transparencies - Rencontres de Moriond

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

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

[previous]

GAME:

Gamma

Astrometric

Measurement

Experiment

Space-time curvature parameter



Apparent star position variation

Light deflection close to the Sun

Space mission

Approach: build on flight inheritance from past missions

[SOHO, STEREO, Hipparcos, Gaia]


Outline of talk:

• Scientific rationale

• The GAME implementation concept

Quick review of historical / scientific framework

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


Scientific rationale of GAME

Goals: Fundamental physics; cosmology; astrophysics

• 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


Classical tests of general relativity [Einstein, 1900+]

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);

…




• The classical tests on General Relativity

• Light deflection from spacetime curvature






Spacetime curvature around massive objects

1.5

1".74 at Solar limb



8.4

 rad

G: Newton’s gravitational constant

1  



1

   GM c 2 d

1



1

 cos

 cos

 d: distance Sunobserver

M: solar mass

0.5

c: speed of light



: angular distance of the source to the Sun

0

0 1 2 3 4

Distance from Sun centre [degs]

5 6

Light deflection



Apparent variation of star position, related

 to the gravitational field of the Sun

 in Parametrised Post-Newtonian (PPN) formulation






• The Dyson - Eddington - Davidson experiment (1919)





Dyson-Eddington-Davidson experiment (1919) - I

Moon

Real (curved) photon trajectories

Negative sample from

Eddington's photographs, presented in 1920 paper

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)


Dyson-Eddington-Davidson experiment (1919) - II

Repeated throughout

XX century

Precision achieved:

~10%

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

Authors

Dyson & al.

Dodwell & al.

Freundlich & al.

Mikhailov van Biesbroeck van Biesbroeck

Schmeidler

Schmeidler

TMET

Year

1920

1922

1929

1936

1947

1952

1959

1961

1973

Deflection ["]

1.98 ± 0.16

1.77 ± 0.40

2.24 ± 0.10

2.73 ± 0.31

2.01 ± 0.27

1.70 ± 0.10

2.17 ± 0.34

1.98 ± 0.46

1.66 ± 0.19

Limiting factors:

• Need for natural eclipses

• Atmospheric turbulence

•

Portable instruments

Short exposures, high background

Large astrometric noise

Limited resolution, collecting area


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


Improvements achievable with adaptive optics

10

0

10

-1

10

-2

Full deflection

Differential over 10"

Differential over 100"

Future multi-conjugate AO system

AO recovers at most 1-2 orders of magnitude



GAME needs space!

10

-3

10

-4

2 4 6

Angle to Sun centre [deg]

8 10

Large, state-of-theart solar telescope equipped with high performance

Adaptive Optics







•

Current experimental findings on






Current experimental results on  …

Hipparcos

Earth Different observing conditions: global astrometry , estimate of full sky deflection on survey sample

Sun

Precision achieved: 3e-3

Cassini

Radio link delay timing,



/



~1e-14

(similarly for Viking, VLBI: Shapiro delay effect, “temporal” component)

[B. Bertotti et al., Nature 2003]

Cassini

Precision achieved: 2e-5








•

Cosmological implications of





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

Taking advantage of PPN limit, e.g. for f(R) theories…



PPN

R



1

 f '



  f



"

2

  f "

2

 

2

,



R

PPN 

1



1

4





2 f f

'

'

 

 





3 f f

"

"

 

 

2

 d



PPN

R d







[Capozziello & Troisi 2005]

Alternative formulation:



PPN

R



1







 f " dR d







2

Zf '



2



 f " dR d







2

,



R

PPN 

1



1

4













2 Zf f '



'



3



 f " f " dR d

 dR d







2

 d

 dR

 dR d















[Capone & Ruggiero 2010]

Local measurements

 cosmological constraints









•

Science bonus: additional topics


Additional science topics - I

Fundamental physics experiments in the Solar System

 planetary physics

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


Additional science topics - II

Astrophysics of planet-star transition region

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]


Additional science topics - III

Monitoring of Solar corona and asteroids

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)


Additional science topics - IV

Complementary

GR tests: measurement of

 from Mercury orbit

2



2

  

Same instrument

 cross-calibration


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


Outline of talk:

• Scientific rationale

• The GAME implementation concept

Description focus on

 measurement

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


The GAME concept (I)

Observer in space with CCD technology

A space mission in the visible range to achieve

• long permanent artificial eclipses

• no atmospheric disturbances, low noise


The GAME concept (II)

Base Angle of ~4° between

Lines of Sight (LOS) N and S

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


M. Gai - GAME

Mission profile

Sun-synchronous orbit,

1500 km elevation

 no eclipse

100% nominal observing time

Stable solar power supply and thermal environment

 instrument structural stability

La Thuile, Rencontres de Moriond XLVI, 2011 28

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

South

North

Peak displacement between stars @



2°:

466 mas

Largest signature over



10° along the ecliptic, i.e. about



10 days


Key issues of GAME

•

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


Two-epoch observation sequence (I)

Deflection  measurement

Calibration fields,   0

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


Two-epoch observation sequence (II)

Field superposition to ease differential measurement



•

Observation sequence

• Fully differential measurement

•




•


•



Fully differential measurement (I)

Epoch 1

Epoch 1



2: deflection modulation switched between field pairs

Epoch 2


Fully differential measurement (II)

Basic equations referred to stars in Fields 1, 2, 3, 4; Epochs 1, 2



 

F 1 ; E 1

 

F 2 ; E 1

 





 

F 1 ; E 2

 

F 2 ; E 2

 

  

F 1 , F 2



   

E 1 ; E 2





Star separation variation: deflection

 

F 3 ; E 2

 

F 4 ; E 2

 



  

F 3 ; E 1

 

F 4 ;



+ instrument [base angle]

E 1

 

  

F 3 , F 4



   

E 1 ; E 2



ADDITIVE variations of Base Angle COMPENSATED

M. Gai - GAME

Base Angle



: hardware separation between observing directions


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



•



•

Precision on image location



•


•



Precision on image location

  

4





X



1

SNR



: Standard deviation of image location



: Effective wavelength of observation

Statistics

Diffraction

X: Root Mean Square size of the aperture

Signal to Noise Ratio

 photons, RON, background

N: Number of photons collected

SNR



N

>1 : Instrumental factor of degradation (geometry, sampling, …)

 can be a small fraction of pixel/image size

[Gai et al., PASP 110, 1998]


Precision on image separation x

1

Arc length defined by composition of individual locations



2 x

2

 x

1

 x

2



 

2

 

1

 

2

 

2

Precision related to



Instrument resolution

 Source magnitude

 Average on # arcs



Pupil size



Exposure time }



Field of view

Observing strategy



•



•



• The Fizeau interferometer/coronagraph

•


•



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


Beam distribution (front)

N and S stellar beams retained, separated by geometric optics

Sun photons rejected either at first or second surface

M. Gai - GAME

Apodisation


Beam distribution (rear)

Secondary mirror + light screen

Larger beams from opposite-to-Sun (Out-ward) directions



/2 injected into the telescope with acceptable vignetting

Simultaneous observation: multiplex + systematics rejection


Imaging performance

Monochromatic PSF

(



= 600 nm)

Polychromatic PSF

(T = 6000 K)


Beam Combination (I)

M. Gai - GAME

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


Beam Combination (II)

Proposed solution:

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

M. Gai - GAME

Near-monolithic assembly

High dimensional stability over mission lifetime

90



115 mm 2 Zerodur prototype



•



•




•

Elementary astrometric performance

•



Elementary astrometric performance

Precision on a

15 mag star:

< 1 mas

[Gai et al., PASP 110, 1998]

Band :



_0 = 650 nm,



= 120 nm

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



•



•




• PSF of the phased array

•

Photon limited mission performance


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}


Small mission version

Pupil map

N S

Entrance slit (solid)

Output slit (dotted)

Optics size: ~0.5



0.7 m

Front mask size: ~0.7



0.8 m


Overall layout

(small mission version)

Korsch, 4 mirrors,

EFL = 19.50 m, visibility > 95% over

20



20 arcmin field; distortion < 1e-4

[Loreggia et al., SPIE 2010]


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

[Gai et al., SPIE 2009]

[on average Galactic plane stellar density from GSCII]

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 map

Overall diameter: ~1.5 m

Individual diameter: 7 cm

Simultaneous observation of 4 Sunward + 4 outward fields


10:35:08

Hole on M1 = 0.7 m

Hole on M3 = 0.4 m

Beam

Combiner

M1

M2

Optical configuration

FP

SF1_SCHOTT

BSM24_OHARA

M3

2.0 m M4 471.70 MM


Photon limited medium mission performance

Error budget: photon limit + 30% systematics

10 -7 level reached in one year observation

5 years mission:







ESA M3 proposal:

Cosmic Visions

2015-2025

[not approved!



]







3 .

9



10



8


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 - GAME

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


1.5

Deflection range

1

GAME:

 

~ 0.5 arcsec

0.5

GAIA:



~ 2-20 mas

0

0 1 2 3


4

GAME observes sky regions with deflection

10

-1 larger (by 10-100) than that seen by Gaia

10

-2

Minimum correlation among variables

M. Gai - GAME

0 50 100



150

Sensitivity: amplitude of deflection / angular precision

Location precision @ V = 15 mag

S







 

Gaia:

GAME:



(



) ~ 300

 as



S = 7 ~ 70



(



) ~ 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)


Beam footprint superposition on M1

Sun-ward fields

Out-ward fields

Vignetting on M2

M. Gai - GAME

Vignetting of out-ward beams on both M1 and M2

Vignetting on M1


Coronagraphic + baffling section


transparencies - Rencontres de Moriond

Gravitation Astrometric

Measurement Experiment

GAME:

Gamma

Astrometric

Measurement

Experiment

READY TO PLAY

AGAIN? [Y/N]

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Measurement Experiment

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Astrometric

Measurement

Experiment

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