Submillimeter emission associated with candidate protoplanets

TL;DR

This paper reports the discovery of submillimeter emission from a dusty circumplanetary disk around PDS 70 c and identifies a potential dust source near PDS 70 b, providing insights into planet formation environments.

Contribution

First detection of submillimeter emission associated with a young protoplanet, revealing properties of its circumplanetary disk and identifying a new potential dust source near another planet.

Findings

Detected submillimeter emission from PDS 70 c's circumplanetary disk.

Identified a new compact continuum source near PDS 70 b.

Estimated dust mass and disk-to-planet mass ratio for PDS 70 c.

Abstract

We present the discovery of a spatially unresolved source of sub-millimeter continuum emission ($\lambda=855$ $\mu$m) associated with a young planet, PDS 70 c, recently detected in H$\alpha$ emission around the 5 Myr old T Tauri star PDS 70. We interpret the emission as originating from a dusty circumplanetary disk with a dust mass between $2\times10^{-3}$ and $4.2 \times 10^{-3}$ Earth masses. Assuming a standard gas-to-dust ratio of 100, the ratio between the total mass of the circumplanetary disk and the mass of the central planet would be between $10^{-4}-10^{-5}$. Furthermore, we report the discovery of another compact continuum source located $0.074''\pm0.013''$ South-West of a second known planet in this system, PDS 70 b, that was previously detected in near-infrared images. We speculate that the latter source might trace dust orbiting in proximity of the planet, but more sensitive observations are required to unveil its nature.

Tables

Table 1. Table 1: Adopted parameters for PDS70 b and PDS70 c

Name	Mp/MJ	$L_p/L_{\odot }$	a/au	$\dot{M}/\left(M_J{\text{yr}}^{-1}\right)$
PDS70 b	5–9	$1.6\times {10}^{-4}$	20.6$\pm$1.2	$2\times {10}^{-8}$
PDS70 c	4–12	$1.6\times {10}^{-4}$	34.5$\pm$2.0	$1\times {10}^{-8}$

Table 2. Table 2: Relative astrometry of PDS70 b and c. The listed uncertainties correspond to a 1 σ 𝜎 \sigma confidence interval.

\topruleDate	Instrument/Filter/${\lambda }_0$ ($\mu$m)	$\delta$RA (mas)	$\delta$Dec (mas)	Sep. (mas)	PA (deg)	Reference
Astrometry of PDS70 b
2012-03-31	NICI/L’/3.78	58.7$\pm$10.7	-182.7$\pm$22.2	191.9$\pm$21.4	162.2$\pm$3.7	Keppler et al. (2018)
2015-05-03	SPHERE/H3/1.67	83.9$\pm$3.6	-178.5$\pm$4.0	197.2$\pm$4.0	154.9$\pm$1.1	Keppler et al. (2018)
2015-05-31	SPHERE/H2/1.59	89.4$\pm$6.0	-178.3$\pm$7.1	199.5$\pm$6.9	153.4$\pm$1.8	Keppler et al. (2018)
2016-05-14	SPHERE/K1/2.11	90.2$\pm$7.3	-170.8$\pm$8.6	193.2$\pm$8.3	152.2$\pm$2.3	Keppler et al. (2018)
		86.2$\pm$5.4	-164.9$\pm$6.6	186.1$\pm$7.0	152.4$\pm$1.5	Haffert (2019)
2016-06-01	NACO/L’/3.80	94.5$\pm$22.0	-164.4$\pm$27.6	189.6$\pm$26.3	150.6$\pm$7.1	Keppler et al. (2018)
		86.7$\pm$7.3	-159.1$\pm$9.3	181.2$\pm$10.0	151.4$\pm$2.0	Haffert (2019)
2018-02-24	SPHERE/K1/2.11	109.6$\pm$7.9	-157.7$\pm$7.9	192.1$\pm$7.9	147.0$\pm$2.4	Müller et al. (2018)
2018-06-20	MUSE/H$\alpha$/0.656	96.8$\pm$25.9	-147.9$\pm$25.4	176.8$\pm$25.0	146.8$\pm$8.5	Haffert (2019)
Astrometry of PDS 70 bsmm
2017-12-03	ALMA/855 cont	51.1$\pm$4.4	-203.3$\pm$4.8	-	-	this work
2017-12-03	ALMA/855 CO	54.9$\pm$4.6	-204.2$\pm$4.3	-	-	this work
Astrometry of PDS70 c
2016-05-14	SPHERE/K1/2.11	-207.8$\pm$6.9	55.7$\pm$5.7	215.1$\pm$7.0	285.0$\pm$1.5	Haffert (2019)
2016-06-01	NACO/L’/3.80	-247.8$\pm$9.9	58.5$\pm$8.9	254.1$\pm$10.0	283.3$\pm$2.0	Haffert (2019)
2018-06-20	MUSE/H$\alpha$/0.656	-233.7$\pm$25.0	28.8$\pm$26.7	235.5$\pm$25.0	277.0$\pm$6.5	Haffert (2019)
Astrometry of PDS 70 csmm
2017-12-03	ALMA/855 cont	-213.1$\pm$3.5	47.0$\pm$4.9	-	-	this work
2017-12-03	ALMA/855 CO	-202.9$\pm$4.5	46.8$\pm$4.6	-	-	this work

Equations

$$T_{CPD}^4=T_{acc}^4+T_{irr,p}^4+T_{irr,\star }^4.$$

$$T_{irr,p}^4=\frac{\mu L_p}{4\pi \sigma r^2},$$

$$T_{acc}^4=\frac{3G{M}_p\dot{M}}{8\pi \sigma r^3}\left[1-{\left(\frac{r_p}{r}\right)}^{1/2}\right].$$

Full text

cirucmstellar disks, circumplanetary disks

††journal: ApJL, Accepted on June 14, 2019††facilities: ALMA

1 Introduction

According to current theories, as the mass of a forming planet increases above $\sim$10 Earth masses (M⊕), the planet is expected to open a partially depleted gap in the circumstellar disk (Crida et al., 2006). Material flowing through the gap that enters the region where the gravity of the planet dominates over that of the host star, i.e., the planet Hill sphere, is trapped in orbit forming a rotating circumplanetary disk (hereafter CPD) (Ward & Canup, 2010). In analogy with the star formation process, circumplanetary material is expected to lose angular momentum due to turbulence and viscosity, and accrete onto the planet at a rate between $10^{-4}$ and $10^{-8}$ Jupiter masses (MJ) per year for a period of time comparable with the life time of the circumstellar disk, i.e., a few Myr (Lubow & Martin, 2012). Consequently, for a planet like Jupiter, more than 50% of its mass might have passed through a CPD.

In addition to regulating the final mass of giant planets, CPDs are the birth place of satellites such as the main moons of Jupiter and Saturn. The density, temperature, and viscosity of a CPD is expected to control the formation, composition, and architecture of the system of satellites (Canup & Ward, 2009). However, the limited number of moon systems in the Solar system and the lack of exo-moon discoveries limit our understanding of how their formation occurs. The recent realization that Europa might harbor conditions suitable for life under its icy surface (Pappalardo et al., 2013) stresses the importance to study how moons of giant planets form.

Gas accretion through CPD and the irradiation from both the host star and the central planet might warm up gas and dust making the CPD bright at infrared and (sub)millimeter wavelengths (Isella et al., 2014; Szulágyi et al., 2018; Zhu et al., 2018). Furthermore, the gas falling onto the planet and/or its CPD might reach temperatures of thousands of Kelvin and emit Hydrogen recombination lines (e.g., H$\alpha$) and UV continuum emission (Zhu, 2015; Marleau et al., 2017; Aoyama et al., 2018)

To date, a few giant planet candidates still embedded in their parental circumstellar disks have been claimed (e.g., Kraus & Ireland, 2012; Reggiani et al., 2018; Sallum et al., 2015), but most still lack confirmation. The most outstanding case is the PDS 70 system, which comprises of a $\sim$5 Myr old low mass ($M_{\star}=0.76M_{\odot}$) T Tauri star at a distance of 113.4 pc (Müller et al., 2018, and references therein) surrounded by a disk with a large inner cavity. A planetary-mass companion was detected within the cavity at multiple near-infrared wavelengths ($1.0\mu\textrm{m}<\lambda<3.8\mu\textrm{m}$) and at different epochs between 2012 and 2018 (Keppler et al., 2018; Müller et al., 2018). This companion, PDS 70 b, was also detected in the H$\alpha$ line ($\lambda=0.656$ $\mu$m; Wagner et al., 2018), suggesting that it is accreting gas. Recently, a second companion candidate, PDS 70 c, was discovered in VLT/MUSE observations in the H$\alpha$ line (8-$\sigma$ detection, Haffert, 2019). The two planets orbit at about 23 au and 35 au from the central star and have masses estimated to range between 4 and 12 MJ, while the observed H$\alpha$ line indicates a mass accretion rate of about $10^{-8}$ MJ yr*-1*. PDS 70 was recently observed at the wavelength of 855 $\mu$m with ALMA by Keppler et al. (2019), who found that most of the circumstellar dust is confined in a large dust ring characterized by a radius of 74 au. Furthermore, ALMA observations reveal the presence of an inner disk with a radius smaller than 10 au, and a faint spur of dust extending from the outer ring toward the inner disk. Interestingly, the latter feature was observed at the position of PDS 70 c, though the existence of this planet was not known at the time the ALMA data were published. Hydrodynamical modelling of the gas kinematics presented in this paper suggested the presence of an additional low-mass companion beyond the orbit of PDS 70 b to account for the large gap extent. No emission was reported at the location of PDS 70 b, implying an upper limit of about 0.01 $M_{\earth}$ for the dust component of a possible CPD.

In Section 2 of this letter, we show that an improved calibration of existing ALMA observations of PDS 70 reveals that the dust spur identified by Keppler et al. (2019) is a compact source of emission spatially separated from the dust ring and located at the position of PDS 70 c. Furthermore, we report the detection of a continuum emission close, but not coincident, to the position of PDS 70 b. We label these two sources PDS 70 csmm and PDS 70 bsmm, respectively. In Section 3, we argue that PDS 70 csmm might probe dust emission from a CPD and, by comparison with simple CPD models, we estimate a dust mass between $2\times 10^{-3}$ and $4.2\times 10^{-3}$ M⊕. In Section 4 we discuss the main caveat affecting this estimate and speculate about the nature of PDS 70 bsmm. We conclude by summarizing our findings in Section 5.

2 Observations

The results presented in this letter are based on an improved calibration of the ALMA band 7 ($\lambda=855$ $\mu$m) observations of PDS 70 published in Keppler et al. (2019) and Long et al. (2018). The source was initially observed in August 2016 (project ID:2015.1.00888.S) using an array configuration characterized by baselines extending between 15 m and 1.5 km, and it was observed again between the 2nd and the 6th of December 2017, (project ID:2017.A.00006.S) using a more extended array configuration with baselines between 15 m and 6.9 km. The combination of the two sets of observations probes angular scales between about 0.025″ and 12″, corresponding to spatial scales between 2.8 au and 1360 au at the distance of PDS 70. The ALMA correlator was configured to observe both continuum and molecular line emission, but here we focus on the continuum emission. We refer to Keppler et al. (2019) for a discussion of the observed CO emission.

Observations taken at the two different epochs were calibrated using the ALMA pipeline and imaged by us using the procedure described in Andrews et al. (2018). One key step of the imaging process is the self-calibration of the continuum visibilities which allows to correct short time-scale phase fluctuations and improve the imperfect long-time scale phase calibration derived from observations of a nearby point-source. Differently from Keppler et al. (2019), we find that self-calibration does improve the continuum image and results in a 40% increase in the peak signal-to-noise ratio (snr). Furthermore, in imaging the ALMA data we discovered that the observations acquired in 2016 were calibrated by the ALMA pipeline using an incorrect gain calibrator flux, which resulted in overestimating the flux density of the PDS 70 disk by about 25%. The self-calibration and imaging was performed in CASA 5.1.1 following the procedure presented in Appendix A.

We imaged both single epoch and the combined ALMA data using Briggs weighting with robust parameters varying from 2 (which mimics natural weighting) to -0.3 (lower values result in significantly higher noise). In Figure 1, we show images of the PDS 70 disk obtained from the combined data using $robust=2$ and 0.3. These maps most clearly reveal the presence of faint substructures in continuum emission. However, we stress that our results do not depend on the assumed weighting scheme, and, in particular, that the compact sources of continuum emission discussed below were identified with the adopted range of weightings in both the combined and 2017 data alone.

The map generated using $robust=2$ has an rms noise of 18 $\mu$Jy beam*-1* and achieves an angular resolution (FWHM of the synthesized beam) of 0.093″$\times$ 0.074″. In the following, we will refer to this image as the natural image. Conversely, the map generated with $robust=0.3$ (i.e., the robust image) has a slightly higher noise (rms=19 $\mu$Jy beam*-1*) but achieves better angular resolution (FWHM=0.067″$\times$ 0.050″). Overall, the natural and robust images show the same disk morphology that agrees with the results presented in Keppler et al. (2019).

The main feature is a bright elliptical ring with semi-major axis of about 0.65″, semi-minor axis of 0.4″, position angle of the semi-major axis of about 158° (as measured from North toward East), and a flux density of 177 mJy. Assuming that the dust ring is intrinsically circular, the measured aspect ratio implies a disk inclination of 52°. The continuum intensity varies along the ring. In the natural image, the intensity reaches a maximum of 2.5 mJy beam*-1* at a position angle of 325° and a minimum of 1.7 mJy beam*-1* at a position angle of 94°. A similar relative variation in measured in the robust image. A second feature of the continuum emission is a central component characterized by a flux density of 0.7 mJy. A 2D elliptical Gaussian fitting of the emission returns a beam deconvolved semi-major axis of 0.10″$\pm$0.01″, a semi-minor axis of 0.08″$\pm$0.01″, and a position angle of 177°$\pm$15°. The inclination and position angle of the central component appear to be consistent with those of the dust ring. These two features were discussed in details in Keppler et al. (2019) and will not be further analyzed here.

For the rest of the paper, we focus on the discussion of two additional sources of continuum emission detected inside the dust cavity. The first, labelled PDS 70 bsmm, has a peak intensity of 100$\pm$18 $\mu$Jy beam*-1* (snr $\sim 5.5$) and 73$\pm$19 $\mu$Jy beam*-1* (snr $\sim 3.8$) in the natural and robust images, respectively. A 2D Gaussian fit of PDS 70 bsmm indicates that the source is much smaller than the synthesized beam, suggesting a beam-deconvolved physical diameter $\lesssim 4$ au. The second source, labeled PDS 70 csmm, is better seen in the robust image where it is spatially separated from the dust ring (see also Appendix B). PDS 70 csmm has a peak intensity of 106$\pm$19 $\mu$Jy beam*-1* (snr $\sim 5.6$) and its morphology is also consistent with a point source.

The astrometric positions of PDS 70 bsmm and PDS 70 csmm are calculated with respect to the center of the disk which is defined as the center of the innermost component of continuum emission as well as the center of rotation as inferred from the 12CO J=3-2 line emission. These measurements, which are discussed in Appendix C, lead to consistent results (Table 2). PDS 70 bsmm and PDS 70 csmm are both separated by 0.21″ from the center of the disk and are located at position angles of about 165° and 283°, respectively.

3 Data analysis

3.1 Comparing optical, NIR, and sub-mm astrometry

Figure 2 compares the relative astrometric positions of PDS 70 bsmm and PDS 70 csmm to those of PDS 70 b and PDS 70 c measured in 2016 and 2018 (see Table 2). It must be noted that the position of the ALMA sources are relative to the center of the 855 $\mu$m continuum emission and CO kinematics as discussed in Appendix C. Conversely, the optical and NIR astrometry is measured relative to the stellar position. In order to compare these measurements, we must therefore assume that the star is at the center of the disk.

The position of PDS 70 csmm is in agreement with the optical and NIR position of PDS 70 c (see also Figures 1 and 8). At the estimated orbital radius 34.5 au, the orbital period of PDS 70 c should be 230 yr implying an angular yearly motion of about 0.008″ in the clockwise direction, assuming a circular and coplanar orbit. This is consistent with the shift observed between 2016 and 2018. PDS 70 bsmm appears to be located South-West of PDS 70 b at an angular distance of 0.074″$\pm$0.013″, as calculated by comparing the ALMA position with the closest NIR epoch (2018-02-24 from Müller et al., 2018). This offset, which is also visible in the overlay between ALMA and VLT/SPHERE observations shown in Figure 1, suggests that PDS 70 bsmm and PDS 70 b might have different physical origins (see Section 4). Although the present analysis has a caveat that the ALMA reference position might not correspond to the position of the central star, a substantial offset would be required to reconcile the difference and introducing such an offset would lead to a disagreement in positions of PDS 70 c and PDS 70 csmm. Future ALMA observations capable of imaging the innermost disk regions in greater details might better pinpoint the position of the central star relative to the circumstellar material.

3.2 Estimating the CPD dust mass

The agreement between the position of PDS 70 csmm and its optical/NIR counterpart, and the fact that the sub-mm emission is spatially unresolved at the sensitivity and resolution of current observations, strongly suggest that PDS 70 cmm traces warm dust emission from a CPD. This hypothesis is supported by the detection of H$\alpha$ line emission attributed to accreting gas (Figure 8, Haffert, 2019). The planet itself would emit at sub-millimeter wavelengths, however we calculate that its 855 $\mu$m flux should be less than 0.1 $\mu$Jy (assuming planet effective temperatures and radii as in Müller et al., 2018).

The spatially integrated flux measured by ALMA can be used to estimate the mass of the CPD. Following Isella et al. (2014), we assume that CPDs are vertically isothermal with a radial temperature profile ($T_{CPD}$) controlled by the sum of internal viscous heating ($T_{acc})$ and external irradiation from both the central planet ($T_{irr,p}$) and the host star ($T_{irr,\star}$), so that

[TABLE]

We assume a stellar luminosity $L_{\star}=0.36L_{\odot}$ (Müller et al., 2018), while the physical parameters for PDS 70 c (and b) are listed in Table 1. The luminosity of PDS 70 c is not known, but because the masses and ages of PDS 70 b and PDS 70 c are thought to be similar, we assume that they might also have similar luminosities.

The stellar irradiation at the position of PDS 70 c might depend on the geometry of the inner part of the circumstellar disk, as this might occult the planets from direct stellar radiation, and on the amount of stellar light scattered by the circumstellar dust ring toward the planet itself (see, e.g. Turner et al., 2012; Isella & Turner, 2018). In first approximation, a lower limit of $T_{irr,\star}$ might correspond to the midplane temperature of an optically thick circumstellar disk, where all the stellar light is absorbed in the disk surface and re-processed toward the disk midplane (Chiang & Goldreich, 1997). At the orbital radius of PDS 70 c, this approximation gives $T_{irr,\star}=20$ K. Conversely, an upper limit for $T_{irr,\star}$ corresponds to the equilibrium temperature of a black body embedded in the unattenuated stellar radiation, which gives $T_{irr,\star}=80$ K.

The temperature due to the irradiation from the planet scales with the distance $r$ as

[TABLE]

where $\mu=0.1$ is the assumed aspect ratio of the CPD, $L_{p}$ is the planet luminosity, and $\sigma$ is the Stefan-Boltzmann constant. Assuming $L_{p}=1.6\times 10^{-4}$ L⊙ and $T_{irr,\star}=80$ K, we find that $T_{irr,p}>T_{irr,\star}$ at $r<0.1$ au. Instead, if we assume $T_{irr,\star}=20$ K, $T_{irr,p}>T_{irr,\star}$ for $r<1.0$ au.

Finally, the temperature due to viscous heating is

[TABLE]

For the parameters of PDS 70 c, $T_{acc}$ varies between 1/3 and 1/7 of $T_{irr,p}$, suggesting that viscous heating might have a very marginal role.

From the CPD temperature derived using Equations 1, 2, 3, and the lower and upper limits of $T_{irr,\star}$, we calculate the expected CPD continuum emission at 855 $\mu$m using Equation 4 in Isella et al. (2014). To this end, we assume a CPD inclination equal to that of the circumstellar disk ($i=51.7\arcdeg$, Keppler et al., 2019), and a dust surface density proportional to $r^{-1}$. Isella et al. (2014) showed that the slope of the surface density profile has a little effect on the total disk flux. We assume an inner disk radius equal to the planet radius, which is estimated to be about 3 Jupiter radii based on the planet temperature and luminosity, and a dust opacity of 3.5 cm2 g*-1* (Keppler et al., 2019). We calculate continuum fluxes for a grid of models characterized by dust masses ($M_{d}$) between $10^{-3}$ M⊕ and $10^{-1}$ M⊕, and disk outer radii between 0.3 au and 3 au. Theoretical models predict that CPDs should be truncated between 1/3 and 1/2 of the planet Hill radius ($R_{H}=a\sqrt[3]{M_{p}/3M_{\star}}$) (Quillen & Trilling, 1998). For the estimated mass range of PDS 70 c, the CPD outer radius might therefore be between 1.4 au and 3 au.

CPD models that match the 855 $\mu$m continuum flux of PDS 70 cmm (106 $\mu$Jy) are shown in Figure 3. As expected, the inferred dust mass depends on the disk temperature so that more dust is needed to explain the observed flux if the disk is colder. If $R_{out}\gtrsim 1$ au, the dust mass is almost independent on the disk outer radius, and it reaches values of $2\times 10^{-3}$ M⊕ and $4.2\times 10^{-3}$ M⊕ in the high and low temperature models, respectively. This behaviour is due to the fact that, in this regime, CPDs are mostly optically thin at 855 $\mu$m. As a consequence, the dust emission scales linearly with the dust mass but is independent on the emitting area. For example, the dust surface density of the CPD model characterized by $T_{irr,\star}=20$ K, $M_{d}=4.3\times 10^{-3}$ M⊕, and $R_{out}=1.25$ au ($R_{out}=0.3R_{H}$ for M${}_{p}=4$ MJ), is $\Sigma_{d}\simeq 0.015\textrm{g\, cm}^{-2}(\textrm{au}/r)$, which, for the adopted dust opacity, corresponds to an optical depth below 1 for $r>0.05$ au.

If the CPD outer radius is smaller than 1 au, the dust mass required to explain the observed emission leads to higher, more optically thick, surface densities. In the limit of $\tau\gg 1$, the disk flux scales linearly with the emitting area (i.e., $F\propto R_{out}^{2}$), and iso-flux curves turn from horizontal to vertical. The transition between optically thin and thick regime, as well as the minimum outer radius compatible with the observations, depend on the disk temperature. We find that the CPD of PDS 70 c might have an outer radius as small as 0.35 au (0.08$R_{H}$ for M${}_{p}=4$ MJ) if $T_{\star,irr}=80$ K, and about 0.6 au (0.15$R_{H}$) if $T_{\star,irr}=20$ K.

The same procedure can be applied to estimate the mass and outer radius of a CPD around PDS 70 b, although astrometric measurement might suggest that the observed sub-millimeter emission might have a different origin. In this case, the measured 855 $\mu$m flux would correspond to dust masses between $1.8\times 10^{-3}$ M⊕ and $3.2\times 10^{-3}$ M⊕ for optically thin disks larger than $\sim$0.7 au, or a minimum outer radius of 0.2 au if the emission is optically thick.

4 Discussion

Inferring the existence and measuring the properties of CPDs is important to constrain both planet and moon formation models. The detection of a compact source of sub-mm emission at the position of PDS 70 c confirms the hypothesis that the H$\alpha$ line emission recently detected by Haffert (2019) probes gas accreting onto a young planet from a CPD. The constraints set on the dust mass suggest that the CPD might have a relatively low mass compared to that of the planet. Using a standard gas-to-dust ratio of 100, the total mass of the CPD would be $10^{-4}-10^{-5}$ times the mass of the planet, unless the CPD is so small ($R_{out}\lesssim 0.1R_{H}$) to become optically thick. For comparison, the minimum mass of solids required to form Jupiter’s Galilean moons is $6.5\times 10^{-2}$ M⊕. This corresponds to a total gas mass of about 2% of the mass of Jupiter. Theoretical models for the formation and evolution of giant planets (e.g. Ward & Canup, 2010) predict low CPD/planet mass ratios only toward the end of the planet accretion phase, and after the planet has accreted most of its mass.

In discussing the comparison between theory and observations, the caveats related to the measurement of the CPD mass can not be neglected. Similarly to the case of circumstellar disks, the main source of uncertainty in calculating dust masses from sub-millimeter fluxes resides in the limited knowledge of the dust opacity. The assumed value of 3.5 cm2 g*-1* is appropriate for dust grains with chemical composition typical of those observed in the interstellar medium and a MRN grain size distribution ($n\propto a^{-3.5}$) with a maximum grain size extending a few millimeters (Birnstiel et al., 2018). However, while millimeter-sized grains have been observed in circumstellar disks, it is unclear whether they might exist in a CPD. For example, in the case of PDS 70, it is thought that the observed circumstellar dust ring might trap most of the large dust grains so that the material flowing from the circumstellar to the circumplanetary disk might be depleted in solids, and, in particular, in mm-size grains. Furthermore, mm-size grains in the CPD are expected to quickly drift inward as a result of the gas drag (Zhu et al., 2018). As counter arguments, small solids in the CPD might collide and grow in size to form larger particles (Shibaike et al., 2017), and local maxima in the gas density could slow down the inward radial drift of dust particles, as observed in several circumstellar disks (see, e.g., Dullemond et al., 2018). However, if for any reason the maximum grain size in the CPD is smaller than about than 100 $\mu$m, the true dust opacity might be a factor of several lower than the adopted value, and, consequently, the dust mass might be a factor of several larger. Future multi-wavelength ALMA observations that measure the spectral slope of the CPD continuum emission will help breaking the degeneracy related to the grain size distribution. Furthermore, observations of both optically thin and thick molecular lines could be used to constrain the gas density and temperature, allowing for a more quantitative comparison between observations and models.

The last item of discussion concerns the nature of PDS 70 bsmm. Its proximity to PDS 70 b suggests that the observed continuum emission might be somehow related to the planet. Due to the uncertainties on the position of the host star in the ALMA images, we cannot exclude that the sub-millimeter continuum arises for circumplanetary dust. This was already discussed in Section 3. One possibility to explain the offset might be that PDS 70 bsmm traces dust particles trapped at the Lagrangian point L5, about $60^{\circ}$ behind PDS 70 b in azimuth along its orbit. Numerical simulations predict that if the disk viscosity is low ($\alpha<10^{-4}$) solid particles might be trapped at this Lagrangian point for more than 1000 orbits (Lyra et al., 2009; Ricci et al., 2018; Zhang et al., 2018). In the case of PDS 70 b, this would imply particle lifetimes larger than about $10^{5}$ years. Such a possibility, however, prefers an inclined orbit ($\sim 20^{\circ}$) with respect to the disk midplane, assuming that the direction of the ascending node aligns with the circumstellar disk’s position angle and that optical/NIR and sub-mm emissions arise from the midplane. Future long-term follow-up observations will better constrain the orbital parameters of PDS 70 b and help examine this possibility. As an alternative, we speculate it might be possible that optical/NIR traces emission from a jet similar to the ones from accreting protostars (e.g., Hartigan et al., 2011). However, in order to explain the red-shifted H$\alpha$ emission reported by (Haffert, 2019), the magnetic dipole of the planet must by substantially misaligned ($>40\arcdeg$) with respect to the circumstellar disk. In either case, deep follow-up observations in both optical/NIR and sub-mm wavelengths are highly desired to elucidate the nature of this source.

5 Conclusions

We presented the detection of 855 $\mu$m continuum emission at the position of the planet PDS 70 c that we attribute to dust emission from a CPD. This result supports the hypothesis that this planet is still in its accretion phase (Haffert, 2019). We have shown that the sub-mm flux measured at the position of PDS 70 c constrains the total dust mass to be between $2\times 10^{-3}$ M⊕ and $4.2\times 10^{-3}$ M⊕, if the CPD outer radius is larger than about 0.3$R_{H}$ as predicted by theory. Taken at face value, our results indicate that the mass of PDS 70 c CPD might be very low compared to that of the planet ($M_{d}/M_{p}\sim 10^{-4}-10^{-5}$). Such low mass ratio and the low mass accretion rate measured by Haffert (2019) suggest that the PDS 70 c might have already accreted most of its final mass. We reported the detection of another compact source of continuum emission (PDS 70 bsmm) located about 0.074″ away from PDS 70 b, the other known planet of this system, for which we do not currently have any robust interpretation.

The discovery of a CPD at sub-mm wavelengths paves the way for the characterizations of the environment surrounding giant planets in the act of forming, and for the study of the interaction between the circumstellar and the circumplanetary disk. Furthermore, the presented ALMA observations demonstrate the capability to measuring orbital parameters of young planets at (sub)-millimeter wavelengths. We argue that optical, NIR, and (sub)millimeter observations are highly complementary because they probe diverse aspects of planet accretion processes and are affected by different systematic errors. The relative astrometric accuracy of ALMA observations is comparable to that achieved in the optical/NIR and is not contaminated by direct or scattered stellar light, which might mislead the interpretation of short wavelength observations. However, the offset between PDS 70 b and PDS 70 bsmm shows that ALMA observations alone might not be sufficient to identify planets in the act of forming. As ALMA and existing optical telescopes are reaching their full imaging capabilities, forthcoming observations of nearby circumstellar disks characterized by cavities and gaps like those observed in PDS 70 might reveal more newborn planets interacting with their natal disk. Such observations are fundamental to investigating the processes responsible for the formation of planetary systems.

We acknowledge A. Muller, S. Haffert, J. de Boer and A. Vigan for kindly sharing their VLT (SPHERE and MUSE) reductions. We tank the anonymous referee for helping improving the manuscript. A. I. acknowledges support from the National Science Foundation under grant No. AST-1715719. M.B. acknowledges funding from ANR of France under contract number ANR-16-CE31-0013 (Planet Forming disks). R.T. acknowledges support from NSF grants AST-1514670 and NASA NNX16AB48G. J.B. acknowledges support from NASA grant NNX17AE31G. L.P. acknowledges support from CONICYT project Basal AFB-170002 and from FONDECYT Iniciación project #11181068. M.K. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 730562 (RadioNet). S.F. acknowledges an ESO Fellowship.

Appendix A Self-calibration

In this section, we provide detailed information about the main steps involved in the self-calibration of the ALMA observations of PDS 70. The entire self-calibration, starting from the archival data and ending with the continuun images presented in this paper, can be reproduced using the python script available at http://obelix.rice.edu/~ai14/PDS70/. The script was written for the version 5.1.1 of the Common Astronomy Software Applications package (CASA) and was not tested on the more recent versions of the software.

A.1 Self-calibration of 2015.1.00888.S data

Following the procedure discussed in Andrews et al. (2018), we started by calculating antenna based complex phase gains for the data acquired in the more compact array configuration, i.e. those from project 2015.1.00888.S. Using the task tclean, we generated an image of the continuum emission adopting Briggs weighting with a robust parameter equal to 0.5, resulting in a synthesized beam with a FHWM of 0.19″$\times$0.15″(see left panel of Figure 4). We used multi-scale cleaning with scales equal to 0 (point source), 1, 3, and 6 $\times$ the beam FWHM, a cleaning threshold of 1 mJy beam*-1* that corresponds to 8$\times$ the rms noise level of the resulting image, and an elliptical mask with a semi-major axis of 1.7″, a semi-minor axis of 1.1″, and a position angle of 160°. Setting the cleaning threshold to several times the noise level is important to avoid the addition of spurious components to the model used to self-calibrate the data, and minimize the effect of the adopted mask. We verified that using smaller or larger masks do not affect the results of the self-calibration. This initial continuum image has a rms noise of 0.13 mJy beam*-1* and a peak intensity of 10.1 mJy beam*-1*, corresponding to a peak signal-to-noise ratio (snr) of $\sim$78. Using the task gaincal we calculated phase gains based on the clean component model generated by tclean on a time interval equal to the scan length (solint = "inf", combine=""). Phase gains were calculated independently for each polarization (gaintype="G") and for each spectral window in order to correct for any phase offset between different correlations and spectral bands. The task applycal was then used to apply the phase gain correction to the data. Particular attention should be paid to set the spwmap parameter to properly map the spectral phase gain solutions to the corresponding spectral windows of the ALMA data. This first iteration of phase calibration led to a reduction of about 35% in the rms noise, and an increase of about 4% and 70% in the peak emission and peak snr, respectively. A second iteration of phase self-calibration was then performed using a solution interval of 120 s and averaging on both polarizations (gaintype="T") and spectral windows (combine="spw"). This led to a further reduction of about 24% in the rms noise, but a marginal ($\sim$1%) increase in the peak intensity. The continuum image obtained after the second self-calibration iteration is shown in the right panel of Figure 4.

A.2 Joint self-calibration

After correcting 2017.A.00006.S data for the source proper motion, we combined them with 2015.1.00888.S self-calibrated data and generated a cleaned image using a robust parameter of 0.6, resulting in a beam FWHM of 0.076″$\times$0.059″, and a cleaning threshold of 0.15 mJy beam*-1*, corresponding to 8$\times$ the rms noise of the resulting image. This initial image of the combined data (central panel of Figure 5) has a rms noise level of $\sim$0.020 mJy beam*-1* and a peak intensity of 1.6 mJy beam*-1*, corresponding to a peak snr of about 77. Using this image, we self-calibrated the combined data by averaging both on polarizations and spectral windows adopting solution intervals of 900 s, 120 s and 30 s. The final image (right panel of Figure 5) has an rms of 0.018 mJy beam*-1* and a peak intensity of 1.73 mJy beam*-1*, corresponding to a peak snr of 96. Overall, for a robust parameter of 0.6, the self-calibration of the continuum led to a reduction of about of 18% in the rms noise, and an increase of about 14% and about 40% in the peak intensity and peak snr, respectively. We found that shorter solution intervals lead to higher noise. We also found that amplitude self-calibration does not provide any improvement of the image quality, and for this reason it was not applied.

Appendix B Subtraction of a symmetric ring emission

To expose the morphology of PDS 70 csmm, we subtract the much brighter dust ring and central component from the observed continuum emission, assuming that they are symmetric. The subtraction is performed in the Fourier space using the following procedure. First, we spatially shift the observations to minimize the asymmetry of the continuum emission relative to the phase center. This step is performed by searching for the phase shift that minimizes the imaginary part of the continuum visibilities. The phase shift is defined as $\exp[-2\pi i(u\delta\mathrm{RA}+v\delta\mathrm{Dec})]$, where $u$ and $v$ are the spatial frequencies, and $\delta\mathrm{RA}$ and $\delta\mathrm{Dec}$ define the translation in the image plane. We perform a $\chi^{2}$ minimization and find a minimum for $\delta\mathrm{RA}=0.0119\arcsec$ and $\delta\mathrm{Dec}=0.0116\arcsec$. The second step consists in calculating the inclination and position angle of the disk that minimize the dispersion of the deprojected visibilities calculated on circular annuli in the Fourier space. A $\chi^{2}$ minimization returns a minimum for an inclination of 49.9°  and a position angle of 159.9°. The third step consists in deprojecting the observed visibilities using the derived inclination and position, calculating the azimuthally averaged profile as a function of the uv-distance, and subtracting it from each visibility point. Finally, the azimuthally averaged visibilities and the residual visibilities are imaged using the same procedure adopted for the observations to map the symmetric and asymmetric components of the emission. The images obtained using a robust parameter equal to 0.3 are shown in Figure 6. The image obtained from the residuals of the visibility subtraction more clearly shows the crescent along the dust ring and PDS 70 csmm, which appears as a point source 0.21″ away from the center of a disk at a position angle of 283°. A 2D Gaussian fitting to PDS 70 csmm indicates that the emission is not spatially resolved, implying therefore a source diameter $\lesssim 4$ au.

Appendix C Astrometric measurements

In Table 2, we report the relative astrometric measurements of PDS 70 b and c, as measured by Keppler et al. (2018), Müller et al. (2018) and Haffert (2019), as well as the relative position of PDS70 bsmm and csmm. The latter were calculated using only the observations acquired in December 2017 to avoid spatial smearing caused by orbital motion. We measure the positions of PDS70 bsmm and csmm relative to both the center of the disk calculated based on the innermost component of the continuum emission and on the disk rotation probed by the 12CO J=3-2 line emission. In the first case, we imaged ALMA 2017 continuum data using robust parameters between 2 and 0.6 and measured the center of the central component of the continuum emission (see Section 2) through a 2D Gaussian fit. The average of these measurements defines the center of the continuum emission. Since images corresponding to different robust parameters are not independent, the uncertainty on the position of the reference point is assumed to be equal to the uncertainty on the position of the center as measured in the robust=2 image. The same procedure was adopted to calculate the position of PDS 70 bsmm and PDS 70 csmm. For the latter, we only used images generated with robust parameters of 0.6 and 0.7 to avoid confusion with the nearby dust ring. The center of rotation of the disk is calculated by fitting a Keplerian rotation pattern to 12CO J=3-2 images obtained using natural weighting, as well as robust parameters of 0.7 and 1. The CO observations were presented in Keppler et al. (2019) while the fitting procedure is described in Teague (2019). The centers of the continuum emission and of the disk rotation are shown in Figure 7 and coincide within their uncertainties.

Appendix D Complementary observations.

In Figure 8, we show the overlay between the ALMA images of the 855 $\mu$m continuum emission and the VLT/SPHERE NIR image published in Müller et al. (2018) (left panels), and the VLT/MUSE H$\alpha$ image published in Haffert (2019) (right panels).