Sub-millimeter brightness of early star-forming galaxies
aa r X i v : . [ a s t r o - ph . C O ] N ov Mon. Not. R. Astron. Soc. , 1–9 (2011) Printed 14 November 2018 (MN L A TEX style file v2.2)
Sub-millimeter brightness of early star-forming galaxies
Hidenobu Yajima ⋆ , Masayuki Umemura , Masao Mori Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Lab, University Park, PA 16802, USA Center for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Japan
Accepted ?; Received ??; in original form ???
ABSTRACT
Based on a three-dimensional model of an early star-forming galaxy, we explorethe evolution of the sub-millimeter brightness. The model galaxy is employed froman ultra-high-resolution chemodynamic simulation of a primordial galaxy by Mori& Umemura, where the star formation rate (SFR) is ∼
10 M ⊙ yr − at t age . . ⊙ yr − at t age > . T dust &
35 K. In the LBG phase, the continuous supernovae drive dust grains faraway from star-forming regions. Then, the grains cannot absorb much radiation fromstars, and becomes into a cold state close to the CMB temperature. Consequently,the dust temperature decreases with the evolutionary time, where the mass-weightedmean temperature is T dust = 26 K at t age = 0.1 Gyr and T dust = 21 K at t age =1.0 Gyr. By this analysis, it turns out that the sub-millimeter brightness is higher inthe LAE phase than that in the LBG phase, although the dust-to-gas ratio increasesmonotonically as a function of time. We derive the spectral energy distributions byplacing the model galaxy at a given redshift. The peak flux at 850 µ m is found to be S ∼ . − . > z >
2. This means thatALMA can detect an early star-forming galaxy with SFR of ∼
10 M ⊙ yr − by lessthan one hour integration with 16 antennas. Key words: radiative transfer – ISM: dust, extinction – galaxies: evolution – galaxies:formation – galaxies: high-redshift – methods: numerical
Exploring the properties of early star-forming galaxies is oneof key themes to elucidate the galaxy formation process. Thefashion of star formation in galaxies can significantly changedust properties. In young galaxies, type-II supernovae cre-ate dust, and also change the dust size and component(Dwek 1998; Todini & Ferrara 2001; Bianchi & Schneider2007; Nozawa, Kozasa, & Habe 2006; Nozawa et al. 2007).In addition, UV radiation from young stars is effectively ab-sorbed by dust and therefore determines the temperatureof dust grains. Besides, the dust can affect the star forma- ⋆ E-mail: [email protected](HY); [email protected](MU);[email protected](MM) tion efficiency itself via hydrogen molecule formation and thecooling by thermal emission. Accordingly, dust propertiessuch as amount, temperature, size and composition shouldtightly correlate with the star formation history. Hence, un-derstanding the dust properties is a significant issue in thestudy of galaxy evolution.So far, the sub-millimeter (sub-mm) flux from dis-tant galaxies has been detected at redshifts of 0 . −
4. These galaxies are called sub-mm galaxies (SMGs)(e.g., Smail, Ivison, & Blain 1997; Hughes et al. 1998;Barger et al. 1998; Eales et al. 1999; Ivison et al. 2000;Daddi et al. 2009). However, the observed galaxies are lim-ited to extremely luminous starburst galaxies, where the starformation rate (SFR) is ∼ ⊙ yr − , from the restric-tion by the detection limit of the facility (e.g., Borys et al. c (cid:13) Yajima et al. .
100 M ⊙ yr − ) at high redshifts (which mean z & ∼ . −
100 M ⊙ yr − ) like Lyman alpha emitters (LAEs)and Lyman break galaxies (LBGs) by using newly devel-oped facilities (Tamura et al. 2009; Stanway et al. 2010).Although Tamura et al. (2009) did not detect notable sub-mm flux from LAEs and LBGs in the SSA22 region withinthe detection limit of S ∼ z ∼ < .
85 mJy from stacked data. Hence, withrecent sub-mm telescopes (e.g. Hershel, AzTEK), it seemsvery difficult to detect sub-mm flux from high-z star-forminggalaxies with SFR <
100 M ⊙ yr − . Moreover, the determi-nation of dust temperature is a hard task in the obser-vational study, because it requires the flux data at manywavelengths in sub-mm band. Hence, one often assumes thedust temperature to speculate spectral energy distributions(SED). Then, the estimation of L IR by integrating specu-lated SED suffer from the uncertainty of the assumed dusttemperature. The uncertainty leads to the misestimation ofSFR and dust amount. A theoretical model may help torelate the observed sub-mm flux with the dust propertiesin star-forming galaxies. Such attempts have been made byseveral authors (e.g., Takagi, Vansevicius, & Arimoto 2003;Dayal, Hirashita, & Ferrara 2010). Takagi et al. (2003) con-structed an SED model of dusty star-forming galaxiesby solving the radiative transfer in spherical symmetry.Dayal et al. (2010), based on cosmological SPH simulations,employed homogeneous distributions of stars and dust inan identified LAE. Recently, Mori & Umemura (2006) haveshown through ultra-high-resolution numerical simulationsthat interstellar media in early star-forming galaxies becomequite clumpy as a result of multiple supernovae. Hence,to construct the SED for early star-forming galaxies, it isimperative to solve three-dimensional radiative transfer inclumpy interstellar media.Here, we theoretically explore the dust amount andtemperature in star-forming galaxies by solving three-dimensional radiative transfer, based on a chemodynamicsimulation of a primordial galaxy by Mori & Umemura(2006). Since the model galaxy well reproduces the observedproperties of Lyman alpha emitters (LAEs) at t age . . t age > . H = 70km s − Mpc − , Ω M = 0 . Λ = 0 .
7. In §
2, the modeland numerical method are described. In §
3, the results ondust properties in early star-forming galaxies are presented.In §
4, the detectability by ALMA is discussed. § Our model galaxy is a supernova-dominated star-forminggalaxy simulated by an ultra-high-resolution (1024 fixedCartesian grids) chemodynamics calculation coupled withthe collisionless dynamics of star particles. The simulationpursues the early evolution ( < × years) of a primevalgalaxy as an assemblage of sub-galactic condensations of5 . × M ⊙ , building up a system with the total mass of10 M ⊙ [see Mori & Umemura (2006) for the simulationdetails].The star formation rate (SFR) of the model galaxy is11 M ⊙ yr − at t age = 0 . ⊙ yr − at t age = 0 . ⊙ yr − at t age = 0 . ⊙ yr − at t age = 1 Gyr. The metal and dust in the galaxy is enrichedby the continuous type II supernovae due to vigorous starformation, and exhibits complex inhomogeneous dust distri-butions (figure 1 in Yajima et al. 2009).According to the Lyman α luminosity, the early evolu-tionary stage is divided into two phases: one is the LAE-phase ( t age . . t age > . α emission comes fromthe cooling radiation by interstellar gas, and the luminosityreaches 2 . × erg s − at t age = 0 . . × erg s − at t age = 0 . t age > . α luminosity quickly declines to several 10 erg s − that is lower than the detection limit, and theSED is dominated by stellar continuum. This phase appearslike LBGs. The model galaxy at this phase has stellar age( ∼ − × yr) and mass ( ∼ − × M ⊙ ) similarto typical LBGs at z ∼
3, while it is older and more mas-sive than typical LBGs at z & z & Spitzer
IRAC, and show the similar age and massto our model galaxy (Eyles et al. 2007; Stark et al. 2009).Therefore, our model galaxy at a later phase is probablycorresponding to typical LBGs for z ∼
3, and a massivesubset of LBGs for z & The radiation from young stars propagates in the highlyinhomogeneous interstellar media containing dust. We com-pute the three-dimensional radiative transfer (RT) of stellarradiation to derive the dust temperature. The RT calcula-tions are done as the post-processing for each evolutionarystage of model galaxy. For the purpose, the data of the hy-drodynamic simulations are coarse-grained into 128 Carte-sian grids.The RT scheme used in this paper is the Authentic Ra-diation Transfer (ART) method which is originally devel-oped by Nakamoto, Umemura, & Susa (2001). The proce-dure is basically the same as that in Yajima et al. (2009);Yajima, Choi, & Nagamine (2011). Our ART method isbased on the long-characteristic method. Usually, the short-characteristic method is computationally less costly thanthe long-characteristic method, by an order of N which isa grid number in the linear dimension. However, the short-characteristic method suffers from numerical diffusion effect. c (cid:13) , 1–9 ub-millimeter brightness of early star-forming galaxies The ART method is devised to reduce the computationalcost to a level similar to the short-characteristic method withkeeping the accuracy equivalent to the long-characteristicmethod. Hence, the present method allows us to calculatethe transfer of radiation from a large number of sources.In this work, the RT equation is solved along 16384 rayswith uniform angular resolution from each star particle. Thenumber of star particles is 3 − . × . Hence, we carryout the RT calculation for ∼ − rays for each snapshot.We map individual star particles to nearest grids, and setradiation rays in an isotropic fashion from each star particle. We distribute the interstellar dust in proportion to themetallicity, assuming the size distribution of dn d /da d ∝ a − . (Mathis, Rumpl, & Nordsieck 1977), where a d is theradius of a dust grain. We suppose the grain size in therange of 0 . − . µ m as our fiducial model. The dust massin a cell is calculated by a following simple relation betweenmetallicity and dust (Draine et al. 2007), m d = 0 . m g ZZ ⊙ , (1)where m d , m g , and Z are the dust mass, gas mass, andmetallicity in a cell. The density in a dust grain is assumedto be that of silicate-like grains, 3 g cm − . The optical depthby dust is given by dτ dust = Z Q ( a d , ν ) πa (cid:18) dn d da d (cid:19) da d ds, (2)where Q ( a d , ν ) and n d are the absorption coefficient factorand the grain number density, respectively. We adopt the Q -value of silicate grain derived in Draine & Lee (1984).Of course, there are some options for the dust model.The present dust model is motivated by the supernova dustmodel in Nozawa et al. (2007). In their model, the small dustgrains of . . µ m are readily destroyed in shock wave, sothat the typical size becomes ∼ . µ m. On the other hand,Todini & Ferrara (2001) pointed out that the typical sizecould be reduced to ∼ . µ m for the first grains in theearly universe. The number density of dust grains increaseswith decreasing dust size for the constant amount of dust,while the absorption cross section decreases with the dustsize. In Figure 1, the extinction per unit dust mass is com-pared between ∼ . µ m and ∼ . µ m dust. As seen inFigure 1, the absorption efficiency does not change appre-ciably with changing the dust size. Therefore, the infraredluminosity and dust temperature are not so sensitive to thedust size. Actually, in a test calculation for 0 . µ m dust,the temperature decreases by just a few K. The difference inthe peak flux at 850 µ m is a few per cent, because the peakof thermal emission shifts toward 850 µ m with decreasingtemperature.On the other hand, the Calzetti’s law A λ A V = . − .
857 + 1 . /λ ) + 1for 0 . µ m λ . µ m0 . − .
156 + 1 . /λ − . /λ + 0 . /λ ) + 1for 0 . µ m λ < . µ m , (3) (Calzetti et al. 2000) is frequently used for dust extinc-tion in local galaxies. In Figure 2, the extinction curve of ourdust model is compared to the Calzetti’s law. Our modelis somewhat flatter than the Calzetti’s law in UV-opticalrange. However, even if we use Calzetti’s extinction curve,the infrared luminosity does not significantly change fromour model. Actually, by a test calculation, we find that therelative difference is twenty per cent for IR luminosity, andthe difference in dust temperature is ∼ a few K. We evaluate the dust temperature T dust by solving the ra-diative equilibrium between heating by photo-absorption (Γ)and cooling by thermal emission (Λ), which are given byΓ = Z Z πJ ν Q ( a d , ν ) πa dn d da d da d dν + k CMB
Λ =
Z Z π a B ν ( T dust ) Q ( a d , ν ) dn d da d da d dν , (4)where J ν and k CMB are the mean intensity of stellar radia-tion and the heating term by CMB radiation, respectively.We simplify the right side of this equation as follows (e.g.,Evans 1994),
Z Z π a B ν ( T dust ) Q ( a d , ν ) dn d da d da dν ∼ π ¯ a n d ¯ QσT , (5)where σ is the Stefan-Boltzmann constant, ¯ a d is the meandust size weighted by the size distribution function,¯ a d = R a d dn d da d da d R dn d da d da d . (6)The ¯ Q is a mean Q -value weighted by the Planck function,¯ Q ( T dust ) = R B d ( T dust , ν ) Q (¯ a d , ν ) dν R B d ( T dust , ν ) dν . (7)Then, we obtain the dust temperature by T dust = (cid:18) Γ4 π ¯ a ¯ n d ¯ Qσ (cid:19) / . (8) In Figure 3, we present the time variation of dust compo-nent as a function of the galactic evolution time. Figure 3(a)shows the dust-to-gas mass ratio ( D ). The ratio increasesmonotonically with the galaxy evolution owing to continu-ous supernovae. D is 4 × − (corresponding to the metal-licity Z = 4 × − Z ⊙ , where Z ⊙ is the solar metallicity) at0.1 Gyr and reaches 0 . × − ( Z = 0 . Z ⊙ ) at 1.0 Gyr.Figure 3(b) shows the total dust mass in the modelgalaxy. The dust mass is 1 . × M ⊙ at 0.1 Gyr, and then(6 − × M ⊙ at > > ∼
50 per cent at t age = 1 . c (cid:13) , 1–9 Yajima et al.
Figure 1.
Dust-absorption cross-section per unit dust mass.Solid and dash lines show the cross section of 0 . µ m and 0 . µ msilicate dust, respectively. The Q-value of silicate dust is takenfrom Draine & Lee (1984). Figure 2.
The dust extinction curve. Solid and dash lines showthe dust model in this paper and Calzetti’s law (Calzetti et al.2000), respectively.
Our model shows that the metallicity reaches the levelof 0 . Z ⊙ < Z < . Z ⊙ in the late phase of LAE. Veryrecently, Nakajima et al. (2011) assessed the metallicity ofLAEs to be Z & . Z ⊙ , which is significantly higher thanwas previously thought for LAEs. This is concordant withour results.Figure 3(c) shows the radiation energy absorbed bydust, and Figure 3(d) shows the absorbed fraction to thetotal radiation energy emitted by stars. The model galaxyhas a blue SED owing to young stars, and the absorptionefficiency by dust decreases steeply with increasing wave-length. Thus, most of energy absorbed by dust is attributedto UV-optical continuum radiation from stars in the rangeof λ ∼ − Figure 4 shows the dust temperature distributions, when themodel galaxy is placed at z = 3. The dust temperature is T dust ∼
35 K near star-forming regions, while T dust ∼
10 Kfar from there. In an early phase ( t age = 0.1 - 0.3 Gyr),the high-temperature regions are distributed extensively ac-cording to the distributions of star-forming regions. In alater phase ( t age = 0.5 - 1.0 Gyr), the distributions of high-temperature dust are confined into the central regions as aresult of the dynamical evolution of star-forming regions.We statistically study the dust temperature distribu-tions. Figure 5 shows the mass fraction of dust in a giventemperature range. In an early stage, dust is confined in eachsub-halo, and therefore it is distributed near star-forming re-gions. Thus, at t age = 0 . T dust >
35 K, and the mass fraction is broadlydistributed in the range of T dust = 10 −
40 K. Thereafter,the dusty gas is blown away by supernova explosions andis distributed diffusely in the extended regions. Then, apart of dust, which is far from young stars, cannot absorbmuch radiation energy, and therefore becomes in a coolerstate. Hence, in a later phase, dust with high temperatureof T dust >
35 K disappears, and the dust temperature fallsin the range of T dust ≈ −
30 K.Figure 6 shows the mean temperature as a function ofevolution time. Filled and open circles are the mass weightedmean temperatures and the energy weighted ones, respec-tively. The mass weighted mean is ∼
24 K in the LAE phase,while ∼
20 K in the LBG phase. The energy weighted meanis ∼
31 K in the LAE phase, while ∼
26 K in the LBGphase. The high-temperature dust emits thermal radiationmore effectively than colder one owing to the higher Q-value and the strong temperature-dependence of emissivity.Hence, the energy weighted mean temperatures are higherby ∼
5K than the mass weighted ones. The mean temper-atures decline with the evolution time especially in earlyphases. This is intimately relevant to the sub-mm brightnessof the galaxy. Recently, Hwang et al. (2010) have studied thedust properties of galaxies with L IR = 10 L ⊙ in the red-shift range 0 . . z . .
8, and found the dust temperature tobe T dust ∼ −
50 K. Amblard et al. (2010) have found thatthe average dust temperature is 28 ± . ± .
6. These temperaturesare comparable to the dust temperature in our calculations.
We compute the intrinsic spectral energy distributions(SED) of the stellar component in the model galaxy by usingthe population synthesis code P´EGASE v2.0 (Fioc & Rocca1997). We place the model galaxy at several redshifts. Theinitial mass function (IMF) is assumed to be that by Salpeter(1955) in the mass range of 0 . − M ⊙ . Also, the effects bythe age and metallicity of stellar population are incorporatedby interpolating the table generated by P´EGASE. The dusttemerature is primarily determined by the UV continuumfrom OB stars with & M ⊙ . For the Salpeter IMF in therange of 0 . − M ⊙ , the mass fraction of stars with & M ⊙ is 0.267. If we suppose the range of 0 . − M ⊙ , the frac-tion is 0.287. Hence, the upper bound of mass range is notso significant on determining the dust temperature. c (cid:13) , 1–9 ub-millimeter brightness of early star-forming galaxies Figure 3. upper left : Dust-to-gas mass ratio as a function of evolution time. upper right : Total dust mass as a function of evolutiontime. The dust mass is estimated in proportion to metallicity. lower left : Radiation energy absorbed by dust as a function of evolutiontime (filled circles). Open circles are intrinsically radiated energy from stars. lower right : The absorbed fraction to the total radiatedenergy as a function of the dust mass.
In this work, at first, we derive the intrinsic SED of stel-lar component by P´EGASE, and correct the SED by incor-porating the dust extinction through three-dimensional RTsimulations. Then, we evaluate the dust temperature andthe thermal emission following the equation (7). Finally, weget the emergent SED by combining the dust absorption-corrected stellar SED with the thermal emission from dust.Fig. 7 shows the resultant SED of the model galaxy inthe observed frame after making the K-correction. As wellknown, λ & Here, we see the time variations of the sub-millimeter bright-ness, focusing on the flux at 850 µ m. Figure 8 shows thetotal flux at 850 µ m in observed frame ( S ). Interestingly,the sub-millimeter brightness is peaked at 0.3 Gyr (LAEphase), independent of the assumed redshift. As alreadyshown in Figure 3(a), the dust-to-gas ratio (metallicity) in-creases monotonically with time. But, the sub-millimeterbrightness does not increases according to the increase ofmetallicity. This is because, in the LAE phase, dust grainsare concentrated on clumpy star-forming regions and there-fore the dust grains can be effectively heated up by stel-lar radiation. On the other hand, the continuous supernovaedrive dust grains far away from star-forming regions at > . z . If the galaxy is at z .
3, the total fluxat 0.1 Gyr is smaller than that at 0.5 Gyr and 1.0 Gyr,although the total absorbed energy is nearly equal. Thisis due to the fact that the flux of 850 µ m is sensitive tothe dust temperature. The spectral shape of dust emissionis basically that of the black body, although the Q -valueaffects the shape to some degree. The temperature, whichexhibits a peak at 850 µ m in the observed frame, is 13 .
65 Kfor a galaxy at z = 3. As seen in Figure 6, the mass-weightedmean temperature declines with the evolution time, and thetemperature at 0.5 Gyr and 1.0 Gyr is closer to 13.65 Kthan that at 0.1 Gyr. Therefore, we conclude that the lowsub-mm flux in an earlier LAE phase is not attributed to thelow dust amount but rather to the higher dust temperature.For higher galaxy redshifts, the absolute flux decreases ofcourse with increasing redshift. But, the difference of theflux between 0 . µ m in the observed frame is corresponding to shorterwavelengths. Here, we assess the feasibility to detect early star-forminggalaxies with SFR of ∼
10 M ⊙ yr − by Atacama Large Mil-limeter/submillimeter Array (ALMA). In the present sim- c (cid:13) , 1–9 Yajima et al.
T(K)
10 17 35
Figure 4.
The distributions of dust temperature when the model galaxy is placed at z = 3. The color shows dust temperature. Figure 9.
The map of brightness temperature at λ = 850 µ m in the model galaxy, assuming the galaxy to be located at z = 3. Thelinear scale of each panel is 16 . . . (cid:13) , 1–9 ub-millimeter brightness of early star-forming galaxies Figure 5.
Mass fraction of dust to the total amount in a giventemperature range. The bin size is 5 K.
Figure 6.
The mean temperature of dust as a function of evo-lution time. Open and filled circles are the energy weighted meanand the mass weighted mean, respectively. ulation, the total flux of 850 µ m in the LBG phase is S = 0 . ∼ . z = 3. Somelensed LBGs have been detected at sub-millimeter, and show S = 0 .
40 mJy and
SF R ∼
10 M ⊙ yr − at z = 2 . S = 0 .
39 mJy and
SF R ∼
24 M ⊙ yr − (cB58 : Baker et al. 2004), or S =0 .
65 mJy and
SF R ∼ ⊙ yr − at z = 2 . Figure 7.
Spectral energy distributions of the model galaxy inthe observed frame after the K-correction is made. Different linestyle corresponds to a different redshift at which the model galaxyis placed (solid: z = 2, dot: z = 3, dash: z = 4, long-dash: z = 5and dot-dash: z = 6). Figure 8.
Total flux at 850 µ m in the observed frame as a func-tion of evolution time. We set the model galaxy at each redshift(circle: z = 2, triangle: z = 3, square: z = 4, cross: z = 5 andstar: z = 6).c (cid:13) , 1–9 Yajima et al. : Kneib et al. 2005). Our results match these observationswell. Also, Stanway et al. (2010) showed the upper limit ofsub-millimeter flux, S < .
85 mJy, for LBGs at z = 5.Our prediction is under their upper limit, and thereforehigher sensitivity is required to detect sub-mm flux fromLBGs at z &
5. On the other hand, there are a few brightLBGs detected at sub-millimeter which show S ∼ − SF R ∼ −
200 M ⊙ yr − (Belokurov et al. 2007;Coppin et al. 2007; Chapman & Casey 2009). These maybe more massive and dusty star-burst systems.In Fig. 9, the map of the brightness temperature at λ = 850 µ m is shown for the model galaxy placed at z = 3.The brightness temperature T b is given by T b = 11 . (cid:18) λ µ m (cid:19) (cid:18) θ × (cid:19) − (cid:18) F mJy (cid:19) mK . (9)The higher T b traces the star-forming regions. Clumpyclouds with higher T b are distributed over an extended areain the LAE phase ( t age = 0 . − . t age = 0 . − . T b in the originalresolution of simulations that corresponds to θ ∼ . T b ∼ . −
40 mK, where the high T b regions are of &
20 mK. The integration time required todetect extended sources of ∼
20 mK with the angular res-olution of θ ∼ .
13” is assessed to be ∼ ∼
13 arcsec . At a later phase, the modelgalaxy becomes as compact as ∼ . Hence, the num-ber of beams to cover the area will be quite large. Even forthe later compact phase, the required time to cover the areawill be a few hundred hours. Thus, the observations withthe angular resolution of ∼ .
13” do not seem achievable totrace the sub-mm structure for early star-forming galaxies.The lower panels of Figure 9 show T b in the coarse-grained resolution of θ ∼ . T b regions show & ∼ ∼
60 minute integra-tion. If an early star-forming galaxy is observed, some beamsmay detect sub-mm flux by the integration of less than 1hour. Thus, the detection of clumpy sub-mm features of anearly star-forming galaxy seems feasible. Moreover, obser-vations with lower angular resolution of &
1” allow us tostudy the statistics of high- z sub-mm sources, e.g., the lu-minosity function of sub-mm galaxies. ALMA will detectthe sub-millimeter flux from LBGs at z ∼ ∼
10 minuteintegration with 16 antennas. Even for a galaxy at z = 6,ALMA can detect it by ∼
60 minute integration.Recently, Dayal et al. (2011) have estimated a bit lowerflux at 850 µ m than the present prediction. They have as-sumed homogeneous distributions of stars and dust for anLAE identified in a cosmological simulation. Compared toour results, it implies that the clumpiness of star-formingregions and interstellar medium significantly contributes tothe enhancement of the sub-mm brightness. We have performed three-dimensional radiative transfer cal-culations on high-resolution hydrodynamic simulations withinhomogeneous metal enrichment. Then, we have exploredthe dust temperature and sub-mm flux in a high-redshiftstar-forming galaxy. Attention has been concentrated on thesub-mm properties of LAE and LBG phases. The star for-mation rate (SFR) is ∼
10 M ⊙ yr − in the LAE phase, andseveral M ⊙ yr − in the LBG phase. As a result, we havefound that dust grains concentrated on clumpy star-formingregions can effectively absorb UV radiation from stars in theLAE phase, and then the grains are heated up to T dust & t age ∼ . µ m. The flux is found to be S ∼ . − . > z >
2. Even for z = 6, the sub-mm flux does notdecrease largely because of negative K-correction. With an-gular resolution of θ ∼ . &
1” allow us to detect high-z sub-mmsources by ∼
10 minute integration with 16 antennas ofALMA. Therefore, we can study clumpy sub-mm featuresof an early star-forming galaxy and also the statistics of theluminosity function of sub-mm galaxies with ALMA.
ACKNOWLEDGMENTS
We are grateful to K. Nagamine, A. Inoue, Y. Miyamoto andM. Ouchi for valuable discussion and comments. We thankthe anonymous referee for useful comments. Numerical sim-ulations have been performed with the
FIRST simulator and
T2K-Tsukuba at Center for Computational Sciences, in Uni-versity of Tsukuba. This work was supported in part by the
FIRST project based on Grants-in-Aid for Specially Pro-moted Research by MEXT (16002003) and JSPS Grant-in-Aid for Scientific Research (S) (20224002), (A) (21244013),and (C) (18540242).
REFERENCES
Amblard A., et al., 2010, A&A, 518, L9+Austermann J. E., et al., 2010, MNRAS, 401, 160Barger A. J., Cowie L. L., Sanders D. B., Fulton E.,Taniguchi Y., Sato Y., Kawara K., Okuda H., 1998, Natur,394, 248Baker, A. J., Tacconi, L. J., Genzel, R., Lehnert, M. D.,Lutz, D., 2004, ApJ, 604, 125Belokurov, V., 2007, ApJ, 671, L9 c (cid:13) , 1–9 ub-millimeter brightness of early star-forming galaxies Bertoldi F., et al., 2007, ApJS, 172, 132Bianchi S., Schneider R., 2007, MNRAS, 378, 973Borys C., et al., 2004, MNRAS, 352, 759Borys C., Chapman S., Halpern M., Scott D., 2003, MN-RAS, 344, 385Calzetti, D., Armus, L., Bohlin, R. C., Kinney, A. L.,Koornneef, J., Storchi-Bergmann, T., 2000, ApJ, 533, 682Chapman S. C., Blain A. W., Smail I., Ivison R. J., 2005,ApJ, 622, 772Chapman, S. C. and Casey, C. M., 2009, MNRAS, 398,1615Coppin K., et al., 2006, MNRAS, 372, 1621Coppin, K. E. K., et al., 2007, ApJ, 665, 936Daddi E., et al., 2009, ApJ, 694, 1517Dayal P., Hirashita H., Ferrara A., 2010, MNRAS, 403, 620Draine B. T., Lee H. M., 1984, ApJ, 285, 89Draine B. T., et al., 2007, ApJ, 663, 866Dwek E., 1998, ApJ, 501, 643Eales S., Lilly S., Gear W., Dunne L., Bond J. R., HammerF., Le F`evre O., Crampton D., 1999, ApJ, 515, 518Eales S. A., et al., 2010, A&A, 518, L23Evans A., 1994, The dusty universe, Evans, A., ed.Eyles, L. P., Bunker, A. J., Ellis, R. S., Lacy, M., Stanway,E. R., Stark, D. P., Chiu, K., 2007, MNRAS, 374, 910Fioc M., Rocca V. B., 1997, A& A, 326, 950Greve T. R., Ivison R. J., Bertoldi F., Stevens J. A., DunlopJ. S., Lutz D., Carilli C. L., 2004, MNRAS, 354, 779Hatsukade B., et al., 2011, MNRAS, 411, 102Hughes D. H., et al., 1998, Nature, 394, 241Hwang H. S. et al., 2010, MNRAS, 409, 75Ivison R. J., Smail I., Barger A. J., Kneib J.-P., BlainA. W., Owen F. N., Kerr T. H., Cowie L. L., 2000, MN-RAS, 315, 209Kneib J., Neri R., Smail I., Blain A., Sheth K., van derWerf P., Knudsen K. K., 2005, A&A, 434, 819Laurent G. T., et al., 2005, ApJ, 623, 742Mathis J. S., Rumpl W., Nordsieck K. H., 1977, ApJ, 217,425Mori M., Umemura M., 2006, Nature, 440, 644Nakajima K., et al., 2011, ArXiv e-printsNakamoto T., Umemura M., Susa H., 2001, MNRAS, 321,593Nozawa T., Kozasa T., Habe A., 2006, ApJ, 648, 435Nozawa T., Kozasa T., Habe A., Dwek E., Umeda H., Tom-inaga N., Maeda K., Nomoto K., 2007, ApJ, 666, 955Perera T. A., et al., 2008, MNRAS, 391, 1227Salpeter E. E., 1955, ApJ, 121, 161Scott K. S., et al., 2008, MNRAS, 385, 2225Smail I., Ivison R. J., Blain A. W., 1997, ApJ, 490, L5Stanway E. R., Bremer M. N., Davies L. J. M., LehnertM. D., 2010, MNRAS, 407, L94Stark, D. P., Ellis, R. S., Bunker, A., Bundy, K., Targett,T., Benson, A., Lacy, M., 2009, ApJ, 697, 1493Takagi T., Vansevicius V., Arimoto N., 2003, PASJ, 55, 385Tamura Y., et al., 2009, Nature, 459, 61Todini P., Ferrara A., 2001, MNRAS, 325, 726Verma, A., Lehnert, M. D., F¨orster Schreiber, N. M., Bre-mer, M. N., Douglas, L., 2007, MNRAS, 377, 1024Weiß A., et al., 2009, ApJ, 707, 1201 Yajima H., Umemura M., Mori M., Nakamoto T., 2009,MNRAS, 398, 715Yajima, H., Choi, J.-H., Nagamine, K., 2011, MNRAS, 412,411 c (cid:13)000