Modeling of Lyman-alpha Emitting Galaxies and Ionized Bubbles at the Era of Reionization

0.42 MB·

by  Hidenobu Yajima

Draftversion January23,2017
PreprinttypesetusingLATEXstyleemulateapjv.8/13/10
MODELING OF LYMAN-ALPHA EMITTING GALAXIES AND IONIZED BUBBLES AT THE ERA OF
REIONIZATION
Hidenobu Yajima1,2, Kazuyuki Sugimura2, Kenji Hasegawa3,
1FrontierResearchInstitute forInterdisciplinarySciences,TohokuUniversity,Sendai,Miyagi980-8578, Japan
2AstronomicalInstitute, TohokuUniversity,Sendai,Miyagi980-8578,Japanand
3GraduateSchoolofScience,NagoyaUniversity,Furo-cho,Chikusa-ku,Nagoya, Aichi464-8602, Japan
7
Draft version January 23, 2017
1
0 ABSTRACT
2
UnderstandingLyα emitting galaxies(LAEs)canbe a keyto revealcosmicreionizationandgalaxy

n formation in the early Universe. Based on halo merger trees and Lyα radiation transfer calculations,
a we model redshift evolution of LAEs and their observational properties at z 6. We consider
J ≥
ionized bubbles associated with individual LAEs and IGM transmission of Lyα photons. We find

9 that Lyα luminosity tightly correlates with halo mass and stellar mass, while the relation with star
1 formation rate has a large dispersion. Comparing our models with the observed luminosity function
by Konno et al. (2014), we suggest that LAEs at z 7 have galactic wind of V & 150 kms−1
out
] and Hi column density of N & 1020 cm−2. Numbe∼r density of bright LAEs rapidly decreases as
A HI
redshiftincreases,due to bothlowerstarformationrateandsmallerHii bubbles. Our modelpredicts
G
futurewidedeepsurveyswithnextgenerationtelescopes,suchasJWST,E-ELTandTMT,candetect
. LAEs at z 10 with a number density of n a few 10−6 Mpc−3 for the flux sensitivity of
h 10−18 ergcm∼−2s−1. By combining these surveLyAsEw∼ith future×21-cm observations, it could be possible
p
to detect both LAEs with L & 1042 erg s−1 and their associated giant Hii bubbles with the size
- Lyα
o &250 kpc at z 10.
∼
r Subject headings: radiative transfer – line: profiles – galaxies: evolution – galaxies: formation –
t
s galaxies: high-redshift
a
[

1 1. INTRODUCTION 2000; Iye et al. 2006; Gronwall et al. 2007; Ouchi et al.
2008, 2010; Bond et al. 2011; Ciardullo et al. 2012;
v One of the major challenges in today’s astronomy is
Yamada et al. 2012). Ouchi et al. (2010) indicated
1 revealing cosmic reionization history with galaxy evolu-
7 tion. Recent CMB observations suggested cosmic reion- that LAEs were hosted in halos with the halo mass
5 ization occurred at z 8 11 (Komatsu et al. 2011; Mh ∼ 1011 M⊙ by the clustering analysis (see also,
5 Planck Collaboration et∼al. 2−014, 2016). Gunn-Peterson Gawiser et al. 2007). Verhamme et al. (2008) suggested
0 tests by the observations of high-redshift QSOs indi- that LAEs were not dust-enriched well yet so that Lyα
. photons escaped from galaxies against dust attenua-
1 cated cosmic reionization completed at z 6 (e.g.,
∼ tion (see also, Yajima et al. 2014). These suggest LAEs
0 Fan et al. 2006). However, the ionization history of
are likely to be in the early phase of galaxy evolu-
7 integer-galacticmedium(IGM)hasnotbeenunderstood
tion (e.g., Mori & Umemura 2006). In addition, LAEs
1 yet. Recent observations of high-redshift galaxies at
are one of major populations of galaxies contributing
: z & 7 are gradually unveiling the cosmic star formation
v the cosmic star-formation density in the early Universe
history (Ouchi et al. 2010; Bouwens et al. 2012, 2015;
i (Ciardullo et al. 2012).
X Oesch et al. 2015, 2016), and have allowed us to spec-
LAEs also have been used as a tool to investigate
ulate the cosmic reionization history (Robertson et al.
r
the early Universe (Iye et al. 2006; Vanzella et al. 2011;
a 2015). Yet, even considering the above observational
Ono et al. 2012; Shibuya et al. 2012; Finkelstein et al.
constraints, various reionization histories remain viable
2013;Zitrin et al.2015;Song et al.2016b). Numberden-
(Cen 2003; Yajima & Khochfar 2015). One of the main
sityofLAEsrapidlydecreasesatz &7(Ono et al.2012;
uncertaintiesislow-massgalaxyformationwiththe halo
massMh lessthan∼1012 M⊙. Duetotheirhighernum- Kgaolanxnioesetwaerl.e2s0i1g4n)ifi,cinadnitclaytaintgtetnhuaatteLdyαdufleuxtoesnferuotmraslohmye-
ber density and the higher escape fraction of ionizing
drogen in the IGM (e.g., Kashikawa et al. 2006). Mean-
photons from them (Razoumov & Sommer-Larsen 2010;
while, LAEs themselves could provide sufficient ionizing
Paardekooperet al.2013;Yajima et al.2011,2014),low-
photons into the IGM (Yajima et al. 2009, 2014), and
mass galaxies can be responsible for main ionizing
someof themcouldmake giantHiibubbles thatallowed
sources. However, the detection sensitivities of current
Lyα photons to reach us. In this case, galaxies can be
observationsarenotsufficienttoconstraintheformation
observed as LAEs. In practice, the most distant LAE
of low-mass galaxies. Therefore it is important to the-
has been observed even at z = 8.68 (Zitrin et al. 2015).
oretically investigate the formation of low-mass galaxies
Thus,LAEscanbe the keyobjectsinunderstandingthe
and their contribution to cosmic reionization.
galaxy formation and cosmic reionization.
Mostofhigh-redshiftlow-massgalaxiesareobservedas
Inthiswork,weinvestigatetheevolutionofLAEswith
Lyαemitters(LAEs;Hu & McMahon1996;Steidel et al.
their associated Hii bubbles. By modeling both LAEs
[email protected] and Hii bubbles simultaneously, we estimate Lyα lumi-
nosityfunctions(LFs),numberdensityofLAEs,sizedis- The relation between stellar and halo mass can be
tribution of Hii bubbles, and the relation between Lyα written as dMstar = dlogMstar Mstar. The abundance
flux and the size of Hii bubble. These estimations are matching anadlMyshis by BdelohgrMoohziMethal. (2013) indicated
uSspeafcuelTfoerlesfcuotpuree(JoWbsSeTrv)aitsiognoainlgmtiossbioenlas.unJchaemdeastW20e1b8b, that ddlologgMMsthar ∼ const for Mh . 1012 M⊙. In addi-
and aims to observe galaxies at z 10. Its high sensi- tion, Behroozi & Silk (2015) showed the weak depen-
tivityofspectroscopywillmakeitp∼ossibletodetectLyα dence of Mstar on halo mass and redshift at the mass
bflluexs.frLomategraolanx,ie3s0-imf thcleayssdgisrtoruibnudteteilnescgoiapnets,HtihiebEubu-- range Mh M∼h1011 −1013 M⊙, although MMsthar increases
ropean Extremely Large Telescope (E-ELT), the Thirty with Mh at Mh . 1011 M⊙ (see also, Moster et al.
2013; Kravtsov et al. 2014). Therefore we here assume
Meter Telescope (TMT), and the Giant Magellan Tele-
scope (GMT), will investigate galaxies at z 10 sta- dMstar const. Thus, we estimate SFR from the growth
tistically. In addition, several 21-cm observat∼ional mis- radtMehof∼halo mass with a constant tuning parameter α,
sionsareongoing,e.g.,theLOwFrequencyARray(LO- i.e., SFR = αdMh. In order to estimate the growth
dt
FAR; Harker et al. 2010), and Murchison Widefield Ar- of halos, we use halo merger trees based on an ex-
ray (MWA; Lonsdale et al. 2009). In future, Square tended Press-Schechter formalism (Somerville & Kolatt
Kilometer Array phase-2 (SKA-2; Dewdney et al. 2009) 1999;Khochfar & Burkert2001,2006). Thehalomerger
will perform large-scale 21-cm tomography. Since 21- trees include 5000 realizations with the halo mass range
cm emission comes from Hi gas, detections of holes of of 109 1013 M⊙ at z = 6. In this work, we al-
21-cm signal indicate giant Hii bubbles around galaxies. low star−formation only for halos with the mass M >
h
Therefore, a combination of 21-cm and galaxy observa- 108 M⊙, because star formation in less massive halos
tions will provide fruitful information about the cosmic can be significantly suppressed due to UV background
reionizationandgalaxyformation(e.g.,Lidz et al.2009). or internal stellar feedback (e.g., Okamoto et al. 2008;
Theoretically large-scale simulations showed that Hasegawa & Semelin 2013). In deriving statistical prop-
galaxies made patchy ionization structures in an inside- erties, e.g., cosmic SFR density, stellar mass density
out fashion (e.g., Iliev et al. 2006, 2012; Mellema et al. and LF, we sum the contribution of each merger tree
2006;Trac & Cen2007;Ocvirk et al.2016),whereaslow- with normalizationfactorsthat reproduce the halo mass
density void regions would be ionized first, in the so- function of Sheth & Tormen (2002). We determine the
calledoutside-infashion,ifAGNswerethemainionizing tuning parameter by using observed cosmic SFR den-
sources. However, AGNs are unlikely to be main ion- sity and stellar mass density at z 7 8. Figure 1
izing sources because of the rapid decrease of observed shows our modeled SFR and stellar∼mas−s density with
number density at redshift z > 4 (e.g., Richards et al. observations. We choose the parameter α by the least
2006), although the contribution of faint AGNs is still squarefittingtothe fourpointsofthe observations. The
underthedebate(Madau & Haardt2015;Yoshiura et al. observed SFR and stellar mass densities consider only
2016). Thus, in this paper, we model LAEs assuming galaxies with MUV < 17 and Mstar 108 M⊙, respec-
the reionization model with the inside-out fashion. In tively. Therefore, we c−onsider only th≥e galaxies satisfy-
ordertounderstandcosmicreionizationtheoretically,we ing the above criteria for the fitting. The best fit value
need high spatial resolutionto follow the detailed physi- is α=3.3 10−3. Note that, so far there is no available
calprocesses ofinterstellar medium, as well as largevol- data about×dMstar at z & 9 and α can change with halo
ume to consider large-scale inhomogeneity of ionization dMh
mass and redshift. However, for simplicity, we assume
structure. Even current numerical simulations cannot
α is constant. Following the above way, we derive star
resolve such a wide dynamic range. For that reason,
formation history from each halo merger tree.
in this work, we semi-analytically investigate the cos-
We also derive UV LFs by converting SFR to UV
mic reionization and galaxy formation based on simple
structure formationmodels and radiative transfer calcu- flux with Lν,UV = 0.7 × 1028 erg s−1 1 MS⊙FRyr−1
lations. We use the cosmological parameters, ΩΛ = 0.7, (Madau et al.1999). Figure2showsourmo(cid:16)deledLFsa(cid:17)t
ΩM =0.3, Ωb =0.045 and h=0.7(Komatsu et al. 2011; z 7and 8with thosefromthe recentobservationby
Planck Collaboration et al. 2016). Bo∼uwens e∼t al. (2015). The observationindicated that a
The paper is organized as follows. We describe our part of UV flux are absorbed by dust with the escape
models of star formation and Hii bubbles in 2. In 3, fraction f 0.6. Our modeled LFs match the ob-
wepresenttheresults,whichincludetheLyαp§roperti§es, servationewsce,lUlVwi∼th the same UV escape fraction.
LFsofLAEsandredshiftevolutionofnumberdensityof Galaxies ionize the IGM as star formation proceeds.
LAEs. We discuss the relation between the Lyα flux of Inaone-zoneapproximation,weestimatetimeevolution
galaxiesandthesizesofHiibubblesin 5,andsummarize of cosmic ionization degree (Barkana & Loeb 2001),
§
in 6.
§ dQ 1
HII = n˙γ f α C(1+z)3n0Q , (2)
2. MODEL dt n0H ion esc,ion− B H HII
Inthecurrentstandardpictureofstructureformation, where Q is the volume fraction of Hii, n0 is the
halos grow via minor/major mergers. In our model, the present-dHaIyIhydrogennumberdensity( 2 10−H7cm−3),
star formation rate (SFR) in a halo is assumed to be n˙γ is the intrinsic ionizing photon em∼iss×ivity per unit
proportional to the growth rate of the halo as follows: ion
volume, α is the case-B recombination rate, C is a
B
clumpiness factor of IGM, and f is escape fraction
dM dM dM esc,ion
star star h
SFR= = . (1) of ionizing photons, which is a free parameter here. We
dt dM dt
h
2
estimate n˙γ from star formation history of each halo
ion
byusingStarburst99withtheSalpeterinitialmassfunc-
tion with the metallicity of 10−2 Z⊙. The reionization
history is shown in the upper panel of Figure 3. As
f increases, the IGM is ionized earlier. We as-
esc,ion
sume the recombination rate for T = 104 K (α =
B
2.6 10−13 cm3 s−1)andC =3,as suggestedby numer-
×
ical simulations (Pawlik et al. 2009; Jeon et al. 2014).
Thecosmicreionizationhistoryisregulatedbyf .
esc,ion
Free electrons produced by the cosmic reionization con-
tribute to the Thomson scattering optical depth (τ ) of
e
CMB photons, defined as
zrec dt
τ = σ n (z)c dz, (3)
e T e
dz
Z0 (cid:12) (cid:12)
(cid:12) (cid:12)
where zrec = 1100 is the redshift (cid:12)at t(cid:12)he time of recom-
(cid:12) (cid:12)
bination. In this work, we assume the single ionization
fraction of helium is the same as the one for hydrogen
at z 3, and the double ionization takes place at z < 3
≥
(e.g.,Wyithe et al.2010;Inoue et al.2013). Recentsim-
ulations show that indeed the fraction of Heii is close
to the Hii fraction at high redshifts, although the ion-
Figure 1. Upper panel: Star formation rate density. Red
ization fraction of helium is slightly lower than the one line represents our modeled star formation history based on the
for hydrogen (Ciardi et al. 2012). The top panel of Fig- halo merger trees. Triangle symbols show the observation by
ure 3 represents the ionization history of hydrogen gas Bouwensetal.(2015). Theobservedstarformationratedensities
areestimatedbyintegratingtheluminosityfunctionsintherange
with the different fesc,ion. The bottom panel of Figure 3 ofMUV≤−17. Ourmodelalsoconsideronlythegalaxiesbrighter
shows τe with different fesc,ion. The Thomson scatter- thanthesamelimitingmagnitude. Lowerpanel: Stellarmassden-
ing optical depth τ increases with redshift in a way de- sity. Redlineisthecumulatedstellarmassofourmodelconsidering
pending on f edue to the different ionization histo- only the galaxies with Mstar ≥ 108 M⊙. Triangle symbols show
esc,ion theobservationbySongetal.(2016a),whointegratedthederived
ries. We find fesc,ion = 0.2 nicely reproduces the CMB stellarmassfunctionsforgalaxieswithMstar≥108 M⊙.
observation (Planck 2016). Therefore, in this work, we
adopt f = 0.2 with no redshift evolution. In fact,
esc,ion
Yajima et al.(2014)showedf isconstantwithred-
esc,ion
shift and 0.2 by cosmological simulations with radia-
∼
tive transfer calculations.
3. RESULTS
3.1. Evolution of ionized bubbles around galaxies
We follow the growth history of Hii bubbles around
individual galaxies with the star formation efficiency α
and f estimated above. Sizes of Hii bubbles evolve
esc,ion
with ionizing photon emissions, recombination, and cos-
mic expansion as follows (Cen & Haiman 2000):
dR3 3N˙γ f
HII =3H(z)R3 + ion esc,ion Cn (z)α R3 ,
dt HII 4πn (z) − H B HII
H
(4)
where H(z) is the Hubble constant at specific redshifts,
and N˙γ is intrinsic ionizng photon emissivity of each
ion
galaxy. The ionizing fronts can propagate up to the
Stro¨mgren radius during the recombination time scale
(Spitzer 1978). The recombination time scale is t
rec
1 0.5 Gyr 1+z −3, which is longer than th∼e
αBnH ∼ 11
typical time scale over which SFR changes more than
(cid:0) (cid:1)
factor 2. Therefore, Hii bubbles do not reach the
∼
equilibrium state, and we need to consider SFR history
to estimate the sizes of Hii bubbles at given redshifts.
Figure 2. UV luminosity functions. Open squares and circles
We estimate probability distribution function (PDF) of
represent observed LBGs at z ∼ 7 and ∼ 8 by Bouwens etal.
the sizes of ionized bubbles (RHII) as shown in Fig- (2015).
ure 4. In our model, higher mass halos tend to pos-
sess larger ionized bubbles. Due to the decrease in the
number density of halos on the high-mass end of a halo
3
Figure 3. Upperpanel: Ionizationhistory. Differentlinesshow
ionizationhistorieswithdifferentescapefractionsofionizingpho-
tons. Lower panel: Thomson scattering optical depth. Different Figure 4. Probabilitydistributionfunctions ofsizesofHiibub-
lines are estimated with different ionization histories presented in bles associated with individual galaxies. Vertical dash lines are
the upper panel. Yellow shade represents the estimation by the correspondingtotheviewingangleof1arcmin.
CMBobservation(PlanckCollaborationetal.2016).
scattering process. However, if dust mainly distributes
mass function (Sheth & Tormen2002), the PDF ofRHII in Hi gas clumps, fesc,Lyα does not become lower than
rapidly decreases at larger RHII. Although the ioniz- fesc,UV because Lyα photons are scattered by hydrogen
ing front does not reach the size of Stro¨mgren sphere on surface of the clumps before interacting with dust.
drsitca∝tor(N˙oiγfons)i1z/e3s(1of+Hzi)i−b2,ubitblceasn. bAesurseeddshasiftadreocurgehasiens-, fCoirarodbuslelroveetdaLl.A(E2s01a2t)zindic2a.teIdntahdadtitfieosnc,,Lycαos∼mofleosgci,UcaVl
the IGM density decreases while the number density of simulations of Yajima et∼al. (2014) showed that f
esc,Lyα
massive halos with higher ionizing photon emissivity in- was & 0.6 and similar to f at z & 6. Therefore, in
esc,UV
creases. Therefore, the tail of PDF in the large-RHII this work, we assume that fesc,Lyα =fesc,UV =0.6.
end shifts to larger R at lower redshift. Future 21 Next, we estimate IGM transmission as a function of
HII
cm observations, e.g., SKA-2, is supposed to probe the wavelength. As in Cen & Haiman (2000), we divide the
IGM ionization structure with the angular resolution of paths along which Lyα photons travel from galaxies to
1′. Therefore,atz .10,the tail ofPDFatlargeR us into the two parts, i.e., outside and inside ionized
HII
∼
can be observationally investigated in future. The halo bubbles,andseparatelyestimate eachcontribution. The
numberdensitymonotonicallyincreasesasthehalomass transmission outside ionized bubbles is estimated as fol-
decreasesatafixedredshift. Sincethe sizeofHiibubble lows:
is positively related with halo mass as will be shown in zi dt
Section 3.3, it seems that the PDFs in the small-RHII τ(λobs,zs)= dzc nH(z)xHIσLyα[λobs/(1+z)],
end monotonically increase as RHII decreases. However, Zzr dz
there are peaks in the PDFs, below which they decrease (6)
amsaRssHfIoIrdestcarerafsoersm. aTthioisnisimcapuosseeddbinytthhiestwhroerskh.oldofhalo where zi ∼ zs − RHIIR×H(1+z). Here, zr is redshift when
the cosmic reionization completes, which we set z = 6,
r
z is redshift when Lyα photons pass through ionizing
3.2. Lyα luminosity functions i
front,z isredshiftofgalaxy,σ isthescatteringcross
s Lyα
Absorptionofionizing photons by interstellar medium sectionfor Higas,andR is the size ofthe cosmological
H
within galaxies results in Lyα emissions via recombina- horizon at z . We assume the outside of the bubble is
s
tion processes, while escaped photons cause the cosmic completely neutral, i.e., x = 1. The σ is estimated
HI Lyα
reionization as shown in the previous section. The Lyα by (Verhamme et al. 2006)
luminosity (L ) is estimated by
Lyα −1
T 2 H(x,a)
LLyα =0.68(1.0−fesc,ion)fesc,LyαǫLyαN˙iγon, (5) σLyα[λ]=1.041×10−13 104 K √π . (7)
(cid:18) (cid:19)
where f is the escape fraction of Lyα photons
esc,Lyα We set T = 104 K in this work. Here, H(x,a) is the
from galaxies, ǫ = 10.2 eV is the energy of a Lyα
Lyα Voigt function,
photon. The escape fraction of Lyα photons f
esc,Lyα
can be lower than fesc,UV because the path length of a +∞ e−y2
Lyα photons until escape can be longer due to multiple H(x,a)= dy (8)
π (x y)2+a2
Z−∞ −
4
where x (ν ν )/∆ν , ν = 2.466 1015 Hz is ies by combining cosmologicalSPH simulations with ra-
0 D 0
≡ − ×
the line-center frequency, ν is the Doppler width, a = diationtransfercalculations. Thesecolumndensities are
D
∆ν /(2∆ν ), ∆ν = 9.936 107 Hz is the natural line optically thick to ionizing photons, hence not consistent
L D L
×
width. We here use the fitting formula of H(x,a) given with f = 0.2. However, recent simulations showed
esc,ion
by Tasitsiomi (2006). ionizing photons mostly escape along ionized holes cre-
Even inside ionized bubbles, a tiny fraction of neutral ated by radiative and SNe feedback (e.g., Yajima et al.
hydrogensexist. WeestimatetheIGMtransmissionfrom 2009, 2011; Kimm & Cen 2014). Thus, f of 20 %
esc,ion
ionizing front to virial radius with the neutral fraction can be considered as the fraction of viewing angle along
under the ionization equilibrium state, which star forming regions are not covered by Hi gas.
For simplicity, we do not take account of the effect of
C r 2 N˙γ −1 1+z 3 such holes on line profiles. Note that, however,Lyα line
xHI =1.5×10−5(cid:18)3(cid:19)(cid:18)kpc(cid:19) 1050iosn−1! (cid:18) 8 (cid:19) . porroofitlheesrsdoemtaeiwlehdasttrcuhcatnugreeidnuHeitogatsh(eDhijoklsetsr,ac&lumKprainmeessr
(9) 2012).
Notethat,theopticaldepthoutsidetheionizedbubbleis The shaded regions in Figure 6 represent the LFs us-
dominant in our work. The IGM transmission is mostly ing different Lyα line profiles with the velocity range
almost zero at λ . λ , where λ = 1216 ˚A is the wave- from V = 300 km s−1 to 300 km s−1. The best
0 0 out
length of Lyα line center. fit velocities a−re 180 km s−1 (model A), 190 km s−1
ConsideringtheIGMtransmission,wederiveLyαLFs, (model B), and 110 km s−1 (model C), as summarized
and compare them with the observation of Konno et al. in Table 1. Only model A with the velocity range
(2014). Depending on the shape of Lyα line profile, the V 150 300 km s−1 can reproduce the observed
out
IGM transmission significantly changes. Even with re- LF w∼ell. Th−erefore we suggest LAEs are likely to have
centdeepspectroscopies,however,itisdifficultto deter- high Hi column density with & 1020 cm−2 and outflow-
mine intrinsic Lyα line profiles, i.e., before the IGM ex- ing Hi gas with velocity &150 km s−1. The Lyα profile
tinction (e.g., Ouchi et al. 2010). The intrinsic Lyα line monotonically shifts to redder one as the outflow veloc-
profiledependsonthephysicalnatureofgalaxies,e.g.,Hi ity increases in model A as shown in Figure 5. On the
column density and velocity field (e.g., Verhamme et al. otherhand,asthe Hicolumndensity decreases,the Lyα
2006). In this work, we calculate intrinsic Lyα line pro- profilemovesbacktothelinecenterfrequencyatspecific
filesbyLyαradiationtransfersimulationsusingthecode velocity of < 300 km s−1. This is because Lyα photons
developed in Yajima et al. (2012b), and study the phys- canescapefromthecloudbeforeshiftingtolongerwave-
ical nature of LAEs through the comparison with the lengthdue to loweropticaldepth. In this work,the best
observation (Konno et al. 2014). The intrinsic line pro- fit velocities for model B and C roughly correspond to
files are calculated based on spherically outflowing gas those producing the Lyα profiles shifted farthest away.
cloud models with the following velocity structure, In addition, the width of line profile becomes smaller as
the Hi column density decrease. Even with the best fit
r
velocities, the number densities of LAEs in the model B
V(r)=V , (10)
out
R and C are smaller than the observation because of the
(cid:18) edge(cid:19)
narrower line profiles resulting in lower IGM transmis-
where Redge is the edge of the spherical cloud and Vout sion. Hence, in order to get higher IGM transmission to
is the outflow velocity at Redge. Although the simu- reproduce the LF, LAEs are likely to have the column
lated profiles do not depend on Redge, here we consider densityhigherthan 1020 cm−2. Thus,inthiswork,we
Redge Rvir. Figure 5 shows the modeled line profiles consider model A as∼our fiducial model.
∼
with various outflowing velocities. The Lyα line profiles Emergent Lyα line profiles are shown in Figure 7.
get the asymmetric shape with a peak at redder wave- As Hi column density decreases, intrinsic Lyα line pro-
lengthfortheoutflowvelocityfield,becauseLyαphotons filesbecomenarrowerandpeakpositionsshifttoshorter
at bluer wavelength are scattered by Hi gas due to the wavelength. IGM transmission increases with wave-
Doppler shift. As NHI increases, the line profiles are ex- length because photons with long wavelength redshift
tended, and the peak frequency shift farther from the early to avoid from being scattered by the IGM, while
line center frequency. For the inflow velocity field, the Lyαfluxneartheline centeris reducedefficiently bythe
Lyα line profile becomes the mirror symmetric shape to IGMscattering. FWHMsoftheemergentlineprofilesare
the one for outflow with the same absolute value of the 1.5˚A(modelA),8.9 10−1˚A(modelB)and5.2 10−2˚A
velocity. × ×
(model C). Therefore it is difficult to distinguish the
With the simulated intrinsic line profiles, we can esti-
different column density models in the current spectro-
mate Lyα LFs for given N and V . In this work, we
HI out scopicobservationwiththeresolutionofR 1000 2000
infer typical N and V of LAEs by comparing mod- ∼ −
HI out (e.g., Shibuya et al. 2012). Future high-dispersion spec-
eled LFs with the observed one by Konno et al. (2014).
troscopies with R 2000, e.g., Prime Focus Spectro-
Figure 6 show the LFs. Here we calculate the LFs for ≫
graph on Subaru or JWST, will be able to reveal the
three Hi column density models, N = 2 1020 cm−2
HI detailed shape of profile.
(model A), N = 2 1019 cm−2 (mo×del B), and
HI Line profiles in inflowing gas models result in the un-
NHI = 2 1018 cm−2 (×model C). The column density derproductionof observable LAEs, because mostof Lyα
×
of model A is corresponding to Damped Lyman-α Sys- photonsarescatteredbytheIGM.Thisisconsistentwith
tems (DLAs: Wolfe et al. 2005). Yajima et al. (2012a) the observation by Ouchi et al. (2010), which indicated
showed that DLAs distributed at lines of sight passing LAEs at z =6.6 are likely to have outflowing gas by the
star-forming regions in high-redshift star-forming galax-
5
Figure 5. Lyα line profiles from expanding spherical gas clouds with the velocity field as V(r) = Vout(cid:16)Rerdge(cid:17), where Redge is the
radius of clouds and Vout is the velocity at Redge. The different panels show the Lyα profiles considering different Hi column densities:
NHI = 2×1020 cm−2 (panel A), 2×1019 cm−2 (panel B), and 2×1018 cm−2 (panel C). The different lines represent the different
expanding velocities at Redge. The φ(λ) is normalized to be unity when it is integrated over the wavelength. The φ(λ) of panel (B) and
(C)isartificiallyreducedbyafactor2and10.
composite spectrum. In addition, Shibuya et al. (2014) minosity and R tightly correlate with M . The
HII star
measuredoutflowvelocitiesofindividualLAEs atz 2, L -M relationdoesnotchangewith redshiftsignif-
Lyα star
∼
andindicatedthatLAEswerelikelytohaveoutflowwith icantly,while theR -M becomessmallerasredshift
HII star
V &150 kms−1. increases. ThisisbecauseHubble constant(i.e.,expand-
out
Next we estimate the redshift evolution of LF based ing velocity of IGM) becomes large at higher redshift.
onthe modelA with V =180kms−1. Figure8 shows Therefore, although R decreases as redshift increases
out HII
the modeled LFs at z =7,8,10 and 12. Note that, here due to higher IGM density, the IGM transmission does
weusethesamelineprofileforallhalosandredshift. At not decreases significantly. Thus, Lyα luminosity does
higherredshifts,typicalSFRissmallerduetolowerhalo not depend sensitively on redshift.
mass and halo growth rate. In addition, as redshift in- The detection sensitivity of recent observations of
creases,typicalsizeofHiibubblesdecreases,resultingin LAEsatz 7 8wascorrespondingtoLyαluminosityof
the lowerIGM transmission. As a result, the LF rapidly &3 1042∼erg−s−1 (Ono et al.2012;Shibuya et al.2012;
×
shifts to the fainter side at higher redshifts. Finkelstein et al.2013;Vanzella et al.2011;Konno et al.
2014;Zitrin et al.2015). Inourmodel,medianandmin-
3.3. Relation between Lyα luminosity and stellar mass
imum stellar masses producing L 3 1042 erg s−1
Lyα
Figure 9 shows the sizes of Hii bubbles and Lyα lumi- at z =7.3 are 6.5 109 and 1.5 108∼M⊙×, respectively.
nosities considering the IGM transmission. Lyα proper- × ×
Therefore, by considering the relation M 3.3
star
ties are calculated by using the Lyα profile of model A. 10−3 M , we suggest that the observed LAEs at∼z =7×.3
h
Tplhe.eWsheadseesertehpartesReHntIItthieghrtalnygceoorrfe2l5a%te−w7it5h%stienlltahremsaamss-, tshheoumldedbieanhohsatleodminahssalioss1w.9ith1M01h2≥M4⊙.6. ×1010 M⊙,and
as R M1/3, while the relation with SFR shows a ×
HII ∝ star 3.4. Redshift evolution of number density of observable
large dispersion.
LAEs
SFR rapidly increase by major merger. However,
R is not so sensitive to the short-time fluctuation So far the Lyα line has been used as the most strong
HII
of SFR because of the longer time-scale for reaching tool to confirm the redshift of distant galaxy candidates
the ionization equilibrium state. As a result, the rela- (e.g.,Iye et al. 2006; Finkelstein et al. 2013; Zitrin et al.
tion between R and SFR shows the large dispersion. 2015). However,itiswidely thoughtthatLAEsatz >9
HII
High-redshift galaxies have been observed as so-called are difficult to be detected because of the IGM opac-
Lyman-break galaxies (LBGs: Bouwens et al. 2012), via ity. Here, we estimate the number density of LAEs
the Lyman-break technique so far. Our results indicate (n ) with higher Lyα flux than specific thresholds.
LAE
LBGs at z & 7 with similar UV brightness can have Figure 10 shows the number density of LAEs with
different Lyα fluxes due to the scatter of IGM transmis- F 10−17,10−18 and 10−19 erg s−1 cm−2. The
Lyα
≥
sion. At z = 15, our sample is limited by the stellar detection limits of current observations with a reason-
mass of galaxies Mstar 109 M⊙. In our model, since able integration time are 10−17 erg s−1 cm−2 (e.g.,
∼ ∼
the stellar mass is simply proportional to halo mass as Shibuya et al. 2012). As explained in Sec. 3.2, the
M 3.3 10−3 M , this means that there is no pro- number density of bright LAEs monotonically decreases
star h
genito∼rs wit×h Mh & 3 1011 M⊙ at z = 15 in our halo with increasing redshift. Given the detection limits of
sample,whichisconstr×uctedtohavethemassrangefrom 10−17 ergs−1 cm−2,widefieldsurveysof 1003 Mpc3 are
109 to 1013 M⊙ at z =6. able to detect LAEs up to z 8.5. This is consistent
∼
In contrast to the SFR-R relation, both Lyα lu- with recent observed LAEs at z . 9 (Finkelstein et al.
HII
6
Figure 6. Lyα luminosity functions (LFs) at z =7.3. Square symbols represent the observed LF of LAEs at z =7.3 by Konnoetal.
(2014). DifferentpanelsshowmodeledLFsbasedonLyαlineprofilestodifferentHicolumndensities. Magentaandcyanshadesshowthe
rangeofLFsconsideringLyαlineprofilewithdifferentoutflow andinflowvelocitywiththerange0∼±300kms−1. Blacksolidlinesare
bestfittedones totheobservation. Blackdashlineintheleftpanel showstheLFbeforeconsideringIGMtransmission.
Figure 8. Lyα luminosity functions at z = 7.3,8,10 and 12.
OpensquaresshowobservedLAEsatz=7.3(Konnoetal.2014).
200 km s−1, the number density of LAEs with F
Lyα
10−18 erg s−1 cm−2 at z 10 is a few 10−6 Mpc−≥3.
Figure 7. Lyα lineprofiles. Red solidlines show emergent line AsshowninFigure9,brig∼htLAE∼sarehos×tedinmassive
profiles of a halo of 5.9×1011 M⊙ at z=7.3, which evolves to a halos. The median halo and stellar mass of LAEs with
halo of 1.0×1012 M⊙ at z = 6.0. Intrinsic Lyα luminosity of F 10−18 erg s−1 cm−2 at z = 10 are 1.1 1012
the halo is 1.3×1043 ergs−1. Emergent luminosities after IGM Lyα ≥ ×
transmissionareshowninthepanels. Blackdashlinesaretheline and 3.5 109 M⊙, respectively. It was suggested that
×
profilesbeforeconsideringIGMtransmission. the observed LBG at z = 11.1, GNz11, had the stellar
mass of 109 M⊙ (Oesch et al. 2016), which is corre-
sponding∼to F 0.2 10−18 erg s−1 cm−2 in our
Lyα
2013; Oesch et al. 2015; Zitrin et al. 2015). The LAEs model. Hence, it w∼ill be c×hallenging to detect Lyα flux
with FLyα 10−17 at z 10 are quite rare, with from GNz11 even by future spectroscopies with the line
n 1 ≥2 Gpc−3. ∼ sensitivity of F 10−18 erg s−1 cm−2.
LAE Lyα
∼ − ∼
Spectroscopies of next generation telescopes, e.g., Different line profile models predict different number
JWST, are supposed to achieve the sensitivity of densities of observable LAEs. The IGM transmission
10−18 erg s−1 cm−2 with a reasonable integration tim∼e. becomes more sensitive to the intrinsic Lyα line profile
If galaxies at z 10 have outflowing gas with v & models, since the typical size of Hii bubbles gets smaller
∼
7
Table 1
Modelparameters
Model NHI/cm2 Vout/kms−1
A 2×1020 180
B 2×1019 190
C 2×1018 110
fesc,ion=0.2
fesc,UV =0.6
fesc,Lyα=0.6
NOTES.—ForeachHicolumndensity, theoutflow velocityis
chosentoreproducetheobservedluminosityfunctionofLAEat
z=7.3(Konnoetal. 2014). Escapefractionsofionizing,UVand
Lyαphotons aresameforallmodels.
we estimate the total kinetic energy of outflowing gas as
Figure 9. Upper panel: Sizes of Hii bubbles as a function of
stellarmassandSFR.Green,redandbluelinesrepresentmedian 1M V2 f e N GMhMgas. (11)
values to galaxies at z = 8,10 and 15, respectively. The shades 2 gas out ∼ conv SN SN− R
show quartiles at each bin. Lower panel: Lyα luminosity as a vir
functionofstellarmassandSFR.
Here M = (1 ǫ)M0 is gas mass after star forma-
gas − gas
tion, M = ǫM0 is stellar mass, M0 is initial gas
star gas gas
mass, ǫ M /M0 is a star formation efficiency with
with increasing redshift. As a result, the difference of ≡ star gas
respecttotheinitialgasmass,f istheconversioneffi-
conv
n amongmodelA,BandCbecomeslargerathigher
LAE ciencyfromtotalsupernovaenergyto kinetic one ofgas,
redshift, and more than order unity at z 10. Future e 2 1051 erg is the releasedenergy for eachsuper-
∼ SN
observation would also allow us to discriminate intrinsic ∼ ×
nova (e.g., Hamuy 2003), and N is the number of su-
SN
line profiles,whichinturnprovideinformationaboutHi pernova. For Salpeter-like IMF, N 1 10−2Mstar =
column density and outflow velocity, by comparing the SN ∼ × M⊙
observed number density of LAEs with the theoretical 1 10−2 ǫ Mgas. By using the star formation effi-
models. × 1−ǫ M⊙
Even next generation telescopes, e.g., GMT, E-ELT, ciency ǫ, w(cid:16)e sim(cid:17)ply estimate Vout as
TMT, will be difficult to have the sensitivity of
10−19 erg s−1 cm−2. However,if future telescopes some∼- V2 +v2 1.4 103 km s−1 ǫ 12 f12 , (12)
how achieve such a high sensitivity, wide field surveysof out esc ∼ × 1 ǫ conv
1003 Mpc3 would be able to reach LAEs at z 12. q (cid:18) − (cid:19)
∼In this work, we consider isolated Hii bubble∼s asso-
ciated with individual LAEs in the estimation of IGM where vesc ≡ 2RGvMirh is the escape velocity of a halo.
transmission. However, at lower redshift, Hii bubbles Next we obqtain fconv as a function of ǫ. Recently
can be overlapped each other (e.g., Iliev et al. 2012; Kim & Ostriker(2015)showedthefinalmomentumpro-
Hasegawa & Semelin 2013; Ocvirk et al. 2016). The duced by a single SN with the energy of 1051 erg as
soivoenr.laTppheisdeHffieictbuwbiblllebseciannveesntihgaantceedtihneHIaGsMegatwraanesmt aisl-. follows: p = 2.8 × 105 kms−1 M⊙ 1 cnmH−3 −0.17 (see
also, Cioffi et al. 1988; Thornton et al. 1998). In this
(in preparation) by combining large-scale N-body with (cid:0) (cid:1)
work, we ignore the weak density dependence and as-
small scale radiative-hydrodynamicssimulations.
sume n 1 cm−3. Since the final momentum is al-
H
∼
4. DISCUSSION most linearly proportional to the injected SN energy
(Cioffi et al. 1988; Kimm & Cen 2014), we approximate
4.1. Condition for galactic outflow from LAEs
the total momentum produced by multiple SNe as fol-
As shown in Section 3.2, high-redshift LAEs are likely lows: P = p eSNNSN , where e N is the total en-
to have galactic wind with V & 150 km s−1. Here 1051 erg SN SN
we roughly derive the conditioonutfor making gas outflow ergy of super(cid:16)novae. (cid:17)Therefore, using E = P2 , we
with V & 150 km s−1 in a spherical gas cloud model. 2Mgas
out derive f = E =16 ǫ . Note that f can not
Supernova (SN) feedback can be responsible for causing conv ESN 1−ǫ conv
strong outflow in high-redshift low-mass galaxies (e.g., exceed unity according t(cid:16)o the(cid:17)energy conservation. For
Kimm & Cen 2014; Kimm et al. 2015). In the assump- that reason, we set f = 1 at ǫ 0.06 because the
conv
≥
tion that supernovae give feedback to all gas uniformly, above expression gives f > 1. Thus, Equation 12 is
conv
8
Figure 10. Number density of LAEs as a function of redshift. Red, blue and green lines show the number densities of LAEs with
FLyα ≥ 10−18 ergcm−2s−1 obtained assuming Lyα line profiles of model A, B and C, respectively. Black dash and dot lines are the
number density of LAEs with FLyα ≥ 10−17 ergcm−2s−1 and FLyα ≥ 10−19 ergcm−2s−1 obtained assuming the Lyα line profile of
modelA.
written by using ǫ as follows: tend to have higher ionizing photon emissivity and in-
trinsic Lyα luminosity for a fixed size of Hii bubbles at
5.5 103 km s−1 ǫ higherredshift. Thecombinationoftheseeffectsleadsto
× 1−ǫ the weak redshift dependence in the L -R relation.
qVo2ut+ve2sc ∼1.4×103 km s−1 (cid:16)1−ǫǫ(cid:17)12if ǫ<0.06 foofrT≥hze1yealrlco1mw0.isnhaaTdnhedidstrhreeeggifloionunxrecopofrrer≥seesnp1to0sn−Ltd1yh8sαeetvroigHewItsIhi−ne1gLcamAngE−l2es
(cid:16) (cid:17)if ǫ 0.06. with as∼sociated Hii bubbles that are detectable both as
 ≥ (13) LAEs and holes in 21-cm signal by future galaxy ob-
We find that the condition of ǫ 0.04 is required to servations by JWST and 21-cm tomography by SKA-
cause the galactic outflow with V ∼ = 180 kms−1 from 2, respectively. Future 21-cm observations will be able
out
a halo with Mh = 4.6 1010 M⊙ at z = 7.3 which is to probe giant Hii bubbles around bright LAEs with
minimum halo mass to×produce the observable Lyα lu- F &10−18 erg s−1 cm−2 at z 10.
Lyα
minosity 3 1042 erg s−1. We can also convert the The differential brightness tem∼perature δT caused
b
∼ ×
tuning parameter α in our star formation model to ǫ, by galaxies shows inner positive and outer negative
as ǫ αΩ /Ω 0.02. This is roughly similar to the ring-like structure (e.g., Chen & Miralda-Escud´e 2004;
M b
∼ ∼
value estimated above. As halo mass increases, higher ǫ Yajima & Li 2014). The detailed structure depends on
is required to cause galactic outflow. Here we have es- SED. If galaxies host X-ray sources like AGNs, the pos-
timated ǫ assuming all gas has same outflow velocity in itive region is extended due to partial photo-ionization
the simple spherical cloud model. For example, in the heating. Therefore, future 21-cm observations may also
caseofdiskgalaxies,onlyapartofgascanbe evacuated give us information about nature of X-ray and UV
along the normal direction to galactic disk as shown in sources in bright LAEs.
numerical simulations (e.g., Agertz et al. 2011). In this
case, strong outflow can be caused even with smaller ǫ 5. SUMMARY
because piled gas mass can be lower.
We present models of Lyα emitting galaxies (LAEs)
with IGM transmission considered at the era of reion-
4.2. Relation between Lyα luminosity and size of ization. Based on halo merger trees and a simple star
ionized bubble
formationmodel,we estimate cosmicstarformationand
LAEscanbe responsiblefor ionizingsourcesofcosmic cosmic reionization history. Our model uses 5000 real-
reionization (e.g., Yajima et al. 2009, 2011, 2014). Fig- izations of halo merger trees with the halo mass range
ure 11 showsLLyα as a function ofthe size ofassociated from Mh = 109 to 1013 M⊙ at z = 6. As a result,
Hii bubble R . The Lyα luminosity steeply increases our model reproduces the observed cosmic star forma-
HII
with R due to higher IGM transmission for large Hii tion densities, stellar mass densities, luminosity func-
HII
bubbles. The relation between L and R does not tions of Lyman-break galaxies with a tuning parameter,
Lyα HII
significantly change with redshift. IGM gas density in- α( SFR/dMh)=3.3 10−3. Our modeled star forma-
creases with redshift as ρ (1+z)3, resulting in lower tio≡n history,dwtith an es×cape fraction of ionizing photons
∝
IGM transmission at higher redshift. However, galaxies f =0.2, also provides a cosmic reionizationhistory
esc,ion
9
numerical simulations were performed on the computer
cluster, Draco, at Frontier Research Institute for Inter-
disciplinary Sciences of Tohoku University. This work
is supported in part by MEXT/JSPS KAKENHI Grant
Number 15H06022 (HY) and 15J03873(KS).
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ACKNOWLEDGMENTS
Jeon,M.,Pawlik,A.H.,Bromm,V.,&Milosavljevi´c,M.2014,
We thank Akira Konno and Masami Ouchi for pro- MNRAS,440,3778
viding us their recent observational data. We are Kashikawa,N.,Shimasaku,K.,Malkan,M.A.,Doi,M.,Matsuda,
Y.,Ouchi,M.,Taniguchi,Y.,Ly,C.,Nagao,T.,Iye,M.,
grateful to Masayuki Umemura, Akio Inoue, Yoshiaki
Motohara,K.,Murayama,T.,Murozono,K.,Nariai,K.,Ohta,
Ono, Takatoshi Shibuya, Daisuke Nakauchi and Sadegh
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Khochfar for valuable discussion and comments. The ApJ,648,7
10