Behind the Coronagraphic Mask

Behind the coronagraphic mask

Frantz MartinacheCEAO Research FellowSubaru Telescope Paris, 10/10/29, Spirit of Lyot 2010

A new approach to look for companions in the so-called “super resolution” regime

Take care of an ill-posed problem

I = O ⊗ PSF Eliminate the PSF out of the equation

the ADI way... the exAO way...

Thalman et al, 2009, ApJ, 707, 123 Guyon et al, 2009, PASP, 122, 71

... or use interferometry!

Interferometry produces good observable quantities

1

Φ2-1

Φ3-2

Φ1-3

2

3

Not about producing the best image possible, but

about extractingobservable quantities

(closure-phase) that do not depend on

phase residuals

Φ(2-1) = Φ(2-1)0 + (φ2-φ1)

Φ(3-2) = Φ(3-2)0 + (φ3-φ2)

Φ(1-3) = Φ(1-3)0 + (φ1-φ3)

measured = intrinsic + atmospheric

Σ

Jennison, R. C. 1958, MNRAS, 118, 276

Ditch these dirty images, keep clean information only!

Example of Palomar closure-phase data

40 % strehl0.3 deg scatter

stability ~ λ/1000all passive !

The best “picture” you can give of one or more companions around a star is a series of astrometric data:

separation, PA, contrast with associated uncertainties

A new regime of angular separations

50 100 150 200 250Projected separation (mas)

5.0

5.5

6.0

6.5

L co

ntra

st li

mit

GJ 517

GJ 559.1GJ 617B

HD 108767B

HD 187748

V383 Lac

NIRC2 L’interferogram

powerspectrum

HD 187748

2 3 4 5 6 7Projected separation (AU)

0

20

40

60

80

Com

pani

on m

ass

dete

ctio

n lim

it (M

J)

50 Myr

150 Myr

V383 Lac

2 3 4 5 6Projected separation (AU)

0

20

40

60

80

Com

pani

on m

ass

dete

ctio

n lim

it (M

J) 50 Myr 150 Myr

HD 108767B

2 3 4 5 6Projected separation (AU)

0

20

40

60

80

Com

pani

on m

ass

dete

ctio

n lim

it (M

J)

40 Myr

260 Myr

GJ 617B

0.5 1.0 1.5 2.0 2.5Projected separation (AU)

0

20

40

60

80

Com

pani

on m

ass

dete

ctio

n lim

it (M

J)

100 Myr

1000 Myr

GJ 559.1

2 4 6 8Projected separation (AU)

0

20

40

60

80

Com

pani

on m

ass

dete

ctio

n lim

it (M

J)

20 Myr

120 Myr

GJ 517

1 2 3 4Projected separation (AU)

0

20

40

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80

Com

pani

on m

ass

dete

ctio

n lim

it (M

J)

50 Myr 50 Myr

Martinache et al, in prep

examples of NRM detection limits:

Strengths and limitations of NRM

Self-calibration properties of closure phase make NRM “bullet-proof”

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NRM onboard JWST in the TGS-TFI.

If anything goes wrong with the primary, this might be the only instrument that

will still work

But: it requires a non-redundant pupil.Is there anything comparable we could do

without masking at all?

Sivaramakrishnan et al, Astro2010T, 40

Φ(2-1) = Φ(2-1)0 + (φ2-φ1)Φ(3-2) = Φ(3-2)0 + (φ3-φ2)Φ(1-3) = Φ(1-3)0 + (φ1-φ3)

... ... ... ... ... ...Φ(k-l) = Φ(k-l)0 + (φk-φl)

... ... ... ... ... ...

Matrix form anyone?

A more “general” formalism

Φ Φ0= + φA ×

measured Fourierphase

“true” Fourierphase

transfermatrix

pupilphaseerrors

For a non-redundant array:The transfer matrix is essentially filled with zeroesExcept: per line, one +1, one -1

Closure phase relations are one example of a left-hand operator K, so that KxA produces rows of zeros.

Redundant scenarios

non-redundant

full aperture

Φ = Φ0 + 1 Δφ

Φ = Φ0 + Arg(ejΣi Δφi)

Im

Re

Additionof phasors

BUT: with a reasonably well corrected aperture, this complicated (non sortable) expression can be linearized, and becomes:

Φ = Φ0 + Σi ΔφiOur linear model still holds... just need a slightly more filled transfer matrix.

Determine the HST transfer matrix

0 50 100 150 200 250

0

50

100

150

200

250

discretize the HST pupil0 50 100 150

0

50

100

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NICMOS Image

0 50 100 150

0

50

100

150

(u,v)-plane Ker-phase histogram

-200 -100 0 100 200Ker-phases (degree)

0

10

20

30

40

50

60

70

# in

bin

CalibratorBinary (GJ164)

GJ 164 Ker-phases

-200 -100 0 100 200Kernel-phases (degrees)

-200

-100

0

100

200

Best

fit b

inar

y m

odel

(deg

ree)

corresponding UV coverage

Count the baselines contributing to each

UV pointand fill up a line of A

with -1, 0, 1

A =

... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ...

... 0 +1 -1 ... 0 -1 ...

In this example,A is a rectangular 155 x 366 matrix, manageable on a

netbook

Kernel-phase

Idea: construct a new operator K so that KxA = 0, but how?By hand? Painful, but manageable if not too big...Or use a tool more versatile: Singular Value Decomposition (SVD)

Rows of K form a basis for the left null space of A

The SVD of AT= U x W x VT gives it all: the columns of V that correspond to zero singular values (Wi = 0) do the trick

These new closure-phase relations are called Ker-phases

Martinache, 2010, ApJ, 724, 464

For each frame:Read the Fourier-phase informationAssemble into Ker-phases using the relations identified earlier... Then:do some statistics (frame-to-frame variability), propagate errors... and you’re done!

NIC1 datacube

Data reduction

FT

uv-plane

0 50 100 150

0

50

100

150

NICMOS Image

0 50 100 150

0

50

100

150

(u,v)-plane Ker-phase histogram

-200 -100 0 100 200Ker-phases (degree)

0

10

20

30

40

50

60

70

# in

bin

CalibratorBinary (GJ164)

GJ 164 Ker-phases

-200 -100 0 100 200Kernel-phases (degrees)

-200

-100

0

100

200

Best

fit b

inar

y m

odel

(deg

ree)

NICMOS 1 data analysis

Martinache, 2010, ApJ, 724, 464

- 4 frame dataset on SAO 179809 (1998)- 8 frame dataset on GJ 164 (2004)

Best fit Parameters:Separation: 88.2 masP.A: 100.6 degreescontrast: 9.1

Performance of the approach

Projected probability density function

70 80 90 100Angular sep (mas)

98

100

102

104

Posi

tion

Angl

e (d

eg)

70 80 90 100

98

100

102

104

Projected probability density function

70 80 90 100Angular sep (mas)

4

6

8

10

12

Con

trast

ratio

70 80 90 100

4

6

8

10

12

Projected probability density function

98 100 102 104Position Angle (deg)

4

6

8

10

12

Con

trast

ratio

98 100 102 104

4

6

8

10

12

NICMOS data contrast detection limits

100 150 200 250 300 350Angular separation (mas)

200

400

600

Con

trast

ratio

0.900

0.900 0.900

0.990

0.990

0.999

0.999

Detection Detection limits

Parameters:Separation: 88.2 +/- 3 masP.A: 100.6 +/- 0.3 degreecontrast: 9.1 +/- 1.2

1.1 λ/D

Limits based on MC simulationsfrom errors measured on a dataset acquired on a single star.

Martinache, 2010, ApJ, 724, 464

Concluding remarks

The technique is still at an early stage but is usable today

Moderate contrast detection with good astrometric precision was demonstrated within λ/D

- dozens of NICMOS archive datasets await re-analysis:> new detections in the super-resolution regime> improved detection limits

- new ground based L- and M-band observing programs should also benefit this technique