A Space-Based Observational Strategy for Characterizing the First

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Jack Keywords: .Ytls hnablinyasltr h Uni- the later, years billion a than less Yet ). 7 1,5 baa Loeb Abraham eateto lmt n pc cecsadEgneig U Engineering, and Sciences Space and Climate of Department 3 5 ai Rapetti David , eateto hsc n srnm,Uiest fCalifor of University Astronomy, and Physics of Department 5 rzn tt nvriy colo at n pc Explora Space and Earth of School University, State Arizona agNhan Bang , 1. 6 omlg:dr gs eoiain rtsas-csooy obse cosmology: - stars first reionization, ages, dark cosmology: ainlRdoAtooyOsraoy 2 deetRa,C Road, Edgement 520 Observatory, Astronomy Radio National INTRODUCTION A 1 10 AAISUIGTERDHFE 1C LBLSPECTRUM GLOBAL 21-CM REDSHIFTED THE USING GALAXIES T ihr Bradley Richard , E eateto hsc,Bakt aoaoy meilColl Imperial Laboratory, Blackett Physics, of Department ; tl mltajv 05/12/14 v. emulateapj style X 11 ≈ 13 il 1958 Field pc cec nttt,45 antSre,Sie25 Bou 205, Suite Street, Walnut 4750 Institute, Science Space 80 8 alArsaeCroain 60Cmec tet Boulder Street, Commerce 1600 Corporation, Aerospace Ball 8 etrfrAtohsc,6 adnS. S5,Cmrde MA Cambridge, 51, MS St., Garden 60 Astrophysics, for Center 1,6 biu Datta Abhirup , 2 − eateto hsc,Uiest fClrd,Budr CO Boulder, Colorado, of University Physics, of Department 1,9 dadJ Wollack J. Edward , 0 ilo er fe the after years million 500 ob&Fraet 2013 Furlanetto & Loeb 4 ila Purcell William , AAGdadSaeFih etr rebl,M 07,USA 20771, MD Greenbelt, Center, Flight Space Goddard NASA 9 AAAe eerhCne,Mfft il,C 43,USA 94035, CA Field, Moffett Center, Research Ames NASA ,poie nob- an provides ), 12 5 ninIsiueo ehooy noe ni and India Indore, Technology, of Institute Indian seiecdby evidenced as 6 et Tauscher Keith , 1,12 rf eso a 4 2017 24, May version Draft oahnPritchard Jonathan , Mather 13 4 O839 USA 80309, CO ai Newell David , ABSTRACT nsai Fialkov Anastasia , ). srpyia n lntr cec,Uiest fColora of University Science, Planetary and Astrophysical 1,2 hog h n fteER(e.g., EoR Ages in- the Dark to of the end us from the range permits through evolutionary CMB large the a against vestigate depth measured optical signal effective ing an With galaxies. of and stars first e oiosi srnm n Astrophysics, and Astronomy in Horizons in-astronomy-and-astrophysics. http://www.nap.edu/catalog/12951/new-worlds-new-hor New rse ta.2015 2015 al. et Presley 2015a al. et 2010 (e.g., Rogers 2013 antenna single & a man either for target 2010 servational Loeb & Pritchard 2010 Wyithe & Morales the up light to objects “first the Universe” by caused (EoR) Reionization ionization ( of intergalactic complete Epoch Universe’s the was before early (IGM) the medium into window servable rud sn the using grounds tvnFurlanetto Steven , opei orpin n oa ai msin.The emissions. radio solar and corruption, nospheric 1 h 1c l-k rgoa inl( signal global or all-sky 21-cm The dsaeo h esitd2-msetu r distinct are spectrum 21-cm redshifted the of state ed ≈ lc oe hc oieadha h ihredshift high the heat and ionize which – holes black g i tLsAgls o nee,C 09,USA 90095, CA Angeles, Los Angeles, Los at nia iest fMcia,AnAbr I419 USA 48109, MI Arbor, Ann Michigan, of niversity in ..Bx860,Tme Z827 USA 85287, AZ Tempe, 876004, Box P.O. tion, %adsniiiyt o eprtrs h result- the temperatures, low to sensitivity and 1% .Faue ntesetu a rvd h first the provide may spectrum the in Features ). ; fteeoho h rtsasadglxe (10 galaxies and stars first the of epoch the of R srpyisDcdlSre:NwWorlds, New Survey: Decadal Astrophysics NRC iso rmtebih oerud.Ti allows This foregrounds. bright the from mission o inletato,w oe h foreground, the model we extraction, signal For . evtoso h lblsetu iharealizable a with spectrum global the of servations otke l 2014 al. et Voytek tt fhdoe a n hspoie tracer a provides thus and gas hydrogen of state n 13 ohsclprmtr eg G rpris first properties, IGM (e.g. parameters rophysical ai Draper David , endb h offiinsascae ihthese with associated coefficients the by defined 10 1 lrVleDcmoiinaaye.Uiga Using analyses. 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Figure 1. Evolution of a slice of the Universe, from early times (left, upper panel) to late times (right) as well as several different models for the corresponding 21-cm spectrum relative to the CMB (lower panel). The red lines are conservative estimates with Pop II (metal-rich) stars only, while the black curves assume that Pop III (metal-free) star formation also occurs, but only in low-mass galaxies where atomic cooling is inefficient. The dashed and solid black curves assume that Pop III stars are distinct from Pop II stars in their emission properties – 100 times brighter in the UV (dashed) and in the UV + X-ray emissions (solid), respectively. The dashed red curve assumes stellar properties corresponding to low redshift Pop II stars whereas the solid red curve corresponds to metallicities of 5% solar. Designations B, C and D indicate the redshift corresponding to the ignition of first stars, the formation of initial black hole accretion, and the onset of reionization, respectively. See Section 6 for further discussion. Figure adapted from Pritchard & Loeb (2010) using the new reference models from Mirocha et al. (2017). constraints on the birth and nature of the first luminous tion, and emission driven by solar emissions and the objects (e.g., Furlanetto 2006). Such an experiment for solar wind (Davies 1990; Liu et al. 2011; Polygiannakis 21-cm cosmology is analogous to the COBE measurement et al. 2003). At 50 km above the lunar farside, >90 dB of the CMB blackbody spectrum, which set the stage for of radio frequency interference (RFI) attenuation pro- more detailed studies of spatial fluctuations by WMAP duces an environment quiet to <1 mK (e.g., McKinley and Planck. et al. 2013). In addition, the Moon shields the instru- In this paper, we describe a space-based strategy for ment (about half the time) from variable solar emission observations of the 21-cm global signal that probes the caused by flares and coronal activity (e.g., Mercier & time of formation and the characteristics of the first stars Trottet 1997). Therefore, observations above the night- and galaxies. We demonstrate how signal extraction us- time, pristine, radio-quiet lunar farside (as verified by ing a realizable radiometer system and Bayesian statis- RAE-2, Alexander & Kaiser 1976) bypass the challenges tical techniques, in the presence of strong galactic and presented by the Earth and the Sun and provide an op- extragalactic foregrounds, can measure spectral features timal site for measurements of the global 21-cm signal. and constrain the physical properties of the first lumi- The key insight permitting the Cosmic Dawn signal nous objects. We use the new detailed design of the to be detected in the presence of bright foregrounds is Dark Ages Radio Explorer (DARE) to illustrate how the that once the Moon blocks solar effects and terrestrial 21-cm spectrum can be extracted from the foreground RFI, the foregrounds are significantly different in their using a feasible observational strategy. characteristics from the expected 21-cm spectral signal. DARE is proposed to conduct observations between The 21-cm monopole strength is about four orders of 40 and 120 MHz in an orbit around the Moon with magnitude weaker than the Galactic foreground. How- data taken only above the lunar farside. On Earth, the ever, the 21-cm signal is separable from the foreground ionosphere corrupts low frequency observations (see e.g., because it is spatially uniform at angular scales &10◦ Vedantham et al. 2014; Vedantham & Koopmans 2015; (e.g., Bittner & Loeb 2011; Liu et al. 2013), unpolarized, Rogers et al. 2015; Sokolowski et al. 2015b; Datta et al. and has distinct spectral features whereas the observed 2016 and references therein) due to refraction, absorp- foreground varies spatially, exhibits polarized emission, The 21-cm Global Signal 3 and is spectrally featureless. The 21-cm cosmological from the wide range of theoretical models consid- signal can then be extracted using algorithms similar to ered. DARE’s present-day observing strategy uti- those employed for CMB observations implemented via lizes four quiet-sky pointing directions away from a Markov Chain Monte Carlo framework (Harker et al. the galactic center. 2012, 2016). Our signal extraction pipeline is centered around The paper is organized as follows. In Section 2, we • introduce and summarize the space-based observational a Singular Value Decomposition (SVD) approach, strategy. In Section 3, an overview of the stellar mod- which allows us to robustly separate the 21-cm sig- els for the sky-averaged 21-cm signal used to develop the nal from the additional contributions to the mea- observational strategy is presented. Section 4 describes surement by using orthogonal modes of variation the nature and brightness of astronomical foregrounds of each component. These modes are determined which must be considered in efforts to measure the much from well-characterized training sets constructed weaker Cosmic Dawn signal. Section 5 provides a synop- from either theory or measurements. sis of the new design for DARE. Section 6 describes our We constructed a detailed end-to-end observation model software pipeline for signal extraction. In Section 7, we that generates simulated antenna temperatures using our discuss the physical parameters (and their uncertainties) models for the diffuse foregrounds and the 21-cm spec- associated with the first stars, black holes, and galaxies trum, and the predicted telescope pointing, Moon lo- that are expected to be measured using the 21-cm all-sky cation, and instrument characteristics. Unlike previous spectrum. Section 8 presents a summary of the potential papers (e.g., Mirocha et al. 2015; Harker et al. 2016), use of the 21-cm background to detect the first luminous which assumed perfect knowledge of the instrument, this objects in the early Universe. new process accounts for and propagates the uncertainty 2. in the instrumental parameters to the signal extraction SUMMARY OF THE OBSERVATIONAL pipeline. Our instrument sensitivity metric is defined as STRATEGY the RMS uncertainty of the extracted 21-cm spectrum, Here we briefly describe key aspects of our observa- averaged over the observation band. Our requirement tional strategy. The following sections will provide de- for this metric is to keep it below 20 mK for all models tails about each item, as well as their relevance to the processed with our pipeline. overall tactic. The core components of the strategy are as follows: 3. MODELS FOR THE 21-CM GLOBAL SIGNAL In this section we discuss the global 21 cm signal, and We incorporate a wide range of theoretical models describe the broad set of physical models that are incor- • (> 1.5 104) from two different classes of possible × porated into our analysis strategy. signals, differing by the generation of stars whose The 21-cm global signal arises from the radiation ef- contribution dominates the behavior of the signal fects produced by the first stars, accreting black holes, (Pop II or Pop III). We show that the DARE in- and galaxies on the surrounding IGM. X-ray and UV strument in orbit of the Moon can effectively dif- emission from these objects and their descendants heated ferentiate between these models using our Bayesian and ionized the tenuous gas that lies between galaxies, inference pipeline. culminating in the Epoch of Reionization several hun- dred Myrs later. The 21-cm background can be used to We realistically model the diffuse foregrounds ac- measure these radiation effects with the hyperfine line • counting for spatial variations of their spectral in- of the neutral hydrogen (HI) gas pervading the Uni- dex, which is estimated from all-sky, publicly avail- verse. The expansion of the Universe redshifts these pho- able maps at two frequencies (45 and 408 MHz). tons from earlier epochs to lower observed frequencies, ν The new DARE reference instrument design in- =1420/(1 + z) MHz (e.g., at z = 30, ν = 45 MHz). Im- • corporates (1) an optimized antenna with on-orbit portantly, this frequency-redshift relation enables a di- beam calibration, (2) the replacement of Dicke rect reconstruction of the history of the Universe as a switches for bandpass calibration with a pilot function of time from the 21-cm spectrum. frequency tone system capable of high dynamic Figure 1 shows some example predictions (amongst range monitoring of gain variations and measure- those currently allowed) for the 21-cm spectrum during ments of the system reflection coefficients, and the Dark Ages and Cosmic Dawn. The brightness tem- (3) polarimetric observations to provide a model- perature of this 21-cm signal is given by (e.g., Madau independent measure of the beam-averaged fore- et al. 1997b; Shaver et al. 1999; Furlanetto et al. 2006) grounds. The observations, performed from the radio-quiet zone above the Moon’s farside, will be 1/2 Ts TCMB 1+ z enabled through a unique “frozen” 50 125 km lu- δTb 27xHI − nar equatorial orbit (Plice et al. 2017×). The nom- ≃ Ts 10 − (1) inal observation time corresponds to 800 hours, ∂ v 1 (1 + δ ) r r mK , which results in radiometric noise integration to the B (1 + z)H(z) 1.7 mK level at 60 MHz. The instrument provides data with the frequency range (40 120 MHz), where xHI is the fraction of neutral gas, T is the 21- − s spectral resolution (50 kHz), beam characteristics cm spin temperature, TCMB is the CMB temperature, ◦ ( 60 FWHM at 60 MHz), and polarization re- δB is the baryon overdensity (taken here to be δB 0), quired≈ to measure the spectral features expected and H(z) is the Hubble parameter. The last term∼ in 4 Burns et al. this equation includes the effect of the peculiar velocities (by e.g., JWST) in the coming years can be immediately with line of sight velocity derivative ∂rvr. Since we will incorporated into the model, and will act to mitigate de- measure the spatially averaged δTb, the effects of the last generacies between Pop II and Pop III sources. More term in Equation 1 are negligible for observations of the subtle features of the signal, such as its asymmetry, may 21-cm global signal (e.g., Bharadwaj & Ali 2004; Barkana also reveal the presence of Pop III despite uncertainties & Loeb 2005). in the calibration of Pop II models (Mirocha et al., in Several important physical processes drive the evolu- preparation). tion of δTb with redshift. These include: (1) UV radi- It is also worth noting that the 21-cm global signal ation from the first stars, which “activates” the spin- traces the collective effects of all sources in the redshift flip signal through the Wouthuysen-Field mechanism ranges illustrated in Figure 1, which form a mostly unre- (Wouthuysen 1952; Field 1958); (2) X-ray heating, likely solved sea of fainter objects that likely dominate the total generated by gas accretion onto the first black holes; and emissivity of the early Universe. The red curves in Figure (3) ionizing photons from the first galaxies (which de- 1 are calibrated to match the latest luminosity function stroy the neutral hydrogen). measurements from HST (which probe relatively bright The relevant radiation backgrounds grow at different galaxies that can be resolved) and CMB optical depth times, so their interplay creates distinct features in the (τe) measurements from Planck (Mirocha et al. 2017), spectrum (Furlanetto et al. 2006; Pritchard & Loeb 2010; with variations arising solely due to differences in the Mesinger et al. 2011). When the first stars appear, their adopted properties of galaxies beyond the current de- UV radiation drives Ts toward the cold temperatures tection threshold. JWST and future CMB missions will that are characteristic of IGM gas (z 35 22 across our further constrain the bright-end of the galaxy luminosity ∼ − range of models; Region B in Figure 1), triggering a deep function and τe, respectively, and will thus enhance the absorption trough (Madau et al. 1997a). Shortly after, sensitivity of the 21-cm global signal to Pop III stars and black holes likely formed, e.g., as remnants of the first their remnants in faint galaxies. stars (z 25 12 across our range of models; Region C). The signal models described in this section are used to The energetic∼ − X-ray photons from these accreting black create the signal training set, an essential component of holes travel great distances, eventually ionize H and He our observational strategy from which the signal extrac- atoms, and produce photo-electrons that deposit some of tion pipeline calculates the main modes of variation of their energy as heat in the IGM (Shull & van Steenberg the signal. The new data expected from JWST and from 1985; Furlanetto & Johnson Stoever 2010), transforming CMB missions will constrain parameter space, which will the 21-cm signal from absorption into emission as the gas allow us to restrict the training set and reduce parameter becomes hotter than the CMB (Region D). The emission degeneracies and covariances. See Section 6 for more de- peaks as photons from these stars and black holes ionize tails on the training set and its effect on the uncertainty the IGM gas (z < 12), eventually eliminating the spin- of our signal estimate. flip signal. The dashed red curve in Figure 1 assumes that the ef- 4. FOREGROUNDS ficiency and properties of star formation in early galaxy Here, we discuss the origin and properties of the fore- populations (Sun & Furlanetto 2016; Mirocha et al. 2017) grounds expected in the 21-cm measurement from lunar and the relationship between X-ray luminosity and star orbit, which are modeled and accounted for in our signal formation rate are the same as at later times (Mineo et al. extraction pipeline. 2012b). There are several reasons to expect that this Pop II model is conservative, i.e., that it underestimates the total production rate of UV and X-ray photons. For ex- 4.1. Galaxy/Extragalactic Foregrounds ample, it assumes solar metallicity, though stars in high-z Beam-averaged diffuse sky foregrounds represent the galaxies are likely forming in metal-poor environments, strongest contributors to any highly redshifted 21-cm which can boost their UV (Eldridge & Stanway 2009) measurement for a space-based experiment. The most and X-ray outputs (Brorby et al. 2016). The solid red important arises from our Galaxy (Shaver et al. 1999). In curve in Figure 1 assumes that galaxies have metallici- addition, a “sea” of Extragalactic sources appear as an- ties (Z) 5% of solar, which results in a shallower absorp- other diffuse, spectrally-featureless power-law foreground tion feature due to enhanced X-ray emission (assuming (at DARE’s resolution) and contributes 10% of the to- ∼ the Brorby et al. 2016 LX -SFR-Z relation). Alterna- tal sky brightness temperature (Figure 2). The emission tively, the black curves include a simple model for Pop from these foregrounds is produced by synchrotron radi- III stars, in which low-mass halos (below atomic cooling ation that intrinsically has a smooth frequency spectrum threshold) can produce UV and X-ray photons (neglected (e.g., Bernardi et al. 2015; Petrovic & Oh 2011). On top by red curves). Boosts of 100 in the efficiency of the of the spectral smoothness, the foregrounds are spatially UV (dashed black) and also the X-ray luminosity (solid variable (inset in Figure 2). Their featureless spectrum black) of Pop III stars relative to Pop II result in a va- and spatial variability contrast with the spectral features riety of qualitatively different predictions for the global and spatial uniformity of the 21-cm spectrum, making 21-cm signal. Pop III models that resemble our black them separable (Liu et al. 2013; Switzer & Liu 2014). curves should be relatively straightforward to distinguish Theoretical models predict that the foreground is well from Pop II-only models for an experiment like DARE approximated by a third-order polynomial to levels below (see Section 6 and Figure 7). At this stage, our ability the amplitude of the 21-cm global signal, especially over to label each set of curves as being Pop II- or Pop III- low-foreground regions (Bernardi et al. 2015). Smooth- dominated assumes that the current Pop II models are ness over a frequency range much broader than 40-120 well calibrated (Mirocha et al. 2017). New measurements MHz is supported by sky models produced from measure-∼ The 21-cm Global Signal 5

Redshift (z) 30 24 20 17 14 12

105

3 Galactic (non-thermal) 10 Galactic reflected Extragalactic off moon Moon (thermal) 101

(K) Galactic free-free b T 21-cm (absorption) 10−1 21-cm (emission)

DARE baseline 10−3 Lunar dust impact mission sensitivity

40 50 60 70 80 90 100 110 120 ν (MHz)

Figure 2. The Galactic and Extragalactic spectra for a typical region away from the Galactic center. The Galaxy spectrum also reflects off the Moon (Evans 1969). The Moon’s thermal emission at low radio frequencies arises from cold, uniform subsurface layers. The effects of hyperkinetic dust impacts on the spacecraft in orbit of the Moon are unimportant. The red curve illustrates the spectral features in the 21-cm spectrum, where the dashed part of the curve corresponds to emission and the solid to absorption for this log-linear plot. Inset: A Mollweide projection of the sky at 408 MHz (Haslam et al. 1982) along with a DARE beam FWHM white contour. ments that cover the range 10 MHz - 5 THz (de Oliveira- also estimate the beam chromaticity by modulating the Costa et al. 2008; Zheng et al. 2017; Sathyanarayana Rao beam-averaged foregrounds through rotation of the an- et al. 2017). These models rely on, at most, five compo- tenna about the boresight axis. This technique is dis- nents to describe the spectral content of the foreground cussed in Section 5. This represents a significant ad- over several decades in frequency. Global measurements vancement over previous simulations. For instance, in from the Experiment to Detect the Global EoR Signa- Harker et al. (2016), the beam was taken to be Gaussian ture (EDGES), Sonda Cosmológica de las Islas para la and the integrated foreground was assumed to perfectly Detección de Hidrógeno Neutro (SCI-HI), Shaped An- 5 i follow a polynomial of the form ln (T )= i=0 ai ln (ν) . tenna measurement of the background RAdio Spectrum Finally, we note that the low foreground areas of the (SARAS), and Large-Aperture Experiment to Detect the sky are polarized to a few percent (. 5%)P (Jelićet al. Dark Ages (LEDA) provide further validation of the in- 2014, 2015; Lenc et al. 2016). Our dual polarization intrinsic foreground smoothness (Rogers & Bowman 2008; strument directly measures this intrinsic sky polariza- Mozdzen et al. 2017; Voytek et al. 2014; Patra et al. 2015; tion. At the same time, this polarization is minimized Bernardi et al. 2016). through dilution produced by our wide antenna beam, In our strategy, we use a diffuse foreground model pro- and also averaged down by our scanning strategy, which duced from all-sky observations taken at two frequen- includes antenna rotation. cies, 45 and 408 MHz (Haslam et al. 1982; Guzmán et al. 2011), in order to account for spatial variations in the 4.2. Other Foregrounds spectral index. 21-cm cosmology experiments in lunar orbit will also The spectrally smooth foreground is altered via detect emission from the Moon via the antenna back- the frequency-dependent antenna response (Vedantham lobe. The lunar spectrum is comprised of (1) thermal et al. 2014; Bernardi et al. 2015; Mozdzen et al. 2016). emission from a 100 m subsurface layer (i.e., electrical The beam directivity of finite-sized, wideband anten- skin depth of the∼ regolith) (Salisbury & Fernald 1971; nas does not remain constant across frequency (Rumsey Keihm & Langseth 1975) and (2) reflected Galactic emis- 1966). This beam “chromaticity” impacts the observed sion, requiring a parameter in the data analysis pipeline spectrum of the spatially-dependent foregrounds. The to describe the Moon’s reflectivity (Davis & Rohlfs 1964; variation with frequency of the beam shape and directiv- Vedantham et al. 2015). ity imprints spectral structure into the beam-averaged Other processes have a minor effect on the spectrum. response that is not intrinsic to the foregrounds. Hyperkinetic impacts of dust from the interplanetary As part of our strategy, chromaticity is addressed by medium and the lunar exosphere on the spacecraft sur- minimizing instrumental design effects and making pre- face generate radio transients (e.g., Meyer-Vernet 1985); cise beam measurements on the ground and on-orbit. We but the dust distribution around the Moon (e.g., Stubbs 6 Burns et al. et al. 2010), the capacitance of the spacecraft, and solar wind conditions produce most of its emission at frequen- 2 2 P = g F (η T + (1 η )T )(1 Γ )+ Toff , cies < 40 MHz (Figure 2; Le Chat et al. 2013). | | l A − l Ap − | A| Bright, transient, nonthermal emission from Jupiter (2) and Io also occur at <40 MHz (Panchenko et al. 2013; where P is the raw power measured by the instrument, g Cecconi et al. 2012); however, at 40-120 MHz, the an- and Toff represent the system gain and radiometric off- tenna temperature observed by an instrument like that set respectively, ηl accounts for the antenna and balun 2 proposed for DARE is only 1 mK for Jupiter (Zarka losses at physical temperature TAp,1 ΓA accounts for 2004). Jupiter, and other astronomical∼ sources such as the reflection coefficient of the antenna,−| and| F 2 is the Cas A (similarly beam-diluted), may introduce low-level throughput of the receiver front end accounting| | for mul- spectral effects due to scattering off the spacecraft. Elec- tiple reflections between the receiver and antenna. The tromagnetic analysis, incorporating accurate models of instrument calibration activities consist of using ground, the spacecraft, must be used to assess and calibrate these on-board and on-orbit calibration to invert the forward effects as part of the signal extraction pipeline. instrument response model and provide an estimate of Finally, atoms (e.g., carbon) in cold, diffuse gas in the the antenna temperature TA. Milky Way (and possibly in the IGM) produce radio re- During science observations, the receiver is calibrated combination lines (RRLs; Peters et al. 2011; Morabito continuously using the pilot tone injection receiver ar- et al. 2014). These lines are sharp ( 10 kHz wide), but chitecture. The calibration system generates tones at 5 spaced at known intervals of 1 MHz.∼ Spectral chan- frequencies simultaneously across the band to adequately≈ nels containing RRLs constitute∼ a negligible fraction of sample the frequency range. The tones are each within the data and may be discarded. Removal of potential a single 50 kHz spectrometer bin, and thus produce neg- RRLs from the 21-cm spectrum will drive the spectral ligible degradation in spectral performance. The nomi- resolution of the science instrument. Also, beam dilu- nal calibration cycle consists of a sequence of four states tion is expected to significantly reduce any impact from which are enabled for 10 seconds each: 1) high-level tones recombination lines. directed toward the receiver, 2) low-level tones directed toward the receiver, 3) high-level tones directed toward the antenna, and 4) low-level tones directed toward the 5. THE DARE SCIENCE INSTRUMENT antenna. The gain of the receiver is computed by differ- encing instrument-measured power from the high- and To illustrate how the cosmological 21-cm spectrum low-level injected tones toward the receiver divided by can be extracted from the foregrounds, we use the new the difference in effective input brightness temperature science instrument proposed for DARE (Figure 3). In of the tones characterized during pre-flight calibration. Burns et al. (2012), we outlined a very basic approach Likewise, the tones injected toward the antenna afford for idealized, lunar-based 21-cm cosmology observations. an on-board measurement of the antenna reflection com- We have now advanced the fidelity of the instrument puted in a similar fashion. model to evaluate measurements of the spectrum and 2 The terms Toff , ηl, and F in Equation 2 are com- constrain parameters for the first luminous objects at the puted based on ground measurements| | and the on-orbit significance level presented in Section 2, in the presence trending of the receiver gain and reflection coefficient. of realistic and well modeled uncertainties. The DARE antenna and receiver are designed to min- Figure 4 shows a block diagram of the current DARE imize temperature variations by limiting exposure to the instrument design, which consists of four subsystems: solar flux and lunar albedo. For the antenna, thermal (1) an antenna composed of a pair of crossed biconical baffles, as shown in Figure 3, result in a predicted phys- dipoles above a ground plane that provides dual polariza- ical temperature change over the lunar orbit of 10◦C al- tion with low reflection coefficient (-12 dB average across lowing DARE to maintain a nearly constant beam di- the band) and beam chromaticity (the beam directiv- rectivity. The front-end receiver includes a proportional- ity spectral knowledge goal is 20 ppm, see below); (2) ∼ integral-derivative temperature control to provide pre- a thermally-controlled receiver with a calibration archi- dicted thermal stability of 0.1◦C, thus reducing receiver tecture that utilizes precise continuous-wave frequency systematics to meet DARE’s calibration and stability re- tones optimized to yield a frequency response that meets quirements. DARE’s RMS criterion; (3) a spectrometer with a wide A novel feature of the current design is on-orbit cal- bandwidth and digital receiver that provides the spec- ibration of the antenna directivity. Measurements of tral resolution and Stokes processing of the V and H the beam will be obtained by receiving 3 narrow- channels; and (4) an instrument electronics subsystem band, circularly-polarized signals spaced across≥ the band, to interface with the spacecraft. The expectation for the transmitted from a large antenna on the Earth as DARE instrument envelopes the hardware performance of sys- orbits the Moon above the nearside. The spacecraft (and tems on the ground (e.g., EDGES, Bowman & Rogers antenna) is slowly rotated while it continuously receives 2010; Cosmic Twilight Polarimeter, CTP, Nhan et al. these signals. The received signal power at each fre- 2017) and in space (Global Precipitation Measurement 2 quency as a function of antenna pointing will produce a Microwave Imager, GMI ). slice through the beam power pattern. The transmitted We model the forward instrument response following signals will also reflect off the lunar regolith and return to that used by EDGES (Monsalve et al. 2017) as: the same antenna on Earth to correct for ionospheric effects. The in-situ beam measurement system is currently

2 being baselined to use the 140-foot radio telescope at the https://pmm.nasa.gov/gpm/ﬂight-project/gmi Green Bank Observatory, operating with 50% aperture The 21-cm Global Signal 7

Figure 3. An artistic rendering of the DARE observatory. The science instrument thermal shield surrounds the antenna (shown transparent for clarity). The antenna consists of a pair of dual, crossed bicones. Beneath the antenna support structure is a deployed ground plane which aids in shaping the beam directivity. Below the instrument is the spacecraft bus including the solar panels and telemetry system.

Dual Bicone Antenna ANTS-Antenna Subsystem Support Structure Ground V H Plane Balun Balun ThermalThe rma l Ground Plane Shield Deployment

IES - Instrument Pilot Tones Electronics & Noise Subsystem LNA LNA Diodes Front-End Thermal Receiver Calibration Control Amp Amp Assembly Filter Filter

RS-Receiver Amp Amp Back-End Receiver Subsystem Filter Filter

ADC ADC SS-Spectrometer Power Subsystem

FPGA FPGA

Figure 4. DARE instrument block diagram. DARE consists of four subsystems: dual polarization antenna, pilot tone calibration receiver, high resolution digital spectrometer, and a standard instrument electronics module for power, data handling, and instrument control that interfaces with the spacecraft. efficiency, transmitting 10 kW of power, and using 10 ization arms of the antenna. This modulation results in second averaging. induced polarization that tracks and measures the beam- Another innovation in the current design of DARE is averaged foreground spectrum, without relying on e.g., polarization measurements to constrain and distinguish polynomial model fits, and is insensitive to the spatially the beam-averaged foregrounds from the unpolarized HI uniform 21-cm signal. CMB polarization measurements signal (Nhan et al. 2017). Our observation strategy in- use analogous modulation approaches, achieving stabil- corporates rotation of the antenna about the boresight ity and systematic control required for µK polarimetric axis to modulate the signals captured by the two polar- sensitivity (e.g., Bennett et al. 2003; Bischoff et al. 2013). 8 Burns et al.

The on-orbit measurements of the antenna directivity ν indicate the sky direction and frequency channel, re- and the induced polarization technique enable us to an- (r) √ spectively, and σr(ν) = TA,D(ν)/ ∆ν∆t is the thermal ticipate a knowledge of the beam-averaged foregrounds noise level in the data for a given frequency bin of width at a level of 20 ppm. This represents an important ∼ ∆ν centered on ν integrated over a time ∆t. advancement that allows us to achieve our goal of <20 (r) mK RMS spectral uncertainty on the extracted 21-cm We model TA,M (ν) as a linear combination of (di- models. mensionless) principal modes derived from SVD analyses (Switzer & Liu 2014; Paciga et al. 2013; Vedantham 6. EXTRACTING THE COSMIC 21-CM SPECTRUM et al. 2014), In this section we demonstrate an essential aspect n m of our observational strategy: how our data analysis (r) (r) TA,M (ν,γ)= (γ21)ifi(ν)+ (γsys)j gj(ν) , (4) pipeline is able to separate the 21-cm signal from fore- i=1 j=1 grounds measured through a realizable instrument. We X X model each of these components, signal along with the where fi(ν) and gj (ν) are the SVD signal and system- foreground and instrument systematics, as described be- atic modes, respectively, and (γ21)i and (γsys)j (both low. with units K) are the coefficients associated with each of In our previous work (Harker et al. 2012, 2016 here- them. We fit the entire parameter space, γ = [γ21,γsys], after H12 and H16), we developed a foundation for a simultaneously (using the emcee code; Foreman-Mackey 21-cm signal extraction pipeline using a Markov Chain et al. 2013) in order to account for the covariance be- Monte Carlo (MCMC) framework. However, we assumed tween all parameters and ensure self-consistency. This an idealized instrument with exact knowledge of most in- MCMC calculation efficiently and robustly obtains the strument systematics and the form of the beam-averaged full posterior distribution. foreground. We have now significantly expanded the ini- In this work, we utilize n = 6 (signal) and m = 7 tial analyses of H12 and H16 by implementing a robust (systematic) SVD modes because they are able to fit SVD modeling scheme based upon a pragmatic end-to- our fiducial models to within the thermal noise level end instrument model (Section 5). Specifically, the cur- achieved through 800 hours of integration. For future rent pipeline (which will be released to the community analyses, however, we are developing a novel technique in a later publication) incorporates the following aspects that will choose the optimal number of modes to use in for the first time: the pipeline. The details of this key advancement will be described in forthcoming works (Tauscher et al., in Full simulations of the antenna beam-weighted prep.; Rapetti et al., in prep.). • foreground. These simulations are based upon The systematic modes gj(ν) are derived from 10,000 beam patterns calculated by the CST electromag- simulated datasets which vary the foreground and in- netic simulation package3 and our diffuse fore- strument within expected uncertainties. This process ground model, described in Section 4. utilizes Equation 2, its inverse, and the fiducial values of the calibration and beam-weighted foreground param- A calibration model, based upon expected lab mea- eters (Tauscher et al. in prep.). Currently, the signal • surements and uncertainties, that includes all pa- modes fi(ν) are derived from input training sets of 21- rameters in Equation 2. The instrument model de- cm spectrum simulations (15,000 and 960, respectively) scribed in H12 included only the antenna reflection based on two well-motivated ranges of physical models coefficient. (primordial Pop II and Pop III stars; see Section 3).4 In A modeling scheme, detailed below, based upon future work, the signal models will be combined into a • the implementation of SVD on well-characterized single training set. training sets for both the signal and a complete The Bayesian nature of the MCMC permits the incor- set of instrument and foreground systematics. The poration of key prior knowledge on the instrument cal- SVD technique independently determines the main ibration and foregrounds when retrieving the posterior modes of variation in the signal and systematics. probability distribution of the model parameters. In the The MCMC algorithm then simultaneously fits all instrument simulations, we account for all the identified the coefficients associated with the SVD modes to uncertainties and priors, including a 50 mK constraint extract the signal. This is a major improvement on the beam-averaged foregrounds from measurements over our previous use of polynomials (Fourier se- of the induced polarization. Even though, at this stage, ries) to fit the foreground (reflection coefficient). the induced polarization is used only as a prior on the antenna temperature, TA, in future work, all four Stokes The MCMC algorithm in the pipeline samples the like- parameters will be included in the likelihood function. lihood function Figure 5 shows the SVD modes used in this work. The 2 left and middle panels contain the signal modes for the Nr Nν (r) (r) 1 TA,D(νi) TA,M (νi,γ) models of primordial Pop II and Pop III stars, respec- ln L(γ)= − , (3) tively. For the purpose of reducing the covariance be- −2 σ (ν ) r=1 i=1 " r i # X X 4 Each set of simulations was derived by randomly sampling where T (r) (ν) and T (r) (ν) are the antenna tempera- the parameter space surveyed in Mirocha et al. (2017), with the A,D A,M addition of two parameters that describe the UV and X-ray photon 4 ture spectra for the data (D) and the model (M), r and production efficiency in minihalos (i.e., those with Tvirial < 10 K). The Pop III models include only those with Region D extrema in 3 https://www.cst.com/ emission. The 21-cm Global Signal 9

PopII signal modes PopIII signal modes Systematic modes 0.4 0.25 0.2 0.2 0.00 0.0 0.0 −0.25 g (ν) g (ν) −0.2 −0.2 1 5 f1(ν) f4(ν) f1(ν) f4(ν) −0.50 g2(ν) g6(ν) )[dimensionless] )[dimensionless] )[dimensionless] ν ν f (ν) f (ν) ν f (ν) f (ν) g (ν) g (ν) ( 3 7

( 2 5 ( 2 5 j

i −0.4 i f f −0.4 g −0.75 f3(ν) f6(ν) f3(ν) f6(ν) g4(ν)

40 60 80 100 120 40 60 80 100 120 40 60 80 100 120 Frequency (MHz) Frequency (MHz) Frequency (MHz)

Figure 5. Left panel: the 6 principal SVD signal modes derived from 21-cm spectrum simulations of models based on primordial Pop II stars. Middle panel: the same but for signal models based on primordial Pop III stars. Right panel: the 7 principal SVD systematic modes derived from simulations of the instrument plus foreground. Each panel contains a set of orthonormal models, i.e. the curves represent only dimensionless shapes which are then multiplied by coeﬃcients with units of temperature (K). The ability to separate the 21-cm signal from DARE’s systematics hinges on the ability to distinguish between the signal modes, fi(ν), and the systematic modes, gj (ν).

PopII model covariance PopIII model covariance 1 1 2 2 10−1

i 3 i 3 ) )

21 4 21 4 −2 γ 10 γ ( 5 ( 5 6 6 ] ] 1 2 1 2 −2 2 [K 2 10 [K

j 3 j 3 ) ) 4 4 sys sys γ γ

( 5 ( 5 6 6 7 7 10−3 10−3 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3 4 5 6 7 (γ21)i (γsys)j (γ21)i (γsys)j

Figure 6. Covariance matrices for the 6 SVD signal parameters, (γ21)i for i ∈ {1, 2,..., 6}, and the 7 SVD systematic parameters, (γsys)j for j ∈ {1, 2,..., 7}, used for fitting the primordial Pop II (left panel) and Pop III (right panel) stellar models. For ease of viewing, the absolute values of the covariances are shown. The vertical and horizontal black lines separate the regions with covariances between signal parameters (top left) and systematic parameters (bottom right). The other two regions are symmetric and show the covariances between parameters multiplying signal and systematic modes. tween our parameters, γ, it is important that the SVD ances between the signal parameters, which depend on systematic modes are as orthogonal as possible (i.e. have the level of overlap between the signal and systematic a minimal dot product) with the SVD signal modes. modes. This will be explored in detail in upcoming work When comparing one signal mode with the systematic (Tauscher et al., in prep.). mode of the same order (color) in Figure 5, we note that In summary, for the DARE instrument parameters dis- the shapes of the modes are sufficiently different to en- cussed in Section 5 and 800 hours of total integration able a clean extraction of the signal (see Figure 7). above the lunar farside, our signal extraction pipeline Figure 6 shows the covariance matrix of the 6 signal recovers the spectra and uncertainties for two represen- parameters, (γ ) with i 1, 2, ..., 6 , and the 7 sys- tative models (Pop II and Pop III star models) shown in 21 i ∈ { } tematic parameters, (γsys)j with j 1, 2, ..., 7 . The Figure 7. In addition to the 21-cm signal, the pipeline top left corners within each of the 4 regions∈ { in both} pan- simultaneously fits the SVD modes of the receiver, beam, els of Figure 6 demonstrate that the lowest order signal and foreground utilizing prior information and on-orbit modes have enough similarities in shape with the first 3-4 measurements. With an average RMS of 17 mK, we re- systematic modes to generate only modest covariances. cover the major features in the spectra and≈ differentiate By simultaneously fitting all parameters, γ, and between different stellar population models. marginalizing over the systematic parameters, γsys, we are able to clearly separate the signal from the systemat- 7. PHYSICAL PARAMETER ESTIMATION ics despite those covariances, as shown in Figure 7. The With the calibrated spectra and uncertainties in Figure widths of the uncertainty bands result from the covari- 7, it is straight-forward to estimate when the first lumi- 10 Burns et al.

Figure 7. The extracted 21-cm spectra with 68% confidence intervals for models with primordial Pop II (red) and Pop III (black) stars expected using the DARE instrument parameters and 800 hours of observation. The dark bands represent thermal (statistical) noise from the sky. The total uncertainty, including statistical plus systematic effects from the instrument and foreground, is shown by the lighter bands, which are dominated by the covariance between the SVD signal and systematic modes. nous objects ignited and began reionizing the Universe. dominate the UV background; if, for example, Pop III Since redshift maps directly to frequency, measurements star formation is efficient, we should expect features of of the extrema frequencies from the 21-cm spectrum de- the signal to occur at lower frequencies (higher redshift) termine when major events occurred in a mostly model- than if Pop II stars dominate the background because independent fashion (Harker et al. 2016). The frequency Pop II stars form in more massive halos which do not of the Region B extremum (νB ) determines the z at become abundant until relatively late times (low red- which the UV background activates the 21-cm transi- shift). DARE’s sensitivity can separate the effects of tion (i.e., first stars ignition). This clean and accurate the broad classes of Pop II and Pop III stellar models measurement delineates the nature of the first stars, es- considered in this work (see Figures 1 and 7), subject to pecially considering that no observational bounds cur- the assumed calibration of the Pop II contribution (see rently exist. Using a Pop III model as a working example, Section 3; Mirocha et al. 2017) and the model for Pop III DARE will extract νB with a 1% (0.4 MHz) uncertainty stars. A useful metric for gauging the influence of Pop (68% confidence). Similarly, the redshift when the first III is the ratio of UV production efficiencies for Pop III black holes began accretion is measured from the Region compared to Pop II stars, ξ ξ /ξ . The value α ≡ α,III α,II C extremum frequency (νC ) with 1% (0.6 MHz) uncer- of ξα,II is drawn from the BPASS models (Eldridge & tainty. The redshift of the beginning of reionization is Stanway 2009) assuming solar metallicity, while ξα,III is measured from the extremum νD with 2% (2 MHz) un- allowed to vary freely. DARE constrains ξα,III with 25% certainty. Different models (Figure 1) yield similar un- uncertainty in Figure 8. certainties for the extrema frequencies.5 The characteristics of the first X-ray sources (Region C The characteristics of the first stars and galaxies, along in Figure 1) are inferred from the ratio of X-ray heating with the history of the early Universe, are determined efficiencies between Pop III and Pop II stars. Analo- from modeling of the calibrated spectrum. First, the his- gous to the UV constraints, the Pop III X-ray efficiency, tory of reionization in the early Universe is characterized ξX,III , is allowed to vary freely, while ξX,II is anchored by the HI fraction (xHI ) and the IGM kinetic tempera- to the local relation between X-ray luminosity and SFR ture (TK) at z 11. Our modeling of features in Region (Mineo et al. 2012a) assuming high-mass X-ray binaries D using DARE’s∼ sensitivity yields uncertainties of 5% are the dominant source. DARE can measure ξX,III and 10% for xHI and TK, respectively. with 15% uncertainty (see Figure 8). Further model- Next, the features in the 21-cm spectrum at the lowing plus multi-wavelength observations (e.g., the cosmic est frequencies depend upon the stellar populations that X-ray background; Fialkov et al. 2017) may help to bet- ter constrain the identity of the Universe’s first X-ray sources, whether they be black hole X-ray binaries, hot 5 Note that the extrema locations are determined from the full signal model on each step of the MCMC, i.e., these quantities have gas in star-forming galaxies, or proto-quasars. not assumed a cubic spline form for the signal as in some previous Finally, before concluding, we emphasize that these works (Harker et al. 2012). Pop III models are quite simple, as, for example, they ne- The 21-cm Global Signal 11

55 (MHz)

C 54 ν 150

53 X, II 125 /ξ 108 100

(MHz) 105

X, III 75 D ν 102 ξ 50 99 35 36 37 53 54 55 56 50 75 100 125 150 νB (MHz) νC (MHz) ξα, III/ξα, II

Figure 8. The panels illustrate examples of constraints on the global 21-cm extrema frequencies (left), UV photon production efficiency (ξα) and X-ray heating efficiency (ξX ) between models with Pop III and Pop II stars (right) using the calibrated 21-cm spectrum. Dotted black lines indicate the “true” input values. The contours are at the 68% confidence intervals using 23 (black) and 30 (blue) mK average RMS uncertainties over the observed band. glect an explicit treatment of feedback. As a result, the accreting black holes along with the redshift of the be- interpretation of the precise value of ξα,III /ξα,II may be ginning of reionization can be inferred to within a few considerably more complex in practice, but the finding percent. The 21-cm signal is also uniquely sensitive≈ to that both values are non-zero is robust. the different radiation effects produced by Pop II and Pop III stellar models. Specifically, the UV production and 8. CONCLUDING REMARKS X-ray heating efficiencies can be constrained, thus deter- mining which stellar population was dominant within the To achieve the science potential of 21-cm global spec- first galaxies. Finally, the history of reionization in the tral observations, we proposed an observational strategy early Universe can be characterized by the redshift evo- that carefully considers the local environment, the instru- lution of the HI ionization fraction (xHI ) inferred from ment, and the methods for signal extraction. A lunar- the 21-cm spectrum. orbiting experiment above the Moon’s farside has the Accurate parameter estimation is a core capability re- best probability of measuring the 21-cm spectrum since quired for 21-cm global signal observations and inter- this environ is free of ionospheric effects and human- pretations. Bayesian methods have significant potential generated radio frequency interference. for 21-cm observations (Greig et al. 2016; Bernardi et al. Signal extraction in the presence of bright foregrounds 2016). They have proven to be successful for other exper- is the greatest challenge for all observations of the 21-cm iments targeting weak signals, including CMB observa- cosmological spectrum. Utilizing Singular Value Decom- tions (Planck Collaboration et al. 2016a,b) and the LIGO position to model the foreground and instrument along gravitational wave detections (Abbott et al. 2016; Veitch with a Markov Chain Monte Carlo numerical inference et al. 2015). The next step in the analyses of the global technique to survey parameter space, we showed that it 21-cm spectrum is to construct a likelihood function al- is possible to accurately recover the expected features in lowing differentiation between differing physical models the spectrum in the presence of bright foregrounds with for the first halos. Similarly, modeling different levels the instrument characteristics of the Dark Ages Radio of structure in the beam-convolved foregrounds needs a Explorer (DARE) for 800 hrs of integration. To sepa- ≈ refined Bayesian approach. This is a highly computation- rate the signal from the foreground, the antenna system ally intensive process. We are refining and extending our must be well-characterized requiring temperature con- SVD modeling approach towards these goals. In addi- trol and precise beam directivity measurements on the tion, recent developments of Nested Sampling algorithms ground and in-space. In addition, a model-independent for high dimensional parameter spaces which operate in constraint on the foreground from polarimetric observa- massively parallel computer architectures (Handley et al. tions is an important element in the signal extraction. 2015) have great potential for 21-cm cosmology applica- From the extracted 21-cm spectrum (including confi- tions. dence intervals), we showed that meaningful constraints In conclusion, measurements of spectral features in the can be placed upon the physical parameters of primordial 21-cm spectrum will answer key science questions from radiating objects. The redshift for the commencement the NRC Astrophysics Decadal Survey: “What were the of first star formation and X-ray emission from the first 12 Burns et al.

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