Stellar Atmosphere and Magnetism Observing with the ngVLA
Masumi Shimojo1,2
1National Astoronomical Observatory of Japan,
2–21–1 Osawa, Mitaka, Tokyo 181–8588
2
Department of Astronomical Science, School of Physical Science,
The Graduate University of Advanced Studies (SOKENDAI),
2–21–1 Osawa, Mitaka, Tokyo 181–8588
masumi.shimojo@nao.ac.jp

Abstract
The thermal radio emission that might come from the chromosphere of the F, G, and K-type main-sequencestars is detected with the large interferometers recently. However, their sensitivities are not enough for investigatingstellar atmosphere and magnetism statistically yet. The next-generation Very Large Array (ngVLA) would bring
revolutionary progress to the studies by its unprecedented higher sensitivity. Moreover, its polarization precision
would be enough for investigating stellar magnetism using circular polarization signals. In this article, we predictthe potential of the ngVLA for investigating stellar atmosphere and magnetism based on solar microwave data anddiscuss what preparations are needed for maximizing scientific results from ngVLA stellar observations.
Key words: stars: activity — stars: atmosphere — stars: magnetic field — radio continuum: stars

Atacama Large Millimeter/submillimeter Array (ALMA) and
Karl G. Jansky Very Large Array (JVLA), the thermal radio
emission from the F, G, and K-type main-sequence stars thatmight come from their chromosphere was detected recently(Villadsen et al. 2014; Liseau et al. 2015; Suresh et al. 2020).
However, the sensitivity of these instruments is not enoughfor investigating the chromosphere and magnetism of the stars
statistically. The next-generation Very Large Array (ngVLA)
would bring revolutionary progress to stellar atmosphere studies by its unprecedented higher sensitivity. Moreover, its polarization precision would be enough for investigating stellar
magnetism using circular polarization signals. In this article,
we predict the potential of the ngVLA for investigating stellar chromosphere and magnetism based on solar microwave
data and discuss what stellar information we can obtain fromngVLA data.

1. Introduction
The activity of a central star is one of the critical keys
for considering the habitable zone of its exo-solar system.
Especially, stellar wind, flares, and EUV radiation: these phenomena are crucial to comprehend the exoplanet’s atmosphere,
and the estimation of their influences is essential to understandthe exoplanet’s habitability. Based on the knowledge about ourSun, the phenomena should strongly depend on stellar magnetic activities. So, stellar magnetism is a fundamental issueof this subject. Additionally, understanding the stable component of the stellar chromosphere is also essential because most
UV radiation that affects the higher atmosphere of exoplanets
comes from the layer.
Studies of such phenomena and structures were done mainlywith emission and absorption lines within optical and UV
ranges (Linsky 2017). The radio emission is not used for thestudies except for very few cases, even when the radio photosphere with microwave would be located in the stellar chromosphere. The reason for lacking studies using the microwave
is that the emission from the main-sequence stars is not brightenough for detecting with most current radio telescopes except
for active stars and high mass-loss stars. In the case of active
stars, the high-energy electrons created by stellar activities fill
the star’s magnetosphere. Hence the strong microwave emission comes from the electrons, and we cannot obtain information about its chromosphere from the microwave emission ofactive stars (Güdel 2002). The radio photosphere of a highmass-loss star is formed by its stellar wind and ejectors. As aresult, the radio photosphere’s size is significantly larger than
the star’s size, then the radio flux from the star is bright enoughfor detection (Wright & Barlow 1975; Blomme 2011). So, themicrowave emission from such stars also does not show theirchromosphere.
Thanks to the high sensitivity of the large interferometers:

2. Microwave spectra from the Sun and stars
The monitoring observations of the solar flux density in the
microwave range started in the late 1940s. Around 20 institutes had carried out the monitoring radio observation of
the Sun in the 1970s(Tanaka et al. 1973). However, atpresent (Feb. 2021), only a few institutes continue to report
the daily flux densities of the Sun with the microwave range(1∼10 GHz), and the famous F10.7 (2.8 GHz) index is oneof them(Covington 1969). The other famous one is the
Toyokawa-Nobeyama Radio Polarimeters (NoRP). The NoRP
is constructed for measuring the total flux density and circularpolarization degree of the Sun at 1, 2, 3.75, 9.4, 17, 34, and 80
GHz (Tanake & Kakinuma 1957; Nakajima et al. 1985). The
daily solar flux densities at 1, 2, 3.75, 9.4, and 17 GHz havebeen reported monthly via the Internet1 , and the oldest data
1

1

https://solar.nro.nao.ac.jp/norp/

2of NoRP is the solar flux density at 3.75 GHz in November
1951 (Tanake et al. 1953). Therefore, the NoRP’s solar flux
database covers 70 years, in other words, six solar cycles.
Figure 1 shows the microwave spectra obtained with NoRP
at solar maxima and minima. The right panel shows the microwave spectra at the solar minima of Cycle 20, 21, 22, 23,
and 24. Shimojo et al. (2017) revealed no difference in the
spectra of solar minima of the recent five solar cycles basedon the plot. Since the spectra were observed at the deepest solar minima, which means no sunspot and no active region, it
presents the spectrum of thermal emission from the radio photosphere of each frequency. Zirin et al. (1991) observed thecenter of the Sun that is a quiet region with the 27-m antennaof the Owens Valley frequency-agile interferometer, using the“total power” mode. Figure 2 is their result, the spectra ofQuiet Sun, and it is basically the same as the right panel of
Figure 1 even when the units are different. Each frequency
component in the spectrum comes from the radio photosphereof each observing frequency located in the transition region andchromosphere. Hence, the spectrum reveals the height profileof the temperature and density of the solar atmosphere, andmicrowave is one of the key observables for investigating theheight structure of a stellar atmosphere.
1000

Fig. 2. Observed brightness temperature as a function of frequency(×), compared to the result of Fuerst (1980). The soled line is thebest fit. (Zirin et al. 1991)

1000
Cycle 20: 1GHz 41.2 / 2GHz 50.1 / 4GHz 76.9 / 9GHz 262.8 [SFU]
Cycle 21: 1GHz 43.2 / 2GHz 52.6 / 4GHz 76.7 / 9GHz 257.2 [SFU]
Cycle 22: 1GHz 44.3 / 2GHz 52.4 / 4GHz 75.9 / 9GHz 254.3 [SFU]
Cycle 23: 1GHz 47.7 / 2GHz 56.1 / 4GHz 79.8 / 9GHz 261.2 [SFU]

Flux (SFU)

Flux (SFU)

Cycle 24: 1GHz 44.5 / 2GHz 52.0 / 4GHz 76.8 / 9GHz 259.5 [SFU]

100

100

Fig. 3. Left: flux spectra for τ Ceti. Right: stellar disk-averaged brightness temperature spectra. Both columns: non-detections are shown as
downwards arrows marking the 99% confidence upper limits and detections as points with 1σ error bars. The plots also show the solar spectrafrom White (2004) for solar minimum (solid line) and solar maximum(dotted line). (Villadsen et al. 2014)

Cycle 19: 1GHz 141.6 / 2GHz 191.2 / 4GHz 233.0 / 9GHz 384.1 [SFU]
Cycle 20: 1GHz 94.8 / 2GHz 108.1 / 4GHz 134.7 / 9GHz 307.2 [SFU]
Cycle 21: 1GHz 127.9 / 2GHz 167.7 / 4GHz 182.2 / 9GHz 338.9 [SFU]
Cycle 22: 1GHz 142.2 / 2GHz 189.9 / 4GHz 206.2 / 9GHz 357.2 [SFU]
Cycle 23: 1GHz 137.3 / 2GHz 173.3 / 4GHz 198.9 / 9GHz 368.5 [SFU]
Cycle 24: 1GHz 99.9 / 2GHz 123.2 / 4GHz 143.9 / 9GHz 304.7 [SFU]

10
0

2

4
6
Frequency (GHz)

8

10

10
0

2

4
6
Frequency (GHz)810

Fig. 1. Monthly mean microwave spectra in the months at the solar
maximum (left panel) or minimum (right panel) in each solar cycle.
The colors indicate the number of the solar cycle. 1 SFU equals to 104
Jy. (Shimojo et al. 2017)

Thanks to the high sensitivity of the JVLA, we can detect
the thermal emission from the radio photosphere of solar-typestars now. Figure 3 shows the microwave spectrum of τ Ceti
(Villadsen et al. 2014). The solid and dotted lines in Figure
3 are the same as the right panel and left panel of Figure 1,
respectively. The spectrum should reveal its atmosphere, but
most data points of current data are the upper limits. So, thesensitivity of the JVLA is not enough for investigating the stellar atmosphere even when the star is located only 3.65 pc fromus.
The ngVLA would have the potential to induce revolutionary change to the situation. Carilli et al. (2018) investigated thepossibility of imaging stellar radio photosphere with ngVLA
and presented that the radio photosphere of 538 main-sequencestars included 370 F, G, and K-type stars, can be detected
and resolved with 85 GHz. Although we need to evaluate
the detectability with lower frequencies, we might obtain mi-

crowave spectra of the radio photosphere of a hundred mainsequence stars, like Figure 1 and Figure 2, with the ngVLA.
Such datasets should reveal the varieties of the stellar atmosphere and progress our understanding significantly.
As mentioned before, Figure 2 and the right panel of Figure
1 show the spectra of the Quiet Sun and reveal the hight structure of temperature and density in the chromosphere and transition region. However, it is the “averaged” spectrum evenwhen it is the solar spectrum because the atmospheric layers have fine structures and dynamics that cannot be resolved
with most solar radio telescopes, as shown with the Hinodesatellite (Hinode Review Team et al. 2019). Hence, the relation between a stellar microwave spectrum and the hight structures of its atmosphere is not simple, and the relationship is
not understood well even in the solar atmosphere (Shibasaki
et al. 2011). Recently, solar observations with the ALMA
(Shimojo et al. 2017; White et al. 2017) reveal fine structures and dynamics in the mm-wave photosphere located in
the chromosphere . On the other hand, thanks to the progressof Radiative-MagnetoHydroDynamics (R-MHD) simulations,
we can reproduce the structures and dynamics of the layers in
the computers. Therefore, the comparison studies between thesolar ALMA data and the solar atmosphere models included

3
the R-MHD simulations become active for solving the relation between the solar microwave spectrum and solar atmosphere now (Martı́nez-Sykora et al. 2020; Wedemeyer et al.
2020; Alissandrakis et al. 2020; Eklund et al. 2020). The modeling works in solar physics are very important for understanding stellar data obtained with the ngVLA.
The difference between the microwave spectra shown in theleft and right panels of Figure 1 shows the microwave component from active regions. To emphasis the component, we show
the different spectrum between solar maximum and minimumin the right panel of Figure 4. The spectrum consists of twoemissions; one is the thermal emission from the dense coronalplasma, and the other one is the gyroresonance emission above
sunspots. The component of gyroresonance emission dominants around 5 GHz (Schmahl & Kundu 1998).
Spectra of Solar Max. & Min.

Difference
200

100

10
0

2
4
6
8
Frequency [GHz]10

3. Circular polarization signal from the Sun and stars
The strength of gyroresonance depends on the polarizationof electromagnetic waves and magnetic field vectors. The extraordinary mode (x mode) of electromagnetic wave gyrates
about the magnetic field with the same sense of rotation as anelectron and resonates strongly with the thermal electrons. On
the other hand, the other mode, the ordinary mode (o mode),gyrates about the magnetic field with the opposite sense tothat of the electron, and its resonance with thermal electrons
is weaker than the x mode. Therefore, there is a difference between the optical depths of the modes, and the gyroresonanceemission is a circular-polarized wave basically. It means thatthe circular polarization signal from the gyroresonance emission has the information of the direction of magnetic field vectors. Then, what do the total circular polarization signals fromthe whole Sun show us? It is a crucial question for understanding stellar circular polarization data obtained with the ngVLA.

150

AR10960 / 3.75GHz Stokes-I
110

100
100

50
0

2
4
6
8
Frequency [GHz]10

Stokes-I Flux [SFU]

C23 Max - C24 Min. [SFU]

Flux [SFU]

1000

upper panel in Figure 5, which shows solar rotation.

Fig. 4. Left: Microwave spectra at Solar Maximum (Plus marks, 8
July 2014) and Solar minimum (dashed line) observed with the NoRP.
Right: Difference between the maximum and minimum. The dash-lineis the hand-writing line of the spectrum of gyro-resonance component.

8070
24-May29-May03-Jun08-Jun13-JunStart Time (24-May-07 00:00:00)

18-JunAR10960 / 3.75GHz Circular Polarization Degree21Pol. Degree [%]The thermal electrons gyrated by v × B force resonant withelectromagnetic waves when the gyro frequency and its higher
harmonics equals the frequency of the electromagnetic wave.
The resonance causes increasing the opacity with the frequency, and the resonant plasma emits electromagnetic waves
based on the physical temperature of the plasma. The gyro frequency is 2.8 × B MHz, where B is the magnetic field strength
measured in Gauss. Considering that the harmonic numbers
should be 1, 2, or 3 for solar plasma, the resonance for the GHz
range occurs in the corona only above sunspots. So, strong
magnetic fields are essential for microwave emission with gyroresonance. The gyroresonance emission is reviewed by Dulk
(1985) and White & Kundu (1997). To understand its in detail,we recommend reading these papers.
Considering these solar studies, the gyroresonace emission
in the GHz range comes only from strong magnetic fields,
like the above starspots, and includes the information of stellar magnetic fields. Due to the rigid relation between magnetic
fields and gyroresonance, the peak frequency of the gyroresonace emission indicates the averaged magnetic fields above
starspots. It will be a crucial achievement for stellar physics.
For the study, we also need the microwave spectrum of the starwhen its activity is low. Hence, we need to observe the star
every day during its rotation period and create a plot like the

90

0

-1

-2
24-May29-May03-Jun08-Jun13-JunStart Time (24-May-07 00:00:00)

18-JunFig. 5. Upper panel: the time profile of the solar flux density at 3.75
GHz observed with NoRP. The time range is from 24 May to 22 June
2007. Lower panel: the time profile of the circular polarization degree.

At first, to consider the most straightforward case for understanding the circular polarization data, we selected the period that an active region passed the solar disk from west to
east. Figure 5 shows the total solar flux density and circular polarization degree at 3.75 GHz from 24 May to 28 June
2007. Although there were two decayed active regions with4
weak magnetic fields, a major active region on the solar disk
was only “NOAA10960”, and most contribution of microwave
comes from this active region. The active region appeared fromthe east limb on 1 June, passed the central meridian on 7 June,
and went to behind the limb on 13 June. The period is near
the solar minimum of Cycle 23, and then the active region andits sunspots are not so big and not with strong magnetic fields,comparing the active regions in solar maxima. Nevertheless,the variation of the circular polarization degree is around ±1% (see the lower panel of Figure 5). It is good news because
the 1 % polarization signal should be easily detected with thengVLA which polarization dynamic range is 35 dB at the center of the field (Murphy et al. 2020).
As shown in Figure 5, the time variation of the polarization is not simple. The peak time of circular polarization is
not the same as that of solar flux density. Usually, an active region has two sunspot groups, preceding sunspots and following
sunspots, and they have opposite magnetic polarity. The circular polarization signals from both sunspots are canceled out ofeach other. Hence, the circular polarization degree decreases
when both sunspots appear on the disk. When the active region
locates near the limb, the resonance layer above a spot is occulted by the limb or the layer above the other spot. Due to theocculting, the circular polarization degree increases (the left
panels of Figure 6). Therefore, if we obtain the time profile ofstellar microwave emission with circular polarization continuously during its rotation period, we would know the magnetic
configuration on the stellar disk even when we cannot resolve
the star.

The relation between stellar spots andGyro-resonance emission(Stokes-I&V)
spot with+ polarity

spot with- polarity

Stokes-I :/ Stokes-V: ＋

Stokes-I: Max / Stokes-V: ~0

Stokes-I:/ Stokes-V: ー

Stokes-I: Strong / Stokes-V: ~0

Fig. 6. The relation between stellar spots and gyroresonance emission.
Left three panels: the case of one active region with a pair of preceding
and following spots on the stellar disk, Right panel: many stellar spot
on the disk.

Figure 5 and the left panels of Figure 6 is the simplest case,as mentioned before, and actual stellar activities are not so simple. As shown in the right panel of Figure 6, it is easily imagined that many spots appear on the stellar disk. In this case,intense microwave flux by gyroresonance emission would beobserved during the whole rotation period, but the circular polarization degree is always very small. As described above,the successive observations during the rotation period are very
critical for investigating the stellar magnetism using microwave
and its circular polarization data.
White & Kundu (1997) mentioned that the gyroresonanceemission strongly depends on the magnetic configuration of anactive region, and the angle between the magnetic field vector
and line of the sight. Hence, actually, we need the modelingprocess to re-construct the stellar magnetic field distribution
from microwave data with circular polarization. Unfortunately,such studies in solar physics are not carried out because we canresolve the Sun with microwave using the radio interferometers. We should prepare the modeling for ngVLA stellar observations. Fortunately, we have much data on solar microwave
data and solar magnetograms. While there are many works forthe preparation, there might not be critical issues for developing the modeling.
4. The possibility of microwave emission from othersources
We discussed the microwave emission and its origin, assuming that the emission comes from the chromosphere or
corona of a central star until now. However, the assumption
is not always correct. As already mentioned in the Section“Introduction”, the high-energy electrons and dense stellar
wind emit microwave. So, we need to distinguish the emissions before discussing the chromosphere and magnetism of
the star. We discuss the issue of the data selection as ending
remarks.
When the target is a non-active star, in other words, the occurrence rate of stellar flares is low, we can easily avoid thenon-thermal emission from a stellar flare using the time variation. If the size of flare loops is smaller than a few times thestar’s size, the flare duration is shorter than or similar to the
Alfven transit time2 of the star in corona considering the flaremodel based on magnetic reconnection (Shibata & Magara2011). So, we can identify the period of the flare during theobservations.
We cannot exclude the microwave emission from stellar
wind using the time variation because it is stable. To exclude
the stars that its microwave emission from stellar wind dominates, we need to obtain the broad-band spectrum (1 ∼ 20
GHz) in the microwave range because its spectrum has a significant difference from the chromosphere (Suresh et al. 2020).
Obtaining broad-band spectra is crucial not only for investigating the stellar chromosphere and magnetism but also for thedata selection.
The possible other source is an exoplanet. If there is a planetwith strong magnetic fields, like Jupiter, the planet would be astrong microwave emitter (de Pater et al. 1997). In this case, weneed to compare the source position and observing time withthe planet orbit and its phase and identify the emission source,
like done by Bastian et al. (2018).
As mentioned above, we need to deal carefully with theobserving data for identifying the emission source, but there
is no doubt that the ngVLA has the potential for the significant progress of stellar atmosphere and magnetism studies. To
achieve superior scientific results, the stellar atmosphere model
based on solar atmosphere studies is essential, as mentioned
before. We should start the preparation in the planning andconstruction phase of the ngVLA project.
2

The time scale at the Sun is about 20 minutes.

5
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