VLBI in the SKA era
Lecture onvery long baseline interferometry

Hiroshi Imai
Amanogawa Galaxy Astronomy Research Center,
Graduate School of Science and Engineering /Center for Education, Institute for Comprehensive Education,
Kagoshima University

JST Sakura Program for international collaboration inradio astronomy between Japan and South Africa

Lecture contents

2vWhy VLBI?
– VLBI specifications– VLBI requirements and constraints• Hardware• Software• Operation

vUniqueness of VLBI
– Science cases– International collaborations in science and VLBI operationvChallenges of VLBI in the SKA era– Global VLBI alliance– Ultimate accuracy / massive astrometry– Time domain astronomy in VLBIJST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Why VLBI? ー specifications ー3𝜃!"#$ ≈ 𝜆⁄𝐵$#%

M87*
Sgr A*JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Why VLBI?
– ultimate angular resolution

4vAngular resolution ~ shortest fringe spacing– Extreme case 1: RadioAstron (2013—2019)••

SpectrR (spacecraft) — ground telescopesθbeam~ 7 μas (almost one baseline) @22 GHz– Extreme case 2: Event Horizon Telescope (EHT)• Up to 7 long-baseline sites• θbeam~ 20 μas @345 GHz informationvInstead of sensitivity and image quality– Limited number of long baselines• Limited common sky on the Earth• Limited coherence (integration) time

– Limited observation time slots• Limited available time of large telescopes• Limited observation cadence
JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Special equipment for VLBI

5v Purpose: getting fringe visibilities–––Detecting weak signals (with radio telescopes in general)
Heterodyne receiving for wave correlation••

Recording digitized time-series wave patterns at a high speed
Frequency conversion for more convenient recording•••

Antenna gains and system noise temperaturePhase information à complex correlation (90°phase shift)
Getting correlation à delay tracking and fringe stopping

Measuring visibility amplitudes and phases in correlatorv Keep the necessary information stably– High stability in frequency and time reference• High stability frequency standard• Loop-back circuits• Time stamp: 1PPS (pulse per second) signals

v Record/get a priori information– Antenna gains and system noise temperatures– Weather, time system, ITRF, etc.

JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

VLBI system: VERA (VLBI Exploration of Radio Astrometry) 6Atmosphere(dry air, water vapor, ionosphere）

Telescope optics
Receiving system(for sky and calibration signals)
Signal transmission
Telescope
driving system

Back end

Front end

Recording system (recording, spectroscopy)
System operation
JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Information transfer in a VLBI station
Antenna optics
Wave guide

Receiverfeed, polarizer,OMT (orthomode transducer)
LNA (low-noise amplifier)Radio frequency signals
Calibration signals
Local frequency
signal generator

MixingReference signals(5 MHz / 10 MHz)IF (Intermediate frequency)
converter,
Band pass filter
Analog/digital sampler
Digital filter
JST Sakura Program for radio astronomy collaboration

7

GPS

Time comparator
1PPS

Frequency
standard(H maser)
Phase calibration
signal detector
Formatter
RecorderHiroshi Imai, Kagoshima University

Frequency conversion
in each station

82⎡⎣VRF (t ) +VLO (t − τ LO )⎤⎦ = V 2 (t ) +V 2 (t − τ LO ) + 2VRF (t ) VLO (t − τ LO )RFLO

VRF (t ) VLO (t − τ LO ) = ARF cos {ω RF t } ALO cos {ω LO (t − τ LO )}ARF ALO ⎡⎤=cos
ωt+ωt−
τ+cos
ω
t−
ωt−
τ
()(){}{}RFLO
LORFLOLO ⎦2 ⎣= A cos {(ω RF + ω LO )t − ω LOτ LO } + A cos {(ω RF − ω LO )t + ω LOτ LO }Filtered out

where A = ARF ALO

USB and/or LSB

USB (upper side band) and LSB (lower side band)

USB: νIF= νRF-νLO → νRF= νLO+νIF
LSB: νIF= -(νRF-νLO) → νRF= νLO-νIFDelay tracking and fringe rotation
for fringe phase tracking

9𝝓𝒌 = 𝟐𝝅 𝝊𝐑𝐅 − 𝝊𝐋𝐨 𝝉𝒌 − 𝝉𝐢𝐧𝐬𝐭 = 𝟐𝝅𝝊𝐑𝐅 𝝉𝒌 − 𝟐𝝅𝝊𝐑𝐅 𝝉𝐢𝐧𝐬𝐭 − 𝟐𝝅𝝊𝐋𝐨 𝝉𝒌 − 𝟐𝝅𝝊𝐋𝐨 𝝉𝒌Observed in k-th baseline
Fringe phase 𝝓Frequency conversion inheterodyne
radio signal receiving

Fringe(phase)
stopping

Delaytracking

Baseband width

Correlated𝜐!

𝜐! + 𝐵Radiofrequency

VLBI requirements and constraints

10vHardware requirements / constraints– Frequency / clock stability 𝜎 ≈ 𝜐𝜎 𝜏 ≈ 𝜎 𝜏 ≪ 1&' ()*+ ()*• στ ≪ 10-12 s in τint or σν /ν ≪ 10-12 for ν≈10 GHz and τint ≈100 s• H-maser frequency standard (σν /ν ≈ 10-15) is necessary.
• Optical lattice clock (σν /ν ≈ 10-18) is newly applicable to VLBI.

– High speed digital sampling
SKA1 (~2027) ★
EHT (2017) ★

Gbps=giga bits per second

OCTAD/OCTADISK2(2022)★
Fig. 9.20 of TMS
JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

VLBI requirements and constraints

11vSoftware requirements / constraints– Correlator• High data damp rate
– Higher dispersion spectroscopy– Wider field of view

• Polarization handling and polarimetry (Stokes I,Q,U,V)– Pipeline data processing∂Δτ g
1 ≤ Δφ FoV (ν ) ≈ 2πνΔτ g ≈ 2πν
Tint∂t∂Δτ g Dω e Δθ FoVc≈
, Δθ FoV ≤∂tc
2πν Dω eTint• Loading raw data
• Data flagging• Selecting reference data
• Fringe amplitude calib.
and• Fringe phase calib.
1 ≤ Δφ FoV (ν %) ≤ 2πΔνΔτ g where ν % = ν + Δν• Image synthesis
DΔθ FoVc• Source findingΔτ ≈, Δθ ≤g

JST Sakura Program for radio astronomy collaboration

cFoV2πΔν DHiroshi Imai, Kagoshima University

VLBI requirements and constraints

12vVLBI operation requirements / constraints– Scheduling VLBI stations• Middle-size telescopes dedicated for VLBI monitoring(e.g., VERA, KVN, VLBA)– Advanced skills requested to users for operation• Selecting clock parameter (delay, delay rate offsets)
calibrators large angular offsets from target• Selecting fringe calibrators short angular offset from target• Selecting flux / polarization calibrators very rare

VLBI calibrators are not ideal ones (bright, compact, stable).
– Data shipping• Physically shipping recorded medias via air cargo• Custom, security issue• Slow internet transportation
JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Uniqueness of VLBI
– Science Cases—

13v Imaging in ultimate angular resolution– Shadows of super-massive blackholes– Lunching points of AGN (active galactic nucleus) jets
M87*, Sgr A*v High precision astrometry– Trigonometry (up to 10 kpc) of non-thermal sources(including maser sources)– Secular motions of radio sources– See also Nakagawa’s lecturev Mapping compact structures ininterstellar / circumstellar / circumnuclear medium– Astrophysical maser sources (in movies)– Compact objects in deep universe (and solar neighborhood)v VLBI for time domain astronomy (localization)– Fast transients: fast radio bursts (FRBs)– Slow transients: super novae, novae, radio burst, maser bursts

JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Shadows ofsuper-massive black holesEHT Collaboration 2022

EHT Collaboration 201914Credit: EHTv Millimeter (~1.3 mm) VLBI à θbeam~20 μasv Ultra-high sensitivity– Large apertures: ALMA-VLBI, LMT (Large Millimeter Telescope)– Ultra-high speed signal recording: 32 Gbps

v New imaging technique– Sparse modelling– Variability (4—30 min) modeling

JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Lunching point of an AGN jet

15

Precession of the M87 jet(due to a blackhole spin?)(EAVN Collaboration 2023)
Hiroshi Imai, Kagoshima University

10 kilo-parsec scaleradio trigonometry 16

Nagayama et al. (2020)

VERA detects
the annual parallax ofSgr A* (Galactic Center)(Oyama et al. 2024)
See also Nakagawa’s lecture

JST Sakura Program for radio astronomy collaboration

Movies of astrophysical masers

10 mas

50 mas

SiO masers in Orion Source I(Mattheus et al. 2009)
JST Sakura Program for radio astronomy collaboration

SiO masers around TX Cam(Gonidakis et al. 2013)17

Movies of astrophysical masers
Absolute motions

Relative motions w.r.t the star

20 mas❌: star (BX Cam) from Gaia EDR3

H2O masers around BX Cam (Xu et al. 2022)
JST Sakura Program for radio astronomy collaboration18

Localizations of key sources
Detections of fast radio bursts (FRBs)
Using
pulse-gatedvisibilities

12 ms

6 ms

120 MHz(1600—1720 MHz)Using
2s-integrated
visibilities

FRBs localization
in VLBI
Marcote et al. (2020)
JST Sakura Program for radio astronomy collaboration

19

Variety of (fast) radio transients

20

Ex.1
3.2 Gbps⇩
400 M samples/sor 200 MHz
bandwidth
in 16 levels(8 bits)
Ex.2

τduration=10-7 s@100 MHz

Nimmo et al. (2021)
JST Sakura Program for radio astronomy collaboration

τduration=10-3 s@1GHz320 Mbps
⇩40 M samples/sor 20 MHzbandwidthin 16 levels(8 bits)

RRATs=Rotating radio transients
Hiroshi Imai, Kagoshima University

International collaborations inscience and VLBI operation

21v Limited opportunities of VLBI observations in the world
against other astronomical observations for …..

– a variety of key compact targets that should be monitored(>> a few hours, over decades)– a large fraction of VLBI sources that request high sensitivity andimage quality

v Limited budget and human resources in individual countries,
including Japan, may cause– long delays (>> 1 month) of data deliver since VLBI observations
through data correlation– long time (>> 1 year) for paper publications if working alonev VLBI is one of the clearest style of international
collaborations and friendship built from exchanging scientificideas to scientific publications through array construction
and operation.
JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Challenges of VLBI in the SKA era

22vToward the Global VLBI alliancev Toward ultimate accuracy / massive astrometryv Time domain astronomy in VLBIJST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Toward the Global VLBI Alliance23

How to organize
different VLBI networks
and SKA-VLBI
as a global VLBI network?

••••
•
•

Variety of newopportunities forjobs andcollaborative
projects

Proposal handling
Scheduling
Correlation
Data archive
Publications
VLBI schools

JIV-ERIC & SKA Organisation 2020
JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Towardultimate accuracy astrometry

24

AIC/ATC =advancedionospheric/troposphericcalibration
techniqueDR =dynamic range
PR =
phase
referencing
SFPR =
sourcefrequency(switching)phasereferencing

Rioja & Dodson 2020
JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Toward 1-μas accuracy astrometry

25

Scanning multiple calibrators
around astrometric target

2024年1月25日

Rioja & Dodson (2023)

日本SKA協会ウェビナーシリーズ

Ultimate accuracy / massive
astrometry

26

v Ultimate accuracy (σ~1 μas) astrometry– Feasible at high frequency bands (>5 GHz)
– Trigonometry of Large/Small Magellanic Clouds(50 kpc/60 kpc)
– ~1 pc-accuracy level pulsar (<1 kpc) astrometry for
improving detectability of gravitational waves fromsuper-massive blackhole binaries (P≳1 year)– Detections of astrometric microlensing events

v Massive (>> 1000 targets) astrometry (σ~10 μas)
– Feasible at low frequency bands (< 2 GHz)
– 3D kinematics of individual nearby star-forming regions probed
by young stellar objects (YSOs, non-thermal sources)– 3D kinematics of the Galactic Nuclear Disk and Bulge probed
by long-period variable stars (OH masers)– 3D kinematics of Large/Small Magellanic Clouds (OH masers)
JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Time domain astronomy in VLBI27

v Technology of automatedprocessing for transient
buffer data
– Largest beam with single
dishes– Synthesizing multiple
interferometer beams in
realtime (see right)– Syntesizing multiple
VLBI beams in offline– Channelization should
also be taken into account.

v VLBI scheduling fortransients– Alerts of VLBI transients– Rules for transient VLBI
JIV-ERIC & SKA Organisation 2020
JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Maser Monitoring Organisation
(M2O)

28

A Keplerian disk with afour-arm spiral birthing
an episodically accretinghigh-mass protostar
Burns et al. (2023)
https://www.masermonitoring.com

v Synergy for single-dishmonitoring of methanol masers
and multi-wavelength
observations
v Follow-ups byVLBI
observations
in target-ofopportunity(ToO) triggers
JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University

Summary and future perspectives

29

v Variety of efforts in VLBI toward the SKA era– Variety of science goals yielded with even a single VLBI arraye.g., VERA dedicated for astrometry– Variety of stages of international collaborations built from designinga VLBI array to scientific project through construction and operation ofthe VLBI array– One of the best suitable models of peaceful international cooperationv Challenges of VLBI toward the SKA era– Complexity of VLBI array operation– Technical challenges in ultimate accuracy and massive astrometry– Sustainable development of VLBI arrays and their science cases– Sustainable human interactions in young generation

JST Sakura Program for radio astronomy collaboration

Hiroshi Imai, Kagoshima University