HI constraints from the cross-correlation of eBOSS galaxies and Green Bank Telescope intensity maps
Laura Wolz, Alkistis Pourtsidou, Kiyoshi W. Masui, Tzu-Ching Chang, Julian E. Bautista, Eva-Maria Mueller, Santiago Avila, David Bacon, Will J. Percival, Steven Cunnington, Chris Anderson, Xuelei Chen, Jean-Paul Kneib, Yi-Chao Li, Yu-Wei Liao, Ue-Li Pen, Jeffrey B. Peterson, Graziano Rossi, Donald P. Schneider, Jaswant Yadav, Gong-Bo Zhao
MMNRAS , 1–16 (2020) Preprint 10 February 2021 Compiled using MNRAS L A TEX style file v3.0
Hi constraints from the cross-correlation of eBOSS galaxies andGreen Bank Telescope intensity maps
Laura Wolz ★ , Alkistis Pourtsidou , Kiyoshi W. Masui , , Tzu-Ching Chang , , ,Julian E. Bautista , , Eva-Maria Müller , Santiago Avila , , David Bacon ,Will J. Percival , , , Steven Cunnington , Chris Anderson , Xuelei Chen ,Jean-Paul Kneib , Yi-Chao Li , Yu-Wei Liao , Ue-Li Pen , Jeffrey B. Peterson ,Graziano Rossi , Donald P. Schneider , , Jaswant Yadav , Gong-Bo Zhao , Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91101, USA California Institute of Technology, Pasadena, CA 91125, USA Academia Sinica Institute of Astronomy and Astrophysics, Roosevelt Rd, Taipei 10617, Taiwan Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France Institute of Cosmology & Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth, PO1 3FX, United Kingdom Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH Departamento de Física Teórica, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Cantoblanco, Madrid, Spain Instituto de Física Teorica UAM-CSIC, Universidad Autónoma de Madrid, 28049 Cantoblanco, Madrid, Spain Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, ON N2L 3G1, Canada Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada Perimeter Institute for Theoretical Physics, 31 Caroline St. North, Waterloo, ON N2L 2Y5, Canada Department of Physics, University of Wisconsin Madison, 1150 University Ave, Madison WI 53703, USA National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Federale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland Department of Physics & Astronomy, University of the Western Cape, Cape Town 7535, South Africa Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George St., Toronto Ontario, M5S 3H8, Canada Department of Physics, Carnegie Mellon University. Pittsburgh. PA, USA Department of Astronomy and Space Science, Sejong University, 209, Neungdong-ro, Gwangjin-gu, Seoul, South Korea Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA Central University of Haryana, Jant-Pali, Mahendergarh - 123031, India
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We present the joint analysis of Neutral Hydrogen (Hi) Intensity Mapping observations withthree galaxy samples: the Luminous Red Galaxy (LRG) and Emission Line Galaxy (ELG)samples from the eBOSS survey, and the WiggleZ Dark Energy Survey sample. The Hi intensitymaps are Green Bank Telescope observations of the redshifted 21cm emission on 100 deg covering the redshift range 0 . < 𝑧 < .
0. We process the data by separating and removingthe foregrounds present in the radio frequencies with FastICA. We verify the quality of theforeground separation with mock realisations, and construct a transfer function to correct forthe effects of foreground removal on the Hi signal. We cross-correlate the cleaned Hi data withthe galaxy samples and study the overall amplitude as well as the scale-dependence of the powerspectrum. We also qualitatively compare our findings with the predictions by a semi-analyticgalaxy evolution simulation. The cross-correlations constrain the quantity Ω Hi 𝑏 Hi 𝑟 Hi , opt at aneffective scale 𝑘 eff , where Ω Hi is the Hi density fraction, 𝑏 Hi is the Hi bias, and 𝑟 Hi , opt the galaxy-hydrogen correlation coefficient, which is dependent on the Hi content of the optical galaxysample. At 𝑘 eff = . ℎ / Mpc we find Ω Hi 𝑏 Hi 𝑟 Hi , Wig = [ . ± . ( stat ) ± . ( sys )] × − for GBT-WiggleZ, Ω Hi 𝑏 Hi 𝑟 Hi , ELG = [ . ± . ( stat ) ± . ( sys )] × − for GBT-ELG,and Ω Hi 𝑏 Hi 𝑟 Hi , LRG = [ . ± . ( stat ) ± . ( sys )] × − for GBT-LRG, at 𝑧 (cid:39) .
8. Wealso report results at 𝑘 eff = . ℎ / Mpc and 𝑘 eff = . ℎ / Mpc. With little information onHi parameters beyond our local Universe, these are amongst the most precise constraints onneutral hydrogen density fluctuations in an underexplored redshift range.
Key words: cosmology: observations – galaxies:evolution – large-scale structure of theUniverse – radio lines: galaxies – methods: statistical – data analysis ★ E-mail:[email protected] © a r X i v : . [ a s t r o - ph . C O ] F e b L. Wolz et al.
The redshifted 21cm emission from Neutral Hydrogen (Hi) gasprovides an alternative view into the structure, dynamics, and evo-lution of galaxies. Hi gas is the fundamental fuel for molecular gasand star formation and plays an essential role in galaxy formationand evolution and models thereof. Blind Hi surveys of the localUniverse provide constraints on the Hi abundance via the Hi massfunction (Jones et al. 2020; Zwaan et al. 2003) and the global Hiabundance Ω Hi = ( . ± . ) − ℎ (Martin et al. 2010). Spectralstacking techniques have also been used (see e.g. Hu et al. 2019 andreferences therein).Targeted deep surveys investigate the Hi scaling relations withgalaxy properties such as stellar mass, star formation activity, orstar formation efficiency with multi-wavelength data. It has beeninferred that cold gas properties are tightly related to their star-forming properties and less to their morphology, with scatter on therelations being driven by inflows mechanisms and dynamics (Cooket al. 2019; Chen et al. 2020). Hi gas has been found to stronglyanti-correlate with stellar mass, particularly when traced by NUV-rcolour (Catinella et al. 2018). Multiple studies on the Hi deficiencyin high density regions such as the VIRGO cluster confirm the highimpact of environment on atomic gas abundance (see Cortese et al.2011; Dénes et al. 2014; Reynolds et al. 2020). Bok et al. (2020)studied environmental effects using an infra-red selected sample ofHi detections finding a reduced scatter in scaling relations for iso-lated galaxies. Some investigations have been made into the relationbetween Hi and its host halo mass to constrain a Hi halo occupationdistribution, see for example Guo et al. (2020) or Paul et al. (2018).The most important limitations of all blind and targeted Hi surveysare their sensitivity limitations on relatively Hi-rich galaxy samples,as well as volume-limited sample sizes. Additionally, there is littleinformation on Hi abundances and scaling relations beyond our lo-cal Universe (Crighton et al. 2015; Padmanabhan et al. 2016; Huet al. 2019).The technique of Hi intensity mapping has been proposedto perform fast observations of very large cosmic volumes in awide redshift range. Intensity mapping does not rely on detectingindividual galaxies, but instead measures the integrated redshiftedspectral line emission without sensitivity cuts in large voxels onthe sky, whith the voxel volume determined by the radio telescopebeam and frequency channelisation, see e.g. (Battye et al. 2004;Chang et al. 2008; Wyithe & Loeb 2009; Mao et al. 2008; Petersonet al. 2009; Chang et al. 2010; Seo et al. 2010; Ansari et al. 2012).Using the Hi signal as a biased tracer for the underlying matterdistribution, it is possible to probe the large-scale structure of theUniverse, and constrain both, global Hi properties and cosmologicalparameters. Particularly, the amplitude of the Hi intensity mappingclustering signal scales with the global Hi energy density Ω HI andcan constrain it for various redshifts.The next few years will see data from a number of Hi inten-sity mapping experiments, for example the proposed MeerKLASSsurvey at the Square Kilometre Array (SKA) precursor MeerKAT(Santos et al. 2017; Wang et al. 2020), an Hi survey at the 500mdish telescope FAST (Hu et al. 2020), and multiple surveys with theSKA using the single-dish mode of operation (Battye et al. 2013;Bull et al. 2015; Santos et al. 2017; SKA Cosmology SWG et al.2020). Other international experiments include the CHIME project(Bandura et al. 2014), HIRAX (Newburgh et al. 2016), and Tianlai(Li et al. 2020b; Wu et al. 2020).The observed intensity maps suffer from foreground contam-ination from Galactic and extra-galactic sources. Our own Galaxy emits high synchroton and free-free emission up to three ordersof magnitude brighter than the redshifted 21cm line (Matteo et al.2002), which need to be subtracted from the data (see e.g. Wolzet al. 2014; Alonso et al. 2015; Shaw et al. 2015; Olivari et al.2016; Cunnington et al. 2019; Carucci et al. 2020). To-date, theintensity mapping signal has not been detected in auto-correlationdue to calibration errors, radio frequency interference, residual fore-grounds and noise systematics (Switzer et al. 2013, 2015; Harperet al. 2018; Li et al. 2020a). The impact of the contaminations can bereduced by cross-correlating the Hi signal with optical surveys. Thefirst successful detection with Green Bank Telescope (GBT) datahas been achieved at 0 . < 𝑧 < . 𝑧 = . Ω Hi and linear Hi bias 𝑏 Hi ,finding Ω Hi 𝑏 Hi 𝑟 Hi , Wig = [ . ± . ] × − , where 𝑟 Hi , Wig is thegalaxy-Hi cross-correlation coefficient. The significance of detec-tion was 7 . 𝜎 for the combined 1hr and 15hr fields observations(Masui et al. 2013).More recently, the Parkes radio telescope reported a cross-correlation detection at 𝑧 (cid:39) . Ω Hi 𝑏 Hi 𝑟 Hi , opt , and also pro-vide estimates for Ω Hi using external estimates for 𝑏 Hi and 𝑟 Hi , opt .The paper is organised as follows: In Section 2, we describe theGBT intensity maps, and the WiggleZ and eBOSS galaxy samples.We also give a brief description of our simulations. In Section 3, weoutline the application of the FastICA technique to the GBT maps,as well as the construction of the foreground transfer function. InSection 4 we present and discuss our cross-correlation results. InSection 5 we derive the Hi constraints. We conclude in Section 6. MNRAS000
The redshifted 21cm emission from Neutral Hydrogen (Hi) gasprovides an alternative view into the structure, dynamics, and evo-lution of galaxies. Hi gas is the fundamental fuel for molecular gasand star formation and plays an essential role in galaxy formationand evolution and models thereof. Blind Hi surveys of the localUniverse provide constraints on the Hi abundance via the Hi massfunction (Jones et al. 2020; Zwaan et al. 2003) and the global Hiabundance Ω Hi = ( . ± . ) − ℎ (Martin et al. 2010). Spectralstacking techniques have also been used (see e.g. Hu et al. 2019 andreferences therein).Targeted deep surveys investigate the Hi scaling relations withgalaxy properties such as stellar mass, star formation activity, orstar formation efficiency with multi-wavelength data. It has beeninferred that cold gas properties are tightly related to their star-forming properties and less to their morphology, with scatter on therelations being driven by inflows mechanisms and dynamics (Cooket al. 2019; Chen et al. 2020). Hi gas has been found to stronglyanti-correlate with stellar mass, particularly when traced by NUV-rcolour (Catinella et al. 2018). Multiple studies on the Hi deficiencyin high density regions such as the VIRGO cluster confirm the highimpact of environment on atomic gas abundance (see Cortese et al.2011; Dénes et al. 2014; Reynolds et al. 2020). Bok et al. (2020)studied environmental effects using an infra-red selected sample ofHi detections finding a reduced scatter in scaling relations for iso-lated galaxies. Some investigations have been made into the relationbetween Hi and its host halo mass to constrain a Hi halo occupationdistribution, see for example Guo et al. (2020) or Paul et al. (2018).The most important limitations of all blind and targeted Hi surveysare their sensitivity limitations on relatively Hi-rich galaxy samples,as well as volume-limited sample sizes. Additionally, there is littleinformation on Hi abundances and scaling relations beyond our lo-cal Universe (Crighton et al. 2015; Padmanabhan et al. 2016; Huet al. 2019).The technique of Hi intensity mapping has been proposedto perform fast observations of very large cosmic volumes in awide redshift range. Intensity mapping does not rely on detectingindividual galaxies, but instead measures the integrated redshiftedspectral line emission without sensitivity cuts in large voxels onthe sky, whith the voxel volume determined by the radio telescopebeam and frequency channelisation, see e.g. (Battye et al. 2004;Chang et al. 2008; Wyithe & Loeb 2009; Mao et al. 2008; Petersonet al. 2009; Chang et al. 2010; Seo et al. 2010; Ansari et al. 2012).Using the Hi signal as a biased tracer for the underlying matterdistribution, it is possible to probe the large-scale structure of theUniverse, and constrain both, global Hi properties and cosmologicalparameters. Particularly, the amplitude of the Hi intensity mappingclustering signal scales with the global Hi energy density Ω HI andcan constrain it for various redshifts.The next few years will see data from a number of Hi inten-sity mapping experiments, for example the proposed MeerKLASSsurvey at the Square Kilometre Array (SKA) precursor MeerKAT(Santos et al. 2017; Wang et al. 2020), an Hi survey at the 500mdish telescope FAST (Hu et al. 2020), and multiple surveys with theSKA using the single-dish mode of operation (Battye et al. 2013;Bull et al. 2015; Santos et al. 2017; SKA Cosmology SWG et al.2020). Other international experiments include the CHIME project(Bandura et al. 2014), HIRAX (Newburgh et al. 2016), and Tianlai(Li et al. 2020b; Wu et al. 2020).The observed intensity maps suffer from foreground contam-ination from Galactic and extra-galactic sources. Our own Galaxy emits high synchroton and free-free emission up to three ordersof magnitude brighter than the redshifted 21cm line (Matteo et al.2002), which need to be subtracted from the data (see e.g. Wolzet al. 2014; Alonso et al. 2015; Shaw et al. 2015; Olivari et al.2016; Cunnington et al. 2019; Carucci et al. 2020). To-date, theintensity mapping signal has not been detected in auto-correlationdue to calibration errors, radio frequency interference, residual fore-grounds and noise systematics (Switzer et al. 2013, 2015; Harperet al. 2018; Li et al. 2020a). The impact of the contaminations can bereduced by cross-correlating the Hi signal with optical surveys. Thefirst successful detection with Green Bank Telescope (GBT) datahas been achieved at 0 . < 𝑧 < . 𝑧 = . Ω Hi and linear Hi bias 𝑏 Hi ,finding Ω Hi 𝑏 Hi 𝑟 Hi , Wig = [ . ± . ] × − , where 𝑟 Hi , Wig is thegalaxy-Hi cross-correlation coefficient. The significance of detec-tion was 7 . 𝜎 for the combined 1hr and 15hr fields observations(Masui et al. 2013).More recently, the Parkes radio telescope reported a cross-correlation detection at 𝑧 (cid:39) . Ω Hi 𝑏 Hi 𝑟 Hi , opt , and also pro-vide estimates for Ω Hi using external estimates for 𝑏 Hi and 𝑟 Hi , opt .The paper is organised as follows: In Section 2, we describe theGBT intensity maps, and the WiggleZ and eBOSS galaxy samples.We also give a brief description of our simulations. In Section 3, weoutline the application of the FastICA technique to the GBT maps,as well as the construction of the foreground transfer function. InSection 4 we present and discuss our cross-correlation results. InSection 5 we derive the Hi constraints. We conclude in Section 6. MNRAS000 , 1–16 (2020)
BOSS - GBT Hi intensity mapping cross-correlations The Hi intensity mapping data from the Green Bank Telescope(GBT) used in this study is located in the 1hr field of the Wig-gleZ Dark Energy survey at right ascension 5 . ° < RA < . ° and declination − . ° < DEC < . ° . This field was observedwith the receiver band at 700 < 𝜈 <
900 MHz, which results ina 21cm redshift range of 0 . < 𝑧 < .
0. The data is divided into 𝑁 𝜈 =
256 frequency channels with width 𝛿𝜈 = .
78 MHz, afterrebinning from the original 2048 correlator channels. The observa-tional spatial resolution of the maps, quantified by the full widthhalf maximum (FWHM) of the GBT telescope beam, evolves fromFWHM ≈ .
31 deg at 𝜈 =
700 MHz to FWHM ≈ .
25 deg at 𝜈 =
900 MHz. The maps are pixelised with spatial resolution angleof 𝛿𝜃 ≈ 𝛿𝜙 = .
067 deg, which results in 𝑁 RA =
217 pixels in rightascension and 𝑁 DEC =
119 pixels in declination. The pixel sizewas chosen such that approximately 4 pixels cover the beam at mid-frequency 𝜈 ≈
800 MHz, and the instrumental noise can be approx-imated as uncorrelated between pixels. The maps are an extendedversion of the previously published observations described in Masuiet al. (2013) with added scans to increase the area to 100 deg andsurvey depth to 100 hrs total integration time collected from 2010-2015. The details on Radio Frequency Interference (RFI) flagging,calibration, and map making procedures can be found in Masui et al.(2013); Switzer et al. (2013); Masui (2013).As described in previous studies, the GBT intensity maps suffera number of instrumental systematic effects. To reduce the impactof the systematic effects, the following measures have been taken: • RFI and resonance: The data is contaminated by RFI and twotelescope resonance frequencies. Figure 1 shows the mean absolutetemperature of each channel as a function of redshift. The red lineshows the initial data with strong RFI contamination at the lowestredshift as well as towards the highest redshift end. The two tele-scope resonances can be seen at 𝜈 =
798 MHz and 𝜈 =
817 MHzwhich corresponds to the dips in amplitude seen at 𝑧 = .
78 and 𝑧 = .
74. To minimise these effects, we dismiss the lowest 30 chan-nels in redshift and the intervals around the resonances before theforeground removal. • Sub-seasons: The time-ordered data is divided into 4 seasons { A , B , C , D } . Thermal noise is uncorrelated between these seasons,which have been chosen to have similar integration depth and cov-erage (Switzer et al. 2013). More specifically, the Gaussian sam-pling noise and time-dependent RFI in each season are independent,however, observational systematics in seasons can correlate. The in-dividual season data is shown as faded purple and yellow lines inFigure 1. • Masking: The noise properties are highly anisotropic towardsthe spatial edges of the map due to the scanning strategy and result-ing anisotropic survey depth. We therefore mask out 15 pixels perside, which significantly reduces residual anisotropic noise in theforeground subtracted maps. About an order of magnitude decreaseof the mean temperature of the maps is found comparing the orig-inal and masked foreground subtracted data marked by the purpleand yellow lines in Figure 1. The solid purple and yellow lines showthe signal averaged over the four seasons, and the faded lines aroundthem show the individual seasons. • Beam: The beam of the instrument can be approximated by asymmetric Gaussian function with a frequency-dependent FWHMwith maximum FWHM max ≈ .
31 deg. In order to aid the dataanalysis as well as to minimise systematics caused by polarisation leakage of the receiver (Switzer et al. 2013), we convolve the datato a common Gaussian beam with FWHM = . max , whichresults in an angular resolution of FWHM = .
44 deg.Figure 1 shows that even after applying these measures and re-moving foregrounds modelled by 36 Independent Components, themean temperature of the Hi maps is about an order of magnitudehigher than the theoretically predicted Hi brightness temperature.We model this following Chang et al. (2010) and Masui et al. (2013)as: 𝑇 HI = . Ω HI − (cid:18) Ω 𝑚 + Ω Λ ( + 𝑧 ) − . (cid:19) − . (cid:18) + 𝑧 . (cid:19) . mK (1)which is shown as the green dotted line. We are unable to directlydetect the Hi signal with our current pipeline in this systematicsdominated data. In this study, we consider three galaxy samples overlapping with theHi intensity maps in the 1hr field. We use the WiggleZ Dark EnergySurvey galaxy sample based on Blake et al. (2011) as previouslypresented in Masui et al. (2013). And, for the first time, we usethe SDSS Emission Line Galaxy (ELG) and Luminous Red Galaxy(LRG) sample of the eBOSS survey (DR16) for the Hi-galaxy cross-correlation analysis.In Figure 2, we show the spatial footprint of each survey in the1hr field, where dark patches indicate unobserved regions and thered lines mark the edge masking as part of the systematics mitigationof the GBT data. The LRG and WiggleZ samples both have areduced spatial overlap with the GBT data as it has unobservedregions, however, since we introduce the red mask, this effect issomewhat diminished. The ELG sample has the most completeoverlap with the GBT data.
WiggleZ - The WiggleZ galaxies are part of the WiggleZ DarkEnergy Survey (Drinkwater et al. 2010), a large-scale spectroscopicsurvey of emission-line galaxies selected from UV and optical imag-ing. These are active, highly star-forming objects, and it has beensuggested that they contain a large amount of Hi gas to fuel theirstar-formation. The selection function (Blake et al. 2010) has an-gular dependence determined primarily by the UV selection, andredshift coverage favouring the 𝑧 = . eBOSS ELG - The extended Baryon Oscillation SpectroscopicSurvey (eBOSS; Dawson et al. 2016), is part of the SDSS-IV ex-periment (Blanton et al. 2017), and has spectroscopically observed173 ,
736 ELGs in the redshift range 0 . < 𝑧 < . eBOSS LRG - Luminous Red Galaxies were observed byeBOSS from a target sample selected (Prakash et al. 2015) fromSDSS DR13 photometric data (Albareti et al. 2017), combined withinfrared observations from the WISE satellite (Lang et al. 2016). MNRAS , 1–16 (2020)
L. Wolz et al.
Figure 1.
Mean of the absolute temperature of the GBT intensity maps as a function of redshift, binned into 256 frequency channels. The solid lines represent themean over the 4 GBT seasons with original data (red), the FastICA foreground subtracted data with 𝑁 IC =
36 (purple), and the masked, FastICA foregroundsubtracted data with 𝑁 IC =
36 (yellow). The faded purple and yellow lines indicate the individual seasons. The green dotted line represents the analyticalbrightness temperature prediction from Equation 1, the pink dashed line the averaged temperature of the lognormal simulations used for the foreground removaltransfer function (see Section 3 for details), and the teal dashed line the numerical prediction from the DARK SAGE simulation described in Section 2.
This sample was selected to be composed of large, old, strongly-biased galaxies, typically found in high mass haloes. In total, thesample contains 174 ,
816 LRGs with measured redshifts between0 . < 𝑧 < .
0. In our analysis we do not combine the eBOSS LRGswith the 𝑧 > . 𝑁 ( 𝑧 ) , where we binned the data according to the frequency binsof the GBT intensity mapping data. This implies that the bin sizeis constant in frequency rather than redshift, and the co-movingvolume of the bins evolves with redshift. The line-of-sight resolutionis very high with an average redshift bin size of 𝛿𝑧 ≈ . 𝑧 ∼ .
6, and that the density of the LRGs dropssignificantly faster with redshift compared to the other samples.The eBOSS ELG distribution is at higher redshift and peaks around 𝑧 ∼ . 𝑧 ∼ .
0. As the low redshift end of the intensity maps is significantlycontaminated by RFI, we lose the peak of the LRG and WiggleZsample in the cross-correlation. The total number of galaxies for thesamples is significantly reduced from 𝑁 Wig , all = 𝑁 LRG , all = 𝑁 ELG , all = 𝑁 Wig = 𝑁 LRG = 𝑁 ELG = In order to examine the underlying astrophysics of Hi-galaxy cross-correlations, we use the online service “Theoretical Astrophysical Observatory” (TAO ) to create a mock galaxy catalogue. We createthe galaxy distribution using the semi-analytic galaxy formationmodel DARK SAGE (Stevens et al. 2016) run on the merger treesof the Millennium simulation (Springel et al. 2006) with box ofcomoving side length of 500 Mpc / ℎ . DARK SAGE is a modifiedversion of SAGE (Croton et al. 2006), which includes a pressure-based description of the atomic and molecular gas components ofthe cold gas based on an advanced computation of disk structureand cooling processes. DARK SAGE is calibrated to reproduce theStellar, Hi and H2 Mass Functions as well as the fraction of Hito stellar mass as a function of stellar mass as observed at 𝑧 = . < 𝑧 < .
0, and the same spatial andredshift binning as the GBT data.We post-process the galaxy catalogue from TAO to create Hiintensity maps as well as the three optical galaxy samples. We applythe same resolution-motivated mass cut as in Stevens et al. (2016)and only use galaxies with 𝑀 ∗ > . 𝑀 sun for our analysis. Thismight be a slightly conservative choice compared to, for example,Spinelli et al. (2020), but the specific purpose of this simulationis to examine the Hi content of the galaxy samples rather than theuniversal properties of the Hi maps.For the Hi intensity maps, we sum the Hi mass 𝑀 𝑖, HI of allgalaxies falling into the same pixel 𝑖 with spatial dimension 𝛿𝜙 = 𝛿𝜃 = .
067 deg and the same frequency bins as the data, wherewe also include redshift space distortions via line-of-sight peculiarvelocities of the galaxies. We transform the maps in brightness https://tao.asvo.org.au/ MNRAS000
067 deg and the same frequency bins as the data, wherewe also include redshift space distortions via line-of-sight peculiarvelocities of the galaxies. We transform the maps in brightness https://tao.asvo.org.au/ MNRAS000 , 1–16 (2020) BOSS - GBT Hi intensity mapping cross-correlations Figure 2.
Spatial footprint of the galaxy samples.
From top to bottom:
WiggleZ, ELG, and LRG samples. The survey window is binned on the samespatial pixelisation as the GBT data with pixel size of 𝛿 𝜃 = 𝛿 𝜙 = .
067 deg. temperature using 𝑇 HI ( 𝑥 𝑖 ) = 𝐴 ℏ 𝑐 𝜋𝑚 H 𝑘 B 𝜈 ( + 𝑧 𝑖 ) 𝐻 ( 𝑧 𝑖 ) 𝑀 𝑖, HI 𝑉 pix , (2)with ℏ the Planck constant, 𝑘 B the Boltzmann constant, 𝑚 H theHydrogen atom mass, 𝜈 HI the rest frequency of the Hi emission line, 𝑐 the speed of light, 𝐴 the transition rate of the spin flip, and 𝑉 pix the co-moving volume of the pixel at mid-redshift. We also removethe mean temperature ¯ 𝑇 Hi of each map to create over-temperaturemaps. We then convolve the resulting maps with a Gaussian beamwith FWHM = .
44 deg.Based on our galaxy lightcone catalogue, we additionally cre-ate optical, near-infrared and UV band emissions for each galaxywith the Spectral Energy Distribution (SED) module of TAO, usingthe Chabrier Initial Mass Function (Conroy & van Dokkum 2012).
Figure 3.
Galaxy density distribution with redshift. The solid lines representthe mean of the random catalogues used to determine the selection function,and the markers show the data points of the samples.
Figure 4.
The galaxy density of the mock galaxy samples from the DARKSAGE simulation as a function of redshift.
The SED is based on the star-formation history primarily dependenton stellar mass, age, and metallicity of each galaxy. Galaxy pho-tometry is applied after the construction of the SED. In our case,we use the SDSS filter { 𝑔, 𝑟, 𝑖, 𝑧 } , and the Galex near ultra-violetfilter NUV and FUV, as well as the near-infrared filter IRAC1 as anapproximation for the WISE filter W1.We apply the same observational colour cuts to the simulatedlightcone to create mock galaxy samples resembling the eBOSSLRG, eBOSS ELG and WiggleZ selections, following the approachin Wolz et al. (2016a). Details on the target selection are given inAppendix A.In Figure 4, we show the redshift distribution of the resultingmock galaxy samples from the semi-analytic simulation. We notethat the overall galaxy numbers are off by several factors as thereare many observational subtleties that can not be replicated by ourapproach. In addition, the eBOSS ELG-like sample peaks at slightlylower redshift around 𝑧 ∼ . MNRAS , 1–16 (2020)
L. Wolz et al.
Figure 5.
The Hi mass 𝑀 HI of our mock galaxy lightcone as a function ofgalaxy colour, ( NUV − 𝑟 ) . The full light cone of 𝑁 = . · galaxieswith 𝑀 ∗ > . 𝑀 sun spanning 0 . < 𝑧 < . abundance in the galaxy samples and examine their impact on thecross-correlation power spectrum. Particularly, we investigate thenon-linear shape the correlations and the amplitude of the predictedcross-shot noise. We only perform qualitative rather than quanti-tative comparisons between the power spectra of the semi-analyticsimulation and the data.In Figure 5, we present the galaxy colour to Hi mass dia-gram, where we use the combination of Galex-NUV and SDSS- 𝑟 filter to project the galaxies onto the red-blue colour scale. TheNUV- 𝑟 colour division has been shown to be a good proxy forthe star formation activity of the objects, see e.g. Cortese et al.(2011). We can see that all three samples occupy different spaces inthe colour diagram with WiggleZ galaxies testing the bluest, mosthighly star-forming objects that are also rich in Hi gas. The ELGsample contains slightly less blue systems with lower star formationand also spanning a wider range of Hi masses. The LRG selectionincorporates objects more red in colour, however, since objects aresupposed to be large and luminous enough for detection at such highredshift, these are still relatively Hi rich. Fast Independent Component Analysis (FastICA) (Hyvärinen1999) is one of the most popular methods for 21cm foregroundcleaning and has been tested on simulated data (Chapman et al.2012; Wolz et al. 2014; Cunnington et al. 2019) as well as real datafrom the GBT (Wolz et al. 2016b) and LOFAR (Hothi et al. 2021).As with most foreground removal methods, FastICA exploits thefact that the foregrounds dominated by synchrotron and free-freeemission smoothly scale in the line-of-sight direction (frequency)(Oh & Mack 2003; Seo et al. 2010; Liu & Tegmark 2011), whereasthe Hi signal from the Large Scale Structure follows a near-Gaussianapproximation with frequency. We apply FastICA to the GBT in-tensity mapping data cube in order to remove the foregrounds andnon-Gaussian systematics and noise. We provide a brief summaryof the method here, and refer the interested reader to Wolz et al.(2014, 2016b) for more details.FastICA is a blind component separation method designed to divide a mixture of signals into its individual source components,commonly referred to as the “Cocktail Party problem”. It operates onthe assumption that the observed signal is composed of statisticallyindependent sources which are mixed in a linear manner. Morespecifically, the technique solves the linear problem 𝒙 = A 𝒔 + 𝜖 = 𝑁 IC ∑︁ 𝑖 = 𝒂 𝒊 𝑠 𝑖 + 𝜖, (3)where 𝒙 is the mixed signal, 𝒔 represents the 𝑁 IC independent com-ponents (ICs), and A the mixing matrix. 𝜖 is the residual of theanalysis. The amplitude of each IC 𝑠 𝑖 is given by the mixing modes 𝒂 𝒊 . FastICA separates the signal into components by using theCentral Limit theorem, such that the non-Gaussianity of the prob-ability density function of each IC is maximized. This implies thatFastICA by definition does not incorporate Gaussian-distributedcomponents into A 𝒔 . Any Gaussian distribution of the mixed signal 𝒙 will be left in the analysis residual 𝜖 .In our application of FastICA, the input data is of dimension 𝑁 pix × 𝑁 𝜈 and the algorithm constructs the mixing matrix A withdimension 𝑁 IC × 𝑁 𝜈 and the ICs 𝒔 with dimension 𝑁 pix × 𝑁 IC .FastICA incorporates any features with frequency correlation,such as point sources, diffuse foregrounds and non-Gaussian noiseand systematics into the ICs. It also identifies frequency-localisedRFI contributions with weak correlations, as they usually exhibitstrong non-Gaussian spatial features. The residual of the componentseparation should, in theory, only contain the Hi signal and theGaussian telescope noise.The number of ICs ( 𝑁 IC ) used in the component separationis a free parameter and can not be determined by FastICA. In thefollowing sub-sections, we carefully examine the sensitivity of theforeground-subtracted data to different choices of 𝑁 IC , ensuring thatour results do not depend on this choice. Foreground subtraction with FastICA and its applications to sim-ulations has been thoroughly investigated by many studies, but thevast majority of simulations published to date have been highlyidealised and do not included any instrumental effects other thanGaussian noise. In this idealised setting, FastICA has been found tovery effectively remove foregrounds for low numbers of ICs startingfrom 𝑁 IC =
4. We note that these numbers also depend on the so-phistication of the foreground models, for example, see Cunningtonet al. (2020a) for 𝑁 IC > 𝑁 IC , thealgorithm incorporates more subtle signals as well as more lo-cal features into the components. This can significantly reduce thepresence of noise and systematics in the data, however, it could alsolead to Hi signal loss.In the following, we investigate the signal loss for differentnumbers of 𝑁 IC in the presence of systematics and use the method-ology presented in Switzer et al. (2015) to construct the transferfunction to correct for Hi signal loss. In absence of a telescope sim-ulator for the (unknown) systematics, we obtain the transfer func-tion by injecting mock Hi signal from simulations into the observedmaps before foreground removal. We then process the combinedmaps with FastICA, and determine the Hi signal loss by cross-correlating the cleaned maps with the injected Hi simulation. In MNRAS000
4. We note that these numbers also depend on the so-phistication of the foreground models, for example, see Cunningtonet al. (2020a) for 𝑁 IC > 𝑁 IC , thealgorithm incorporates more subtle signals as well as more lo-cal features into the components. This can significantly reduce thepresence of noise and systematics in the data, however, it could alsolead to Hi signal loss.In the following, we investigate the signal loss for differentnumbers of 𝑁 IC in the presence of systematics and use the method-ology presented in Switzer et al. (2015) to construct the transferfunction to correct for Hi signal loss. In absence of a telescope sim-ulator for the (unknown) systematics, we obtain the transfer func-tion by injecting mock Hi signal from simulations into the observedmaps before foreground removal. We then process the combinedmaps with FastICA, and determine the Hi signal loss by cross-correlating the cleaned maps with the injected Hi simulation. In MNRAS000 , 1–16 (2020)
BOSS - GBT Hi intensity mapping cross-correlations Figure 6.
The signal loss function Δ ( 𝑘 ) for the foreground subtraction withFastICA for different numbers of ICs 𝑁 IC . Note that Δ = . { A , B , C , D } to highlightthe sensitivity of the transfer function to the individual season-dependentsystematics. order to reduce noise, we use the average of 100 Hi realisationsand we also subtract the cleaned GBT data from the combined databefore cross-correlating with the injected signal.We describe the process in detail below: • We create 𝑁 𝑚 =
100 mock simulations 𝑚 𝑖 of lognormal halodistributions using the python package powerbox (Murray 2018)with a halo mass limit of 𝑀 ℎ, min = . • We populate each dark matter halo with a Hi mass following asimple Hi halo mass relation as in Wolz et al. (2019). • We grid the Hi mass of each halo to the same spatial andfrequency resolution as the GBT data at medium redshift 𝑧 ≈ . • We convert the Hi grid into brightness temperature 𝑇 HI usingEquation 1, re-scale the overall averaged temperature to the sameorder of magnitude as the theory prediction with Ω HI = . × − ,and convolve the data with a constant, symmetric Gaussian beamwith FWHM = .
44 deg. • We add each mock Hi brightness temperature realisation 𝑚 𝑖 to each GBT season 𝑗 ∈ { 𝐴, 𝐵, 𝐶, 𝐷 } of the GBT data to createcombined cubes ( 𝑑 𝑗 + 𝑚 𝑖 ) . • We run FastICA with 𝑞 number of independent componentson each sub-dataset as ICA 𝑞 ( 𝑑 + 𝑚 ) , where 𝑞 ∈ { , , , } . • We subtract the original, cleaned GBT data cube to obtain thecleaned mock simulations ˜ 𝑚 𝑗𝑞𝑖 = ICA 𝑞 ( 𝑑 𝑗 + 𝑚 𝑖 ) − ICA 𝑞 ( 𝑑 𝑗 ) .In this study, we focus on the impact on Hi signal loss throughforeground subtraction on the cross-correlation. In order to approx-imate this effect, we examine the cross-power spectrum 𝑃 of theforeground removed mock ˜ 𝑚 𝑞 with the original mock 𝑚 . We de-fine the signal loss function Δ per season 𝑗 for different 𝑞 = 𝑁 IC averaged over all realisations as Δ 𝑗𝑞 ( 𝑘 ) = (cid:205) 𝑁 𝑚 𝑖 𝑃 ( ˜ 𝑚 𝑗𝑞,𝑖 , 𝑚 𝑖 )( 𝑘 ) (cid:205) 𝑁 𝑚 𝑖 𝑃 ( 𝑚 𝑖 )( 𝑘 ) . (4)In an ideal situation without any signal loss, Δ 𝑗𝑞 ( 𝑘 ) is equal to unityacross all scales. Note that here, Δ is defined as the Hi signal lossfunction on the Hi-galaxy cross-correlation.In our analysis, the signal loss is corrected via the transfer function of the cross-correlation defined as Θ 𝑗𝑞 = ( Δ 𝑗𝑞 ) − . We showthe signal loss function in Figure 6. For all tested 𝑁 IC , there issome significant degree of signal loss ranging between 10% − 𝑘 < . ℎ Mpc − . This can be explained con-sidering the survey geometry, as these scales are mostly tested byline-of-sight modes which are highly affected by diffuse foregroundsubtraction. Even for increasing numbers of ICs in the subtraction,the transfer function converges towards unity on smaller scales.However, for very high number 𝑁 IC =
36, there is signal loss onall scales of the power spectrum. Note that the divergent behaviourfrom 𝑘 > ℎ Mpc − is due to the effect of the beam on these scales,and they are not considered in our final analysis. We can see thatin general, the amplitude of the transfer function of season B issomewhat higher than the others, which suggests that this seasonmight suffer more from systematic effects. We use the inverse-noise weighted power spectrum estimator asdescribed in Wolz et al. (2016b). For the cross-correlation of twotracers 𝑎 and 𝑏 , that is:ˆ 𝑃 𝑎𝑏 ( (cid:174) 𝑘 𝑙 ) = 𝑉 Re { ˜ 𝛿 𝑎 ( (cid:174) 𝑘 𝑙 ) · ˜ 𝛿 𝑏 ( (cid:174) 𝑘 𝑙 ) ∗ } (cid:205) 𝑁 pix 𝑗 = 𝑤 𝑎 ((cid:174) 𝑥 𝑗 ) · 𝑤 𝑏 ((cid:174) 𝑥 𝑗 ) , (5)with ˜ 𝛿 the Fourier transform of the weighted density field 𝑤 ((cid:174) 𝑥 𝑗 ) 𝛿 ((cid:174) 𝑥 𝑗 ) of the tracer, 𝑁 pix the total number of pixels, 𝑤 ((cid:174) 𝑥 𝑗 ) theweighting function, and 𝑉 the survey volume. For Hi intensity maps, 𝑤 ((cid:174) 𝑥 𝑗 ) is given by the inverse noise map of each season. For galaxysurveys, the total weighting factor is 𝑤 ((cid:174) 𝑥 𝑗 ) = 𝑊 ((cid:174) 𝑥 𝑗 ) 𝑤 opt ((cid:174) 𝑥 𝑗 ) ,where 𝑤 opt ((cid:174) 𝑥 𝑗 ) is given by optimal weighting function 𝑤 opt ((cid:174) 𝑥 𝑖 ) = /( + 𝑊 ((cid:174) 𝑥 𝑖 ) × ¯ 𝑁𝑃 ) , with 𝑃 = ℎ − Mpc , and the selectionfunction 𝑊 ((cid:174) 𝑥 𝑗 ) . We derive the selection function for each sam-ple from binning the random catalogues. The redshift evolution ofthese is shown as dashed lines in Figure 3, and the spatial footprintin Figure 2. We note, that we do not use any additional weightingfunctions for the galaxy power spectrum.Equation 5 holds for Hi-auto, galaxy-auto, as well as Hi-galaxycorrelations. For galaxy power spectra, we additionally remove theshot noise weighted by the selection function as described in Blakeet al. (2011). The 1-d power spectra ˆ 𝑃 ( 𝑘 ) are determined by aver-aging all modes with 𝑘 = | (cid:174) 𝑘 | within the 𝑘 bin width.In the following, we use ˆ 𝑃 to indicate the estimated powerspectrum, and 𝑃 for the theory prediction. All power spectra areestimated using the redshift range 0 . < 𝑧 < .
95 with 𝑁 𝜈 = 𝑁 RA =
187 and 𝑁 DEC =
89. We use the flatsky approximation at mid-redshift 𝑧 = .
78, resulting in a volumeof 𝑉 = . · ( Mpc / ℎ ) . Note, that we do not correct for gridingeffects with our power spectrum estimator since the power spectrumis dominated by the beam from 𝑘 ∼ ℎ Mpc − . In this section, we present the Hi power spectrum to visualise theimpact of the foreground subtraction and the transfer function. InFigure 7, we show the Hi power spectrum in auto-correlation ˆ 𝑃 𝑖 HI foreach season 𝑖 , as well as the cross-correlation between the seasonsˆ 𝑃 𝑖 𝑗 HI for all investigated numbers of ICs 𝑁 IC ∈ { , , , } . Wepresent the Hi power spectrum with foreground subtraction correc-tion, where we use Θ 𝑖 as an approximation to correct the auto-powerspectrum 𝑖 , and Θ 𝑖 Θ 𝑗 to correct for the cross-season correlation 𝑖 𝑗 . MNRAS , 1–16 (2020)
L. Wolz et al.
As expected, the auto-power spectrum is dominated by instrumentnoise whose amplitude is higher than the Hi signal. Unlike othersubtraction techniques like PCA, FastICA cannot remove and mit-igate effects of Gaussian telescope noise. Hence, 𝑃 𝑖 HI can be usedas an estimate for the noise present in the data and we use the aver-aged auto-power spectrum ˆ 𝑃 autoHI , q ( 𝑘 ) = (cid:205) 𝑖 ˆ 𝑃 𝑖 HI , q ( 𝑘 )/ 𝜎 HI , q ( 𝑘 ) = ˆ 𝑃 autoHI , q ( 𝑘 )/ √︁ 𝑁 modes , (6)with 𝑁 modes the number of 𝑘 modes sampled in the survey volume,and 𝑞 the number of ICs, 𝑁 IC . As we use the auto-correlationbetween seasons as proxy for the noise on the Hi power spectrum,an extra scaling of √ 𝑁 IC on all scales. We are therefore confident that these two choicesof ICs in the foreground subtraction are removing sufficient fore-grounds. We use 𝑁 IC =
20 as a conservative choice with minimalHi signal loss, and possibly higher residual systematics and noise.Whereas 𝑁 IC =
36 is a more assertive choice in the subtractionresulting in lower noise properties with higher levels of Hi signalloss.
In Figure 8, we show the galaxy power spectra ˆ 𝑃 g ( 𝑘 ) of our samplesin auto- as well as cross-correlation. Note that our power spectrumestimator is not optimised for galaxy surveys and we do not usethe galaxy power spectra for a quantitative analysis. Only the auto-galaxy power spectra are shot noise removed, as we do not assumea sample overlap between galaxy surveys.The error bars on the auto-correlation are estimated as 𝜎 g ( 𝑘 ) = √ 𝑁 modes (cid:18) ˆ 𝑃 g ( 𝑘 ) + 𝑛 g (cid:19) , (7)where 𝑁 modes is again the number of independent 𝑘 modes in thesurvey volume, and 𝑛 g is the galaxy density of the samples, com-puted as 𝑛 g = 𝑁 g / 𝑉 , with 𝑁 g the number of galaxies and 𝑉 thesurvey volume. The cross-galaxy error bars are estimated as 𝜎 𝑖 𝑗 g ( 𝑘 ) = √︁ 𝑁 modes (cid:118)(cid:117)(cid:116) ˆ 𝑃 𝑖 𝑗 g ( 𝑘 ) + (cid:32) ˆ 𝑃 𝑖 g ( 𝑘 ) + 𝑛 𝑖 g (cid:33) (cid:32) ˆ 𝑃 𝑗 g ( 𝑘 ) + 𝑛 𝑗 g (cid:33) . (8)In the upper panel of Figure 8, we can see that the ELG and Wig-gleZ samples are similarly biased across scales, with tentativelyan opposite trend in the scale-dependent behaviour. This result isin agreement with theory, as the WiggleZ and ELG samples tracesimilar populations of galaxies. The bias of the LRG sample is sig-nificantly higher, which is again as expected as this sample tracesmore quiescent, early-type objects in denser environments. The lower panel of Figure 8 shows the cross-correlation be-tween the galaxy samples, similarly to Anderson et al. (2018). Theidea being that the bluer, star-forming samples (ELG and WiggleZ)trace the dark matter in a similar manner to Hi, therefore the shapeof the blue-red correlation power spectrum could also be used asa qualitative estimate of the Hi-LRG cross power spectrum. In ourdata, most notably, the WiggleZ-LRG power spectrum exhibits adrop in amplitude for smaller scales which is not seen for the othertwo spectra. In Figure 10, we present the Hi-galaxy cross-power spectra in abso-lute power for the three galaxy samples and different numbers of ICsin the foreground subtraction. The error bars on these power spectraare determined by the errors on the galaxy sample, see Equation 7,and the Hi data, see Equation 6, combined as 𝜎 𝑞 g , HI ( 𝑘 ) = √︁ 𝑁 modes √︄ ˆ 𝑃 𝑞 g , HI ( 𝑘 ) + ˆ 𝑃 𝑞 HI ( 𝑘 ) (cid:18) ˆ 𝑃 g ( 𝑘 ) + 𝑛 g (cid:19) , (9)with 𝑞 the number of ICs { , , , } . We note that the Hi dataerrors dominate the total cross-power error budget.We can see in all three panels of Figure 9, that the amplitudeof the cross-power signal is not very sensitive to the foreground re-moval parameters within the error bars. We do not observe a drop inamplitude with increasing numbers of ICs, and we are confident thatwe correctly account for Hi signal loss with our transfer function,particularly, within the large errors of the GBT data. Generally, asthe amplitude of the noise of the GBT data is decreased with in-creasing 𝑁 IC , the detection of the signal becomes more statisticallysignificant and the error bars decrease with increasing componentsremoved. In Figure 10, we show the cross-correlation of the threegalaxy samples for fixed 𝑁 IC =
36 in comparison.The GBT-WiggleZ cross-correlation in the upper panel of Fig-ure 10, is detected for both 𝑁 IC = ,
36 on scales 0 . < 𝑘 < . ℎ Mpc − . Qualitatively, the middle panel showing the ampli-tude of the GBT-ELG correlation looks very similar, but the de-tection seems more noise dominated on the larger scales, around 𝑘 ≈ . ℎ Mpc − . The GBT-LRG correlation shown in the lowestpanel demonstrates a detection of the signal for 𝑁 IC =
36. At thesmallest scales around 𝑘 ∼ ℎ Mpc − , the amplitude of the cor-relation signal drops off and the power spectrum is highly noisedominated. Anderson et al. (2018) reported a drop in amplitude inthe cross-correlation of the Parkes Hi intensity maps with the redsub-sample 2dF galaxies. However, the signal-to-noise ratio of theGBT-LRG measurements is not large enough to confirm this trend.The cross-correlation of WiggleZ-LRG galaxies as shown inFigure 8 supports that this would be an expected result for our data.The negligible power of the correlation of the Hi intensity mapswith the LRG galaxy sample on small scales, implies that the LRGgalaxies that contribute to these scales are Hi deficient. The powerspectrum signal on these scales originates from galaxy pairs mostlikely part of the same halo in a dense cluster environment. The Hideficiency of these types of quiescent galaxies has been predicted intheory and observed for the local Universe. Our work is an indicatorfor this trend for cosmological times.We will make more quantitative estimates for the significanceof the detections when we present our derived Hi constraints inSection 5. MNRAS000
36. At thesmallest scales around 𝑘 ∼ ℎ Mpc − , the amplitude of the cor-relation signal drops off and the power spectrum is highly noisedominated. Anderson et al. (2018) reported a drop in amplitude inthe cross-correlation of the Parkes Hi intensity maps with the redsub-sample 2dF galaxies. However, the signal-to-noise ratio of theGBT-LRG measurements is not large enough to confirm this trend.The cross-correlation of WiggleZ-LRG galaxies as shown inFigure 8 supports that this would be an expected result for our data.The negligible power of the correlation of the Hi intensity mapswith the LRG galaxy sample on small scales, implies that the LRGgalaxies that contribute to these scales are Hi deficient. The powerspectrum signal on these scales originates from galaxy pairs mostlikely part of the same halo in a dense cluster environment. The Hideficiency of these types of quiescent galaxies has been predicted intheory and observed for the local Universe. Our work is an indicatorfor this trend for cosmological times.We will make more quantitative estimates for the significanceof the detections when we present our derived Hi constraints inSection 5. MNRAS000 , 1–16 (2020)
BOSS - GBT Hi intensity mapping cross-correlations Figure 7.
The absolute value of the Hi power spectrum of the GBT intensity maps for different number of ICs in the foreground subtraction. All power spectraare transfer function corrected. We show the auto-correlation between the seasons marked with crosses, and the season cross-correlation with circles. Thereare a few negative data points (indicated by stars), which demonstrate the high noise on the measurements. Note that these measurements are about an order ofmagnitude higher than theory predictions and should be treated as upper limits which is in agreement with (Switzer et al. 2015).
We use our simulations for qualitative interpretation of our results.We use the same redshift range with ¯ 𝑧 ≈ .
78 to estimate the powerspectra of our mock data, however, we do not mask the edges of thedata which results in a bigger volume of 𝑉 = . · ( Mpc / ℎ ) . Wedo not include any noise and instrumental effects in this simulationsuite as we focus on understanding the implication from galaxyevolution on the cross-correlation signal.In Figure 11 from top to bottom, we show the power spectrafor the galaxy samples, the cross-galaxy and the Hi-galaxy correla-tions. The shapes and amplitudes of the galaxy power spectrum arecomparable to the data power spectrum. We presume that the fluc-tuations of the mock LRG sample are due to the low galaxy density.The cross-galaxy power spectra are comparable to the data measure-ments, with a drop in amplitude at smaller scales 𝑘 > . ℎ Mpc − .In the bottom panel of Figure 11 we show the resulting mockHi-galaxy cross-correlation. We note that the overall amplitude islower than the data due to a lower Ω HI than data measurementssuggest. The simulations predict the amplitude of all power spectraat the same level of magnitude. We show the beam-convolved mockas well as a unconvolved power spectrum, to demonstrate the effectof the Hi shot noise, as predicted in Wolz et al. (2017). The amplitudeof the cross-shot noise is proportional to the ensemble averaged Himass of the respective galaxy sample. Our simulation predicts thehighest shot noise amplitude for the Hi-WiggleZ correlation, andvery similar levels for both eBOSS samples. However, on the scalesunaffected by the GBT telescope beam, the shot noise does not havea measurable effect, in particular when considering the signal-to-noise ratio of our data. Notably, we do not find a drop in amplitude ofthe Hi-LRG correlation. This could suggest, that the drop could becaused by an unknown observational effect, which we were unableto identify with our tests given the large uncertainties of the data, or, alternatively, that our selection of mock LRG galaxies or the modelitself misses some features and our mock sample can not fullyrepresent the data. We hope to investigate this interesting feature infuture work with less noise-dominated Hi intensity maps. We perform several tests of our analysis pipeline listed in this sec-tion. For these tests, we examine the covariance matrix of the datacomputed as C 𝑞 = 𝐶 𝑞 ( 𝑘 𝑖 , 𝑘 𝑗 ) = 𝑁 𝑚 ∑︁ 𝑚 ( 𝑃 𝑞𝑚 ( 𝑘 𝑖 ) − ¯ 𝑃 𝑞 ( 𝑘 𝑖 ))( 𝑃 𝑞𝑚 ( 𝑘 𝑗 ) − ¯ 𝑃 𝑞 ( 𝑘 𝑗 ) 𝑁 𝑚 (10)where the number of independent components 𝑞 = { , , , } ,¯ 𝑃 the averaged power spectrum over all realisations, and 𝑁 𝑚 thenumber of realisations. We can derive an estimate for error barsfrom the diagonal as 𝜎 𝑞𝑖 = √︃ C 𝑞𝑖𝑖 . • Mode correlation from fastICA: We derive the covarianceof the data to determine the statistical independence between 𝑘 bins. We use the power spectra 𝑃 ( ˜ 𝑚 𝑗𝑞,𝑖 , 𝑚 𝑖 )( 𝑘 ) of the foreground-subtracted lognormal simulations ˜ 𝑚 𝑗𝑞,𝑖 with the original simulation 𝑚 𝑖 , and compute the covariance matrix. We find no significant off-diagonal correlations between the modes 0 . < 𝑘 < . ℎ Mpc − considered in our analysis. We also compute the errors from thediagonal of the inverted covariance matrix to determine the addi-tional error introduced from the foreground removal. We find thatthis contribution is more than 2 orders of magnitude lower than theanalytical errors based on noise and cosmic variance as determinedby Equation 6. We therefore can safely neglect this contribution inthe present analysis. MNRAS , 1–16 (2020) L. Wolz et al.
Figure 8.
The galaxy power spectrum of the eBOSS LRG, eBOSS ELG andWiggleZ samples.
Top : The auto-power spectra of the individual samples,with higher amplitude in the LRG sample and similar amplitudes of the ELGand WiggleZ samples, reflecting the different biases of the samples.
Bottom:
The cross-correlation between galaxy samples. We observe a drop in smallscale amplitude for the LRG-WiggleZ correlation. • Randoms null test: We correlate the GBT sub-season datawith the 𝑁 𝑚 =
100 random WiggleZ catalogues used to derive theselection function. As expected, we find a signal consistent withzero within the error bars. We also derive the covariance matrixfrom the mocks and find that the error bars 𝜎 cov are in agreementwith the empirically derived 𝜎 g , HI in Equation 9. • Shuffled null test: We correlate the GBT sub-season data withthe three galaxy samples which are each re-shuffled in redshift toremove the correlation. As expected, we find all signals consistentwith zero within the error bars.
Here, we are present our derived Hi constraints from the cross-correlation power spectra analysis (summarised in Table 1). Beforedoing so, we briefly review the findings of Masui et al. (2013),who measured the GBT maps cross-correlation with the WiggleZ15hr and 1hr fields. Fitting in the range of scales 0 . ℎ Mpc − <𝑘 < . ℎ Mpc − , they found 10 Ω Hi 𝑏 Hi 𝑟 = . ± .
05 forthe combined, 10 Ω Hi 𝑏 Hi 𝑟 = . ± .
08 for the 15hr field and10 Ω Hi 𝑏 Hi 𝑟 = . ± .
07 for the 1hr field (which is the one we areconsidering in this paper). For a more restrictive range of scales,their combined measurement was 10 Ω Hi 𝑏 Hi 𝑟 = . ± .
07. Notethat Masui et al. (2013) used Singular Value Decomposition (SVD)
Figure 9.
The GBT Hi intensity mapping cross-correlation with the galaxysamples for different numbers of ICs in the foreground subtraction. Notethat all power spectra were estimated at the same 𝑘 , and the staggered 𝑘 values in the plots are for illustration purposes only. From top to bottom:
Hi-WiggleZ, Hi-ELG, and Hi-LRG cross-correlation power spectrum. for their foreground removal, but we use FastICA here followingWolz et al. (2016b). Our transfer function construction methods areidentical. We note that the errors quoted are statistical, and Masuiet al. (2013) also estimated a ± .
04 systematic error representingtheir 9% absolute calibration uncertainty. We will adopt the samesystematic error in our analysis.In this paper we will explore different ranges of scales, byperforming fits for three cases:
Case I , with 0 . ℎ Mpc − < 𝑘 < . ℎ Mpc − . Case II , with 0 . ℎ Mpc − < 𝑘 < . ℎ Mpc − , and Case III , with 0 . ℎ Mpc − < 𝑘 < . ℎ Mpc − . Considering dif-ferent ranges of scales is motivated by the fact that, while small MNRAS000
Case I , with 0 . ℎ Mpc − < 𝑘 < . ℎ Mpc − . Case II , with 0 . ℎ Mpc − < 𝑘 < . ℎ Mpc − , and Case III , with 0 . ℎ Mpc − < 𝑘 < . ℎ Mpc − . Considering dif-ferent ranges of scales is motivated by the fact that, while small MNRAS000 , 1–16 (2020)
BOSS - GBT Hi intensity mapping cross-correlations Figure 10.
The GBT Hi intensity mapping cross-correlation with the galaxysamples in comparison. Note that all power spectra were estimated at thesame 𝑘 , and the staggered 𝑘 values in the plots are for illustration purposesonly. scales (high 𝑘 ) contain most of the statistical power of the measure-ment, the beam and model of nonlinearities become less robust as 𝑘 increases.In Figure 12 we show the measured GBT-WiggleZ power spec-trum, concentrating on the results with 𝑁 IC = ,
36. In the bottompanel, we perform a simple null diagnostic test by plotting the ratioof data and error. This shows that most of the measurements in therange of scales with high signal-to-noise ratio are more than 1 𝜎 positively away from 0. For our fiducial IC=36 results for Case I,corresponding to the same range of scales considered in Masui et al.(2013), the detection significance is estimated to be 4 . 𝜎 (we notethat in Masui et al. (2013) this was found to be 7 . 𝜎 but for thecombined 1hr and 15hr fields observations). We show similar plotsfor the GBT-ELG and GBT-LRG cross-correlations in Figure 13and Figure 14, respectively. We note that our null tests suggest thatthe GBT-LRG detection is the most tentative of the three. Indeed,estimating the detection significance for GBT-ELG and GBT-LRG,we find 4 . 𝜎 and 2 . 𝜎 , respectively, for Case I. In Table 1 we showthe detection significance for 𝑁 IC =
36 for all Cases. We see thatthe detection significance for the GBT-LRG cross-correlation con-siderably improves when considering the restricted ranges of scales,Cases II and III.To relate the measured power spectra with a theory model andderive the Hi constraints, we use Equation 1 to express the mean21cm emission brightness temperature 𝑇 Hi as a function of Ω Hi . Weobserve the brightness contrast, 𝛿𝑇 = 𝑇 Hi 𝛿 Hi . We also assume thatthe neutral hydrogen and the optical galaxies are biased tracers ofdark matter, but we also include a galaxy-Hi stochastic correlationcoefficient 𝑟 Hi , opt . To compare the theoretical prediction with themeasurements, we follow a procedure similar to the one describedin Masui et al. (2013): • We assume a fixed Planck cosmology (Ade et al. 2016). • We assume a known galaxy bias 𝑏 opt at the mean redshift 𝑧 (cid:39) .
8, with opt corresponding to WiggleZ (Blake et al. 2011),eBOSS ELGs, and eBOSS LRGs (Alam et al. 2020) depending onthe galaxy sample we cross-correlate the Hi maps with. That is, 𝑏 Wig = . 𝑏 ELG = . 𝑏 LRG = . • We include non-linear effects to the matter power spectrum 𝑃 m ( 𝑘 ) using CAMB (Lewis et al. 2000) with
HALOFIT (Smith et al.2003; Takahashi et al. 2012) and also include (linear) redshift spacedistortions as ( + 𝑓 𝜇 ) (Kaiser 1987), where 𝑓 the growth rate Figure 11.
The power spectra of our simulation suite.
Top:
The auto-galaxypower spectra of the three galaxy samples. The mock-ELG and WiggleZpower spectra are of similar amplitude, whereas the mock-LRG exhibits ahigher bias, consistent with the data.
Middle:
The cross-galaxy power spec-tra of the mock samples. Similarly to the data, we see a possible drop inamplitude on smaller scales for the LRG-WiggleZ correlation.
Bottom:
TheHi-galaxy cross-correlation, beam-convolved and with no beam to demon-strate the effect of the cross-shot noise. The dashed-dotted lines indicate theshot noise amplitude. of structure and 𝜇 the cosine of the angle to the line-of-sight.When spherically averaged to compute the matter power spectrummonopole, 𝑃 𝛿 𝛿 ( 𝑘 ) , this RSD factor gives an amplitude boost of 1 . • We then construct an empirical cross-power spectrum model
MNRAS , 1–16 (2020) L. Wolz et al.
Figure 12.
Top : The measured GBT-WiggleZ cross-correlation power spec-trum. We show two cases with 20 and 36 Independent Components usedin FastICA for the Hi maps foreground cleaning, corrected with the corre-sponding transfer functions. We also show the best-fit models from Table 1(Cases I, II, and III) for 𝑁 IC = Bottom : A null diagnostic test plottingthe ratio of data and error.
Figure 13.
Top : The measured GBT-ELG cross-correlation power spectrumfor 𝑁 IC = ,
36. We also show the best-fit models from Table 1 (Cases I,II, and III) for 𝑁 IC = Bottom : A null diagnostic test plotting the ratio ofdata and error.
Figure 14.
Top : The measured GBT-LRG cross-correlation power spectrumfor 𝑁 IC = ,
36. We also show the best-fit models from Table 1 (Cases I,II, and III) for 𝑁 IC = Bottom : A null diagnostic test plotting the ratio ofdata and error. 𝑃 Hi , g given by (Masui et al. 2013): 𝑃 Hi , g ( 𝑘 ) = 𝑇 Hi 𝑏 Hi 𝑏 g 𝑟 Hi , opt 𝑃 𝛿 𝛿 ( 𝑘 ) . (11)The model is run through the same pipeline as the data to includeweighting, beam , and window function effects, as described inWolz et al. (2016b). We will comment further on our modellingchoices at the end of this section. • We fit the unknown prefactor Ω Hi 𝑏 Hi 𝑟 Hi , opt to the data. Weperform fits for all three ranges of scales (Cases I, II, and III inTable 1). We find a good reduced 𝜒 ∼ 𝑘 < . ℎ Mpc − (where there are too few modes in the volume)does not make a discernible difference to our results. • We report our Ω Hi 𝑏 Hi 𝑟 Hi , opt at three different effective scales 𝑘 eff , which are estimated by weighting each 𝑘 -point in the cross-power by its ( S best − fit / N ) , for Cases I, II, and III. As we alreadymentioned, we do this because most of our measurements lie atthe nonlinear regime. Assigning an effective scale also allows for abetter interpretation of the implications for the values of 𝑟 Hi , opt .Our derived constraints are shown in Table 1, for 𝑁 IC = 𝑁 IC =
36 (for the smaller 𝑁 IC cases the errors are too largedue to residual foreground variance). In the GBT-WiggleZ Case I,we find excellent agreement with the Masui et al. (2013) results forthe 1hr field, 10 Ω Hi 𝑏 Hi 𝑟 Hi , Wig = . ± .
07. Using this case asour benchmark, the lower result in the GBT-ELGs case implies asmaller correlation coefficient between these galaxies and Hi, and The telescope beam is modelled as a Gaussian with transverse smooth-ing scale 𝑅 . This is related to the beam angular resolution, 𝜃 FWHM , by 𝑅 = 𝜒 ( 𝑧 ) 𝜃 FWHM /( √ ) , with 𝜒 ( 𝑧 ) being the radial comoving distanceto redshift 𝑧 . In cross-correlation, the beam induces a smoothing in thetransverse direction as e − 𝑘 𝑅 ( − 𝜇 )/ . MNRAS000
07. Using this case asour benchmark, the lower result in the GBT-ELGs case implies asmaller correlation coefficient between these galaxies and Hi, and The telescope beam is modelled as a Gaussian with transverse smooth-ing scale 𝑅 . This is related to the beam angular resolution, 𝜃 FWHM , by 𝑅 = 𝜒 ( 𝑧 ) 𝜃 FWHM /( √ ) , with 𝜒 ( 𝑧 ) being the radial comoving distanceto redshift 𝑧 . In cross-correlation, the beam induces a smoothing in thetransverse direction as e − 𝑘 𝑅 ( − 𝜇 )/ . MNRAS000 , 1–16 (2020) BOSS - GBT Hi intensity mapping cross-correlations Table 1.
Best-fit and 1 𝜎 statistical errors on 10 Ω Hi 𝑏 Hi 𝑟 Hi , opt at a mean redshift 𝑧 (cid:39) . 𝑁 IC = ,
36, together with the effective scale 𝑘 eff and detectionsignificance for 𝑁 IC =
36 (Cases I, II, and III; see main text for details).
GBTxWiggleZ GBTxELGs GBTxLRGs 𝑘 eff [ ℎ / Mpc ] Case I [ 𝑘 < . ℎ / Mpc ]NIC=20: . ± .
09 0 . ± .
06 0 . ± .
06 -
NIC=36: . ± .
08 (4 . 𝜎 ) 0 . ± .
06 (4 . 𝜎 ) 0 . ± .
06 (2 . 𝜎 ) 0.48 Case II [ 𝑘 < . ℎ / Mpc ]NIC=20: . ± .
12 0 . ± .
09 0 . ± .
09 -
NIC=36: . ± .
09 (4 . 𝜎 ) 0 . ± .
09 (4 . 𝜎 ) 0 . ± .
08 (4 . 𝜎 ) 0.31 Case III [ 𝑘 < . ℎ / Mpc ]NIC=20: . ± .
17 0 . ± .
12 0 . ± .
12 -
NIC=36: . ± .
12 (4 . 𝜎 ) 0 . ± .
11 (5 𝜎 ) 0 . ± .
10 (4 . 𝜎 ) 0.24 even smaller in the GBT-LRGs case. The results imply that redgalaxies are much more weakly correlated with Hi on the scaleswe are considering, suggesting that Hi is more associated withblue star-forming galaxies and tends to avoid red galaxies. Thesame trend is followed in the restricted ranges of scales Cases IIand III, albeit with different derived best-fit amplitudes. This is inqualitative agreement with what was found in Anderson et al. (2018)when separating the 2dF survey sample into red and blue galaxies,albeit at a much lower redshift 𝑧 = .
08. The effective scales ofthe three Cases are different: Case I has 𝑘 eff = . ℎ / Mpc, CaseII has 𝑘 eff = . ℎ / Mpc, and Case III has 𝑘 eff = . ℎ / Mpc.The different derived best-fit amplitudes are within expectation as 𝑟 Hi , opt and 𝑏 Hi are predicted to be scale-dependent. Therefore, wealso expect that if another survey targets larger (linear) scales, e.g. 𝑘 < . ℎ / Mpc, it will derive different Ω Hi 𝑏 Hi 𝑟 Hi , opt .We can proceed with the interpretation of our results makingsome further assumptions. First of all, since the correlation coeffi-cient 𝑟 <
1, our results put a lower limit on Ω Hi 𝑏 Hi . It would alsobe interesting to attempt to determine Ω Hi from our measurementstaking some external estimates for 𝑏 Hi and 𝑟 Hi , opt . The linear biasof Hi is expected to be ∼ .
65 to ∼ 𝑟 Hi , Wig = . 𝑘 eff for Case III, whichis the case where nonlinearities are expected to be milder), we canestimate 𝑟 Hi , ELG ∼ . 𝑟 Hi , LRG ∼ .
6. Combining these valueswith the results in Table 1 and our knowledge of the galaxy samplesbiases, we get the Ω Hi estimates shown in Figure 15. These areshown together with other available constraints from the literature(Braun 2012; Zwaan et al. 2005; Rao et al. 2006; Lah et al. 2007;Martin et al. 2010; Rhee et al. 2013; Hoppmann et al. 2015; Huet al. 2019). For a recent compilation of Ω Hi measurements in theredshift range 0 < 𝑧 <
5, see Hu et al. (2019).As a final note, we caution the reader that these estimates arecrude given the number of assumptions we have made. In principle,the degeneracy between Ω Hi and 𝑏 Hi can be broken with the use ofredshift space distortions (Wyithe 2008; Masui et al. 2013), but weneed higher quality Hi intensity mapping data with a much bettersignal-to-noise ratio to achieve this (Masui et al. 2010; Pourtsidouet al. 2017). We also stress that while our empirical model (Equa-tion 11) has provided an acceptable statistical fit to our data sets, itis not appropriate for high-precision future data. Following what isdone in optical galaxy surveys (see e.g. Blake et al. (2011); Beutleret al. (2014)), with better data we would need to use more sophis-ticated models and perform a comprehensive Hi power spectrummultipole expansion analysis (Cunnington et al. 2020b). For exam-ple, for the cross-correlation case a more appropriate model to use Figure 15.
Estimates for Ω Hi from this work compared to other measure-ments in the literature. All our estimates are at the central redshift 𝑧 = . 𝑘 eff = . ℎ / Mpc) for deriving these estimates. Ourassumptions and methodology are detailed in the main text. would be: 𝑃 Hi ,𝑔 ( 𝑘, 𝜇 ) = 𝑇 Hi 𝑏 𝑔 𝑏 Hi [ 𝑟 Hi , opt + ( 𝛽 Hi + 𝛽 𝑔 ) 𝜇 + 𝛽 Hi 𝛽 𝑔 𝜇 ] + ( 𝑘 𝜇𝜎 𝑣 / 𝐻 ) 𝑃 m ( 𝑘 ) , (12)with 𝛽 𝑖 = 𝑓 / 𝑏 𝑖 and 𝜎 𝑣 the velocity dispersion parameter. Further,to appropriately model the power spectrum at scales above 𝑘 ∼ . ℎ Mpc − at 𝑧 ∼ 𝑟 Hi , opt , and construct perturbation theory basedmodels (Villaescusa-Navarro et al. 2018; Castorina & White 2019)including observational effects (Blake 2019; Soares et al. 2021). Tosummarise, with our currently available measurements we are veryconstrained in the number of parameters we can simultaneouslyfit, and we cannot break any degeneracies unless we use severalassumptions and external estimates, hence our empirical choice ofmodel. In this work, we performed the first ever comparison of the Hi inten-sity mapping detections in cross-correlation with multiple galaxysurveys. We use an extended version of the previously publishedGBT Hi intensity mapping data located in the 1hr field in combina-tion with the WiggleZ Dark Energy Galaxy survey, and the SDSSeBOSS ELG and LRG samples.For the GBT data, we subtract the foregrounds and mitigate
MNRAS , 1–16 (2020) L. Wolz et al. some systematics via FastICA for 𝑁 IC ∈ { , , , } . In addition,for the first time for FastICA, we construct a transfer function forthe Hi signal loss via mock simulations. We find that there can bea high signal loss up to 50% for 𝑘 < . ℎ Mpc − , as foregroundremoval affects the line-of-sight modes on these scales for all 𝑁 IC .The transfer function converges towards unity for smaller scales,however, for 𝑁 IC =
36, we find there is a minimum of 20% signalloss on all scales. The amplitude of the transfer function variesbetween seasons, indicating that the systematics strongly affect theHi signal loss.For the Hi intensity mapping auto-power spectrum, we findthat the amplitude of the cross-season power spectrum convergesfor increasing number of ICs. The amplitude is in agreement withprevious work in Masui et al. (2013); Switzer et al. (2013); Wolzet al. (2016b), and should be interpreted as an upper limit for detec-tion. We investigate the shapes of the galaxy cross-power spectrum,particularly, the correlation between the WiggleZ and the LRG data.We observe a drop in amplitude on the small scales 𝑘 ≈ . 𝑁 IC of our foreground subtraction. We find a signifi-cant drop in amplitude in the Hi-LRG correlation at large scales, inagreement with previous findings in Anderson et al. (2018).We construct a mock data set including Hi information andoptical galaxy magnitudes based on the outputs of the semi-analyticmodel DARKSAGE and qualitatively compare the results to ourdata. Our mock catalogues predict the WiggleZ sample to containthe Hi-richest galaxies. Due to the selection of bright objects, theLRG sample also has relatively Hi-rich objects, and the averagedmass is in a similar range as the ELG sample. The simulationsconfirm a drop in amplitude in the LRG-WiggleZ correlation, butnot in the Hi-LRG correlation. This could be due to failure of oursimulation (not matching selection of our galaxies), or the decreasein amplitude caused by observational effects. The present signal-to-noise ratio is not high enough to investigate this further.Finally, we use the cross-correlation measurements to con-strain the quantity Ω Hi 𝑏 Hi 𝑟 Hi , opt , where Ω Hi is the Hi densityfraction, 𝑏 Hi is the Hi bias, and 𝑟 Hi , opt the galaxy-hydrogen cor-relation coefficient. We consider three different ranges of scales,which correspond to three different effective scales 𝑘 eff for our de-rived constraints. At 𝑘 eff = . ℎ / Mpc we find Ω Hi 𝑏 Hi 𝑟 Hi , Wig = [ . ± . ( stat ) ± . ( sys )] × − for GBT-WiggleZ, Ω Hi 𝑏 Hi 𝑟 Hi , ELG = [ . ± . ( stat ) ± . ( sys )] × − for GBT-ELG, and Ω Hi 𝑏 Hi 𝑟 Hi , LRG = [ . ± . ( stat ) ± . ( sys )] × − for GBT-LRG, at 𝑧 (cid:39) .
8. We also report results at 𝑘 eff = . ℎ / Mpc and 𝑘 eff = . ℎ / Mpc. The best-fit amplitudes and1 𝜎 statistical errors for all these cases are shown in Table 1. Ourresults are amongst the most precise constraints on neutral hydrogendensity fluctuations in a relatively unexplored redshift range, usingthree different galaxy samples.Our findings as well as our developed simulations and dataanalysis pipelines will be useful for the analysis of forthcoming Hiintensity mapping data, and for the preparation of future surveys. ACKNOWLEDGEMENTS
Author contributions : L.W. and A.P. conceived the idea, de-signed the methodology, led the data analysis, and drafted the paper.All authors contributed to the development and writing of the paper,or made a significant contribution to the data products.
MNRAS , 1–16 (2020)
BOSS - GBT Hi intensity mapping cross-correlations DATA AVAILABILITY
The raw GBT intensity mapping data (the observed time streamdata) is publicly available according to the NRAO data pol-icy, which can be found at https://science.nrao.edu/observing/proposal-types/datapolicies . The data prod-ucts, such as maps and foreground removed maps, are not publiclyavailable at this point and access needs to be requested via the GBTIntensity Mapping collaboration. We foresee a public release of theGBT data products once the analysis of the maps is finalised andthe results are published in scientific journals.The SDSS-IV DR16 data is available at . The DR16 LSS catalogues are pub-licly available: https://data.sdss.org/sas/dr16/eboss/lss/catalogs/DR16/ . APPENDIX A: SAMPLE SELECTION FOR OPTICALMOCK GALAXIES
For our sample selection in the simulation, we use the selectionwhich includes the magnitude limits of the observations as well asthe target selection.For WiggleZ, we use the selection cuts outlines in Drinkwateret al. (2010), as we have previously done in Wolz et al. (2016b).The selection is based on the GALEX UV filters NUV and FUV, aswell as the SDSS 𝑟 filter, as follows.NUV < . < 𝑟 < − . < ( NUV − 𝑟 ) < . (A1)For eBOSS ELG, we follow21 . <𝑔 < . (− . ( 𝑟 − 𝑧 ) + . ) < ( 𝑔 − 𝑟 ) < ( . ( 𝑟 − 𝑧 ) + . )( . ( 𝑔 − 𝑟 ) + . ) < ( 𝑟 − 𝑧 ) < (− . ( 𝑔 − 𝑟 ) + . ) . (A2)For eBOSS LRG, we follow , where we use the infra red filterIRAC1 as a close approximation for the WISE filter. ( . <𝑖 < . )( 𝑧 < . )( IRAC1 < . )( 𝑟 − 𝑖 ) > . )( 𝑟 − IRAC1 ) > ( 𝑟 − 𝑖 )) . (A3) REFERENCES
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