An general introduction to optical interferometry with science highlights

Antoine Mérand - VLTI programme scientist [email protected] - Office 5.16 Introduction to interferometry - Dec 2019 2 Angular separation

Introduction to interferometry - Dec 2019 3 Diffraction in a telescope

(wave amplitude)

http://en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle

Introduction to interferometry - Dec 2019 4 Point spread function

Point Spread Function of a circular aperture is the so-called Airy pattern. Its first null has an angular radius of 1.22λ/D

Introduction to interferometry - Dec 2019 5 Atmospheric effects Atmospheric turbulence limits angular resolution to ~0.5” in the visible (independent of telescope diameter)

Short exposure / atmospheric turbulence

Introduction to interferometry - Dec 2019 6 Diffraction of partial apperture

"On the Theory of Light and Colours” Thomas Young, 1801

Introduction to interferometry - Dec 2019 7 Young’s double slit experiments a1+b1 – a2+b2: optical path difference In phase: white fringe a1 a2 Ø (a1+b1-a2-b2)%λ = 0 Out of phase: dark fringe

Ø (a1+b1-a2-b2)%λ= λ/2 b1 b2 http://www.falstad.com/ripple/

Introduction to interferometry - Dec 2019 8 Spatial information in fringes �⃗ direction to the object � Optical path difference Ø �⃗. � = B. �in � ≈ ��

Phase of the fringes contains � = �⃗. � information about �⃗ (α) B 1 Fringe corresponds to �⃗. �(≈ α�) = � ⇒ � ≈ �/�

Introduction to interferometry - Dec 2019 9 Object’s geometry affects the phase and amplitude of the fringes

Fringe patterns for each point in the object add up in the focal plane and produce a fringe pattern with reduced contrast and shifted in phase:

Reduced fringes’ contrast ⟺ Object is resolved

Fringes’ phase offset ⟺ Object’s photocentre shift

Introduction to interferometry - Dec 2019 10 Formulation The fringes’ amplitude and phase is called the complex visibility. It is the spatial coherence of the source The complex visibility is the normalized Fourier transform of the image I(x,y,λ): ∬ �(�, �, �)�()/���� � �, �, � = ∬ � �, �, � ���� van Cittert - Zernike theorem Ø Baseline vector � = �, � [same unit as λ] Ø Pointing vector �⃗ = �, � [in rad]

Introduction to interferometry - Dec 2019 11 Telescopes, Interferometers: the same thing?

Telescope Interferometer Low-pass spatial Band-pass spatial coherence filter coherence filter Recombines all Records all frequencies observed frequencies measured separately Image intuitively Data remain in the connects to object coherence space (convolution by PSF) (visibilities)

Introduction to interferometry - Dec 2019 12 Single baseline gives very limited information

Binaries separated by �, 2�, 3�, � … have same visibilities for a given single B Image is 2D and baseline is 1D

� = �⃗. � B

Introduction to interferometry - Dec 2019 13 Centro-symmetric images

For a centro-symmetric image, Fourier transform becomes an Hankel transform:

Case for a uniform disk:

λ=1μm

Introduction to interferometry - Dec 2019 14 Recover the phase information The atmosphere induces phase jitter >> wavelength Sum of phases in a triangle are immune to the turbulence: closure phase

CP = (ɸ12+φa) + ɸ23 + (ɸ31-φa) = ɸ12 + ɸ23 + ɸ31

Introduction to interferometry - Dec 2019 15 Binary star

The Fourier transform is linear:

f2

f1 x y

3 Telescopes with several spectral channels (e.g. VLTI/AMBER) allow to un-ambiguously measure a binary separation and flux ratio.

Kraus+ 2009 The Messenger 136

Introduction to interferometry - Dec 2019 16 B ~ 140m λ ~ 2.2μm λ/B ~ 3mas

Introduction to interferometry - Dec 2019 17 Principles of operations

Coherence length ~ λR Introduction to interferometry - Dec 2019 18 Delay Line

Introduction to interferometry - Dec 2019 19 Telescopes

4 x AT (1.8m) equipped with vis-AO Relocatable: B=8m to B=130m

4 x UT (8.2m) equipped with vis and nir AO

Introduction to interferometry - Dec 2019 20 VLTI instruments (4T) https://www.eso.org/sci/facilities/paranal/instruments.html PIONIER Ø H band (λ~1.6μm), R~50 GRAVITY Ø K band (λ~2.2μm), R~20, 500 and 4000 Ø Fringe tracker (up to 2” off-axis) MATISSE Ø L,M,N bands (λ~3 to 12μm), R~30, 500, 1000 amd 3500 Ø GRAVITY as a fringe tracker (GRA4MAT)

Introduction to interferometry - Dec 2019 21 Spectral capabilities

Eta Car (LBV) GRAVITY spectrum (Gravity Collaboration 2018)

Be Star MATISSE spectrum (Meilland A., priv. comm.)

Introduction to interferometry - Dec 2019 22 Differential visibilities

CO lines in Mira-type star (Wittkowski+ 2018)

Star only (expected)

CO envelop

star Visibility drops in a line -> object is larger

Introduction to interferometry - Dec 2019 23 Differential phases Spectro-interferometry gives complementary information to spectroscopy Fringes’ contrast drops

as object gets resolved spectrum Fringes differential phase follows the photocenter Fringes’s phase

Introduction to interferometry - Dec 2019 24 Differential phase application Measuring the orbital motion of the Broad Line Region in the quasar 3C273 (z=0.158) Knowing the distance, the mass of the central object 8 can be estimated: 2.6±1.1 10 M☉

GRAVITY collaboration, 2019a

Introduction to interferometry - Dec 2019 25 3C273 modeling

GRAVITY collaboration, 2019a

Introduction to interferometry - Dec 2019 26 Beating the diffraction? BLR of 3C-273 found to be 46±10μas λ/B = 2.2μm/140m ~ 3.2mas

GRAVITY collaboration, 2019a

Introduction to interferometry - Dec 2019 27 Beating the diffraction? Differential phase is measured better than 1º 360º of phase corresponds to 1 wavelength Differential phase is measured better than λ/360 Actual resolution for 1º is λ/B/360 ~ 10μas

Introduction to interferometry - Dec 2019 28 Diffraction limit

Definitions for a telescope of 2.44λ/D diameter D: Ø Airy pattern first null at radius 1.22λ/D Ø Aperture is a lowpass (spatial) filter of cutoff λ/D Limitation depends how well you know your PSF Ø Telescopes can achieve astrometry << λ/D in a field Ø … but deconvolution does not work much below λ/D

Introduction to interferometry - Dec 2019 29 Imaging reconstruction In practice, (u,v) plane is sparsly filled Ø n(n-1)/2 baseline, (n-1)(n-2)/2 closure phases Visibility interpolation and regularisation (priors) are needed: Ø Image positivity, edge-preserving smoothness, total variation, maximum entropy, etc. Very useful when morphology is not known a priori Limitations:

Ø Largest to smallest scales: λ/Bmax -> λ/Bmin 2 Ø Number of pixels ~ (Bmax/Bmin) Ø Dynamic range ~ 1/precision on visibility or phase

Introduction to interferometry - Dec 2019 30 Imaging at VLTI

Moveable telescopes in three 4T configurations

Bmin=8m to Bmax=130m → ~16x16 image 6V/3CP per observtions: 8 observations per config

Introduction to interferometry - Dec 2019 31 Some VLTI images

AGB pi1 Gru (Paladini+ 2018) post-AGB IRAS 08544-4431 YHG V766 Cen (Hillen+ 2016) (Wittkowski+ 2017) PIONIER PIONIER PIONIER

RSG Antares CO line (Ohnaka+ 2017) LBV Eta Car, HeI line (GRAVITY Collab 2018)

AMBER & GRAVITY GRAVITY AMBER High mass proto-star IRAS17216-3801 (Kraus+ 2017) 20mas

Introduction to interferometry - Dec 2019 32 Do one always needs imaging? Different approachs: Ø Morphological fit Ø Physics based model (simulation) Additional observables very useful (SED, spectroscopy…)

Synthetic image, visibilities and modeling disks images spectra for a fast rotating star using analytical functions (Domiciano de Souza+ 2018) (Lazareff+ 2017) Introduction to interferometry - Dec 2019 33 Binary star

The Fourier transform is linear:

f2

f1 x y

3 Telescopes with several spectral channels (e.g. VLTI/AMBER) allow to un-ambiguously measure a binary separation and flux ratio.

Kraus+ 2009 The Messenger 136

Introduction to interferometry - Dec 2019 34 Detection of gravitational reddening around Sgr A*

Radial velocity deviation to the apparent orbit:

GRAVITY collaboration, 2018a

Credit: ESO/M. Kornmesser

Introduction to interferometry - Dec 2019 35 Galactic Centre

Resolving a GRAVITY collaboration, 2018a binary in astrometry and radial velocity gives the mass and the distance Best distance and mass to the Galactic Centre

Introduction to interferometry - Dec 2019 36 Detection of LSCO around Sgr A*

GRAVITY collaboration, 2018a GRAVITY collaboration, 2018b

Material falling on the last stable circular orbit around the black hole

Introduction to interferometry - Dec 2019 37 Microlensing

� (Dong+19) �, � (Zang+20)

� = 0.495 ± 0.063 �⨀ � = 429 ± 21 �� � = 19 ± 3 �⊕ ��� = 0.77 ± 0.04 ��

� = and � =

Introduction to interferometry - Dec 2019 38 Spectroscopy and astrometry of exoplanets

100x improvement HR 8799 e VLTI/GRAVITY on astrometry and spectral resolution compared to AO AO b Pic b

GRAVITY Collaboration CO (In preparation) 2.0 2.2 2.4 µm GRAVITY Collaboration+ 2019

Introduction to interferometry - Dec 2019 39 Field of View Interferometers use spatial filters for telescopes: Ø Single mode fibers Ø Trade between loosing flux / high contrast fringes Field-of-view limited to diffraction limit of single telescope

Introduction to interferometry - Dec 2019 40 Field of View In K-band, FoV: 50 mas on UTs, 250 mas on ATs Makes it hard to connect to AO images Ø FoV VLTI ~ pixel AO Can also be turned into an advantage: off-axis attenuation Ø Point your fiber on (faint) Sgr A* / exoplanets Ø (bright) S2 / host stars get attenuated, up to few 100 Ø Bright is reference for faint, even if interferometer lacks dynamix range

Introduction to interferometry - Dec 2019 41 Why Interferometry? Unmatched angular resolution Ø Staying the visibility space allows accurate measurements (astrometry, differential spectra, …) Ø Precision in V allows super resolution, much better than λ/B Limitations: Ø Sensitivity compared to imaging / spectroscopy (but K~19 in the GC or exoplanets, with reference) Ø Dynamic range of few 100 Ø Field of View: diffraction limit of the telescope (UTs~50mas; ATs~250mas in K-band) Ø Image reconstruction requires lots of 4T time Ø Complicated visibility modelling (especially with spectra)

Introduction to interferometry - Dec 2019 42