Hydrogen Radio Recombination Lines from Accreting Planets
Jun Hashimoto, 1,2,3 Yuhiko Aoyama, 4,5,6 Ruobing Dong 7 Beibei Liu 8
1Astrobiology Center, National Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
2
Subaru Telescope, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan3
Department of Astronomy, School of Science, Graduate University for Advanced Studies (SOKENDAI), Mitaka, Tokyo 181-8588, Japan
4
Department of Earth and Planetary Science, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo
113-0033, Japan
5
Institute for Advanced Study, Tsinghua University, Beijing 100084, People’s Republic of China
6
Department of Astronomy, Tsinghua University, Beijing 100084, People’s Republic of China
7
Department of Physics & Astronomy, University of Victoria, Victoria, BC, V8P 1A1, Canada
8
Department of Physics, Zhejiang University, 38 Zheda Road,Hangzhou 310027, China
jun.hashimto@nao.ac.jp

Abstract
Gas giant planet gains its mass via mass accretion from the parent protoplanetary disk, and thus, investigating
planetary accreting processes helps understanding of planet formation. The ngVLA with an extinction-free accreting
planet tracer of hydrogen radio recombination lines would solve long standing problems in planet formation: when,
where, and how planets form in the disk. The detection of any accreting signatures from planets also serves as asmoking-gun evidence of planet-origin in sub-structures of the disk. Note that long exposure time such as tens tohundreds of hours is necessary to significantly detect HRRL from accreting planets with the ngVLA.
Key words: planets and satellites: formation — planets and satellites: gaseous planets — accretion, accretion
disks — radio lines: planetary systems

1.

Accreting planets embedded in protoplanetary disks

Gas giant planet forms in a protoplanetary disk, and gains
its mass via mass accretion from the parent disk until its hoststar loses its gas disk (e.g., Hayashi et al. 1985). As predictedby planet population synthesis models (e.g., Ida & Lin 2004),
when the gas accretion onto planets is sufficiently large, gas
giant planets can form more than sub-Jovian planets. On theother hand, microlensing observations show that the number of
sub-Jovian planets is dominant in the planetary mass function(Suzuki et al. 2018). The mass accretion onto a planet determines the final mass of the planet (e.g., Tanigawa & Ikoma
2007) and thus investigating the planetary mass accretion process informs our understanding of planet formation.
When the gas giant planet is embedded in the disk, it is predicted to create a gap in the disk by planet–disk interactions(e.g., Lin & Papaloizou 1986). The gas in the disk spiraling flows onto the planet and its circumplanetary disk throughthe gap from higher latitude in the parent protoplanetary disk
(Figure 1; e.g., Tanigawa et al. 2012; Szulágyi et al. 2014).
This accreting flow is referred to as ‘meridional flow’, andhas been observed by ALMA (Teague et al. 2019). Since
the meridional accreting flow in the gap is supersonic becauseof its velocity close to free-fall one, the accreting gas shocks
on the planet and its circumplanetary disk. When the velocity of accreting gas is fast enough (more than ∼30 km/s;
Aoyama et al. 2018), the gas temperature by shocks reaches
4high enough (>∼10 K) to ionize atomic hydrogen. When freeelectrons recombine and cascade to the ground state or excite
neutral hydrogen via collision, they produce line emission suchas Hα at λ =6562.8 Å. Gas giant planets PDS 70b and c emit-ting Hα have been directly observed by Magellan/MagAO andVLT/MUSE (Wagner et al. 2018; Haffert et al. 2019).

Fig. 1. Schematic illustration of meridional flows in the circumplanetary emvironment at the edge-on view taken from Aoyama et al. (2018).

Analyzing recombination line emissions from accreting
planets provides useful physical quantities such as a dynamical
mass of the planet, an accretion rate, a value of extinction, anda filling factor (ff ; a fraction of emitting areas of the recombination line at the surface of the planet and its circumplanetarydisk; Aoyama et al. 2019; Hashimoto et al. 2020). While
numerical simulations predict that an accreting planet embedded in the protoplanetary disk may have a large filling factor

2[Vol. ,(>
∼1) due to meridional flows (e.g., Szulágyi et al. 2018), analyses of observed Hα from accreting planets PDS 70b and cembedded in the parent disk revealed small values of ff ∼0.01(Aoyama et al. 2019; Hashimoto et al. 2020). These small values indicate that the Hα emitting areas are localized at the surfaces of PDS 70b and c, and suggest that accreting processesof PDS 70b and c would be similar with stellar ones such as
magnetospheric accretion or boundary-layer accretion.
Despite the successes of investigating Hα and many efforts
to search for Hα from accreting planets (e.g., Cugno et al.
2019; Zurlo et al. 2020), robust detections of planetary Hαhave been reported in only PDS 70b and c to date. This may
be due to heavy extinction by dust grains over the planet in
the protoplanetary disk because emission lines at optical wavelengths are severely affected by dust extinction (Szulágyi et al.
2020). On the other hand, hydrogen recombination lines canbe found at radio wavelengths for the higher principal quantum number levels (n >∼ 20). For ngVLA at 1–116 GHz, there
are roughly 135 hydrogen radio recombination lines (HRRL)<of principal quantum numbers 40 <∼ n ∼ 175 at the α transition, i.e., H40α to H175α. At radio wavelengths, dust extinction in the protoplanetary disk is negligible except muchdenser regions in the inner disk at r <∼1 au. The disadvantage of HRRL is its much lower intensity comparing with Hα.
Figure 2 shows expected intensity ratios of planetary accreting
emission lines at Hnα relative to Hα (Aoyama et al. 2018),
e.g., I(H40α)/I(Hα) ∼ 4×10−10 . The ngVLA with the muchbetter sensitivity and spatial resolution may remedy this disadvantage and place HRRL as a paramount tracer of accreting
planets.
100
10-1
10-2

Flux ratio of Hn to Hα

10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10

5

10
15
20
25
30
35
Principal quantum number of lower level

4045Fig. 2. Intensity ratios of Hnα to Hα calculated by the one-dimensional radiative hydrodynamic model in Aoyama et al.
(2018), assuming the free-fall velocity v0 of 40 km/s andthe number density of hydrogen nuclei n0 of 1013 cm−3 .

2.

Detection of HRRL from accreting planets by ngVLA

In this section, We discuss some science cases (§ 2.1 to 2.4),
and describe the brief feasibility study of detecting HRRL fromaccreting planets by ngVLA (§ 2.5).
2.1.

Origin of sub-structures in the disks

ALMA has revealed sub-structures including gap/ring, spiral, and crescent structures in tens of protoplanetary disks.
Most of them are the gap/ring structures (e.g., Andrews et al.
2018). Though a number of possible mechanisms have been
discussed to explain the gap/ring structures, the origin is still
under debate. One exciting hypothesis is disk–planet interactions (e.g., Lin & Papaloizou 1986). However, robust detections of young planets in the gap are PDS 70b and c todate (e.g., Haffert et al. 2019), possibly due to large dust extinction at optical and near-infrared (NIR) wavelengths (e.g.,
Szulágyi et al. 2020). In addition to class II objects, the disks
around class 0/I objects also shows the gap/ring structures (e.g.,
HL Tau; ALMA partnership et al. 2015). It is much harder tosearch for planets around class I objects at optical/NIR wavelengths because of much heavier dust extinction of tens ofmagnitudes at optical wavelengths. On the other hand, HRRL
serves as the dust-extinction free tracer of accreting planets.
The ngVLA observations of HRRL could help understandingof the origin of the gap/ring structures.
2.2.

Ice and gas giant planets

The core accretion scenario (e.g., Hayashi et al. 1985) predicts that gas giant planet forms when its core reaches the critical mass of ∼10 M⊕ and triggers rapid gas accretion from theprotoplanetary disk. In our Solar system, though Uranus and
Neptune (ice giant planet) have their masses of >∼10 M⊕ , they
do not have massive gas like Jupiter. These facts may invokethat the critical mass distinguishing ice and gas giant planets ishigher than theoretical predictions. The demographics of themass of accreting planets embedded in the disk would provide
clues of the boundary core mass, and might test the planet formation theory.
The gap/ring structures have been most commonly found in
sub-structures in the disks. While the gap width and depth in
the protoplanetary disk have been used to estimate planetary
masses (e.g., Zhang et al. 2018; Lodato et a. 2019), theseproperties of gaps might be insufficient to enable unique constraints on the measurements of planetary masses, due to thedegeneracies of planetary mass with disk viscosity and aspectratio (Fung et al. 2014). On the other hand, analyses of HRRL
allows to derive the dynamical mass of planets (Aoyama et al.
2019; Hashimoto et al. 2020):
RPlanet v02,(1)
2G
where RPlanet , v02 , and G are a planetary radius, the free-fallvelocity, and the gravitational constant, respectively. The valueof v02 can be estimated by fitting the line profile because theline profile is a function of the free-fall velocity and the number
density of hydrogen nuclei n0 as shown in Figure 3.
MPlanet =No. ]

31

2.3.

(v0 km/s, n0 cm-3)(40, 1011)(80, 1011)(120, 1011)

Normalized energy fux density

0.8

0.6

0.4
1/e

0.2

0
-200

-150

-100

-50
0
50
Doppler velocity (km/s)

100

150

200

10-10

Energy fux density (erg/s/cm2/Hz)

How do gas giant planets evolve ?

The mass of the gas giant planet is determined by massaccretion. In the early phase of planet formation, rapid gas
accretion and/or meridional accretion would take place (e.g.,
Tanigawa et al. 2012; Szulágyi et al. 2014), possibly witha large mass accretion rate (ṀPlanet ) and a large filling factor (ff ), because circumplanetary environment consists of sufficient material. On the other hand, in the end of planet formation, when the gap in the disk curved by the planet is deep
enough, accretion flows from the disk onto planets could be reduced with small values of ṀPlanet and ff . The latter could be
supported by PDS 70b and c (Aoyama et al. 2019; Hashimoto
et al. 2020). To test this hypothesis of evolution of gas giant
planet, the relationship between the gas surface density at theplanetary radial location in the gap and the values of ṀPlanet& ff might be helpful.
The gas surface density can be estimated by ALMA. The
values of ṀPlanet and ff are derived as follows (Aoyama et al.
2019):(40, 1011)(40, 1012)(40, 1013)

10-11
10-12
10-13
10-14
10-15
10-16
10-17
10-18
-100

It has long been thought that gas giant planet formation takes
for a few Myr (Pollack et al. 1996). The discovery of substructures plausibly induced by planets in disks around class II
objects at >∼1 Myr old (e.g., Andrews et al. 2018) is still inagreement with the predicted timescale (e.g., Wimarsson et al.
2020). However, recent ALMA observations have revealed thatclass I objects with ages of < 1 Myr also possess ring/gap disks(e.g., ALMA partnership et al. 2015; Sheehan et al. 2018;
Segura-Cox et al. 2020). Particularly, these sub-structures arelocated at a few tens of AU from their central hosts. Theoreticalstudies suggested that the growth timescale of the cores of giant
planets increases with radial distances, mainly (if not all) due
to the prolonged orbital time (Ida & Lin 2004, Goldreich et al.
2004, Liu & Ji 2020). Thus, it would be even more challenging
to form gas giant planets at distant disk locations within 1 Myr.
The core accretion theory, including planetesimal accretion andpebble accretion, will need to be revisited, if accreting giant
planets can indeed be found around such young Class I objects
from ngVLA/HRRL observations.
2.4.

10-9

When and where do gas giant planets form?

-500Doppler velocity (km/s)

50

2
LHnα = 4πRPlanet
ff IHnα ,(2)2ṀPlanet = µn0 v0 ff (4πRPlanet
),

(3)

100

Fig. 3. Spectral profile of H40α with different velocity (top; 40, 80, and120 km/s with n0 = 1011 cm−3 ) and density (bottom; 1011 , 1012 , and1013 cm−3 with v0 = 40 km/s). The spectral width is ∼ v0 /2, excepting the case of high density. At high density, the flux is saturated at theenergy density determined by Planck’s law. Namely, near the line center, the optical depth is enough to make the radiation black-body like.

where LHnα , RPlanet and IHnα are the luminosity of HRRL
Hnα, the planetary radius, and the Hnα energy flux per unit
area calculated with the free-fall velocity v0 and the number
density of hydrogen nuclei n0 by using the model in Aoyama
et al. (2018), respectively. The value of µ is the mean mass perhydrogen nucleus, µ = 2.3 × 10−24 g.
2.5.

Expected flux of planetary HRRL

We calculate the expected line flux of H40α (99.0 GHz)
from accreting planets by using the one-dimensional radiative hydrodynamic model developed in Aoyama et al. (2018).
Assuming that a 1 MJup planet is embedded in the protoplanetary disk at a distance of 140 pc (the free-fall velocity
v0 of 40 km/s, the number density of hydrogen nuclei n0 of
1013 cm−3 , a filling factor ff of unity, and a planetary radius

4[Vol. ,of 2 RJup ), the expected line flux of H40α is 18 µJy. Since
the line width roughly corresponds to half of the free-fall velocity of 40 km/s, the expected SNR at one channel of 10 km/s
is roughly 3 with 100 h on source time. The line sensitivity at
10 km/s of the ngVLA is 32 µJy/beam at 93 GHz. Above assumption of n0 =1013 cm−3 is similar to that of PDS 70b andc, whose mass accretion rate is 5 × 10−7 MJ yr−1 (Hashimoto
et al. 2020). Regarding the filling factor, it is expected to alarger value of >∼1 in case of meridional flows (e.g., Szulágyi
et al. 2018). Our feasibility study suggests that the detectionof HRRL with the ngVLA is very challenging, whereas if thesensitivity of the receivers could be improved by a factor of 10,
we only need 10 h of on source time.
3.

Bright-240 km/s

N3″ (303 au)

E-60 km/s

Searching for HRRL by ALMAHRRL can be observed with ALMA. At band 1 to 10 (i.e.,
35–950 GHz) in ALMA, there are ∼40 lines of HRRL (H19α
to H57α). In ALMA archival data, some observations of protoplanetary disks contain HRRL in their observing setups bychance. One good example would be DSHARP (Disk Substructures at High Angular Resolution Project; Andrews et al.
2018) which is one of the ALMA large projects (program ID:
2016.1.00484.L). DSHARP is a deep, high resolution (35 mas,or 5 au) survey of the 240 GHz continuum and 12CO J=2-1
line emission from 20 nearby stars, and its spectral setup contains H30α at 231.9 GHz. Figure 4 shows the channel mapsof H30α in HD 163296 system (a mass of 2.0 M , a distance of 101 pc) taken by part of the DSHARP project. We do
not find significant signals of H30α around HD 163296. Theline sensitivity at 10 km/s bandwidth in HD 163296 reaches∼350 µJy/beam, which is roughly one order magnitude higher
than that of ngVLA (e.g., 32 µJy/beam at 93 GHz).
4.

Faint

Synergy with other observations

We can search for infrared emission from planets with dynamically constrained masses from HRRL. If they can be detected (e.g., PDS 70b and c, Keppler et al. 2018, Mesa et al.
2019), we will be able to constrain planetary evolutionary models (Fortney et al. 2007, Spiegel & Burrows 2012), as different models (e.g., “hot start” or “cold star”) predict different
infrared fluxes for planets with the same mass at the same age.
At the moment, detecting infrared emission from planets forming in disks are still very difficult. In the future, with the help
of JWST and TMT, it is expected that more PDS 70 b like detections will be made.
References
ALMA Partnership, Brogan, C. L., Pérez, L. M., et al. 2015, ApJL,
808, L3
Andrews, S. M., Huang, J., Pérez, L. M., et al. 2018, ApJL, 869, L41
Aoyama, Y., Ikoma, M., & Tanigawa, T. 2018, ApJ, 866, 84
Aoyama, Y., & Ikoma, M. 2019, ApJL, 885, L29
Cugno, G., Quanz, S. P., Hunziker, S., et al. 2019, A&A, 622, 156
Fortney, J. J., Marley, M. S., & Barnes, J. W. 2007, ApJ, 659, 1661
Fung, J., Shi, J.-M., & Chiang, E. 2014, ApJ, 782, 88,
Goldreich, P., Lithwick, Y., & Sari, R. 2004, ARA&A,42, 549

N

3″ (303 au)

E
120 km/s

3″ (303 au)N
E-180 km/s

N3″ (303 au)

E
0 km/sN

3″ (303 au)

E
180 km/s

3″ (303 au)NE-120 km/s

N3″ (303 au)

E
60 km/sN

3″ (303 au)

E
240 km/s

3″ (303 au)

N
E

Fig. 4. Channel maps of H30α in the HD 163296 system observed
as part of the DSHARP project (Andrews et al. 2018). Black ellipse denotes the ring at 155 au. Beam size is 74 × 61 mas at
PA of 80.4◦ , and the noise level is ∼350 µJy/beam at 10km/s bin.

Haffert, S. Y., Bohn, A. J., de Boer, J., et al. 2019, Nature Astronomy,
3, 749Hashimoto, J., Aoyama, Y., Konishi, M., et al. 2020, AJ, 159, 222
Hayashi, C., Nakazawa, K., & Nakagawa, Y. 1985, in Protostars andPlanets II, ed. D. C. Black & M. S. Matthews, 1100–1153
Ida, S., & Lin, D. N. C. 2004, ApJ, 604, 388
Keppler, M., Benisty, M., Müller, A., et al. 2018, A&A,617, A44
Lin, D. N. C., & Papaloizou, J. 1986, ApJ, 307, 395
Liu, B. B., & Ji, J. H. 2020, RAA,20, 164
Lodato, G., Dipierro, G., Ragusa, E., et al. 2019, Monthly Notices of
the Royal Astronomical Society, 486, 453
Mesa, D., Keppler, M., Cantalloube, F., et al. 2019, A&A,632, A25
Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124,
62
Segura-Cox, D. M., Schmiedeke, A., Pineda, J. E., et al. 2020,
Natur,586, 228
Sheehan P. D., & Eisner J. A., 2018, ApJ, 857, 18
Spiegel, D. S., & Burrows, A. 2012, ApJ, 745, 174
Suzuki, D., Bennett, D. P., Ida, S., et al. 2018, ApJL, 869, L34
Szulágyi, J., Morbidelli, A., Crida, A., & Masset, F. 2014, ApJ, 782,
65
Szulágyi, J., Cilibrasi, M., & Mayer, L. 2018b, ApJL, 868, L13
Szulágyi, J., & Ercolano, B. 2020, ApJ, 902, 126
Tanigawa, T., & Ikoma, M. 2007, apj, 667, 557
Tanigawa, T., Ohtsuki, K., & Machida, M. N. 2012, ApJ, 747, 47
Teague, R., Bae, J., & Bergin, E. A. 2019, Nature, 574, 378
Wagner, K., Follete, K. B., Close, L. M., et al. 2018, ApJL, 863, L8
Zhang, S., Zhu, Z., Huang, J., et al. 2018, ApJL, 869, L47
Zurlo, A., Cugno, G., Montesinos, M., et al. 2020, A&A, 633, A119