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Exploring Cosmic Origins with CORE: Survey requirements and mission design

J. Delabrouille, P. de Bernardis, F. R. Bouchet, A. Achúcarro, P. A. R. Ade, R. Allison, F. Arroja, E. Artal, M. Ashdown, C. Baccigalupi, M. Ballardini, A. J. Banday, R. Banerji, D. Barbosa, J. Bartlett, N. Bartolo, S. Basak, J. J. A. Baselmans, K. Basu, E. S. Battistelli, R. Battye, D. Baumann, A. Benoît, M. Bersanelli, A. Bideaud, M. Biesiada, M. Bilicki, A. Bonaldi, M. Bonato, J. Borrill, F. Boulanger, T. Brinckmann, M. L. Brown, M. Bucher, C. Burigana, A. Buzzelli, G. Cabass, Z. -Y. Cai, M. Calvo, A. Caputo, C. -S. Carvalho, F. J. Casas, G. Castellano, A. Catalano, A. Challinor, I. Charles, J. Chluba, D. L. Clements, S. Clesse, S. Colafrancesco, I. Colantoni, D. Contreras, A. Coppolecchia, M. Crook, G. D'Alessandro, G. D'Amico, A. da Silva, M. de Avillez, G. de Gasperis, M. De Petris, G. de Zotti, L. Danese, F. -X. Désert, V. Desjacques, E. Di Valentino, C. Dickinson, J. M. Diego, S. Doyle, R. Durrer, C. Dvorkin, H. -K. Eriksen, J. Errard, S. Feeney, R. Fernández-Cobos, F. Finelli, F. Forastieri, C. Franceschet, U. Fuskeland, S. Galli, R. T. Génova-Santos, M. Gerbino, E. Giusarma, A. Gomez, J. González-Nuevo, S. Grandis, J. Greenslade, J. Goupy, S. Hagstotz, S. Hanany, W. Handley, S. Henrot-Versillé, C. Hernández-Monteagudo, C. Hervias-Caimapo, M. Hills, M. Hindmarsh, E. Hivon, D. T. Hoang, D. C. Hooper, B. Hu, E. Keihänen, R. Keskitalo, K. Kiiveri, T. Kisner, T. Kitching, M. Kunz, H. Kurki-Suonio, G. Lagache, L. Lamagna, A. Lapi, A. Lasenby, M. Lattanzi, A. M. C. Le Brun, J. Lesgourgues, M. Liguori, V. Lindholm, J. Lizarraga, G. Luzzi, J. F. Macìas-Pérez, B. Maffei, N. Mandolesi, S. Martin, E. Martinez-Gonzalez, C. J. A. P. Martins, S. Masi, M. Massardi, S. Matarrese, P. Mazzotta, D. McCarthy, A. Melchiorri, J. -B. Melin, A. Mennella, J. Mohr, D. Molinari, A. Monfardini, L. Montier, P. Natoli, M. Negrello, A. Notari, F. Noviello, F. Oppizzi, C. O'Sullivan, L. Pagano, A. Paiella, E. Pajer, D. Paoletti, S. Paradiso, R. B. Partridge, G. Patanchon, S. P. Patil, O. Perdereau, F. Piacentini, M. Piat, G. Pisano, L. Polastri, G. Polenta, A. Pollo, N. Ponthieu, V. Poulin, D. Prêle, M. Quartin, A. Ravenni, M. Remazeilles, A. Renzi, C. Ringeval, D. Roest, M. Roman, B. F. Roukema, J. -A. Rubino-Martin, L. Salvati, D. Scott, S. Serjeant, G. Signorelli, A. A. Starobinsky, R. Sunyaev, C. Y. Tan, A. Tartari, G. Tasinato, L. Toffolatti, M. Tomasi, J. Torrado, D. Tramonte, N. Trappe, S. Triqueneaux, M. Tristram, T. Trombetti, M. Tucci, C. Tucker, J. Urrestilla, J. Väliviita, R. Van de Weygaert, B. Van Tent, V. Vennin, L. Verde, G. Vermeulen, P. Vielva, N. Vittorio, F. Voisin, C. Wallis, B. Wandelt, I. Wehus, J. Weller, K. Young, M. Zannoni

arXiv:1706.04516v1astro-ph.IMastro-ph.CO

TL;DR

The paper asks how a future space survey can fully exploit CMB polarisation to address open questions in cosmology and fundamental physics. It develops the performance requirements and design of CORE, whose lensing reconstruction can reduce lensing B-mode power by 70% and improve primordial gravitational-wave amplitude errors by a factor of 2.5.

  • Problem

    CMB polarisation remains incompletely measured, while inflation, dark matter, dark energy, anomalies, and physics beyond the standard model motivate improved observations.

  • Method

    The paper derives survey requirements and evaluates CORE’s space-mission design, scanning strategy, frequency coverage, foreground control, and systematic-error mitigation.

  • Results

    70% reduction in lensing B-mode power yields a factor of 2.5 improvement in the error on the amplitude of primordial gravitational waves.

  • Takeaways & Limitations

    CORE is intended to provide broad, high-precision CMB polarisation measurements that complement ground observations and constrain cosmology across multiple science goals.

  • Takeaways & Limitations

    If r ≪ 0.001, primordial inflationary B-mode detection may remain out of reach, although precise polarisation measurements retain scientific value.

Abstract

from arXiv · show

Future observations of cosmic microwave background (CMB) polarisation have the potential to answer some of the most fundamental questions of modern physics and cosmology. In this paper, we list the requirements for a future CMB polarisation survey addressing these scientific objectives, and discuss the design drivers of the CORE space mission proposed to ESA in answer to the "M5" call for a medium-sized mission. The rationale and options, and the methodologies used to assess the mission's performance, are of interest to other future CMB mission design studies. CORE is designed as a near-ultimate CMB polarisation mission which, for optimal complementarity with ground-based observations, will perform the observations that are known to be essential to CMB polarisation scienceand cannot be obtained by any other means than a dedicated space mission.

1 Introduction

CMB observations have established ΛCDM but leave fundamental questions about inflation, dark matter, dark energy, anomalies, and physics beyond the standard model. The paper motivates CORE as an ESA medium-size space mission to obtain the sensitivity and measurements needed to exploit CMB polarisation.

  • CMB anisotropy studies have driven precise constraints on the ΛCDM standard cosmological model, while fundamental questions remain unresolved.
  • CMB photons preserve information from the recombination epoch, making additional observations a probe of the early Universe and its subsequent interactions.
  • Planck’s roughly 50 µK.arcmin polarisation sensitivity was insufficient, whereas near-optimal exploitation requires a few µK.arcmin or better.
  • Although suborbital experiments target primordial and lensing B modes, the field widely accepts that a space mission is needed to fully exploit CMB polarisation.
  • The paper specifies performance requirements and design options for CORE, an ESA medium-size mission proposed for launch before 2030.

2 Overview of CORE

CORE is a multi-frequency polarimetric space mission designed to measure CMB E and B modes while separating foreground emission and controlling systematic effects. Its instrument, orbit, passive cooling, and scan strategy are jointly chosen to provide broad frequency coverage, high sensitivity, and repeated measurements.

  • CORE observes 19 frequency bands from 60 to 600 GHz, with angular resolution ranging from about 18′ to 2′, targeting CMB E and B modes.
  • The instrument combines 2100 cryogenically cooled KIDs with a 1.2-m crossed-Dragone telescope to achieve about 1.7 µK.arcmin aggregate CMB polarisation sensitivity.
  • Passive cooling and a symmetric spacecraft geometry reduce detector background and thermal modulation, improving sensitivity especially above 220 GHz.
  • The baseline scan uses a roughly 2-minute spin, approximately 4-day precession, and one-year revolution, with each pixel observed at many detector orientations.

3 Scientific objectives

CORE’s scientific objectives span inflation, tests of ΛCDM and particle physics, cosmic structures, foregrounds, galaxy evolution, and large-scale cosmological anisotropies. Its central promise is that improved CMB polarisation measurements can test inflationary scenarios, clarify cosmological tensions, and probe matter and fundamental physics.

  • Inflation: CORE aims to constrain the mechanisms that generated primordial inhomogeneities, especially through inflation and its predicted primordial tensor perturbations.The tensor-to-scalar ratio r parameterizes the relative amplitude of tensor to scalar perturbations.
  • The cosmological model and fundamental physics: The mission will test ΛCDM, investigate apparent tensions, and seek signatures of extensions to the standard particle and interaction model.The motivation includes unresolved discrepancies such as the roughly 2.4σ difference between Planck-inferred and Cepheid-plus-supernova estimates of the Hubble constant.
  • Structures and legacy science: CORE will probe gravitationally lensed matter, foreground emission, galaxy evolution, and cosmic dipoles, extending CMB science beyond primordial anisotropies.Its objectives include mapping matter through CMB lensing, understanding polarisation foregrounds and dust-obscured star formation, and testing isotropy and homogeneity with dipoles.
  • Inflation: Detecting or ruling out r ≃0.001 would test large-field inflationary models beyond the expected reach of suborbital experiments alone.A non-detection would rule out all large-field models, while a detection could distinguish among some currently favoured models.
  • Inflation: CORE also targets spectral tilt, its scale dependence, non-Gaussian signatures, and, if primordial B modes are detected, the tensor spectral index.These observables provide inflationary constraints beyond measuring the tensor-to-scalar ratio.
  • The cosmological model and fundamental physics: High signal-to-noise CMB maps and lensing measurements could reduce cosmological-parameter errors by an order of magnitude or more and improve extension-dependent figures of merit by up to 10^7.These improvements would help assess whether existing tensions reflect new physics, statistical fluctuations, or systematic errors; CORE combined with Euclid and DESI is projected to reach σ(Mν) = 16 meV.

4 Survey requirements

The survey requirements prioritize a near-ultimate space mission that reaches sensitivity and angular resolution set by CMB science, foreground separation, delensing, and fundamental limits. CORE is designed to complement ground observations by providing full-sky, multi-frequency polarisation measurements that ground experiments cannot obtain alone.

  • Foregrounds: Foreground residuals must be reduced by at least 3 orders of magnitude at ℓ≃10, 2 at ℓ≃100, and 1 at ℓ≃1000; ground surveys can exploit at most ≲25% of the sky.
  • Why space: A space mission avoids atmospheric absorption, emission, and fluctuations, while its mapping speed is at least 100 times better than from the ground.
  • Frequency channels: The survey requires at least ten frequency channels, preferably more, to model synchrotron and thermal-dust foregrounds with redundancy and consistency checks.
  • Survey strategy: The mission is intended to deliver reference-quality polarisation data by focusing on observations out of ground-based reach and limiting performance by cosmic variance, foreground separation, and delensing rather than instrumentation.
  • Sensitivity and angular resolution: An angular resolution of ≲4′ and noise below ≲2 µK.arcmin are required for the ultimate E-mode measurement, which remains signal dominated almost to ℓ≃3000.
  • Sensitivity and angular resolution: The target sensitivity is 1.7–2.5 µK.arcmin, with angular resolution better than about 30′ for primordial B modes, ≲8′ for most lensing B modes, and ≲4′ for optimal E/B measurements.
  • Frequency channels: CORE spans approximately 65–400 GHz for CMB and foreground measurements, while high-frequency channels can construct CIB maps used for independent B-mode delensing validation.

5 Mission design

CORE’s mission design uses an L2 orbit and redundant, full-sky scanning to control contamination, instrumental systematics, noise, and polarisation-angle errors. The baseline omits an onboard HWP and relies on spacecraft scanning to meet the observing requirements.

  • Mission constraints: An ESA M-class implementation constrains CORE to a total project budget below approximately EUR 700 million and compatibility with the Ariane 6.2 launcher.The ESA contribution has a EUR 550 million cost cap, with remaining funding from national agencies and possible international partners.
  • Orbit: L2 is the baseline orbit because it keeps the Sun, Earth, and Moon away from the telescope line of sight, reducing sidelobe stray-light risk.The paper notes that sidelobe contamination is difficult to assess reliably before launch, motivating risk reduction by design.
  • Observing strategy: The observing strategy covers the complete sky repeatedly, with varied polarisation angles and observation times to control leakage, calibration drift, and low-frequency noise.Requirements include evenly distributed polarisation angles, short- and long-timescale revisits, stable thermal conditions, and approximately uniform integration over the sky.
  • Observing strategy: CORE must keep the line of sight away from the Sun, Earth, and Moon while maintaining thermal stability and revisiting distant pixels faster than long-term instrumental instabilities.These constraints target stray-light pickup, temperature-driven effects, gain drifts, and other low-frequency systematics.
  • Polarisation modulation: The baseline favours no HWP, so scanning alone must provide the polarisation-angle coverage and systematic control that active modulation would otherwise simplify.An onboard spinning or stepped HWP would rotate polarisation without rotating the spacecraft, but introduces drawbacks affecting mission performance and feasibility.
  • Performance: The 145-GHz baseline channel has about 3 µK.arcmin sensitivity near the ecliptic poles, about 6 µK.arcmin near the plane, and a median of about 5 µK.arcmin.Most pixels have sensitivity between 4 and 6 µK.arcmin; the noise-map spectra are compared with the homogeneous-coverage theoretical estimate.

6 Payload

CORE’s payload design combines passive shielding, telescope geometry, polarization-modulation choices, cooling, and scan constraints to control stray light and systematic effects while preserving scientific performance.

  • Thermal and spacecraft geometry: The payload module stays behind a Sun screen, with symmetry and a shadow-cone geometry preventing direct solar illumination during scanning.The service module and payload are thermally separated, while the Sun, Earth, and Moon remain on the same side of the screen.
  • Telescope design: The telescope size is set by angular-resolution and sidelobe-rejection requirements, linking aperture choice to both imaging and stray-light control.The beam diameter scales approximately as θ_beam ≃ 70λ/D, while the FWHM is about half that for full aperture illumination.
  • Shielding against sidelobe stray light: Sidelobe shielding forces stray radiation through multiple reflections, adding at least one order of magnitude of rejection and likely more.The focal plane receives sky radiation through the telescope or after reflections on mostly absorptive screens; these screens also increase detector and cooler loading.
  • Shielding against sidelobe stray light: A 1-mK temperature fluctuation in a payload 1% coupled to the detectors generates a 10-µK signal, making absorptive screens preferably as cold as possible.Absorptive screens increase the load on detectors and the active cooling chain, and their temperature fluctuations can create internal stray-light emission.
  • Polarization modulation: Using an HWP as the first optical element restricts aperture size and therefore degrades angular resolution, optical throughput, component separation, de-lensing, and sidelobe rejection.Large half-wave plates are technically challenging, while smaller apertures increase far-sidelobe pickup and reduce scientific reach.
  • Polarization modulation: CORE omits a half-wave plate because the authors judge a no-HWP design easier and scientifically better after weighing modulation benefits against technical risks.Rotating HWPs introduce cryogenic, magnetic, calibration, and systematic-effect challenges; stepped HWPs also do not mitigate low-frequency noise and long-term instability.
  • Cooling chain: The active cooling chain requires a redundancy strategy because cooler failure is a single-point mission risk, but redundancy itself introduces thermal drawbacks.The baseline uses pulse-tube, Joule–Thomson, and dilution refrigeration stages.
  • Scan and payload constraints: At 0.5 RPM, spacecraft spin momentum is approximately 105 Nms, requiring two reaction wheels and constraining the typical allowed spin rate to less than approximately 2 RPM.Reaction-wheel storage and star-sensor accuracy jointly limit the scan rate, so the scan strategy and payload design represent a compromise among constraints.

7 Controlling systematic effects

CORE controls systematic effects through calibrated, deprojected mapmaking and scanning strategies that model beam, detector, pointing, and bandpass mismatches. Simulations show beam asymmetry and bandpass mismatch can be reduced to levels compatible with the mission sensitivity under stated assumptions.

  • Angular-response systematics: CORE combines ground calibration, theoretical modelling, in-flight calibration, and deprojection to control intensity leakage into polarisation maps.The instrument model includes beam and detector-response properties, which are refined through calibration and mapmaking.
  • Angular-response systematics: Beam ellipticity generates intensity-to-polarisation leakage through scan-direction intensity gradients when measurements with different orientations are combined.The leakage coefficients depend on the amplitude and direction of the intensity-beam ellipticity.
  • Angular-response systematics: 0-pointing and detector-response parameters can be corrected in mapmaking when the instrument is perfectly calibrated, while residual beam terms require fitted nuisance parameters.The treatment assumes systematic parameters remain constant long enough to construct substantial sky maps.
  • Angular-response systematics: Beam-asymmetry corrections developed for CORE reduce their impact well below the mission sensitivity target.This result is reported for the CORE-specific correction approach demonstrated in simulations and analysis studies.
  • Bandpass mismatch: Bandpass mismatch causes intensity leakage because detectors weight astrophysical components differently across frequency bands, with spatially varying emission laws further complicating calibration.Synchrotron, thermal dust, and CMB spectra produce coefficient differences of a few percent, and the effect can be severe for low-level primordial B modes.
  • Bandpass mismatch: One iteration of component separation and linear inversion reduces bandpass-mismatch effects to the required mission-sensitivity level when inter-band mismatch is no worse than for Planck.Intensity component maps are inserted into the detector model, after which the sky signal and mismatch parameters are solved jointly.

8 Options

The options analysis defines MiniCORE as a descoped mission retaining observations unavailable by other means, while identifying upgrades that improve sensitivity, angular resolution, or foreground and CIB mapping. The minimal option remains scientifically useful but lacks clear margins and redundancy.

  • Descoping options: MiniCORE prioritises clean full-sky CMB maps, high-frequency foreground maps, and CIB maps for delensing in complementarity with ground observations.These capabilities target scales dominated by foreground emission and cosmic variance while supporting ground-based measurements at finer angular scales.
  • Descoping options: 900 detectors, an 80 cm aperture, a 3-year mission, and a reduced frequency range define a possible MiniCORE configuration.The associated table assumes a 3-year mission, 30% fractional bandwidth, 60% optical efficiency, and optics cooled to 85 K.
  • Descoping options: 3.2 µK.arcmin aggregate CMB sensitivity leaves MiniCORE adequate for lensing B modes with S/N ≃1.5, while the primordial recombination bump is below noise for r <∼0.006.The full-array sensitivity is slightly less than 2 times worse than CORE in map noise and 4 times worse in power.
  • Descoping options: MiniCORE is considered the minimal next-generation CMB polarisation space mission because further descoping would not adequately address CORE’s science goals.The option does not clearly satisfy the margins-and-redundancy requirement, although extending the mission could improve final sensitivity.
  • Performance upgrades: 1.5 µK.arcmin using 130–220 GHz channels, or 1.3 µK.arcmin for the full array, is achievable by making all detectors dual-polarisation.This improvement reduces the noise level by a factor of 2 in channels centred at ν ≥115 GHz.
  • Performance upgrades: Multi-chroic detectors could increase detector counts by 2–3 and potentially reach 1 µK.arcmin or better, provided foreground residuals improve comparably.Larger apertures and added high-frequency channels would additionally improve resolution and dust, infrared-source, cluster, and CIB science.

9 Discussion

The discussion positions CORE as a space mission combining low noise, angular resolution, frequency coverage, and scan-based systematic control for inflationary, lensing, foreground, and broader cosmological science. Its design is intended to complement ground observatories while fitting an ESA medium-class mission context.

  • Science performance: CORE’s resolution and low noise target σr = 0.0004, distinguishing inflationary models with r ≪0.001 from r = 0.003.The mission design specifically aims to avoid an ambiguous hint around r = 0.002 ± 0.001.
  • Science performance: 70% reduction in lensing B-mode power improves the error on primordial gravitational-wave amplitude by a factor of 2.5 through CORE lensing reconstruction.Delensing is presented as essential for reaching the targeted inflationary sensitivity.
  • Foreground control: CORE’s frequency bands have sufficient per-band sensitivity to measure Galactic emission, which is necessary because foregrounds can exceed low-ℓ primordial B modes by orders of magnitude.The discussion highlights unknown foreground complexity as a central challenge for primordial B-mode measurements.
  • Cosmological reach: Post-CORE constraints could reduce the allowed cosmological parameter space by ∼10^7 relative to Planck 2015 and by 10^5 relative to Planck 2015 plus future BAO measurements.The mission’s angular resolution is optimised for broad science within an ESA M-class budget.
  • Systematic control: CORE’s scan strategy is designed to discriminate polarimetric systematic errors without requiring a continuously rotating half-wave plate.The alternative would add technical risk, cost, and schedule consequences, especially for the required broad frequency coverage.
  • Space-ground complementarity: Comprehensive exploitation of CMB polarisation requires space-based observations when foregrounds, cosmic variance, and systematics dominate over raw sensitivity.Ground-based high-resolution observations remain complementary, particularly at high multipoles.
  • Space-ground complementarity: Combining a spectrometer such as PIXIE, an imager such as CORE, and a high-resolution ground observatory would provide powerful complementary CMB observations.The proposed combination spans distinct observing capabilities for the next decade.

10 Conclusion

CMB polarisation measurements are needed to address unresolved questions about inflation, dark matter, dark energy, and the completeness of cosmological understanding. CORE is designed as a space mission that combines broad, sensitive polarisation mapping with systematic-effect control and complementary ground observations.

  • Science requirements: Detailed CMB polarisation observations remain necessary because most useful sky scales have not been mapped with high signal-to-noise in polarisation.The target is full-sky coverage across scales down to about 2′ and sensitivity of a fraction of a µK.arcmin.
  • Science requirements: Space observations provide the precision and accuracy needed to control foregrounds, cosmic variance, and instrumental systematics in future polarisation surveys.Ground observations remain complementary, extending angular resolution to smaller scales.
  • CORE design: CORE maps 19 frequency channels from 60 to 600 GHz with 2100 cryogenically cooled detectors and reaches 1.7 µK.arcmin polarisation sensitivity after four years.Its angular resolution spans 2–18′, while repeated coverage and frequency redundancy support systematic and foreground checks.
  • CORE design: Repeated sky coverage, stable scanning, and joint estimation of sky emission and instrumental response are used to minimise and correct systematic effects.The mission observes from a Lissajous orbit around Sun–Earth L2 and repeatedly scans the full sky over four years.
  • Mission options: A descoped CORE configuration could reduce the aperture to 80 cm, halve the detector count, and remove channels below 100 GHz while preserving most essential polarisation science.This option would increase dependence on high-quality ground measurements; dual-polarisation, multichroic detectors, or a larger aperture could instead improve the survey.
  • Additional science: CORE’s polarisation maps also support studies of Galactic magnetic fields, galaxy clusters, lensed dusty galaxies, protoclusters, and future astrophysical investigations.The paper describes these as additional science goals beyond the mission’s primary CMB polarisation optimisation.

A.1 Atmosphere and detector sensitivity

Atmospheric emission increases detector loading and introduces time-dependent noise for ground observations, whereas space detectors operate in a colder, quieter environment. Under the stated assumptions, one space detector can match the sensitivity of roughly 100–200 ground detectors, with space especially important outside atmospheric windows.

  • Detector loading: Ground-based detectors receive additional loading from atmospheric emissivity, while space detectors benefit from a colder and quieter observing environment.The comparison assumes 3% emissive ground optics, 0.5 mm precipitable water vapour, and Planck-like space-telescope emissivity.
  • Mapping speed: 100–200 ground-based detectors provide sensitivity equivalent to one space-borne detector within atmospheric windows under the stated assumptions.The comparison ignores atmospheric fluctuations, ground pickup, and other systematics that further degrade ground-based performance.
  • Frequency coverage: Outside atmospheric windows and above 300 GHz, ground observations are extremely challenging, making space the apparent option for sensitive few-arcminute mapping over large sky areas.These regions lie near major O2 and H2O lines or at frequencies where atmospheric transmission is poor.
  • Detector sensitivity: At 150 GHz, space-detector noise levels are 49, 43, and 40 µKCMB·√s for the stated payload-temperature cases.These estimates are slightly better than, but generally consistent with, Planck 143 GHz polarisation-detector sensitivities of 50–53 µKCMB·√s.

A.2 Required observing time and focal-plane area

Reaching 5 µK.arcmin full-sky polarisation sensitivity requires far fewer detector-years and a much smaller focal plane from space than from the ground. Space is most area-efficient near 170–200 GHz, while the ground optimum is 150 GHz.

  • Observing time: 500–1000 detector-years are required from space to reach 5 µK.arcmin full-sky polarisation sensitivity, compared with about 10^5 detector-years on the ground.The requirement scales proportionally to 1/σ^2 and the observed sky fraction.
  • Focal-plane area: A focal plane of roughly 10 cm is required in space, compared with around 1 m on the ground, for comparable full-sky performance.The space estimate assumes a single-mode pixel and filling factor κ^2 = 9.
  • Observing time: For four years of observation, about 200–300 space detectors are needed at 100–150 GHz, whereas the ground requires roughly two orders of magnitude more detectors.This is the detector-count comparison shown for the same 5 µK.arcmin full-sky target.
  • Focal-plane area: Dual-polarisation and multichroic detectors can reduce focal-plane size, with dual-polarisation trichroic detectors providing an example factor-of-six reduction.The reduction applies provided optical efficiency is not worse than for single-frequency, single-polarisation detectors.
  • Frequency choice: The most efficient space frequency range is 170–200 GHz, while 150 GHz is optimal from the ground in sensitivity per focal-plane area.The space optimum depends somewhat on payload temperature.

A.3 Atmospheric emission fluctuations

Atmospheric emission fluctuates with precipitable water vapour and temperature, producing noise that is especially problematic for large-scale CMB polarisation. Stable low-water-vapour sites help, but space is required for low-noise, few-arcminute, large-area observations above 300 GHz.

  • Atmospheric variability: Atmospheric emission varies across time and sky because of inhomogeneous precipitable water vapour and temperature.For a 300 K atmosphere with 2% emissivity, the total emission is about 6 KRJ, while 0.1% temperature inhomogeneities generate about 6 mKRJ fluctuations.
  • Impact on polarisation: Atmospheric fluctuations cannot be ignored for large-scale CMB polarisation because B modes are more than 10^3 times fainter than temperature anisotropies.The relative faintness of B modes makes atmospheric noise relevant even when detector white noise is lower.
  • Ground limitations: Ground observations up to 300 GHz are theoretically possible from Antarctica or the Atacama plateau under very low precipitable water vapour and stable conditions.Broad-band observations above 300 GHz remain very challenging because of atmospheric-emission fluctuations.
  • Space requirement: A space mission is the only viable option for low-noise, few-arcminute, large-sky-area observations at sub-millimetre wavelengths.Stratospheric balloons avoid atmospheric noise but provide only short observing durations.

B.1 Main requirements and design drivers

The scanning strategy must balance sky coverage, crossing angles, and polarization-angle diversity. CORE adopts α = 30° and β = 65° to support broad detector coverage and varied scan orientations.

  • Scanning regimes: When α > β, scan annuli intersect at large angles and provide varied detector orientations across the sky.Annuli separated by about β degrees in time also generate large-angle crossings for most observed pixels.
  • Scanning regimes: When α < β, rings connect distant pixels quickly but intersect at smaller angles.This regime therefore trades rapid long-distance connections against crossing-angle diversity.
  • Baseline choice: CORE sets α = 30° and β = 65°, giving α + β = 95° so all focal-plane detectors can observe the complete sky.The choice follows the need to increase the angular sum beyond the earlier α = β = 45° concept.

B.2 Practical constraints

CORE’s practical design constraints couple thermal stability, stray-light avoidance, full-sky coverage, orbit selection, and communications. The baseline orbit and scan geometry are chosen to satisfy these constraints without excessive proximity of bright bodies to the line of sight.

  • Thermal and illumination constraints: Maintaining the precession axis anti-solar keeps integrated solar illumination on the spacecraft’s thermal-control surfaces constant.The payload is kept symmetrical to stabilize illumination of the solar panels and outer V-groove screen.
  • Thermal and illumination constraints: The Sun must not illuminate the inner V-grooves or payload, while Earth and Moon must not directly illuminate the detector array.These screening requirements constrain the allowable precession angle α.
  • Sky coverage: Full-sky mapping requires α + β to exceed the focal-plane radius, while excessively large values bring the Sun, Earth, and Moon too near the line of sight.For CORE’s field of view of roughly 5° radius, α + β = 95° is appropriate.
  • Communications: Data transfer requires a steerable antenna to point toward Earth while cancelling the spacecraft’s spin and precession.Phased-array and mechanical-pointing systems are identified as possible implementations.
  • Orbit selection: The maximum orbit radius decreases from about 860,000 km at α = 30° to 400,000 km at α = 45° and 260,000 km at α = 50°.A large Lissajous orbit requires lower Δv and less propellant, although launcher capacity is not a major mission driver.

B.3 Sampling

The sampling design links spin and precession periods to beam-scale coverage and sky accumulation. CORE’s baseline provides 199 samples per second along the scan, 3.75′ maximum cross-scan spacing, and 45% sky coverage per precession.

  • Co-scan sampling: 199 samples per second, or about 5 ms per sample, results from Ns = 4 samples per beam for a 4′ beam with β = 65° and Tspin = 120 s.This is the co-scan sampling rate for the CORE baseline.
  • Cross-scan sampling: The baseline maximum cross-scan sampling step is θ⊥ = 3.75′ for Tspin = 120 s, Tprec = 4 days, and α = 30°.This is not quite sufficient for the highest-frequency channels, for which a faster spin of about 1 RPM would be preferable.
  • Cross-scan sampling: The cross-scan step should ideally be about one quarter of the beam size.Most of the sky has a smaller spacing than the quoted maximum, which occurs along the spin-axis trajectory.
  • Sky coverage: 45% of the sky is covered by each precession for α = 30° and β = 65°.One-precession coverage is the spherical area between colatitudes |α − β| and α + β.
  • Sky coverage: Figure 14 compares four-day single-detector coverage for CORE’s baseline and a LiteBIRD-like strategy using √s per HEALPix pixel.The figure uses Nside = 512 and shows full maps plus a gnomonic detail around Galactic coordinates (0°, −50°).

B.4 Optimisation

CORE’s scan optimization compares two angle-period combinations that cover the same area per precession but differ strongly in sampling uniformity and operational demands. The selected baseline is a compromise among cross-scan sampling, thermal hardware, and attitude-control constraints.

  • Compared strategies: Case A uses α = 30°, β = 65°, Tspin = 120 s, and Tprec = 4 days, whereas Case B uses α = 65°, β = 30°, Tspin = 600 s, and Tprec = 93 minutes.Case B represents a LiteBIRD-like option considered for comparison.
  • Compared strategies: Both strategies cover the same sky area during one precession, but only Case A meets the required cross-scan sampling relative to pixel size.The time evolution of coverage depends on the ratio Tprec/Tspin.
  • Coverage uniformity: Case B leaves large gaps between scans and produces a highly inhomogeneous observing-time distribution after four days.The gaps gradually fill as precessions accumulate, but the resulting map is less uniform.
  • Parameter trade-offs: Matching CORE’s 3.75′ cross-scan sampling with α = 65° and β = 30° requires Tprec/Tspin ≃ 5220.With Tspin = 10 minutes, this implies Tprec = 36 days; with Tprec = 4 days, Tspin must be about 1.1 minutes.
  • Parameter trade-offs: The final CORE parameters compromise among scan performance, the additional solar panels and V-groove redesign required at α = 65°, and the greater attitude-control demands of Tspin = 1.1 minutes.A 36-day fill time would also be suboptimal for cross-comparing maps obtained at different mission epochs.
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