Physics & Astronomy Faculty Publications Physics and Astronomy

6-11-2018

On the Radio Detectability of Circumplanetary Discs

Zhaohuan Zhu University of Nevada, Las Vegas, [email protected]

Sean M. Andrews Harvard-Smithsonian Center for Astrophysics

Andrea Isella Rice University

Follow this and additional works at: https://digitalscholarship.unlv.edu/physastr_fac_articles

Part of the Astrophysics and Astronomy Commons

Repository Citation Zhu, Z., Andrews, S. M., Isella, A. (2018). On the Radio Detectability of Circumplanetary Discs. Monthly Notices of the Royal Astronomical Society, 479(2), 1850-1865. http://dx.doi.org/10.1093/mnras/sty1503

This Article is protected by copyright and/or related rights. It has been brought to you by Digital Scholarship@UNLV with permission from the rights-holder(s). You are free to use this Article in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/ or on the work itself.

This Article has been accepted for inclusion in Physics & Astronomy Faculty Publications by an authorized administrator of Digital Scholarship@UNLV. For more information, please contact [email protected]. MNRAS 479, 1850–1865 (2018) doi:10.1093/mnras/sty1503 Advance Access publication 2018 June 11

On the radio detectability of circumplanetary discs

Zhaohuan Zhu,1‹ Sean M. Andrews2 and Andrea Isella3 1Department of Physics and Astronomy, University of Nevada, Las Vegas, 4505 S. Maryland Pkwy, Las Vegas, NV 89154, USA 2Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA 3Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, TX 77005, USA

Accepted 2018 June 6. Received 2018 May 29; in original form 2017 August 24

ABSTRACT Discs around young planets, so-called circumplanetary discs (CPDs), are essential for planet growth, satellite formation, and planet detection. We study the millimetre and centimetre emission from accreting CPDs by using the simple α disc model. We find that it is easier to detect CPDs at shorter radio wavelengths (e.g. λ 1 mm). For example, if the system is 140 pc away from us, deep observations (e.g. 5 h) at ALMA Band 7 (0.87 mm) are sensitive to as small as 0.03 lunar mass of dust in CPDs. If the CPD is around a Jupiter mass planet 20 au away from the host star and has a viscosity parameter α 0.001, ALMA can detect this −10 −1 disc when it accretes faster than 10 M yr . ALMA can also detect the ’minimum mass sub-nebulae’ disc if such a disc exists around a young planet in young stellar objects. However, to distinguish the embedded compact CPD from the circumstellar disc material, we should observe circumstellar discs with large gaps/cavities using the highest resolution possible. We also calculate the CPD fluxes at VLA bands, and discuss the possibility of detecting radio emission from jets/winds launched in CPDs. Finally we argue that, if the radial drift of dust particles is considered, the drifting time-scale for millimetre dust in CPDs can be extremely short. It only takes 102–103 yr for CPDs to lose millimetre dust. Thus, for CPDs to be detectable at radio wavelengths, mm-sized dust in CPDs needs to be replenished continuously, or the disc has a significant fraction of micron-sized dust or a high gas surface density so that the particle drifting time-scale is long, or the radial drift is prevented by other means (e.g. pressure traps). Key words: radiation mechanisms: thermal – planets and satellites: detection – planet-disc interactions – protoplanetary discs – brown dwarfs – radio continuum: planetary systems – submillimetre: planetary systems.

Seibert & Artymowicz 1999; Ayliffe & Bate 2009;Szulagyi´ et al. 1 INTRODUCTION 2016). The planet can continue to grow with material being accreted During their formation, giant planets are expected to be surrounded through the CPDs. by dense discs made of gas and dust called circumplanetary discs Studying CPDs is crucial for understanding satellite formation (CPDs). The orbital properties of regular satellites around giant (e.g. Heller et al. 2014), and even habitability of life on satellites planets in our solar system support the existence of CPDs in the (e.g. Europa and Enceladus; Waite et al. 2017). The density and past. All medium and large satellites of giant planets in our solar temperature structure of CPDs affect the satellite size and compo- systems, except the captured satellite Triton, have prograde orbits sition (e.g. Heller & Pudritz 2015). If the CPD is too hot for water that are nearly coplanar with the planet’s equator. Furthermore, the to condense, the satellites will be made mostly of dust grains with gradient in the amount of ices in the Galilean satellites is consistent little subsurface water ocean (Canup & Ward 2002). Forming large with satellite formation in a warm disc. satellites and multiple satellites in resonance (e.g. Galilean satel- Theoretical studies suggest that, after the runaway phase of giant lites) can lead to geological activity, providing energy sources for planet formation, the planet’s atmosphere detaches from the planet’s early life (Peale 1999). Hill sphere and shrinks significantly (Papaloizou & Nelson 2005). Despite their importance, finding CPDs in other young stellar Material that falls into the planet’s Hill sphere will spin around the objects (YSOs) is challenging since these discs are a lot fainter planet, forming CPDs to conserve the angular momentum (Lubow, than the central star. On the other hand, when CPDs are actively accreting, they can be as bright as a late M-type/early L-type brown dwarf (Quillen & Trilling 1998;Zhu2015). Unlike the SEDs of a brown dwarf, the SEDs of accreting CPDs are a lot redder, peaking  E-mail: [email protected]

C 2018 The Author(s)

Downloaded from https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839Published by Oxford University Press on behalf of the Royal Astronomical Society by Library Periodicals user on 15 August 2018 Circumplanetary disc detection 1851

−12 −1 −8 −1 at mid-infrared. Thus, to detect CPDs in protostellar systems, we from 10 M yr to 10 M yr ), α can vary from 0.0001 to need to image the young stellar system at mid-infrared, adopting 0.1. high-contrast imaging techniques capable of blocking most of the The disc inner radius is assumed to be the Jupiter radius (RJ), stellar light. With such observational strategy, a few red sources and the outer radius of the CPD (Rout) is assumed to be 1/3 of the within circumstellar discs have been discovered (LkCa 15b: Kraus Hill radius of the planet (Quillen & Trilling 1998;Martin&Lubow 1/3 & Ireland 2012; HD100546b: Quanz et al. 2013; Currie et al. 2015, 2011), or Rout = 1/3 × rp(Mp/3M∗) .Inthispaper,weuseR to but see Rameau et al. 2017, HD169142b: Biller et al. 2014; Reggiani represent the radius in the CPD (the distance to the planet), and r et al. 2014) and their photometries at infrared bands are consistent to represent the radius in the circumstellar disc (the distance to the with accreting CPDs (Zhu 2015; Zhu, Ju & Stone 2016). Besides central star). For a Jupiter mass planet at rp=5, 20, and 80 au from the photometry, another observational signature of accretion discs is the solar mass star, Rout is 0.12, 0.46, and 1.85 au. On the other Hα emission lines (Calvet & Gullbring 1998; Muzerolle, Hartmann hand, if the planet is 10 Jupiter mass but to be surrounded by the &Calvet1998; Muzerolle, Calvet & Hartmann 2001; Zhou et al. same sized CPDs (Rout=0.12, 0.46, and 1.85 au), this more massive 2014). So far, LkCa 15b is the most promising candidate for the planet needs to be at rp=2.4, 9.3, and 37.2 au from the solar mass accreting CPDs since both the accretion indicators, Hα line and star. near-IR thermal emission, have been detected (Sallum et al. 2015). With these disc parameters (M˙p, α, Rin,andRout), we can cal- Besides optical and infrared observations, radio observations can culate the disc structure by solving coupled radiative transfer and potentially detect the CPDs too. Using the parameterized models, hydrostatic equilibrium equations as in D’Alessio et al. (1998). Isella et al. (2014) suggest that ALMA can detect CPDs with mass However, such detailed CPD models are not necessary at the cur- −4 down to 5 × 10 MJ and size down to 0.2 au. With numerical sim- rent stage where these parameters are still highly uncertain. Thus in ulations, Zhu et al. (2016) suggest that the central star can induce this paper, we make approximations to simplify the calculations. spiral shocks in CPDs and the dissipation of the shocks can lead to Given the MpM˙p, the viscous theory suggests that the disc effec- CPD accretion. Applying this accretion disc model to the CPD can- tive temperature follows (e.g. from Hartmann 1998) didates mentioned above (HD100546b, HD169142b, LkCa 15b), 3GM M˙ R 1/2 all these CPD candidates should be detectable by ALMA (Zhu et al. T 4 = p p 1 − in , (1) 2016). In this paper, we extend Isella et al. (2014) with detailed eff 8πσR3 R disc vertical structure calculations to show whether CPDs can be where R is the disc inner radius and we assume R = 0.1 R ∼ R . detected by ALMA and future generation radio telescopes such as in in J To derive the disc midplane temperature, we assume that the disc the Next Generation VLA (ngVLA, Selina et al. 2018). In Section 2, vertical temperature along the height (z) follows Hubeny (1990), we introduce the analytical disc model. The results are presented in Section 3. Finally, after short discussions in Section 4, the paper is 3 T (z)4 = T 4 τ + T 4 , (2) summarized in Section 5. 8 eff R ext

where τ R is the Rosseland mean optical depth at z,andText is the 2 METHOD background temperature due to the external irradiation. Here we include both the heating from ISM and the irradiation from the To calculate the radio emission from CPDs, we first need to con- 4 = 4 + 4 = planet as Text TISM Tirr. We choose TISM 10 K and assume struct a disc model. Following the α disc theory, and similarly to that Tirr could be due to the radiation from either the central bright circumstellar discs (D’Alessio et al. 1998), the structure of a CPD is planet or the disc boundary layer.1 The planet or the boundary layer ˙ determined by the disc accretion rate (Mp), the viscosity parameter will irradiate the disc at a large incident angle. The incident angle is − (α), and the disc inner and outer radius (Rin, Rout), as long as the tan 1(H/R) to the first order (Kenyon & Hartmann 1987). With H/R planet mass (Mp), temperature (Tp), and radius (Rp) are given. Un- ∼ 0.1 (Zhu et al. 2016), we assume that the disc receives 1/10th of fortunately, we don’t have many, if any, observational constraints the irradiation luminosity in the direction perpendicular to the disc on these parameters. Thus, we narrow down the parameter space us- surface. Thus, ing either order-of-magnitude estimates or theoretical results from 1/4 numerical calculations. Lirr Tirr = . (3) To form a Jupiter mass planet within the lifetime of the gaseous σ 40πR2 circumstellar discs (∼106 yr), the average CPD accretion rate (M˙ ) p When we consider the irradiation from a bright planet, we assign Lirr −6 −1 ˙ −5 2 −1 is 10 MJ yr . In this paper, we vary MpMp from 10 MJ yr as the planet’s luminosity based on the ’hot start’ planet model (e.g. −8 2 −1 ˙ to 10 MJ yr . We choose MpMp as a fundamental parameter Marley et al. 2007; Spiegel & Burrows 2012). When we consider the since M M˙ determines the disc effective temperature for a viscous p p irradiation from the boundary layer, we adopt Lirr = GMpM˙p/(2Rp) heating-dominated disc (equation 1). However, for the radio emis- since half of the accretion energy is released at the boundary layer. ˙ sion calculation, Mp and Mp become degenerate when the disc is The disc midplane temperature is then optically thin or irradiation dominated (Sections 3.1, 3.2, and 4.1). 1/2 Thus, we normally also specify M whenever M M˙ is given. 9GMpM˙pκR Rin p p p T 4 = 1 − + T 4 , (4) Another important parameter for determining the disc structure is c 128πσR3 R ext the viscosity coefficient: α parameter. The first-principle hydrody- namical simulations by Zhu et al. (2016) suggest that spiral shocks where κR is the Rosseland mean opacity and we choose the nominal = 2 induced by the star can lead to efficient angular momentum trans- value of κR 10 cm /g. port in CPDs. In this accretion scenario, the value of α parameter depends on the disc accretion rate due to the thermal feedback. For 1We have ignored the irradiation from the protoplanetary disc and the central a disc accreting at a higher rate, the disc is hotter, leading to more- star. Such irradiation can be important if the planet is close to the central opened spiral shocks so that the shock-driven accretion is more star (e.g. 5 au, see discussion in Section 4.1). On the other hand, as shown in efficient with a higher α. Over a wide range of accretion rates (M˙ p Sections 3.2 and 4.1, irradiation makes little difference on the radio emission.

Downloaded from https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839 MNRAS 479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 1852 Z. Zhu, S. M. Andrews, and A. Isella

Using the viscous disc theory, we also have Thus, ⎧ 1/4 1/2 ⎪ 3 κR 4 + 4 M˙p Rin ⎪ T T if τmm > 0.5 ν = 1 − , (5) ⎨ 8 κmm eff ext 3π R T = (8) b ⎪ ⎩⎪ 2T τ if τ < 0.5 = 2 = 3 c mm mm where ν αcs,iso/ and GMp/R in the α disc model. With equations (1)–(5), we can solve  numerically. On the where τ = 0.5κ . Then, we can calculate the flux emitted at other hand, we can also approximate the solution with analytical mm mm every disc radius, using I = 2kT /λ2. After integrating the whole formulae in the following way. First, if we ignore T , we can solve b ext disc, the total CPD emission at mm is derived. We want to caution  analytically as that, by using the opacity law above and applying the same opacity law throughout the disc, we assume that the dust-to-gas mass ratio 3 1/5 1 3/5 27/5 σGM M˙ μ 4/5 R 2 is 1/100 and the dust is perfectly coupled to the gas. As shown in  = p p 1 − in , (6) 6/5 4 3 3 Section 4.6, the perfect coupling is only correct for micron sized 3 α π κRR  R particles. If particles are large enough to decouple from the gas, we could have dramatically different conclusions (Section 4.6). where μ and R are the mean molecular weight and the gas constant, We can also calculate the averaged brightness temperature at mm respectively. Considering that the disc is mostly cold, we choose μ over the whole CPD surface, = 2.4. On the other hand, if we ignore the viscous heating and assume Tc is dominated by Text, we can solve  as Rout Tb2πRdR = Rin Tb 2 . (9) πRout M˙ μ  = P . (7) 3παText This averaged brightness temperature can be compared with the brightness temperature limit of the telescope to estimate if the disc In reality, both viscous heating and external irradiation contribute to is detectable by ALMA or ngVLA. For example, let’s assume 1-h Tc, and a larger Tc will result in a smaller  (equation 5). Thus, we ALMA band 7 observation has a 0.7 K noise level, and the desired choose  as the minimum of  derived from equations (6) and (7). observational beam size is 0.03 arcsec. And we want to observe a With the  determined, we can calculate the midplane temperature CPD that is 20 au from the central star and 140 pc away from us. using equation (4). The angular size of the CPD will be 0.006 arcsec, which will be Knowing the disc surface density and the vertical temperature smaller than the observational beam by a factor of 5. We also know structure (equation 2), we can finally calculate the disc radio con- that the predicted averaged brightness temperature for this CPD tinuum emission flux. We also calculate the brightness temperature is 380 K from Table 1. Then, the diluted brightness temperature (Tb) as an alternative measure of the intensity of the source. In within one observational beam, or antenna temperature, will be this paper, we define the brightness temperature as the equivalent 380/52=15.2 K, and we can get an S/N=(15.2/0.7)=22 detection temperature a black body would have in order to be as bright as with 1-h integration. the observed brightness at a particular wavelength. Thus, it is the Tables 1 and 2 summarize the fluxes and the averaged brightness property of the source. To represent the power actually received by temperatures for all our cases when the source is 140 pc away (e.g. the antenna, we use antenna temperature defined as the temperature in the Taurus star-forming region). The planet mass is assumed to of a black body that would produce the same power as the antenna be 1 MJ in Table 1,and1 MJ or 10 MJ in Table 2.Table1 shows the output. When the source is spatially resolved, the antenna temper- discs in the viscous limit, which means that the planet is faint (e.g. ature coincides with the brightness temperature. When the source it had a ’cold start’) and the viscous heating determines the disc is unresolved, the antenna temperature will be the product of the temperature structure. For such viscous discs, the disc’s effective brightness temperature of the source and the dilution factor. The temperature only depends on the product of Mp and M˙p (equation 1), dilution factor is the ratio between the solid angle of the source and and, when the disc is optically thick at mm, the mm emission will the solid angle of the beam. only depend on MpM˙p.Thus,weuseMpM˙p, α,andRout as three First, we calculate the disc’s optical depth at the given radio wave- fundamental parameters. However, when the disc is optically thin length (τ mm = κmm/2). Although the disc is normally optically or is irradiated by the bright planet, the flux will also depend on Mp thick with the Rosseland mean opacity, it can be optically thin at (equations 6 and 7, more discussion in Sections 3.2 and 4.1). millimetre wavelength (mm) and centimetre wavelength (cm) con- In Table 1, under each temperature and flux column, there are sidering the significantly lower dust opacity at the radio wavelength two sub-columns: ’b.’ refers to the cases that consider the boundary range. We adopt the mass opacity from Andrews et al. (2012), κmm layer irradiation (Lirr = Lacc = GMpM˙p/(2Rin)), and “no b.” refers = 0.034 × (0.87mm/λ)cm2 g−1, which assumes a dust-to-gas mass to the cases without considering the boundary layer irradiation. ratio of 0.01. When the disc is optically thick at mm, the disc’s Table 2 shows the cases where the planet is bright (e.g. the planet brightness temperature at mm (Tb) will equal the disc’s temperature has a ’hot start’) and the irradiation from the central planet to the at τ mm (z) = 1. When the disc is optically thin at mm, we can cal- disc is important for determining the disc temperature. Three planet −3 −4 −5 culate the brightness temperature by integrating the product of the luminosities (Lirr = 10 , 10 , 10 L) have been considered. In temperature, opacity, and density along the disc height. Considering Table 2, we list results with both Mp = 1MJ and Mp = 10MJ. Notice most of the disc mass is at the midplane and most radio emission that with Mp = 10MJ, the disc with Rout = 0.46 au corresponds to comes from the material at the midplane in the optically thin limit, aCPDatrp=9.3 au instead of rp =20 au. When the irradiation is −5 the brightness temperature is then simply the disc’s midplane tem- weak (e.g. Lirr = 10 L), viscous heating dominates and the flux perature weighted by the disc optical depth. of CPDs with Mp = 1MJ in Table 2 is similar to those in Table 1.

Downloaded fromMNRAS https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 Circumplanetary disc detection 1853 (10mm) b T (3mm) b T 17.58 7.78 8.04 2.35 2.43 3mm) . (1 b T 1f6.98 85mm) . (0 b T JyKKKKKKKK μ Jy μ Jy μ Jy μ Jy μ Jy μ Jy μ F(0.85 mm) F(1.3 mm) F(3 mm) F(10 mm) Jy μ no b. b. no b. b. no b. b. no b. b. no b. b. no b. b. no b. b. no b. b. L 3 L − 10 . The left three columns are input parameters, while other columns are derived quantities. J M 1 J disc = M M p M out au R α Viscous discs with 1 − p ˙ yr M 2 J p M 1e-81e-81e-8 1e-41e-8 1e-11e-8 1e-21e-8 0.12 1e-31e-8 0.46 1e-41e-8 0.46 3.5e-4 1e-11e-8 0.46 7.0e-6 1e-2 0.46 0.002 5.6e-5 1e-3 1.85 0.002 3.8e-4 1e-4 1.85 0.002 2.4e-3 1.3e1 1.85 1.4e-1 0.002 1.9e-5 1.85 0.002 1.8e-4 1.3e1 1.3 1.5e-1 0.002 1.6e-3 1.1e1 0.002 1.3e-2 6.9e1 3.9e-2 6.2 3.1e-1 0.002 1.3e1 1.5 0.002 7.2e1 3.0 4.3e-2 3.2e-1 2.8e1 6.2 3.3 3.7e-1 2.3e2 2.4e1 3.1e-3 8.6e-2 3.0e1 3.2 4.1e-1 9.2e-1 2.4e2 3.5e-3 9.1e-2 2.5e1 3.7 3.0e-2 8.0 8.4e-1 9.3e-1 8.5e-5 6.9e1 7.0e-3 2.3 2.7e-1 3.4e-2 8.9e-1 3.1e-2 9.5e-5 7.4e-3 7.2e1 8.4 3.1e-1 8.0e-4 6.8e-2 3.1e-2 2.4 1.9e-4 0.04 7.4e-3 6.1 6.6e-1 9.1e-4 7.2e-2 67.51 2.0e-4 6.9e-2 0.05 8.3e-3 6.9e-1 1.8e-3 0.42 68.27 6.3 0.01 7.2e-2 1.8e-2 3.70 1.9e-3 0.03 0.48 75.07 22.25 1.7e-1 0.01 1.9e-2 0.06 4.18 0.03 75.62 1.8e-1 23.37 0.28 0.58 0.00 0.06 2.48 59.84 0.01 4.72 17.88 0.31 0.61 0.00 60.27 0.04 2.80 18.76 0.01 4.89 0.12 0.38 0.00 22.51 9.39 0.04 1.10 0.00 3.30 0.14 0.40 0.00 22.65 9.80 0.02 1.24 3.42 0.00 0.04 0.17 0.00 3.10 0.02 0.33 1.53 0.04 0.18 0.00 0.01 3.23 0.37 1.59 0.05 0.01 0.48 0.05 0.49 Table 1. M 1e-51e-51e-5 1e-11e-5 1e-21e-5 1e-31e-5 0.12 1e-41e-5 0.12 1e-11e-5 0.12 8.7e-5 1e-21e-5 0.12 5.5e-4 1e-31e-5 0.46 1.570 3.5e-3 1e-41e-5 0.46 1.570 2.2e-2 1e-11e-5 0.46 1.570 6.1e-4 4.2e1 1e-2 0.461e-6 1.570 3.8e-3 7.3e1 1e-3 1.851e-6 1.570 2.4e-2 7.3e1 1e-4 4.3e1 1.851e-6 1.570 1.5e-1 7.3e1 7.4e1 1e-1 1.851e-6 1.570 4.2e-3 1.0e2 7.4e1 1.3e1 1e-2 1.851e-6 1.570 2.7e-2 4.2e2 7.4e1 3.5e1 1e-31e-6 1.570 1.7e-1 4.2e2 0.12 1.2e2 3.5e1 1.3e1 1e-41e-6 1.570 4.2e2 0.12 4.4e2 3.5e1 1.1 3.5e1 1e-11e-6 1.570 2.3e2 0.12 4.4e2 3.0e1 2.2e-5 3.5e1 1e-21e-6 1.6e3 1.2 0.12 4.4e2 1.8e2 1.4e-4 3.5e1 1e-31e-6 1.570 2.4e3 7.3 0.46 2.9e2 2.0e2 0.157 8.7e-4 3.4e1 1e-41e-6 8.0 0.46 2.0e3 2.0e2 0.157 5.5e-3 1.9e2 1e-11e-6 1.2 8.0 2.4e3 0.46 2.7e3 6.4e1 0.157 1.5e-4 2.0e2 1e-2 5.2 7.4 2.5 0.461e-7 5.2e2 0.157 9.6e-4 2.0e2 3.5e1 1e-3 2.1e1 8.1 1.851e-7 2.7e3 1.1e3 0.157 6.1e-3 3.3e-2 8.2e1 4.1e1 1e-4 4.6e1 8.1 1.851e-7 0.157 3.8e-2 3.0e-1 6.3e2 4.1e1 4.6e1 3.6e1 2.2e1 5.6 2.9 1e-1 1.851e-7 0.157 3.3e-2 1.1e-3 1.1e3 9.8e-1 1.2e3 1.1e1 4.2e1 4.7e1 5.3 1e-2 1.851e-7 0.157 3.0e-1 6.7e-3 9.8e-1 9.5e1 4.9e1 4.2e1 4.7e1 1.2e1 6.7e-1 1e-31e-7 0.157 9.8e-1 4.2e-2 7.0e-2 2.4e2 1.2e3 0.12 2.6e2 1.4e1 219 2.0e1 1.5 1e-41e-7 0.157 9.8e-1 2.7e-1 4.5 2.4e2 0.12 1.1e2 380 6.9e-1 5.7e1 2.0e1 1.2e1 6.8 1e-11e-7 0.157 7.9e-2 5.6 2.7e1 0.12 2.5e2 380 2.6e2 2.7e2 5.5e-6 2.0e1 1e-21e-7 3.2 0.157 225 2.2e2 0.12 2.5e2 380 2.8e1 3.5e-5 1.6 2.0e1 136 1e-31e-7 4.6 1.4 384 1.5e-1 1.3e3 1.1 0.46 3.1e1 1.1e2 0.016 2.2e-4 33 2.7e2 1.2e1 1e-41e-7 5.6 384 1.3e3 4.5 0.46 2.8e2 1.1e2 0.016 1.4e-3 3.1e1 1e-1 159 4.01e-7 1.2e-1 1.9e-1 384 4.5 0.46 1.5e3 142 5.3e-1 0.016 3.8e-5 1.2e2 3.2e1 1e-2 1.3e1 422 7.5 136 1.6 1.1 0.46 1.5e31e-8 6.5e1 0.016 2.4e-4 1.2e2 1e-3 38 1.3e-1 422 136 5.0 4.5 2.5 4.57 1.85 2.6e-1 6.4e-11e-8 4.5e2 0.016 1.5e-3 163 2.3e1 1e-4 1.8e1 422 3.2e1 4.5 140 1.851e-8 6.4e2 48 0.016 9.6e-3 3.3e-2 8.0e1 2.3e1 425 142 3.3e-3 2.6e1 8.8 33 3.2e-1 1.5e-1 1e-1 1.85 0.016 1.6e-4 2.7e-1 5.2e2 425 142 5.90 2.3e1 1.9e1 23 5.3 1.2 2.7 1e-2 1.85 0.016 3.3e-2 1.3e-3 3.5e-3 48 5.5e-1 7.0e2 76 1.1e1 425 2.3e1 2.6e1 145 7.0e-3 1.8e-1 5.4 1e-3 6.1e-1 475 151 0.016 2.7e-1 1.0e-2 8.4e1 55 0.12 4.6e1 6.4e-1 3.05 40 9.6 520 151 0.016 5.5e-1 6.7e-2 7.0e-2 1.3e2 0.12 1.5e2 1.4e1 181 8.7e-3 1.1e1 1.2e-2 1.5 1.5 27 26 7.1e-1 520 0.016 3.2 0.12 55 9.1e1 213 78 6.5e-1 5.2e1 85 1.4e-6 2.9 477 6.7 155 0.016 7.6e-2 2.8e1 1.4e2 213 1.5e-2 3.92 54 1.5e2 8.7e-6 1.6e-2 1.1e1 3.65 522 155 9.7 3.2 3.4e-1 25 185 2.3e2 2.6e1 0.002 5.5e-5 1.5 522 29 10 77 3.2 1.4 216 1.5e-1 8.0e2 3.3e-4 3.1e1 1.9e-2 213 6.3e1 186 0.002 54 3.2 31 24 1.1e1 88 4.2e-1 1.35 216 4.58 2.5 2.6e2 703 5.4e-2 186 0.002 59 2.8e1 1.0 142 3.8 1.2e-1 1.8e-1 3.9e-4 30 8.8e2 703 5.4e-1 6.5e1 0.54 2.7e-2 1.1e1 237 7.8 8.1e-1 1.6 18 12 80 77 189 7.0e-2 6.8e1 1.73 214 59 2.41 34 1.3e-1 237 30 4.7 24 2.5 2.4 4.56 189 2.6e-1 2.77 6.2e-1 3.6e2 3.4e-2 704 144 1.4e1 66 8.9e-1 1.1 0.63 1.5e-2 12 27 704 7.6e1 239 3.3e-3 8.6 0.41 204 26 3.2e-1 19 1.5e-1 3.01 85 80 7.4e-4 3 2.3e-1 3.9e2 239 6.6e-2 5.66 3.34 66 1.4e1 22 252 4.9 2.0e-2 2.6 3.2e-2 31 3.4e-3 73 0.36 69 7.0e-3 1.7e-1 5.8 6.4e-1 9.2e-4 293 2.3e-1 7.3e-2 14 31 4.4e1 1.05 0.52 6.0e-1 1.2e-3 3.3e-2 205 3.07 30 293 1.81 87 85 6.9e-2 8 8.5e-3 1.2e-2 1.4 26 69 24 7.0e-1 253 0.42 1.8e-3 4 0.39 120 74 6.1e-1 1.6e-3 4.7e1 293 6.4 34 1.31 120 7.4e-2 1.4e-2 3.79 30 2.18 1.7e-2 4 3.63 293 2.0e-3 22 74 3.3e-5 87 0.15 1.4 0.49 8 27 90 10 43 1.4 121 1.6e-1 3.3e-4 1.9e-2 0.31 195 27 23 121 1.38 0.78 0.06 4.3e-5 4.41 35 395 33 0.18 1.2e-1 1.8e-1 3.8e-4 0.26 105 25 76 5 0.56 133 1.5 18 11 45 0.28 0.39 91 2 1.69 116 0.95 195 0.06 2.41 29 1.2e-1 24 4.74 2.78 0.05 396 0.32 37 106 0.62 12 16.24 134 29 3.3e-3 0.36 0.42 0.24 0.04 19 117 2.92 48 3 5.28 3.20 20 0.11 0.05 3 3.4e-3 17.94 0.37 142 39 165 0.19 13 0.04 1.06 0.51 0.28 29 68 3.24 1.82 49 24.46 8 17.26 0.14 22 0.41 3 142 0.24 165 30 0.02 1.28 25.37 3.60 18.72 2.09 4 0.03 68 57 0.16 8 10 0.08 0.02 0.32 167 11.02 1.47 0.79 31 0.04 0.18 23 58 0.10 4 11.91 0.01 10 0.38 2 1.63 0.91 167 0.05 3.93 0.02 27 23 0.01 0.45 0.24 3 0.05 2 4.21 0.03 0.50 0.27 27 3

Downloaded from https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839 MNRAS 479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 1854 Z. Zhu, S. M. Andrews, and A. Isella 5 − 10 4 − (3mm) 10 b T 3 − 10 5 − 10 4 − 3mm) . 10 (1 b T 3 − 10 5 − 10 4 − 85mm) . 10 (0 b T 3 − 10 5 − Jy K K K K K K K K K . μ 10 L 3 − 4 − Jy ,10 μ 10 (3 mm) L F 4 − 3 ,10 − Jy μ 10 L 5 − 10 5 − Jy = μ 10 irr L 4 − Jy μ 10 (1.3 mm) F 3 − Jy μ 10 5 − Jy μ 10 in the third row refer to cases with 4 3 − Jy − μ 10 (0.85 mm) F , and 10 3 4 − Jy − μ 10 ,10 5 − 5 J − M 10 disc M 3 J − M 10 out au R J α M Irradiated discs. The values of 10 1 1 = − p p ˙ yr M M 2 J p M M 1e-51e-51e-5 1e-11e-5 1e-2 0.121e-5 1e-3 0.121e-5 8.7e-5 1e-4 0.121e-5 5.5e-4 1e-1 0.12 8.7e-51e-5 3.5e-3 1e-2 0.46 5.5e-41e-5 2.2e-2 1e-3 0.46 4.3e1 3.5e-31e-5 6.1e-4 1e-4 0.46 7.4e1 2.2e-21e-5 3.8e-3 1e-1 0.46 7.4e1 4.2e1 6.1e-41e-5 2.4e-2 1e-2 1.85 7.4e1 7.3e1 3.8e-3 1.5e-1 1e-31e-6 1.85 1.1e2 7.3e1 2.4e-2 4.2e1 3.6e-3 1e-41e-6 1.85 4.3e2 7.3e1 1.5e-1 7.3e1 2.7e-21e-6 1.85 1e-1 4.3e2 1.0e2 4.2e-3 7.3e1 1.3e1 1.7e-11e-6 1e-2 4.3e2 4.2e2 2.7e-2 7.3e1 3.5e1 0.121e-6 1.1 1e-3 2.9e2 4.2e2 1.7e-1 1.0e2 3.5e1 0.12 1.3e11e-6 2.1e-5 1e-4 1.9e3 4.2e2 4.2e2 3.5e1 0.12 3.5e11e-6 1.4e-4 1e-1 2.6e3 2.4e2 4.2e2 3.3e1 0.12 3.5e1 1.3e1 2.2e-5 1.11e-6 8.7e-4 1e-2 1.7e3 4.2e2 1.9e2 0.46 3.5e1 3.5e1 1.4e-41e-6 5.5e-3 1e-3 2.4e3 2.3e2 2.0e2 0.46 3.0e1 3.5e1 8.7e-41e-6 1.2 9.6e-5 6.5 1e-4 2.6e3 1.6e3 2.0e2 0.46 1.8e2 3.5e1 3.8e1 5.5e-31e-6 7.4 8.7e-4 1e-1 2.4e3 8.1e1 0.46 2.0e2 3.0e1 4.4e1 1.5e-41e-6 8.1 6.1e-3 1e-2 2.4e3 6.0e2 1.85 2.0e2 1.8e2 4.4e1 1.2 3.5e1 9.6e-4 5.5 8.1 3.8e-2 1e-31e-7 1.2e3 1.85 6.9e1 2.0e2 1.5e1 7.3 4.1e1 6.1e-3 2.8 4.0e-4 1e-41e-7 2.4e3 1.85 5.3e2 2.0e2 2.1e1 1.2e2 8.0 4.1e1 3.8e-2 3.5e1 3.9e-31e-7 1.85 1.1e3 1e-1 6.5e1 1.2 4.6e1 5.2 2.8e2 8.0 1.4e1 9.6e-4 4.1e1 3.6e-21e-7 1.2e3 1e-2 5.2e2 7.3 4.6e1 2.1e1 2.8e2 2.6 1.0e2 6.7e-3 4.1e1 1.3e1 0.12 2.7e-11e-7 1e-3 1.1e3 8.0 4.6e1 3.2e1 2.4e2 4.2e-2 1.2e1 2.0e1 0.12 223 6.71e-7 1.1e3 1.9 2.5e-6 1e-4 8.0 5.5e1 4.6e1 2.9e2 2.4e2 2.1e1 2.7e-1 9.6e1 2.0e1 0.12 1.2e1 3821e-7 2.4e-5 1e-1 2.5 2.7e2 1.7e3 3.1e1 4.6e1 220 2.4e2 0.12 2.0e1 382 4.2 5.5e-61e-7 2.1e-4 1e-2 1.1e3 4.9e1 140 2.0e3 5.8 2.7e2 4.6e1 380 2.4e2 3.6e1 0.46 2.0e1 382 1.2e1 1.6 3.5e-51e-7 1.4e-3 1e-3 2.6e2 140 1.4e3 219 380 2.8e1 1.3e2 0.46 2.0e1 7.6e-1 37 2.2e-41e-7 1.0e-5 1e-4 2.7e2 136 140 1.5e3 4.9e1 380 380 2.4e2 1.3e2 0.46 3.0e1 3.9 2.0e1 1.4e-31e-7 1.2 9.9e-5 6.9 1e-1 5.4 136 161 2.6e2 7.1e-1 380 1.3e3 0.46 1.1e2 1.5 3.2e1 9.0 2.9e-51e-7 34 4.6 9.6e-4 1e-2 136 136 2.6e2 424 380 1.4e3 8.4e1 1.85 38 1.1e2 2.9e1 3.2e1 2.4e-4 4.6 159 8.7e-3 1e-3 136 6.2e-1 424 5.791e-8 3.3 6.0e2 1.85 53 1.1e2 1.1 2.5e1 1.5e-3 6.1 1.5e-1 422 4.0e-5 143 1.6 1e-4 136 424 2.6e2 331e-8 8.8e2 1.85 7.8e1 8.6 1.1e2 159 1.5e1 4.5 2.5e1 34 9.6e-3 3.1 2.1e-1 422 4.0e-4 154 4.951e-8 1.85 5.0e2 1e-1 2.0e1 1.3e-1 422 3.4e-1 1.2e2 4.5 49 140 1.2e-4 2.3e1 422 4.0e-3 1541e-8 77 53 6.8e2 1e-2 6.8e1 1.1 2.8e1 25 422 5.2 2.4e2 1.5e1 2.0e-1 152 1.1e-3 1.6 2.3e1 4.62 0.12 3.9e-2 33 4761e-8 8.0 3.2e-1 140 1.2e-1 1e-3 4.6e2 4.5 1.9e1 422 2.7 1.1e2 152 9.6e-3 1.2e1 0.12 3.3 48 521 761e-8 151 2.5e-7 1e-4 3.85 6.4e2 4.5 1.7e-1 2.6e1 3.2e1 49 23 1.6e2 475 6.7e-2 1.3e1 1.4e1 0.12 199 7.0 87 521 2.7e-11e-8 28 151 2.0 2.5e-6 1e-1 34 6.0e1 7.3e-1 1.5 2.9e2 1.8e1 520 8.9e1 0.12 1.0e1 227 188 3.30 7.7e-7 1.7e-21e-8 76 57 475 2.5e-5 1e-2 2.5 1.8e2 1.6e3 3.2e1 2.6e1 520 23 183 3.3 1.4e2 0.46 1.1e1 227 188 4.88 48 85 4.3 7.2e-61e-8 520 7.0e-1 2.4e-4 25 1e-3 187 3.08 5.0e1 6.5 2.8e2 215 28 3.6e1 0.46 91 4.5e-1 7.9e-2 1.6e-2 1.8 5.5e-51e-8 9.6 520 1.0e-6 54 1e-4 187 1.5e2 11 4.46 1.1e3 182 215 3.0e1 1.0e2 0.46 91 1.70 1.1e1 7.8e-1 40 85 186 3.5e-4 6.5e-11e-8 57 1.0e-5 1e-1 25 3.2 4.4e-1 4.7e1 7.7e-2 214 2.5e2 0.46 3.3e1 1.4e-2 4.1 79 27 186 3.1e-6 1.461e-8 1.0e-4 6.7 1e-2 3.81 54 5.7 10 155 1.5e2 7.5e-1 214 8.6e2 1.85 7.2e1 0.65 1.5 1.3 3.0e1 79 9.1 3.1e-5 33 2.9 9.9e-4 54 14 1e-3 4.1e-1 7.4e-2 248 3.93 1.36 8.4e1 1.85 35 9.2e-1 2.8e1 1.6e-1 3.21 2.9e-4 143 4.0e-6 22 68 1e-4 77 7.0e-1 248 10 0.63 5.95 3.7 5.6e2 1.85 40 6.4e1 1.8e1 2.4e-3 6.4 1.6e-1 3.6e-2 2.2e-2 238 3.70 4.0e-5 13 1.6 54 77 9.1e-1 31 2.94 1.6e-1 1.85 8.1e1 1.1 8.9 142 1.5e1 2.6 29 1.2e-5 3.3 2.2e-1 238 4.0e-4 67 5.52 0.58 19 97 4.6e2 1.9e1 1.5e-1 237 3.5e-2 3.6e-1 1.1e2 2.2e-2 30 3.20 2.51 1.2e-4 1.4e1 4.0e-3 68 12 8.9e-1 1.6e-1 79 97 7.4e1 3.3e-1 28 237 5.5 1.5e1 2.1e-1 0.43 1.2e-3 1.6 4.78 66 27 1.39 18 298 1.1 8.5 3.4e-1 2.57 1.3e-1 3.4e-2 87 3.8e2 2.5 2.1e-2 1.5e1 3.0 9.8e1 1.1e-2 1.1e1 7.5e-2 4.6e-2 67 3.3 28 298 0.41 3.3e-1 74 87 1.27 3.99 2.0e-1 3.2e1 23 293 1.4e1 7.1 2.42 35.77 10 0.52 3.1e-1 1.8e-3 28 2.0 85 5.7e1 166 7.4e-2 7.4e-1 1.5 2.8e2 4.5e-2 1.4e1 293 0.38 8.3e1 166 1.09 66 3.70 3.3e-1 8.0 31.76 1.8e-2 73 42 293 2.09 85 2.5 3.2e1 22 3.3 0.51 4.98 1.8e-3 0.18 4.3 8 78.11 293 7.3e-1 7.2e-2 24 83 128 3.22 4.4e-2 5.4e1 6.9 2.7e2 26.98 128 1.11 3.5e1 4.5e-1 9.3e-2 1.7e-2 1.9 112 32 0.18 37.93 13 51.48 4.76 0.48 3.1e1 1.78 1.7e-3 24.06 6.4 1.05 0.07 6.9e-1 3.7e-3 75 121 22 3.2 4.5e-1 8 9.3e-2 4.6e1 121 2.5e2 106 3.2e1 34.79 1.6e-2 0.16 4.3 44.20 21.39 1.65 0.34 4.26 31 6.3 11 0.91 0.41 0.07 0.66 1.6 3.7e-3 9.1 18.26 28.77 33.32 151 79.18 15 74 105 4.3e-1 9.2e-2 172 4.03 1.44 8.2e1 1.3 9.3e-1 0.33 2.9e1 3.30 10.64 0.40 45 54.58 27.46 10 23.00 0.64 0.06 5.81 4.0 3.6e-3 124 1.7e-1 3.7e-2 7.6e-3 139 3.89 9.47 0.31 13 48.71 9.2e-1 3.15 25.24 7.9e1 9.0 17.39 0.39 3.2 0.04 38 5.64 0.61 1.2 75.68 0.05 117 0.15 21.06 8.11 1.6e-1 134 3.6e-2 3.6e-1 7.5e-3 3.63 2.82 26.39 12 9.1e-1 61.48 13.2 Table 2.

Downloaded fromMNRAS https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 Circumplanetary disc detection 1855 5 − 10 4 − (3mm) 10 b T 3 − 10 5 − 10 4 − 3mm) . 10 (1 b T 3 − 10 5 − 10 4 − 85mm) . 10 (0 b T 3 − 10 5 − y K K K KKKKK JyK μ 10 4 − Jy μ 10 (3 mm) F 3 − Jy μ 10 5 − Jy μ 10 4 − Jy μ 10 (1.3 mm) F 3 − Jy μ 10 5 − Jy μ planet at 2.3, 9.3, and 37 au from the central solar mass star. 10 J M 4 − Jy μ 10 (0.85 mm) F 3 − Jy μ 10 5 J − M 10 disc M 3 J − M 10 out au R of 0.12, 0.46, d 1.85 au corresponds to CPDs around a 10 out R α continued , J – M 1 10 − p ˙ yr = M 2 J p p M 1e-51e-51e-5 1e-11e-5 1e-2 0.121e-5 1e-3 0.121e-5 3.5e-5 1e-4 0.121e-5 2.2e-4 1e-1 0.12 3.5e-51e-5 1.4e-3 1e-2 0.46 2.2e-41e-5 8.7e-3 1e-3 0.46 1.6e1 1.4e-31e-5 2.4e-4 1e-4 0.46 7.4e1 8.7e-31e-5 1.5e-3 1e-1 0.46 7.4e1 1.6e1 2.4e-41e-5 9.6e-3 1e-2 1.85 7.4e1 7.3e1 1.5e-3 6.1e-2 1e-31e-6 1.85 4.1e1 7.3e1 9.6e-3 1.6e1 1.2e-3 1e-41e-6 1.85 2.8e2 7.3e1 6.1e-2 7.3e1 1.0e-21e-6 1.85 1e-1 4.3e2 3.6e1 1.7e-3 7.3e1 6.7e-2 4.71e-6 1e-2 4.3e2 2.7e2 1.1e-2 7.3e1 3.0e1 0.12 4.2e-11e-6 1e-3 9.6e1 4.2e2 6.7e-2 3.5e1 3.5e1 0.121e-6 7.2e-6 1e-4 8.0e2 4.2e2 4.2e-1 2.7e2 3.5e1 0.12 3.0e1 4.61e-6 5.5e-5 1e-1 2.6e3 8.6e1 4.2e2 1.2e1 0.12 3.5e1 8.7e-61e-6 3.5e-4 1e-2 2.6e3 6.8e2 4.2e2 8.8e1 0.46 3.5e1 3.0e1 5.5e-51e-6 2.2e-3 1e-3 2.4e3 7.6e1 4.6 2.0e2 0.46 1.0e1 3.5e1 3.5e-41e-6 3.1e-5 2.2 1e-4 2.4e3 6.5e2 2.0e2 0.46 8.4e1 3.5e1 1.7e1 2.2e-31e-6 3.3 2.9e-4 1e-1 2.4e3 2.7e1 0.46 2.0e2 4.0e-1 4.4e1 6.1e-51e-6 9.9 8.1 2.4e-3 1e-2 2.4e3 2.3e2 1.85 2.0e2 8.3e1 4.4e1 1.5e1 3.8e-4 1.9 8.1 1.5e-2 1e-31e-7 1.2e3 3.8e-1 1.85 2.4e1 2.0e2 3.3 4.1e1 2.4e-3 1.3e-4 4.9 1e-4 9.6e-11e-7 1.2e3 1.85 2.0e2 2.0e2 4.5e1 8.0 4.1e1 1.5e-2 1.5e1 8.0 1.2e-3 3.8e-11e-7 1.85 1.1e3 1e-1 2.1e1 4.5e1 1.7 2.6e2 8.0 3.3e-4 4.1e1 8.4e-1 1.2e-21e-7 1.1e3 1e-2 1.9e2 3.3 4.6e1 2.8e2 3.9e1 2.6e-3 4.6 4.1e1 0.12 1.0e-1 5.1 851e-7 1e-3 1.1e3 8.0 4.5e1 1.0e1 7.7 2.2e2 1.7e-2 8.2e-1 2.0e1 0.12 6.2e-1 2.21e-7 7.9e-7 1e-4 1.1e3 8.0 2.0e1 4.6e1 9.8e1 2.4e2 1.1e-1 3.5e1 2.0e1 0.12 3821e-7 7.7e-6 1e-1 1.4e2 83 3.9 8.1e2 5.2e-1 1.0e1 4.5e1 2.1e2 13 0.12 2.0e1 382 4.5 2.1e-61e-7 7.2e-5 1e-2 7.6 2.7e2 1.7e1 2.0e3 2.0 9.3e1 4.6e1 380 2.4e2 1.3e1 0.46 2.0e1 382 1.4e-51e-7 5.5e-4 1e-3 4.8e-1 1.3e2 140 7.2e2 380 9.0e1 0.46 82 2.0e1 2.4e-1 12 9.4 8.7e-51e-7 1.4 3.2e-6 1e-4 2.6e2 140 1.5e3 1.6e1 380 380 8.4e1 4.4 1.3e2 0.46 1.1e1 2.0e1 91 5.5e-4 5.0e-21e-7 3.2e-5 2.3 1e-1 1.8 136 1.3e2 2.3e-1 380 6.2e2 0.46 7.6e1 1.8e1 9.6e-61e-7 3.0 3.1e-4 11 1e-2 136 58 2.6e2 380 1.4e3 2.8e1 1.85 16 1.1e2 2.9 370 4.3e-2 4.4e-1 3.2e1 1.3 8.6e-5 87 9.9 4.6 2.9e-3 1e-3 136 2.1e-1 1.941e-8 2.4e2 1.85 53 7.3e1 5.1e-1 424 1.5e1 6.1e-4 2.2 1.3e-5 1e-4 136 56 3671e-8 8.8e2 3.9e-1 1.85 53 2.6e1 3.9e-2 1.1e2 424 2.9 2.5e1 14 3.8e-3 9 6.8e-2 1.3e-4 1.74 5.0 2.8 422 86 5.0e-11e-8 154 1.85 2.2e2 1e-1 1.1 1.1 4.5e1 4.5 49 3.7e-5 1.4e1 367 8.7 1.3e-3 56 3.8e-1 4221e-8 154 6.8e2 1e-2 11 2.4e1 2.8e1 1.8 2.3e2 6.5e-2 49 3.6e-4 2.3e1 1.54 0.12 422 1.2e-2 152 13 4.8e-11e-8 8 216 1e-3 1.9e2 2.9 4.2e1 3.3e-3 4.8 1.1e-1 0.12 422 66 9.2e-1 1.0 152 48 2.6 26 5.6 911e-8 521 7.9e-8 1e-4 6.4e2 4.5 5.9e-2 2.6e1 151 1.0e1 7.5 1.6e2 2.6e-2 10 1.4e1 0.12 1.28 6.5e-1 2.3 1.4e-1 214 481e-8 521 7.9e-7 1e-1 2.1e1 1.0e-1 151 9.9e1 8 11 8.3e-1 3.6e1 0.12 227 520 64 25 182 2.5e-7 5.5e-31e-8 2.3e-1 1.15 7.9e-6 1e-2 1.4e2 79 214 4.5 7.6e2 6.0e-1 1.0e1 1.4e-1 2.6e1 56 1.0 1.4e2 0.46 1.1e1 227 4.6 520 188 2.4e-61e-8 9 7.7e-5 8.9e-2 1e-3 7.3 1.9e1 520 2.2 9.6e1 57 215 180 1.02 15 1.3e1 0.46 63 2.5e-2 9 4 5.3e-3 2.3e-1 25 2.1e-51e-8 3.2e-7 1e-4 5.1e-1 1.3e-1 1.2e2 520 7.0e2 215 187 52 8.2e1 0.46 91 77 1.1e1 2.5e-1 0.56 9.9 1.59 1.4e-41e-8 1.4 3.2e-6 180 1e-1 1.0 1.7e1 2.5e-2 214 9.0e1 4.2 54 0.46 1.2e1 32 4.8e-3 2.1e-1 86 13 1.0e-6 5.3e-2 1.2e-21e-8 9 8 3 3.2e-5 186 2.4 1e-2 0.50 1.9 1.1e2 2.4e-1 214 52 6.2e2 1.85 6.8e1 1.49 1.7e1 79 9.9e-6 2.8 3.2e-4 1e-3 62 2.4e-2 1.26 0.21 54 2.8e1 1.85 16 31 2.9e-1 2.9 0.44 1.0e1 5.2e-2 248 4.9e-2 4.9e-1 1.1e-2 1.4 9.6e-5 72 1.3e-6 11 1e-4 2.3e-1 1.28 5 36 2.00 3 2.3e2 1.85 40 6 6.0e1 5.1e-1 248 1.5e1 8.6e-4 2.3 7.0e-3 1.20 1.3e-5 0.20 77 2.9e-1 55 238 68 5.1e-2 4.1e-1 1.85 2.7e1 4.1e-2 31 1.1e-2 2.4 15 3.7e-6 1.1 6.9e-2 1.3e-4 1.90 5.0 34 2.9 238 69 1.04 5.1e-1 2.2e2 1.3 4 10 4.4e1 6.9e-3 30 1.09 3.7e-5 0.19 6 1.2e1 237 9.0 1.3e-3 12.12 2.8e-1 5.1e-2 54 67 0.17 3.8e-1 2.6e1 1.1e-1 2.1 6.7e-2 97 3.7e-4 1.70 0.97 237 13 5.0e-1 33 11.19 197 2.0e2 2.3 6.7e-3 1.0 4.1e1 3.6e-3 0.82 4.9 94.07 0.14 1.1e-1 2.4e-2 68 1.4e-2 0.16 8 4 1.1 28 2.8 3 28 0.83 5.3 66 1.1e-1 298 6.4e-2 1.0e1 7.7 87 1.32 6.7e-1 2.3 1.4e-1 9.37 190 78.53 0.79 5.7e-4 0.13 2.1e1 0.45 1.1e-1 2.4e-2 9.7e1 1.4e-2 11 0.16 3.9e1 166 293 58 8.8e-1 25 1.0e-1 8 5.6e-3 2.4e-1 1.25 3 70.56 189 4.8 6.4e-1 0.71 1.0e1 1.4e-1 42 0.12 85 1.0 0.42 4.9 7.96 5.6e-4 1.0e-1 2.3e-2 6.8 1.4e-2 14.57 2.0e1 293 2.3 9.5e1 128 1.12 0.11 10 1.3e1 2.9e-2 56 0.36 5.5e-3 0.06 2.3e-1 25 67.48 0.36 7.35 112 5.9e-1 1.4e-1 4 1.0e1 32 13.74 3 5.4e-4 0.58 1.63 0.02 0.11 1.2e-3 56.38 1.4 0.34 0.06 74.50 1.0 2.9e-2 1.8e1 121 9.3e1 4.0 1.2e1 6.16 35 5.2e-3 9 2.2e-1 106 5.5e-2 51.00 11.62 1.2e-2 0.55 2.1 0.13 0.10 31 51.48 0.31 1.57 0.02 0.05 4 1.2e-3 2.9 3.45 31.73 15.53 2.9e-2 1.29 0.21 105 2.8e1 30 2.9e-1 0.49 1.2e1 172 0.05 5.3e-2 5.0e-1 1.2e-2 9.90 1.4 26.74 44.20 5 0.13 3.18 14.12 1.46 0.02 36 2.00 1.2e-3 2.4e-3 24.39 1.25 0.05 0.21 3 2.9e-1 9.31 139 4.6e-1 2.7e1 4.8e-2 29 1.1e-2 62.40 2.9 2.67 12.64 0.12 1.1 1.95 5 30 0.02 1.07 0.01 0.04 1.3 7.91 2.4e-3 51.85 1.19 0.20 134 12.29 2.9e M Table 2 M

Downloaded from https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839 MNRAS 479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 1856 Z. Zhu, S. M. Andrews, and A. Isella

3 RESULTS Fig. 3 shows the total flux at 0.85 mm (ALMA band 7) for CPDs with R = 0.46 au, or equivalently CPDs at a = 20 au with M In Section 3.1, we first present the results without including the out p p = 1M and M∗ = M. The flux is scaled by assuming that the sys- irradiation from the planet to the disc (cases in Table 1). Then, in J tems are 140 pc away from us. The two most plausible α values Section 3.2, we present the results that consider the planet irradiation (α=0.001, and 0.01 as in Zhu et al. 2016) are shown. The horizontal (cases in Table 2). line is the 5σ detection level (56 μJy beam−1) achieved by ALMA band7observationwith5hofintegrationonsource.2 Since the CPD won’t be spatially resolved by either ALMA or ngVLA (the 3.1 Viscous heating-dominated discs maximum CPD we calculated is 1.85 au in radius), the total CPD Without the planet irradiation, the disc thermal structure is solely flux will be just received by one observational beam. In this case, determined by the viscous accretion. The disc structure for CPDs we can compare the CPD’s total flux with the RMS of ALMA or −5 −1 with M˙p = 10 MJ yr and Mp = 1MJ is shown in Fig. 1.Two ngVLA to determine if the CPD is detectable. As shown in the cases with different α values (α = 0.01 and 0.001) are presented. figure, the flux is independent of the α value when the accretion −3/5 ˙ = −5 2 −1 The disc surface density follows R ,asinequation(6).With rate is high (MpMp 10 MJ yr ), since the discs are optically a smaller α (upper panels), the disc surface density is higher in thick under such high accretion rates. When the accretion rate gets order to maintain the same accretion rate. Since this disc is al- lower, the discs become optically thin at mm/cm and their brightness most optically thick at mm within 2 au, the brightness temperature depends on their surface density. The discs with lower α values (tri- at mm is always higher than the effective temperature calculated angles) are brighter since they have higher surface density. Overall, with the Rosseland mean opacity. With a higher α (lower pan- CPDs at 20 au should be detectable with ALMA unless the disc’s ˙ = −7 2 −1 els), the surface density is lower and the outer disc becomes opti- accretion rate is very low MpMp 10 MJ yr and α is large cally thin at mm, so that the brightness temperature drops off faster (α ≥ 0.01). there. We summarize our results of Table 1 in Fig. 4.Fromlefttoright, The figure also suggests that the midplane temperature at the Rout is 0.12 au, 0.46 au, and 1.85 au, or equivalent to a CPD around very inner disc (<0.03 au or 60 RJ) can be higher than the dust a Jupiter mass planet that is 5 au, 20 au, and 80 au away from a sublimation temperature (∼1500 K). Dust will sublimate at the solar mass star. Both Table 1 and Fig. 4 clearly show that the disc’s inner disc and the disc will be ionized. The ionized plasma at the radio emission decreases dramatically at longer wavelengths. In the inner disc can also radiate at mm from bound-free and free-free optically thin limit with the above opacity law, the flux will decrease emission. In this paper, we have ignored these effects and simply as λ−3 (the opacity and thus the optical depth decreases as λ−1 and assume that the brightness temperature from the bound-free and the intensity per unit optical depth decreases as λ−2 following the free-free emission at the inner disc is the same as the brightness Rayleigh–Jeans law). At VLA bands, the disc is normally 1–3 orders temperature calculated using dust opacity. To be self-consistent, of magnitude fainter compared with the flux at ALMA bands. On the we should use bound-free and free-free opacities to calculate the other hand, the RMS noise of VLA is less than a factor of 3 smaller disc thermal structure and use this new disc structure to estimate than the RMS noise of ALMA.3 Thus, ALMA will be much more the disc emission at submm (such approach has been adopted in sensitive to CPDs than VLA. On the other hand, detecting CPDs circumstellar disc studies, such as in Zhu, Hartmann & Gammie with VLA is still possible for some cases (e.g. CPDs accreting 2009). However, such calculation is not necessary for the purpose at high rates with Rout=1.85 au shown in Fig. 4 or CPDs with of this work, because, as we will show in Section 4.1, most of the strong jets Section 4.3). Eventually ngVLA may be as sensitive radio emission actually comes from the outer disc, and changing the as ALMA for detecting CPDs. The upper panels of Fig. 4 show inner radius from RJ to 100 RJ has little effect on the radio emission. the flux at ALMA band 7 (0.85 mm, red) and 6 (1.3 mm, black), On the other hand, free-free emission from the jet and wind may be while the lower panels show the flux at ngVLA bands at 3 mm and important, which will be discussed in Section 4.3. 10 mm. The horizontal lines are the 5σ detection levels achieved With the brightness temperature known, we can calculate the flux by 5 h integration at each band. For ngVLA, we assume the 1-h at each radius and integrate the total flux in the disc. Fig. 2 shows noise RMS is 1.48 μJy beam−1 at 3 mm and 0.39 μJy beam−1 at the integrated flux as a function of the disc outer radius Rout.The 10 mm. Only discs with α=0.001 (triangles) and α = 0.01 (squares) solid curves are for the case shown in the upper panels of Fig. 1 are shown in the figure. Fig. 4 suggests that it is easier to detect having a lower α value, while the dashed curves are for the case CPDs at shorter radio wavelengths, and CPDs will also be bigger shown in the bottom panels of Fig. 1 having a higher α value. The and brighter when they are farther away from the star. With α vertical dotted lines label the three different disc sizes Rout = 0.12, = 0.001, Mp = 1MJ,andM∗ = M, 5 h observation can safely 0.46, and 1.85 au, which correspond to a CPD around a Jupiter detect CPDs that are more than 20 au away from the central star −7 −1 mass planet at 5, 20, and 80 au from the central solar mass star. As and accreting at M˙p 10 MJ yr .Ifα = 0.01, 5 h observation clearly demonstrated in Fig. 2, when the disc is optically thick at can detect CPDs at 20 au away from the star and accreting at −6 −1 a particular wavelength, the flux is independent of the disc surface M˙p 10 MJ yr . 1.27 density and the integrated flux roughly scales as Rout . This scaling 1.25 is roughly consistent with the theoretical expectation (Rout ), which can be derived by integrating 2πRTb to Rout with Tb sharing the −3/4 same scaling as Teff for an optically thick disc (∝R , equation 2Using ESO ALMA sensitivity calculator for a source that transits overhead, (1)). −1 = the 1-h RMS noise level of ALMA band 7 (345 GHz) is 25 μJy beam and Thus, a CPD at rp 80 au is almost 34 times brighter than the the 1-h RMS noise level of ALMA band 6 (230 GHz) is 16 μ Jy beam−1,as- = CPD at rp 5 au as long as it is optically thick. On the other hand, suming the maximum bandwidth (7.5 GHz per polarization) for 43 antennas 0.58 when the disc becomes optically thin, the flux scales as Rout . Thus, in the ’automatic’ weather conditions. a CPD at 80 au will only be 5 times brighter than the CPD at 5 au 3Using the VLA exposure calculator, we derive that the 1-h RMS noise of when the disc is optically thin. the A array Q band observation is 10 μJy beam−1.

Downloaded fromMNRAS https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 Circumplanetary disc detection 1857

−5 −1 Figure 1. The disc surface density (left-hand panels) and temperatures (right-hand panels) for viscous heating-dominated CPDs with M˙p = 10 MJ yr , Mp = 1MJ,andα = 0.001 (upper panels) or α = 0.01 (lower panels). Disc effective temperature, midplane temperature, and brightness temperature at 0.85 mm and 3mm are shown in the right-hand panels.

Figure 3. The flux at 0.85 mm (ALMA band 7) for viscous heating- Figure 2. The integrated flux as a function of the disc outer radius Rout. M˙p −5 −1 dominated CPDs with different accretion rates. The systems are assumed to is 10 MJ yr and Mp = 1MJ. The disc is assumed to be viscous heating be 140 pc away from us. Cases with two different α values are shown. The dominated, and thus the planet irradiation is not considered. The black and planet mass is assumed to be 1 M and the planet is 20 au away from the red curves show the flux at 0.85 mm and 3 mm, respectively. The solid J central star (R = 0.46 au). The horizontal line (56 μJy beam−1)isthe5σ curves are for the case with α = 0.001 while the dashed curves are for the out detection level at ALMA band 7 with 5 h integration. case with α = 0.01. The vertical dotted lines label the three different disc sizes Rout =0.12, 0.46, and 1.85 au. When the disc becomes optically thin at a particular wavelength, the flux increases slower with Rout.Thefluxis calculated assuming that the CPD is 140 pc away from us.

Downloaded from https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839 MNRAS 479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 1858 Z. Zhu, S. M. Andrews, and A. Isella

Figure 4. The flux for viscous heating-dominated CPDs with different accretion rates. The upper panels show fluxes at 0.85 mm and 1.3 mm (red and black symbols, respectively). The red and black dashed lines indicate the 5σ level achieved by ALMA, respectively, at 0.85 mm and 1.3 mm with 5 h of integration on source. The lower panels show fluxes at 3 mm and 10 mm (red and black symbols, respectively). The red and black dashed lines (3.31 μJy beam−1 and 0.87 μJy beam−1) indicate the 5σ level achieved by 5 h ngVLA observation with the assumed RMS noise level at these two bands (1-h RMS noise of 1.48 −1 −1 μJy beam at 3 mm and 0.39 μJy beam at 10 mm). From left to right panels, Rout are 0.12 au, 0.46 au, and 1.85 au, which correspond to ap of 5 au, 20 au, and 80 au for a Jupiter mass planet around a solar mass star. Triangles are the cases with α=0.001 while squares are the cases with α=0.01.

3.2 Irradiated discs 4 DISCUSSION When the irradiation from the planet dominates the viscous heat- −1/2 −1 4.1 CPD models with different assumptions ing, Tc follows R and  follows R (equations 3 and 7). For −9/10 comparison, Tc and  of the viscously heated disc follow R Our calculations suggest that CPDs should be detectable by ALMA and R−3/5 (equations 4 and 6). The disc structure for both vis- (note the caveat in Section 4.6). Here we will explore how the cous heating-dominated and irradiation-dominated discs is shown calculated flux will change if we relax some of our assumptions. in the left-hand panel of Fig. 5. The disc surface density drops more Our disc model in Section 2 (equation 1) assumes a zero torque sharply when the irradiation starts dominating the viscous heating. inner boundary, which means that the disc rotates at the local Kep- On the other hand, the right-hand panel of Fig. 5 shows that the lerian speed at the inner boundary. In reality, the Keplerian rotating brightness temperature and the mm/cm flux do not change much disc joins the slowly rotating planet through a boundary layer or between the irradiated and viscous cases. This is because Tc ×  magnetosphere channels. Unless the planet has strong magnetic follows R−1.5 for both the viscously heated and irradiated discs, and fields (more discussion in Zhu 2015), a boundary layer will form Tc ×  is proportional to the brightness temperature when the disc between the disc and the planet, where half of the accretion energy is optically thin. This looks like a coincidence, but it is the direct (Lacc = GMpM˙p/Rp) is released. This boundary layer could irradi- cause from the viscous accretion theory. Equation (5) suggests that ate and heat up the CPD. To include this effect, we set Lirr = 0.5Lacc in equations (1)–(7). The resulting mm/cm flux from such discs is M˙ μ shown on the right side of each Tb and flux column in Table 1.We T  = p (10) c 3πα can see that the irradiation has little effect on the mm emission. Only when the disc accretion rate is low and α is large (in other words, the surface density is low), the irradiation can increase the when R  Rin. Thus, whatever the heating mechanism is, Tc ×  total flux by 20 per cent. is unchanged and directly determined by M˙p. As shown in Table 2, −3 If the CPD is close to the star, the irradiation from the star and the flux difference between cases with Lirr = 10 L and cases −5 with L = 10 L is normally < 10 per cent. In rare cases, the the circumstellar disc can be significantly stronger. At 5 au, the irr ∼ difference can go up to 30 per cent. circumstellar disc has a temperature of 100 K. We thus calculate the radio emission from CPDs with TISM=100 K, which mimics the

Downloaded fromMNRAS https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 Circumplanetary disc detection 1859

Figure 5. The radial profiles of the disc surface density and brightness temperature for discs without irradiation (dashed curves) and with irradiation (solid curves). For the irradiated cases, the central planet is assumed to have the luminosity of 0.001 L.

On the other hand, we expect CPD’s mm/cm flux is sensitive to Rout instead of Rin, since most mm/cm emission comes from the outer disc. We demonstrate this point in Fig. 6.EvenwithRi=100RJ,the mm/cm flux is almost unchanged. Our models assume that Rout is 1/3 of the Hill radius, which is supported by many theoretical studies (Quillen & Trilling 1998; Martin & Lubow 2011). However, in case Rout is smaller than this value by a factor of 2, the total flux will only decrease by a factor ∝ 1.27 of 2.4 if the disc is optically thick (F Rout ) or by a factor of 1.5 ∝ 0.58 if the disc is optically thin (F Rout , the scaling laws are given in Fig. 2). Finally, we study how the mm/cm flux changes with different Mp. Since the disc’s effective temperature only depends on MpM˙p, at a given MpM˙p, the flux will be independent of Mp when the disc is optically thick at mm/cm. On the other hand, Tc depends on ˙ 1/2 MpMp (equation 10). Thus, when the disc is optically thin, mm/cm −1/2 ˙ flux should roughly scale with Mp at a given MpMp.Thishas Figure 6. The flux at 1.3 mm (ALMA band 6) for CPDs with different ˙ = −5 2 −1 beenshowninFig.6. With MpMp 10 MJ yr fixed, the flux accretion rates. All these cases have α=0.001, and Rout = 0.46 au. Cases with from the CPD around a 10MJ planet is almost the same as the flux different background irradiation (T ), planet irradiation, planet masses ISM from the CPD around a 1 M planet since the disc is optically thick. (M ), and inner radii (R ) are shown. The horizontal line (36 μJy beam−1) J p i ˙ = −7 2 −1 = is the 5σ detection level at ALMA band 6 with 5 h integration. But with MpMp 10 MJ yr ,thefluxfromtheMp 10MJ case is a factor of ∼3 smaller than the Mp = 1MJ case. Overall, our calculated mm/cm flux is robust and it is not affected irradiation from the star and the circumstellar disc. The fluxes are by the boundary layer, the irradiation, the inner disc radius, and only shown as the plus signs in Fig. 6. As expected from the argument mildly affected by M . in Section 3.2, such strong irradiation has little effect on the disc’s p radio emission. The irradiation onto the disc can also be strong if the planet is 4.2 Radio flux from minimum mass sub-nebula model bright by itself (e.g. it has a ’hot start’). But as shown in Table 2 and Section 3.2, irradiation does not change the mm emission sig- Although we have little observational constraints on CPDs around nificantly because the flux in the optically thin limit only depends young planets, we can use satellites around Jovian planets in our so- on the accretion rate and is independent of the heating mechanism. lar system to study CPDs that were in our solar system. Several CPD The mm emission from the CPDs irradiated by a Lirr = 0.001 L models have been constructed to understand satellite formation in planet is shown in Fig. 6 as the star signs and they are quite similar our solar system 5 billion years ago. In one model, by spreading the to the non-irradiated case. mass of Galilean satellites into a mini disc around Jupiter, the ’min- Then, we explore how the mm emission changes if we vary Rin in imum mass sub-nebula’ disc was constructed (Lunine & Stevenson the model. The size of a young Jupiter mass planet could be larger 1982; Mosqueira & Estrada 2003). Such model has a high gas sur- 5 −2 than RJ if it starts with a high internal energy (Marley et al. 2007). face density of few× 10 gcm . The disc surface density and A young planet may also have strong magnetic fields, truncating temperature in Mosqueira & Estrada (2003) are plotted in the left- the CPD far away from the planet. For the emission at near-IR and hand and middle panel of Fig. 7. In this model, the disc is assumed mid-IR, Zhu (2015)hasshownthattheIRfluxisverysensitiveto to have the same temperature along the vertical direction. We calcu- Rin since most near-IR/mid-IR emission comes from the inner disc. late the disc brightness temperature and integrate the total mm/cm

Downloaded from https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839 MNRAS 479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 1860 Z. Zhu, S. M. Andrews, and A. Isella

Figure 7. The minimum mass sub-nebula model and its mm/cm emission. The disc surface density and temperature (Mosqueira & Estrada 2003)areshown in the left-hand and middle panel. The middle panel also shows the brightness temperature at 0.85 mm and 3 mm. Since the disc has a uniform temperature vertically and the disc is optically thick, the brightness temperature equals the disc midplane temperature. The integrated mm/cm emissions for discs with different Rout are shown in the right-hand panel. The horizontal lines are the 5-h 5σ detection levels for ALMA and ngVLA.

emission from the disc (the right-hand panel of Fig. 7). Surprisingly, emission, the exact coefficient and the power in equation (11) is suchadiscat5au(soRout ∼0.12 au) is even detectable by ALMA. very uncertain. The extrapolated flux can be off by more than one Thus, if the ’minimum mass sub-nebula’ disc once existed around order of magnitude. Nevertheless, this provides a rough estimate of our Jupiter, we will be able to detect such a disc in a young solar sys- the possible radio emission from the disc. tem analog 140 pc away. In reality, the circumstellar material may confuse the detection even with ALMA’s highest resolution unless a deep gap has been carved out (more discussion in Section 4.5). 4.4 Constraining CPD properties On the other hand, the other satellite formation model, so-called If there is ALMA detection of discs around planetary mass objects, ’gas-starved’ disc model (Canup & Ward 2002), has a much lower we can use our disc models to constrain CPD properties. We take the surface density. The ’gas-starved’ disc model is basically an α disc ˙ ∼ × −7 −1 recent ALMA detection of the disc around OTS44 (a 12MJ object) as model with Mp 2 10 MJ yr , so its mm/cm emission can be −12 −1 an example (Bayo et al. 2017). OTS44 accretes at 8×10 M yr . found from our main set of models. We will be able to detect such Thus, M M˙ ∼ 10−7M2 yr−1. The source is detected at ∼100μJy CPDs if they are 20 au away from the central star with α<0.01. p p J with one beam at ALMA Band 6 (1.3 mm). Since the disc is un- resolved by ALMA with the beam of 0.16 arcesc, the disc size is 4.3 Radio emission from CPD jets and winds smaller than 13 au with the distance of 160 pc. All our models satisfy −7 2 −1 this size constraint. Under the Mp = 10MJ, MpM˙p ∼ 10 M yr , Most astrophysical accretion discs, from AGNs to protostars, pro- J and Lirr = 0.001 L category in Table 2,wefindthat∼100μJy at duce jets and winds that are observable at both radio and optical −4 1.3 mm corresponds to the disc with Rout ∼ 1auifα = 10 .This wavelengths. Thus, accreting CPDs could also produce jets and disc has a mass around 0.01 MJ. We can also estimate the disc mass winds. MHD simulations by Gressel et al. (2013) have indeed sug- if α is not 10−4. For example, under the same set of disc parameters gested that disc winds can be launched in CPDs. To estimate the −3 but with α = 10 , the CPD with Rout = 1.85 au has a flux of 28 μJy centimetre free-free emission of jets launched in CPDs, we extrapo- −3 and a mass of 1.3 × 10 MJ. As discussed in Section 3.1, the flux late the relationship for protostellar jets given in Anglada, Rodr´ıguez 0.58 scales as Rout when the disc is optically thin, and the mass scale & Carrasco-Gonzalez (2015), 1 = as Rout for strongly irradiated discs. Thus, to emit 100μJy, the α −3 2 0.6 10 disc has an outer radius of 17 au and also a mass of 0.01MJ. Fν d Lbol = 0.008 (11) The disc mass and mm emission for all our models are given mJy kpc2 L in the left-hand panel of Fig. 8. We can see that the 5 h ALMA −3 −4 to the planetary mass regime. With Lbol = 1.57 × 10 L in our Band 7 observation can probe CPDs having 10 MJ of gas, which ˙ = −5 2 −1 MpMp 10 MJ yr model, we can estimate that Fν from the jet is equivalent to 0.026 lunar mass of dust assuming the dust-to-gas is 8.48 μJy at cm if d = 140 pc. The flux of 8.48 μJy is detectable mass ratio of 1/100. There is a loose correlation between the disc by ngVLA. Thus, when we have CPD observations with ngVLA in mass and the mm emission. Thus, by using such correlation, we can future, we may need to separate the flux from the disc and the flux estimate the disc mass from its mm emission. From Table 2,wesee from the jet using the radio spectral index, similar to the practice we that the flux at ALMA Band 7 is roughly 3 times larger than the are carrying out in the circumstellar discs (e.g. Carrasco-Gonzalez´ flux at Band 6. Thus, for OTS 44, the flux at ALMA Band 7 should et al. 2016). Recently, this approach has been applied to the pre- be around 300 μJy. Using Fig. 8, the estimated disc mass for OTS transitional disc HD 169142 to reveal an ionized central source, 44 is again 0.01MJ. which could be due to the photoionization of the inner disc, an On the other hand, OTS 44 is a free-floating planetary mass independent object or an ionized jet (Mac´ıas et al. 2017). object whose outer disc radius is unconstrained. For a planetary We caution that, although brighter objects are expected to have mass object orbiting around a central star, its outer radius is limited stronger free-free wind/jet emission since brighter objects normally to 1/3 of its Hill radius. Thus, knowing the planet’s position with have stronger accretion that powers stronger wind/jet and free-free respect to the central star, Rout can also be estimated with some

Downloaded fromMNRAS https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 Circumplanetary disc detection 1861

Figure 8. Left: The disc mass and submm emission (at 0.85 mm) for our models. Right: The disc outer radius and submm emission (at 0.85 mm) for our models. The filled points are discs with Mp = 1MJ (from Table 1 without boundary irradiation) while the open points are discs with Mp = 10MJ (from Table 2 −5 with little irradiation, Lirr = 10 L). In the right-hand panel, the distance of the planet from the central star is plotted on the top axis (assuming a Jupiter mass planet around a solar mass star) and the three Rout (0.12, 0.46, and 1.85 au) are slightly shifted horizontally to show overlapping points. The horizontal line in the left-hand panel is the 5-h 5σ detection level for ALMA Band 7. The two dotted lines in the right-hand panel represent the flux from the fiducial circumstellar disc (equation 13) and the flux that is a factor of 1000 smaller than the fiducial case, assuming the ALMA Band 7 observation with the 0.03 arcsec resolution.

assumptions about the planet and the stellar mass. Then, both the −5 2 −1 10 MJ yr .ThenTable1 suggests that the disc should be around CPD’s radio flux and Rout are known. We plot the mm emission and 400 μJy at ALMA Band 7, which is consistent with the estimate Rout for all our models in the right-hand panel of Fig. 8. from numerical simulations in Zhu et al. (2016). Finally, we caution We can apply this figure to the recent ALMA tentative detection that we have assumed perfect coupling between dust and gas so far. of the point source within HD 142527 (Boehler et al. 2017). HD If we relax this assumption, the discs without radio detections may 142527 system is ∼156 pc away from us. The point source candi- still have a lot of gas despite very little dust, and HD 169142b may date is at 50 au from the central star and has the flux of 0.80 mJy be faint at radio bands (more discussion in Section 4.6). at 0.88 mm . The right-hand panel of Fig. 8 suggests that the upper flux limit from the CPDs at ∼ 50 au is ∼ 2 mJy. Thus, the detected flux is consistent with the emission from the CPD. Since the mea- 4.5 The resolution requirement sured flux is close to the upper limit of all the models, the CPD In most above cases, the planet/brown dwarf is not embedded in the candidate is almost optically thick at mm and the M M˙ should be p p circumstellar disc so there is little confusion between the tiny disc 10−7M2 yr−1 based on the figure. If the inner radius of the CPD is J around the brown dwarf/planet and the circumstellar disc around 1 R , the CPD should be brighter than 17.2 magnitude at the mid-IR J the central star. In reality, we want to discover CPDs within circum- M band (Zhu 2015), which can be studied by JWST in future. stellar discs or gaps of circumstellar discs. Then, we need to not We can also use the right-hand panel of Fig. 8 to constrain the only detect CPDs but also have enough spatial resolution to separate non-detection of discs around GSC 0614-210 b (Bowler et al. 2015), them from circumstellar discs. The emission from the background DH Tau b (Wolff et al. 2017), and GQ Lup B (MacGregor et al. 2017; circumstellar disc or cavity/gap can be simply estimated assuming Wu et al. 2017) by ALMA. The accretion rates of these discs have the disc is optically thin, which is normally a good approximation been measured with various techniques. DH Tau b has an accretion −12 −1 for the circumstellar disc region beyond 10 au. Suppose the circum- rate of 3.2×10 M yr (Zhou et al. 2014), GQ Lup B has an −12 −11 −1 stellar disc has a surface density and temperature structure of (r) accretion rate of 10 to 10 M yr (Wu et al. 2017)(butsee = × × −9.3 −1 and T(r), the brightness temperature will be tb(r) T(r) κmm Zhou et al. 2014 which derive an accretion rate of 10 M yr .), = −1 −10.8 −1 (r). If we choose a fiducial model with (r) 1.78 (r/100 au) g and GSC 0614-210 b has an accretion rate of 10 M yr (Zhou −2 = −1/2 = −8 −7 2 −1 cm and T(r) 22.1(r/100 au) K, which is a α 0.01 disc et al. 2014). Thus, MpM˙p in these discs are ∼10 − 10 M yr . −8 −1 J around a solar mass star accreting at 10 M yr and roughly con- Assuming these discs fill 1/3 of their Hill radius, the non-detection sistent with the protoplanetary discs in Ophiuchus (Andrews et al. may suggest that α 0.001 in these discs. 2009), we have HD 169142b is another CPD candidate 20 au away from the central 1.65 M star. If its L-band emission comes from the accret- = × (r) T 0.87mm tb(λ) 1.34 − . (12) ingCPD(Reggianietal.2014), Zhu (2015) estimate that MpM˙p is 1.78gcm 2 22.1K λ

Downloaded from https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839 MNRAS 479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 1862 Z. Zhu, S. M. Andrews, and A. Isella

Then, assuming the mm beam size is θ and the source is 140 pc where Torb = 2π/vK. For irradiation-dominated discs, we have  = −1 −0.5 away, the radio flux will be 0(R/au) and T = T0(R/au) . For the particular case where Mp = ˙ = −8 −1 = 2 1MJ, Mp 10 MJ yr ,andα 0.001 (as in Fig. 5), we have (r) T 0.87mm θ = −2 = F (λ) = 87μJy × . (13) 0 0.2gcm and T0 40K. Putting these values into equation −2 1.78gcm 22.1K λ 0.03 (16) and assuming Ts < 1, we derive the particle drift time-scale With (r) = 1.78 (r/100 au)−1gcm−2 and T(r) = 22.1(r/100 au)−1/2 1/2 1mm 0 40K Mp −1.5 τ = 47.8 yr, (17) K, F(λ) follows r and it is plotted in the right-hand panel of Fig. 8 drift −2 s 0.2gcm T0 10MJ assuming the 0.03 arcsec resolution. Clearly with such high disc sur- face density, it is difficult to detect any CPD within 20 au with 0.03 which is extremely short. For a comparison, the gas accretion time- arcsec resolution. To detect CPDs at 20 au, the radio flux from the scale is circumstellar disc within the telescope beam needs to be suppressed R2 M 1/2 R 0.001 40K = = 5 p by at least 2–3 orders of magnitude. Such suppression can be phys- τgas 10 yr . (18) ν 10MJ au α T0 ical due to the decrease of the surface density from the gap-opening process, or can be observational such as using a smaller telescope The drift time-scale of mm particles in CPDs is 3 orders of beam. However, there is a limit of using a smaller beam. When the magnitude smaller than the drift time-scale of mm particles in cir- CPD starts to be spatially resolved, decreasing the beam size won’t cumstellar discs. For the circumstellar disc around a solar mass star, ∼ ∼ increase the contrast between the CPD and the circumstellar discs. the central object mass is 1000MJ, T0 is 200 K, 0 is 1000 g −2 α = τ ∼ × 5 For the CPD at 20 au away from the central star, Rout is 0.46 au and cm if 0.001. Thus, drift is 5 10 yr for 1 mm dust par- the diameter is thus 0.92 au, so that this limiting spatial resolution is ticles. The drift time-scale for the disc around a solar mass star is 0.92 au/140 pc = 0.0066 arcsec. We will achieve the maximum con- shown in the left-hand panel of Fig. 9. As the disc’s surface density trast between the CPD and the background circumstellar disc at this decreases and the mass of the central object drops, τ drift decreases resolution. This is where ngVLA has more advantage than ALMA significantly. For the 10 MJ planet accreting at a low rate (shown in with similar sensitivity level but much higher angular resolution. the right-hand panel of Fig. 9), the drift time-scale for 1 mm parti- Another advantage of using a high spatial resolution is that we cles is only 1000 yr. Such fast drift speed is consistent with Pinilla can separate the gap region from the smooth circumstellar disc. A et al. (2013), who studied discs around brown dwarfs with dust co- giant planet at rp can induce a gap that can extend from 0.5 rp to 2 agulation/fragmentation code, and has been used to explain the dust rp. If we can spatially resolve the gap, we can gain the maximum mass-central star mass relationship in brown dwarf discs (Pascucci contrast between the gap and the CPD. We can also gain a higher et al. 2016). This fast radial drift is also consistent with the lack of contrast if the CPD is at the outer disc where the circumstellar disc mm emission from GSC 0614-210 b (Bowler et al. 2015), DH Tau has a lower surface density and a lower temperature, as shown by b (Wolff et al. 2017), and GQ Lup B (MacGregor et al. 2017;Wu the dotted line in the right-hand panel of Fig. 8). Thus, to detect et al. 2017). It also suggests that there may still be a lot of gas in CPDs, we should observe discs with large gaps/cavities using the these discs, which can be probed by future ALMA molecular line highest resolution possible. observations. Fig. 10 shows the drift time-scale for discs around a Jupiter mass planet. The 1 mm particles will drift to the central star within 1000 yr −9 −1 4.6 The drift of mm/cm dust particles even in discs accreting at 10 M yr . The drift time-scale is −11 −1 <100 yr when the disc accretes at 10 M yr . The upper panels So far we have assumed that dust and gas are perfectly coupled. In show the irradiation-dominated cases while the bottom panels show reality, dust particles feel the aerodynamic drag force from the gas the viscous heating-dominated cases. Clearly, independent of the and drift radially in discs. The aerodynamic drag force depends on heating mechanism, the drift time-scale for mm particles is very particle size and is normally parametrized using the dimensionless short.4 dust stopping time (T ). The radial drift speed is s The meter barrier in protoplanetary discs becomes the millimetre T −1v − ηv barrier in CPDs. v = s R,g K , (14) R,d + −1 Thus, it is unlikely that we will detect mm/cm signals from discs Ts Ts around planetary mass objects unless: where vR,g is the gas radial velocity, vK is the midplane Keplerian =− 2 −1 (1) There is a significant population of micron sized dust. At velocity, and η (R Kρg) ∂Pg/∂R is the ratio between the gas pressure gradient and the stellar gravity in the radial direction mm/cm wavelengths, the opacity of micron-sized dust is only sev- (Weidenschilling 1977; Takeuchi & Lin 2002). eral times smaller than that of mm-sized dust (D’Alessio, Calvet & When the particle size is smaller than the mean free path of a Hartmann 2001). Thus, if all the dust in the CPD is in the micron- molecule (which is the case for the problem studied here), the drag sized range, the CPD can still have detectable radio emission, al- force is in the Epstein regime and Ts can be written as (e.g. Espaillat though the flux will be weaker than our current estimate. et al. 2014) (2) Or, the disc has a high surface density so that the mm-sized dust has a smaller stopping time and the drift time-scale is long. ρ s 100gcm−2 T = 1.55 × 10−3 p , (15) This means that the disc either accretes at a high rate or the α is s −3 1gcm 1mm g small.

where ρp is the dust particle density, s is the dust size, and g is the disc gas surface density. 4When particles settle to the disc midplane or have significant pile up, the With equations (14) and (15), we can calculate the dust drift feedback from dust to gas becomes important. Then streaming instability time-scale (Youdin & Goodman 2005) will operate to regulate the dust-to-gas mass −1 ratio, and dust will still drift fast radially (slower by a factor of 2 than the R Ts + T τ = = s T , (16) speed without including the feedback; Bai & Stone 2010)). drift ∂lnP 2 orb vR,d g H 2π ∂lnR R

Downloaded fromMNRAS https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 Circumplanetary disc detection 1863

Figure 9. The drift time-scale for the disc around a solar mass object having Lirr = L (the left-hand panel) and the disc around a 0.01 M object having Lirr = 0.001 L (the right-hand panel). In both cases, the disc is irradiation dominated and α is assumed to be 0.001.

−3 Figure 10. The drift time-scale for discs around a 1 MJ planet. The discs are either irradiation dominated (Lirr = 10 L, upper panels) or viscous heating dominated (Lirr = 0, bottom panels.). Discs that accrete at high and low rates are shown in the left- and right-hand panels.

(3) Or, dust is continuously being replenished into the disc. The radial drift. For example, if the radial drift time-scale is 102 yr replenishment could come from the accretion streams from the while the gas accretion time-scale is 105 yr, the dust-to-gas mass circumstellar disc, or infalling envelope, or dust fragmentation due ratio will be 1000 times smaller than the ISM value (0.01) even with to collisions between bigger dust particles.5 On the other hand, the the continuous replenishment of dust and gas. dust replenishing rate needs to be very high to compensate the fast (4) Or, there are structures in the gaseous CPD (e.g. pressure traps) that can slow down or even trap dust particles in the disc (e.g. mini HL Tau like CPDs in HL Tau gaps). In the CPD simulations 5 The real situation can be a lot more complicated since dust particles may by Zhu et al. (2016), rings and vortices have indeed been observed be trapped at the gap edge induced by the planet and won’t flow into the (e.g. figs 3 and 4 in that paper) due to the shock driven accretion. circumplanetary disc.

Downloaded from https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839 MNRAS 479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 1864 Z. Zhu, S. M. Andrews, and A. Isella

Although these features are transient, they may slow down particle Although ALMA may have enough sensitivity to detect CPDs, it radial drift. is difficult to distinguish the unresolved CPDs from the background circumstellar disc. Only if a deep gap/cavity has been carved out or Another possibility for the existence of dust is that CPDs are in the CPD is far away from the central star, we can distinguish them the debris disc stage so that there is little gas in the disc (dust-to-gas from the circumstellar disc using ALMA’s highest resolution. The mass ratio 1 and dust drift is slow). Since we are interested in high-resolution requirement is where future long baseline arrays CPDs that are actively accreting, this is beyond the scope of this such as the ngVLA would provide the greatest advantage compared paper. to ALMA. Overall, it is more likely to detect discs around planetary mass Finally, we find that mm/cm dust particles drift extremely fast objects if the discs are accreting at a relatively high rate (surface in CPDs. Within most of our parameter space, It only takes 100– density is higher so that the dust drift time-scale is longer) and 1000 yr for mm dust particles to drift to the central star. The meter being fed continuously (e.g. through circumstellar discs, infalling barrier in protoplanetary discs becomes the millimetre barrier in envelope, etc.). It is less likely to find discs around isolated planetary circumplanetary discs. Thus, to detect CPDs at radio wavelengths, mass objects that are accreting at a low rate. CPDs need to have a large population of micron-sized dust, a high On the other hand, OTS44 is isolated and does not have a high gas surface density, mechanisms to trap/slow down dust particles, accretion rate either. The mm particles should have already drifted or mechanisms to replenish mm particles efficiently. We have also to the central planetary mass object (the right-hand panel of Fig. 9). commented on recent ALMA detection or non-detection of discs Based on the drift time-scale argument, we suggest that the ALMA around planetary mass objects. Based on the particles’ drift time- detection by Bayo et al. (2017) indicates that most dust may be at the scale argument, the radio emission may come from micron-sized micron-sized range, or the disc has sub-structures, or the gas surface dust only, or the dust-to-gas mass ratio is significantly smaller than density is very high so that the dust-to-gas mass ratio is significantly 0.01 in these discs, or the disc has substructures to trap dust particles. lower than 1/100. The latter scenario can be tested if its gas mass These can be tested by future observations. can be constrained from ALMA molecular line observations. Another interesting source is FW Tau b (Kraus et al. 2014), ∼ which is an 10 MJ companion 330 au away from the central ACKNOWLEDGEMENTS 0.2-0.3 M binary. ALMA has detected a strong emission (∼1.78 mJy) at 1.3 mm (Kraus et al. 2015), implying 1–2 earth mass of Z.Z. would like to thank Enrique Macias Quevedo, Catherine Espail- lat for helpful discussions. The work is stimulated by the discussion dust in the disc. This amount of dust mass implies 1 MJ mass of gas (10 per cent of the central object mass) in the disc with the of the ’Science Use Cases’ for ngVLA. Z.Z. acknowledges support assumption that the dust-to-gas mass ratio is 1/100. Considering the from the National Aeronautics and Space Administration through gravitational instability will limit the gas mass, it is unlikely that the the Astrophysics Theory Program with Grant No. NNX17AK40G. dust-to-gas mass ratio can be significantly lower than 1/100 in this A. I. acknowledges support from the National Aeronautics and disc. We suggest that most of the radio emission may come from Space Administration Grant No. NNX15AB06G. micron-sized dust in this disc, or there are structures in the disc to slow down the particle radial drift. REFERENCES

Andrews S. M., Wilner D. J., Hughes A. M., Qi C., Dullemond C. P., 2009, 5 CONCLUSION ApJ, 700, 1502 Andrews S. M. et al., 2012, ApJ, 744, 162 We have constructed simple α disc models to study radio emission Anglada G., Rodr´ıguez L. F., Carrasco-Gonzalez C., 2015, Proc. Sci., ˙ −8 2 −1 from CPDs. A large disc parameter with MpMp from 10 MJ yr Radio Jets in Young Stellar Objects with the SKA. SISSA, Trieste, −5 2 −1 −4 −1 to 10 MJ yr , α from 10 to 10 ,andRout from 0.1 to 1.85 au PoS(AASKA14)121 has been explored. Ayliffe B. A., Bate M. R., 2009, MNRAS, 397, 657 We find that radio observations are more sensitive to CPDs at Bai X.-N., Stone J. M., 2010, ApJ, 722, 1437 shorter wavelengths (e.g. ALMA Band 7 and above). The radio Bayo A. et al., 2017, ApJ, 841, L11 emission by viscous discs is almost independent of the inner disc Biller B. A. et al., 2014, ApJ, 792, L22 radius and the irradiation by the star or the planet. If the system is Boehler Y., Weaver E., Isella A., Ricci L., Grady C., Carpenter J., Perez L., 2017, ApJ, 840, 60 140 pc away from us, deep observations at ALMA Band 7 could Bowler B. P., Andrews S. M., Kraus A. L., Ireland M. J., Herczeg G., Ricci detect CPDs around a Jupiter mass planet at 20 au from the host star, L., Carpenter J., Brown M. E., 2015, ApJ, 805, L17 −10 −1 when the disc accretes at a rate of 10 M yr with α 0.001 Calvet N., Gullbring E., 1998, ApJ, 509, 802 −9 −1 or at a rate of 10 M yr with α 0.01. When the CPDs are Canup R. M., Ward W. R., 2002, AJ, 124, 3404 closer or farther away from the star, Rout is proportional to Rp and Carrasco-Gonzalez´ C. et al., 2016, ApJ, 821, L16 1.27 we can scale our calculated flux accordingly: the flux scales as Rout Currie T., Cloutier R., Brittain S., Grady C., Burrows A., Muto T., Kenyon 0.58 when the CPD is optically thick, and as Rout when it is optically S. J., Kuchner M. J., 2015, ApJ, 814, L27 thin. Radio emission from CPD Jets or winds may be detectable by D’Alessio P., Canto¨ J., Calvet N., Lizano S., 1998, ApJ, 500, 411 ngVLA in future. D’Alessio P., Calvet N., Hartmann L., 2001, ApJ, 553, 321 We also discuss the radio emission from various CPD models Espaillat C. et al., 2014, in Beuther H., Klessen R. S., Dullemond C., Henning T., eds, Protostars and Planets VI. Univ. Arizona Press, Tucson, that were constructed to understand the Galilean satellite formation p. 497 in our solar system. With the ’minimum mass sub-nebula’ model, Gressel O., Nelson R. P., Turner N. J., Ziegler U., 2013, ApJ, 779, 59 ALMA has the sensitivity to detect the CPD if it is >5aufrom Hartmann L., 1998, Accretion Processes in Star Formation. Cambridge Univ. the central star. If we use the ’gas-starved’ disc model, ALMA has Press, Cambridge, NY enough sensitivity to detect the CPD if it is >20 au away from the Heller R. et al., 2014, Astrobiology, 14, 798 central star with α<0.01. Heller R., Pudritz R., 2015, ApJ, 806, 181

Downloaded fromMNRAS https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018 Circumplanetary disc detection 1865

Hubeny I., 1990, ApJ, 351, 632 Quanz S. P., Amara A., Meyer M. R., Kenworthy M. A., Kasper M., Girard Isella A., Chandler C. J., Carpenter J. M., Perez´ L. M., Ricci L., 2014, ApJ, J. H., 2013, ApJ, 766, L1 788, 129 Quillen A. C., Trilling D. E., 1998, ApJ, 508, 707 Kenyon S. J., Hartmann L., 1987, ApJ, 323, 714 Rameau J. et al., 2017, AJ, 153, 244 Kraus A. L., Ireland M. J., 2012, ApJ, 745, 5 Reggiani M. et al., 2014, ApJ, 792, L23 Kraus A. L., Ireland M. J., Cieza L. A., Hinkley S., Dupuy T. J., Bowler B. Sallum S. et al., 2015, Nature, 527, 342 P., Liu M. C., 2014, ApJ, 781, 20 Selina R. J. et al., 2018, preprint (arXiv:1806.08405) Kraus A. L., Andrews S. M., Bowler B. P., Herczeg G., Ireland M. J., Liu Spiegel D. S., Burrows A., 2012, ApJ, 745, 174 M. C., Metchev S., Cruz K. L., 2015, ApJ, 798, L23 Szulagyi´ J., Masset F., Lega E., Crida A., Morbidelli A., Guillot T., 2016, Lubow S. H., Seibert M., Artymowicz P., 1999, ApJ, 526, 1001 MNRAS, 460, 2853 Lunine J. I., Stevenson D. J., 1982, ICARUS, 52, 14 Takeuchi T., Lin D. N. C., 2002, ApJ, 581, 1344 MacGregor M. A. et al., 2017, ApJ, 835, 17 Waite J. H. et al., 2017, Science, 356, 155 Mac´ıas E., Anglada G., Osorio M., Torrelles J. M., Carrasco-Gonzalez´ C., Weidenschilling S. J., 1977, MNRAS, 180, 57 Gomez´ J. F., Rodr´ıguez L. F., Sierra A., 2017, ApJ, 838, 97 Wolff S. G. et al., 2017, AJ, 154, 26 Marley M. S., Fortney J. J., Hubickyj O., Bodenheimer P., Lissauer J. J., Wu Y.-L. et al., 2017, ApJ, 836, 223 2007, ApJ, 655, 541 Youdin A. N., Goodman J., 2005, ApJ, 620, 459 Martin R. G., Lubow S. H., 2011, MNRAS, 413, 1447 Zhou Y., Herczeg G. J., Kraus A. L., Metchev S., Cruz K. L., 2014, ApJ, Mosqueira I., Estrada P. R., 2003, ICARUS, 163, 198 783, L17 Muzerolle J., Hartmann L., Calvet N., 1998, AJ, 116, 455 Zhu Z., 2015, ApJ, 799, 16 Muzerolle J., Calvet N., Hartmann L., 2001, ApJ, 550, 944 Zhu Z., Hartmann L., Gammie C., 2009, ApJ, 694, 1045 Papaloizou J. C. B., Nelson R. P., 2005, A&A, 433, 247 Zhu Z., Ju W., Stone J. M., 2016, ApJ, 832, 193 Pascucci I. et al., 2016, ApJ, 831, 125 Peale S. J., 1999, ARA&A, 37, 533 Pinilla P., Birnstiel T., Benisty M., Ricci L., Natta A., Dullemond C. P., Dominik C., Testi L., 2013, A&A, 554, A95 This paper has been typeset from a TEX/LATEX file prepared by the author.

Downloaded from https://academic.oup.com/mnras/article-abstract/479/2/1850/5035839 MNRAS 479, 1850–1865 (2018) by Library Periodicals user on 15 August 2018