M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, 20111 Gravitation Astrometric Measurement Experiment M. Gai - INAF-Osservatorio Astronomico di Torino

M. Gai - GAME La Thuile, Rencontres de Moriond XLVI, 2011 1

Gravitation Astrometric Measurement Experiment

M. Gai - INAF-Osservatorio Astronomico di Torino

On some Fundamental Physics results achievable through astronomical

techniques…

Goal of GAME: to 10-7-10-8; to 10-5-10-

6


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]


• Scientific rationale

• The GAME implementation concept

Outline of talk:Outline of talk:

Goal of GAME: to 10-7-10-8; to 10-5-10-6

Quick review of historical / scientific framework


Scientific rationale of GAMEScientific 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


1. 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+]











0 1 2 3 4 5 60

0.5

1

1.5

Distance from Sun centre [degs]

De

flect

ion

an

gle

[arc

sec]

cos1

cos11

2

dc

GM

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











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


Repeated throughout XX century

Precision achieved: ~10%

Limiting factors:

• Need for natural eclipses

• Atmospheric turbulence

• Portable instruments

Deflection ["]Year Authors

1.66 ± 0.19 1973TMET

1.98 ± 0.46 1961Schmeidler

2.17 ± 0.34 1959Schmeidler

1.70 ± 0.10 1952van Biesbroeck

2.01 ± 0.27 1947van Biesbroeck

2.73 ± 0.31 1936Mikhailov

2.24 ± 0.10 1929Freundlich & al.

1.77 ± 0.40 1922Dodwell & al.

1.98 ± 0.16 1920Dyson & al.

Short exposures, high background

Large astrometric noise

Limited resolution, collecting area

[A. Vecchiato et al., MGM 11 2006]

Dyson-Eddington-Davidson experiment (1919) - II


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 10100 degradation

Measurement performance loss vs. space: 10^5 10^6


2 4 6 8 10

10-4

10-3

10-2

10-1

100

Angle to Sun centre [deg]

Def

lect

ion

[arc

sec]

Full deflectionDifferential over 10"Differential over 100"

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!











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











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



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…

d

d

RfRf

RfRf

RfRf

Rf PPNRPPN

RPPNR 22

2

"3'2

"'

4

11,

"2'

"1

d

dR

dR

d

d

dRfZf

d

dRff

d

dRfZf

d

dRf

PPNR

PPNR 22

2

"3'2

"'

4

11,

"2'

"

1

Alternative formulation:

[Capone & Ruggiero 2010]











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


Additional science topics - II

Upper limits on masses of massive planets and brown dwarfs

• Nearby (d < 30-50 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


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


Additional science topics - IV

Complementary GR tests:

measurement of from Mercury orbit

Same instrument cross-calibration

22


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


• Scientific rationale

• The GAME implementation concept

Outline of talk:Outline of talk:

Goal of GAME: to 10-7-10-8; to 10-5-10-

6

Description focus on measurement


A space mission in the visible range to achieve

•long permanent artificial eclipses

•no atmospheric disturbances, low noise

The GAME concept (I)The GAME concept (I)

Observer in space with CCD technology


The GAME concept (II)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


Mission profile

Sun-synchronous orbit,

1500 km elevation

no eclipse

Stable solar power supply and thermal environment instrument structural stability

100% nominal observing time


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


Observing calendar

Convenient observing periods: ~June + December


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]


Astrometric signature at 2° ecliptic latitude

Peak displacement between stars @ 2°: 466 mas

Largest signature over 10° along the ecliptic, i.e. about 10 days

South

North


• 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 GAMEKey issues of GAME


Two-epoch observation sequence (I)Two-epoch observation sequence (I)

Two measurements epochs to modulate deflection on fields F1, F2 (Sun“switched”on/off)

Deflection measurement

Calibration fields, 0


Two-epoch observation sequence (II)Two-epoch observation sequence (II)

Field superposition to ease differential measurement











Fully differential measurement (I)Fully differential measurement (I)

Epoch 12: deflection modulation switched between field pairs

Epoch 1

Epoch 2


2;12,12;22;11;21;1 EEFFEFEFEFEF

2;14,31;41;32;42;3 EEFFEFEFEFEF Star separation variation: deflection + instrument [base angle]

ADDITIVE variations of Base Angle COMPENSATED

Fully differential measurement (II)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


Fully differential measurement (III)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











PrecisionPrecision on image on image location location

SNRX

1

4

NSNR

: 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

DiffractionStatistics

[Gai et al., PASP 110, 1998]

can be a small fraction of pixel/image size


PrecisionPrecision on image on image separationseparation

Arc length defined by composition of individual locations

x1 x2

22

12

212 xxxx

Precision related to

Instrument resolution Pupil size

Source magnitude Exposure time

Average on # arcs Field of view }

Observing strategy











Solution: Fizeau-like interferometerSolution: 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


Beam distribution (front)Beam distribution (front)

N and S stellar beams retained, separated by geometric optics

Apodisation

Sun photons rejected either at first or second surface


Beam distribution (rear)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


Imaging performance

Monochromatic PSF ( = 600 nm)

Polychromatic PSF (T = 6000 K)


Beam Combination Beam Combination (I)(I)

N and S stellar beams folded onto telescope optical axis by beam combiner: Two flat, pierced mirrors set at fixed angle


Beam Combination Beam Combination (II)(II)

Proposed solution:

Pierced prism hosting one optical surface and supporting flat mirror e.g. by silicon bonding (LISA)

90115 mm2 Zerodur prototype

Near-monolithic assembly

High dimensional stability over mission lifetime











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]







• PSF of the phased array


Key issues of Key issues of GAMEGAME


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}


Pupil mapPupil map

N S

Entrance slit (solid)

Output slit (dotted)

Optics size: ~0.50.7 m

Front mask size: ~0.70.8 m

Small mission version


Overall Overall layoutlayout

[Loreggia et al., SPIE 2010]

Korsch, 4 mirrors,

EFL = 19.50 m,

visibility > 95% over

2020 arcmin field;

distortion < 1e-4

(small mission version)(small mission version)


Photon limited small mission performance

~1 million 15 mag stars required to achieve 1 as cumulative

2e-6 equivalent precision on

Observing time required: 20 + 20 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 2 + 2 months over 2 years

[Gai et al., COSPAR 2010; Vecchiato et al., COSPAR 2010]


Medium mission version

Pupil mapPupil map

Overall diameter: ~1.5 m

Individual diameter: 7 cm

Simultaneous observation of 4 Sun-ward + 4 outward fields


10:35:08

New lens from CVMACRO:cvnewlens.seq Scale: 0.05 08-Oct-10

471.70 MM

M2

M1

M3

M4

FP

BSM24_OHARA

SF1_SCHOTT

2.7 m

2.0 m

Hole on M1 = 0.7 m

Hole on M3 = 0.4 m

Optical Optical configuratioconfiguratio

nn

Beam Beam CombinerCombiner


Photon limited medium mission performance

5 years mission: 4e-8 precision on 5e-6 precision on

ESA M3 proposal: Cosmic Visions 2015-2025

[not approved! ]

8109.3

Error budget: photon limit + 30% systematics

10-7 level reached in one year observation


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


GAME OVER

READY TO PLAY AGAIN?

[Y/N]


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


0 1 2 3 40

0.5

1

1.5


De

flect

ion

an

gle

[arc

sec]

0 50 100 150

10-2

10-1


De

flect

ion

an

gle

[arc

sec]

GAIA: ~ 2-20 mas

Deflection range

GAME: ~ 0.5 arcsec

GAME observes sky regions with deflection larger (by 10-100) than that seen by Gaia

Minimum correlation among variables


Sensitivity: amplitude of deflection / angular precision

Location precision @ V = 15 mag

Gaia: () ~ 300 as S = 7 ~ 70

GAME: () ~ 400 as S = 1250

More than one order of magnitude of improvement

S

Lower number of measurements (stars) required by GAME

Lower sensitivity to systematic errors (deflection signal ~0".5, ~ PSF size)


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 Beam footprint superposition on M1on M1


Coronagraphic + baffling section

Documents

M. Gai - GAMELa Thuile, Rencontres de Moriond XLVI, 20111 Gravitation Astrometric Measurement Experiment M. Gai - INAF-Osservatorio Astronomico di Torino