Properties of reionization-era galaxies from JWST luminosity functions and 21-cm interferometry
Jaehong Park, Nicolas Gillet, Andrei Mesinger, Bradley Greig
MMNRAS , 1–10 (2018) Preprint 5 September 2019 Compiled using MNRAS L A TEX style file v3.0
Properties of reionization-era galaxies from
JWST luminosity functions and 21-cm interferometry
Jaehong Park, (cid:63) Nicolas Gillet Andrei Mesinger, and Bradley Greig, , Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy ARC Centre of Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO 3D), University of Melbourne, VIC 3010, Australia School of Physics, The University of Melbourne, Parkville, VIC 3010, Australia
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Next generation observatories will enable us to study the first billion years of our Uni-verse in unprecedented detail. Foremost among these are 21-cm interferometry withthe Hydrogen Epoch of Reionization Arrays (HERA) and the Square Kilometre Array(SKA), and high- z galaxy observations with the James Webb Space Telescope ( JWST ).Taking a basic galaxy model, in which we allow the star formation rates and ionizingescape fractions to have a power-law dependence on halo mass with an exponentialturnover below some threshold, we quantify how observations from these instrumentscan be used to constrain the astrophysics of high- z galaxies. For this purpose, wegenerate mock JWST
LFs, based on two different hydrodynamical cosmological sim-ulations; these have intrinsic luminosity functions (LFs) which turn over at differentscales and yet are fully consistent with present-day observations. We also generatemock 21-cm power spectrum observations, using 1000h observations with SKA1 and amoderate foreground model. Using only
JWST data, we predict up to a factor of 2-3improvement (compared with
HST ) in the fractional uncertainty of the star forma-tion rate to halo mass relation and the scales at which the LFs peak (i.e. turnover).Most parameters regulating the UV galaxy properties can be constrained at the levelof ∼ % or better, if either (i) we are able to better characterize systematic lens-ing uncertainties than currently possible; or (ii) the intrinsic LFs peak at magnitudesbrighter than M UV ∼ < − . Otherwise, improvement over HST -based inference is mod-est. When combining with upcoming 21-cm observations, we are able to significantlymitigate degeneracies, and constrain all of our astrophysical parameters, even for ourmost pessimistic assumptions about upcoming
JWST
LFs. The 21-cm observationsalso result in an order of magnitude improvement in constraints on the EoR history.
Key words: cosmology: theory – dark ages, reionization, first stars – diffuse radiation– early Universe – galaxies: high-redshift – intergalactic medium
Recent years have witnessed remarkable progress in under-standing the timing of the epoch of reionization (EoR).Aided primarily by high-redshift QSO spectra (e.g. Mort-lock et al. 2011; McGreer et al. 2015; Ba˜nados et al. 2018)and the optical depth to the cosmic microwave background(CMB) (e.g. Planck Collaboration et al. 2016b, 2018), wecan estimate that the mid-point of the EoR (when thevolume-averaged neutral fraction was ¯ x HI = . ) was around z ∼ . ± , (e.g. Mitra et al. 2015; Planck Collaborationet al. 2016b; Greig & Mesinger 2017a; Price et al. 2018;Gorce et al. 2018) with a maximum of a few percent of the (cid:63) E-mail: [email protected] (JP)
IGM remaining neutral by z = (McGreer et al. 2015; al-though the final overlap stages can extend to z ∼ –6; Lidzet al. 2007; Mesinger 2010; Keating et al. 2019).The next few years will see us moving away from puttingpoints on the ¯ x HI vs. z plane, towards a deeper understand-ing of the galaxies that are responsible for the EoR. Thiswill primarily be enabled by two ground-breaking observa-tions: (i) near infrared high- z galaxy studies with the JamesWebb Space Telescope ( JWST ; Gardner et al. 2006) and(ii) measurements of the 3D structure of the EoR withnext-generation 21-cm interferometers like Hydrogen Epochof Reionization Array (HERA ; DeBoer et al. 2017) and http://reionization.org © a r X i v : . [ a s t r o - ph . C O ] S e p J. Park et al.
Square Kilometre Array(SKA ; Mellema et al. 2013; Koop-mans et al. 2015).Although JWST will enable resolved spectroscopy ofhigh- z galaxies, such detailed studies will be limited to rel-atively bright and rare objects (e.g. Stark 2016; Shapleyet al. 2017; Williams et al. 2018; Chevallard et al. 2019).The bulk of the high- z galaxy population will be studiedprimarily by counting the number per volume which fall ina given non-ionizing UV magnitude bin, the so-called rest-frame UV luminosity functions (UV LFs). JWST should ex-tend our knowledge of high-z LFs by pushing one to twomagnitudes deeper than current observations with Hubble(e.g. Salvaterra et al. 2011; Dayal et al. 2013; Shimizu et al.2014; O’Shea et al. 2015; Finkelstein 2016; Wilkins et al.2017; Cowley et al. 2018; Tacchella et al. 2018; Williamset al. 2018; Yung et al. 2019). This will allow us to pushblank field LFs to magnitudes fainter than M UV ∼ > − ; suchfaint magnitudes are currently accessible only through clus-ter lensing, and are thus susceptible to large systematic un-certainties including lens modeling and completeness correc-tions (e.g. Bouwens et al. 2016; Livermore et al. 2016; Ateket al. 2018; Ishigaki et al. 2017).On the other hand, the 21-cm line from neutral hydro-gen will enable us to map the intergalactic medium (IGM)on large-scales, during the first billion years. From theselarge-scale 21-cm structures, we can indirectly infer averageproperties of high-redshift galaxies, albeit with some degen-eracies (e.g. McQuinn et al. 2007; Pober et al. 2015; Greig& Mesinger 2015, 2017b; Ross et al. 2019). These propertiesinclude the stellar mass fraction, the gas fraction, the starformation rate, the escape fraction, X-ray luminosities, etc.In Park et al. (2019) we showed that high- z LFs and 21-cm interferometry are complementary observations, helpingus nail down the properties of high- z galaxies, and amelio-rating the degeneracies present when each is considered sep-arately. We used current LF observations obtained with the Hubble telescope, combining them with a mock 21-cm obser-vation from a 1000h integration with the HERA instrument.
In this work, we quantify the additional constraints on high-zgalaxy properties available with deeper LF observations, suchas might be expected from JWST.
This paper is organized as follows. In § §
3. In §
4, we summarize our results. We assume a standard Λ CDMcosmology based on
Planck h , Ω m , Ω b , Ω Λ , σ , n s )=(0.678, 0.308, 0.0484, 0.692,0.815, 0.968). Unless stated otherwise, we quote all quanti-ties in comoving units, and when we refer to the UV mag-nitude, this corresponds to the rest-frame 1500˚A AB mag-nitude. As in Park et al. (2019), we compute the likelihood of ourmodel parameters using two main data sets: the rest-frameUV LFs at high- z and mock 21-cm power spectra (PS) mea-surements. The main difference in this work is that instead of https://astronomers.skatelescope.org − − − − − − − M UV − − − φ / m ag / M p c Mock - F Mock - BGillet et al . (2019) Figure 1.
Simulated luminosity functions at z = . These simu-lations were used to build the two sets of mock JWST
LFs shownin Fig. 2. These were chosen because they agree with current con-straints (the 68% C.L. from Gillet et al. 2019 are denoted withthe shaded area) but are very different at the ultra faint end. using current LFs observations from
Hubble , we use deepermock LFs, roughly corresponding to what we should getwith
JWST .In addition to these two mock data sets, we also includein our likelihood calculation the two most robust constraintson EoR timing currently available: (i) the electron scatter-ing optical depth to the CMB, τ e = . ± . ( σ ) from(Planck Collaboration et al. 2016b); and (ii) the upper limitof the neutral fraction, ¯ x HI < . + . ( σ ) at z = . fromthe fraction of dark pixels in QSO spectra (McGreer et al.2015). These EoR timing measurements allow a rough es-timate of the ionizing escape fraction, when combined alsowith the observed LFs (e.g. Kuhlen & Faucher-Gigu`ere 2012;Mitra et al. 2013; Mitra et al. 2015; Robertson et al. 2013,2015; Price et al. 2016), but become superfluous when 21-cmobservations become available (Park et al. 2019). Our mock LFs are taken from the GAlaxy Formation Forthe EoR (GAFFER) simulation suite (Gillet et al. in prep).GAFFER is comprised of ∼
800 fully-coupled hydro-radiativetransfer cosmological simulations aiming to characterize thegrowth of dwarf galaxies during the EoR. Using the numeri-cal code EMMA (Aubert et al. 2015), we vary five astrophys-ical/numerical parameters governing galaxy formation: thestar formation efficiency, the ISM over-density threshold forstar formation, the supernova feedback efficiency, the sub-grid ionizing escape fraction, and the mass of the numericalstar particle. For more details on how these parameters af-fect the star formation and feedback models in EMMA, werefer the reader to Deparis et al. (2016, 2019) and Depariset al in prep. Most of the simulation boxes are 10Mpc on
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WST and 21-cm constraints on the first galaxies a side, with halos above ∼ × M (cid:12) being resolved with > dark matter particles.For each simulation, we compute the correspondingLFs by assuming a constant conversion factor between agalaxy’s star formation rate (averaged over the previous 10Myr) and its 1500˚A UV luminosity: (cid:219) M ∗ = K UV × L UV ,with K UV = . × − M (cid:12) yr − / erg s − Hz − consistent witha Salpeter IMF with a ∼
10% solar metalicity (c.f. Kenni-cutt 1998; Madau & Dickinson 2014). We do not modeldust; thus our mock LFs would correspond to dust-correctedones. However, since we concern ourselves with faint galax-ies which dominate the photon budget during reionization,dust is unlikely to require a large correction over our magni-tude range (e.g. Finkelstein et al. 2012; Dunlop et al. 2013;Bouwens et al. 2015b; Cullen et al. 2017; Wilkins et al. 2017;Yung et al. 2019; Ma et al. 2019; Vogelsberger et al. 2019).From the GAFFER simulation suite, we select two sim-ulations to use as mock
JWST
LFs. These two simulationshave LFs which are both within 1 σ of current observationalconstraints (e.g. Gillet et al. 2019; see Fig. 1) but were chosento have different behavior at the faint end, due to differentstrengths of SNe and photo-heating feedback from reioniza-tion (Gillet et al. in prep). Detecting a turnover at brightermagnitudes with JWST would be easier than detecting itat fainter magnitudes; thus we take these two models tobracket the expected range. Below we denote mock obser-vations based on the simulation with a turnover at brightermagnitudes with the suffix “-B”, and those based on the sim-ulation with a turnover at fainter magnitudes with the suffix“-F”.Mock observations are constructed from the galaxynumber densities, φ ( M uv ) , in these two simulations. For con-sistency, we use the same galaxy number counts to makeboth JWST and
HST mock LFs, varying only the uncer-tainties (by construction, the
HST mocks are entirely con-sistent with current
HST observations). The uncertaintiesfor
HST are the same ones we used in Park et al. (2019),allowing for a direct comparison. These uncertainties werebased on the observational data from Bouwens et al. (2016)for redshift 6, Bouwens et al. (2015a) for redshifts 7 and 8,and Oesch et al. (2017) for redshift 10. The same magni-tude bins are used. In each bin, the error is evaluated as themaximum of the observational uncertainty ( σ OBS ) and thePoisson error in the bin due to the finite simulation volumeof the simulations ( σ P ). Over most of the range of interest,specifically M UV > − , the observational uncertainties dom-inate over the cosmic variance. Moreover, we enforce thatthe uncertainty has to be greater than 20% of the galaxydensity ( σ ≥ . φ , taking this to be a systematic “floor” (R.Bouwens, private communication).The mock JWST
LFs are then built by extending the
HST
LFs 1.5 magnitudes deeper. Although in principle, er-ror bars should be computed considering specific volumes ofspecific observational programs, simply extending the
HST
LFs by 1.5 mags is a reasonable approximation for what isachievable with
JWST (Finkelstein 2016; R. Bouwens and We note that had we chosen a longer time-frame over which toaverage the SFR, the drop at faint magnitudes ( M UV > -10) seen inFig. 1 would be less steep; however, this does not have a notableeffect on the observable luminosity range. P. Oesch, private communication). Specifically, we take: σ JWST ( M UV ) = σ HST ( M UV − . ) if M UV > − . σ HST ( M UV ) if M UV < − . φ ( M UV ) if − < M UV < − . (1)with the Poisson-dominated bright-end taken to have thesame errors as are currently available for HST , and the in-termediate regime having 20% systematic errors, similar towhat is available currently from
HST programs.The resulting mock LFs are shown in Fig. 2, for both
HST and
JWST error bars, as well as for both of our simula-tions. As mentioned previously, LFs which have an intrinsicturnover at fainter (brighter) magnitudes are denoted withthe qualifiers “-F” (“-B”).
We create a mock cosmic 21-cm signal using the publiccode . (Mesinger & Furlanetto 2007;Mesinger et al. 2011) generates the evolved density and cor-responding peculiar velocity fields by applying second orderLPT (e.g. Scoccimarro 1998) on a high-resolution realizationof a Gaussian random field. Then, estimates theionization field from the density field using an excursion-setapproach (e.g. Furlanetto et al. 2004), while the spin temper-ature evolution is computed by integrating the cosmic X-rayand soft UV backgrounds back along the lightcone for eachsimulation cell. We use the latest version introduced in Parket al. (2019), allowing us to tie the galactic radiation sourcesto the corresponding UV LFs (c.f. http://homepage.sns.it/mesinger/Videos/parameter_variation.mp4 ). Here webriefly summarize the free parameters in the model; for moredetails on the simulation and the astrophysical parameters,readers are referred to Park et al. (2019).We assume the average properties of high- z galaxies de-pend on their host dark matter halo mass (e.g. Behroozi &Silk 2015; Sun & Furlanetto 2016; Dayal & Ferrara 2018;Salcido et al. 2019). Specifically, we parametrize the typicalstellar mass of galaxies with a power law dependence on thetotal halo mass, M h : M ∗ ( M h ) = f ∗ , (cid:18) M h M (cid:12) (cid:19) α ∗ (cid:18) Ω b Ω m (cid:19) M h (2)where f ∗ , is the normalization (i.e. the fraction of galacticbaryons in stars for halos with a mass of M (cid:12) ) and α ∗ isthe power-law index. Then, the star formation rate (SFR) isdefined as (cid:219) M ∗ ( M h , z ) = M ∗ t ∗ H ( z ) − , (3)where H ( z ) − is the Hubble time and t ∗ is a free parameterregulating the star formation time-scale.Similarly we define the ionizing UV escape fraction as f esc ( M h ) = f esc , (cid:18) M h M (cid:12) (cid:19) α esc , (4)where f esc , is the normalization of the escape fraction and α esc is a power-law index. https://github.com/andreimesinger/21cmFAST MNRAS , 1–10 (2018)
J. Park et al. − − − − − M UV − − − − φ / m ag / M p c Mock
HST - F z = 6 z = 8 z = 8 z = 10 − − − − − M UV Mock
JWST - F − − − − − M UV Mock
HST - B − − − − − M UV Mock
JWST - B Figure 2.
HST and
JWST
LF mock observations used for parameter recovery. LFs corresponding to the simulation with a turnover atbrighter (fainter) magnitudes are denoted with “-B” (“-F”).
Since small halos are unable to host star-forming galax-ies due to their limited gas reservoir from inefficient coolingand/or feedback (e.g. Shapiro et al. 1994; Giroux et al. 1994;Hui & Gnedin 1997; Barkana & Loeb 2001; Springel & Hern-quist 2003; Okamoto et al. 2008; Mesinger & Dijkstra 2008;Sobacchi & Mesinger 2013), we introduce a duty cycle quan-tifying the fraction of halos which host galaxies via f duty ( M h ) = exp (cid:18) − M turn M h (cid:19) , (5)Here M turn is a characteristic mass below which the fractionof halos hosting stars/galaxies exponentially decreases. Forreference, M turn ∼ M (cid:12) at z ∼ for a virial temperatureof K (corresponding to the atomic cooling threshold).The corresponding rest-frame UV LFs are calculated as: φ ( M UV ) = (cid:20) f duty d n d M h (cid:21) (cid:12)(cid:12)(cid:12)(cid:12) d M h d M UV (cid:12)(cid:12)(cid:12)(cid:12) , (6)where d n / d M h is the halo mass function. To calculate the d M h / d M UV term, we assume a linear dependence of the 1500˚A UV luminosity to the star formation rate: (cid:219) M ∗ ( M h , z ) = K UV × L UV , just as we did when constructing the mock LFsfrom the GAFFER simulations.We thus have six free parameters which regulate theemission of UV photons: f ∗ , , α ∗ , f esc , , α esc , M turn and t ∗ . We introduce two additional parameters to characterizethe X-ray emission of high- z galaxies, L X < / SFR and E ,which we describe below.It is expected that X-rays, through their long mean freepaths, are a dominant source of heat in the neutral IGM,outside of the HII regions which surround the nascent galax-ies (e.g. Pritchard & Furlanetto 2007; McQuinn & O’Leary2012; Mesinger et al. 2013; Madau & Fragos 2017; Eideet al. 2018). computes the angle-averaged spe-cific X-ray intensity (in units of erg s − keV − cm − sr − ) ineach simulation cell at a given spatial position and redshift.We parametrize the typical emerging X-ray SED of high- z galaxies via their integrated soft-band ( < ) luminosityper SFR (in units of erg s − M − (cid:12) yr ), L X < / SFR = ∫ E d E e L X / SFR , (7)where L X / SFR is is the specific X-ray luminosity perunit star formation escaping the host galaxies in units of erg s − keV − M − (cid:12) yr , taken here to be a power law with en-ergy index α X = (e.g. Fragos et al. 2013; Mineo et al. 2012;Das et al. 2017) and E is an additional free parameter cor-responding to the X-ray energy threshold below which pho-tons are absorbed inside the host galaxies, never managingto escape and heat the IGM.We compute a mock observation from a simulation boxof
500 Mpc on a side with a grid, downsampled from initial conditions. Our default astrophysical parame-ters used for the mock simulation are listed in Table 1; theseparameters are consistent with the mock UV LFs as shownbelow and discussed in Gillet at al. in prep.From the light-cone of this simulation, we compute the3D power spectra in 12 segments, sliced along the red-shift/frequency axis in equal comoving volumes. As in Parket al. (2019), we compute the thermal and cosmic variancenoise on the power spectrum at each redshift using the pub-lic code (Pober et al. 2013, 2014). For this,we assume the ‘moderate’ foreground removal strategy fromPober et al. (2014) which restricts the computation of the21cm PS to modes outside of the foreground ‘wedge’. Fur-ther, this assumes coherent summation over redundant base-lines in order to reduce thermal noise (Parsons et al. 2012).For this work, we assume a single 1000hr tracked scan withthe SKA. We model the SKA using the recent SKA SystemBaseline Design document We combine the above mentioned data sets within a fullyBayesian framework, obtaining parameter constraints withthe public Monte Carlo Markov Chain (MCMC) samplerof 3D EoR/CD simulations, (Greig & Mesinger2015, 2017b; Greig & Mesinger 2018). At each parametersample, computes the corresponding 21-cm PS,UV LFs, and reionizaton history, comparing them with ourdata sets using a χ likelihood and a flat prior over the pa-rameter ranges shown in the figures below. The likelihoods https://github.com/jpober/21cmSense http://astronomers.skatelescope.org/wp-content/uploads/2016/09/SKA-TEL-SKO-0000422 02 SKA1 LowConfigurationCoordinates-1.pdf https://github.com/BradGreig/21CMMC MNRAS000
500 Mpc on a side with a grid, downsampled from initial conditions. Our default astrophysical parame-ters used for the mock simulation are listed in Table 1; theseparameters are consistent with the mock UV LFs as shownbelow and discussed in Gillet at al. in prep.From the light-cone of this simulation, we compute the3D power spectra in 12 segments, sliced along the red-shift/frequency axis in equal comoving volumes. As in Parket al. (2019), we compute the thermal and cosmic variancenoise on the power spectrum at each redshift using the pub-lic code (Pober et al. 2013, 2014). For this,we assume the ‘moderate’ foreground removal strategy fromPober et al. (2014) which restricts the computation of the21cm PS to modes outside of the foreground ‘wedge’. Fur-ther, this assumes coherent summation over redundant base-lines in order to reduce thermal noise (Parsons et al. 2012).For this work, we assume a single 1000hr tracked scan withthe SKA. We model the SKA using the recent SKA SystemBaseline Design document We combine the above mentioned data sets within a fullyBayesian framework, obtaining parameter constraints withthe public Monte Carlo Markov Chain (MCMC) samplerof 3D EoR/CD simulations, (Greig & Mesinger2015, 2017b; Greig & Mesinger 2018). At each parametersample, computes the corresponding 21-cm PS,UV LFs, and reionizaton history, comparing them with ourdata sets using a χ likelihood and a flat prior over the pa-rameter ranges shown in the figures below. The likelihoods https://github.com/jpober/21cmSense http://astronomers.skatelescope.org/wp-content/uploads/2016/09/SKA-TEL-SKO-0000422 02 SKA1 LowConfigurationCoordinates-1.pdf https://github.com/BradGreig/21CMMC MNRAS000 , 1–10 (2018)
WST and 21-cm constraints on the first galaxies − . . . α ∗ l og ( M t u r n ) . . . t ∗ − − − l og ( f e s c , ) − − − log ( f ∗ , ) − . − . . α e s c − . . . . α ∗ log ( M turn ) . . . t ∗ − − − log ( f esc , ) − . − . . . α esc confidence level HST - F + τ e +the dark-fraction JWST - F + τ e +the dark-fraction JWST - F30 + τ e +the dark-fraction − − z = 6 95% confidence level JWST - F z = 7 95% confidence level z = 8 95% confidence level − − − − − − − M UV − − φ / m ag / M p c z = 10 95% confidence level − − − − − − − M UV z = 12 95% confidence level − − − − − − − M UV z = 15 95% confidence level z . . . . . . ¯ x H I HST - F + τ e +the dark-fraction JWST - F + τ e +the dark-fraction JWST - F30 + τ e +the dark-fraction Figure 3.
Corner plot showing parameter constrains for the mock UV LFs (see legend): 1D marginalized PDFs and 2D marginalizedjoint posterior distributions are shown along the diagonal and in the bottom left corner, respectively. Blue dashed lines, green solid linesand brown dot-dashed lines represent per cent confidence levels for constraints using data sets of the mock HST -F, the mock
JWST -Fand the mock
JWST -F30, respectively. Top-right panels: Recovered per cent confidence levels of the LFs corresponding to the posteriorof our model. Shaded regions with the cross hatch (blue, ‘ + ’), shaded regions (green) and shaded regions with ‘ × ’ hatch (brown) representconstraints using the mock HST -F, the mock
JWST -F and the mock
JWST -F30, respectively. Middle-right: Corresponding constraints onthe global evolution of the IGM neutral fraction, x H i ( z ) with the same legends (note that these almost entirely overlap, highlighting thatimproved LF constraints will not aid in nailing down the EoR history, provided the escape fraction is allowed to be a free functional).Note that together with the listed data sets we also use (i) the electron scattering optical depth to the CMB from Planck Collaborationet al. (2016b); and (ii) the upper limit of the neutral fraction at z = . from the dark fraction of pixels in QSO spectra (McGreer et al.2015). for each data set are multiplied together when computingthe posterior. For the 21-cm PS, we include a Gaussianerror on the PS in each bin to account for simulation inac-curacy (e.g. Zahn et al. 2011), adding it in quadrature withthe sample variance. For all runs, we include the additionalEoR timing constraints mentioned above: (i) the electronscattering optical depth to the CMB τ e = . ± . ( σ ) from Planck Collaboration et al. (2016b); and (ii) the upperlimit of the neutral fraction ¯ x HI < . + . ( σ ) at z = . from McGreer et al. (2015). In Fig.3, we show constraints on our six astrophysical param-eters describing the UV emission of galaxies: f ∗ , , α ∗ , f esc , , α esc , M turn and t ∗ , constructed using the “faint end” turnoverLFs, for both HST and
JWST . As discussed previously, ifthe turnover is at faint magnitudes, it is more difficult to bedetectable even with
JWST ; therefore the “-F” LFs can beconsidered the “pessimistic” scenario.The marginalized posteriors are shown in the corner plot on the left side, while the corresponding recovered UVLFs are shown in the upper right, with the EoR history inthe middle right. As noted in the legend, blue / green linesand shaded areas denote posteriors constructed using
HST -F /
JWST -F data sets. All data sets additionally include τ e and the dark fraction measurements. The marginalized 1Dconstraints are also written in Table 1.Using HST -F LFs, we recover the trends already notedin in Park et al. (2019). Although here we use a mock
HST -F observation to directly compare against the
JWST -F forecast, the mock
HST -F is by construction consistentwith current observations (c.f. Fig. 1), and so the agreementwith Park et al. (2019) is understandable. Most notably,we find that
HST -F LFs are unable to constrain the flat-tening/turnover scale, M turn , encoding the halo mass belowwhich star formation becomes inefficient. They only providean upper limit, ruling out log ( M turn ) (cid:46) . at per centconfidence level. The constraints on the scaling of the stellarmass with halo mass is reasonable, with a fractional uncer-tainty in the relevant parameters of order tens of percent MNRAS , 1–10 (2018)
J. Park et al. (c.f. Table 1). The ionizing escape fraction is only poorlyconstrained, with the normalization parameter f esc , hav-ing a σ fractional uncertainty of ∼ per cent, while itsdependence on halo mass is completely unconstrained (asevidenced by the flat marginalized PDF over α esc , consis-tent with our priors).Considering the JWST -F LFs, we note that the con-straints are not very different for the escape function pa-rameters (as is expected since we are not directly addinginformation on the ionizing photon budget). However, therecovery of parameters describing star formation is (mod-estly) improved. Specifically, we note that the σ fractionaluncertainty for α ∗ is reduced by a factor of 2. This is be-cause the reduced errors of the mock JWST
LFs tighten theslope of the LFs (see Fig. 2). Together with the reduced er-rors, the extended faint-end provides additional informationon the abundance of faint galaxies, which translates to asomewhat tighter upper limit on log ( M turn ) (cid:46) . at per cent confidence level. This improvement is more notablewhen looking at the corresponding recovered LFs in the up-per right panels. We see explicitly that our mock JWST -FLFs allow us to rule out models which predict a turnover at M UV < − . In the previous section, we noted that if the intrinsic LFsturn over at faint magnitudes ( M UV ∼ > − ), JWST
LFs willonly modestly improve on our current knowledge of averagegalaxy properties, as obtained with
HST
LFs. The largestimprovement comes in the form of improved constraints on α ∗ and a somewhat tighter upper limit on the turnover scale.Here we consider a more ”optimistic” JWST -F fore-cast, labeled
JWST -F30. This forecast is based on the sameintrinsic LFs, “-F”, but we assume that uncertainties canbe reduced, e.g. due to an improved understanding of thedominant systematic uncertainties. To illustrate this, wesimply reduce the errors of each LF bin to of theirfiducial values, discussed previously, keeping the 20% mini-mum error. In other words, in each magnitude bin we take σ JWST − F30 = max [ σ JWST − F , . φ ] .Fig. 4 shows the resulting JWST
LFs, and the corre-sponding parameter constraints are shown in Fig. 3 withthe label
JWST -F30. The most notable improvement is on log ( M turn ) . As evidenced by the 1D PDF, the constraintson the turnover mass are significantly tightened, which is incontrast to the mock JWST -F LFs which only provide anupper limit. Moreover, the σ fractional uncertainty for α ∗ isreduced by ∼ per cent, compared with the mock JWST -FLFs. A careful reader can note that the recovered fractional uncer-tainty on α ∗ is a factor of two larger than quoted in Park et al.(2019). This is due to the fact that our mock observation comesfrom a fairly small simulation box, 10 Mpc on a side. The re-sulting Poisson noise for the brightest galaxies is larger than wasquoted in the Bouwens et al. (2016) observations that were usedin Park et al. (2019), resulting in weaker recovery on the halomass scaling of the stellar mass. − − − − − M UV − − − − φ / m ag / M p c Mock
JWST - F30 z = 6 z = 7 z = 8 z = 10 Figure 4.
Mock LFs assuming an optimistic error budget,obtained by reducing the fiducial
JWST uncertainties by 30%.The intrinsic number densities are taken from the faint turnovermodel.
We now show the resulting constraints for the mock LFswith the turnover at brighter magnitudes (i.e.,
HST -B and
JWST -B from Fig. 2) in Fig. 5. Comparing
JWST -B re-sults to those of
JWST -F, we note a large improvement inthe inference of the turnover scale. This is understandable,since the “-B” LFs intrinsically turn over at scales whichapproach the
JWST sensitivity thresholds. This is reflectedalso in the recovered luminosity functions (upper right pan-els in Fig. 5), which understandably show stronger evidenceof a turnover than was the case for
JWST -F in the previ-ous figure. Specifically, we recover log ( M turn ) = . + . − . ( σ ). This fractional uncertainty of ∼ per cent is compara-ble to the constrains achievable with the reduced error barLFs discussed in § JWST if either we are able to better characterize systematiclensing uncertainties than currently possible, or the intrinsicLFs peak at M UV ∼ < − . In the previous sections, we saw that if the LFs turn overat M UV ∼ > − (our “-F” models), a dramatic improvementin inference using JWST observations is unlikely, given ourfiducial uncertainties. Here we additionally add mock 21-cmPS observations, to see if parameter inference is improved,for these “pessimistic” LFs. We also extend our parame-ter space to include the afore-mentioned X-ray parameters,which drive the Epoch of Heating, observable with 21-cm.The resulting corner plot is shown in Fig. 6. Adding themock 21-cm observation results in a marked improvementin all parameter constraints, as expected from Park et al.(2019). We find the 21-cm signal dominates constraints on log ( M turn ) , t ∗ , log ( f esc , ) , α esc , log ( L X < / SFR ) and E . On the other hand, the LFs dominates constraints on MNRAS000
JWST -F in the previ-ous figure. Specifically, we recover log ( M turn ) = . + . − . ( σ ). This fractional uncertainty of ∼ per cent is compara-ble to the constrains achievable with the reduced error barLFs discussed in § JWST if either we are able to better characterize systematiclensing uncertainties than currently possible, or the intrinsicLFs peak at M UV ∼ < − . In the previous sections, we saw that if the LFs turn overat M UV ∼ > − (our “-F” models), a dramatic improvementin inference using JWST observations is unlikely, given ourfiducial uncertainties. Here we additionally add mock 21-cmPS observations, to see if parameter inference is improved,for these “pessimistic” LFs. We also extend our parame-ter space to include the afore-mentioned X-ray parameters,which drive the Epoch of Heating, observable with 21-cm.The resulting corner plot is shown in Fig. 6. Adding themock 21-cm observation results in a marked improvementin all parameter constraints, as expected from Park et al.(2019). We find the 21-cm signal dominates constraints on log ( M turn ) , t ∗ , log ( f esc , ) , α esc , log ( L X < / SFR ) and E . On the other hand, the LFs dominates constraints on MNRAS000 , 1–10 (2018)
WST and 21-cm constraints on the first galaxies Table 1.
Summary of the median recovered values with σ errors for the eight free parameters, obtained from our MCMC procedurefor each combination of data sets listed below. Note that together with the listed data sets we also use (i) the electron scattering opticaldepth to the CMB from Planck Collaboration et al. (2016b); and (ii) the upper limit of the neutral fraction at z = . from the darkfraction of pixels in QSO spectra (McGreer et al. 2015). We note that the fiducial values are used for generating the mock 21-cm signal;LFs are taken independently from the GAFFER simulations. Parameters log ( f ∗ , ) α ∗ log ( f esc , ) α esc log ( M turn ) t ∗ log (cid:16) L X < SFR (cid:17) E [ M (cid:12)] [ erg s − M − (cid:12) yr ] [ keV ] Fiducial values (21-cm only) − .
155 0 . − . − .
20 9 .
00 0 . .
50 0 . HST -F − . + . − . . + . − . − . + . − . − . + . − . . + . − . . + . − . . . JWST -F − . + . − . . + . − . − . + . − . − . + . − . . + . − . . + . − . . . JWST -F30 − . + . − . . + . − . − . + . − . − . + . − . . + . − . . + . − . . . HST -B − . + . − . . + . − . − . + . − . − . + . − . . + . − . . + . − . . . JWST -B − . + . − . . + . − . − . + . − . − . + . − . . + . − . . + . − . . .21-cm + JWST -F − . + . − . . + . − . − . + . − . − . + . − . . + . − . . + . − . . + . − . . + . − . − . . . α ∗ l og ( M t u r n ) . . . t ∗ − − − l og ( f e s c , ) − − − log ( f ∗ , ) − . − . . α e s c − . . . . α ∗ log ( M turn ) . . . t ∗ − − − log ( f esc , ) − . − . . . α esc confidence level HST - B + τ e +the dark-fraction JWST - B + τ e +the dark-fraction − − z = 6 95% confidence level JWST - B z = 7 95% confidence level z = 8 95% confidence level − − − − − − − M UV − − φ / m ag / M p c z = 10 95% confidence level − − − − − − − M UV z = 12 95% confidence level − − − − − − − M UV z = 15 95% confidence level z . . . . . . ¯ x H I HST - B + τ e +the dark-fraction JWST - B + τ e +the dark-fraction Figure 5.
The same as Fig. 3, but for the mock
HST -B and
JWST -B LFs. Purple dashed lines and Turquoise solid lines represent per cent confidence levels for constraints using data sets of the mock HST -B and the mock
JWST -B, respectively. Shaded regions with thecross hatch (purple, ‘ + ’) and shaded regions (turquoise) represent constraints using the mock HST -B and the mock
JWST -F, respectively. α ∗ , as evidenced by the almost identical 1D PDFs of α ∗ from the mock 21-cm + JWST -F LFs and from the mock
JWST -F LFs only. Constraints on f ∗ , are comparablysourced by both observations. In summary, the σ frac-tional uncertainties on our parameters from the combineddata sets are [ log ( f ∗ , ) , α ∗ , log ( f esc , ) , α esc , log ( M turn ) , t ∗ , log ( L X < / SFR ) , E ] = ( , , , , . , , . , . )per cent.The most dramatic improvement is seen in the EoRhistory (middle right panel). With 21-cm observations, wewill know the EoR history to within ∆ z ( ¯ x HI ) ∼ < . ( σ ) over MNRAS , 1–10 (2018)
J. Park et al. − . . . α ∗ l og ( M t u r n ) . . . t ∗ − − − l og ( f e s c , ) − . − . . α e s c l og ( L X < k e V S F R ) − − − log ( f ∗ , ) . . . E [ k e V ] − . . . . α ∗ log ( M turn ) . . . t ∗ − − − log ( f esc , ) − . − . . . α esc
38 40 42 log ( L X < SFR ) confidence level JWST - F + τ e +the dark-fraction
21 cm + JWST - F + τ e +the dark-fraction . . . E [keV]19 . . . . ( N HI ) [cm − ]10 − − z = 6 JWST - F z = 7 z = 8 − − − − − − − M UV − − φ / m ag / M p c z = 10 − − − − − − − M UV z = 12 95% confidence level − − − − − − − M UV z = 156 8 10 12 z . . . . . . ¯ x H I Fiducial model confidence level
JWST - F + τ e +the dark-fraction
21 cm + JWST - F + τ e +the dark-fraction Figure 6.
Same as Fig. 3, but including also constraints available from adding mock 21-cm observations (see legend). most of the EoR. This is a order of magnitude improvementover our current state of knowledge: ∆ z ( ¯ x HI ) ∼ < . Next generation observatories will enable us to study thefirst billion years of our Universe in unprecedented detail.Foremost among these are 21-cm interferometry with HERAand SKA, and high- z galaxy observations with JWST . Herewe quantify how observations from these instruments canbe used to constrain the astrophysics of high- z galaxies. Forthis purpose, we generate mock JWST
LFs, based on two dif-ferent hydrodynamical cosmological simulations; these haveintrinsic LF which turn over at different scales and yetare fully consistent with present-day observations. Likewise,we generate mock 21-cm power spectra, using the semi-numerical code combined with a moderate fore-ground model and 1000h thermal noise with the SKA1-lowinstrument. We assume a simple astrophysical model for thehigh- z galaxy population, in which the star formation rateand ionizing escape fraction are power-law functions of halomass, and there is an exponential suppression of star forminggalaxies below some threshold halo mass. We find that if the LFs turn over at magnitudes fainterthan M UV ∼ > − , we must significantly improve on our un-derstanding of systematic lensing uncertainties in order for JWST
LFs to dramatically improve our understanding ofthe faint galaxies, beyond what we have currently with
HST
LFs. However, if LFs intrinsically turn over at magnitudesbrighter than M UV ∼ < − , then the turn over scale can beeasily recovered to within a few percent, and uncertaintieson the star formation rate to halo mass relation can be de-creased by ∼ .Additionally including 21-cm observations would im-prove constraints significantly, even for our most pessimistic JWST scenario. The two observations are complementary,with JWST dominating constraints on the star formationrate to halo mass relation, and 21-cm dominating constraintson the ionizing escape fraction, turn over scale, and the EoRhistory.
ACKNOWLEDGEMENTS
We thank R. Bouwens, S. Finkelstein and P. Oesch for en-lightening discussions about approximating
JWST
LF un-certainties. This project has received funding from the Euro-
MNRAS000
MNRAS000 , 1–10 (2018)
WST and 21-cm constraints on the first galaxies pean Research Council (ERC) under the European Union’sHorizon 2020 research and innovation program (grant agree-ment No. 638809 – AIDA – PI: Mesinger). The results pre-sented here reflect the authors’ views; the ERC is not re-sponsible for their use. The simulations used to generatethe mock LFs were computed as part of the PRACE tier-0grant GAFFER (project no. 2016163945). We acknowledgePRACE for awarding us access to Curie at GENCI@CEA,France. REFERENCES
Atek H., Richard J., Kneib J.-P., Schaerer D., 2018, preprint,( arXiv:1803.09747 )Aubert D., Deparis N., Ocvirk P., 2015, MNRAS, 454, 1012Ba˜nados E., et al., 2018, Nature, 553, 473Barkana R., Loeb A., 2001, Phys. Rep., 349, 125Behroozi P. S., Silk J., 2015, Astrophysical Journal, 799Bouwens R. J., et al., 2015a, Astrophysical Journal, 803, 1Bouwens R. J., Illingworth G. D., Oesch P. A., Caruana J., Hol-werda B., Smit R., Wilkins S., 2015b, ApJ, 811, 140Bouwens R. J., Oesch P. A., Illingworth G. D., Ellis R. S., Ste-fanon M., 2016, The Astrophysical Journal, 843, 129Chevallard J., et al., 2019, MNRAS, 483, 2621Cowley W. I., Baugh C. M., Cole S., Frenk C. S., Lacey C. G.,2018, MNRAS, 474, 2352Cullen F., McLure R. J., Khochfar S., Dunlop J. S., Dalla VecchiaC., 2017, MNRAS, 470, 3006Das A., Mesinger A., Pallottini A., Ferrara A., Wise J. H., 2017,MNRAS, 469, 1166Dayal P., Ferrara A., 2018, Phys. Rep., 780, 1Dayal P., Dunlop J. S., Maio U., Ciardi B., 2013, MNRAS, 434,1486DeBoer D. R., et al., 2017, PASP, 129, 045001Deparis N., Aubert D., Ocvirk P., 2016, in SF2A-2016: Proceed-ings of the Annual meeting of the French Society of Astron-omy and Astrophysics. pp 399–402Deparis N., Aubert D., Ocvirk P., Chardin J., Lewis J., 2019,A&A, 622, A142Dunlop J. S., et al., 2013, MNRAS, 432, 3520Eide M. B., Graziani L., Ciardi B., Feng Y., Kakiichi K., Di Mat-teo T., 2018, MNRAS, 476, 1174Finkelstein S. L., 2016, Publ. Astron. Soc. Australia, 33, e037Finkelstein S. L., et al., 2012, ApJ, 756, 164Fragos T., et al., 2013, ApJ, 764, 41Furlanetto S. R., Zaldarriaga M., Hernquist L., 2004, ApJ, 613, 1Gardner J. P., et al., 2006, Space Sci. Rev., 123, 485Gillet N. J. F., Mesinger A., Park J., 2019, arXiv e-prints, p.arXiv:1906.06296Giroux M. L., Sutherland R. S., Shull J. M., 1994, ApJ, 435, L97Gorce A., Douspis M., Aghanim N., Langer M., 2018, A&A, 616,A113Greig B., Mesinger A., 2015, Monthly Notices of the Royal As-tronomical Society, 449, 4246Greig B., Mesinger A., 2017a, MNRAS, 465, 4838Greig B., Mesinger A., 2017b, Monthly Notices of the Royal As-tronomical Society, 472, 2651Greig B., Mesinger A., 2018, MNRAS, 477, 3217Hui L., Gnedin N. Y., 1997, MNRAS, 292, 27Ishigaki M., Kawamata R., Ouchi M., Oguri M., Shimasaku K.,Ono Y., 2017, The Astrophysical Journal, 854, 73Keating L. C., Weinberger L. H., Kulkarni G., HaehneltM. G., Chardin J., Aubert D., 2019, arXiv e-prints, p.arXiv:1905.12640Kennicutt Jr. R. C., 1998, ARA&A, 36, 189 Koopmans L., et al., 2015, Advancing Astrophysics with theSquare Kilometre Array (AASKA14), p. 1Kuhlen M., Faucher-Gigu`ere C. A., 2012, Monthly Notices of theRoyal Astronomical Society, 423, 862Lidz A., McQuinn M., Zaldarriaga M., Hernquist L., Dutta S.,2007, ApJ, 670, 39Livermore R. C., Finkelstein S. L., Lotz J. M., 2016, The Astro-physical Journal, 835, 1Ma X., et al., 2019, MNRAS, p. 1267Madau P., Dickinson M., 2014, ARA&A, 52, 415Madau P., Fragos T., 2017, ApJ, 840, 39McGreer I. D., Mesinger A., D’Odorico V., 2015, MNRAS, 447,499McQuinn M., O’Leary R. M., 2012, ApJ, 760, 3McQuinn M., Lidz A., Zahn O., Dutta S., Hernquist L., Zaldar-riaga M., 2007, MNRAS, 377, 1043Mellema G., et al., 2013, Experimental Astronomy, 36, 235Mesinger A., 2010, MNRAS, 407, 1328Mesinger A., Dijkstra M., 2008, MNRAS, 390, 1071Mesinger A., Furlanetto S., 2007, ApJ, 669, 663Mesinger A., Furlanetto S., Cen R., 2011, Monthly Notices of theRoyal Astronomical Society, 411, 955Mesinger A., Ferrara A., Spiegel D. S., 2013, MNRAS, 431, 621Mineo S., Gilfanov M., Sunyaev R., 2012, MNRAS, 419, 2095Mitra S., Ferrara A., Choudhury T. R., 2013, MNRAS, 428, L1Mitra S., Roy Choudhury T., Ferrara A., 2015, Monthly Noticesof the Royal Astronomical Society: Letters, 454, L76Mortlock D. J., et al., 2011, Nature, 474, 616O’Shea B. W., Wise J. H., Xu H., Norman M. L., 2015, ApJ, 807,L12Oesch P. A., Bouwens R. J., Illingworth G. D., Labbe I., StefanonM., 2017, The Astrophysical Journal, 855, 105Okamoto T., Gao L., Theuns T., 2008, MNRAS, 390, 920Park J., Mesinger A., Greig B., Gillet N., 2019, MNRAS, 484, 933Parsons A., Pober J., McQuinn M., Jacobs D., Aguirre J., 2012,ApJ, 753, 81Planck Collaboration et al., 2016a, A&A, 594, A13Planck Collaboration et al., 2016b, A&A, 596, A108Planck Collaboration et al., 2018, arXiv e-prints, p.arXiv:1807.06209Pober J. C., et al., 2013, AJ, 145, 65Pober J. C., et al., 2014, ApJ, 782, 66Pober J. C., et al., 2015, ApJ, 809, 62Price L. C., Trac H., Cen R., 2016, preprint, ( arXiv:1605.03970 )Price D. C., et al., 2018, MNRAS, 478, 4193Pritchard J. R., Furlanetto S. R., 2007, MNRAS, 376, 1680Robertson B. E., et al., 2013, ApJ, 768, 71Robertson B. E., Ellis R. S., Furlanetto S. R., Dunlop J. S., 2015,ApJ, 802, L19Ross H. E., Dixon K. L., Ghara R., Iliev I. T., Mellema G., 2019,MNRAS,Salcido J., Bower R. G., Theuns T., 2019, arXiv e-prints, p.arXiv:1908.00552Salvaterra R., Ferrara A., Dayal P., 2011, MNRAS, 414, 847Scoccimarro R., 1998, MNRAS, 299, 1097Shapiro P. R., Giroux M. L., Babul A., 1994, ApJ, 427, 25Shapley A. E., et al., 2017, ApJ, 846, L30Shimizu I., Inoue A. K., Okamoto T., Yoshida N., 2014, MNRAS,440, 731Sobacchi E., Mesinger A., 2013, MNRAS, 432, L51Springel V., Hernquist L., 2003, MNRAS, 339, 312Stark D. P., 2016, ARA&A, 54, 761Sun G., Furlanetto S. R., 2016, Monthly Notices of the RoyalAstronomical Society, 460, 417Tacchella S., Bose S., Conroy C., Eisenstein D. J., Johnson B. D.,2018, ApJ, 868, 92Vogelsberger M., et al., 2019, arXiv e-prints,MNRAS , 1–10 (2018) J. Park et al.
Wilkins S. M., Feng Y., Di Matteo T., Croft R., Lovell C. C.,Waters D., 2017, MNRAS, 469, 2517Williams C. C., et al., 2018, ApJS, 236, 33Yung L. Y. A., Somerville R. S., Finkelstein S. L., Popping G.,Dav´e R., 2019, MNRAS, 483, 2983Zahn O., Mesinger A., McQuinn M., Trac H., Cen R., HernquistL. E., 2011, MNRAS, 414, 727This paper has been typeset from a TEX/L A TEX file prepared bythe author. MNRAS000