figure table

# The Hydrogen Intensity and Real-time Analysis eXperiment: 256-Element Array
Status and Overview

Devin Crichton  Institute for Particle Physics and Astrophysics, ETH Zürich,
Zürich, Switzerland  School of Mathematics, Statistics, & Computer Science,
University of KwaZulu-Natal, Durban, South Africa  Astrophysics Research
Centre, University of KwaZulu-Natal, Westville Campus, Durban 4000, South
Africa  Moumita Aich  School of Mathematics, Statistics, & Computer Science,
University of KwaZulu-Natal, Durban, South Africa  Astrophysics Research
Centre, University of KwaZulu-Natal, Westville Campus, Durban 4000, South
Africa  Adam Amara  Institute of Cosmology & Gravitation, University of
Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth PO1 3FX, UK
Institute for Particle Physics and Astrophysics, ETH Zürich, Zürich,
Switzerland  Kevin Bandura  LCSEE, West Virginia University, Morgantown, WV
26506, USA  Center for Gravitational Waves and Cosmology, West Virginia
University, Morgantown, WV 26505, USA  Bruce A. Bassett  African Institute for
Mathematical Sciences, 6 Melrose Road, Muizenberg, 7945, South Africa
Department of Maths and Applied Maths, University of Cape Town, Rondebosch,
Cape Town, 7700, South Africa  South African Astronomical Observatory,
Observatory, Cape Town, 7925, South Africa  Carlos Bengaly  Département de
Physique Théorique, Université de Genève, 1211 Genéve 4, Switzerland
Observatório Nacional, 20921-400, Rio de Janeiro - RJ, Brazil  Pascale Berner
Institute for Particle Physics and Astrophysics, ETH Zürich, Zürich,
Switzerland  Shruti Bhatporia  High Energy Physics, Cosmology & Astrophysics
Theory Group, University of Cape Town, Cape Town, South Africa  Martin Bucher
Université de Paris, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France
LPENS, Ecole Normale Supérieure, 75005 Paris, France  School of Mathematics,
Statistics, & Computer Science, University of KwaZulu-Natal, Durban, South
Africa  NITheCS, Stellenbosch, South Africa  Tzu-Ching Chang  NASA Jet
Propulsion Laboratory, Californita Institute of Technology, Pasadena, CA, USA
H. Cynthia Chiang  Department of Physics, McGill University, Montreal, Quebec
H3A 2T8, Canada  School of Mathematics, Statistics, & Computer Science,
University of KwaZulu-Natal, Durban, South Africa  Jean-Francois Cliche
Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada
Carolyn Crichton  Département de Physique Théorique, Université de Genève,
1211 Genéve 4, Switzerland  School of Mathematics, Statistics, & Computer
Science, University of KwaZulu-Natal, Durban, South Africa  Astrophysics
Research Centre, University of KwaZulu-Natal, Westville Campus, Durban 4000,
South Africa  Romeel Dave  Institute for Astronomy, University of Edinburgh,
Royal Observatory, Edinburgh EH9 3HJ, UK  Department of Physics and Astronomy,
University of the Western Cape, Cape Town 7535, South Africa  South African
Astronomical Observatory, Observatory, Cape Town, 7925, South Africa  Dirk I.
L. De Villiers  Department of Electrical and Electronic Engineering,
Stellenbosch University, Stellenbosch 7600, South Africa  Matt Dobbs
Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada
Aaron M. Ewall-Wice  Department of Astronomy, University of California,
Berkeley, CA, USA  NASA Jet Propulsion Laboratory, Californita Institute of
Technology, Pasadena, CA, USA  Scott Eyono  School of Mathematics, Statistics,
& Computer Science, University of KwaZulu-Natal, Durban, South Africa
Astrophysics Research Centre, University of KwaZulu-Natal, Westville Campus,
Durban 4000, South Africa  Christopher Finlay  Département de Physique
Théorique, Université de Genève, 1211 Genéve 4, Switzerland  South African
Astronomical Observatory, Observatory, Cape Town, 7925, South Africa
Department of Maths and Applied Maths, University of Cape Town, Rondebosch,
Cape Town, 7700, South Africa  African Institute for Mathematical Sciences, 6
Melrose Road, Muizenberg, 7945, South Africa  Sindhu Gaddam  School of
Mathematics, Statistics, & Computer Science, University of KwaZulu-Natal,
Durban, South Africa  Astrophysics Research Centre, University of KwaZulu-
Natal, Westville Campus, Durban 4000, South Africa  Ken Ganga  Université de
Paris, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France  Kevin G.
Gayley  Department of Physics, University of Wisconsin-Madison, Madison, WI
53706, USA  Kit Gerodias  Department of Physics, McGill University, Montreal,
Quebec H3A 2T8, Canada  Tim B. Gibbon  Centre for Broadband Communication,
Nelson Mandela Metropolitan University, P.O Box 77000, Port Elizabeth 6031,
South Africa  Austine Gumba  School of Mathematics, Statistics, & Computer
Science, University of KwaZulu-Natal, Durban, South Africa  Astrophysics
Research Centre, University of KwaZulu-Natal, Westville Campus, Durban 4000,
South Africa  Neeraj Gupta  Inter-University Centre for Astronomy and
Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007, India  Maile Harris
Department of Physics, Yale University, New Haven, CT, USA  Heiko Heilgendorff
School of Mathematics, Statistics, & Computer Science, University of KwaZulu-
Natal, Durban, South Africa  Astrophysics Research Centre, University of
KwaZulu-Natal, Westville Campus, Durban 4000, South Africa  Matt Hilton
School of Mathematics, Statistics, & Computer Science, University of KwaZulu-
Natal, Durban, South Africa  Astrophysics Research Centre, University of
KwaZulu-Natal, Westville Campus, Durban 4000, South Africa  Adam D. Hincks
David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto,
50 St. George Street, Toronto, ON M5S 3H4, Canada  Pascal Hitz  Institute for
Particle Physics and Astrophysics, ETH Zürich, Zürich, Switzerland  Mona
Jalilvand  Department of Physics, McGill University, Montreal, Quebec H3A 2T8,
Canada  Département de Physique Théorique, Université de Genève, 1211 Genéve
4, Switzerland  Roufurd P.M. Julie  South African Radio Astronomy Observatory,
2 Fir Street, Observatory, Cape Town, 7925, South Africa  Zahra Kader  School
of Mathematics, Statistics, & Computer Science, University of KwaZulu-Natal,
Durban, South Africa  Astrophysics Research Centre, University of KwaZulu-
Natal, Westville Campus, Durban 4000, South Africa  Joseph Kania  Department
of Physics and Astronomy, West Virginia University, Morgantown, WV 26505, USA
Center for Gravitational Waves and Cosmology, West Virginia University,
Morgantown, WV 26505, USA  Dionysios Karagiannis  Department of Physics and
Astronomy, University of the Western Cape, Cape Town 7535, South Africa  Aris
Karastergiou  Astrophysics, University of Oxford, Denys Wilkinson Building,
Keble Road, Oxford OX1 3RH, UK  Department of Physics and Astronomy,
University of the Western Cape, Cape Town 7535, South Africa  SKA SA, 3rd
Floor, The Park, Park Road, Pinelands 7405, South Africa  Department of
Physics and Electronics, Rhodes University, PO Box 94, Makhanda 6140, South
Africa  Kabelo Kesebonye  School of Mathematics, Statistics, & Computer
Science, University of KwaZulu-Natal, Durban, South Africa  Astrophysics
Research Centre, University of KwaZulu-Natal, Westville Campus, Durban 4000,
South Africa  Piyanat Kittiwisit  Department of Physics and Astronomy,
University of the Western Cape, Cape Town 7535, South Africa  Jean-Paul Kneib
Institute of Physics, Laboratory of Astrophysics, École Polytechnique Fédérale
de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland  Kenda
Knowles  School of Mathematics, Statistics, & Computer Science, University of
KwaZulu-Natal, Durban, South Africa  Astrophysics Research Centre, University
of KwaZulu-Natal, Westville Campus, Durban 4000, South Africa  Department of
Physics and Electronics, Rhodes University, PO Box 94, Makhanda 6140, South
Africa  Emily R. Kuhn  Department of Physics, Yale University, New Haven, CT,
USA  Martin Kunz  Département de Physique Théorique, Université de Genève,
1211 Genéve 4, Switzerland  Roy Maartens  Department of Physics and Astronomy,
University of the Western Cape, Cape Town 7535, South Africa  Institute of
Cosmology & Gravitation, University of Portsmouth, Dennis Sciama Building,
Burnaby Road, Portsmouth PO1 3FX, UK  Vincent MacKay  Department of Physics,
University of Toronto, Toronto, Canada  Dunlap Institute for Astronomy &
Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S
3H4, Canada  Stuart MacPherson  Durban University of Technology, Engineering
and the Built Environment, P.O. Box 1334, Durban, 4000 South Africa  Christian
Monstein  Institute for Particle Physics and Astrophysics, ETH Zürich, Zürich,
Switzerland  Kavilan Moodley  School of Mathematics, Statistics, & Computer
Science, University of KwaZulu-Natal, Durban, South Africa  Astrophysics
Research Centre, University of KwaZulu-Natal, Westville Campus, Durban 4000,
South Africa  V. Mugundhan  School of Mathematics, Statistics, & Computer
Science, University of KwaZulu-Natal, Durban, South Africa  Astrophysics
Research Centre, University of KwaZulu-Natal, Westville Campus, Durban 4000,
South Africa  Raman Research Institute, India  Warren Naidoo  School of
Mathematics, Statistics, & Computer Science, University of KwaZulu-Natal,
Durban, South Africa  Astrophysics Research Centre, University of KwaZulu-
Natal, Westville Campus, Durban 4000, South Africa  Arun Naidu  Astrophysics,
University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
Laura B. Newburgh  Department of Physics, Yale University, New Haven, CT, USA
Viraj Nistane  Département de Physique Théorique, Université de Genève, 1211
Genéve 4, Switzerland  Amanda Di Nitto  Department of Physics, McGill
University, Montreal, Quebec H3A 2T8, Canada  Deniz Ölçek  Department of
Physics, McGill University, Montreal, Quebec H3A 2T8, Canada  Xinyu Pan
Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada
Sourabh Paul  Department of Physics and Astronomy, University of the Western
Cape, Cape Town 7535, South Africa  Jeffrey B. Peterson  Department of
Physics, Carnegie Mellon University, Pittsburgh, PA, USA  Elizabeth Pieters
Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada
Carla Pieterse  Department of Electrical and Electronic Engineering,
Stellenbosch University, Stellenbosch 7600, South Africa  Astrophysics
Research Centre, University of KwaZulu-Natal, Westville Campus, Durban 4000,
South Africa  Aritha Pillay  Durban University of Technology, Engineering and
the Built Environment, P.O. Box 1334, Durban, 4000 South Africa  Anna R.
Polish  Department of Physics, Yale University, New Haven, CT, USA  Liantsoa
Randrianjanahary  Department of Physics and Astronomy, University of the
Western Cape, Cape Town 7535, South Africa  Alexandre Refregier  Institute for
Particle Physics and Astrophysics, ETH Zürich, Zürich, Switzerland  Andre
Renard  Dunlap Institute for Astronomy & Astrophysics, University of Toronto,
50 St. George Street, Toronto, ON M5S 3H4, Canada  Edwin Retana-Montenegro
School of Mathematics, Statistics, & Computer Science, University of KwaZulu-
Natal, Durban, South Africa  Astrophysics Research Centre, University of
KwaZulu-Natal, Westville Campus, Durban 4000, South Africa  Ian H. Rout
Astrophysics Research Centre, University of KwaZulu-Natal, Westville Campus,
Durban 4000, South Africa  Cyndie Russeeawon  Department of Physics and
Electronics, Rhodes University, PO Box 94, Makhanda 6140, South Africa
Alireza Vafaei Sadr  Département de Physique Théorique, Université de Genève,
1211 Genéve 4, Switzerland  Benjamin R.B. Saliwanchik  Department of Physics,
Brookhaven National Laboratory, Upton, NY, USA  Department of Physics, Yale
University, New Haven, CT, USA  Ajith Sampath  School of Mathematics,
Statistics, & Computer Science, University of KwaZulu-Natal, Durban, South
Africa  Astrophysics Research Centre, University of KwaZulu-Natal, Westville
Campus, Durban 4000, South Africa  Pranav Sanghavi  LCSEE, West Virginia
University, Morgantown, WV 26506, USA  Center for Gravitational Waves and
Cosmology, West Virginia University, Morgantown, WV 26505, USA  Mario G.
Santos  Department of Physics and Astronomy, University of the Western Cape,
Cape Town 7535, South Africa  South African Radio Astronomy Observatory, 2 Fir
Street, Observatory, Cape Town, 7925, South Africa  Onkabetse Sengate  School
of Chemistry and Physics, University of KwaZulu-Natal, Durban, South Africa
Astrophysics Research Centre, University of KwaZulu-Natal, Westville Campus,
Durban 4000, South Africa  J. Richard Shaw  Department of Physics and
Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
Jonathan L. Sievers  Department of Physics, McGill University, Montreal,
Quebec H3A 2T8, Canada  School of Chemistry and Physics, University of
KwaZulu-Natal, Durban, South Africa  Oleg M. Smirnov  Department of Physics
and Electronics, Rhodes University, PO Box 94, Makhanda 6140, South Africa
SKA SA, 3rd Floor, The Park, Park Road, Pinelands 7405, South Africa  Kendrick
M. Smith  Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5,
Canada  Ulrich Armel Mbou Sob  Department of Physics and Electronics, Rhodes
University, PO Box 94, Makhanda 6140, South Africa  Raghunathan Srianand
Inter-University Centre for Astronomy and Astrophysics, Post Bag 4,
Ganeshkhind, Pune 411 007, India  Pieter Stronkhorst  Hartebeesthoek Radio
Astronomy Observatory, P. O. Box 443, Krugersdorp 1740, South Africa
Dhaneshwar D. Sunder  School of Mathematics, Statistics, & Computer Science,
University of KwaZulu-Natal, Durban, South Africa  Astrophysics Research
Centre, University of KwaZulu-Natal, Westville Campus, Durban 4000, South
Africa  Simon Tartakovsky  Department of Physics, McGill University, Montreal,
Quebec H3A 2T8, Canada  Russ Taylor  Department of Astronomy, University of
Cape Town, Cape Town, South Africa  Department of Physics and Astronomy,
University of the Western Cape, Cape Town 7535, South Africa  Peter Timbie
Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
Emma E. Tolley  Institute of Physics, Laboratory of Astrophysics, École
Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290
Versoix, Switzerland  Junaid Townsend  Department of Physics and Astronomy,
University of the Western Cape, Cape Town 7535, South Africa  Will Tyndall
Department of Physics, Yale University, New Haven, CT, USA  Cornelius Ungerer
Astrophysics Research Centre, University of KwaZulu-Natal, Westville Campus,
Durban 4000, South Africa  ArioGenix(Pty) Ltd, Pretoria, South Africa  Jacques
van Dyk  Department of Physics, McGill University, Montreal, Quebec H3A 2T8,
Canada  Pronex Engineering Management Consultants CC, Pretoria, South Africa
Astrophysics Research Centre, University of KwaZulu-Natal, Westville Campus,
Durban 4000, South Africa  Gary van Vuuren  Durban University of Technology,
Engineering and the Built Environment, P.O. Box 1334, Durban, 4000 South
Africa  Keith Vanderlinde  Dunlap Institute for Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada
David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto,
50 St. George Street, Toronto, ON M5S 3H4, Canada  Thierry Viant  Institute
for Particle Physics and Astrophysics, ETH Zürich, Zürich, Switzerland
Anthony Walters  School of Mathematics, Statistics, & Computer Science,
University of KwaZulu-Natal, Durban, South Africa  Astrophysics Research
Centre, University of KwaZulu-Natal, Westville Campus, Durban 4000, South
Africa  Jingying Wang  Department of Physics and Astronomy, University of the
Western Cape, Cape Town 7535, South Africa  Amanda Weltman  High Energy
Physics, Cosmology & Astrophysics Theory Group, University of Cape Town, Cape
Town, South Africa  Patrick Woudt  Department of Astronomy, University of Cape
Town, Cape Town, South Africa  Dallas Wulf  Department of Physics, McGill
University, Montreal, Quebec H3A 2T8, Canada  Anatoly Zavyalov  David A.
Dunlap Department of Astronomy & Astrophysics, University of Toronto, 50 St.
George Street, Toronto, ON M5S 3H4, Canada  Zheng Zhang  Université de Paris,
CNRS, Astroparticule et Cosmologie, F-75013 Paris, France  LPENS, Ecole
Normale Supérieure, 75005 Paris, France

###### Abstract

The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) is a radio
interferometer array currently in development, with an initial 256-element
array to be deployed at the South African Radio Astronomy Observatory (SARAO)
Square Kilometer Array (SKA) site in South Africa. Each of the 6 m, $f/0.23$
dishes will be instrumented with dual-polarisation feeds operating over a
frequency range of 400–800 MHz. Through intensity mapping of the 21 cm
emission line of neutral hydrogen, HIRAX will provide a cosmological survey of
the distribution of large-scale structure over the redshift range of
$0.775<z<2.55$ over $\sim$15,000 square degrees of the southern sky. The
statistical power of such a survey is sufficient to produce $\sim$7 percent
constraints on the dark energy equation of state parameter when combined with
measurements from the Planck satellite. Additionally, HIRAX will provide a
highly competitive platform for radio transient and HI absorber science while
enabling a multitude of cross-correlation studies. In these proceedings, we
describe the science goals of the experiment, overview of the design and
status of the sub-components of the telescope system, and describe the
expected performance of the initial 256-element array as well as the planned
future expansion to the final, 1024-element array.

###### keywords:

21 cm, intensity mapping, cosmology, dark energy, radio transients,
interferometers

*Devin Crichton<EMAIL_ADDRESS>
##  1 Introduction

In recent years, the statistical distribution of large-scale structure in the
late-time universe has been measured with increased precision. Current state-
of-the-art measurements primarily come from baryon acoustic oscillation (BAO)
studies from galaxy and Lyman-$\alpha$ surveys as well as weak lensing
probes[1, 2, 3, 4, 5, 6, 7]. However, tomographic measurements in the
visible/infrared bands become increasingly difficult beyond $z\sim 1$,
requiring complex optical systems and long integration times. Intensity
mapping with the 21 cm (1420.4 MHz) line of neutral hydrogen has the potential
to push beyond these limitations, with observations in the range of
$0<z\lesssim 30$ being achievable with current and planned instruments. The
abundance of hydrogen and the optically thin nature of the emission will
enable detailed tomographic measurements of the distribution of matter over
large, cosmological volumes[8, 9, 10]. In the post-reionisation epoch, by
observing the BAO feature in the matter power spectrum, intensity mapping
enables cosmological measurements that can break parameter degeneracies in
current combinations of early-universe and late-time measurements, as well as
constrain the dynamical nature of dark energy over the transition from matter-
dominated to dark-energy dominated expansion.

Modern advances in computer and communication hardware as well as the
relatively simple, low-frequency receivers required for these observations
have motivated the development of large, $\sim$100–1000 element interferometer
arrays such as CHIME[11], CHORD[12], HERA[13], PUMA[14], and Tianlai[15]. Such
telescopes focus their sensitivity on cosmologically relevant angular scales,
favouring compact arrays with “redundant” configurations, where the
constituent radio telescopes are placed with regular spacing. This type of
array architecture additionally provides a natural platform for the detection
and monitoring of radio transients, with wide fields of view, fast mapping
speeds, and the real-time processing power required for fast radio burst (FRB)
detection and pulsar searches, as demonstrated by CHIME in, e.g. Refs. 16, 17,
18, 19, 20.

Figure 1: HIRAX will observe $\sim$15,000 deg2 of the southern sky, shown by
the region enclosed by the white dashed lines. The survey footprint overlaps
many existing and forthcoming surveys such as those of CHIME[11], DES[4],
KiDS[6], DESI[21] and Advanced ACTPol[22]. The entirety of the sky area shown
is contained within the Rubin/LSST[23] survey footprint and is accessible to
the SKA[24] and its precursors. The background colorscale shows Galactic
emission from the Planck 353 GHz map.

The Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX)[25] is a new
radio interferometer array that will employ a compact, redundant layout. HIRAX
is currently funded for the construction of an initial 256-element array
(HIRAX-256) that will comprise a subset of the planned 1024-element array. The
telescope will conduct a large 21 cm intensity mapping survey, targeting
cosmological constraints on the dark energy equation-of-state parameters,
while additionally operating as a platform for transient and HI absorber
searches. The cosmological survey requires careful control of systematics due
to significant risk of contamination by residuals from foregrounds, which are
up to six orders of magnitude brighter in power. The radio transient detection
pipeline for HIRAX will focus on searches for FRBs and millisecond pulsars.
FRBs are currently under intense study since the nature of their emission
processes is not yet understood. HIRAX-256 is expected to detect multiple FRBs
per week and future proposed HIRAX outrigger sites with very long baselines
($\sim$1000 km) will aid in the localisation of FRB detections to within 0.1
arcseconds. Pulsar searches will be performed on beam-formed data at full
baseband, allowing for searches over a wide parameter space. Additionally, the
flexible digital backend will allow for the monitoring of known pulsars
(aiding existing pulsar timing studies) as well as upchannelizing to $\sim$3
kHz spectral resolution, which will be used to conduct a blind Hi absorber
search. Such a search will provide an informative accounting of the state of
cold gas in galaxies out to $z\sim 2.5$, encompassing the peak of the global
star-formation rate density at $z\sim 2$. Finally, as shown in Figure 1, the
$-60^{\circ}\lesssim\delta\lesssim 0^{\circ}$ declination range of the HIRAX
survey has significant overlap with a range of other large surveys of the
southern and equatorial sky, thus enabling a wide range of potential cross-
correlation studies. These include optical/infrared galaxy and lensing surveys
from eBOSS[26], DES[4], KiDS[6], HSC[27], DESI[21], Rubin/LSST[23], Euclid[28]
and Roman[29] as well as ground based cosmic microwave background (CMB)
surveys from Advanced ACTPol[22], SPT-3G[30] and the Simons Observatory[31].

These science goals are highly synergistic with those of the SKA[24] and its
precursors. For example, the combined MeerKLASS[32] and HIRAX intensity
mapping surveys will have the potential to produce a cosmological analysis
over a redshift range of $0\lesssim z\lesssim 2.5$, with contrasting
systematic challenges from the differing observing modes and instruments. The
blind Hi absorber surveys with HIRAX will extend observations beyond the
redshift limits of ongoing surveys, such as the MeerKAT Absorption Line Survey
(MALS[33]), to investigate the relationship between cold atomic gas and the
evolution of star formation and AGN activity.

In these proceedings, we present the current status and design of HIRAX-256,
as well as the analysis work that has been done to inform these design
choices. In Section 2 we introduce the instrument and briefly outline the
various sub-components. Section 3 overviews the forecasted cosmological
constraints and current analysis methodologies. In Section 4 we describe how
forecasts and analysis of simulated data have constrained the design of the
instrument, and finally in Section 5 we discuss the current status of the
project.

##  2 Instrument and Subsystems

###  2.1 Overview

Figure 2: Artist’s impression of the HIRAX array in the Karoo desert.

The overall design of HIRAX is driven by optimizing sensitivity to the
restricted range of angular scales corresponding to the BAO signature. The BAO
science goals thus naturally dictate the high-level instrument configuration.
The redshift range $0.775<z<2.55$, which captures the onset of the influence
of dark energy on the expansion rate at $z\sim 2$, sets the observing
frequency range of 400–800 MHz. The 150 Mpc BAO characteristic length
corresponds to angular scales of $3^{\circ}$–$1.3^{\circ}$ at 400–800 MHz,
thus setting a minimum baseline length range of 15–60 m. Along the line of
sight, the BAO characteristic length translates into frequency scales of 12–20
MHz, thus setting an absolute minimum requirement of $\sim$100 frequency
channels over 400–800 MHz. Finally, because the BAO signal is faint ($\sim$0.1
mK), the instrument must have a large collecting area and low system
temperature. The basic HIRAX instrument parameters are summarized in Table 1,
and a rendering of the array is shown in Figure 2. The HIRAX array, which will
initially consist of 256 elements, will be installed at the South African
Radio Astronomy Observatory (SARAO) site in the Karoo Desert, South Africa, at
$30^{\circ}41^{\prime}47^{\prime\prime}$ S,
$21^{\circ}34^{\prime}20^{\prime\prime}$ E. From this site, HIRAX will be able
to access $\sim$15,000 deg2 of the southern sky, as illustrated in Figure 1.

To keep the total data volume at a manageable level, we will take advantage of
the redundant configuration of HIRAX to average visibilities within groups of
nominally identical baselines. A continuous few-day buffer of the full set of
raw visibilities will be stored while the calibration and averaging process is
performed, after which the raw data will be deleted. This averaging process is
highly sensitive to differences in telescope pairs, since even small
mismatches may couple with Galactic emission, which is up to $10^{3}$ times
greater in amplitude than the BAO signal, subsequently offsetting the
calibration and introducing systematic errors in the observations. Redundant
radio telescope arrays that average visibilities early in this way, such as
HIRAX, therefore operate in a unique regime that demands precise control—not
merely characterization—over possible departures from redundancy. The
methodology for deriving the HIRAX instrument specifications is discussed in
further detail in §4.

The degree to which baselines are redundant and the angular scales over which
that redundancy is distributed are important considerations in determining the
optimal HIRAX array layout. Evaluating array layouts that strike a balance
between redundancy and more uniform $uv$-plane coverage[34] is an active area
of study. Key factors favouring maximal redundancy include reduced raw data
rate and ease of redundant calibration, whereas key factors favouring less
than maximal redundancy include the array chromatic response, taking into
account dish-feed and dish-dish coupling across the array, and the impact of
instrument errors that cause systematic departures from redundancy.

Figure 3 illustrates the HIRAX signal chain. At the focus of each telescope
dish, the incoming radio signals are received and amplified by a dual-
polarization active feed, band limited to 400–800 MHz, and converted to
optical light with an RF over optical fibre (RFoF) transmitter. The optical
signals from all dishes are transmitted to a central processing hub and
converted back into RF using RFoF receivers, passed through a second stage of
400–800 MHz filtering, and then digitized. HIRAX employs ICE boards [35] for
digitizing and channelizing the RF inputs, and performing the corner turn
operation before the data are passed to the GPU X-engine for correlation.

Parameter | Value
---|---
Number of dishes | 256
Dish diameter | 6 m
Dish focal ratio | 0.23
Collecting area | 7200 m2
Frequency range | 400–800 MHz
Frequency resolution | 1024 channels, 390 kHz
Field of view |  $5^{\circ}$–$10^{\circ}$
Resolution |  $0.2^{\circ}$–$0.4^{\circ}$
Target system temperature | 50 K
Table 1: HIRAX instrument parameters for the initial 256-element array. Figure
3: HIRAX signal chain schematic. In each dish, an active dual-polarization
feed receives and amplifies incoming radio signals. The signals are filtered,
further amplified, and converted to optical light with an RFoF transmitter at
the dish focus. Optical fibre transports the signals to an RFoF receiver,
which converts the signals back into RF and applies additional amplification
and filtering before digitization. An ICE-based system performs the
digitization, channelizing, and corner turn. The data are then passed to the
GPU X-engine for correlation.

###  2.2 Dishes and Mounting Structure

Each HIRAX telescope will have a parabolic reflector with a diameter of 6 m
and focal ratio of $f/0.23$. The dish size was chosen to maximize collecting
area over the minimum baseline lengths, and the low focal ratio allows the
entire receiver support structure to sit below the aperture plane, thus
reducing cross-talk between neighboring dishes. Each dish will be supported by
a mounting structure that is stationary in azimuth and that can be manually
repointed in zenith angle over a range of $\pm 30^{\circ}$ to incrementally
build up sky coverage. The HIRAX redundancy requirements have strict
implications for the allowed tolerances on the dish surface and the mount
alignment, which impact the on-sky beam shape and pointing, respectively. In
general, the requirements on dish and mount precision are far more stringent
than the requirements on accuracy. The precision requirements are discussed in
further detail in §4.

Dish fabrication methods using composite materials with an embedded reflective
layer are well suited for meeting the HIRAX requirements while being cost
effective. Fabricating all of the dishes using a small number of molds ensures
that variations across the array are kept to a minimum. Composite materials
also have high strength-to-weight ratios and are therefore excellent
candidates for minimizing gravitational distortion of the dish surfaces as the
telescopes are repointed. One prototype composite dish has been installed at
the HIRAX test site at the Hartebeesthoek Radio Astronomy Observatory
(HartRAO), and other prototyping efforts are currently underway. Further
details about the HIRAX prototype dishes and design are available in Ref. 36.

###  2.3 Dual-Polarization Cloverleaf Feed

HIRAX will use a dual-polarization cloverleaf feed based on the design that
was developed for CHIME[37]. In contrast to the CHIME feed, which is passive,
the HIRAX feed is active. Each polarization of the HIRAX feed consists of a
balun that uses an Avago MGA-16116 dual amplifier, providing a gain of 22 dB,
and the difference between the ouputs are amplified by 21 dB using a Mini-
Circuits PSA4-5043+. Each feed is mounted inside a cylindrical can, which
circularizes the beam and helps reduce cross-talk. Each feed and can assembly
will be supported at the dish focus with a radio-transparent central column
that extends upward from the vertex. The column will provide environmental
protection by fully enclosing the feed assembly, and the cables will be routed
along the boresight axis to minimize their impact on beam asymmetry and
sidelobe levels. Measurements of the noise performance of the HIRAX feed and
its repeatability is described in Ref. 38.

###  2.4 Radio Frequency Over fibre System

Signals received by the HIRAX feed are band limited to 400–800 MHz and passed
through an additional 22 dB amplification stage before being intensity
modulated on an optical carrier at the focus using an RFoF transmitter.
Optical fibres carry these signals to a central processing hub, where RFoF
receivers convert the signals back into RF. The RF signals are subsequently
amplified and filtered again (25 dB gain, 400–800 MHz) before being passed to
the digitizer. For the long length of the HIRAX cable runs from the telescopes
to the central hub, especially looking ahead to the planned 1024 element
array, the combination of RFoF electronics and optical fibres provide a more
cost-effective solution than copper coaxial cables. The RFoF transmitter and
receiver design is based on technology that was developed by CHIME[39]
(although ultimately unused in the final experimental configuration). The
transmitter contains a laser diode (AGX Technologies, FPMR3
series111http://www.agxtech.com/PDF/FPMR3+w+Isolator+Rev1.9.pdf) that is
intensity modulated by the incoming RF signal, and the receiver contains a
photodetector (AGX Technologies, PPDD
series222http://www.agxtech.com/PDF/PPDA+R5.6.pdf) that converts the
transmitted optical signal into RF.

###  2.5 ICE-based F-Engine

The digital back end for HIRAX consists of an FX correlator, with the F-engine
comprised of an ICE-based digitisation and channelisation system[40, 35]. The
F-engine for HIRAX-256 will be made up of 32 ICE boards, each processing 16
inputs from 8 dual-polarisation feeds. These ICE boards are contained in two
ICE crates, each hosting 16 boards. Briefly, the ICE boards use FPGA-based
electronics to digitize the incoming signals from the RFoF system at a
precision of 8 bits over the full 400 MHz of bandwidth. For the channelisation
step, these digitised signals are processed by a polyphase filter bank and FFT
based pipeline, producing the 1024 frequency channels (390 kHz wide) that are
passed to the correlator. This system also performs the real-time corner-turn
operation, which arranges the outgoing data such that each node of the
X-engine receives data streams from all inputs over the subset of the
bandwidth to be processed by that node. These streams are transferred to the
GPU-based X-Engine over a dedicated 40 Gbps network. For the 1024 element
array, this system will be scaled up to 128 ICE boards and 8 ICE crates. For
HIRAX-256, this system will process an incoming bandwidth of 1.65 Tbps, with
the 1024 element being capable of processing 6.6 Tbps.

###  2.6 GPU Correlator

The HIRAX-256 X-engine is a dense, GPU-based system consisting of 8 nodes,
each processing 128 channels or 50 MHz of bandwidth. These nodes will perform
full, $N^{2},$ correlation of the incoming data streams from all 512 inputs
using a pair of NVIDIA A40 GPUs in each node. The full specifications of each
of these correlator nodes is shown in Table 2.

Parameters | Value
---|---
Motherboard | GIGABYTE G482-Z52
Processor | 2 $\times$ AMD EPYC™ 7452, 32 cores each
RAM | 1TB
GPU | 2 $\times$ NVIDIA A40, PCIe 4.0
F-Engine Network | 4 $\times$ SILICOM PE31640G2QI71-QX4 - 2 $\times$ 40 Gbps
Outgoing Data Network | 2$\times$25 Gbps
Table 2: HIRAX-256 correlator node specifications. The HIRAX-256 X-engine is
comprised of eight these nodes.

This system will produce raw visibility data for each baseline with an
integration time of $\sim$10s. Additional outputs from these nodes will
include formed beams for the FRB and Hi absorber search pipelines as well as
for the pulsar search and monitoring systems. This system represents a very
dense and powerful correlator, processing 1.6 Tbps of data in a single rack,
eight times more bandwidth per node than the CHIME X-engine [41]. This has
largely been enabled by making use of the increased I/O performance of PCIe
4.0 for both the GPU and network card interconnects. The X-engine makes use of
the kotekan[42, 43] software also used by CHIME and CHORD. The correlator will
be scaled up for the 1024-element array, potentially with an even denser
layout depending on hardware developments.

###  2.7 On-site Science Data Processing

Both the visibility data and the beam-formed data from the X-engine will be
sent to the on-site science data processing (SDP) system. This system will
handle the initial calibration and baseline stacking operations for the
cosmological analysis, produce data products for the Hi absorber studies and
perform the real-time transient searches. Additionally, it will manage and
accumulate incoming housekeeping data streams for later use. Reduced data
products will be synchronised to off-site computing centres for further
processing and long-term storage.

##  3 Data Analysis Methodology

###  3.1 Cosmological Survey

HIRAX will operate as a survey instrument to map the large volumes required
for precise measurements of the BAO signal. The 21 cm cosmology science goals
largely drive the system requirements (§4) for the array as a whole and the
constituent telescopes. Here, we begin by outlining the top-level survey
parameters that are required to meet the HIRAX BAO science goals.

To reduce cosmic variance, HIRAX will survey $\sim$15,000 deg2 from
declinations $-60^{\circ}\lesssim\delta\lesssim 0^{\circ}$ (Figure 1) over a
four year period with an observing efficiency of $\sim$50%. The time per
pointing will be chosen to deliver a survey sensitivity uniform in declination
to within 1.5%. To probe the 21 cm power spectrum on BAO scales requires
sensitivity to radial wavenumbers in the range $0.03<k_{\parallel}<0.2$
Mpc${}^{-1},$ which can be achieved with the specified bandwidth and
channelisation, and sensitivity to transverse wavenumbers in the range
$0.05<k_{\perp}<0.16$ Mpc${}^{-1},$ which can be achieved with baseline
separations covering a minimum range of 8 m to 110 m, as can be seen in Figure
4(a). The HIRAX survey sensitivity is shown in Figure 4(b), which demonstrates
that HIRAX is optimised to measure BAO scales where it is competitive with
other planned intensity mapping and galaxy redshift surveys. For more details
on the calculation of these sensitivity estimates, see Refs. 9, 44.

Figure 4:  (a) Angular scales accessible to HIRAX baselines as a function of
frequency. The background colour scale represents the BAO feature in the 21 cm
power spectrum assuming line-of-sight modes, $k_{\parallel},$ corresponding to
correlations over 15 MHz in frequency. The blue curve shows approximately
where non-linear effects become significant. This demonstrates the importance
of HIRAX’s short baselines, and hence compact layout, for measuring the BAO
feature. (b) Comparison of HIRAX’s power spectrum sensitivity as a function of
$k_{\perp}$ with that of SKA-MID surveys, in single dish (SD) and
interferometer (IF) mode, shown alongside shot noise estimates from upcoming
spectroscopic galaxy surveys from DESI, Euclid and Roman. The upper panel
shows the BAO feature in the power spectrum as a function of $k_{\perp}$ at
$z=1.2$. Differences in sensitivity due to different survey areas, and hence
cosmic variance contributions, are not accounted for here.

####  3.1.1 Fisher Forecasts

We evaluate the cosmological constraints that can be achieved with HIRAX using
the Fisher forecast method following the approach of Ref. 9. For reviews on
observational approaches to constraining cosmological parameters with BAO
measurements, see Refs. 45, 46, 47. Our analysis is restricted on small scales
to linear modes, on large transverse scales by the minimum baseline length,
and on large radial scales by filtering of foreground modes below
$k_{\parallel}^{FG}\sim 0.01\text{ Mpc}^{-1}$. In Figure 5(a) we show
forecasts for the measurement of the BAO signal in the power spectrum,
demonstrating that HIRAX should resolve this feature with high significance.
This in turn leads to percent level constraints on the volume-averaged
distance measure, $D_{V}(z)=\left[czD^{2}_{M}(z)/H(z)\right]^{1/3}$, in
several redshift bins as shown in Figure 5(b). Also shown in Figure 5(b) is a
compilation of recent BAO constraints from SDSS galaxy, quasar and
Lyman-$\alpha$ surveys[48, 1, 49, 50, 51, 52, 53, 54, 55].

Figure 5: Forecast constraints on (a) the BAO feature of the matter power
spectrum, (b) distance scale, $D_{V}$ evolution, (c) dark energy equation of
state parameters $w_{0}$ and $w_{a}$, (d) large-scale structure parameters
$\sigma_{8}$ and $\Omega_{M}$, for HIRAX-256 and HIRAX-1024. Parameter
contours shown represent 68% confidence intervals and, for the parameter
constraints, a prior based on Planck[56] results has been added. We note that
the change in degeneracy direction for the $\Omega_{M}$ and $\sigma_{8}$
contours between HIRAX-256 and HIRAX-1024 is due to the different relative
contributions of the Planck prior to the combined constraints.

We explore cosmological parameter constraints for three different cosmological
models, $\Lambda$CDM, $w$CDM and $w_{0}w_{a}$CDM. Here $w$CDM allows for
variation in a fixed dark energy equation-of-state parameter, $w$, while
$w_{0}w_{a}$CDM, fits for an evolving equation-of-state
$w(a)=w_{0}+(1-a)w_{a}$, as in Ref. 45. Marginalized constraints on a subset
of the full parameter set are shown in Table 3 for the HIRAX 256-element and
1024-element arrays including priors based on constraints from the Planck
Satellite[56]. These are compared to current state-of-the-art constraints from
the eBOSS cosmology analysis[2], which are combined with constraints from
Planck, Pantheon SNe Ia[57] and DES Y1[58].

In Figures 5(c) and 5(d) we show marginalized parameter contours for the dark
energy equation-of-state parameters as well as large-scale structure
parameters $\Omega_{M}$ and $\sigma_{8},$ respectively, for both the HIRAX
256-element and 1024-element arrays with Planck priors. The computed dark
energy figures of merit (FoM[45]), corresponding to the inverse of the area
enclosed by the 68% confidence contours in the marginalized $w_{0}-w_{a}$
constraints, are 60 for HIRAX-256 and 360 for HIRAX-1024. This is competitive
with other planned dark energy experiments[9]. We note that the Planck prior
dominates the $\Omega_{M}$ constraint but that the HIRAX 1024-element array,
in particular, can further constrain $\Omega_{M}$ and $\sigma_{8}$.

HIRAX-256 \+ Planck | $\sigma_{8}$ | $\Omega_{\Lambda}$ | $w_{0}$ | $w_{a}$
---|---|---|---|---
$\Lambda$CDM | 0.00441 | 0.0039 | - | -
$w$CDM | 0.0047 | 0.0042 | 0.0739 | -
$w_{0}w_{a}$CDM | 0.0053 | 0.0043 | 0.1223 | 0.4332
HIRAX-1024 \+ Planck |  |  |  |
$\Lambda$CDM | 0.0027 | 0.0034 | - | -
$w$CDM | 0.0028 | 0.0036 | 0.0316 | -
$w_{0}w_{a}$CDM | 0.0038 | 0.0037 | 0.0506 | 0.1965
eBOSS \+ Planck \+ SNe Ia \+ Lens. |  |  |  |
$\Lambda$CDM | 0.0056 | 0.0047 | - | -
$w$CDM | 0.0092 | 0.0066 | 0.027 | -
$w_{0}w_{a}$CDM | 0.0093 | 0.0069 | 0.073 | 0.5200
Table 3:  Marginalized 68% cosmological parameter forecast constraints for the
HIRAX experiment compared to current eBOSS[2] results for $\Lambda$CDM, $w$CDM
and $w_{0}w_{a}$CDM cosmologies.

####  3.1.2 Cosmological Analysis Pipeline Status

We can obtain more realistic forecasts for HIRAX 21 cm power spectrum
constraints using detailed telescope simulations. We adopt the $m$-mode
approach[59, 60, 61], which is appropriate for a drift-scan instrument such as
HIRAX. Decomposing daily scans into $m$-modes along the sidereal time
direction allows us to decouple these modes and analyse them independently,
which makes the analysis of large arrays computationally tractable. The
simulated visibility, ${\bm{v}}={\mathbf{B}}\,\bm{a}+{\bm{n}},$ can be
written, for all baselines and frequencies, as a sum of the sky signal,
$\bm{a},$ processed by the instrument response or so-called beam transfer
matrix, $\mathbf{B},$ and instrument noise, ${\bm{n}}$. The beam transfer
matrix encodes information about the telescope beam and pointing, the baseline
layout, and the instrument noise. Here, we consider a Gaussian primary beam
but directivities estimated from electromagnetic simulations of the HIRAX
antenna[36] can also be used in the simulation pipeline. The input sky model
comprises simulated 21cm fluctuations with Gaussian statistics and simulated
Galactic and extragalactic foregrounds. Currently, these are generated using
Gaussian random field realisations of an input 21 cm power spectrum as well as
a Galactic foreground model based on that of Ref. 62 with the large-scale
spatial distribution of the signal constrained to be similar to that of the
Haslam 408 MHz map[63]. Future efforts include making use of a more
sophisticated signal model based on an empirical Hi halo model applied to
$n$-body simulations. Given an instrument model and survey specification, the
beam transfer matrix can be computed and is used to generate synthetic
visibility data. In the results shown here, we use a compact grid of
7$\times$7 dishes (covering the most cosmologically relevant angular scales)
and assume a survey conducted over declinations from $-40^{\circ}$ to
$-20^{\circ}$ through 7 repointings of the array. The noise is scaled such the
the redundancy of the baselines of this 7$\times$7 sub-array are equivalent to
that of the 1024 element array with a survey length of four months of
integration time per-pointing.

The process of estimating a power spectrum from simulated data is adapted
closely from Ref. 60 but we briefly outline it here. In the results shown
here, the simulated visibilities are assumed to have negligible calibration
residuals but the inclusion of a realistic calibration pipeline and handling
for data excised due to, e.g., radio-frequency interference, is being
developed. The visibility dataset is then compressed by filtering out modes
that the HIRAX baselines are insensitive to using singular value
decomposition. The next step involves deprojecting galactic and extra-galactic
foregrounds, which is the main challenge for a detection of 21cm intensity
fluctuations. Foreground removal relies on smooth spectral behaviour of the
foregrounds and involves high-pass spectral filtering of the data to retain
primarily the high-frequency spectral 21cm modes. Here, we apply a
Karhunen–Loève filter based on an ideal instrument with perfect statistical
knowledge of the foregrounds. The power spectrum, binned in $k_{\parallel}$
and $k_{\perp},$ is then estimated from the filtered data.

The plots in Figure 6 show examples of the estimated power spectra constraints
using the $m$-mode approach for a Gaussian beam in four different uniform
frequency bands. In this case, the mixing matrix for an unwindowed estimator
is used. See Ref. 61 for a detailed discussion on different quadratic power
spectrum window functions. At the relevant scales of interest as mentioned
above and depending on frequency channel considered, we expect to recover the
binned power spectrum with relative error from $5\%$ to $8\%$ in the
approximate range of $0.05<k<0.10~{}h~{}{\rm Mpc}^{-1}$, noting that the set
of baselines considered in these simulations also affects these limits. A
minimum-variance power spectra estimator reduces the uncertainties by about a
factor of two, at the price of a more complicated correlation structure
between the bins. In future work, estimated cosmological constraints will be
derived from these power spectrum estimates, and contrasted with the Fisher
matrix results in Section 3.1.1.

Figure 6: Estimated relative errors in recovered $P(k_{\parallel},k_{\perp})$
band-powers (from diagonal elements of the derived covariance matrices) over
100 MHz sub-bands spanning the HIRAX bandwidth using the $m$-mode pipeline. A
foreground filter has been applied here assuming ideal knowledge of the
instrument.

####  3.1.3 Systematics Analysis

We have additionally extended the above analysis to examine the effect of
unmodeled systematics on the extraction on accurate power spectra. This
involves injecting systematic perturbations to the simulated visibilities by
assuming distributions of systematic parameters that affect the primary beam,
pointing or array layout of the simulated telescope. For the primary beams,
electromagnetic simulations of the HIRAX dish-feed systems have been
performed[36], including parameter sweeps of physical tolerances of the system
under investigation such as feed positioning relative to the dish. Linear
models for the perturbations arising from small changes in these tolerances on
the beam directivities are then constructed and propagated to the visibilities
which are run through the power spectrum estimation pipeline. For layout-based
effects such as errors in dish positioning, a similar approach is used where
the linear order perturbation on the visibilities due to these uncertainties
are propagated through the pipeline. In both cases care is taken to keep track
of systematic correlations between baselines due to sharing systematics from
the same dishes. This analysis was used to inform aspects of the system level
requirements outlined below, in Section 4.

###  3.2 Beamforming and Real-time Analysis

HIRAX will sum the channelized baseband data from the array elements to form
beams on the sky for use in the transient/FRB, pulsar, and Hi absorber
searches. The HIRAX beamforming will be fully described in future work, but we
provide a brief overview here.

For a calibrated, planar array, the summing reduces to a Fourier transform,
where each location on the sky corresponds to a frequency-dependent $k$. For
regularly spaced antennas, Fast Fourier transforms (FFTs) can be used at
single frequencies. However, FFTs naturally pick out integer values of $k$ and
therefore require additional steps to align the beams across frequencies.
Alternatively, one can directly sum the antenna data in a slow Fourier
transform. For a close-packed array, there are roughly as many independent
beams inside the primary beam as there are antennas. In the simplest
implementation, each beam is the sum over $n$ antennas, and with $n$ beams,
the total computational cost becomes an order $n^{2}$ matrix multiplication.
The visibilities already cost $n^{2}$ to generate, and so the brute-force
beamforming at worst increases the computational burden on the correlator by a
constant, order-unity factor. Modern GPUs are sufficiently performant at low
bit-depth matrix multiplications that the brute force beamforming is
attractive for a 256-element array. For 4-bit operations, the NVIDIA RTX 3090
as well as the NVIDIA A40s in use in the HIRAX-256 X-engine are capable of
over 500 TOPS. On paper, a single GPU has enough processing power to form 256
formed beams from 256 HIRAX antennas, and preliminary GPU kernels are within a
factor of two of the theoretical limit.

With the decision to use a brute-force beamformer, we can now describe how the
HIRAX beamforming will work. The beam-crossing time is relatively short for
HIRAX ($\sim$1 minute) and so we will use tracking beams that follow sources
as they transit the primary beam. The RMS per-antenna errors introduced by
using 4-bit arithmetic are $\sim$3∘ with an RMS amplitude fractional error of
$0.035$. Since the data from the F-engine arrive as 4-bit integers, and the
errors introduced by 4-bit beamforming are small, we plan to use 4-bit
arithmetic to do the beamforming. The beamforming phases will be updated
approximately every second. We plan to beamform the intensity data only, using
both $XX$ and $YY$ polarization, and do not plan to form real-time cross-polar
beams. Since many scientific uses of the formed beams require higher frequency
resolution than that provided by the F-engine, the formed beams will be
upchannelized (see, e.g., Refs. 64, 65) before being squared and summed to
produce high frequency-resolution power beams. These upchannelized beams can
then either be integrated in the X-engine for the 21cm absorber search, or
passed to the FRB back-end for the FRB search. We additionally will send a
small number ($\sim$10) of non-squared beams to the pulsar back-end for the
pulsar search. This gives the pulsar back-end the option of carrying out
coherent de-dispersion for millisecond pulsar searches. The utility of
HIRAX-256 for pulsar studies is still under study but we expand upon the
planned FRB survey below.

####  3.2.1 Fast Radio Burst Survey

The HIRAX fast radio burst (FRB) survey will use the search pipeline developed
for CHIME[64]. Briefly, the formed, upchannelized beams will be sent to a
separate search engine, where they will be incoherently searched for transient
events. The search will be carried out by a computationally efficient tree-
dedispersion algorithm. Detected FRBs will be flagged, and baseband data will
be written to disk for off-line analysis. The instantaneous detection
threshold will be around 10 $\sigma$, though the exact threshold will need to
be tuned on-site and will depend on the false positive rate from local RFI. At
256 dishes, HIRAX has similar collecting area and sensitivity to CHIME, and so
we expect the redshift and DM distributions will be similar to the CHIME FRB
catalog[19]. With a smaller field of view, we expect an event rate roughly
half of CHIME’s, or about 1 FRB per day.

We will build a minimum of two outrigger stations in order to localize FRBs
detected by HIRAX to sub-arcsecond accuracy. The central goal is to localize
the FRBs to within a host galaxy for the large majority of HIRAX FRBs.
Additionally, with $\sim$1000 km baselines, we hope to localize FRBs to tens
of milliarcseconds (mas) for studies of FRB environments within their host
galaxies. Bandwidth constraints prevent us from continuously streaming
baseband data, so the outriggers will store 1-2 minutes of baseband data in
memory (45 GB/s/dish required). When the core detects an FRB, it will send a
trigger to the outriggers that will then write their baseband data to disk,
for off-line correlation. Post-processing of the core data will typically
result in a higher SNR than the initial detections. Reasons include the
ability to reform a beam directly on the FRB, coherently de-disperse the data,
and expend more effort on RFI mitigation. We expect 15 $\sigma$ to be typical
for the post-processed SNR. We target 5 $\sigma$ detections between the core
and each outrigger station, which results in outrigger station sizes of 16-24
dishes. At a fixed false-positive rate, there is an increase required in the
SNR due to the possibly large phase space over which one is searching for
possible FRBs. For 2-dimensional searches using narrow-band, very long
baseline interferometry data, this factor can be large. However, since we are
targeting a detection by each station when correlated against the core, the
result is a single timing offset from broad-band data, so calculations show
the phase-space effect is small for HIRAX. Further, the bulk of the expected
false positives arise from small enough timing errors that we would still
localize the FRB to the correct galaxy.

Localizations will be fundamentally tied to astronomical calibrators, and we
plan to be able to calibrate using observations up to $\sim$ 1 hour after the
FRBs occur. We have demonstrated moderately-priced off-the-shelf clock systems
that are capable of holding the sub-ns timing accuracy we need on multi-hour
timescales[66]. At HIRAX frequencies, ionospheric corrections are important,
and we plan to use a combination of astrometric calibrators, GNSS satellites,
and real-time publicly available ionospheric maps. The worst-case scenario of
using publicly available ionosphere maps/models corresponds to a typical
uncertainty of a few tenths of a TEC unit,333The total electron content or TEC
of the ionosphere is reported in units of $10^{16}e^{-}/m^{2}$. 1 TEC unit
corresponds to a DM of $3.3\times 10^{-7}$. which translates to roughly 1
nanosecond. For outrigger separations of $\sim 1000$ km, this corresponds to a
60 mas error, and so we do not expect the ionosphere to limit our ability to
assign FRBs to host galaxies.

##  4 Instrument Requirements

With the science requirements and analysis methods described in §3, we can now
define the following high-level system requirements for the HIRAX array. The
system requirements are derived by propagating the higher level science
requirements, starting from the top-level requirement on the dark energy FoM,
to lower level system requirements based on the simulations methodology
described in §3. The survey and array layout system requirements were
described in §3.1, and here we focus on the requirements for the ensemble of
telescopes comprising the array. Since there are typically multiple system
requirements that are derived from any given individual science requirement,
we consider tradeoffs in tolerances for the system requirements to allocate
the error budget. Across the HIRAX array, we find that the gains must be
stable to 1% over 1-minute integrations across the full bandwidth, relative
bandwidths must be stable to 0.75% over the beam crossing time, and the
tolerance on the primary beam FWHM must be 0.05% across the full bandwidth. In
addition, the dishes should have an aperture efficiency of 0.7, the antenna
cross-talk should contribute an excess noise level of no more than 10 K on the
two shortest dish separations, and the antenna spill should have a maximum
noise level of 5 K at 400 MHz, increasing to 10 K at 800 MHz. Finally,
telescope pointing and positioning must be repeatable across the array: we
require that the dish boresight vectors must be parallel within $5^{\prime}$
RMS, the foci of all dishes must lie in a plane with $<5$ mm RMS deviation
orthogonal to the plane, and the foci must form a regularly spaced grid with
separation distances precise to $<2.5$ mm RMS. We note that the analyses used
to derive these constraints were based on science targets for the 1024-element
array as the requirements will be fixed across the expected array deployments.

The system requirements for the array as a whole form the foundation for
defining more specific requirements for the HIRAX telescope mechanical
structure, comprising the dish, mount, and receiver support structure. In
total, we have defined over 60 specifications that are discussed in detail in
the HIRAX telescope mechanical assembly requirements document, which is
available online.444https://hirax.ukzn.ac.za/wp-
content/uploads/2021/08/HIRAX_REQ001_002_V1_Baselined-signed.pdf Broadly
speaking, tolerances related to redundancy fall into two general categories:
pointing or positioning error, and beam error. Pointing and positioning errors
are analyzed with a simple geometric model of the telescope to compute the
error stackup. Starting with the requirements for boresight vector parallelism
and foci positioning within a plane, the error budget is allocated to various
telescope sub-components in accordance with the mechanical difficulty of
meeting each target. The telescope parameters that are governed by this
geometric error stackup include the dish vertex position relative to the
elevation axis, orthogonality of the dish boresight vector and elevation axis,
position and alignment angle of the elevation axis within the array, and the
elevation pointing angle. Errors in the beam shape are assessed with
electromagnetic simulations of the dish, receiver, and receiver support
structure. We use CST Studio Suite555https://www.3ds.com/products-
services/simulia/products/cst-studio-suite/ to simulate the impact of the
receiver position with respect to the dish focus, receiver orientation angle
relative to the boresight vector, and deviations in the dish surface with
respect to the average best-fit paraboloid. Table 4 summarizes the target
precision values for the most important telescope mechanical parameters.

Telescope mechanical parameter | Target precision (RMS)
---|---
Receiver position relative to focus | 0.5 mm
Receiver orientation relative to boresight vector |  $2.5^{\prime}$ polar and azimuthal
Dish surface deviations | 1 mm
Dish vertex position relative to elevation axis | 1 mm
Orthogonality of boresight vector and elevation axis | $1^{\prime}$
Elevation axis position within the array | 0.5 mm in array plane
| 1 mm out of array plane
Elevation axis alignment within the array | $1^{\prime}$
Elevation pointing angle | $1^{\prime}$
Table 4: Target precision values for HIRAX telescope mechanical structure

##  5 Current Status and Conclusions

The design of most aspects of the 256-element HIRAX deployment have been
finalised and site development is expected to commence in 2022. Currently,
multiple hardware testing activities are underway, with instrumented prototype
$f/0.38$ and $f/0.25$ dishes deployed at HartRAO for RF front-end
characterisation, and parallel efforts in progress at Dominion Radio
Astrophysical Observatory and the Green Bank Observatory. Beam
characterisation analyses using drone-based and holographic measurements are
being carried out. The design of the F- and X-engine systems are complete and
the 256-element X-engine is assembled, with one node deployed at the Bleien
Observatory for trial operation using on-sky data. A significant milestone has
been reached in the finalisation of the specification for the telescope
mechanical system, with the expectation that initial deployed dishes making
use of the final design should be assembled for testing in 2022.

HIRAX-256 will be a powerful instrument for 21 cm cosmology, radio transient,
and Hi absorber science. While much emphasis has been placed on the control of
systematics from a priori studies, we expect the analysis of the initial on-
sky data to be extremely informative for progressing the analysis techniques
in use as well as the design of future 21 cm experiments.

### Acknowledgments

This work is based on the research supported in part by the National Research
Foundation of South Africa (Grant Numbers 98772, 128919, 107797, 120809,
120700) and in part by grant numbers 200021_192243, 200020_182231,
IZLSZ2_170907, 20FL21_186180 and 20FL20_201479 from the Swiss National Science
Foundation. AR, DC, TV, CB, CF, MK, VN, AVS, ET, and JPK acknowledge funding
by the Swiss National Science Foundation. KM acknowledges support from the
National Research Foundation of South Africa. AW and SB acknowledge support
from the South African Research Chairs Initiative of the Department of Science
and Technology and National Research Foundation and from a VC 2020 Future
Leaders award. RM, DK, LR, DdV and CP are supported by the South African Radio
Astronomy Observatory (SARAO) and the National Research Foundation (Grant No.
75415 and 75322) and RM is also supported by the UK STFC Consolidated Grant
ST/S000550/1. WN and DC acknowledge the financial assistance of the South
African Radio Astronomy Observatory (SARAO) towards this research
(www.sarao.ac.za). LN, MH, AP, WT acknowledge support from the National
Science Foundation under Grant No. 1751763. EK acknowledges support by a NASA
Space Technology Research Fellowship. TCC and PB acknowledge support from the
NASA Jet Propulsion Laboratory Strategic R&TD awards. Part of this work was
done at Jet Propulsion Laboratory, California Institute of Technology, under a
contract with the National Aeronautics and Space Administration. The research
of OS is supported by the South African Research Chairs Initiative of the
Department of Science and Technology and National Research Foundation. HCC
acknowledges the support of the Natural Sciences and Engineering Research
Council of Canada (NSERC; RGPIN-2019-04506). ADH acknowledges support from the
Sutton Family Chair in Science, Christianity and Cultures and from the Faculty
of Arts and Science, University of Toronto. AZ was supported by a University
of Toronto Excellence Award. MGS, SP and JT acknowledge support from the South
African Radio Astronomy Observatory (SARAO) and National Research Foundation
(Grant No. 84156). Computations were performed on Hippo at the University of
KwaZulu-Natal, on the Baobab cluster at the University of Geneva and on the
Niagara supercomputer at the SciNet HPC Consortium. SciNet is funded by: the
Canada Foundation for Innovation; the Government of Ontario; Ontario Research
Fund - Research Excellence; and the University of Toronto[67, 68]. This work
made use of the numpy[69], scipy[70], matplotlib[71], and astropy[72, 73]
software packages.

## References

  * [1] S. Alam, M. Ata, S. Bailey, et al., “The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample,” MNRAS 470, 2617–2652 (2017).
  * [2] S. Alam, M. Aubert, S. Avila, et al., “Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory,” Phys. Rev. D 103, 083533 (2021).
  * [3] A. Slosar, V. Iršič, D. Kirkby, et al., “Measurement of baryon acoustic oscillations in the Lyman-$\alpha$ forest fluctuations in BOSS data release 9,” J. Cosmology Astropart. Phys 2013, 026 (2013).
  * [4] DES Collaboration, T. M. C. Abbott, M. Aguena, et al., “Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing,” arXiv e-prints , arXiv:2105.13549 (2021).
  * [5] L. Fu, M. Kilbinger, T. Erben, et al., “CFHTLenS: cosmological constraints from a combination of cosmic shear two-point and three-point correlations,” MNRAS 441, 2725–2743 (2014).
  * [6] C. Heymans, T. Tröster, M. Asgari, et al., “KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints,” A&A 646, A140 (2021).
  * [7] C. Hikage, M. Oguri, T. Hamana, et al., “Cosmology from cosmic shear power spectra with Subaru Hyper Suprime-Cam first-year data,” PASJ 71, 43 (2019).
  * [8] T.-C. Chang, U.-L. Pen, J. B. Peterson, et al., “Baryon Acoustic Oscillation Intensity Mapping of Dark Energy,” Phys. Rev. Lett. 100, 091303 (2008).
  * [9] P. Bull, P. G. Ferreira, P. Patel, et al., “Late-time Cosmology with 21 cm Intensity Mapping Experiments,” The Astrophysical Journal 803, 21 (2015).
  * [10] E. D. Kovetz, M. P. Viero, A. Lidz, et al., “Line-Intensity Mapping: 2017 Status Report,” arXiv e-prints , arXiv:1709.09066 (2017).
  * [11] K. Bandura, G. E. Addison, M. Amiri, et al., “Canadian Hydrogen Intensity Mapping Experiment (CHIME) pathfinder,” in Ground-based and Airborne Telescopes V, L. M. Stepp, R. Gilmozzi, and H. J. Hall, Eds., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 9145, 914522 (2014).
  * [12] K. Vanderlinde, A. Liu, B. Gaensler, et al., “The Canadian Hydrogen Observatory and Radio-transient Detector (CHORD),” in Canadian Long Range Plan for Astronomy and Astrophysics White Papers, 2020, 28 (2019).
  * [13] D. R. DeBoer, A. R. Parsons, J. E. Aguirre, et al., “Hydrogen Epoch of Reionization Array (HERA),” Publications of the Astronomical Society of the Pacific 129, 045001 (2017).
  * [14] A. Slosar, Z. Ahmed, D. Alonso, et al., “Packed Ultra-wideband Mapping Array (PUMA): A Radio Telescope for Cosmology and Transients,” in Bulletin of the American Astronomical Society, 51, 53 (2019).
  * [15] X. Chen, “The Tianlai Project: a 21CM Cosmology Experiment,” in International Journal of Modern Physics Conference Series, International Journal of Modern Physics Conference Series 12, 256–263 (2012).
  * [16] CHIME/FRB Collaboration, M. Amiri, K. Bandura, et al., “Observations of fast radio bursts at frequencies down to 400 megahertz,” Nature 566, 230–234 (2019).
  * [17] CHIME/FRB Collaboration, M. Amiri, K. Bandura, et al., “A second source of repeating fast radio bursts,” Nature 566, 235–238 (2019).
  * [18] CHIME/FRB Collaboration, B. C. Andersen, K. Bandura, et al., “CHIME/FRB Discovery of Eight New Repeating Fast Radio Burst Sources,” ApJ 885, L24 (2019).
  * [19] The CHIME/FRB Collaboration, :, M. Amiri, et al., “The First CHIME/FRB Fast Radio Burst Catalog,” arXiv e-prints , arXiv:2106.04352 (2021).
  * [20] C. Ng, A. Pandhi, A. Naidu, et al., “Faraday rotation measures of Northern hemisphere pulsars using CHIME/Pulsar,” MNRAS 496, 2836–2848 (2020).
  * [21] DESI Collaboration, A. Aghamousa, J. Aguilar, et al., “The DESI Experiment Part I: Science,Targeting, and Survey Design,” arXiv e-prints , arXiv:1611.00036 (2016).
  * [22] S. W. Henderson, R. Allison, J. Austermann, et al., “Advanced ACTPol Cryogenic Detector Arrays and Readout,” Journal of Low Temperature Physics 184, 772–779 (2016).
  * [23] LSST Science Collaboration, P. A. Abell, J. Allison, et al., “LSST Science Book, Version 2.0,” arXiv e-prints , arXiv:0912.0201 (2009).
  * [24] R. Braun, T. Bourke, J. A. Green, et al., “Advancing Astrophysics with the Square Kilometre Array,” in Advancing Astrophysics with the Square Kilometre Array (AASKA14), 174 (2015).
  * [25] L. B. Newburgh, K. Bandura, M. A. Bucher, et al., “HIRAX: a probe of dark energy and radio transients,” in Ground-based and Airborne Telescopes VI, H. J. Hall, R. Gilmozzi, and H. K. Marshall, Eds., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 9906, 99065X (2016).
  * [26] M. R. Blanton, M. A. Bershady, B. Abolfathi, et al., “Sloan Digital Sky Survey IV: Mapping the Milky Way, Nearby Galaxies, and the Distant Universe,” AJ 154, 28 (2017).
  * [27] S. Miyazaki, Y. Komiyama, H. Nakaya, et al., “Hyper Suprime-Cam,” in Ground-based and Airborne Instrumentation for Astronomy IV, I. S. McLean, S. K. Ramsay, and H. Takami, Eds., 8446, 327 – 335, International Society for Optics and Photonics, SPIE (2012).
  * [28] L. Amendola, S. Appleby, A. Avgoustidis, et al., “Cosmology and fundamental physics with the Euclid satellite,” Living Reviews in Relativity 21, 2 (2018).
  * [29] R. Akeson, L. Armus, E. Bachelet, et al., “The Wide Field Infrared Survey Telescope: 100 Hubbles for the 2020s,” arXiv e-prints , arXiv:1902.05569 (2019).
  * [30] B. A. Benson, P. A. R. Ade, Z. Ahmed, et al., “SPT-3G: a next-generation cosmic microwave background polarization experiment on the South Pole telescope,” in Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy VII, W. S. Holland and J. Zmuidzinas, Eds., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 9153, 91531P (2014).
  * [31] P. Ade, J. Aguirre, Z. Ahmed, et al., “The Simons Observatory: science goals and forecasts,” J. Cosmology Astropart. Phys 2019, 056 (2019).
  * [32] M. G. Santos, M. Cluver, M. Hilton, et al., “MeerKLASS: MeerKAT Large Area Synoptic Survey,” arXiv e-prints , arXiv:1709.06099 (2017).
  * [33] N. Gupta, R. Srianand, W. Baan, et al., “The MeerKAT Absorption Line Survey (MALS),” in MeerKAT Science: On the Pathway to the SKA, 14 (2016).
  * [34] J. S. Dillon and A. R. Parsons, “Redundant Array Configurations for 21 cm Cosmology,” The Astrophysical Journal 826, 181 (2016).
  * [35] K. Bandura, A. N. Bender, J. F. Cliche, et al., “ICE: A Scalable, Low-Cost FPGA-Based Telescope Signal Processing and Networking System,” Journal of Astronomical Instrumentation 5, 1641005 (2016).
  * [36] B. R. B. Saliwanchik, A. Ewall-Wice, D. Crichton, et al., “Mechanical and optical design of the HIRAX radio telescope,” in Ground-based and Airborne Telescopes VIII, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 11445, 114455O (2021).
  * [37] M. Deng and D. Campbell-Wilson, “The cloverleaf antenna: A compact wide-bandwidth dual-polarization feed for CHIME,” arXiv e-prints , arXiv:1708.08521 (2017).
  * [38] E. R. Kuhn, B. R. B. Saliwanchik, M. Harris, et al., “Design and implementation of a noise temperature measurement system for the Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX),” arXiv e-prints , arXiv:2101.06337 (2021).
  * [39] J. Mena, K. Bandura, J. F. Cliche, et al., “A Radio-Frequency-over-Fiber link for large-array radio astronomy applications,” Journal of Instrumentation 8, T10003 (2013).
  * [40] K. Bandura, J. F. Cliche, M. A. Dobbs, et al., “ICE-Based Custom Full-Mesh Network for the CHIME High Bandwidth Radio Astronomy Correlator,” Journal of Astronomical Instrumentation 5, 1641004 (2016).
  * [41] N. Denman, M. Amiri, K. Bandura, et al., “A GPU-based Correlator X-engine Implemented on the CHIME Pathfinder,” arXiv e-prints , arXiv:1503.06202 (2015).
  * [42] A. Recnik, K. Bandura, N. Denman, et al., “An Efficient Real-time Data Pipeline for the CHIME Pathfinder Radio Telescope X-Engine,” arXiv e-prints , arXiv:1503.06189 (2015).
  * [43] P. Klages, K. Bandura, N. Denman, et al., “GPU Kernels for High-Speed 4-Bit Astrophysical Data Processing,” arXiv e-prints , arXiv:1503.06203 (2015).
  * [44] D. Alonso, P. G. Ferreira, M. J. Jarvis, et al., “Calibrating photometric redshifts with intensity mapping observations,” Phys. Rev. D 96, 043515 (2017).
  * [45] A. Albrecht, G. Bernstein, R. Cahn, et al., “Report of the Dark Energy Task Force,” arXiv e-prints , astro–ph/0609591 (2006).
  * [46] D. H. Weinberg, M. J. Mortonson, D. J. Eisenstein, et al., “Observational probes of cosmic acceleration,” Phys. Rep. 530, 87–255 (2013).
  * [47] É. Aubourg, S. Bailey, J. E. Bautista, et al., “Cosmological implications of baryon acoustic oscillation measurements,” Phys. Rev. D 92, 123516 (2015).
  * [48] A. J. Ross, L. Samushia, C. Howlett, et al., “The clustering of the SDSS DR7 main Galaxy sample - I. A 4 per cent distance measure at z = 0.15,” MNRAS 449, 835–847 (2015).
  * [49] J. E. Bautista, R. Paviot, M. Vargas Magaña, et al., “The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic correlation function between redshifts 0.6 and 1,” MNRAS 500, 736–762 (2021).
  * [50] H. Gil-Marín, J. E. Bautista, R. Paviot, et al., “The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic power spectrum between redshifts 0.6 and 1.0,” MNRAS 498, 2492–2531 (2020).
  * [51] A. de Mattia, V. Ruhlmann-Kleider, A. Raichoor, et al., “The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the emission line galaxy sample from the anisotropic power spectrum between redshift 0.6 and 1.1,” MNRAS 501, 5616–5645 (2021).
  * [52] A. Raichoor, A. de Mattia, A. J. Ross, et al., “The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: large-scale structure catalogues and measurement of the isotropic BAO between redshift 0.6 and 1.1 for the Emission Line Galaxy Sample,” MNRAS 500, 3254–3274 (2021).
  * [53] J. Hou, A. G. Sánchez, A. J. Ross, et al., “The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the quasar sample in configuration space between redshift 0.8 and 2.2,” MNRAS 500, 1201–1221 (2021).
  * [54] R. Neveux, E. Burtin, A. de Mattia, et al., “The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from the anisotropic power spectrum of the quasar sample between redshift 0.8 and 2.2,” MNRAS 499, 210–229 (2020).
  * [55] H. du Mas des Bourboux, J. Rich, A. Font-Ribera, et al., “The Completed SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations with Ly$\alpha$ Forests,” The Astrophysical Journal 901, 153 (2020).
  * [56] Planck Collaboration, N. Aghanim, Y. Akrami, et al., “Planck 2018 results. VI. Cosmological parameters,” A&A 641, A6 (2020).
  * [57] D. M. Scolnic, D. O. Jones, A. Rest, et al., “The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample,” The Astrophysical Journal 859, 101 (2018).
  * [58] T. M. C. Abbott, F. B. Abdalla, A. Alarcon, et al., “Dark Energy Survey year 1 results: Cosmological constraints from galaxy clustering and weak lensing,” Phys. Rev. D 98, 043526 (2018).
  * [59] J. R. Shaw, K. Sigurdson, U.-L. Pen, et al., “All-sky Interferometry with Spherical Harmonic Transit Telescopes,” The Astrophysical Journal 781, 57 (2014).
  * [60] J. R. Shaw, K. Sigurdson, M. Sitwell, et al., “Coaxing cosmic 21 cm fluctuations from the polarized sky using m-mode analysis,” Phys. Rev. D 91(8), 083514 (2015).
  * [61] A. Liu and J. R. Shaw, “Data Analysis for Precision 21 cm Cosmology,” Publications of the Astronomical Society of the Pacific 132, 062001 (2020).
  * [62] M. G. Santos, A. Cooray, and L. Knox, “Multifrequency Analysis of 21 Centimeter Fluctuations from the Era of Reionization,” The Astrophysical Journal 625, 575–587 (2005).
  * [63] C. G. T. Haslam, C. J. Salter, H. Stoffel, et al., “A 408 MHz all-sky continuum survey. II. The atlas of contour maps.,” A&AS 47, 1–143 (1982).
  * [64] CHIME/FRB Collaboration, M. Amiri, K. Bandura, et al., “The CHIME Fast Radio Burst Project: System Overview,” The Astrophysical Journal 863, 48 (2018).
  * [65] M. Amiri, K. M. Bandura, P. J. Boyle, et al., “The CHIME Pulsar Project: System Overview,” ApJS 255, 5 (2021).
  * [66] J. Mena Parra et al., “A clock stabilization system for CHIME/FRB Outriggers,” (in preparation).
  * [67] C. Loken, D. Gruner, L. Groer, et al., “SciNet: Lessons learned from building a power-efficient top-20 system and data centre,” Journal of Physics: Conference Series 256, 012026 (2010).
  * [68] M. Ponce, R. van Zon, S. Northrup, et al., “Deploying a top-100 supercomputer for large parallel workloads: The niagara supercomputer,” in Proceedings of the Practice and Experience in Advanced Research Computing on Rise of the Machines (Learning), PEARC ’19, Association for Computing Machinery, (New York, NY, USA) (2019).
  * [69] C. R. Harris, K. J. Millman, S. J. van der Walt, et al., “Array programming with NumPy,” Nature 585, 357–362 (2020).
  * [70] P. Virtanen, R. Gommers, T. E. Oliphant, et al., “SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python,” Nature Methods 17, 261–272 (2020).
  * [71] J. D. Hunter, “Matplotlib: A 2d graphics environment,” Computing in Science Engineering 9(3), 90–95 (2007).
  * [72] Astropy Collaboration, T. P. Robitaille, E. J. Tollerud, et al., “Astropy: A community Python package for astronomy,” A&A 558, A33 (2013).
  * [73] Astropy Collaboration, A. M. Price-Whelan, B. M. Sipőcz, et al., “The Astropy Project: Building an Open-science Project and Status of the v2.0 Core Package,” AJ 156, 123 (2018).

###### List of Figures

  1. 1 HIRAX will observe $\sim$15,000 deg2 of the southern sky, shown by the region enclosed by the white dashed lines. The survey footprint overlaps many existing and forthcoming surveys such as those of CHIME[11], DES[4], KiDS[6], DESI[21] and Advanced ACTPol[22]. The entirety of the sky area shown is contained within the Rubin/LSST[23] survey footprint and is accessible to the SKA[24] and its precursors. The background colorscale shows Galactic emission from the Planck 353 GHz map.
  2. 2 Artist’s impression of the HIRAX array in the Karoo desert.
  3. 3 HIRAX signal chain schematic. In each dish, an active dual-polarization feed receives and amplifies incoming radio signals. The signals are filtered, further amplified, and converted to optical light with an RFoF transmitter at the dish focus. Optical fibre transports the signals to an RFoF receiver, which converts the signals back into RF and applies additional amplification and filtering before digitization. An ICE-based system performs the digitization, channelizing, and corner turn. The data are then passed to the GPU X-engine for correlation.
  4. 4  (a) Angular scales accessible to HIRAX baselines as a function of frequency. The background colour scale represents the BAO feature in the 21 cm power spectrum assuming line-of-sight modes, $k_{\parallel},$ corresponding to correlations over 15 MHz in frequency. The blue curve shows approximately where non-linear effects become significant. This demonstrates the importance of HIRAX’s short baselines, and hence compact layout, for measuring the BAO feature. (b) Comparison of HIRAX’s power spectrum sensitivity as a function of $k_{\perp}$ with that of SKA-MID surveys, in single dish (SD) and interferometer (IF) mode, shown alongside shot noise estimates from upcoming spectroscopic galaxy surveys from DESI, Euclid and Roman. The upper panel shows the BAO feature in the power spectrum as a function of $k_{\perp}$ at $z=1.2$. Differences in sensitivity due to different survey areas, and hence cosmic variance contributions, are not accounted for here.
  5. 5 Forecast constraints on (a) the BAO feature of the matter power spectrum, (b) distance scale, $D_{V}$ evolution, (c) dark energy equation of state parameters $w_{0}$ and $w_{a}$, (d) large-scale structure parameters $\sigma_{8}$ and $\Omega_{M}$, for HIRAX-256 and HIRAX-1024. Parameter contours shown represent 68% confidence intervals and, for the parameter constraints, a prior based on Planck[56] results has been added. We note that the change in degeneracy direction for the $\Omega_{M}$ and $\sigma_{8}$ contours between HIRAX-256 and HIRAX-1024 is due to the different relative contributions of the Planck prior to the combined constraints.
  6. 6 Estimated relative errors in recovered $P(k_{\parallel},k_{\perp})$ band-powers (from diagonal elements of the derived covariance matrices) over 100 MHz sub-bands spanning the HIRAX bandwidth using the $m$-mode pipeline. A foreground filter has been applied here assuming ideal knowledge of the instrument.

###### List of Tables

  1. 1 HIRAX instrument parameters for the initial 256-element array.
  2. 2 HIRAX-256 correlator node specifications. The HIRAX-256 X-engine is comprised of eight these nodes.
  3. 3  Marginalized 68% cosmological parameter forecast constraints for the HIRAX experiment compared to current eBOSS[2] results for $\Lambda$CDM, $w$CDM and $w_{0}w_{a}$CDM cosmologies.
  4. 4 Target precision values for HIRAX telescope mechanical structure