Spectral Line Intensity Mapping with Spherex

Spectral Line Intensity Mapping with SPHEREx

Tzu-Ching Chang (JPL/Caltech)

SPHEREx Science Team

Hao-Yi Heidi Wu (Ohio State)

Olivier Doré Cosmology and First Light - December 2015 1 Line Intensity Mapping (IM)

•“Intensity Mapping” (Chang+ 2008, Wyithe & Loeb 2008, Wyithe et al. 2008):

• Measure the collective emission from a large region containing multiple sources, without spatially resolving down to galaxy scales. • Use spectral lines as tracers of structure, retain high frequency resolution thus redshift information. • Measure brightness temperature ﬂuctuations on the sky: just like CMB temperature ﬁeld, but in 3D.

courtesy of Phil Korngut (Caltech) • Low-resolution redshift surveys: economical, large survey volumes. • Confusion-limited. Foreground- limited. 2 Introduction

1.2 Targets for Line-Intensity Mapping

A wide range of spectral lines have been considered for intensity mapping studies [1]. While most work has focussed on the 21-cm line, there is growing interest in the [CII] ﬁne-structure line [2–4], the Ly↵ line [5–8], and rotational CO lines [9–14]. Much of the initial motivation was to probe the epoch of reionization [15] (EoR) at redshift z 10, but increasingly the focus has extended to large-scale structure at lower redshifts. The experimental21cm,⇠ front has beenCO, evolving [CII], rapidly with H severalα, preliminaryLyα detections and a host of new experimental projects, which include an array of suborbital instruments, and at least two major satellite mission concepts [16, 17]. Fig. 2 shows the accessible scales and redshifts of some of these upcoming line-intensity mappingIntensity experiments. Mapping Experiments SpatialScale θ

Figure 2. A representative list of current andRedshift proposed intensity z mapping experiments. The horizontal axis shows the redshift range of each experiment and the vertical axis indicates the range between the maximum resolution of the instrumentIntensity and the total Mapping sky coverage. status report These include (Kovetz+, COPSSII, arXiv:1709.09066 AIM-CO and ) COMAP which will target CO at medium redshifts, CONCERTO, CCAT-p and TIME which target [CII] at EoR redshifts, GBT, CHIME, HIRAX and HERA which target 21cm and SPHEREx which can measure H↵ and Ly↵ over a wide range of redshifts at high-resolution. (Courtesy of Ely Kovetz and Patrick Breysse)

One or more of the lines above is observable from redshifts of order unity to redshifts potentially as high as 20 or more. Under the prevailing ⇤CDM cosmological model, this will make it possible to track the growth of the ﬁrst structures, the reionization of the Universe and the emergence of dark energy (see Fig. 3). The accessible cosmic volume is so large that it may be possible to identify even small deviations from ⇤CDM. Meanwhile, measurements of line-emission over large volumes of space at high redshift may provide a unique window into astrophysical properties such as the star-formation rate and the density of molecular clouds.

IM Status Report 2017 SPHEREx deep ﬁelds: A representative view of the Universe

Peak of Star First galaxies formation z Dark energy Cosmic domination reionization Line Intensity Mapping with SPHEREx

Hα ﬂuctuations at z~1 Lyα ﬂuctuations at z=6.6

Wu et al. Sadoun et al., in prep in prep

50 Mpc 50 Mpc

• SPHEREx will produce 96 spectral images and map 3D intensity ﬂuctuations of multiple line tracers across redshift.

• Simulation work on-going, including multiple emission lines (Hα, Hβ, [OIII], [OII]) at 0 < z < 10 plus stellar continuum, and Lyα radiative transfer calculations during EoR. Line Intensity Mapping with SPHEREx

Fluctuations in Line Emission Power Spectra of Emission Lines

z=2 Clustering amplitude (bias)

Doré et al., arXiv:1412.4872

• SPHEREx will measure statistically the ﬂuctuations of multiple spectral lines associated with cosmic structures across redshift.

• SPHEREx will measure at high SNR the 3D clustering of multiple line tracers and the luminosity-weighted biases. Line Intensity Mapping with SPHEREx

Fluctuations12 in Line Emission SFRD from Hα intensity mapping the cross power spectrum becomes similar to Equation (19) that needs to be replaced by the terms Pcross(k)and ∆Pcross(k). In Figure 8, we show the cross power spectra of Hα, [OIII], [OII] and Hβ lines with the 21-cm line at z = 1.0 ± 0.2. The errors are also shown for the CHIME and Tianlai experiments in solid and dotted bars, respectively. We ﬁnd both the SNRs of the cross power spectra for the CHIME and Tianlai are large enough to be well measured for all of the four lines at z ∼ 1. The SNR of Tianlai is larger than that of CHIME, since it has greater collecting area, more receivers, and higher resolution, as shown in Table 3. Note that the measurable scales of the cross power spectrum are larger than the intensity power spectrum probed by SPHEREx alone (see Figure 6). This is because the spatial and spectral resolutions of CHIME and Tianlai are relatively low, so that only large scales with k<1Mpc−1h can be detected. We ﬁnd that the detectability of SPHEREx cross-

Clustering amplitude (bias) correlated with CHIME or Tianlai is greatly improved compared to the current galaxy×21-cm measurements given by Chang et al. (2010) and Masui et al. (2013). The SNR of SPHEREx×CHIME and Tianlai is ∼30 for Hα, [OIII] and [OII] lines, and it is ∼10 for Hβ line at z ∼ 1. For comparison,Doré et al., the SNRarXiv: is less1412.4872 than 10 for the Fig. 9.— The constraints on the SFRDGong from the et H αal.intensity 2017 as galaxy×21-cm measurements at z ∼ 0.8. measured by SPHEREx. The filled blue triangles, green squares, In Table 4, we tabulate the SNRs of the cross power orange pentagons, red circles and pink inverse triangles aretheob- servational data given in other works (Schiminovich, et al. 2005; spectrum for the four optical lines with CHIME and Oesch et al. 2010; Reddy & Steidel 2009; Bouwens et al. 2014; Tianlai at 0.8 ≤ z ≤ 2.4. As can be seen, the cross Finkelstein et al. 2015). The gray curves show the SFRD given in • SPHERExpower will spectra map have SFR large through SNRs over cosmic the redshift time range, upHopkins to z~5 & Beacom via (2006),Hα andIntensity the gray region Mapping. shows the 2σ C.L. even for the relatively faint Hβ line with SNR>5, and We find that intensity mapping can provide stringent constraints on the SFRD at z ! 4. the foreground line contamination can be reduced sig- • SPHERExnificantly has the by cross sensitivity correlation. Thisto detect indicates thatLyα cross fromkHz EoR, is adopted inferring for SKA1-mid ionizing band photon one. We find production. the correlations of the four lines with the 21-cm line are an SNRs of the cross power spectra between SPHEREx and advantageous method for extracting the intensity fluctu- SKA1-mid are lower than that for CHIME and Tianlai. • See talk ationby Nick signal. Scoville tomorrow afternoon. For instance, SNR=5.7 for Hα × 21 cm at z = 1, which Another similar 21-cm experiment, Hydrogen Intensity is a factor of 5∼6 lower than CHIME and Tianlai. This and Real-time Analysis eXperiment (HIRAX), focuses on is basically due to relatively low spatial resolution for the similar redshift range of 0.8

Figure 10. 2D anisotropic power spectra shown by perpendicular and parallel Fourier modes for the signal (Lyα), foreground (only Hα here), and total observed signal+foreground. We find the 2D signal power spectrum is almost symmetric for k and k , and the redshift distortion effect is relatively small. ForGong+ the foreground 14 power spectrum at low redshift, because the redshift distortion effect is strong and the⊥ shift∥ factor on the foreground k and k are different, the shape of the power • spectrumHigh-z is irregular. Lyα Thisand effect low-z provides H aα way lines to distinguish can thebe signal confused and the foreground in SPHEREx in principle. Thein totalthe power⊥ IM spectrumregime.∥ is similar with the foreground power spectrum, since the amplitude of the signal power spectrum is much lower than the foreground. • (AWe color versionare planning of this figure isto available use in a the combination online journal.) of well-demonstrated techniques: • Masking bright, low-z sources: employed in CMB, CIB, EBL and studied for IM (e.g., Sun+16, are basically consistent with each other, especially for the Hα replaced by and [OSilva+17iii]lines.Themeanintensityofthethreelinesare). I 15 Jy sr 1, I 13 Jy sr 1,andI 24 Jy sr 1, ¯Hα − ¯[O iii] − ¯[O ii] − 2 which∼ are larger than the I∼ 10 Jy sr 1.Theresultsfromthe∼ • Use the anisotropic¯Lyα power− spectrum shape of Lyα and Hα (fromk observing1 toD( zcomovings) LFs in Ly et al. (2007)isingoodagreementswiththeothers,∼ bs (zs ) bs (zs)+ ∥ ˙ → ⎛ 2 2 ⎞ H (z ) D(z ) and wecoordinates) adopt their LFs and to thedistinguish errors to calculate the lines the power (Visbal & Loeb 2010; Gong+14;k + kLidz & Taylors s 2016; ⊥ ∥ spectrumCheng+ and uncertainty 2016 for). the three foreground lines. ⎝# ⎠ 2 At last, we discussed the methods to remove the foreground (ys /yf )k contamination due to low-redshift emission lines. We first bf (zf ) bf (zf )+ ∥ Cross-correlations of different lines at same redshift →(e.g., Visbal⎛ & Loeb2 22010; Gong+12,2 2 ⎞ +17). compared• the power spectrum of the Lyα at z 7tothe (rs /rf ) k +(ys /yf ) k Hα,[Oiii], and [O ii]powerspectrumatlowredshifts,and∼ ⊥ ∥ 1 ⎝D#(z ) ⎠ then• weCross-correlations considered the projection effectwith in galaxy the real survey.tracers The (e.g., Chang+10, Masui+13,˙ f Pullen+13,. +17). power spectrum of the foreground lines becomes larger after × H (zf ) D(zf ) the projection. We then proposed to mask the whole bright pixels with foreground emission above some flux threshold to Here, D(z)isthegrowthfactor.Thenormalexpressionofthe reduce the contamination of the foreground lines in the intensity second term of the bias is fµ2.Heref d ln D/d ln a,wherea mapping. We found that the contamination can be neglected is the scale factor, and µ cos θ,where= θ is the angle between when the flux cut is 1.4 10 20 Wm 2.Thecross-correlation − − the line of sight and the wave-vector= k.Wealsonoticethatthe method is helpful to reduce× or to estimate the contamination, so-called non-gravitational effects can introduce strong redshift- but it is indirect and cannot substitute the masking method in space distortion effect (Zheng et al. 2011;Wyithe&Dijkstra the survey of the intensity mapping. 2011). According to full Lyα radiative transfer calculations, the Lyα emission is dependent on environment (gas density and This work was supported by NSF CAREER AST-0645427 velocity) around LAEs. The observed LAE clustering features and AST-1313319. M.B.S. and M.G.S. acknowledge sup- can be changed by this effect especially at high redshifts. port by FCT-Portugal under grant PTDC/FIS/100170/2008. However, this effect relies on “missing” Lyα photons scattering M.B.S. acknowledges support by FCT-Portugal under grant in relatively close proximity to Lyα emission galaxies, which SFRH/BD/51373/2011. could be recovered by intensity mapping. Therefore, we ignore this effect in our discussion. In Figure 10,weshowthe2Danisotropicpowerspectrum APPENDIX decomposed into k and k for the signal, foreground and the total observations. We⊥ just show∥ the Hα foreground here, since it In Equation (28)ofSection4.1,weseethattheobserved has the lowest redshift among the other two foreground lines and foreground power spectrum is actually anisotropic, i.e., not has the largest effect of the power spectrum projection. We find simply a function of k √k2 + k2. This can in principle the shape of the signal power spectrum is quite symmetric and be used in the foreground= cleaning⊥ ∥ process. In particular, the redshift distortion effect is relatively small, since the signal after the intensity cut, we can check if there is still any comes from high redshifts. However, for the foreground, the strong contamination by looking at the anisotropy of the shape of the spectrum is irregular due to the redshift distortion total power spectrum. In order to check the strength of these and the different factors on the k and k (i.e., rs/rf on k and ⊥ ∥ ⊥ anisotropies caused by the projection effect, we calculate the ys /yf on k )intheprojection.Thiseffectprovidesapotential two-dimensional (2D) anisotropic power spectra for the signal method to distinguish∥ the signal from the foreground and could and foregrounds. Here we also take into account of the linear be helpful to remove the foreground in future high sensitivity redshift-space distortions. In that case, the bias should be experiments.

10 CO/[CII]/Lya synergy Tzu-Ching Chang

Table 3: Experimental Parameters for a Possible Lya Mapping Instrument. Aperture diameter (m) 0.2 2 Survey Area (AS; deg ) 13 Total integration time (hours) 2900 Free spectral range (B ; µ m) 0.85 1.1 l Freq. resolution (l/dl ) 220 Number of pixels in 2D array 72900 FOV per pointing; deg2 0.6 Observational time per pointing (hours) 129.5 PoS(AASKA14)004 Survey volume (Mpc/h)3 8.5 107 ⇥

from an assumed Lya intensity mapping experiment which consists of an aperture array with the parameters described in table 3. The parameters of the 21cm intensity mapping observation with SKA1-LOW are described in Table 1 for z = 8, and the assumed frequency dependence of instrument system temperature Tsys and the collecting area Ae are as follows: Tsys = Tsky + Trec, where 300MHz 2.55 Tsky = 60 n K is the sky temperature in Kelvin, and Trec = 0.1 Tsky + 40K is the instru- 2 ⇤ ment receiver temperature. A = 925 110 m2. The Lya intensity mapping calculation is from Line cross-correlations e n Silva et al. (2013). The forecast shows that the 21cm and Ly cross-power spectra can be de- a tected at high SNR values of (789, 442, 273, 462) for z =(7,8,9,10), respectively, and is shown in Figure 3.

The AstrophysicalH Journal,α x835:273 21cm,(14pp), 2017 February z=1 1 Hα x Lyα, z=6Gong et al. Lyα x 21cm, z=7 17

0.1000 Now thatz = 7 we have simulatedz = 9 21cm and Ly↵ emission in order toz calculate= 8 theirz = 10 respective auto and cross-power 2 ] 1 spectra, as well as investigated parameter e↵ects, we − sr 2 − 0.0100 turn to estimating the detectability of these spectra by cm

1 future probes of the EoR. We ﬁrst discuss the 21cm and − Ly↵ noise auto spectra and then their noise cross-power erg s [

2 spectra in the following sections. π /2

) 0.0010 k ( P

3 4.1. 21 cm Noise Auto Spectrum and Foreground k Wedge

0.0001 In this section, we consider the noise power spectrum 0.1of 21cm emission,1.0 with our signal-to-noise10.0 ratio100.0 (S/N) Heneka+ 17 calculation includingk[h/Mpc cosmic] variance and thermal and instrumental noise. We proceed to integrate the so- Gong+ 17 Figure 3: The SKA1-LOW 21cmcalled and 21cm Lya foregroundcross-power spectra wedge at inz Chang+ our=(7, S/N8,9,10 calculations.) .15 The Lya models are based on Silva et al. (2013). TheInstrument cross-power specifications spectra are predicted are taken to be to detectable match at the> 100 SKA SNR signifi- • At z=5.2-6.6, SPHEREx measures both Lyα andcance Hα level, lines. given the Cross-correlation assumedstage survey 1 parameters (Pritchard et can al. 2015 probe) for line the intensity mapping of the 21cm brightness. temperature during the EoR. scales of Lyα photon scattering in the IGM during EoR. The variance for a (dimensional) 21cm power spectrum estimate for mode k and angle µ between the line of sight and k (McQuinn et al. 2006; Lidz et al. • Cross-correlations with 21cm at z=0.8-2.5 from CHIME/HIRAX,2008 and), when at z=6-8 neglecting8 from systematic SKA1- e↵ects such as im- LOW, respectively probing large-scale structures and ionizing bubbleperfect foregroundevolution removal, during reads EoR. as 2 See talk by Jackie HewittFigure tomorrow 14.H↵ to afternoon Ly↵ cross-correlation. coecient 2 TsysVsur 21 (k, µ)= P21 (k, µ)+ W21 (k, µ) , CCCH↵,Ly↵ of brightness fluctuations at redshift z =10and Btintn (k ) z = 7. Shown is the cross-correlation of the sum of galac- " ? # tic and di↵use IGM fluctuations in H↵ with total Ly↵ fluc- (24) Figure 8. Cross power spectra of the Hα, [O III], [O II], and Hβ lines with the 21 cm linetuations at z =1.0 “Ly 0.2. The↵-tot” errors for and the CHIME with and the Tianlai di experiments↵use IGM are contribution where the first term is due to cosmic variance, the sec- shown as solid• and dottedCross-correlation bars, respectively. The dashed–dotted and dotted curves with denote the e.g. clustering WFIRST and shot-noise terms of theHLS cross power H spectra,α respectively.galaxies at z=1-2, and Euclid deep field Hα and We find Tianlai has smaller errors and higher S/N than CHIME at a given redshift.“Ly Unlike↵-dIGM” the intensity power (top), spectra as probed well by as the theSPHEREx, scattered the 21 cm IGM contribu- ond term describes the thermal noise of the instrument, experiments are restricted by[OII] the relatively galaxies low spatial and spectral for resolutions, signal and the crosstion powervalidation “Ly spectra↵-sIGM” can only be measured (bottom). and at large foreground scales with k < 1Mpc-1 h. mitigation. and the window function W21 (k, µ)includesthelim- as shown in Table 3. Note that the measurable scales of the In Table 4, we tabulate the S/Ns of the cross power ited spectral and spatial instrumental resolution. As we cross power spectrum are larger than the intensity power spectrumtotal forLy the↵ fouremission, optical lines “Ly with↵ CHIME-tot” and in Tianlai both at panels of Fig- spectrum probed by SPHEREx alone (see Figure 6). This is 0.8z 2.4. As can be seen, the cross power spectra have want to consider SKA stage 1, we take B = 8 MHz for because the spatial and spectral resolutions of CHIME and largeure S/14Ns, over the the CCC redshift is range, close even to for onethe relatively both faint at both redshifts the survey bandwidth, a total observing time time of Tianlai are relatively low, so that only large scales with Hβ line with S/N>5, and the foreground line contamination kh< 1 Mpc-1 can be detected. We find that the detectability canz be= reduced 10 and signizficantly= 7, by with cross-correlation. a slight This decrease indicates toward higher tint = 1000 hr, an instrument system temperature of of SPHEREx cross-correlated with CHIME or Tianlai is greatly thatk. cross-correlations When cross-correlating of the four lines with H↵ theemission 21 cm line are with the di↵use Tsys = 400 K, and an e↵ective survey volume of Vsur = improved compared to the current galaxy×21 cm measure- an advantageous method for extracting the intensity fluctuation 2 ments given by Chang et al. (2010) and Masui et al. (2013). signal.(top panel) and the scattered (bottom panel) IGM com- 2 2 21 (z) /Ae , with redshifted 21cm wavelength The S/N of SPHEREx×CHIME and Tianlai is ∼30 for the ponentAnother similar of Ly 21↵ cmemission, experiment, the the Hydrogen CCC sharply Intensity decreases to- Hα, [O III] and [O II] lines, and it is ∼10 for the Hβ line at and Real-time Analysis eXperiment (HIRAX), focuses on the 2 21 (z),⇣ e↵ective area⌘ per antenna Ae = 925m (z = 8), z ~ 1. For comparison, the S/N is less than 10 for the similarward redshift smaller range scales of 0.8 < (higherz < 2.5k as). do There CHIME even and is a turnover galaxy×21 cm measurements at z ∼ 0.8. Tianlaifrom for positive measuring cross-correlation BAO and constraining at dark lower energy k to negative and comoving distance and survey depth and . The antenna distribution enters via the number den- 11 cross-correlation at high k, at both redshifts z = 10 and sity of baselines n (k )=0.8 that observe transverse z = 7. The most prominent decrease of the CCC with ? wavenumber k , which we (simplistically) assume to be k is visible for the di↵use IGM at redshift z = 7 (top ? panel, orchid dots). Interestingly, the redshift behav- constant as in Chang et al. (2015). The window function ior of the CCC for di↵use IGM versus scattered IGM is W21 (k, µ) reads, as in Lidz et al. (2011), as

di↵erent. 2 2 (k /k ,res) +(k /k ,res) The di↵erent behaviors for components of Ly↵ emis- W21 (k, µ)=e k k ? ? , (25) sion when cross-correlated with H↵ emission mostly tracing galactic emission was shown in this section. This with parallel modes k = µk along the line of sight and k 1/2 can be used to single out the IGM contribution to the perpendicular modes k = 1 µ2 k. The spectral ? total Ly↵ emission and distinguish galactic and IGM and spatial instrumental resolution in parallel and per- components of Ly↵ emission. pendicular modes is given by

4. SIGNAL-TO-NOISE RATIO CALCULATION RresH (z) 1 k ,res = = (26) k c (1 + z) x ,res k Outlook

• Spectral Line Intensity Mapping with SPHEREx offers an exciting 3D probe of a signiﬁcant fraction of the Universe.

• Hα, [OIII] IM: tracing cosmic star formation and measuring SFRD at 1 < z < 5. • Lyman-α IM: tracing ionization progress during EoR at z~5.5-8. • SPHEREx IM offers a rich and unique dataset, complementary to EBL and galaxy survey sciences. • Work in progress: • Quantifying systematic effects using light cone simulations of multiple lines and stellar continuum. • Reﬁning Cosmology and EoR science cases with IM including estimate of systematic effects.