999, ApJS, 123, 3
VB acknowledges support from NSF grant AST-1413501. Maccio`A.V.,PaduroiuS.,AnderhaldenD.,SchneiderA.,
TheauthorsthankA.Taylor,M.Vielforhelpfuldiscussions Moore B., 2012, MNRAS, 424, 1105
and A. Mazumdar for help with understanding the particle McLure R. J. et al., 2013, MNRAS, 432, 2696
physics behind WDM. McLure R. J., Dunlop J. S., Cirasuolo M., Koekemoer
A. M., Sabbi E., Stark D. P., Targett T. A., Ellis R. S.,
2010, MNRAS, 403, 960
MitraS.,ChoudhuryT.R.,FerraraA.,2011,MNRAS,413,
REFERENCES
1569
AbazajianK.,AceroM.,AgarwallaS.,Aguilar-ArevaloA., MitraS.,ChoudhuryT.R.,FerraraA.,2012,MNRAS,419,
Albright C., et al., 2012 1480
BarkanaR.,HaimanZ.,OstrikerJ.P.,2001,ApJ,558,482 Moore B., Quinn T., Governato F., Stadel J., Lake G.,
Barkana R., Loeb A., 2001, Phys. Rep., 349, 125 1999, MNRAS, 310, 1147
Benson A. J. et al., 2013, MNRAS, 428, 1774 NavarroJ.F.,FrenkC.S.,WhiteS.D.M.,1997,ApJ,490,
BlumenthalG.R.,FaberS.M.,PrimackJ.R.,ReesM.J., 493
1984, Nature, 311, 517 Oesch P. A. et al., 2010, ApJ, 709, L16
Bode P., Ostriker J. P., Turok N., 2001, ApJ, 556, 93 Oesch P. A. et al., 2013, ApJ, 773, 75
Bolton J. S., Haehnelt M. G., 2007, MNRAS, 382, 325 Pacucci F., Mesinger A., Haiman Z., 2013, MNRAS, 435,
Bond J. R., Szalay A. S., 1983, ApJ, 274, 443 L53
Bouwens R. J. et al., 2010, ApJ, 725, 1587 Parkinson H., Cole S., Helly J., 2008, MNRAS, 383, 557
Bouwens R. J. et al., 2011, ApJ, 737, 90 PawlikA.H.,Milosavljevi´cM.,BrommV.,2011,ApJ,731,
Bouwens R. J. et al., 2014, ArXiv:1403.4295 54
(cid:13)c 0000RAS,MNRAS000,000–000
10
Pawlik A. H., Schaye J., van Scherpenzeel E., 2009, MN-
RAS, 394, 1812
Peebles P. J. E., 1971, Physical cosmology
Planck Collaboration et al., 2014a, A&A, 571, A1
Planck Collaboration et al., 2014b, A&A, 571, A16
RazoumovA.O.,Sommer-LarsenJ.,2010,ApJ,710,1239
Schneider A., Anderhalden D., Maccio` A. V., Diemand J.,
2014, MNRAS, 441, L6
SchultzC.,On˜orbeJ.,AbazajianK.N.,BullockJ.S.,2014,
ArXiv:1401.3769
Sheth R. K., Tormen G., 1999, MNRAS, 308, 119
SlosarA.etal.,2013,J.CosmologyAstropart.Phys.,4,26
Somerville R. S., 2002, ApJ, 572, L23
Songaila A., Cowie L. L., 2010, ApJ, 721, 1448
Subramanian K., Cen R., Ostriker J. P., 2000, ApJ, 538,
528
TeyssierR.,PontzenA.,DuboisY.,ReadJ.I.,2013,MN-
RAS, 429, 3068
VielM.,BeckerG.D.,BoltonJ.S.,HaehneltM.G.,2013,
Phys. Rev. D, 88, 043502
Viel M., Lesgourgues J., Haehnelt M. G., Matarrese S.,
Riotto A., 2005, Phys. Rev. D, 71, 063534
Weinberg D. H., Bullock J. S., Governato F., Kuzio de
Naray R., Peter A. H. G., 2013, ArXiv e-prints
Wise J. H., Cen R., 2009, ApJ, 693, 984
Wyithe J. S. B., Bolton J. S., 2011, MNRAS, 412, 1926
Wyse R. F. G., 2001, in Astronomical Society of the Pa-
cific Conference Series, Vol. 230, Galaxy Disks and Disk
Galaxies, Funes J. G., Corsini E. M., eds., pp. 71–80
Yajima H., Choi J.-H., Nagamine K., 2011, MNRAS, 412,
411
(cid:13)c 0000RAS,MNRAS000,000–000
