The last decade has witnessed remarkable advances in the characterization of the (sub-)millimeter emission from planet-forming disks. Conversely, the study of (sub-)centimeter emission has made more limited progress, to the point that only a few exceptional disk-bearing objects have been characterized in the centimeter regime. This work takes a broad view of the centimeter emission from a large sample with Karl G. Jansky Very Large Array (VLA) observations that is selected from previous Atacama Large (sub-)Millimeter Array (ALMA) surveys of more representative disks in brightness and extent . We report on the detection and characterization of flux at centimeter wavelengths from 21 sources in the Taurus star-forming region. Complemented by literature and archival data, the entire photometry from 0.85 mm to 6 cm is fit by a two-component model that determines the ubiquitous presence of free-free emission entangled with the dust emission. The flux density of the free-free emission is found to scale with the accretion rate but is independent of the outer-disk morphology depicted by ALMA. The dust emission at 2 cm is still appreciable and offers the possibility to extract an unprecedented large set of dust spectral indices in the centimeter regime. A pronounced change between the median millimeter indices (2.3) and centimeter indices (2.8) suggests that a large portion of the disk emission is optically thick up to 3 mm. The comparison of both indices and fluxes with the ALMA disk extent indicates that this portion can be as large as 40 au and suggests that the grain population within this disk region that emits the observed centimeter emission is similar in disks with different sizes and morphologies. All these results await confirmation and dedicated dust modeling once facilities such as next generation VLA (ngVLA) or Square Kilometre Array (SKA)-mid are able to resolve the centimeter emission from planet-forming disks and disentangle the various components.

(Abridged) We present high angular resolution and sensitivity ALMA 3.1 mm and VLA 9.1 mm observations of the disc around CI Tau. These new data were combined with similar-resolution archival ALMA 0.9 and 1.3 mm observations and new and archival VLA 7.1 mm, 2.0, 3.0, and 6.0 cm photometry to study the properties of dust in this system. At wavelengths <3.1 mm, CI Tau's continuum emission is very extended and highly substructured (with three gaps, four rings, and two additional gap-ring pairs identified by non-parametric visibility modelling). Instead, the VLA 9.1 mm data are dominated by a bright central component, only partially (< 50

We present high angular resolution (50 mas) and sensitivity Atacama Large Millimeter/submillimeter Array (ALMA) Band 3 (3.1 mm) and Very Large Array (VLA) Ka band (9.1 mm) observations of the multi-ringed disc around the 3 Myr-old solar-mass star CI Tau. These new data were combined with similar-resolution archival ALMA Band 7 (0.9 mm) and 6 (1.3 mm) observations and new and archival VLA Q (7.1 mm), Ku (2.0 cm), X (3.0 cm), and C band (6.0 cm) photometry to study the properties of dust in this system. At wavelengths <= 3.1 mm, the continuum emission from CI Tau is very extended (>= 200 au) and highly substructured (with three gaps, four rings, and two additional gap-ring pairs identified by non-parametric visibility modelling). In contrast, the VLA Ka band data are dominated by a centrally peaked bright component, only partially (<= 50%) due to dust emission, surrounded by a marginally detected faint and smooth halo. We fitted the ALMA and VLA Ka band data together, adopting a physical model that accounts for the effects of dust absorption and scattering. For our fiducial dust composition ('Ricci' opacities), we retrieved a flat maximum grain size distribution across the disc radius, with a(max) = (7.1 +/- 0.8) x 10(-2) cm that we tentatively attributed to fragmentation of fragile dust or bouncing. We tested, for the first time, the dependence of our results on the adopted dust composition model to assess which mixture can best reproduce the observations. We found that 'Ricci' opacities work better than the traditionally adopted 'DSHARP' ones, while graphite-rich mixtures perform significantly worse. We also show that for our fiducial composition, the data prefer low porosity (<= 70%) grains. This is in contrast with recent claims of highly porous aggregates in younger sources, which we tentatively justified by time-dependent compaction at the fragmentation or bouncing barrier. Our results on composition and porosity are in line with constraints from disc population synthesis models and naturally arise from CI Tau's peculiar spectral behaviour (i.e. the abrupt steepening of its spectral index at wavelengths longer than 3.1 mm), making this disc a unique target to characterise the properties of disc solids and thus ideal for deeper centimetre-wavelength observations and follow-up dust polarisation studies.

Observational surveys of entire star-forming regions have provided evidence of power-law correlations between the disc-integrated properties and the stellar mass, especially the disc mass (Md proportional to M-star(lambda m)) and the accretion rate (M proportional to M-star(lambda acc)). Whether the secular discevolution affects said correlations is still a matter of debate: while the purely viscous scenario has been investigated, other evolutionarymechanisms could have a different impact. In this paper, we study the time evolution of the slopes lambda(m) and lambda(acc) in the wind-drivenand viscous-wind hybrid case and compare it to the purely viscous prediction. We use a combination of analytical calculations, wherepossible, and numerical simulations performed with the 1D population synthesis codeDiskpop, which we also present and release to the community. Assuming M-d(0)proportional to M(star)(lambda m,0 )and M(0)proportional to M(star)(lambda acc,0 )as initial conditions, we find that viscous and hybrid accretion preservethe power-law shape of the correlations, while evolving their slope; on the other hand, magneto-hydrodynamic winds change the shapeof the correlations, bending them in the higher or lower end of the stellar mass spectrum depending on the scaling of the accretiontimescale with the stellar mass. However, we show how a spread in the initial conditions conceals this behaviour, leading to power-lawcorrelations with evolving slopes as in the viscous and hybrid case. We analyse the impact of disc dispersal, intrinsic in the windmodel and due to internal photoevaporation in the viscous case: we find that the currently available sample sizes (similar to 30 discs at 5 Myr)introduce stochastic oscillations in the slopes' evolution, which dominate over the physical signatures. We show that we could mitigatethis issue by increasing the sample size: with similar to 140discs at 5 Myr, corresponding to the complete Upper Sco sample, we would obtainsmall enough error bars to use the evolution of the slopes as a proxy for the driving mechanism of disc evolution. Finally, from ourtheoretical arguments, we discuss how the observational claim of steepening slopes necessarily leads to an initially steeperMd-M star correlation with respect to M-M-star.

While the most exciting explanation of the observed dust asymmetries in protoplanetary disks is the presence of protoplanets, other mechanisms can also form the dust features. This paper presents dual-wavelength Atacama Large Millimeter/submillimeter Array observations of a large asymmetric dusty ring around the M-type star CIDA 9A. We detect a dust asymmetry in both 1.3 and 3.1 mm data. To characterize the asymmetric structure, a parametric model is used to fit the observed visibilities. We report a tentative azimuthal shift of the dust emission peaks between the observations at the two wavelengths. This shift is consistent with a dust trap caused by a vortex, which may be formed by an embedded protoplanet or other hydrodynamical instabilities, such as a dead zone. Deep high-spatial-resolution observations of dust and molecular gas are needed to constrain the mechanisms that formed the observed millimeter cavity and dust asymmetry in the protoplanetary disk around CIDA 9A.

Protoplanetary disks emit radiation across a broad range of wavelengths, requiring a multiwavelength approach to fully understand their physical mechanisms and how they form planets. Observations at sub-millimeter to centimeter wavelengths can provide insights into the thermal emission from dust, free-free emission from ionized gas, and possible gyro-synchrotron emission from the stellar magnetosphere. This work is focused on CX Tau, a ${\sim}0.4\,M_\odot$ star with an extended gas emission and a compact and apparently structureless dust disk, with an average millimeter flux when compared to Class II sources in Taurus. We present observations from the Karl G. Jansky Very Large Array (VLA) across four bands (between 9.0 mm and 6.0 cm) and combine them with archival data from the Atacama Large Millimeter/submillimeter Array (ALMA), the Submillimeter Array (SMA) and the Plateau de Bure Interferometer (PdBI). This multiwavelength approach allows us to separate the dust continuum from other emissions. After isolating the dust thermal emission, we derived an upper limit of the dust disk extent at 1.3 cm which is consistent with theoretical predictions of a radial drift-dominated disk. Centimeter data show a peculiar behavior: deep observations at 6.0 cm did not detect the source, while at 1.3 cm the flux density is anomalously higher than adjacent bands. Intraband spectral indices suggest a dominant contribution from free-free emission, whereas gyro-synchrotron emission is excluded. To explain these observations, we propose a strong variability among the free-free emission with timescales shorter than a month. Another possible interpretation is the presence of anomalous microwave emission from spinning dust grains.

As the classic viscous paradigm for protoplanetary disk accretion is challenged by the observational evidence of low turbulence, the alternative scenario of MHD disk winds is being explored as being potentially able to reproduce the same observed features traditionally explained with viscosity. Although the two models lead to different disk properties, none of them has been ruled out by observations—mainly due to instrumental limitations. In this work, we present a viable method to distinguish between the viscous and MHD framework based on the different evolution of the distribution in the disk mass ( M d )–accretion rate ( M ̇ ) plane of a disk population. With a synergy of analytical calculations and 1D numerical simulations, performed with the population synthesis code Diskpop , we find that both mechanisms predict the spread of the observed ratio M d / M ̇ in a disk population to decrease over time; however, this effect is much less pronounced in MHD-dominated populations compared with purely viscous populations. Furthermore, we demonstrate that this difference is detectable with the current observational facilities: we show that convolving the intrinsic spread with the observational uncertainties does not affect our result, as the observed spread in the MHD case remains significantly larger than in the viscous scenario. While the most recent data available show a better agreement with the wind model, ongoing and future efforts to obtain direct gas mass measurements with Atacama Large Millimeter/submillimeter Array and next-generation Very Large Array will cause a reassessment of this comparison in the near future.

Planet formation imprints signatures on the physical structures of disks. In this paper, we present high-resolution (similar to 50 mas, 8 au) Atacama Large Millimeter/submillimeter Array observations of 1.3 mm dust continuum and CO line emission toward the disk around the M3.5 star 2MASSJ04124068+2438157. The dust disk consists of only two narrow rings at radial distances of 0 47 and 0 78 (similar to 70 and 116 au), with Gaussian sigma widths of 5.6 and 8.5 au, respectively. The width of the outer ring is smaller than the estimated pressure scale height by similar to 25%, suggesting dust trapping in a radial pressure bump. The dust disk size, set by the location of the outermost ring, is significantly larger (by 3 sigma) than other disks with similar millimeter luminosity, which can be explained by an early formation of local pressure bump to stop radial drift of millimeter dust grains. After considering the disk's physical structure and accretion properties, we prefer planet-disk interaction over dead zone or photoevaporation models to explain the observed dust disk morphology. We carry out high-contrast imaging at the L' band using Keck/NIRC2 to search for potential young planets, but do not identify any source above 5 sigma. Within the dust gap between the two rings, we reach a contrast level of similar to 7 mag, constraining the possible planet below similar to 2-4M(Jup). Analyses of the gap/ring properties suggest that an approximately Saturn-mass planet at similar to 90 au is likely responsible for the formation of the outer ring, which can potentially be revealed with JWST.

ABSTRACT Large surveys of star-forming regions have unveiled power-law correlations between the stellar mass and the disc parameters, such as the disc mass $M_{\mathrm{d}} \!-\! {M_{\star }}$ and the accretion rate $\dot{M} \!-\! {M_{\star }}$. The observed slopes appear to be increasing with time, but the reason behind the establishment of these correlations and their subsequent evolution is still uncertain. We conduct a theoretical analysis of the impact of viscous evolution on power-law initial conditions for a population of protoplanetary discs. We find that, for evolved populations, viscous evolution enforces the two correlations to have the same slope, λm = λacc, and that this limit is uniquely determined by the initial slopes λm, 0 and λacc, 0. We recover the increasing trend claimed from the observations when the difference in the initial values, δ0 = λm, 0−λacc, 0, is larger than 1/2; moreover, we find that this increasing trend is a consequence of a positive correlation between the viscous time-scale and the stellar mass. We also present the results of disc population synthesis numerical simulations, that allow us to introduce a spread and analyse the effect of sampling, which show a good agreement with our analytical predictions. Finally, we perform a preliminary comparison of our numerical results with observational data, which allows us to constrain the parameter space of the initial conditions to λm, 0 ∈ [1.2, 2.1], λacc, 0 ∈ [0.7, 1.5].

The formation of multiple stellar systems is a natural by-product of the star-formation process, and its impact on the properties of protoplanetary discs and on the formation of planets is still to be fully understood. To date, no detailed uniform study of the gas emission from a sample of protoplanetary discs around multiple stellar systems has been performed. Here we analyse new ALMA observations at a $\sim$21 au resolution of the molecular CO gas emission targeting discs in eight multiple stellar systems in the Taurus star-forming regions. $^{12}$CO gas emission is detected around all primaries and in seven companions. With these data, we estimate the inclination and the position angle for all primary discs and for five secondary or tertiary discs, and measure the gas disc radii of these objects with a cumulative flux technique on the spatially resolved zeroth moment images. When considering the radius including 95\% of the flux as a metric, the estimated gas disc size in multiple stellar systems is found to be on average $\sim 4.2$ times larger than the dust disc size. This ratio is higher than what was recently found in a population of more isolated and single systems. On the contrary, when considering the radius including 68\% of the flux, no difference between multiple and single discs is found in the distribution of ratios. This discrepancy is due to the sharp truncation of the outer dusty disc observed in multiple stellar systems. The measured gas disc sizes are consistent with tidal truncation models in multiple stellar systems assuming eccentricities of $\sim0.15$-$0.5$, as expected in typical binary systems.

The DSHARP survey evidenced the ubiquity of substructure in the mm dust distribution of large, bright protoplanetary discs. Intriguingly, these datasets have yet higher resolution information that is not recovered in a CLEAN image.We first show that the intrinsic performance of the CLEAN algorithm is resolution-limited. Then analyzing all 20 DSHARP sources using the 1D, super-resolution code Frankenstein (frank), we accurately fit the 1D visibilities to a mean factor of 4.3 longer baseline than the Fourier transform of the CLEAN images and a factor of 3.0 longer baseline than the transform of the CLEAN component models. This yields a higher resolution brightness profile for each source, identifying new substructure interior to 30 au in multiple discs; resolving known gaps to be deeper, wider, and more structured; and known rings to be narrower and brighter. Across the survey, high contrast gaps are an average 14% wider and 44% deeper in the frank profiles relative to CLEAN, and high contrast rings are an average 26% narrower. Categorizing the frank brightness profiles into trends, we find that the relative scarcity of features interior to 30 au in the survey’s CLEAN images is an artifact of resolving power, rather than an intrinsic rarity of inner disc (or compact disc) substructure. Finally the rings in the frank profiles are narrower than the previously inferred deconvolved widths, indicating smaller α/St ratios in the local gas disc.

Context. Observations at millimeter wavelengths of bright protoplanetary disks have shown the ubiquitous presence of structures such as rings and spirals in the continuum emission. The derivation of the underlying properties of the emitting material is nontrivial because of the complex radiative processes involved. Aims. In this paper we analyze new observations from the Atacama Large Millimeter/submillimeter Array (ALMA) and the Karl G. Jansky Very Large Array (VLA) at high angular resolution corresponding to 5 – 8 au to determine the dust spatial distribution and grain properties in the ringed disk of HD 163296. Methods. We fit the spectral energy distribution as a function of the radius at five wavelengths from 0.9 to 9 mm, using a simple power law and a physical model based on an analytic description of radiative transfer that includes isothermal scattering. We considered eight dust populations and compared the models' performance using Bayesian evidence. Results. Our analysis shows that the moderately high optical depth (τ>1) at λ ≤ 1.3 mm in the dust rings artificially lower the millimeter spectral index, which should therefore not be considered as a reliable direct proxy of the dust properties and especially the grain size. We find that the outer disk is composed of small grains on the order of 200 µm with no significant difference between rings at 66 and 100 au and the adjacent gaps, while in the innermost ~30 au, larger grains (≥mm) could be present. We show that the assumptions on the dust composition have a strong impact on the derived surface densities and grain size. In particular, increasing the porosity of the grains to 80% results in a total dust mass about five times higher with respect to grains with 25% porosity. Finally, we find that the derived opacities as a function of frequency deviate from a simple power law and that grains with a lower porosity seem to better reproduce the observations of HD 163296. Conclusions. While we do not find evidence of differential trapping in the rings of HD 163296, our overall results are consistent with the postulated presence of giant planets affecting the dust temperature structure and surface density, and possibly originating a second-generation dust population of small grains.

The 1.33 mm survey of protoplanetary discs in the Taurus molecular cloud found annular gaps and rings to be common in extended sources (> 55 au), when their 1D visibility distributions were fit parametrically. We first demonstrate the advantages and limitations of nonparametric visibility fits for data at the survey's 0.12" resolution. Then we use the nonparametric model in Frankenstein ('frank') to identify new substructure in three compact and seven extended sources. Among the new features we identify three trends: a higher occurrence rate of substructure in the survey's compact discs than previously seen, underresolved (potentially azimuthally asymmetric) substructure in the innermost disc of extended sources, and a 'shoulder' on the trailing edge of a ring in discs with strong depletion at small radii. Noting the shoulder morphology is present in multiple discs observed at higher resolution, we postulate it is tracing a common physical mechanism. We further demonstrate how a super-resolution frank brightness profile is useful in motivating an accurate parametric model, using the highly structured source DL Tau in which frank finds two new rings. Finally we show that sparse (u, v) plane sampling may be masking the presence of substructure in several additional compact survey sources.

Context. Exoplanetary research has provided us with exciting discoveries of planets around very low-mass (VLM) stars (0.08 M⊙ ≲ M* ≲ 0.3 M⊙; e.g., TRAPPIST-1 and Proxima Centauri). However, current theoretical models still strive to explain planet formation in these conditions and do not predict the development of giant planets. Recent high-resolution observations from the Atacama Large Millimeter/submillimeter Array (ALMA) of the disk around CIDA 1, a VLM star in Taurus, show substructures that hint at the presence of a massive planet. Aims. We aim to reproduce the dust ring of CIDA 1, observed in the dust continuum emission in ALMA Band 7 (0.9 mm) and Band 4 (2.1 mm), along with its 12CO (J = 3−2) and 13CO (J = 3−2) channel maps, assuming the structures are shaped by the interaction of the disk with a massive planet. We seek to retrieve the mass and position of the putative planet, through a global simulation that assesses planet-disk interactions to quantitatively reproduce protoplanetary disk observations of both dust and gas emission in a self-consistent way. Methods. Using a set of hydrodynamical simulations, we model a protoplanetary disk that hosts an embedded planet with a starting mass of between 0.1 and 4.0 MJup and initially located at a distance of between 9 and 11 au from the central star. We compute the dust and gas emission using radiative transfer simulations, and, finally, we obtain the synthetic observations, treating the images as the actual ALMA observations. Results. Our models indicate that a planet with a minimum mass of ~1.4 MJup orbiting at a distance of ~9−10 au can explain the morphology and location of the observed dust ring in Band 7 and Band 4. We match the flux of the dust emission observation with a dust-to-gas mass ratio in the disk of ~10−2. We are able to reproduce the low spectral index (~2) observed where the dust ring is detected, with a ~40−50% fraction of optically thick emission. Assuming a 12CO abundance of 5 × 10−5 and a 13CO abundance 70 times lower, our synthetic images reproduce the morphology of the 12CO (J = 3−2) and 13CO (J = 3−2) observed channel maps where the cloud absorption allowed a detection. From our simulations, we estimate that a stellar mass M* = 0.2 M⊙ and a systemic velocity vsys = 6.25 km s−1 are needed to reproduce the gas rotation as retrieved from molecular line observations. Applying an empirical relation between planet mass and gap width in the dust, we predict a maximum planet mass of ~4−8 MJup. Conclusions. Our results suggest the presence of a massive planet orbiting CIDA 1, thus challenging our understanding of planet formation around VLM stars.

The frequency of Earth-sized planets in habitable zones appears to be higher around M-dwarfs, making these systems exciting laboratories to investigate planet formation. Observations of protoplanetary disks around very low-mass stars and brown dwarfs remain challenging and little is known about their properties. The disk around CIDA 1 (~0.1–0.2 M⊙) is one of the very few known disks that host a large cavity (20 au radius in size) around a very low-mass star. We present new ALMA observations at Band 7 (0.9 mm) and Band 4 (2.1 mm) of CIDA 1 with a resolution of ~0.05″ × 0.034″. These new ALMA observations reveal a very bright and unresolved inner disk, a shallow spectral index of the dust emission (~2), and a complex morphology of a ring located at 20 au. We also present X-shooter (VLT) observations that confirm the high accretion rate of CIDA 1 of Ṁacc = 1.4 × 10−8 M⊙ yr−1. This high value of Ṁacc, the observed inner disk, and the large cavity of 20 au exclude models of photo-evaporation to explain the observed cavity. When comparing these observations with models that combine planet–disk interaction, dust evolution, and radiative transfer, we exclude planets more massive than 0.5 MJup as the potential origin of the large cavity because with these it is difficult to maintain a long-lived and bright inner disk. Even in this planet mass regime, an additional physical process may be needed to stop the particles from migrating inwards and to maintain a bright inner disk on timescales of millions of years. Such mechanisms include a trap formed by a very close-in extra planet or the inner edge of a dead zone. The low spectral index of the disk around CIDA 1 is difficult to explain and challenges our current dust evolution models, in particular processes like fragmentation, growth, and diffusion of particles inside pressure bumps.

Class III stars are those in star forming regions without large non-photospheric infrared emission, suggesting recent dispersal of their protoplanetary disks. We observed 30 class III stars in the 1-3 Myr Lupus region with ALMA at ${\sim}856\mu$m, resulting in 4 detections that we attribute to circumstellar dust. Inferred dust masses are $0.036{-}0.093M_\oplus$, ${\sim}1$ order of magnitude lower than any previous measurements; one disk is resolved with radius ${\sim}80$ au. Two class II sources in the field of view were also detected, and 11 other sources, consistent with sub-mm galaxy number counts. Stacking non-detections yields a marginal detection with mean dust mass ${\sim}0.0048M_\oplus$. We searched for gas emission from the CO J=3-2 line, and present its detection to NO Lup inferring a gas mass ($4.9 {\pm} 1.1$) ${\times}10^{-5} M_\oplus$ and gas-to-dust ratio $1.0{\pm}0.4$. Combining our survey with class II sources shows a gap in the disk mass distribution from $0.09{-}2M_\oplus$ for ${>}0.7M_\odot$ Lupus stars, evidence of rapid dispersal of mm-sized dust from protoplanetary disks. The class III disk mass distribution is consistent with a population model of planetesimal belts that go on to replenish the debris disks seen around main sequence stars. This suggests that planetesimal belt formation does not require long-lived protoplanetary disks, i.e., planetesimals form within ${\sim}$2 Myr. While all 4 class III disks are consistent with collisional replenishment, for two the gas and/or mid-IR emission could indicate primordial circumstellar material in the final stages of protoplanetary disk dispersal. Two class III stars without sub-mm detections exhibit hot emission that could arise from ongoing planet formation processes inside ${\sim}1$ au.

ABSTRACT We analyse spatially resolved ALMA observations at 0.9, 1.3, and 3.1 mm for the 26 brightest protoplanetary discs in the Lupus star-forming region. We characterize the discs multiwavelength brightness profiles by fitting the interferometric visibilities in a homogeneous way, obtaining effective disc sizes at the three wavelengths, spectral index profiles, and optical depth estimates. We report three fundamental discoveries: first, the millimetre continuum size–luminosity relation already observed at 0.9 mm is also present at 1.3 mm with an identical slope, and at 3.1 mm with a steeper slope, confirming that emission at longer wavelengths becomes increasingly optically thin. Second, when observed at 3.1 mm the discs appear to be only 9 per cent smaller than when observed at 0.9 mm, in tension with models of dust evolution that predict a starker difference. Third, by forward modelling the sample of measurements with a simple parametric disc model, we find that the presence of large grains ($a_\mathrm{max}\gt 1\,$ mm) throughout the discs is the most favoured explanation for all discs as it reproduces simultaneously their spectral indices, optical depth, luminosity, and radial extent in the 0.9–1.3 mm wavelength range. We also find that the observations can be alternatively interpreted with the discs being dominated by optically thick, unresolved, substructures made of mm-sized grains with a high scattering albedo.

ABSTRACT We present the first ALMA survey of protoplanetary discs at 3 mm, targeting 36 young stellar objects in the Lupus star-forming region with deep observations (sensitivity 20–50 $\mu$Jy beam−1) at ∼0.35 arcsec resolution (∼50 au). Building on previous ALMA surveys at 0.89 and 1.3 mm that observed the complete sample of Class II discs in Lupus at a comparable resolution, we aim to assess the level of grain growth in the relatively young Lupus region. We measure 3 mm integrated fluxes, from which we derive disc-averaged 1–3 mm spectral indices. We find that the mean spectral index of the observed Lupus discs is $\alpha _\mathrm{1-3\, mm}=2.23\pm 0.06$, in all cases $\alpha _\mathrm{1-3\, mm}\lt 3.0$, with a tendency for larger spectral indices in the brightest discs and in transition discs. Furthermore, we find that the distribution of spectral indices in Lupus discs is statistically indistinguishable from that of the Taurus and Ophiuchus star-forming regions. Assuming the emission is optically thin, the low values $\alpha _\mathrm{1-3\, mm}\le 2.5$ measured for most discs can be interpreted with the presence of grains larger than 1 mm. The observations of the faint discs in the sample can be explained without invoking the presence of large grains, namely through a mixture of optically thin and optically thick emission from small grains. However, the bright (and typically large) discs do inescapably require the presence of millimetre-sized grains in order to have realistic masses. Based on a disc mass argument, our results challenge previous claims that the presence of optically thick substructures may be a universal explanation for the empirical millimetre size-luminosity correlation observed at 0.89 mm.