Sky survey telescopes and powerful targeted telescopes play complementary roles in astronomy. In order to investigate the nature and characteristics of the motions of very faint objects, a flexibly-pointed instrument capable of high astrometric accuracy is an ideal complement to current astrometric surveys and a unique tool for precision astrophysics. Such a space-based mission will push the frontier of precision astrometry from evidence of Earth-mass habitable worlds around the nearest stars, to distant Milky Way objects, and out to the Local Group of galaxies. As we enter the era of the James Webb Space Telescope and the new ground-based, adaptive-optics-enabled giant telescopes, by obtaining these high precision measurements on key objects that Gaia could not reach, a mission that focuses on high precision astrometry science can consolidate our theoretical understanding of the local Universe, enable extrapolation of physical processes to remote redshifts, and derive a much more consistent picture of cosmological evolution and the likely fate of our cosmos. Already several missions have been proposed to address the science case of faint objects in motion using high precision astrometry missions: NEAT proposed for the ESA M3 opportunity, micro-NEAT for the S1 opportunity, and Theia for the M4 and M5 opportunities. Additional new mission configurations adapted with technological innovations could be envisioned to pursue accurate measurements of these extremely small motions. The goal of this White Paper is to address the fundamental science questions that are at stake when we focus on the motions of faint sky objects and to briefly review instrumentation and mission profiles.
This paper is the accurate transcription with a very few updates of the White Paper called Summary of science cases with most stringent performance requirements set in each case Program Used Mission Number of Benchmark target EoM precision time (h) fraction objects per field (at ref. mag.) Dark Matter & compact objects 17 000 0.69 102–105 20 (14–22) 10 Nearby Earth-like planets & follow-up 3 500 0.14 < 20 5 (1–18) 0.15 Open observatory 4 000 0.17 10-105 6 (1-22) 1.0 Overall requirements 24 500 1.00 101-105 6 (1-22) 0.15-10 Figures are based on a 4 year mission, thermal stabilisation (+ slew time) is assumed to take 30
Europe has long been a pioneer of astrometry, from the time of ancient Greece to Tycho Brahe, Johannes Kepler, the Copernican revolution and Friedrich Bessel. ESA’s Hipparcos [
An unprecedented microarcsecond relative precision mission will advance European astrometry still further, setting the stage for breakthroughs on the most critical questions of cosmology, astronomy, and particle physics.
The current hypothesis of cold dark matter (CDM) urgently needs verification. Dark matter (DM) is essential to the Λ + CDM cosmological model (ΛCDM), which successfully describes the large-scale distribution of galaxies and the angular fluctuations of the Cosmic Microwave Background, as confirmed by ESA’s Planck mission [
There are a number of open issues regarding ΛCDM on small scales. Simulations based on DM-only predict 1) a large number of small objects orbiting the Milky Way, 2) a steep DM distribution in their centre and 3) a prolate Milky Way halo. However, hydrodynamical simulations, which include dissipative gas and powerful astrophysical phenomena (such as supernovae explosions and jets from galactic nuclei) can change this picture. Quantitative predictions are based on very poorly understood sub-grid physics and there is no consensus yet on the results. Answers are buried at small-scales, which are extremely difficult to probe. A new high precision astrometric mission appears to be the best way to settle the nature of DM and will allow us to validate or refute key predictions of ΛCDM, such as
the DM distribution in dwarf spheroidal galaxies the outer shape of the Milky Way DM halo the lowest masses of the Milky Way satellites and subhalos the power spectrum of density perturbations
These observations will significantly advance research into DM. They may indicate that DM is warmer than ΛCDM predicts. Or we may find that DM is prone to self- interactions that reduces its density in the central part of the satellites of the Milky Way. We may discover that DM has small interactions that reduce the number of satellite companions. Alternatively, measurement of the Milky Way DM halo could reveal that DM is a sophisticated manifestation of a modification of Einstein’s gravity.
Because they are DM-dominated (see Fig. Number of dwarf spheroidal galaxy stars within the field of view of Theia, a high precision astrometry concept, with expected plane-of-sky errors lower than half the galaxy’s velocity dispersion as a function of the galaxy’s estimated mass-to-light ratio within the effective (half-projected-light) radius of the galaxy. Luminosities and total masses within the half-light radii are mainly from [
Simulations from [
Large DM cores could also be attributed however to strong self-interactions. Hence finding evidence for such cores in the faintest dSphs (which are even more DM dominated [
To determine the inner DM distribution in dSphs, one needs to remove the degeneracy between the radial DM profile and orbital anisotropy that quantifies whether stellar orbits are more radial or more tangential in the Jeans equation [ Reconstruction of the DM halo profile of the Draco dSph without (
We remark in addition that a high precision astrometric mission is able to perform follow-ups of Gaia’s observations of dSphs streams of stars if needed. Not only will such a mission provide the missing tangential velocities for stars with existing radial velocities, but it will also provide crucial membership information - and tangential velocities - for stars in the outer regions of the satellite galaxies that are tidally disrupted by the Milky Way.
For almost two decades cosmological simulations have shown that Milky Way-like DM halos have triaxial shapes, with the degree of triaxiality varying with radius ([
Precise measurement of the velocity of distant Hyper Velocity Stars (hereafter HVS) can test these departures from spherical symmetry, independently of any other technique attempted so far (such as the tidal streams). HVSs were first discovered serendipitously [
Because these velocities exceed the plausible limit for a runaway star ejected from a binary, in which one component has undergone a supernova explosion, the primary mechanism for a star to obtain such an extreme velocity is assumed to be a three-body interaction and ejection from the deep potential well of the supermassive black hole at the Galactic Center [
By measuring the three-dimensional velocity of these stars, we will reconstruct the triaxiality of the Galactic potential. In a spherical potential, unbound HVS ejected from the Galactic Center should travel in nearly a straight line, as depicted in Fig. Illustration of the trajectories of hyper velocity stars ejected from Galactic Center for 3 different outer DM halo shapes: oblate ( Expected proper motions of HVS5 under different assumptions about the shape and orientation of the DM halo. The families of models are shown with the halo major axis along the Galactic X- (
Proper motions of several HVSs were measured with the Hubble Space Telescope (HST) by [
Figure Example of a reconstruction of the Galactic halo shape from a high precision astrometry mission (Theia) measurement of proper motion of HVS5. The assumed proper motions correspond to a prolate model with
Statistical studies of high-precision proper motions of HVSs can also constrain departures of the halo shape from spherical ([
Finally, an accurate measurement of HVS velocities may lead to improved understanding of the black hole(s) at the Galactic Center. Indeed, theoretical models show that HVSs will have a different spectrum of ejection velocities from a binary black hole versus a single massive black hole. Gaia has led to the discovery of several candidate hypervelocity stars (ejection velocities of over 550km/s:, [
The orbits of DM particles in halos
Recent work on the orbital properties and kinematic distributions of halo stars and DM particles show that halo stars, especially the ones with lowest metallicities, are relatively good tracers of DM particles [
A central prediction of ΛCDM in contrast to many alternatives of DM, such as warm DM (e.g. [ Face-on view of the evolution of the perturbation of a Galactic Disc due to a DM subhalo of mass 3
These anomalous bulk motions develop both in the solar vicinity [ Astrometric signatures in the proper motion along Galactic latitude of the perturbation of disc stars by a subhalo. The
A field of view of 1∘× 1∘ in the direction of the Galactic Disc has
Gaia DR2 astrometry has led to the discovery of gaps in tidal streams [
In the ΛCDM model, galaxies and other large-scale structures formed from tiny fluctuations in the distribution of matter in the early Universe. Inflation predicts a spectrum of primordial fluctuations in the curvature of spacetime, which directly leads to the power spectrum of initial density fluctuations. This spectrum is observed on large scales in the cosmic microwave background and the large scale structure of galaxies, but is very poorly constrained on scales smaller than 2 Mpc. This severely restricts our ability to probe the physics of the early Universe. A high precision astrometric mission could provide a new window on these small scales by searching for astrometric microlensing events caused by
UCMHs form shortly after matter domination (at
Like standard DM halos, UCMHs are too diffuse to be detected by regular photometric microlensing searches for MAssive Compact Halo Objects (MACHOs). Because they are far more compact than standard DM halos, they however produce much stronger Projected sensitivity of a high precision astrometry mission (Theia) to the fraction of dark matter in the form of ultra-compact minihalos (UCMHs) of mass Limits on the power of primordial cosmological perturbations at all scales, from a range of different sources. A Theia-like mission will provide far stronger sensitivity to primordial fluctuations on small scales than Gaia, spectral distortions or primordial black holes (PBHs). Unlike gamma-ray UCMH limits, a high precision astrometry mission’s sensitivity to cosmological perturbations will also be independent of the specific particle nature of dark matter
The results will be independent of the DM nature, as astrometric microlensing depends on gravity only, unlike other constraints at similar scales based on DM annihilation, from the Fermi Gamma-Ray Space Telescope [
Using the nearest star, Proxima Centauri, astrometry could measure the behaviour of gravity at low accelerations. A high precision astrometry mission with an extended baseline of 10 years and a precision of 0.5
The ultimate exoplanetary science goal is to answer the enigmatic and ancient question, “
Since the discovery of the first Jupiter-mass companion to a solar-type star [
However, transiting or Doppler-detected HZ terrestrial planet candidates (including the discovery of the
Unlike the Doppler and transit methods, astrometry alone can determine reliably and precisely the true mass and three-dimensional orbital geometry of an exoplanet, which are fundamental inputs to models of planetary evolution, biosignature identification, and habitability. By determining the times, angular separation and position angle at periastron and apoastron passage, exquisitely precise astrometric position measurements will allow the prediction of where and when a planet will be at its brightest (and even the likelihood of a transit event), thus (a) crucially helping in the optimization of direct imaging observations and (b) relaxing important model degeneracies in predictions of the planetary phase function in terms of orbit geometry, companion mass, system age, orbital phase, cloud cover, scattering mechanisms, and degree of polarization (e.g. [
Surgical single-point positional precision measurements in pointed, differential astrometric mode (< 1
A core exoplanet program could be comprised of 63 of the nearest A, F, G, K, and M stars (Fig. Minimum masses of planets that can be detected at the center of the HZ of their star for the 63 best nearby A, F, G, K, M target systems. The target systems (either single or binary stars), are ranked from left to right with increasing minimum detectable mass in HZ around the primary system component, assuming equal observing time per system. Thus for binary stars, A and B components are aligned vertically, as they belong to the same system therefore they share the same rank. When the A and B mass thresholds are close the name is usually not explicitly written down to avoid overcrowding. B components that have mass thresholds above 2.2
Furthermore, as the photon noise from the reference stars is the dominant factor of the error budget, the accuracy for binaries increases faster with telescope staring time than around single stars. For binaries, the reference stars only need to provide the plate scale and the reference direction of the local frame, the origin point coordinates are constrained by the secondary/primary component of the binary. Finally, when observing a binary, the astrometry on both components is obtained simultaneously: the staring time is only spent once as both components are within the same field of view (FoV). These two effects combined cause the observation of stars in binary systems to be much more efficient (as measured in
We further stress that the complete census of small and nearby planets around solar-type stars is unique to high-precision astrometry. On the one hand, Sun-like stars have typical activity levels producing Doppler noise of
For the full sample of the nearest stars considered in Fig.
A secondary program can help elucidate other important questions in exoplanetary science.
An example where astrometry breaks the degeneracy. Two simulated planetary systems are around a solar-type star at 10 pc, with two Jupiter-like planets at 0.5 and 2.5 AU (
The brightest Galactic X-ray sources are accreting compact objects in binary systems. Precise optical astrometry of these X-ray binaries provides a unique opportunity to obtain quantities which are very difficult to obtain otherwise. In particular, it is possible to determine the distances to the systems via parallax measurements and the masses of the compact objects by detecting orbital motion to measure the binary inclination and the mass function. With a high precision astrometric mission, distance measurements are feasible for > 50 X-ray binaries
Matter in the NS interior is compressed to densities exceeding those in the center of atomic nuclei, opening the possibility to probe the nature of the strong interaction under conditions dramatically different from those in terrestrial experiments and to determine the NS composition. NSs might be composed of nucleons only; strange baryons (hyperons) or mesons might appear in the core or even deconfined quark matter, forming then a hybrid star with a quark matter core and hadronic matter outer layers; or of pure strange quark matter (a quark star). A sketch of the different possibilities is given in Fig. Sketch of the different existing possibilities for the internal structure of a neutron star. Figure courtesy of [
The key to constraining the NS EoS is to measure the masses and radii of NSs. While masses have been measured for a number of X-ray binary and radio pulsar binary systems (e.g., [ Left: Neutron star mass measurements in X-ray binaries, update from [
A high precision astrometric mission will contribute by obtaining precise mass constraints with orbital measurements [
Other techniques for constraining the NS EoS might also be possible in the future: detecting redshifted absorption lines; determining the NS moment of inertia of systems like the double pulsar J0737–3039; and more detections of tidal deformability from gravitational wave emission during the inspiral of a binary neutron star merger like for GW170817 [
In addition to the goal of constraining the NS EoS, NS masses are also relevant to NS formation and binary evolution. Current evolutionary scenarios predict that the amount of matter accreted, even during long-lived X-ray binary phases, is small compared to the NS mass. This means that the NS mass distribution is mainly determined by birth masses. Determining the masses of NSs in X-ray binaries, therefore, also provides a test of current accretion models and evolutionary scenarios, including the creation of the NSs in supernovae.
BHs are, according to the theory of general relativity, remarkably simple objects. They are fully described by just two parameters, their mass and their spin. Precise masses are available for very few BHs in X-ray binaries. The recent detection of gravitational waves [
Currently, the cutting edge of research in BH X-ray binaries involves constraining BH spins, including the rate of spin and the orientation of the spin axis. Techniques for determining the rate of spin include measuring the relativistic broadening of the fluorescent iron
In 1986 Bohdan Paczyński [ Microlensing event, OGLE3-ULENS-PAR-02, the best candidate for a
Detection of isolated black holes and a complete census of masses of stellar remnants will for the first time allow for a robust verification of theoretical predictions of stellar evolution. Additionally, it will yield a mass distribution of lensing stars as well as hosts of planets detected via microlensing.
The measurement of cosmological distances has revolutionized modern cosmology and will continue to be a major pathway to explore the physics of the early Universe. The age of the Universe (
The tension between the methods can be due to unknown sources of systematics, to degeneracies between cosmological parameters, or to new physics (e.g. [
Significant improvements in lens modeling, combined with long-term lens monitoring, should allow measuring
By performing photometric measurements with the required sensitivity and no interruption, the combination of a high precision astrometric mission and excellent modeling of the lens galaxy, will enable measurement of
These distance measurements can be transferred to nearby galaxies allowing us to convert observable quantities, such as angular size and flux, into physical qualities such as energy and luminosity. Importantly, these distances scale linearly with
The different targets considered for observations with a high precision astrometry mission have been located in Fig. Sky map of the targets considered for observations with a high precision astrometric mission
Several mission profiles have been considered in the last few years focused on differential astrometry, for instance NEAT, micro-NEAT and Theia. Additional new differential astrometry mission configurations adapted with technological innovations will certainly be envisioned to pursue accurate measurements of the extremely small motions required by the science cases in this White Paper.
To address the science described in this white paper, a high precision astrometry mission should stare towards:
dwarf spheroidal galaxies to probe their dark matter inner structure; hyper-velocity stars to probe the triaxiality of the halo, the existence of compact minihalo objects and the time delay of quasars; the Galactic Disc, to probe DM subhalos and compact minihalo objects; star systems in the vicinity of the Sun, to find the nearest potentially habitable terrestrial planets; known X-ray binaries hosting neutron stars or black holes.
For a targeted mission, the objects of interest must be sampled throughout the lifetime of the mission. After re-pointing the telescope and while waiting for stabilization, photometric surveys, e.g. for measurements of
As illustrated in Fig. Expected plane-of-sky velocity errors from a high precision astrometry mission’s proper motions as a function of distance from Earth. These errors respectively correspond to 40 and 1000 cumulative hours of exposures for exoplanets (
A mission concept with an expected Theia-like astrometric precision, as shown in Fig. Estimated RMS precision on a high precision astrometry mission relative parallax (
Table
The Payload Module (PLM) of a high precision astrometric mission must be simple. It is essentially composed of four subsystems: telescope, camera, focal plane array metrology and telescope metrology. In the case of the Theia/M5 concept, they were designed applying heritage from space missions and concepts like Gaia, HST/FGS, SIM, NEAT (proposed for the ESA M3 opportunity), Theia (proposed for the ESA M4 opportunity), and Euclid.
However, achieving microarcsecond differential astrometric precision requires the control of all effects that can impact the determination of the relative positions of the point spread function. The typical apparent size of an unresolved star corresponds to 0.2 arcseconds for a 0.8 m telescope operating in visible wavelengths. The challenge is therefore to control systematic effects to the level of 1 part per 200 000. The precision of relative position determination in the Focal Plane Array (FPA) depends on i) the photon noise, which can be either dominated by the target or by the reference stars; ii) the geometrical stability of the instrument, iii) the stability of the optical aberrations, and iv) the variation of the detector quantum efficiency between pixels. The control of these effects impairs other missions that otherwise could perform microarcsecond differential astrometry measurements, like HST, Kepler, the Roman Space Observatory (previously known as WFIRST), or Euclid, posing fundamental limits to their astrometric accuracy. All these effects must be taken into account in any high precision differential astrometry mission concept.
To address the challenges and fulfil the requirements from Section
The Theia PLM concept consists of a single Three Mirror Anastigmatic (TMA) telescope with a single focal plane (see Fig. Overall layout of the Theia Payload Module concept. Volume is estimated at 1.6 × 1.9 × 2.2
To reach sub-microarcsecond differential astrometry a diffraction-limited telescope, with all aberrations controlled, is necessary. A trade-off analysis was performed between different optical designs, which resulted in two optical concepts that could fulfil all requirements. Both are based on a Korsch TMA telescope; one is an on-axis solution while the second is an off-axis telescope. In both cases only three of the mirrors are powered mirrors. While the on-axis solution adopts a single folding mirror, the off-axis solution adopts two folding mirrors. The on-axis design was the Theia/M5 baseline (Fig. On-axis Korsch TMA option. Ray-tracing and spot diagrams for the entire FoV. This design was adopted as the baseline for the Theia/M5 proposal. EFL is Effective Focal Length
To achieve the precision by centroiding as many stars as possible, a mosaic of detectors (in principle CCD or CMOS) must be assembled on the focal plane (Fig. Concept for the Theia/M5 Camera. Left: concept for the FPA detector plate. Right: overall view of the camera concept
The time baseline (Table Theia’s mission main characteristics Launch date No constraints, allowing launch date in 2029 Orbit Large Lissajous in L2 Lifetime ∙ 4 years of nominal science operations ∙ Technical operations: 6 months orbit transfer plus instrument commissioning and 1 month decommissioning Concept Single spacecraft, single telescope in the PLM, single camera in the focal plane, metrological monitoring of PLM Communication architecture 75 Mbps, 4h/day
Some instrument key features of the Theia concept are presented in Fig. Proposed Theia satellite concept (Thales Alenia Space). FGS: Fine Guidance Sensor; FOG: Fiber Optics Gyroscope; AOCS: Attitude and Orbit Control System,TT&C: Telemetry, Tracking & Control; TWTA: Travelling Wave Tube amplifier Assembly; LGA: Low Gain Antenna; HGA: High Gain Antenna
Observations carried out with a mission dedicated to high precision astrometry will add significant value and will benefit from a number of other ground-based and space missions operating in the 2030s and beyond, including ESA’s Athena, PLATO, Euclid and Gaia missions, ESO’s MICADO and Gravity instruments, CTA, SKA, the NASA/ESA/CSA JWST and the Rubin Observatory (previously known as LSST). For example:
There have been several propositions for a space mission dedicated to high precision astrometry: a 6 meter baseline visible interferometer on a single satellite like SIM or SIM-Lite [
One interesting potential solution to be considered is the nanosat technology and the cost reduction that is linked to it. There is a huge cost difference between cubesats (< 10 M€) and an ESA M-class mission (400 − 500 M€) or NASA MIDEX/Discovery mission (300 − 500 M$). The cubesat technology has matured and many hundreds are launched every year. That technology has now crept into micro-sats that are up to 200 kg and spacecraft bus of this category are now < 5 M€, while only a few years ago they were
Presently, two detector technologies are used: CCD or CMOS. CMOS detectors present a high quantum efficiency over a large visible spectral band that can also reach infrared wavelengths depending on the sensitive layer. CMOS detectors also have programmable readout modes, faster readout, lower power, better radiation hardness, and the ability to put specialized processing within each pixel. On the other hand there are many known detector systematics, even for advanced detectors like the Teledyne H4RG10. The main challenging effects are the following: fluence-dependent PSF, correlated read noise, inhomogeneity in electric field lines and persistence effects (e.g. [
If a Theia-like mission is selected for the 2040’s, detector technology might be different from anything we have in place nowadays. The main requirements are small pixels, low read-out noise (RON) on large format focal plane and mastering intrapixels effects in order to reach the highest precision astrometry. It should be noticed that the development of European detector technology for low-RON and large-format IR and visible detector matrices, like the Alfa detector that ESA is undertaking with Lynred, is of high interest for our science cases.
Traditionally systematic errors have been the major challenge for
Metrology laser-feed optical fibers placed at the back of the nearest mirror to the detectors can be used to monitor distortions of the focal plane array, and to allow the associated systematic errors to be corrected [
In the case of Theia, the telescope metrology subsystem to monitor perturbations to the telescope geometry is based on a concept of a series of simple and independent linear displacement interferometers installed between the telescope mirrors and organized in a virtual hexapod configuration. Existing space-based interferometers from TNO, as the Gaia Basic Angle Monitor (BAM) are already capable of reaching more precise measurements than those required by Theia/M5 – BAM can perform
For telescopes that do not have high stability levels, there are some alternatives. One is the diffractive pupil concept that puts a precision array of dots on the primary, which produces a regular pattern of dots in the focal plane. One way to use the diffractive pupil is to look at a very bright star (0 mag) and record the diffraction pattern interspersed with observations of a much dimmer target star (
To solve fundamental questions like
“ “ “ “
many branches of astronomy need to monitor the motion of faint objects with significantly higher precision than what is accessible today. Through ultra-precise microarcsecond relative astrometry, a high precision astrometry space mission will address the large number of important open questions that have been detailed in this White Paper.
The scientific requirements points toward a space mission that is relatively simple: a single telescope, with metrology subsystems and a camera. Such a mission can fit as an M-class mission, or even at a smaller mission class depending on the final accuracy which is desired.
Some technological challenges must be tackled and advanced: the spacecraft, the focal plane detector and the metrology. We believe that these challenges can be mastered well before 2050 and that they will open the compelling scientific window of the faint objects in motion.
The authors would like to thank the researchers and engineers who are not co-authors of this paper but who have taken part and have brought their contribution to the proposed missions to ESA successive calls: NEAT (M3), micro-NEAT (S1), and Theia (M4 and M5). An extensive list of supporters for the science objectives is given in [
We are grateful to the anonymous referee who helped to improve the quality of the paper with his/her remarks.
Concerning the funding of our work, we would like to acknowledge the support of many agencies or programs. R.B. acknowledges support from NASA’s Virtual Planetary Laboratory lead team under cooperative agreements NNA13AA93A. A.C.M.C. acknowledges support from CFisUC strategic project (UID/FIS/04564/2019). F.C. acknowledges support by the Swiss National Science Foundation (SNSF) and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (COSMICLENS: grant agreement No. 787886). M.F. received support from Polish National Science Centre (NCN) under Grant No. 2017/26/D/ST9/00591. M.F. gratefully acknowledge the support of the Swedish National Space Agency (DNR 65/19, 174/18). D.H. thanks the Swedish National Space Agency (SNSA/Rymdstyrelsen) for their support. A.M. thanks the Portugese Fundação para a Ciência e a Tecnologia (FCT) through the Strategic Programme UID/FIS/00099/2019 for CENTRA. P.S. acknowledges support from the Australian Research Council under grant FT190100814. L.W. acknowledges support from the Polish NCN grants: Harmonia No. 2018/06M/ST9/00311 and Daina No. 2017/27/L/ST9/03221. The OATo team acknowledges partial funding by the Italian Space Agency (ASI) under contracts 2014-025-R.1.2015 and 2018-24-HH.0, and by a grant from the Italian Ministry of Foreign Affairs and International Cooperation (ASTRA). A.C. and F.M. acknowledge support by the LabEx FOCUS ANR-11-LABX-0013. The work of C.J., X.L. and J.P. was supported by the Spanish Ministry of Science, Innovation and University (MICIU/FEDER, UE) through grants RTI2018-095076-B-C21, ESP2016-80079-C2-1-R, and the Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia ’María de Maeztu’) through grants MDM-2014-0369 and CEX2019-000918-M. A.K.-M., A.A., V.C., P.G., P.G., A.M.A., A.M., M.S. were supported by Fundação para a Ciência e a Tecnologia, with grants reference UIDB/00099/ 2020 and SFRH/BSAB/142940/2018 (P.G. only). A.D. and L.O. also acknowledge partial support from the Italian Ministry of Education, University and Research (MIUR) under the Departments of Excellence grant L.232/2016, and from the INFN grant InDark. G.J.W. gratefully acknowledges support of an Emeritus Fellowship from The Leverhulme Trust. EV is supported by Spanish grant PGC2018-101950-B-100.
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See
For an analysis of orbital content of DM halos see [
One target is a binary which is too close for follow-up spectroscopy
with 2 000 hours of observation
Euclid red book:
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