basic! introduction to radio/submm interferometry

2014 La Serena School for Data Science Sebastian Perez @ MAD / Universidad de Chile lecture overview ! 1) a bit of HISTORY: radio astronomy / interferometry 2) motivation - why interferometry? 3) basics: interferometers / visibilities / uv-plane 4) imaging 5) deconvolution 6) power of interferometry via 2 cool examples

La Serena School for Data Science / August 2014 For thousands of years human observation of the Universe was limited to the visible spectrum

Until….. Karl Jansky’s serendipitous discovery an engineer of Bell Laboratories, investigating static that interfered with short wave transatlantic voice transmissions. Using a large directional antenna, Jansky noticed that his analog pen-and-paper recording system kept recording a repeating signal of unknown origin. Since the signal peaked about every 24 hours, Jansky originally suspected the source of the interference was the Sun crossing the view of his directional antenna.

Motivation: why interferometry? ! answer: all has to do with diffraction which is the limiting resolution of your telescope. ! ✓ ! ang res ⇡ D ! largest fully steerable radio dish: GBT with 100m dish

$theta = (21e-2/100) * 206265 / 60 = 7.2 arcminutes :(

to reach 1 arc sec resolution you need a 42 km aperture!!

La Serena School for Data Science / August 2014 studied radio signals emanating from the Sun ! ! built the first multi-element astronomical radio interferometer in 1946. ! production of a number of important radio source catalogues, including the Third Cambridge (3C) Catalogue, which helped lead to the discovery of the first .!

La Serena School for Data Science / August 2014 Motivation: why interferometry? ! there is a need to develop a better technique than just building larger and larger antennas.. ! for an interferometer, resolution is given by

✓ang res $theta = (21e-2/100e3) * 206265 ⇡ B = 0.4 arcsec :)

Aperture synthesis: methodology of synthesising a continuous aperture through summation of separated pairs of antennas.

La Serena School for Data Science / August 2014 The Essential Books NRAO Synthesis Imaging Workshop in Socorro (VLA) every two years

La Serena School for Data Science / August 2014 Interferometers: the basics ALMA • Interferometry: a method to ‘synthesize’ a large aperture by combining signals collected by separated small apertures • An Interferometer measures the interference pattern produced by two apertures, which is related to the source brightness. • The signals from all antennas are correlated, taking into account the distance (baseline) and time delay between pairs of antennas

b stolen from: Nuria Marcelino ALMA ES Proposal Preparation Tutorial Charlottesville, April 26, 2011 5 North American ALMA Science Center two-element interferometer

the most basic interferometer seeks a relation between the the product of the voltages from two separated antennas and the distribution of the brightness of the originating source on the sky

La Serena School for Data Science / August 2014 2.Visibility data C (⌫)= E (~r )E (~r ) 12 h ⌫ 1 ⌫ 2 i Calibration

dxdy V⌫ (~u)= I⌫ (~x)A⌫ (~x)exp[ 2⇡i(~x ~u)] 1 x2 y2 · ZZ p primary beam ~ s ~u = B12/ Sky image

from S. Casassus’ lecture

Escuela de FormaciónLa Serena Planetaria School / for20 Data- 22 Marzo Science 2013 / August / MAD 2014 - Universidad de Chile Visibilities • each V(u,v) contains information on T(l,m) everywhere, not just at a given (l,m) coordinate or within a particular subregion

• each V(u,v) is a complex quantity – expressed as (real, imaginary) or (amplitude, phase)

T(l,m) V(u,v) amplitude V(u,v) phase

6 Fourier transforms are at the heart of interferometry

Jean Baptiste Joseph Fourier FT relationships

scaling

shifting convolution/ ! multiplication !

Thompson, Moran & Swenson (2001) Example 2D Fourier Transforms T(l,m) V(u,v) amplitude

δ function constant

ellipticalGaussian ellipticalGaussian Gaussian Gaussian

narrow features transform into wide features (and vice-versa) stolen from: David Wilner

7 Example 2D Fourier Transforms T(l,m) V(u,v) amplitude

uniform Bessel disk function

sharp edges result in many high spatial frequencies stolen from: David Wilner

8 Amplitude and Phase • amplitude tells “how much” of a certain spatial frequency • phase tells “where” this spatial frequency component is located T(l,m) V(u,v) amplitude V(u,v) phase

stolen from: David Wilner

9 The Visibility Concept

• visibility as a function of baseline coordinates (u,v) is the Fourier transform of the sky brightness distribution as a function of the sky coordinates (l,m)

• V(u=0,v=0) is the integral of T(l,m)dldm = total flux density

• since T(l,m) is real, V(-u,-v) = V*(u,v) – V(u,v) is Hermitian – get two visibilities for one measurement

stolen from: David Wilner 10 The Visibility Concept

stolen from: David Wilner 11 The Visibility Concept

stolen from: David Wilner 12 The Visibility Concept

stolen from: David Wilner 13 The Visibility Concept

14 stolen from: David Wilner The Visibility Concept

stolen from: David Wilner 15 The Visibility Concept

stolen from: David Wilner 16 Inner and Outer (u,v) Boundaries

V(u,v) amplitude V(u,v) phase T(l,m)

V(u,v) amplitude V(u,v) phase T(l,m)

24 2.Visibility data C (⌫)= E (~r )E (~r ) 12 h ⌫ 1 ⌫ 2 i Calibration

dxdy V⌫ (~u)= I⌫ (~x)A⌫ (~x)exp[ 2⇡i(~x ~u)] 1 x2 y2 · ZZ p primary beam ~ s ~u = B12/ Sky image

from S. Casassus’ lecture

Escuela de FormaciónLa Serena Planetaria School / for20 Data- 22 Marzo Science 2013 / August / MAD 2014 - Universidad de Chile Aperture Synthesis Basics

• idea: sample V(u,v) at enough (u,v) points using distributed small aperture

antennas to synthesize a large aperture antenna of size (umax,vmax)

• one pair of antennas = one baseline = two (u,v) samples at a time • N antennas = N(N-1) samples at a time • use rotation to fill in (u,v) plane over time (Sir Martin Ryle, 1974 Nobel Prize in Physics) Sir Martin Ryle 1918-1984 • reconfigure physical layout of N antennas for more samples • observe at multiple wavelengths for (u,v) plane coverage, for source spectra amenable to simple characterization (“multi-frequency synthesis”)

• if source is variable, then be careful

stolen from: David Wilner 17 Two ingredients to get an interferometric image

You need two things...

1 2 Fourier Transform & Deconvolution

(actually, there’s a bit more to it than this, but time is short and so are attention spans)

stolen from: Katherine Blundell Synthesis imaging in a nutshell

The uv-plane sampling function The Fourier Transform of The recovered the true sky brightness ‘dirty’ image distribution

ID(x,y) ⇔ S(u,v) × I(u,v) ⎧ ⎨ ⎩ ⎧ ⎨ ⎩ ⎥ ⎥ ⎥ ⎥ Image plane Fourier plane

A Fourier transform

stolen from: Katherine Blundell Synthesis imaging in a nutshell

FT of the uv-plane sampling function The true sky brightness The recovered distribution ‘dirty’ image (what we want!)

ID(x,y) = Beam ⊗ I(x,y) ⎧ ⎨ ⎩ ⎧ ⎨ ⎩ What we need to Image plane deconvolve

stolen from: Katherine Blundell Examples of Aperture Synthesis Telescopes (for Millimeter Wavelengths)

Jansky VLA SMA

ATCA IRAM PdBI

ALMA CARMA

18 The separation of the VLA antennas is altered every ~4 months. Most extended: A Most compact: D stolen from: Katherine Blundell Dirty Beam Shape and N Antennas

2 Antennas

stolen from: Katherine Blundell 35 Dirty Beam Shape and N Antennas

3 Antennas

stolen from: Katherine Blundell 36 Dirty Beam Shape and N Antennas

4 Antennas

stolen from: Katherine Blundell 37 Dirty Beam Shape and N Antennas

5 Antennas

stolen from: Katherine Blundell 38 Dirty Beam Shape and N Antennas

6 Antennas

stolen from: Katherine Blundell 39 Dirty Beam Shape and N Antennas

7 Antennas

stolen from: Katherine Blundell 40 Dirty Beam Shape and N Antennas

8 Antennas

stolen from: Katherine Blundell 41 Dirty Beam Shape and Super Synthesis

8 Antennas x 2 samples

stolen from: Katherine Blundell 42 Dirty Beam Shape and Super Synthesis

8 Antennas x 6 samples

stolen from: Katherine Blundell 43 Dirty Beam Shape and Super Synthesis

8 Antennas x 30 samples

stolen from: Katherine Blundell 44 Dirty Beam Shape and Super Synthesis

8 Antennas x 107 samples

stolen from: Katherine Blundell 45 Deconvolution Algorithms • an active research area, e.g. compressive sensing methods

• clean: dominant deconvolution algorithm in radio astronomy – a priori assumption: T(l,m) is a collection of point sources – fit and subtract the synthesized beam iteratively – original version by Högbom (1974) purely image based – variants developed for higher computational efficiency, model visibility subtraction, to deal better with extended emission structure, etc.

• maximum entropy: a rarely used alternative – a priori assumption: T(l,m) is smooth and positive – define “smoothness” via a mathematical expression for entropy, e.g. Gull and Skilling (1983), find smoothest image consistent with data – vast literature about the deep meaning of entropy as information content

46 50 Aperture synthesis or synthesis imaging is a type of Interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection.

Observations from the Earth's surface are limited to wavelengths that can pass through the atmosphere. At low frequencies, limited by the ionosphere, which reflects waves with frequencies less than its characteristic frequency. ! Higher frequencies (eg. sub-mm), water vapor is the limiting factor.

La Serena School for Data Science / August 2014 A whole spectrum of radiation! Figure 5: The flags of 20 nations fly over the plaza at the OSF, representing the ALMA partnership. (Credit: J. Di Francesco)

ALMA, an international astronomy facility, is a partnership of Europe, North America and East Asia in cooperation with the Republic of Chile. ALMA is funded in Europe by the European Organization for Astro- nomical Research in the Southern Hemisphere (ESO), in North America by the U.S. National Science Foundation (NSF) in cooperation with the National Research Council of Canada (NRC) and the National Science Council of Taiwan (NSC), and in East Asia by the National Institutes of Natural Sciences (NINS) of Japan in cooperation with the Academia Sinica (AS) in Taiwan. ALMA construction and operations are led on behalf of Europe by ESO, on behalf of North America by the National Radio Astronomy Observatory (NRAO), which is managed by Associ- ated Universities, Inc. (AUI) and on behalf of East Asia by the National Astronomical Observatory of Japan (NAOJ). The Joint ALMA Observa- tory (JAO) provides the unified leadership and management of the con- struction, commissioning, and operation of ALMA.

Array operations are the responsibility of the Joint ALMA Observa- tory (JAO). The telescope array itself is located at the Array Operations Site (AOS) at an elevation of Curves showing5000m. Due the to the transparency limited oxygen at this elevation, of the the atmosphere array is operated from the Operations Support Facility (OSF) at an elevation of 2900 m, with trips to the AOS to install, retrieve, or move equipment and above the ALMAantennas. OSF site site facilitiesas a includefunction the array ofcontrol frequency. room, offices, labs, staff residences, and a contractor camp. The OSF is where ongoing opera- tions, maintenance, and repairs of ALMA antennas and receivers take place. The JAO has a central office in Santiago. The interface between the ob- servatory and the astronomical com- munity is through the ALMA Regional Centers.

Figure 6: Curves showing the transparency of the atmosphere above the ALMA site as a func- tion of frequency. Plotted in blue and black are the transparency values for the 50th and 12.5th percentile conditions respectively averaged over the year. This means that 50% of the time the sky transparency is better than shown in the blue line (corresponding to a precipitable water vapour (PWV) of 1.3 mm), and 1/8 of the time is better than the black line (transparency at 0.5 mm of PWV). The horizontal lines represent the frequency coverage of the ALMA receiver bands. Bands 3, 4, 6, 7, 8 and 9 are available on all an- tennas in Cycle 2. Plots such as this one can be generated via the Science Portal (under “About” -> “Atmosphere Model”) for any fre- quency range and value of water vapor. 4 La Serena School for Data Science / August 2014 ALMA Fiction ALMA - FACT / Chajnantor at 5100 mts ALMA - Chajnantor at 5100 mts Copyright; NatGeo 16 km! telescope

ALMA - Chajnantor at 5100 mts Copyright; NatGeo 16 km! telescope

ALMA - Chajnantor at 5100 mts Copyright; NatGeo The Correlator, ALMA’s central computer, is located in ALMA’s Operations Center on the Chajnantor Plateau. It receives, processes and stores the information sent by the back end.

The Correlator is ALMA’s brain. Here, the data collected by the antennas is processed at a rate of thousands of millions of times per second.

You would need over 3 million laptop computers to carry out the same number of operations per second.

This colossal machine is the world’s most powerful calculator and has been designed especially for ALMA.

The Correlator, ALMA’s central computer, 2009. Credit: ALMA (ESO/NAOJ/NRAO), S. Argandoña.

La Serena School for Data Science / August 2014 2 cool examples: ! HD 142527 - Protoplanetary Disk SS 433 - Stellar Mass (famous) !

La Serena School for Data Science / August 2014 RESEARCH LETTER RESEARCH LETTER

ALMA’s00 view0.1 / HD142527 0.2 0.300 0.1 0.2 0.3 210–1–2210–1–2 2 2 2 2 aba aba CO CO

1 1 1 1

0 0 0 0

–1 –1 –1 –1

–2 Continuum –2 Continuum –2 –2

2 2 2 2 cdcd

Casassus et al. 2013 1 1 1 1 Angular position north (arcsec) Angular position north (arcsec)

0 0 0 0

–1 –1 –1 –1

–2 2 μm –2 2 μm HCO+ HCO+–2 –2

210 –1–2210210 –1–2210–1 –2 –1 –2 Angular position east (arcsec) Angular position east (arcsec) Figure 1 | ALMA observations of HDFigure 142527, 1 with| ALMA a horseshoe observations dust of HD 142527,Supplementary with a horseshoe Fig. 1 for dust an overlay withSupplementary the continuum. Fig.d 1,HCO for an1(4–3) overlay line with the continuum. d,HCO1(4–3) line continuum surrounding a gap that stillcontinuum contains gas. surroundingWe see diffuse a gap CO that gas still containsintensity gas. shownWe by see white diffuse contours CO gas at fractionsintensity of shown 0.1, 0.3, by 0.5, white 0.75 contours and at fractions of 0.1, 0.3, 0.5, 0.75 and in Keplerian rotation (coded in Doppler-shiftedin Keplerian colours), rotation and (coded filamentary in Doppler-shifted0.95 of colours), the peak and intensity filamentary value, 0.40 30.9510220 ofW the per peak beam, intensity overlaid value, on a0.40 3 10220 W per beam, overlaid on a emission in HCO1, with non-Keplerianemission flows near in HCO the star1, with (comparison non-Keplerian flowsred–green–blue near the star image (comparison of HCO1 intensityred–green–blue summed in three image different of HCO colour1 intensity summed in three different colour models illustrative of Keplerian rotationmodels are shown illustrative in Supplementary of Keplerian rotation arebands shown (see in Supplementary Supplementary Fig. 8 for definitions).bands (see Insets Supplementary show magnified Fig. 8 for views definitions). Insets show magnified views Information). The near-infrared emissionInformation). abuts the inner The rim near-infrared of the horseshoe- emission abutsof the the central inner features rim of the that horseshoe- cross the dustof gap. the The central cross features indicates that the cross star the at dustthe gap. The cross indicates the star at the shaped outer disk. The star is at the originshaped of the outer coordinates. disk. The North star is is at up the and originorigin, of the coordinates. with a precision North of is 0.05 up arcsec, and andorigin, the with arrows a precision point at the of 0.05 filaments. arcsec, and the arrows point at the filaments. east is to the left. a, Continuum at 345 GHz,east is with to the specific left. a, intensity Continuum units at in 345 GHz,Inset with to specifica: same intensity as in a, with units a in narrow exponentialInset to a: same scale as highlighting in a, with a the narrow exponential scale highlighting the Janskys per beam. It is shown on an exponentialJanskys per scale beam. (colour It is shown scale). A on beam an exponentialgap-crossing scale (colour filaments. scale). These A beam features appeargap-crossing to grow filaments. from the These eastern features and appear to grow from the eastern and ellipse is shown in the bottom right of b,ellipse and contours is shown are in drawn the bottom at 0.01, right 0.1, of 0.3,b, andwestern contours sides are ofdrawn the horseshoe. at 0.01, 0.1, Contours 0.3, western are at sides 0.0015 of and the horseshoe. 0.005 Janskys Contours per are at 0.0015 and 0.005 Janskys per 0.5, 0.75 and 0.9 times the peak value. The0.5, noise 0.75 level and 0.9 is 1 timess 5 0.5 the mJy peak per value. beam. The noisebeam. level Inset is to1sd5: deconvolved0.5 mJy per beam. models (Supplementarybeam. Inset to d Information): deconvolved of models the (Supplementary Information) of the b, CO(3–2) line intensity shown by whiteb, CO(3–2) contours lineat fractions intensity of shown 0.3, 0.5, by 0.75 white contoursHCO1 emission at fractions (green) of 0.3, at velocities 0.5, 0.75 whereHCO the1 gap-crossingemission (green) filaments at velocities are seen, where the gap-crossing filaments are seen, and 0.95 of the peak intensity value, 2.325and3 0.9510220 ofW the per peak beam. intensity The underlying value, 2.325 3that102 is,20 W from per 3.2 beam. to 4.3 The km underlying s21. Intensitythat maps is, from for the 3.2 blue to 4.3 and km red s2 velocity1. Intensity maps for the blue and red velocity red–green–blue image also shows CO(3–2)red–green–blue line intensity, image but also integrated shows in CO(3–2)ranges line intensity, (see Supplementary but integrated Fig. in 8 for definitions)ranges (see are Supplementary shown in contours, Fig. 8 for with definitions) are shown in contours, with three different velocity bands, whose velocitythree different limits are velocity indicated bands, in the whose spectra velocitylevels limits at 0.5 are and indicated 0.95 times in the the spectra peak values.levels These at 0.5 red and and 0.95 blue times contours the peak are values. an These red and blue contours are an of Supplementary Fig. 8. c, Near-infraredof Supplementary image from Gemini Fig. 8. thatc, Near-infrared traces imagealternative from way Gemini to present that traces the intensityalternative field shown way in d to, but present deconvolved the intensity for field shown in d, but deconvolved for reflected stellar light, shown on a linearreflected scale. We stellar applied light, a circular shown on intensity a linear scale.ease We of visualization. applied a circular intensity ease of visualization. mask to the stellar glare, some of whichmask immediately to the stellar surrounds glare, some the mask. of which See immediately surrounds the mask. See and at a position angle orthogonal toand that at expected a position from angle close-in orthogonal high- to thatemission. expected Indeed, from theclose-in CO 4.67- high-mmemission. emission seen Indeed, in the the inner CO 4.67- disk26mmis emission seen in the inner disk26 is velocity material in Keplerian rotation.velocity Very material blueshifted in Keplerian emission rotation.purely Very Keplerian, blueshifted it does emission not bear thepurely signature Keplerian, of the it disk does winds not bear seen the signature of the disk winds seen could reach out to 0.2 arcsec fromcould the star reach (channel out to at 0.22 arcsec2.4 km from s21 thein star other (channel systems at and22.4 its km orientation s21 in is other the same systems as andthat its of the orientation outer is the same as that of the outer in Supplementary Fig. 2, taking intoin account Supplementary the beam). Fig. A 2, blueshifted taking into accountdisk. An the orthogonal beam). A blueshifted inner disk candisk. also An be discounted orthogonal on inner dynamical disk can also be discounted on dynamical CO(3–2) high-velocity componentCO(3–2) can also be high-velocity seen at the componentbase of this cangrounds also be (Supplementary seen at the base of Information, this grounds section (Supplementary 3). Information, section 3). feature, near the star (at 22.1 km sfeature,21 in Supplementary near the star (at Fig.2 5).2.1 km s21 inIt Supplementary is natural to Fig. interpret 5). the filamentsIt is natural as planet-induced to interpret gap- the filaments as planet-induced gap- The non-Keplerian HCO1 is probablyThe not non-Keplerian consistent with HCO a central1 is probablycrossing not consistent accretion with flows, a central or ‘bridges’.crossing Because accretion the eastern flows, side or ‘bridges’. is the Because the eastern side is the outflow. Stellar outflows are not observedoutflow.27 in Stellar disks outflows with inner are cavities not observedfar27 side,in disks the blueshifted with inner part cavities of thefar eastern side, bridge the blueshifted is directed part towards of the eastern bridge is directed towards and no molecular envelopes (that is,and transition no molecular disks). envelopes For an outflow (that is, transitionthe star and disks). is a Forhigh-velocity an outflow terminationthe star and of the is accretiona high-velocity flow onto termination of the accretion flow onto orientation, the low velocities measuredorientation, by the the lines low imply velocities that measured the the inner by the disk. lines These imply bridges that the are predictedthe inner by disk. hydrodynamical These bridges simula- are predicted by hydrodynamical simula- filaments in HD 142527 would standfilaments still and in HD hover 142527 above would the star standtions still when and hover applied above to planet-formation the star tions feedback when applied in HD to 142527 planet-formation (ref. 7). feedback in HD 142527 (ref. 7). (Supplementary Information, section(Supplementary 3). Even the Information,blueshifted emis- sectionIn 3). these Even simulations, the blueshifted the bridges emis- straddleIn these the simulations, protoplanets the responsible bridges straddle the protoplanets responsible sion is slow by comparison with thesion escape is slow velocity. by comparison A slow disk with wind the escapefor the velocity. dynamical A slow clearing disk wind of the largefor the gap dynamical in HD 142527. clearing They of the are large gap in HD 142527. They are (for example one photoevaporative(for or magnetically example one driven) photoevaporative can also be orclose magnetically to Keplerian driven) rotation can also in be azimuth,close but to Keplerian have radial rotation velocity in com- azimuth, but have radial velocity com- excluded on the basis of the highexcluded collimation on shown the basis by of the the HCO high1 collimationponents of shown>0.1 of by the the azimuthal HCO1 components.ponents of > In0.1 our of data, the azimuthal we see that components. In our data, we see that

192 | | VOL 493 | 10 JANUARY192 | NATURE 2013 | VOL 493 | 10 JANUARY 2013 ©2013 Macmillan Publishers Limited. All©201 rights3 Macmillan reserved Publishers Limited. All rights reserved Casassus et al. 2013 SS433

X-ray binary / ! Companion star: unknown ! Compact object: most likely a Black Hole ! Accretion disc ! Relativistic jets ! 3 main periodicities:

Porb = 13.1 days Pprec = 162 days P nut = 6 days Black hole Carroll & Ostlie (2007) An optical view of a microquasar in the

Why is SS 433 special?

Blundell et al. 2001 SS 433

fraction of a milli-arcsecond resolution! ! (0.12 mas at 0.3 cm) graphical tool for demonstrating the techniques of radio interferometry: Pynterferometer ! (python based) written by A. Avison from ALMA UK arc

La Serena School for Data Science / August 2014