M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Gravitation Astrometric Measurement Experiment M. Gai - INAF-Osservatorio Astronomico di Torino On some Fundamental Physics results achievable through astronomical techniques… Goal of GAME:  to ;  to

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, GAME: Gamma Astrometric Measurement Experiment Space-time curvature parameter  Light deflection close to the Sun Apparent star position variation Space mission Approach: build on flight inheritance from past missions [SOHO, STEREO, Hipparcos, Gaia] [previous]

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Scientific rationale The GAME implementation concept Outline of talk: Goal of GAME:  to ;  to Quick review of historical / scientific framework

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Scientific rationale of GAME The classical tests on General Relativity Light deflection from spacetime curvature The Dyson - Eddington - Davidson experiment (1919) Current experimental findings on  Cosmological implications of  Science bonus: additional topics Goals: Fundamental physics; cosmology; astrophysics

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Perihelion precession of planetary orbit [Mercury]  Eddington’s parameter  2. Light deflection by massive objects (Sun)  Eddington’s parameter  3. Gravitational redshift / blueshift of light “Modern” tests: Gravitational lensing; Equivalence principle; Time delay of electromagnetic waves (Shapiro effect); Frame dragging tests (Lense-Thirring effect); Gravitational waves; Cosmological tests (cosmic background); … Classical tests of general relativity [Einstein, 1900+]

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Scientific rationale of GAME The classical tests on General Relativity Light deflection from spacetime curvature The Dyson - Eddington - Davidson experiment (1919) Current experimental findings on  Cosmological implications of  Science bonus: additional topics Goals: Fundamental physics; cosmology; astrophysics

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Spacetime curvature around massive objects 1".74 at Solar limb  8.4  rad Light deflection  Apparent variation of star position, related to the gravitational field of the Sun   in Parametrised Post-Newtonian (PPN) formulation G: Newton’s gravitational constant d: distance Sun- observer M: solar mass c: speed of light  : angular distance of the source to the Sun

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Scientific rationale of GAME The classical tests on General Relativity Light deflection from spacetime curvature The Dyson - Eddington - Davidson experiment (1919) Current experimental findings on  Cosmological implications of  Science bonus: additional topics Goals: Fundamental physics; cosmology; astrophysics

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Dyson-Eddington-Davidson experiment (1919) - I First test of General Relativity by light deflection nearby the Sun Epoch (a): unperturbed direction of stars S1, S2 (dashed lines) Epoch (b): apparent direction as seen by observer (dotted line) Real (curved) photon trajectories Moon Negative sample from Eddington's photographs, presented in 1920 paper

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Repeated throughout XX century Precision achieved: ~10% Limiting factors: Need for natural eclipses Atmospheric turbulence Portable instruments Deflection ["]YearAuthors 1.66 ± TMET 1.98 ± Schmeidler 2.17 ± Schmeidler 1.70 ± van Biesbroeck 2.01 ± van Biesbroeck 2.73 ± Mikhailov 2.24 ± Freundlich & al ± Dodwell & al ± Dyson & al. Short exposures, high background Large astrometric noise Limited resolution, collecting area [A. Vecchiato et al., MGM ] Dyson-Eddington-Davidson experiment (1919) - II

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Why is space better than ground? Atmospheric imaging limit without adaptive optics: ~1" [seeing ]  10  degradation of individual location performance Atmospheric coherence length in the visible: ~10"  small differential deflection  100  degradation Astrometric decorrelation noise ~0".1  degraded statistics on stars  10  degradation Atmospheric diffusion of Sun light  increased background  10  100  degradation Measurement performance loss vs. space: 10^5  10^6

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Improvements achievable with adaptive optics Large, state-of-the- art solar telescope equipped with high performance Adaptive Optics Future multi-conjugate AO system AO recovers at most 1-2 orders of magnitude  GAME needs space!

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Scientific rationale of GAME The classical tests on General Relativity Light deflection from spacetime curvature The Dyson - Eddington - Davidson experiment (1919) Current experimental findings on  Cosmological implications of  Science bonus: additional topics Goals: Fundamental physics; cosmology; astrophysics

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Cassini Radio link delay timing,  / ~1e-14 (similarly for Viking, VLBI: Shapiro delay effect, “temporal” component) Current experimental results on  … Hipparcos Different observing conditions: global astrometry, estimate of full sky deflection on survey sample Precision achieved: 2e-5 Earth Sun Cassini [B. Bertotti et al., Nature 2003] Precision achieved: 3e-3

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Scientific rationale of GAME The classical tests on General Relativity Light deflection from spacetime curvature The Dyson - Eddington - Davidson experiment (1919) Current experimental findings on  Cosmological implications of  Science bonus: additional topics Goals: Fundamental physics; cosmology; astrophysics

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Cosmological implications  Dark Matter and Dark Energy: explain experimental data  Alternative explanations: modified gravity theories – e.g. f(R)  Possible check: fit of gravitation theories with observations  Check of modified gravitation theories within Solar System Rationale: replacement in Einsten’s field equations of source terms [new particles] on one side with geometry terms [curvature] on the other side

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI,

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Check of gravitation theories within Solar System Local measurements  cosmological constraints [Capozziello & Troisi 2005] Taking advantage of PPN limit, e.g. for f(R) theories… Alternative formulation: [Capone & Ruggiero 2010]

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Scientific rationale of GAME The classical tests on General Relativity Light deflection from spacetime curvature The Dyson - Eddington - Davidson experiment (1919) Current experimental findings on  Cosmological implications of  Science bonus: additional topics Goals: Fundamental physics; cosmology; astrophysics

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Additional science topics - I Light deflection effects due to oblate and moving giant planets: Jupiter and Saturn Monopole and quadrupole terms of asymmetric mass distribution Close encounters between Jupiter and selected quasars and stars Speed of gravity; link between dynamical reference system and ICRF Mercury’s orbit monitoring Perihelion precession determination  PPN  parameter Fundamental physics experiments in the Solar System  planetary physics

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Additional science topics - II Upper limits on masses of massive planets and brown dwarfs Nearby (d < pc), bright (4 < V < 9) stars, orbital radii 3-7 AU Time resolved photometry on transiting exo-planet systems Constraints on additional companions: mass, period, eccentricity [Sample not conveniently observable by Gaia or Corot] Astrophysics of planet-star transition region

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Additional science topics - III Observation in / through inner part of Solar System NEO orbits and asteroid dynamics (a few close encounters) Circumsolar environment transient phenomena (high resolution corona observations) Monitoring of Solar corona and asteroids

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Additional science topics - IV Complementary GR tests: measurement of  from Mercury orbit Same instrument  cross-calibration

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Mercury observability ~6 periods in 2 year period (dotted line) Orbit region accessible to GAME: <30° to Sun Magnitude / pixel fits GAME dynamic range (scaling exposure time) Performance assessment in progress

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Scientific rationale The GAME implementation concept Outline of talk: Goal of GAME:  to ;  to Description focus on  measurement

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, A space mission in the visible range to achieve long permanent artificial eclipses no atmospheric disturbances, low noise The GAME concept (I) Observer in space with CCD technology

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, The GAME concept (II) Experimental approach: Repeated observation of fields close to the Ecliptic Measurement of angular separation of stars between fields Track separation with epoch  distance to Sun Base Angle of ~4° between Lines of Sight (LOS) N and S

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Mission profile Sun-synchronous orbit, 1500 km elevation  no eclipse Stable solar power supply and thermal environment  instrument structural stability 100% nominal observing time

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, GSCII star counts along ecliptic plane Astrometric performance depends on actual number, brightness and spectral type of observed targets (7’ field) “Gaps” due to - extinction / reddening - removal of “blended” stars Average values

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Observing calendar Convenient observing periods: ~June + December

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Field superposition at high stellar density Field crowding manageable due to > high angular resolution: ~0.1 arcsec > magnitude limit to ~16 mag [visible, wide band]

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Astrometric signature at 2° ecliptic latitude Peak displacement between  2°: 466 mas Largest signature over  10° along the ecliptic, i.e. about  10 days South North

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Observation sequence Fully differential measurement Precision on image location Systematic error control: beam combiner The Fizeau interferometer/coronagraph Elementary astrometric performance Photon limited mission performance Key issues of GAME

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Two-epoch observation sequence (I) Two measurements epochs to modulate deflection on fields F1, F2 (Sun“switched”on/off) Deflection  measurement Calibration fields,   0

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Two-epoch observation sequence (II) Field superposition to ease differential measurement

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Observation sequence Fully differential measurement Precision on image location Systematic error control: beam combiner The Fizeau interferometer/coronagraph Elementary astrometric performance Photon limited mission performance Key issues of GAME

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Fully differential measurement (I) Epoch 1  2: deflection modulation switched between field pairs Epoch 1 Epoch 2

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Star separation variation: deflection  + instrument [base angle] ADDITIVE variations of Base Angle COMPENSATED Fully differential measurement (II) Basic equations referred to stars in Fields 1, 2, 3, 4; Epochs 1, 2 Base Angle  : hardware separation between observing directions

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Fully differential measurement (III) Optical scale variation (in each field) Deflection between fields Different collective effects on field images from instrument evolution (focal length, distortion) deflection (field displacement)  simple calibration of MULTIPLICATIVE terms

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Observation sequence Fully differential measurement Precision on image location Systematic error control: beam combiner The Fizeau interferometer/coronagraph Elementary astrometric performance Photon limited mission performance Key issues of GAME

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Precisionon image location Precision on image location  : Standard deviation of image location : Effective wavelength of observation Signal to Noise Ratio  photons, RON, background N: Number of photons collected  : Instrumental factor of degradation (geometry, sampling, …) X: Root Mean Square size of the aperture Diffraction Statistics [Gai et al., PASP 110, 1998]  can be a small fraction of pixel/image size

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Precisionon image separation Precision on image separation Arc length defined by composition of individual locations x1x1 x2x2 Precision related to Instrument resolution  Pupil size Source magnitude  Exposure time Average on # arcs  Field of view } Observing strategy

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Observation sequence Fully differential measurement Precision on image location Systematic error control: beam combiner The Fizeau interferometer/coronagraph Elementary astrometric performance Photon limited mission performance Key issues of GAME

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Solution: Fizeau-like interferometer Solution: Fizeau-like interferometer + coronagraph Goal: achieve higher resolution through small apertures Fizeau interferometer implemented by Pupil Masking: set of elementary apertures cut on pupil of underlying monolithic telescope  cophasing by alignment Coronagraphic techniques applied to each aperture  replication of individual coronagraphs in phased array Geometry optimised vs. astrometry and background

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Beam distribution (front) N and S stellar beams retained, separated by geometric optics Apodisation Sun photons rejected either at first or second surface

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Beam distribution (rear) Larger beams from opposite-to-Sun (Out-ward) directions  /2 injected into the telescope with acceptable vignetting Secondary mirror + light screen Simultaneous observation: multiplex + systematics rejection

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Imaging performance Monochromatic PSF ( = 600 nm) Polychromatic PSF (T = 6000 K)

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Beam Combination (I) N and S stellar beams folded onto telescope optical axis by beam combiner: Two flat, pierced mirrors set at fixed angle

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Beam Combination (II) Proposed solution: Pierced prism hosting one optical surface and supporting flat mirror e.g. by silicon bonding (LISA) 90  115 mm 2 Zerodur prototype Near-monolithic assembly High dimensional stability over mission lifetime

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Observation sequence Fully differential measurement Precision on image location Systematic error control: beam combiner The Fizeau interferometer/coronagraph Elementary astrometric performance Photon limited mission performance Key issues of GAME

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Bright case: 100 s exposures, close to Sun Background: 15.5 mag per square arcsec Faint case: 500 s exposures, away from Sun Background: 19.5 mag per square arcsec Elementary astrometric performance Band: _0 = 650 nm,  = 120 nm Precision on a 15 mag star: < 1 mas [Gai et al., PASP 110, 1998]

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Observation sequence Fully differential measurement Precision on image location Systematic error control: beam combiner The Fizeau interferometer/coronagraph PSF of the phased array Photon limited mission performance Key issues of GAME

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Scaling and tuning GAME geometry Basic concept can be modified to fit  Experiment “scale”: goal  budget  Engineering / technological constraints  Additional science case requirements Example: small mission / medium mission class Performance factors: ~diameter^2, (field of view)^{3/2}

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Pupil map NS Entrance slit (solid) Output slit (dotted) Optics size: ~0.5  0.7 m Front mask size: ~0.7  0.8 m Small mission version

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Overall layout [Loreggia et al., SPIE 2010] Korsch, 4 mirrors, EFL = m, visibility > 95% over 20  20 arcmin field; distortion < 1e-4 (small mission version)

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Photon limited small mission performance ~1 million 15 mag stars required to achieve 1  as cumulative  2e-6 equivalent precision on  Observing time required: days [on average Galactic plane stellar density from GSCII] [Gai et al., SPIE 2009] Observation focused on Galactic centre / anti-centre region: 3e-7 precision on   months over 2 years [Gai et al., COSPAR 2010; Vecchiato et al., COSPAR 2010]

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Medium mission version Pupil map Overall diameter: ~1.5 m Individual diameter: 7 cm Simultaneous observation of 4 Sun- ward + 4 outward fields

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Optical configuration Beam Combiner

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Photon limited medium mission performance 5 years mission: 4e-8 precision on  5e-6 precision on  ESA M3 proposal: Cosmic Visions [not approved!  ] Error budget: photon limit + 30% systematics level reached in one year observation

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Concluding remarks GAME as modern rendition of Dyson, Eddington & Davidson experiment Simple geometry / differential measurement concept Robust rejection of instrumental disturbances Scalable to 10^-7 – 10^-8 precision range Instrument suitable to additional science applications Future steps:  strengthen science case and consortium;  optimise design AND get consensus to implementation

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, GAME OVER READY TO PLAY AGAIN? [Y/N]

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, GAME vs. Gaia Commonality: Use of natural sources (stars) in two (or >2) fields of view Position measurement on CCD images Resolution (image size) ~200 mas GAME peculiarity: Observing instrument in low orbit Payload optimised for  and  measurement Fully differential

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, GAIA:  ~ 2-20 mas Deflection range GAME:  ~ 0.5 arcsec GAME observes sky regions with deflection larger (by ) than that seen by Gaia Minimum correlation among variables

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Sensitivity: amplitude of deflection / angular precision Location V = 15 mag Gaia:  (  ) ~ 300  as  S = 7 ~ 70 GAME:  (  ) ~ 400  as  S = 1250 More than one order of magnitude of improvement Lower number of measurements (stars) required by GAME Lower sensitivity to systematic errors (deflection signal ~0".5, ~ PSF size)

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Sun-ward fields Out-ward fields Vignetting of out-ward beams on both M1 and M2 Vignetting on M2 Vignetting on M1 Beam footprint superposition on M1

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, Coronagraphic + baffling section