Millimeter/submillimeter Array (ALMA), the Karl G. Jansky Very Large Array
(VLA) and the NOrthern Extended Millimeter Array (NOEMA) over the past decade
have now resulted in the first delineation of the evolution of the cold
molecular gas content of galaxies per unit volume as a function of redshift
(e.g., [321, 319, 80, 39], and references therein). Combined with studies of
stellar mass, atomic gas, and the star formation activity, this has now led to
a consensus picture of the evolution of baryons associated with galaxies over
cosmic time and space (e.g., [396]). While the current constraints already
required a major revision of simulations of galaxy evolution, substantial
uncertainties remain due to the limited volumes ($\sim$700,000 Mpc3) and depth
possible with current observatories, as well as the fact that studies were
carried out in different rotational lines of CO, which leaves residual
uncertainties due to gas excitation. With its vastly increased survey speed
and bandwidth, providing simultaneous coverage of multiple CO lines including
continuous coverage of the fundamental CO $J$=1$\to$0 transition (toward which
all cold gas masses are calibrated) at all redshifts and the typically
brightest CO $J$$\geq$3–5 lines out to $z$$>$6, the next generation Very Large
Array (ngVLA; [266]) is expected to push this area of research from a
consensus picture to a precision measurement, both in terms of accuracy of
individual detections and survey volume.

Figure 26: Left: Legacy CO line scan surveys based on $>$1000 hr of dedicated
observations with ALMA, NOEMA, and the VLA over the span of a decade (boxes;
e.g., [321, 319, 80, 396], and references therein), and improvements in the
uncertainties expected due to the vastly improved survey speed of the ngVLA
(blue dashed line and shaded curve). Right: Accessibility of the CO line
ladder for a $z$=6 main sequence galaxy, showing that the ngVLA will have both
the sensitivity and bandwidth to cover six of the seven lowest-$J$ rotational
transitions for studies of CO excitation. Clearly, the ngVLA is required for
the next major breakthrough in this key field of research.

###  2.29 Molecular Line Absorption Against the CMB as a Probe of Cosmological
Parameters

Thematic Areas: $\square$ Stellar Astrophysics $\square$ Solar System,
Planetary Systems and Habitability $\square$ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ Galaxies
and AGN $\square$ ✓ Cosmology, Large Scale Structure and Early Universe
$\square$ ✓ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Dominik A. Riechers Institution: Universität zu Köln Email:
<EMAIL_ADDRESS>
Co-authors: Axel Weiß (MPIfR), Fabian Walter (MPIA), Pierre Cox (IAP)

With the ever-growing precision in measurements of fundamental cosmological
parameters, standard $\Lambda$CDM cosmology has so far stood the test of time.
However, in light of potential complications like the "Hubble Tension" (e.g.,
[323] and references therein), deviations from this simple model are still
important to investigate, since they may provide a pathway toward the
discovery of new fundamental physical phenomena, such as different forms of
dark matter, exotic dark energy, revised prescriptions of gravity, or the
presence of currently unknown particles or coupling processes. One
particularly promising method to study deviations from the standard model are
distortions imprinted on the cosmic microwave background (CMB; e.g., [294]) by
astrophysical sources across a broad range in redshifts. While galaxies have
now been detected out to $z$$>$13 thanks to the James Webb Space Telescope
(JWST; e.g., [113]), powerful methods to study CMB distortions like the
Sunvaey-Zel’dovich effect associated with galaxy clusters remain limited to
$z$$\leq$1 (e.g., [163]). It has recently been established that the
fundamental 110–101 rotational transition of the ortho-H2O molecule can be
used to measure key parameters like the CMB temperature $T_{\rm CMB}$ toward
massive starburst galaxies at redshifts $z$$>$6, where the $T_{\rm CMB}$$>$20
K is sufficient to excite this transition (Figs. 27 and 28; see [322]). While
detections are possible with the best current millimeter-wave interferometers
like the Atacama Large Millimeter/submillimeter Array (ALMA) and the NOrthern
Extended Millimeter Array (NOEMA), the signal is too weak to be spatially
resolved in reasonable integration times (Fig. 27). The lack of spatial
resolution is the currently largest source of uncertainty of the $T_{\rm CMB}$
measurements. The next generation Very Large Array (ngVLA; [266]) will offer
the boost in sensitivity and resolution to provide detailed images of the
absorption signal against the CMB, providing detailed column density
distributions of the H2O vapour. Moreover, the ngVLA will have the sensitivity
to detect the signal in the most massive star-forming galaxies at $z$$>$10
(see Fig. 28), which are expected to be an order of magnitude fainter than
those seen at $z$=4–6.

Figure 27: NOEMA detection of H2O 110–101 absorption toward the $z$=6.34
starburst galaxy HFLS3 (red dashed box; [322]). The line is about twice as
strong as the galaxy’s continuum emission, and thus, absorbs into the CMB.
When the dust spectral energy distribution and size of the galaxy are well
measured, the strength of the absorption only depends on the CMB properties,
in particular its temperature – providing a direct measurement at the redshift
of the galaxy (see Fig. 28). The ngVLA will have the sensitivity and spatial
resolution to resolve the absorption signal, which will result in
substantially more accurate measurements.

Figure 28: Left: Direct measurements of the CMB temperature previously existed
at $z$=0–1 based on the Sunyaev-Zel’dovich effect toward galaxy clusters, and
model-dependent measurements existed for quasar absorption line systems out to
$z$$\sim$3\. H2O 110–101 absorption-based studies offer the potential to
provide such measurements to much higher redshifts. The largest source of
error for the measurement in HFLS3 is the knowledge of the size of the galaxy.
The orange line and shaded area show the best combined fit to all current
data, which is consistent with standard $\Lambda$CDM cosmology (see [322] and
references therein). Right: Depending on the contribution from collisional
excitation, models suggest that for starbursts like HFLS3, the CMB absorption
should be detectable at $z$$>$4.5, and be almost independent of redshift out
to $z$$>$12\. The ngVLA will provide the sensitivity to carry out such
measurements for the most evolved galaxies at $z$$>$10.

###  2.30 VLBI probes of supernovae, supernova factories and starburst
galaxies

Thematic Areas: $\square$ ✓ Stellar Astrophysics $\square$ Solar System,
Planetary Systems and Habitability $\square$ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ ✓ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Eduardo Ros Institution: Max-Planck-Institut für Radioastronomie Email:
<EMAIL_ADDRESS>
Co-authors: Miguel Á. Pérez Torres (Inst. de Astrofísica de Andalucía), Antxon
Alberdi (Inst. de Astrofísica de Andalucía), José C. Guirado (Univ. de
València)

The incorporation of long baselines into the Next Generation Very Large Array
(ngVLA) will enhance its operational capabilities, allowing it to operate in a
manner similar to Very Long Baseline Interferometry (VLBI). This enhancement
will be characterised by significantly improved $(u,v)$-coverage, due to both
the increased number of antennas and the broader frequency range. Known for
its unique ability to study compact radio emission in exceptional detail, VLBI
focuses primarily on stellar surfaces, young stars, supernovae and their
aftermath, such as neutron stars and black holes with companions.

The long baseline options within the ngVLA represent a major leap forward in
structural sensitivity at larger scales compared to current VLBI methods. This
enhancement will allow unprecedented flux density sensitivity on compact
angular scales up to a frequency of about 100 GHz—a significantly unexplored
area of astrophysics for these objects.

With its expanded capabilities, the ngVLA will make a major contribution to
the study of stellar physics. In addition to the instrument’s role in studying
gamma-ray bursts, microquasars, pulsars and supernova remnants, as described
in other sections of this document, it will be essential for studying radio
supernovae and nearby starburst galaxies.

The radio emission from young supernovae is thought to result from the shock
interaction between the supernova ejecta and the circumstellar medium (see
e.g., [354]. Different physical parameters of this medium influence the timing
of the radio peak of supernovae, ranging from early emission, as observed in
SN 1993J in Messier 81 [341, 246], to later emission after ten years, as
expected for superluminous Type I supernovae [116, 97, 249], or even many
years later, as seen in ’regular’ supernova remnants.

In the absence of recent supernova explosions in the Milky Way, starburst
galaxies, particularly Luminous Infrared Galaxies (LIRGs), become prime
targets for supernova observation. LIRGs serve as supernova factories,
providing the opportunity to observe individual supernova explosions across
the electromagnetic spectrum [279].

Leveraging the sensitivity of the ngVLA will significantly increase the number
of core-collapse supernovae detected and observed compared to current studies.
Galaxies such as IC 10, less than 1 Mpc away, NGC 253 (Sculptor) at 3.4 Mpc,
and Messier 82 at about 4 Mpc can have their radio structures resolved. This
is achieved by studying their angular expansion over long periods of time,
providing insights into the morphology and deceleration parameters of the
ejected material. Such observations provide valuable information about the
circumstellar and interstellar environments, as well as the progenitor star.
In addition, the detection of individual radio supernovae and remnants in
circumstellar starbursts [280] provides a reliable estimate of the star
formation rate in nearby galaxies, assists in the identification of Type I-a
radio supernovae, and offers clear insights into the nature of progenitor
systems.

Resolving young supernovae in starburst galaxies at longer distances, such as
Arp 299 at 50 Mpc, NGC 1615 at 68 Mpc, Mrk 321 at 75 Mpc, and Arp 220 at 83
Mpc, will be challenging, but catching supernovae at the moment of explosion,
when they peak at higher frequencies, may help.

It is noteworthy that the study of radio supernovae is closely linked to the
observation of their most energetic multi-wavelength counterparts, namely
gamma-ray bursts and fast radio bursts. This synergy is particularly relevant
in the current era of multi-messenger, transient astronomy (see e.g., [250]).

###  2.31 Zooming into Feedback Engines

Thematic Areas: $\square$ Stellar Astrophysics $\square$ Solar System,
Planetary Systems and Habitability $\square$ ✓ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Peter Schilke Institution: University of Cologne Email<EMAIL_ADDRESS>koeln.de

High-mass stars and clusters provide most of the energy input shaping clouds
on scales from a few pc to few 100 pc, and galaxies in the form of mechanical
(e. g. outflows, stellar winds, expanding H ii regions, and eventually, on
larger scales, supernova explosions) and radiative (e. g. thermal, UV, X-ray,
cosmic ray) feedback. A complete understanding of these processes requires a
detailed study of the small-scale structure (i.e. a few 1000 AU) of the
different feedback engines, since this is the scale where the feedback
originates and its power and properties are determined. The physical and
chemical structure of these cluster-forming habitats is studied using submm/mm
and radio observations sensitive to the dense gas structure and the presence
of embedded newly formed massive stars that inject energy into their
surroundings.

In the last few years, these studies have undergone a major quantum leap,
thanks to new powerful facilities like ALMA and JVLA, which provide unique
higher-resolution and higher-sensitivity observations. This has enabled
detailed studies at 1000 AU scales for some of the most active and energetic
regions in the Galaxy (e. g. SgrB2, W51, NGC6334: [339]; [128]; [338]). The
results show highly fragmented structures fed by dense filaments, with
multiple massive stars forming in a reduced volume and powering energetic
outflows and H ii regions. Using different molecules/isotopologues/excitation
stages and exploiting a combination of optically thick and thin transitions,
it is possible to go beyond the restriction of 2D images and perform a
tomography to restore at least part of the line-of-sight structure.

Using sophisticated excitation analysis of various molecules, in particular of
high and vibrationally excited states, it is possible to determine the local
IR field produced by the embedded star-forming population, otherwise difficult
to determine due to high opacity and extinction (e. g. [390, 53]), and thus to
better constrain the thermal structure of these massive and energetic regions.
These lines have the potential to locate embedded sources that warm the
surrounding dense gas.

Figure 29: VLA observations of $\ell$-type HCN($v_{2}=1,J=13$) lines toward
G10.47 from Rolffs et al. 334.

This is possible because the vibrationally excited states are pumped by IR
radiation and thus, are sensitive to a specific wavelength corresponding to
the energy of the vibrational level. Complex organic molecules are
particularly well suited for this task because they selectively trace the
inner, hotter regions where the dust is hot enough to release those species.
Also, they have, by virtue of their complexity, many rotational lines, which
means that even in a moderately wide spectrum there are many lines that can be
fitted, better constraining the solution; and many vibrational levels spanning
many excitation energies, which allows a finely grained exploration of the IR
field.

While in principle this can be done with ALMA, this method suffers in very
high column density regions, particularly toward disks around high-mass stars,
from the dust being optically thick, even in ALMA Band 3. The solution is to
go to lower frequencies, domain of ngVLA, where e. g. $\ell$-type lines of
vibrationally excited HCN or vibrational satellite lines of HC3N, CH3OH,
C2H5CN and many others are readily observable (see Fig. 29 for observations
with the VLA in 2009).

###  2.32 Studies of fast radio Bursts above 2 GHz with the ngVLA

Thematic Areas: $\square$ Stellar Astrophysics $\square$ Solar System,
Planetary Systems and Habitability $\square$ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ ✓ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Laura G. Spitler Institution: Max-Planck-Institut für Radioastronomie
Email<EMAIL_ADDRESS>
Co-authors: Florian Eppel (JMU Würzburg)

Fast radio bursts (FRBs) are radio transients emitted by so-far unidentified
sources at cosmological distances [75]. Their unknown astrophysical origin (or
origins) is currently one of the biggest mysteries in astronomy, although the
majority of models involve a neutron star [295]. Furthermore, they are also
useful astronomical tools with applications for, e.g., studying the
intergalactic medium (e.g. [243]), measuring cosmological parameters such as
the Hubble constant (e.g. [174]), and testing fundamental physics (e.g. [37]).
Observationally, FRBs are characterized by micro- to millisecond-timescale
emission that has, so far, only been detected at radio frequencies and exhibit
complex and varying time-frequency structure and polarization properties
[282]. A few percent of the known sources have been confirmed to emit multiple
bursts, the so-called “repeaters", which enable a wide-range of follow-up
observations [12, 173].

Identifying an FRB’s host galaxy is critically important for understanding
their astrophysical origins, as well as most of the astrophysical and
cosmological applications. Unambiguous localization requires a precision of
$\sim$arcsecond, and therefore an interferometric radio telescope is necessary
[96]. Several blind, FRB surveys are running commensally on interferometers
including the Jansky Very Large Array (VLA) [220] and the Australian Square
Kilometer Array Pathfinder (ASKAP) [241]. Meanwhile, new interferometers are
being designed and built with the FRBs as a key science case (e.g.
DSA-110101010https://www.deepsynoptic.org/, CHIME/FRB+CHORD [384], Square
Kilometer Array [242]). Note, ASKAP and DSA-110 operates solely around 1.4
GHz, while CHIME/FRB+CHORD observes at $400-800~{}$MHz. What is missing in
most current and future observatories is the ability to discover and localize
FRBs above $\sim$2 GHz. Beyond targeted follow-up of active repeaters, the
nature of FRBs at higher radio frequencies is entirely unexplored. A commensal
FRB search system on the ngVLA would help fill in this gap [221]. The ngVLA
will be the only high-frequency radio instrument with a large field of view
and, simultaneously, the capability to localize FRBs down to $<$arcsecond
precision upon detection. This will enable systematic multi-wavelength (MWL)
surveys of FRBs in synergy with current and future X-ray missions, especially
for the population of once-off FRBs. MWL information is key in understanding
the nature of FRBs, since several FRB models predict associated high-energy
emission [295]. Due to the small beam sizes and/or inaccurate localization
capabilities of the current generation of telescopes, especially once-off
events are difficult to target in today’s MWL programs which focus on the few
known repeaters [343, 293]. The ngVLA will therefore play a key role in
constraining different FRB models and ultimately in revealing the progenitor
of FRBs.

Perhaps even more important for FRB science is the ngVLA’s widefield, high
resolution, high sensitivity imaging capabilities. The presence or absence of
radio emission in the host galaxy coincident with the position of the FRB
source is an important clue in understanding the source’s local environment.
Of particular interest are the so-called “persistent radio sources" (PRS) that
have been associated with two repeaters [247, 415]. In the case FRB 20121102A,
the diameter of the PSR is $<0.7$ pc and detected over a wide frequency range
[69]. The nature of these PRSs is also unclear but may be powered by the
interaction of the FRB source with its environment [248]. The ngVLA’s high
sensitivity will allow the detection of weaker PRSs or provide deeper
constraints over a wider frequency range than other observatories.

###  2.33 Study of the Dense ISM with the ngVLA

Thematic Areas: $\square$ Stellar Astrophysics $\square$ Solar System,
Planetary Systems and Habitability $\square$ ✓ Circuit of Cosmic Matter (incl.
star formation) $\square$ ✓ The Galaxy and the Local Group $\square$ Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: L. Viktor TÓTH Institution: Eötvös University Budapest, Institute of
Physics and Astronomy Email<EMAIL_ADDRESS>
Co-authors: Mika JUVELA, University of Helsinki

As a recent evaluation of ISM simulations by [188] showed, ngVLA observations
may uncover the density and velocity structure of ISM in early phases of
massive protostar formation up to 3kpc.

In studies of star formation (SF), many questions remain open regarding the
formation and filamentary structures of clouds, their fragmentation, and the
mass accretion and the balance between gravity, turbulence, and magnetic
fields across different scales [264, 141]. One also needs a better
understanding of the components of the interstellar medium (ISM) itself, the
gas and dust, which are used as tracers of the SF process and which themselves
undergo significant evolution along the SF process. The understanding of the
high-mass star formation (HMSF) is particularly important, since massive stars
are crucial to many astrophysical processes even at galactic scales, via their
ionising radiation, stellar winds, and the production of heavy elements [195].
High-mass stars are formed in massive ($M>1000$ M⊙, $\Sigma\sim 0.02$ g cm-2)
and mainly cold ($T\sim$10–40 K) clouds [278, 368, 227], which tend to reside
at kiloparsec distances. Therefore, one needs sensitive radio observations of
dust and of molecules on low excitation levels. One also needs the coverage of
a wide range of size scales, ending up at the scale of protostellar cores
(down to disk scales, $\sim$100 au), possible only with ground-based
interferometry.

ngVLA meets many of these requirements. It covers the millimeter range that
includes the low-lying transitions of many key molecules, such as ${\rm
NH}_{3}$, ${\rm HCO^{+}}$ and ${\rm N_{2}H^{+}}$ as well as many deuterated
molecules that are abundant in pre-stellar cores (e.g. DCO+ and ${\rm
N_{2}D^{+}}$). Although single-dish observations are still needed at the
largest scales, the compact ngVLA configurations provide already an almost
complete picture of the more compact almost complete picture of the more
compact HMSF regions (Fig. 30). High sensitivity is also crucial in kinematic
studies, to study the mass flow from cloud scales to individual protostars,
that require a high velocity resolution of $\sim$0.1 km s-1. Simulations have
shown that ngVLA can provide an accurate picture of both the mass distribution
and the velocity field in HMSF regions [188]. For example, for an target at 4
kpc distance, one obtains a good coverage of the scales $\sim$0.01-0.3 pc by
using just the core antenna configuration, while the more extended
configurations can reveal the structure of individual protostellar systems at
the disk scales.

Figure 30: Synthetic ngVLA observations of a massive cloud filament, 6 h
integrations with the core configuration. Shown are line area maps for the
true and ngVLA-observed ${\rm N_{2}H}^{+}$ and ${\rm NH}_{3}$ spectral lines
(frames a-d), the same as correlations shown for ideal observations (including
radiative transfer effects) and synthetic ngVLA observations vs. true values
(frames e-f), and the accuracy of ${\rm NH}_{3}$ kinetic temperature estimates
(frame g; for ideal and for simulated ngVLA line observations).

###  2.34 Star and Planet Formation with ngVLA

Thematic Areas: $\square$ Stellar Astrophysics $\square$ ✓ Solar System,
Planetary Systems and Habitability $\square$ ✓ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Takahiro Ueda Institution: Max Planck Institute for Astronomy Email:
<EMAIL_ADDRESS>
Co-authors: Sebastian Wolf, Univ. Kiel, Mario Flock, MPIA, Tilman Birnstiel,
LMU München

The process of star and planet formation is a complex and fascinating journey
that begins with the gravitational collapse of a molecular cloud core. The
collapse gives rise to the formation of a disk of gas and dust around the
protostar, establishing the initial conditions for planet formation.

Star formation in molecular clouds The magnetic field is anticipated to play a
pivotal role in the core collapse, with its morphology traceable through the
linear polarization of the thermal reemission radiation from aligned dust
grains. The ngVLA is poised to observe dust polarization, providing insights
into the magnetic field morphology and strength on scales of $10^{2}$ to
$10^{3}$ au in nearby star-forming regions along with dust grain properties
such as size and aspect ratio, as well as the involved grain alignment
efficiency and underlying mechanisms. The young forming-disks have moved into
the focus as planet formation was shown to happen early on. The small sizes
and high optical depths [274] require the capabilities of the ngVLA to reveal
the early presence of structure and their origins.

Planet formation in protoplanetary disks After disk formation, an intriguing
focus of the ngVLA lies in observing their future habitable zone ($\sim$ few
au for solar-type stars) with an angular resolution beyond that achievable
with ALMA, providing constraints on the physical conditions for terrestrial
planet formation. Its unprecedented resolution allows for probing the months-
scale time variability of substructures induced by giant planets like Jupiter
[199]. In particular, the ngVLA will offer insights complementary to those
obtained with optical/infared long-baseline interferometry, tracing the upper
disk layers and constraining the vertical disk structure [e.g., VLTI; 156].
Furthermore, as the potential planet-forming regions of selected
protoplanetary disks were found to be optically thick even in the
submillimeter regime [e.g., 406], the lower optical depth in the wavelength
range targeted by the ngVLA will allow for a less ambiguous data analysis.

(Sub-)cm wavelengths are also critical for investigating the dust-size
evolution beyond the millimeter size regime. For example, Rosetta/MIRO
measurements of the comet 67P/Churyumov-Gerasimenko indicate an upper pebble
size of 3-6 mm [56]. Given the wavelength range covered by the ngVLA it will
not only allow tracing this particle size regime, but also exploit the strong
wavelength dependence of the degree and even orientation of the linear
polarization on particle size and particle internal structure [54].

Another pivotal topic involves resolving ambiguities in interpreting
substructures in protoplanetary disks. While ALMA has shown the ubiquity of
these structures, their origin is still under debate. Both, the sensitivity to
the thermal reemission radiation and thus spatial distribution of
millimeter/centimeter-sized pebbles as well as the possibility to constrain
the magnetic field via the Zeeman effect will allow distinguishing between the
potential roles of instabilities, magnetic fields, or embedded planets [see
science case 2.14; 46, 336]. Eventually, the long-wavelength emission of
circumplanetary disks will provide constraints on the final phase of giant
planet formation, i.e., the gas-accretion phase.

Debris disks: Signposts of the evolution of planetary systems The ngVLA also
holds substantial promise for debris disk studies, i.e., the characterization
of the planetary systems through the observations of the dust released from
comets and minor body collisions. As shown by [361], it will provide
particularly valuable constraints on the origin of the phenomenon of hot
exozodiacal dust [3, 198]. Understanding this phenomenon represents an
essential prerequisite for future detection and characterization of exoplanets
in the habitable zone using, e.g., the Habitable Exoplanets Observatory
(HabEx). Moreover, the wavelength dependence of the spatial brightness
distribution of debris disks will not only provide constraints on the location
of planetesimal belts and embedded planets, traced through planet-debris disk
interaction, but even on physical properties of the planetesimals themselves,
e.g., their collisional strength [197].

In summary, the ngVLA stands poised to revolutionize the study of star and
planet formation. By probing magnetic field and grain properties, the ngVLA
will unravel the intricacies of gravitational collapse and disk formation. Its
unprecedented resolution enables exploration of the future habitable zone,
providing valuable insights into the conditions during the formation of
terrestrial planets like our Earth. By resolving ambiguities in interpreting
disk substructures and delving into debris disk studies, the ngVLA emerges as
a powerful tool, offering new perspectives on ongoing, most decisive
scientific debates in the field.

###  2.35 Planet Formation at the Innermost Region of Protoplanetary Disks

Thematic Areas: $\square$ Stellar Astrophysics $\square$ ✓ Solar System,
Planetary Systems and Habitability $\square$ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Takahiro Ueda Institution: Max Planck Institute for Astronomy Email:
<EMAIL_ADDRESS>
Co-authors: Mario Flock, MPIA, Tilman Birnstiel, LMU München, Sebastian Wolf,
Univ. Kiel

Close-in exoplanets are known to be common around Solar-type stars. How are
they formed? Is their formation process different from that of solar system
terrestrial planets? Understanding the formation of these planets is of great
importance in planetary science. One preferential site of rocky
planetesimal/planet formation is the inner edge of the so-called dead zone
[210, 376, 377]. The dead zone is the location where magneto-rotational
instability (MRI [17]) is suppressed because of poor gas ionization [118]. The
inner edge of the dead zone is characterized as the radial location where disk
temperature reaches $\sim 1000$ K, above which thermal ionization of the gas
is effective enough to activate MRI (e.g., [84]).

It is challenging to directly observe the dead-zone inner edge of disks around
few-Myr-old T-Tauri stars because it is too close to the central star.
However, disks around more luminous stars (e.g., Herbig Ae stars) or young
disks with inner regions heated by disk accretion offer ideal laboratories to
test the hypothesis that close-in planets form at the dead-zone inner edge.

Figure 31 (left) shows a simulation of dust evolution around a Herbig Ae star
with a stellar luminosity of $56L_{\odot}$ [378]. The high luminosity
positions the dead-zone inner edge at $\sim 1$ au in the model. The dead-zone
inner edge traps dust particles drifting from outer region because of steep
drop in the gas surface density. The radial dust accumulation results in a
mid-plane dust-to-gas mass ratio reaching unity, triggering the formation of
rocky planetesimals. Figure 31 (right) shows the vertical optical depth at
different observing wavelengths. The optical depth is almost unity at
$\lesssim 3$ mm, while it is fully optically thin at 10 mm except at the peak.

Figure 32 shows the synthetic images of ngVLA observations for the disk model
depicted in Figure 31 [378]. The images include rms noise corresponding to an
integration time of 10 hours. The expected angular resolution is $\sim 0.002$
arcsec and $\sim 0.006$ at Band 6 (100 GHz) and 4 (30 GHz), respectively. A
distinct ring-like structure is visible at $\sim 1$ au with the provided
integration time, highlighting the ngVLA’s potential as a powerful tool to
investigate planet formation in the innermost regions of disks.

Figure 31:  Simulated dust distribution (left) and corresponding optical depth
(right) of the disk around a Herbig Ae star with stellar luminosity of
$56L_{\odot}$. See [378] for more details.  Figure 32:  Synthetic images of
the ngVLA observations on the disk model shown in Figure 31. The on-source
time is assumed to be 10 hrs. See [378] for more details.

###  2.36 From near-infrared to centimeter: comprehensive understanding of the
inner planet-forming region

Thematic Areas: $\square$ Stellar Astrophysics $\square$ ✓ Solar System,
Planetary Systems and Habitability $\square$ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Takahiro Ueda Institution: Max Planck Institute for Astronomy Email:
<EMAIL_ADDRESS>
Co-authors: Mario Flock, MPIA, Tilman Birnstiel, LMU München, Sebastian Wolf,
Univ. Kiel, Karine Perraut, Univ. Grenoble Alpes

The inner regions of protoplanetary disks are of great interest in
astronomical research. The inner regions of these disks have been actively
studied by the Very Large Telescope Interferometer (VLTI) operated by the
European Southern Observatory. The VLTI observes the inner disk regions with
an effective angular resolution down to approximately 2 milliarcseconds at
infrared wavelengths, enabling us to probe the inner edge of dust disks in
typical nearby star-forming regions.

One of the pivotal findings of the VLTI observations is that the emission
sizes at mid-infrared wavelengths (N band; $10.7~{}{\rm\mu m}$) are much
larger than the expectations derived from the full disk model. In contrast,
the observed emission size aligns with the model at the near-infrared
wavelength (Figure 33 right) [139]. One plausible interpretation for this
inconsistency is dust filtration: forming planets trap large dust, depleting
mid-infrared emission within their orbits. The dust filtration is anticipated
to play an important role even in the formation of the Solar system, as
geochemical evidence suggests distinct populations among the building blocks
of Solar system asteroids, potentially spatially separated by proto-Jupiter
[211]. However, from a theoretical perspective, the occurrence of strong dust
filtration remains uncertain due to uncertainties in dust
coagulation/fragmentation processes [359].

The ngVLA holds the promise of directly imaging the inner disk structure, as
depicted in Figure 33 showcasing synthetic images of a disk hosting a
$10M_{\oplus}$ planet at 1 au ($\sim 7$ mas at 150 pc). The lower panels show
the disk model with the turbulence strength parameter $\alpha_{\rm turb}$ of
$10^{-3}$ in which no strong dust filtration occurs. Conversely, the upper
panels exhibit strong dust filtration at $\sim 1$ au due to low turbulence
($\alpha_{\rm turb}=10^{-5}$). The model with dust filtration shows a larger
emission size at the N band. At ngVLA wavelengths, the expectation is to
observe the cavity structure if dust filtration is indeed occurring. The ngVLA
will offer crucial insights into the presence of inner planets, shedding light
on the formation of both the Solar system and exoplanets.

Figure 33:  Synthetic images of the inner planet-forming disks with a
$10M_{\oplus}$ planet at 1 au. The upper panels show the case of $\alpha_{\rm
turb}=10^{-5}$ in which strong dust filtration occurs at $\sim 1$ au, while
the lower panels show the case of $\alpha_{\rm turb}=10^{-3}$ where no strong
dust filtration occurs. The white dashed line denotes the planet orbit. The
cyan dashed line in the middle panels denotes the half-emission radius. The
rightmost figure shows the observed ratio between half-emission radii at K
($2.2~{}{\rm\mu m}$) and N ($10.7~{}{\rm\mu m}$ ) bands [254, 387, 139, 138].

###  2.37 Big Data, surveys, classification

Thematic Areas: $\square$ Stellar Astrophysics $\square$ Solar System,
Planetary Systems and Habitability $\square$ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ ✓Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Eleni Vardoulaki Institution: Thüringer Landessternwarte Tautenburg
Email<EMAIL_ADDRESS>
Co-authors:

Name: Etienne Bonnassieux, JMU Würzburg, Yuri Y. Kovalev, MPIfR

Radio-astronomy has, in the past decades, worked towards building the
infrastructural and technical capacity necessary to reliably create high-
resolution (sub-arcsec), high-sensitivity (collecting areas up to a square
kilometer), and high-fidelity maps of our Universe. In the Southern
hemisphere, this is exemplified in the SKA; the ngVLA will provide a
complementary and worthy successor in the Northern hemisphere. The ultimate
aim is to generalise, over the entire extent of the sky, the work done over
the past decades, from the Cambridge surveys [e.g. 404] which revealed the
large radio sources that inhabit our universe, all the way to multi-wavelength
[e.g. COSMOS; 344] and large sky-surveys [e.g. FIRST, VLASS, EMU, LoTSS; 21,
217, 271, 351, 350], that peered into the deep radio universe probing the
faint active and dominating star-forming galaxy populations. The ngVLA will
provide an unprecedented ability to constrain the underlying physics of this
separation, not on ad-hoc observational criteria but physically-significant
observational tracers.

This ambition comes, of course, with a cost: namely, the size of the
associated data. From antenna voltage correlation, to the computing
requirements for data calibration & reduction, to the storage of the final
data-products with the appropriate quality metrics, metadata and compression
algorithm, as well as the automation and distribution of as much of the
subsequent analysis as possible, the result is the exponential increase of the
requirements for processing capabilities (high-performance computers - HPC;
federated computing) and storage (order of Peta-to-Exabytes). The above is
finally in the context of a paradigm shift in data sharing and knowledge
distribution, with science-ready products and code-sharing following open
science policies [findability, accessibility, interoperability, and
reusability - FAIR; 403]. In this section, we will consider the analysis of
Observatory data-products, e.g. the next-generation ngVLA surveys. By
extending at least three axes of the existing parameter space (resolution,
sensitivity, spectral coverage), the complexity of source-finding,
association/discrimination and finally classification is also increased. Not
only is the classification problem to be solved for a much greater source
density, the complexity of each individual source is increased, including with
the introduction of new source categories as sensitivity thresholds are
reached (e.g. star-formation emission becoming detectable).

To rise to this challenge, three interrelated approaches have proven fruitful
to identify radio sources and their host galaxies, and classify them based on
their properties: a) statistical methods of population study [e.g. 337], which
require a pre-existing, reliable multi-wavelength source association catalogue
- itself a monumental task; b) machine learning (ML) [e.g. 13, 239, 8], vital
to rise to the challenge of next-generation (SKA, ngVLA) catalogues with their
millions of complex, resolved, multi-category radio sources; and c) citizen
science, critical to compile robust training samples, thus enabling
discoveries. The future of radio-astronomy lies in the joint deployment of all
three approaches.

####  2.37.1 Population Statistics:

With high-quality, multi-wavelength data of large populations of astronomical
sources, it is possible to robustly identify meaningful subsets within these
populations. Better spectral coverage makes it more likely to discern
underlying physical mechanisms [88, 344, 95, 94, 201, 140, 355, 30, 257, 386,
385, 146]. This approach has proved fruitful in panchromatic fields like
COSMOS [e.g. 356, 355, 386, 385], to address key aspects of galaxy evolution,
probing back to the epoch of reionisation. These fields’ relatively small sky
area ($\sim$2 deg2) allows for methods of visual inspection to create robust,
enhanced catalogues (including science-ready products (e.g. position of radio
source and host, fluxes, sizes, host properties, environmental parameters).
Reaching deeper sensitivity [2$\mu$Jy/beam, MIGHTEE; 152] reveals a key issue
in radio source identification and classification: the wealth of unrelated,
faint and point-like radio sources around and within larger, diffuse radio
sources impose the need for robust spectro-photometric coverage and efficient
source deblending [e.g. super-deblend 181]. Additionally, as the resolution
and sensitivity of our surveys increase, new, complex emission becomes
detected, while existing point sources might resolve into complex structures
themselves. The performance of current-generation automatic algorithms for
source identification [e.g. BLOBCAT, PyBDSF; 260] is thereby mitigated, hence
the necessity for machine-learning approaches. Formation of deep parsec-scale-
selected complete samples of AGN [e.g., 205, 303, and references therein] will
allow to address pivotal questions related to highly energetic phenomena in
AGN cores including jet formation and collimation, energy extraction, particle
acceleration and neutrino production, and also aid with AGN/SFG disentangling.
Current, now-conventional methods remain vital in this data-intensive radio
era. Even approaches as basic as visual inspection are still needed to
identify, deblend, assemble and classify more complex radio structures, but
quickly show their limits as sample sizes increase. For surveys of the order
of hundreds of thousands to million of radio sources [e.g. EMU, LoTSS; 271,
272, 351, 350, 257, 147], the robust training of reliable ML/AI algorithms is
crucial.

Astrometry and geodesy: A very important aspect of ngVLA long baseline surveys
and AGN studies is that they will enable precise astrometry and geodesy
measurements, linking radio astronomy and the study of astrophysical objects
to interdisciplinary science by providing detailed characterisation of the
Earth (e.g. shape, rotation, gravity, tectonic plate motion). VLBI-compact AGN
form the basis of the most accurate reference frames in radio [68] and optical
[115] bands and are used for precise geodesy measurements [e.g., 284]. Deep
surveys of ngVLA including its long baselines will allow us to significantly
extend the sample of compact extragalactic radio sources forming the frame.
Detailed imaging information will be used to compensate for effects of AGN
structure at parsec-scales which currently provide one of the limitations of
the VLBI reference frame accuracy [e.g., 409].

####  2.37.2 Machine learning:

Automated algorithmic tools have already been developed for radio source
identification and classification [e.g. PyBDSF, Selavy, Aegean, Ceasar,
Profound; 260, 402, 144, 324, 325, 331, 143], but they all face limitations
when dealing with complex radio structures, as recently revealed by
comparative studies for multi-source finders [Hydra; 44, 45]. Algorithms
featuring two-channel identification and classification using radio and
optical/infrared observations of the field are promising: they do not require
prior training, instead relying on dimensionality reduction and sorting
methods. These techniques of unsupervised cataloguing, known as self-
organising maps [e.g. PINK; 302, 117] can efficiently match radio sources to
host galaxies, and are very useful for discovering complex radio structures.
Advances in ML/AI include supervised deep learning convolutional neural
networks [CNN, e.g. CLARAN; 407] which have been used extensively to
automatically identify and classify large samples of radio sources. These
methods are, however, strongly reliant on robust training samples. Although
supervised CNN have been used in the field since 2017, they do come with their
own limitations and costs, such as re-training and adjusting for different
telescopes. Self-supervised learning [e.g. 353] or eXplainable Artificial
Intelligence (XAI) techniques [e.g. LIME; 369], are on the rise because they
aim to address the issues faced by CNNs, i.e. lacking a proper analysis for
overfitting [21]. Given that radio-astronomy applications lie in the weakly
supervised regime ($N_{\rm unlabelled}>>N_{\rm labelled}$), learning using the
significant quantity of unlabelled data could solve some of the shortcomings
in current models - e.g. using physical properties, using both labelled and
unlabelled data, and pre-training without labels [353]. Additionally, XAI
techniques [e.g. LIME 369] can now ensure that the chosen algorithm is optimal
for the task at hand.

In summary, ML/AI methods are a promising tool to handle large samples of
radio sources dealing with millions of galaxies. They remain computationally
expensive, and future technical work should also focus on optimising their CPU
efficiency.

####  2.37.3 Citizen science:

Complementing our advanced algorithms, visual inspection has proven very
valuable to find unexpected and complex sources in large surveys, and valuable
in deblending nearby and complex sources: after all, we wish not only to
associate and classify, but also handle unexpected discoveries.

Projects such as the radio galaxy zoo (RGZ) have been very successful in
training and engaging citizen scientists (zooters), who classified over
100,000 sources, resulting in 14 publications within 10 years. Their
successors for the EMU (Tang & Vardoulaki in prep.) and LoTSS [147] will use
modern approaches [43, 42, 345] to build the workspaces, aiming to provide an
enjoyable experience to the zooters, with the potential for VR developments
allowing grater accessibility of ngVLA images [82]. The results form the basis
of training samples for millions of radio sources, in addition to science-
ready products for research. Such projects have a tremendous educational
value, directly involving students in schools and universities via dedicated
programs.

####  2.37.4 Summary:

To play the classification game one needs a winning hand: a multi-wavelength
and multi-frequency approach, based on ML techniques calibrated through
citizen science engagement.

###  2.38 Constraining the nature of dark matter with strong gravitational
lensing

Thematic Areas: $\square$ Stellar Astrophysics $\square$ Solar System,
Planetary Systems and Habitability $\square$ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ Galaxies
and AGN $\square$ ✓ Cosmology, Large Scale Structure and Early Universe
$\square$ ✓ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Simona Vegetti Institution: Max-Planck-Institut für Astrophysik,
Garching Email<EMAIL_ADDRESS>
Co-authors: Devon M. Powell, MPA

The nature of dark matter is one of the most fundamental puzzles of
contemporary physics, with far-reaching implications, from particle physics to
cosmology and astrophysics in general. As of now, we do not know what dark
matter is. However, we do know that it is not one of the particles in the
Standard Model of particle physics, and several extensions have been proposed
[25].

Different dark matter models make different predictions on the distribution of
dark matter on sub-galactic scales. For example, the cold dark matter (CDM)
model predicts that the Universe should be clumpy down to sub-solar-mass
scales and that a relatively large population of low-mass haloes should exist
[e.g. 358]. On the other hand, warm dark matter (WDM) models predict less low-
mass structure, and in particular, the presence of a minimum halo mass below
which the dark matter distribution should be smooth [e.g. 236]. In fuzzy dark
matter (FDM, i.e. a form of dark matter made of ultra-light bosonic particles)
the dark matter distribution within galaxies is characterised instead by a
stochastic and oscillating granular structure [e.g. 161]. Different dark
matter models also make different predictions on the structure of low-mass
haloes, which are on average less concentrated in WDM and FDM than in CDM.
Self-interacting dark matter (SIDM) predicts the existence of very-dense core
collapsed objects. Measuring the dark matter distribution on sub-galactic
scales is therefore one of the cleanest and most direct way to distinguish
between dark matter models. As most of these structures (either in the form of
low-mass haloes or FDM granules) are expected to be completely dark, they are
best detected and characterised via their gravitational signature on the
images of strongly lensed galaxies and radio jets [see 391, for a review].

The sensitivity of observations of strong lens systems containing resolved
sources, to the dark matter distribution within the lens and along the line of
sight, strongly depends on the angular resolution of the data. The ngVLA in
its long baseline configuration ($>8000$ km), will allow us to probe the dark
matter distribution on sub-kpc scales and detect dark matter haloes with
masses as low as $10^{6}M_{\odot}$, where different dark matter models make
significantly different predictions on the number density of these objects. In
Fig. 34 we show mock ngVLA observations of the gravitational lens system
MG0751+2716 for different array configurations. The long baseline
configuration provides an angular resolution of a few milli-arcseconds, as
required to constrain the dark matter distribution on sub-kpc scales. In Fig.
35 we show the subhalo mass function and the expected mass sensitivity of the
long baseline configuration of the ngVLA to the presence of these objects. It
can be seen that these observations are expected to provide an increase in
sensitivity, compared to other existing facilities, by several orders of
magnitude.

Figure 34: Mock ngVLA observations of the gravitational lens system
MG0751+2716 for different array configurations. Credits: images created by A.
Lategan (U. Pretoria) and J. P. McKean (U. Pretoria, RUG) Figure 35: Subhalo
mass function predicted from CDM (dashed black line) and still viable WDM
models (blue and green solid lines). Vertical lines represents the mass
sensitivity from different observing facilities. Very Long Baseline
Interferometric observations with the ngVLA are expected to be sensitive to
the presence of low-mass haloes with masses as low as $10^{6}M_{\odot}$.
Credits: image created by C. M O’Riordan (MPA).

###  2.39 Sub-Structures in Blazar Jets and Synergetic TeV Observations

Thematic Areas: $\square$ Stellar Astrophysics $\square$ Solar System,
Planetary Systems and Habitability $\square$ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ ✓ Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ ✓ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Christoph Wendel Institution: Julius-Maximilians-Universität Würzburg
Email<EMAIL_ADDRESS>
Co-authors: (names and institutions)

Name: Karl Mannheim (JMU Würzburg), Matthias Kadler (JMU Würzburg)

Jets in active galactic nuclei (AGN) are known to accelerate particles to very
high energies as demonstrated by their bright $\gamma$-ray emission up to TeV
energies. The mechanism of particle acceleration remains disputed but it is
likely to be related to dynamical processes inside an inhomogeneous jet
medium. Indeed, stratified or multi-layered jets are readily motivated by
theory [357] such as the spine-sheath model [125], i.e. a fast-moving, highly
relativistic inner spine that might be surrounded by a mildly relativistic
outer sheath.

When jets propagate and expand, the energy stored in the magnetic field
carried along the jet can be converted via relativistic magnetic reconnection
into kinetic energy of the particles [126, 283]. Due to tearing instabilities,
the reconnection current sheets fragment into plasmoids which confine heated,
highly magnetised and compressed jet medium. The ejected plasmoids radiate
mainly in the X-ray and TeV regime and are embedded in the mini-jet current
sheets along the jet. The superposition of the beamed emission from the small
plasmoids is attributed to the background of a flaring period and is thought
to be lasting for several hours to days. However, plasmoids can merge and grow
to monster plasmoids, whose luminosity is comparable to the entire envelope
luminosity with a variability timescale of several minutes. This mechanism
provides an explanation for the observed ultra-fast, strong flares on top of
broader, weaker envelope emission as shown in the left-hand side panel of Fig.
36 [352, 5].

Relativistic magnetic reconnection can convert a magnetically dominated jet
into a kinetically dominated one, meanwhile changing the velocity and
collimation profile of a jet, which is observable with radio interferometry.
In such a transition region, mini-jets with streets of multiple plasmoids
should be detectable as separate components due to their high brightness
temperatures. However, current very-long-baseline-interferometry arrays lack
either the angular resolution or the dynamic range (cf. right-hand side panel
of Fig. 36). The ngVLA will provide superior information in this respect to
study such filamentary mini-jet sub-structures at the energetic transition
region of AGN jets.

In rare cases, it is already today possible that high-quality spectra at high
or very high energies can put constraints on the origin of the $\gamma$ rays
in blazar jets, e.g. by searching for spectral cut-offs due to absorption or
for narrow spectral bumps or dips due to pair cascades [401]. Major advances
in terms of TeV $\gamma$-ray sensitivity and energy coverage will come from
the imminent Cherenkov Telescope Array [CTA; 4, 86]. Future coordinated ngVLA
and CTA observations can thus reveal a causal connection of ultra-fast TeV
variability and mini-jet activity in the transition region and locate the TeV
$\gamma$-ray emission region of blazar jets as well as inform about the
dominant radiation and particle acceleration processes.

Figure 36: Left: $\gamma$-ray lightcurve of a flaring episode of 3C 279
detected by the Fermi Large Area Telescope in April 2018 [352]. A strong
minute-scale flare arises out of the envelope emission. Right: Event-Horizon-
Telescope image of 3C 279 with compact sub-components marked [196]. At
comparable effective angular resolution (lower frequency but higher signal-to-
noise ratio), the ngVLA will be able to measure also the low-intensity regions
(including their polarisation) between the components.

###  2.40 Antenna positions with a sub-mm repeatability

Thematic Areas: $\square$ Stellar Astrophysics $\square$ Solar System,
Planetary Systems and Habitability $\square$ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ ✓Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Ming Hui Xu Institution: German Research Centre for Geosciences GFZ
Email<EMAIL_ADDRESS>
Co-authors: (names and institutions)

Simone Bernhart, Reichert GmbH, Bonn & BKG, Frankfurt, Hayo Hase, BKG,
Frankfurt

Observations from ngVLA will be able to provide geodetic accuracy at the sub-
mm level so that the antennas are connected to each other with an accuracy
better than 1 mm. For the densely distributed antennas in the ngVLA network,
two major advantages can be used to achieve this high accuracy: 1) phase
delays can be routinely obtained and used for geodetic purposes, and 2)
systematic errors due to troposphere and ionosphere are largely reduced. The
results based on this idea are shown in Fig. 37 for the 120-meter-long
baseline between WETTZ13N and WETTZELL, demonstrating the repeatability at the
sub-mm level [410]. The ngVLA network can be entirely connected by using only
short baselines, and a dedicated solution of these short-baseline observations
will allow us to determine their positions with the sub-mm repeatability.

Because the effects related to source structure are one of the dominating
systematic errors in geodetic VLBI observations [408], another major topic for
geodesy is to study, monitor and model these effects to have really point-like
anchors in the sky, by using both the high-quality image products and the
astrophysical knowledge of modeling the structure of AGNs from ngVLA.

The invariant points of the ngVLA antennas and the axis offsets (between
azimuth and elevation axes) will need to be studied and calibrated based on
geodesy. More opportunities in developing geodesy will be available if there
will be joint observations of ngVLA with existing global geodetic networks to
contribute to the global terrestrial reference frame (TRF). One could select a
sub-network of ngVLA to regularly participate in geodetic observations, and
they could be core stations in the future TRF.

Geodetic positions of the antennas in ngVLA will provide an essential support
for its high-accuracy astrometric/astronomical applications where positions
and motions of the celestial sources are of concern.

Figure 37: Relative position residuals of antenna WETTZ13N with respect to
WETTZELL from three-year VLBI observations. Left: North coordinates v.s. East
coordinates. Right: Up coordinates from phase delays (red) and group delays
(blue).

###  2.41 High-precision $\lambda$-astrometry at mm-wavelengths with the ngVLA

Thematic Areas: $\square$ Stellar Astrophysics $\square$ Solar System,
Planetary Systems and Habitability $\square$ Circuit of Cosmic Matter (incl.
star formation) $\square$ The Galaxy and the Local Group $\square$ ✓ Galaxies
and AGN $\square$ Cosmology, Large Scale Structure and Early Universe
$\square$ Extreme conditions in the cosmos, fundamental astrophysics

Principal Author:

Name: Guang-Yao Zhao Institution: Max-Planck-Institut für Radioastronomie,
Bonn Email<EMAIL_ADDRESS>
Co-authors: Andrei Lobanov, MPIfR

Very long baseline interferometry (VLBI) at millimetre wavelengths is more
challenging than their centimetre counterparts, largely due to the limitations
on the coherence time imposed by the turbulent troposphere [e.g., see review
by 91]. while the ngVLA long baseline array (LBA) will greatly improve the
sensitivity of VLBI observations at frequencies up to 116 GHz, achieving
astrometry using the conventional phase-referencing method would still be
unreachable at the highest frequencies, because this would require fast
switching between sources within a cycle shorter than the coherence time. To
mitigate such an issue, a dedicated method, so-called source-frequency phase
referencing (SFPR), has been established [326]. A typical SFPR calibration
includes a frequency-domain phase solution transfer (FPT), i.e., using a
centimetre observation to calibrate a close-in-time millimetre observation
[256]. Recent successful observations have demonstrated that FPT and SFPR are
ideal for extending the coherence time and achieving relative astrometry at
millimetre wavelengths [e.g., 328, 327, 413, 416, 176].

SFPR requires observations at two or more frequencies to be carried out
(quasi-) simultaneously. This can be achieved by implementing the "quasi-
optical" multi-band receivers [e.g. the Korean VLBI Network 328, 416], fast
frequency switching [e.g., with the VLBA 326, 176], or via the paired antenna
method (subarraying) [e.g., 15, 187]. The technical design of the ngVLA should
be feasible to perform fast frequency switching or subarraying, and thus
enable SFPR observations. Together with the high angular resolution and high
sensitivity of the ngVLA, this will enable astrometric measurements with an
unprecedented level of precision [e.g., 91]. These measurements will have
important impacts on a number of scientific areas including AGN and jet
physics, stellar astrophysics, transient phenomenon, etc [see e.g., 89]

Below we list a few potential scientific applications in studying AGNs and
relativistic jets:

  * •

Linking black holes to their relativistic jets: Thanks to the high dynamic
range of the ngVLA images, it is possible to detect the black hole shadows and
photo rings in nearby galaxies at the higher frequencies of the ngVLA [232,
233]. The emissions from the relativistic jets are usually more prominent at
lower frequencies and show steep spectra. Astrometry across frequency bands
(i.e., $\lambda$-astrometry) using SFPR will enable robust alignments of the
images of the black hole shadow and the relativistic jet. Such alignments
would be critical to discern between different theoretical models for jet
launching in the vicinity of the supermassive black holes (SMBH), whether the
outflows are anchored from the magnetosphere of the black hole [33] or from
the accretion disk [32].

  * •

Studying the magnetic field structure in the ultracompact AGN jets: The VLBI
core of an AGN jet often corresponds to the $\tau$=1 surface at a given
frequency. Due to opacity effects, the location of the core changes with
frequency [e.g., 204]. Measuring this effect, the so-called core shift could
provide information on the physical conditions (e.g., magnetic field strength,
pressure) in the ultracompact jet [lobanov1998]. Besides, robust alignment of
images at different frequencies is required to perform Faraday Rotation
studies, which is key to probing the magnetic field geometry in the jet [e.g.,
91].

  * •

Detection of close binary SMBH systems:  Binary SMBHs are natural products of
hierarchical galaxy formation. Close binaries with less than a parsec
separation would be strong nano-Hz gravitation wave emitters [e.g., 93]. Yet
such systems are difficult to identify, especially when only one SMBH in the
system is radio loud. In this case, the orbital motion of the binary system is
still expected to leave signatures in the astrometric measurements [91,
jiang2023]. The high-accuracy astrometric results of the ngVLA at high
frequencies could allow the identification of binary SMBH candidates that will
be potential targets of the next-generation gravitation wave detectors.
Detailed follow-up studies of binary SMBHs will be helpful in understanding
how galaxies evolve [e.g., 91, 90].

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