Prospects of High Spatial Resolution Observations with ngVLATakayuki Muto
Division of Liberal Arts, Kogakuin University, 1–24–2 Nishi-Shinjuku, Shinjuku, Tokyo 163–8677, Japan
muto@cc.kogakuin.ac.jp

Abstract
We discuss the capability of spatially resolved observations of protoplanetary disks with ngVLA. Using a commonly used protoplanetary disk model, we estimate to what extent ngVLA can resolve the disk structures at a given
distance from the central star. With ngVLA, spatially resolved observations of protoplanetary disks are possible with1 hour integration at the frequencies of 20 GHz or higher, and the spatial resolution can go down to several tens of
milliarcsec. Therefore, ngVLA is capable of obtaining similar quality images of protplanetary disks with ALMA,
while at much lower frequency. Low frequency observations is useful in determing the disk physical structures(i.e., temperature, surface density and dust properties) in tandem with sub-mm ALMA data. Especially, ngVLA
is a unique probe for the disk midplane of Earth-forming region (i.e., several au from the central star) and watersnowline.
Key words: protoplanetary disks — planets and satellites: formation — radio continuum: stars

1. Introduction
Planet formation is one of major problems in astrophysics,
and has been a topic of active debate for more than decades.
Planets are considered to be formed in protoplanetary disks,
which is a cold disk of gas and dust rotating around a youngstar. Dust grains are believed to grow to a planet within thedisk over a few to ten million years.
The structures of protoplanetary disks are key to understandplanet formation. Disk structures indicate where dust grainsare concentrated, or where planets are formed. Until very recently, however, such structures have not been known due totheir small sizes. Typical sizes of protoplanetary disks are of
the order of ∼100 au. Situated at the distance of >∼100 pc, theapparent size of protoplanetary disks is ∼1 asec. Therefore,
it is necessary to have a telescope with the spatial resolutionof at least ∼0.1 asec to observe structures in disks. If we areto observe the scale comparable with our Solar System planets(<∼several tens of au), higher spatial resolution is required.
ALMA has made game-changing discoveries of protoplanetary disk structures thanks to its unprecedented sensitivity
and spatial resolution at sub-mm and mm wavelengths. It is
now known that the disks are full of ring-like structures (e.g.,ALMA Partnership 2015, Andrews et al. 2019) and some disks
show strong asymmetry (e.g., Fukagawa et al. 2013). The
asymmetry of dust particles indicate the location where dust
grains are strongly concentrated and ring gap structures can be
an indirect signature of an already forming planet. We are now
starting to see the planet formation activities in protoplanetarydisks.
There are a number of advantages of going to longer wavelengths in the observations of protoplanetary disks. The mostimportant is that the disk can be optically thin at longer wavelengths. Since dust grains are heavily concentrated in protoplanetary disks, the dust continuum emission can become
optically thick even at sub-mm wavelengths (see Section 2)
and it becomes difficult to observe structures at disk midplane,

where planet formation takes place. Another merit of going tolonger wavelengths is that the it is possible to observe larger
grains, which are more likely to be involved in planet formation. Therefore, ngVLA, a high resolution instrument at mmto cm-wavelengths, is an ideal tool for studying planet formation in protoplanetary disks.
However, emission at longer wavelengths is generally faint.
Therefore, it is important to understand the limitation ofngVLA. In this memo, we discuss what can be observed withcurrently planned ngVLA specification by using a simple disk
model and suggest possible science goals made available withngVLA..
2. Typical Parameters of Protoplanetary Disks
We consider a simple disk model with the power-law radial
distribution of dust grain surface density:( r )−3/2Σd (r) = 10[g/cm2 ](1)
1 au
and temperature:( r )−1/2
T (r) = 300
[K].
(2)
1 au
Here, r is the distance from the central star and numericalfactors are chosen based on the Minimum-Mass Solar Nebulamodel (Hayashi et al. 1985). This disk temperature indicatesthat the disk is geometrically thin, or the ratio of pressure scaleheight h and the disk radius r is much less than unity, i.e.,h/r <∼ 0.1.
We first note that the innermost region of protoplanetarydisks is optically thick at sub-mm wavelength. The opticaldepth of the model disk is given by) ( r )−3/2(ν,τν (r) = 100(3)
103 GHz
1 AU
wherecommonlyused
dustopacityκof10(ν/103 GHz) cm2 /g is assumed (Beckwith et al. 1990)

2[Vol. ,Resolution θ1/2 [mas]1001012.4 GHz
10.58
870.6-8 GHz
0.56
50.51
4.5×105

16 GHz0.13
12.42
146627 GHz
0.05
4.5335041 GHz
0.03
2.77
207

93 GHz
0.02
1.36
126

Table 1. Brightness temperature RMS [K] with 1 hour integraton

with the spectral index β of unity. Only with the estimate of
optical depth, the need of low frequency (long wavelengths)
observations is evident when one has to probe the disk midplane. With this disk model, the expected surface brightnessof the disk when viewed face-on can be calculated as()Tb,ν (r) ∼ T (r) 1 − e−τν (r)(4)

tion, the disk structures at ∼ 30 au from the central star can beresolved down to several tens of milliarcsec, or less than 10 au
at the distance of 100 pc, at frequencies higher than ∼20 GHz.
The structures at ∼3 au from the central star can be resolved
down to ∼ 10 mas, or 1 au at the distance of 100 pc, at thefrequency higher than ∼ 20 GHz.

where Tb,ν (r) is the brightness temperature of the resolved disk
image at the observing frequency of ν.

4. Possible Science Cases

3. Observability with ngVLA
We discuss to what extent the ngVLA can resolve the diskstructure using the typical protoplanetary disk model introduced in the previous section. We calculate the brighness temperature of the disk at a given radius and compare it with the1 hr continuum sensitivity provided in the ngVLA Reference
Design Book (Table 1).
Figure 1 compares the expected signal from protoplanetarydisks with the ngVLA design sensitivity. Each panel shows theRMS noise levels for different beam sizes with 1 hour integration in purple shadows and the expected signal in brightness
temperature at a given radius with lines. For example, the redline in the Panel (a) of Figure 1 indicates the surface brightnessof the disk at the location 10 au away from the central star.
With 100 mas beam, the signal from 10 au from the central starcan be detected with more than 10σ at >∼16 GHz. Since thedisk physical temperature is lower at the outer region of protoplanetary disks, the signal at ∼100 au from the central starcan be detectable only at the highest frequency bands for the
100 mas beam.
Since the typical distance of the nearby star forming regionis >∼100 pc, the beam size of 100 mas corresponds to 10 auscale. With 100 mas beam, therefore, the structures at 100 au
can be well resolved while it is possible to observed only largescale structures at <∼ 30 au region. Therefore, the observabilityof disk structures at low frequency is the competition between
the beam size and sensitivity. For higher spatial resolution, it isnecessary to go for higher frequency where the disk is brighter.
The disk optical depth poses another limit of high resolution
observations of the inner few au part of the disk. In the Panels(b) and (c) of Figure 1, we show the disk signal from <∼3 au.
The curves become flat for high frequency since the disk becoms optically thick and the brightness temperature of the disk
emission is limited by the physical temperature of the emitting
region. For the beam size of 10 mas, or ∼ 1 au at the distanceof 100 pc, the disk signal is detectable for frequency higher
than ∼20 GHz. For the beam size of 1 mas, weak detection isexpected only at the highest frequency of ngVLA bands.
In summary, ngVLA has potential to probe protoplanetary
disk structures down to several au scales. With 1 hour integra-Following up the discussion in the previous section, webriefly present two possible science cases on the spatially resolved observations of protoplanetary disks made available
with ngVLA.
4.1. Disk Dynamical Structures at Neptune-forming Region
With ngVLA, it is possible to resolve the disk at several auscales and the disk emission at r ∼30 au can be detected withmore than ∼ 10σ. At 30 au from the central star, the pressure
scale height of protoplanetary disks is expected to be <∼ 3 auand therefore, the disk structures with the scale comparable tothe pressure scale height can be resolved. Since the pressure
scale height of the disk is the distance traveled by sound wave
within one Kepler rotation period, it can be regarded as thecharacteristic length scales of the dynamical processes in thedisk, such as disk instability and/or disk-planet interaction. For
example, a massive planet embedded in a disk opens a gap withthe width of several pressure scale heights (e.g., Kanagawa etal. 2017).
The spatial resolution is similar to what current ALMA
can typically observe at >∼200 GHz (e.g., ALMA Partnership2015). With ngVLA, we expect have similar quality images atfrequencies ∼10 times lower than ALMA. Having spatially resolved wide band data provides us with rich information about
physical structures of disks. In dust continuum emission, disk
temperature, surface density and dust opacity are always degenerated at a single band observations (see Equation 4). With
multiple band observations of wide frequency coverage, it ispossible to break the degeneracy (Kim et al. 2020). It is important to have both high frequency bands (e.g., ALMA Band 7 orhigher) that probe temperature and the low frequency bands toprobe surface density. With much better spatial resolution andsensitivity than ALMA at 100 GHz, ngVLA will play a crucialrole in understanding icy-planet forming region (r ∼ 30 au) of
protoplanetary disks.
4.2. Disk Overall Structures at Earth-Forming Region
From the results in Section 3, ngVLA is capable of resolving
the disk within r ∼ 3 au by several to ten beams. Therefore,with ngVLA, for the first time, it is possible to spatially resolve
the Earth-forming regions in protoplanetary disks. The structures that extend over the disk scale can be probed. Since the3
Brightness Temperature [K]

No. ]
103

(a) 100mas Beam

1hr RMS
r=100au
r=30au101 r=10au

10-1
10-3
100

101
frequency [GHz]102

Brightness Temperature [K](b) 10mas Beam103

1hr RMS
r=10aur=3au

101

References

Brightness Temperature [K]

-1
10 0
10104

101
frequency [GHz]102(c) 1mas Beam
1hr RMS
r=3au
r=1au

103

102

evolution (e.g., Espaillat et al. 2014). However, some transitional disks have inner disks of less than several au in radius
within their large inner cavities (e.g., Fukagawa et al. 2013,Kudo et al. 2018). This is a mystery since standard viscous
evolution timescale is short at the inner part of the disk. If
there is a planet at the innermost radii, it can prevent disk materials to migrate onto the central star by forming a gap (e.g.,Zhu et al. 2012).
Another interesting feature expected at several au from thecentral star is the snowline, which is a condensation front ofwater ice expected at 2–3 au from the central star. Rocky dust
particles are expected interior to the snowline while icy dust atlarger radii. Rapid change of dust properties will result in thechange of dust opacity and therefore a ring-like feature may
be observed (e.g., Zhang et al. 2015, Okuzumi et al. 2016).
Currently, water snowline is investigated for stars exhibiting
a burst phase (Cieza et al. 2016), where the snowline goes tomuch outer radii due to high activity of the central star. WithngVLA, it will be possible to probe the snowline around normal stars, providing us with insight of planet formation anddust evolution.

101

102

frequency [GHz]Fig. 1. The expected signal and RMS with 1 hour integration for
100 mas (a), 10 mas (b), and 1 mas (c) resolution.

disk is expected to be optically thick at r <∼3 au from the central
star in sub-mm wavelengths, ngVLA will be a unique facility
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There are several interesting observational indications about
the innermost several au region of protoplanetary disks. One
example is the inner disk of transitional disks. A transitional
disk object is the young star having a circumstellar disk withan inner cavity and is considered to be in the late stage of disk

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