High resolution measurements of close binary stars and the Probability Imaging technique

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High resolution measurements of close binary stars and

the Probability Imaging technique

Marcel Carbillet, Claude Aime, E. Aristidi, Gilbert Ricort

To cite this version:

Marcel Carbillet, Claude Aime, E. Aristidi, Gilbert Ricort. High resolution measurements of close binary stars and the Probability Imaging technique. ESO workshop : Science with the VLTI, 1996, Garching, Germany. pp.361. �hal-02480010�

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High resolution measurements of close binary

stars and the Probability Imaging technique

Marcel Carbillet, Claude Aime, Eric Aristidi, and Gilbert Ricort

Departement d'Astrophysique de l'Universite de Nice-Sophia Antipolis URA 709 du CNRS, Parc Valrose, F-06108 Nice cedex 02, France

Abstract. We report in this communicationthe rst experimentalresults in the visible

range obtained by the Probability Imaging technique applied to close binary stars.

Speckle data of the well known binaryDel as well as the newly discovered one Moai1

(Carbillet et al. 1996) are processed. An analysis of the probability density functions, combined with the classical visibility, is used to reconstruct the binary systems.

1 Introduction

An alternative to the computation of moments usualy done in the dierent speckle interferometry techniques is the analysis of the probability density func-tions (pdf) at several points in space in the speckle pattern. This is what

Prob-ability Imaging (PI) does { see Aime (1993). The two-fold pdfP

(2)( 1 ; 2; )

is a function of two random variables of intensity

1 and

2, and a space-lag

. Whatever the value of , the two-fold pdf for a point source has a

symmet-rical structure in

1 and

2; when for

close to the separation vector d, the

two-fold pdf for a binary star has an arrow-head shape with a trend towards a

direction

2of the order of

1, where

is the oriented intensity ratio between

the two components of the binary system, with no ambiguity about their relative position.

2 Gaussian Model

Assuming that the complex amplitude of the wave at the focus of a large tele-scope is a circular Gaussian process, the two-fold pdf of a binary star can be expressed as the product between the two-fold pdf of a point source and a

func-tion Q(

1 ;

2) containing all the information about

. The value of can be

then easily retrieved doing a simple radial integration ofQ.

3 Application

In practice, theQfunction is obtained by dividing the two-fold pdf of the binary

star by the point-source one. If the oriented intensity ratio is not close to 1,

one can computeQ Q

T, where

Q

T is the transpose quantity of

Q. The radial

integration gives thenas well as

1

. Otherwise, if

is close to 1, one only has

to compute the radial integration ofQ, sinceQ Q

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2 Marcel Carbillet, Claude Aime, Eric Aristidi, and Gilbert Ricort

The data processed here were obtained in the red (=650nm) using a

speck-legraph developed by the Aperture Synthesis group of the Observatoire Midi-Pyrenees, and coupled with an intensied CCD video camera and an acquisition system. This instrumentation was set at the Cassegrain focus of the 2m Bernard Lyot telescope of the PicduMidi, France. The complete procedure to obtain the

relevant parametersd,andPA(position angle) uses both the classical visibility

function and the Q function, as shown in Figure1.

28 30 32 34 36 38 200 400 600 800 -15 -10 -5 5 10 15 0 10 20 30 40 50 60 70 80 90 100 110 120 0 128 010 20 30 40 50 6070 80 90 100 110 120 0 128 mR = 6

Observers: E. Aristidi, Y. Bresson, M. Carbillet, B. Lopez - Date: 12/12/1995 ∆t = 20 ms 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 16 0 123 456 789 10 11 12 13 14 15 16 0 16 Q(Ω1,Ω2) ΩQ ( θ ) θ (deg) 20 30 40 50 60 70 => ρ = 0"110+-0"005 Moai 1 • => intensity ratio: α = 1.00+ -0.15 • => diff. of magnitudes: δm = 0.00+ -0.15

and: PA = (213+ -1) deg / (33+ -1) deg

θmax= (45+ -4) deg 0 10 20 30 40 50 60 70 80 90 100 110 120 0 128 0 10 20 30 4050 60 70 8090 100 110 120 0 128 => ρ = 0"220 +- 0"005 β Del mR = 3.6 ∆t = 20 ms 0 10 20 30 40 50 60 0 64 0 10 20 30 40 50 60 0 64 [Q-QT_](Ω 1,Ω2)

• => oriented intensity ratio: α = 0.44+ -0.02

• => diff. of magnitudes: δm = 0.90+ -0.05

and: PA = (289+ -1) deg Observers: E. Aristidi, M. Carbillet, J.-L. Prieur - Date: 10/09/19994

θ (deg) ΩQ-Q T ( θ ) 20 40 60 80 θ_max= (24+ -1) deg (SAO 12917)

Fig.1.Square visibility function,Q Q

T (top) or

Q(bottom) function and the

radial integration of it, forDel (top) and Moai1 (bottom).

4 Perspectives

The possibility to avoid the use of a reference star is under examination, using

the two-fold pdf of the double star computed for?d. We also plan to apply

this technique as a routine for our current speckle observations, and especially for Post-Hipparcos late-type binary star ones { see Aristidi et al. (1996).

References

Aime C. (1993): Trends in Opt.Eng.1, 15

Aristidi E., Lopez B., Carbillet M., et al. (1996): this conference

Carbillet M., Lopez B., Aristidi E. et al. (1996): to appear in Astron. Astrophys.