2.1. Unresolved observations of the inner dusty disk

NIR observations were the basis of the first estimates of disk lifetimes (Haisch, Lada, & Lada Reference Haisch, Lada and Lada2001). With the advent of the Spitzer Space Telescope, large samples covering most of the disks and diskless populations in clusters, extended our knowledge of the dusty inner rim over several AU (see Figure 2). Spitzer data allowed to conduct statistical studies in disk evolution, including ‘transition disks’ (e.g. Sicilia-Aguilar et al. Reference Sicilia-Aguilar2006a; Najita, Strom, & Muzerolle Reference Najita, Strom and Muzerolle2007; Espaillat et al. Reference Espaillat2012). Despite being unresolved, the number of disks observed during the Spitzer cold mission is so overwhelming, that the statistical constraints on disk properties (including the presence of inner holes and gaps) and their lifetimes have provided one of the most complete and general views about the typical structures, dispersal paths, and lifetimes for the disks around solar- and late-type stars (Hartmann et al. Reference Hartmann, Megeath, Allen, Luhman, Calvet, D’Alessio, Franco-Hernández and Fazio2005; Megeath et al. Reference Megeath, Hartmann, Luhman and Fazio2005; Lada et al. Reference Lada2006; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2006a; Hernández et al. Reference Hernández2007, amongst many others). Such unresolved observations are particularly important to study disk dispersal in solar analogues, since dispersing disks around low- and solar-mass stars are very often too faint to be resolved otherwise.

Silicate emission is another tracer of the dust grains in the warm disk atmosphere and a signature of the vertical temperature structure in the disk (Calvet et al. Reference Calvet1992; D’Alessio et al. Reference D’Alessio, Calvet, Hartmann, Franco-Hernández and Servín2006). Although for most disks, the silicate observations are unresolved, it is possible to obtain spatially resolved silicate data (Van Boekel et al. Reference Van Boekel, Waters, Dominik, Dullemond, Tielens and de Koter2004; Juhász et al. Reference Juhász2012). Partly observable from the ground, it was efficiently observed for large samples of objects thanks to Spitzer/IRS, allowing to study the disk mineralogy in a statistically significant way. Even though the silicate emission does not provide information on the global grain properties in the disk, it is a sign of grain processing, heating, mixing, and transport in the disk. Dust processing happens in all protoplanetary disks, ranging from HAeBe (Meeus et al. Reference Meeus, Waters, Bouwman, van denAncker, Waelkens and Malfait2001; Bouwman et al. Reference Bouwman, Meeus, de Koter, Hony, Dominik and Waters2001; Van Boekel et al. Reference Van Boekel2005) to brown dwarf (BD) disks (Apai et al. Reference Apai, Pascucci, Bouwman, Natta, Henning and Dullemond2005; Ricci et al. Reference Ricci2014). Crystalline silicates are not found in the ISM (Kemper, Vriend, & Tielens Reference Kemper, Vriend and Tielens2004) and require very specific conditions for their formation. Thus, the mass fraction of crystals and stochiometry of the silicates can be used to trace the physical conditions in the disk when the material formed, including the temperature, initial chemical composition, grain sizes, velocities, and the time frame for annealing, considering the different chemical reactions that give rise to the production of different silicate components (e.g. silica, forsterite, enstatite; Bouwman et al. Reference Bouwman, Meeus, de Koter, Hony, Dominik and Waters2001; Henning Reference Henning2010). The formation of a silicate feature is also strongly connected to the disk structure, so the size of the emitting region can be estimated even in unresolved observations, considering the strength of the emission in different silicate bands (Kessler-Silacci et al. Reference Kessler-Silacci2007; Bouwman et al. Reference Bouwman2008; Juhász et al. Reference Juhász2010).

The silicate feature is optically thin, which allows to estimate the dust mass and composition fraction in the outer disk layers and, comparing to the continuum, to discern the presence of gaps and holes (Bouwman et al. Reference Bouwman2010) and the presence of large ( ~ 10 μm) grains in the disk atmosphere, used to constrain turbulence and settling (Sicilia-Aguilar et al. Reference Sicilia-Aguilar2007; Pascucci et al. Reference Pascucci, Apai, Luhman, Henning, Bouwman, Lahuis and Natta2009). The lack of strong amorphous silicate features in intermediate-aged disks around M-type stars is interpreted as a sign of grain growth and settling in the innermost disk, which dominates the 10 μm emission (Sicilia-Aguilar et al. Reference Sicilia-Aguilar2007). The lack of trends between crystallinity and other disk and stellar properties (Watson et al. Reference Watson2009; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2007, Reference Sicilia-Aguilar2011) suggests that their formation depends on many factors, including rapid creation and mixing of crystalline silicates on timescales much shorter than those of disk evolution (Ábrahám et al. Reference Ábrahám2009; Juhász et al. Reference Juhász2012). Finally, crystalline silicates could be used as indirect signatures of the presence of planets, related to heating by shocks (Desch et al. Reference Desch, Ciesla, Hood and Nakamoto2005; Bouwman et al. Reference Bouwman2010).

2.2. Inner extent of dust in disks

Although modelling spatially unresolved spectral energy distributions (SED) provides some constraints on the inner disk radius, the most accurate measurements of R_{in, dust} come from spatially resolved interferometric observations of NIR dust emission. These measurements showed that the spatial extent of the hottest dust in disks were not consistent with disk models extending up to the star, and were found to correlate with the squared root of the stellar luminosity as R_{in, dust} ∝ L^1/2 _⋆ (Monnier & Millan-Gabet Reference Monnier and Millan-Gabet2002; Dullemond & Monnier Reference Dullemond and Monnier2010). This correlation was readily explained with the existence of a dust sublimation front at temperatures of 1300–1500K: Most of the NIR dust emission is emitted by a disk rim located at the dust sublimation front (Natta et al. Reference Natta2001; Dullemond, Dominik, & Natta Reference Dullemond, Dominik and Natta2001). The gas inside this rim must be radially optically thin enough to allow a direct irradiation of the rim. More physical models of the rim were proposed, including the physics of dust sublimation (Isella & Natta Reference Isella and Natta2005), multiple dust species and full radiative transfer (Kama, Min, & Dominik Reference Kama, Min and Dominik2009) and detailed hydrodynamics (Flock et al. Reference Flock, Fromang, Turner and Benisty2016). The radial location of the dust rim can provide constraints on the inner disk dust surface density, size distribution, and material through an analytical formula or through detailed models (Kama et al. Reference Kama, Min and Dominik2009; Flock et al. Reference Flock, Fromang, Turner and Benisty2016).

The advent of new instruments at VLTI, such as AMBER and PIONIER, and the use of very long baselines (CHARA), enabled detailed modelling of multi-wavelength observations. These showed that additional material (gas or refractory species) could contribute significantly to the NIR excess (Kraus et al. Reference Kraus2008; Tannirkulam, Harries, & Monnier Reference Tannirkulam, Harries and Monnier2007; Benisty et al. Reference Benisty2010a). Multi-wavelength observations revealed systems with cleared regions (Olofsson et al. Reference Olofsson2011, Reference Olofsson2013; Tatulli et al. Reference Tatulli2011; Matter et al. Reference Matter2014), and optically thin material located inside the gap (Kraus et al. Reference Kraus2012). With a larger number of observations available, the images of the first AU could be reconstructed, unveiling a complex morphology (Renard et al. Reference Renard, Malbet, Benisty, Thiébaut and Berger2010; Benisty et al. Reference Benisty, Tatulli, Ménard and Swain2010b). Although the most detailed studies were focussed on a small samples, recent homogeneous PIONIER observations of HAeBe stars found that very few objects show well-resolved puffed-up rims, so that the sublimation front is rather smooth and not a sharp transition (Lazareff et al. submitted). Large-scale emission, contributing to lower visibilities at short baselines, might indicate cavity walls. Similar findings were derived from a statistical analysis of MIR observations (Millan-Gabet et al. Reference Millan-Gabet2016).

As a cautionary note, resolved observations are subject to interpretation through models that depend on the dust composition and size distribution, on the structure of the rim, on the dust density, and on the temperature. The dust composition and size affects the dust opacity, which controls the local temperature (see Section 7). Observations of different objects, including those with and without inner holes, and combination with multi-wavelength observations to track the gas content and the extended disk structure are a key to put these observations into a broader context.

2.3. Inner extent of molecular gas in disks

Similarly to the hottest dust in the inner disk, the hottest (and innermost, in terms of disk radii) molecular gas emission typically peaks in the NIR with ro-vibrational branches at 2–5 μm (e.g. Figure 7 in Salyk et al. Reference Salyk, Blake, Boogert and Brown2009), or in the UV at 1 300–1 700 Å (France et al. Reference France2011, Reference France2012). With due differences, spatial information on the gas-emitting region can be obtained with interferometry (Eisner et al. Reference Eisner2010; Eisner, Hillenbrand, & Stone Reference Eisner, Hillenbrand and Stone2014), spectro-astrometry (Pontoppidan et al. Reference Pontoppidan2008; Pontoppidan, Blake, & Smette Reference Pontoppidan, Blake and Smette2011; Brittain, Najita, & Carr Reference Brittain, Najita and Carr2015), position-velocity diagrams (Goto et al. Reference Goto2006; Brittain, Najita, & Carr Reference Brittain, Najita and Carr2009; van der Plas et al. Reference van der Plas2009; Carmona et al. Reference Carmona2011), and with high-dispersion spectrographs through fully spectrally resolved velocity profiles (Brown et al. Reference Brown2013; Banzatti & Pontoppidan Reference Banzatti and Pontoppidan2015). For optically thin lines, the strength of NIR gas emission lines is linked to the column density, temperature, and excitation conditions of hot gas in the inner disk. Optically thick lines trace the temperature in the emitting region, which has a complex dependency on the gas density.

The emission from two molecules, H₂ and CO, is especially suited to trace the innermost disk region where molecular gas can survive: They are abundant (being made by the most abundant atoms), they share a similarly high thermal dissociation temperature ( ~ 4500 K) and they can also self-shield to dissociating UV radiation to some extent (Bruderer Reference Bruderer2013a; see Section 2.4).

The NIR CO fundamental ro-vibrational lines are good tracers of the gas in the inner disk because their energy levels are sufficiently populated at the temperatures found at 0.1–10 AU and because their Einstein A coefficients are large, making them much stronger than the NIR H₂ lines (e.g. Carmona et al. Reference Carmona2008; Bitner et al. Reference Bitner2008), which lack a permanent dipole moment. As the CO emission becomes optically thick at low column densities (N_CO ~ 10¹⁶ cm⁻² or N_H ~ 10²⁰ cm⁻²), strong lines are formed even in the upper regions where the dust is optically thin. The CO overtone needs higher column densities and temperatures than CO ro-vibrational to be excited (N_CO ~ 5 × 10²⁰ cm⁻², T > 1 700 K; Bik & Thi 2004), being mostly observed in massive young stars.

UV pumping triggers H₂ emission at 2.12 μm, which can be detected up to 150 AU if the disk is warm and flared (e.g. Carmona et al. Reference Carmona2011). H₂ also has stronger fluorescent transitions (excited by Lyα photons) in the UV that been observed with IUE and HST wavelengths and that are also detectable for CTTS and transition disks (Valenti et al. Reference Valenti, Fallon and Johns-Krull2003; Hoadley et al. Reference Hoadley, France, Alexander, McJunkin and Schneider2015). The main limitation for these observations are the brightness of the target and whether there is still enough gas at a high enough temperature, to produce substantial NIR emission. This poses a general outer limit of ≈ 20 AU to the disk regions that can be studied in the thermal NIR, as well as sensitivity limits of the individual techniques. All considered to date, high-dispersion spectroscopy of NIR CO emission has provided the largest and most informative dataset of molecular gas observations in inner disks (Brown et al. Reference Brown2013; Banzatti & Pontoppidan Reference Banzatti and Pontoppidan2015).

High-dispersion spectroscopy provides a way to characterise the emitting region of gas in disks even at scales not directly spatially resolvable. This is achieved by modelling velocity-resolved line profiles broadened by Keplerian rotation in the disk. The observed velocities depend on Kepler’s law and on the inclination angle, so that emission from smaller orbital radii has higher velocity shifts. The observed line profiles therefore provide measurements of the disk radii where CO is emitting, being ‘spatially-resolved’ through the velocity shifts. To fully spectrally resolve a line from a ≲ 10 AU disk radii, a resolving power of at least 25 000 is required, depending on the disk inclination. In the case of NIR observations, this is currently achieved by high-resolution slit spectrographs such as CRIRES at the ESO-VLT, iSHELL on the IRTF, NIRSPEC at Keck, and IRCS at Subaru. This technique has proven to be efficient in surveys of velocity-resolved CO emission, especially with the advent of CRIRES (e.g. Pontoppidan et al. Reference Pontoppidan, Blake and Smette2011; Brown et al. Reference Brown2013; Banzatti & Pontoppidan Reference Banzatti and Pontoppidan2015). It allows us to study a radial region between 0.05–20 AU in disks around stellar masses ≳ 0.3 M_⊙, based on flux sensitivity limits of CRIRES of ≈ 2–10⁻¹⁶ erg cm⁻² s⁻¹ for an unresolved line with resolution 3.3 km s⁻¹ and a typical line width of 10 km s⁻¹. The minimum column density depends on the assumed gas temperature, the size of the emitting region, and the disk inclination. From observations of HD 139614 (Carmona et al. 2016), the minimum column density detectable at 3σ level was N_H = 5 × 10¹⁹ cm⁻² (N_CO = 5 × 10¹⁵ cm⁻²) for a disk of gas between 0.1–1.0 AU at T = 675–1 500 K inclined 20° around a 1.7 M_⊙ star.

If the emitting region is beyond 10–30 AU in disks at 120–140 pc, CO emission lines can be directly spatially resolved in position-velocity diagrams (Goto et al. Reference Goto2006; Brittain et al. Reference Brittain, Najita and Carr2009; van der Plas et al. Reference van der Plas2009; Carmona et al. Reference Carmona2011). If the emitting region is < 10 AU, information on the spatial scales can be retrieved from the spectroastrometry signature of the line profiles in the 2D spectrum (e.g. Pontoppidan et al. Reference Pontoppidan, Blake and Smette2011; Brown et al. Reference Brown2013; van der Plas et al. Reference van der Plas, van den Ancker, Waters and Dominik2015). Spectroastrometry essentially measures the shift on the centre of the point spread function (PSF) at the position of the emission lines in the 2D spectrum. As the centre of the PSF can be measured with an accuracy of the order of 1/10 of a pixel with CRIRES (with the assistance of adaptive optics), spatial information can be retrieved on spatial scales of the order of 0.01 arcsec (= 1 AU at 100 pc), for bright enough sources. This technique has been successfully implemented in a dozen of disks so far (Pontoppidan et al. Reference Pontoppidan2008, Reference Pontoppidan, Blake and Smette2011; Brittain et al. Reference Brittain, Najita and Carr2015). Its success depends, amongst other things, on the disk inclination and on reaching a good S/N, which strongly limits the observations of faint and low-mass disks. NIR interferometry has been used to detect CO emission at 2.3 μm at disk radii of < 2 AU (Eisner et al. Reference Eisner2010, Reference Eisner, Hillenbrand and Stone2014). The low detection rates with this technique suggested that the most effective range to study CO gas in inner disks is at 4.6–5 μm, where the emission is more frequently found, also for low-mass stars (Goto et al. Reference Goto2006; Brown et al. Reference Brown2013; Banzatti & Pontoppidan Reference Banzatti and Pontoppidan2015).

All the NIR observing techniques mentioned above provide spatial information on CO emission in the inner disks. As they probe the hottest molecular gas, the spatial information is usually regarded as a measurement of the smallest stellocentric distance where the molecular gas survives, which we call R_{in, CO} as being based mostly on observations of CO. These measurements have a high potential to constrain disk structure and evolution, as we will discuss later. In velocity-resolved observations, the velocity at the half width at half maximum (HWHM) of the line provides a measurement of the disk radius close to where the peak line flux is emitted. At smaller disk radii, less than 10% of the line flux is typically emitted, with slight differences depending on how steep line wings are (Banzatti & Pontoppidan Reference Banzatti and Pontoppidan2015). In spectroastrometry, R_{in, CO} is usually taken at the peak of the spectro-astrometric signal, which corresponds to the disk radius that contributes most to the emission (Pontoppidan et al. Reference Pontoppidan2008, Reference Pontoppidan, Blake and Smette2011). Models show that R_{in, CO} from CO ro-vibrational emission corresponds to the location of the maximum CO intensity when a power law for the intensity, or a power-law column density and temperature profiles are assumed. It effectively corresponds to the disk radius where CO emission becomes optically thick. From R_{in, CO} inward to the star, the column density of CO decreases, so the value depends on how the temperature increases at lower radii. For a detection, the decline on surface density should (combined with the decrease on solid angle) be faster that the increase on temperature.

As being based on molecular gas, R_{in, CO} does not imply that no gas is present closer to the star. Atomic gas usually extends inward to the magnetospheric radius to feed stellar accretion, and it is often much easier to detect accretion than molecular gas, especially in low-mass disks (see Section 5).

2.4. R_in > R_subl: the onset of inner disk gaps?

Given that the dust dominates the opacity and controls the amount of UV radiation penetrating the disk, the survival of molecular gas is expected to be linked to the presence of shielding dust. We would thus expect R_{in, dust} and R_{in, CO} to agree with each other in disks, but CO is able to self-shield against UV radiation, surviving down to very low amounts of gas mass even in the total absence of dust grains (e.g. ¹²CO self-shields at N_CO ~ 10¹⁵ cm⁻², corresponding to N_H ~ 10¹⁹cm⁻², assuming standard abundances; van Dishoeck & Black Reference van Dishoeck and Black1988; Bruderer 2013b). Although R_{in, dust} is set by the dust sublimation temperature( ~ 1500 K), R_{in, CO} may be smaller than expected from the thermal dissociation temperature of CO (4 500 K) due to self-shielding. If R_{in, dust} is larger than R_subl,, the dust is removed by means other than dust sublimation. In this case, if R_{in, CO} still matches R_{in, dust}, it means that whatever process is removing dust it is also removing CO gas, because otherwise CO gas should self-shield and exist down to < R_subl,. Therefore, comparison of measured R_{in, dust} and R_{in, CO} to R_subl, can help to understand the physics and processes that regulate the inner disk structure.

In Figure 3, we show measurements of R_{in, dust} from IR interferometry (Anthonioz et al. Reference Anthonioz2015; Menu et al. 2015) and of R_{in, CO} from IR spectroscopy of CO gas (Banzatti & Pontoppidan Reference Banzatti and Pontoppidan2015), as compared to a simplified parameterisation of R_subl, (Dullemond & Monnier Reference Dullemond and Monnier2010, Salyk et al. 2011). The two probes of R_in agree with each other and with R_subl, in most disks around stars with masses < 1.5 M_⊙, supporting the idea that CO survives where dust survives, and that dust survives until it is destroyed by the high temperatures close to the star. R_{in, CO} is much larger than R_subl, in some disks, though, and notably some of them are known to be ‘transitional’ disks from observations of the inner dust (e.g. TWHya). Remarkably, for stellar masses of > 1.5 M_⊙, R_subl, is smaller than both R_{in, dust} and R_{in, CO} in the vast majority of disks. This has been recently interpreted as evidence that most of these disks are forming inner gas and dust holes by means different than dust sublimation (Maaskant et al. Reference Maaskant2013; Banzatti & Pontoppidan Reference Banzatti and Pontoppidan2015; Menu et al. Reference Menu2015b).

Figure 3. Measurements of R_{IR, dust} from IR interferometry (orange points, from Anthonioz et al. Reference Anthonioz2015; Menu et al. Reference Menu2015b) and of R_{IR, CO} from IR spectroscopy of CO gas (red points, from Banzatti & Pontoppidan Reference Banzatti and Pontoppidan2015). The dust/CO radii (R _X ) are normalised to the dust sublimation radii R_subl, expected from models. Large crosses show median values and median absolute deviations for two stellar mass bins.

The combination of observations at different wavelengths can thus help to explore the various possibilities of disk dispersal in the inside-out scenario to understand the physics and connections between gas and dust, and the process of accretion and transport in the innermost disk, all highly relevant for the formation of terrestrial planets and Solar Systems analogues.

3.1. Millimetre continuum interferometry observations

Whereas dust gaps in disks were traditionally identified through a dip in the MIR part of their SED due to the deficit of warm dust (e.g. Strom et al. Reference Strom, Strom, Edwards, Cabrit and Skrutskie1989; Forrest et al. Reference Forrest2004; Calvet et al. Reference Calvet2005; Brown et al. Reference Brown2007), their presence was confirmed through (sub)millimetre interferometric imaging at subarcsecond resolution, using e.g. the SubMillimeter Array (SMA), Plateau de Bure Interferometer (PdBI), and Combined Array for Research in Millimeter-wave Astronomy (CARMA). The millimetre continuum images revealed that dust was indeed depleted from the inner tens of AU of the disk, showing ring-like outer disk structures (e.g. Piétu et al. Reference Piétu, Dutrey, Guilloteau, Chapillon and Pety2006; Dutrey et al. Reference Dutrey2008; Hughes et al. Reference Hughes2009; Brown et al. Reference Brown2009; Isella et al. Reference Isella, Natta, Wilner, Carpenter and Testi2010; Andrews et al. Reference Andrews2011b; see review in Williams & Cieza Reference Williams and Cieza2011). Interestingly, some large mm-dust cavities were found in disks without a clear deficit in their SED, e.g. MWC758, UX Tau A, and WSB 60, possibly due to vertical structure and small/large dust grain segregation (Andrews et al. Reference Andrews2011b).

The image quality of these pioneering interferometers was rather low, due to the small number of antennas, resulting in low u,v-coverage and S/N (typically 10–20 peak S/N ratios). The image results from the Fourier transform of the observed visibilities, using a deconvolution algorithm (cleaning) to suppress the side lobes. Interpretation of these images thus has to be done with care, as the deconvolution process generally does not result in a beam-convolved image, but rather the best attempt of the algorithm to deconvolve the data with incomplete u,v-sampling. The visibility data can be represented in a real and an imaginary component as function of baseline (u,v-distance), usually deprojected along the position angle and inclination of the disk (Berger & Segransan Reference Berger and Segransan2007). The real component represents the radial variations, and for a ring-like structure, it shows an oscillation pattern (following a Bessel function), where the first ‘null’ is a measure of the cavity size (Hughes et al. Reference Hughes2007). Emission in the imaginary component indicates azimuthal asymmetries along the ring: Zero emission indicates an axisymmetric disk. The real and imaginary components are measured with respect to the phase centre, the centre of the disk, so an offset will result in non-zero imaginary emission.

Interpretation of the dust continuum images is usually done by fitting the visibilities (in the u,v-plane) with a radiative transfer model. Typical dust models include a dust surface density profile Σ(r), following a power-law with or without exponential tail, and an inner cut-off at the dust cavity radius. This cut-off is usually taken to be sharp, to simplify the fitting and limit the parameter space, although this is generally considered to be unphysicalFootnote ⁵ . When near infrared excess is measured in the SED, an inner disk is often added by setting Σ(r) to non-zero between the dust sublimation radius and an arbitrary inner disk size (typically 1–10 AU). The inner disk may cast shadows on the gap edge, so this is a crucial part of the interpretation of mm data. As azimuthal asymmetries were usually not significant, a simple assumption of an axisymmetric disk was used, with zero imaginary emission.

The huge increase of sensitivity and u,v-coverage by ALMA has resulted in many high quality images of disk dust gaps at 0.2–0.3 arcsec resolution (e.g. van Dishoeck et al. Reference van Dishoeck, van der Marel, Bruderer, Pinilla, Iono, Tatematsu, Wootten and Testi2015). The high S/N (typically > 100) leaves no doubt about the azimuthally asymmetric nature of some of these disks. The most extreme examples are Oph IRS 48 (van der Marel et al. Reference van der Marel2013) and HD 142527 (Casassus et al. Reference Casassus2013; Fukagawa et al. Reference Fukagawa2013) with contrasts ~ 30–130. Minor azimuthal asymmetries with contrasts of ≲ 2 appear in SR 21 and HD 135344B (Pérez et al. Reference Pérez, Isella, Carpenter and Chandler2014; Pinilla et al. Reference Pinilla2015a). Several clearly axisymmetric dust rings are also found (e.g. Zhang et al. Reference Zhang, Isella, Carpenter and Blake2014; Walsh et al. Reference Walsh2014; van der Marel et al. Reference van der Marel, van Dishoeck, Bruderer, Pérez and Isella2015b, Reference van der Marel2016; Canovas et al. Reference Canovas2016). These structures can be understood in the context of mm-dust trapping in gas pressure bumps (e.g. Whipple Reference Whipple and Elvius1972; Pinilla, Benisty, & Birnstiel Reference Pinilla, Benisty and Birnstiel2012). This is supported by the segregation of small dust grains as seen in scattered light, where observations reveal no or smaller gaps (e.g. Garufi et al. Reference Garufi2013), and the presence of gas inside the dust cavity as shown by ALMA CO observations (e.g. Pontoppidan et al. Reference Pontoppidan2008; Bruderer et al. Reference Bruderer, van der Marel, van Dishoeck and van Kempen2014; Zhang et al. Reference Zhang, Isella, Carpenter and Blake2014; Perez et al. Reference Perez2015; Banzatti & Pontoppidan Reference Banzatti and Pontoppidan2015; van der Marel et al. Reference van der Marel, van Dishoeck, Bruderer, Pérez and Isella2015b, Reference van der Marel2016; Canovas et al. Reference Canovas2016). CO intensity maps (integrated over velocity) can resolve the gas cavities directly at ~ 0.25 arcsec resolution, when their inner radius is large enough (several tens of AU). A quantitative analysis of these data indicates deep gas gaps, with density drops of several orders of magnitude, which are smaller than the dust gaps (van der Marel et al. Reference van der Marel2016 a). However, the amount of gas inside ~ 10 AU remains unconstrained, as the emission at this resolution is dominated by the edge of the gap. NIR observations (Section 2) provide more information about the presence of gas closer to the star. The dust asymmetries may result from azimuthal trapping in a vortex, as a result of Rossby Wave instability in the pressure bump (e.g. Barge & Sommeria Reference Barge and Sommeria1995; Birnstiel, Dullemond, & Pinilla Reference Birnstiel, Dullemond and Pinilla2013; Lyra & Lin Reference Lyra and Lin2013).

Considering the large parameter space and the high S/N, intensity profiles rather than full radiative transfer models are often used to fit these data, especially in azimuthally asymmetries (van der Marel et al. Reference van der Marel2013; Pérez et al. Reference Pérez, Isella, Carpenter and Chandler2014; Walsh et al. Reference Walsh2014; Pinilla et al. Reference Pinilla2015a; van der Marel et al. Reference van der Marel2015a). The edges are generally more consistent with a smooth ring (following a radial Gaussian) rather than a sharp cut-off (Andrews et al. Reference Andrews, Rosenfeld, Wilner and Bremer2011a). Observing the continuum at different wavelengths reveals a wavelength dependency of the cavity size through the shift of the null in the visibilities (e.g. Pinilla et al. Reference Pinilla2015a; van der Marel et al. Reference van der Marel, van Dishoeck, Bruderer, Pérez and Isella2015b) or as radial dependence of the spectral index α, with F _mm ~ ν^α (e.g. Wright et al. Reference Wright2015; Casassus et al. Reference Casassus2015; van der Marel et al. Reference van der Marel2015a), indicating that the larger dust grains are usually more concentrated.

As ALMA is reaching its full capacity, milliarcsecond observations have revealed a possibly different type of gaps in disks: Series of narrow bright and dark rings in the dust continuum of HL Tau and TW Hya (Brogan et al. 2015; Andrews et al. Reference Andrews2016), which are interpreted through a range of possibilities in the context of planet gaps, snowlines, magnetised disks, dust opacity effects, and sintering-induced dust rings (e.g. Dong, Zhu, & Whitney Reference Dong, Zhu and Whitney2015; Zhang, Blake, & Bergin Reference Zhang, Blake and Bergin2015; Banzatti et al. Reference Banzatti2015b; Flock et al. Reference Flock2015; Pinte et al. Reference Pinte2016; Okuzumi et al. Reference Okuzumi, Momose, Sirono, Kobayashi and Tanaka2016).

3.2. Scattered light observations

Scattered light observations in the visible and NIR probe the dust in the surface layers of the disk. At those wavelengths, a relatively small column density of dust is enough to attain a scattering optical depth of the order of unity. These observations mostly trace (sub-)micron sized grains, which are the dominant population of dust at the disk surface, as the strong coupling between small dust grains and gas attenuates their settling towards the midplane. To spatially resolve a disk in scattered light, high-contrast and high-resolution observations are needed. This has biased the sample of detected protoplanetary disks ( ~ 30) towards bright disks around HAeBe stars in the nearest star-forming regions (see Quanz Reference Quanz2015). The primary limit on the stellar brightness is dictated by the adaptive optics system, whereas large disk brightnesses are needed to obtain a relatively high contrast with the stellar luminosity.

Differential imaging techniques are used to overcome the large star-disk flux contrast at small angular separations. Post-processing PSF subtraction initiated the high-contrast imaging by means of coronagraphic Hubble Space Telescope (HST) observations (e.g. Grady et al. Reference Grady1999; Weinberger et al. Reference Weinberger1999). This technique is powerful to resolve the outer disk region, but limits the access to the inner ~ 1 arcsec because of the limited telescope size and the need for a coronagraphic mask. Ground-based facilities like the VLT and Gemini provide dedicated differential imaging instrumentation (e.g. Beuzit et al. Reference Beuzit2006; Macintosh et al. Reference Macintosh2008). Angular differential imaging (ADI) was developed for direct detection of companions, but it can be used for scattered light observations of disks. The principle of ADI is to keep the orientation of the telescope pupil fixed on the detector such that the field of view rotates around the target star. In this way, the disk signal rotates with respect to the quasi-static speckles and a reference PSF can be constructed from the target star itself (Marois et al. Reference Marois, Lafrenière, Doyon, Macintosh and Nadeau2006). This technique is particularly powerful for radially narrow disks, such as debris and edge-on disks (Milli et al. Reference Milli2012) but it may suffer from flux losses by self-subtraction in extended disks (Garufi et al. Reference Garufi2016). Polarimetric differential imaging (PDI) makes use of the polarising nature of dust grains by taking the difference of orthogonally polarised images which subtracts the unpolarised stellar halo and speckles (Canovas et al. Reference Canovas, Rodenhuis, Jeffers, Min and Keller2011; Avenhaus et al. Reference Avenhaus2014a, e.g.). Pioneering works were done by Kuhn, Potter, & Parise (Reference Kuhn, Potter and Parise2001) and Apai et al. (Reference Apai2004), while the first systematic census of protoplanetary disks in PDI was performed with Subaru/HiCIAO by the SEEDS consortium (e.g. Hashimoto et al. Reference Hashimoto2011; Kusakabe et al. Reference Kusakabe2012; Grady et al. Reference Grady2013).

The surface brightness of a disk in scattered light depends both on the disk structure and the scattering properties of the dust grains in the disk surface. For example, a local change in surface density or pressure scale height will affect the irradiation of the disk surface and the amount of light scattered into our line of sight. For inclined disks, the surface brightness is also determined by the dust properties because of the scattering angle dependence on the phase function and the degree of polarisation. Scattered light provides also insight into the dust properties in the disk surface through measurements of disk colour (e.g. Mulders et al. Reference Mulders, Min, Dominik, Debes and Schneider2013; Stolker et al. Reference Stolker2016) and phase function (Stolker et al. subm.). While small (compared to the observed wavelength) grains scatter isotropically, the phase function of larger grains has a forward scattering peak which can manifest itself as a brightness asymmetry of the near and far side of a disk (e.g. Mishchenko, Hovenier, & Travis Reference Mishchenko, Hovenier and Travis2000; Thalmann et al. Reference Thalmann2014). On the other hand, the degree of polarisation typically peaks around scattering angles of 90°, which is near the disk major axis (e.g. Hashimoto et al. Reference Hashimoto2012; Min et al. Reference Min, Rab, Woitke, Dominik and Ménard2016). The combined effect of disk structure, phase function, and degree of polarisation can make the interpretation of polarised surface brightness non-trivial: Disentangling the different effects may require radiative transfer modelling. Here, sub-millimetre observations can help to trace a complete picture of the distribution of small dust, large dust, and gas throughout a disk (see Section 7).

Several types of morphological features and brightness asymmetries have been detected in scattered light (e.g. Casassus Reference Casassus2016). Spiral arms have been observed in a number of transition disks (e.g. Muto et al. Reference Muto2012; Garufi et al. Reference Garufi2013; Wagner et al. Reference Wagner, Apai, Kasper and Robberto2015). Their origins are still debated due to our limited knowledge of their vertical structure, since in principle both global changes of the dust properties and small variations on the disk scale height may account for the observations. The observed spirals can be produced by various mechanisms, including planet/stellar interactions with the disk (e.g. Ogilvie & Lubow Reference Ogilvie and Lubow2002; Boss Reference Boss2006), gravitational instabilities (e.g. Cossins, Lodato, & Clarke Reference Cossins, Lodato and Clarke2009), and shadowing effects (Montesinos et al. Reference Montesinos2016). The visibility of a spiral density wave in scattered light depends on the strength of the temperature and/or surface density perturbation (Juhász et al. Reference Juhász2015). A massive planet can trigger both a primary and secondary spiral arms interior to its orbit (Dong et al. Reference Dong, Zhu, Rafikov and Stone2015), which resembles some of the observed spiral arms (e.g. Benisty et al. Reference Benisty2015).

Brightness asymmetries may also be related to global or local asymmetries in the disk structure. In some cases, a plausible connection between disk surface and midplane can be made when the asymmetry in scattered light and sub-mm dust continuum coincides (e.g. Garufi et al. Reference Garufi2013; Marino et al. Reference Marino2015).

Radial reductions in surface brightness are often interpreted as gaps (e.g. Quanz et al. Reference Quanz2013; Thalmann et al. Reference Thalmann2015; Rapson et al. Reference Rapson, Kastner, Millar-Blanchaer and Dong2015). Nevertheless, a decrease in the scattered light flux does not necessarily relate to a decrease in gas and/or dust surface density but could also be a shadowing effect (e.g. Siebenmorgen & Heymann Reference Siebenmorgen and Heymann2012; Garufi et al. Reference Garufi2014). Local shadowing effects have been detected on a few disks: For example, a warped inner disk (Marino, Perez, & Casassus Reference Marino, Perez and Casassus2015) can produce azimuthal surface brightness reductions, possibly variable on detectable timescales (Pinilla et al. Reference Pinilla2015b; Stolker et al. Reference Stolker2016). Radiative transfer modelling, ideally combined with hydrodynamical simulations, are required to translate scattered light flux into gap depth (e.g Fung, Shi, & Chiang Reference Fung, Shi and Chiang2014; Rosotti et al. Reference Rosotti, Juhasz, Booth and Clarke2016). In gaps opened by planet formation (e.g. Baruteau et al. Reference Baruteau, Beuther, Klessen, Dullemond and Henning2014), the gap depth depends on the planet-to-star mass ratio, the disk aspect ratio, and the turbulence (e.g. Kanagawa et al. Reference Kanagawa2015). Alternative explanations include the effect of snow-lines on the dust surface density (e.g. Zhang et al. Reference Zhang, Blake and Bergin2015; Banzatti et al. Reference Banzatti2015b; Okuzumi et al. Reference Okuzumi, Momose, Sirono, Kobayashi and Tanaka2016), dust evolution (Birnstiel et al. Reference Birnstiel, Andrews, Pinilla and Kama2015), and vortices at dead zone edges (e.g. Varnière & Tagger Reference Varnière and Tagger2006). Non-axisymmetric gap edges in scattered light can be shaped by dynamical disruption by a planet (e.g. Casassus et al. Reference Casassus2012), but they can also be an illumination effect of an inclined gap edge (e.g Thalmann et al. Reference Thalmann2010) or a shadowing effect by a misaligned inner disk (e.g. Thalmann et al. Reference Thalmann2015).

Finally, the detectable size in scattered light is limited by the disk structure and the sensitivity of the instrument. For example, the τ=1 height of a flaring disk will increase with radius as long as the surface density is high enough. This means that, depending on the disk structure, the disk becomes self-shadowed at a given radius and what we observe in scattered light beyond that radius is an optically thin/faint surface layer. Moreover, the illumination by the star decreases as r ⁻², so that disks are not detectable any more in scattered light beyond a certain radius. For PDI scattered light images, the sensitivity rapidly drops down at 1–2 arcsec, whereas observed disks are often larger. On the other hand, HST coronographic scattered light images work better above 2–3 arcsec (Grady et al. Reference Grady2005), although this cannot be applied to disks with sizes < 200–300 AU. The same applies to the very inner part of the disk (at the dust sublimation radius), unachievable with current instrumentation. Very compact disks also remain unresolved with mm imaging and undetectable in scattered light (e.g. Garufi et al. Reference Garufi2014). If there is a class of disks with < 10–30 AU radii (e.g. Woitke et al. Reference Woitke2013), then SPHERE and ALMA would be the right instrument to measure their outer edge.

4.1. The dust mass

The total mass of disk-forming material is distributed between the refractory dust ( ~ 1% by mass) and the volatile gas (remaining ~ 99%). Given the relative ease of broadband continuum observations as compared to spectrally resolved observations of atomic and molecular transitions, dust masses are generally easier to estimate. The total disk mass is then derived scaling up the dust mass by a standard gas-to-dust ratio, Δ_g/d = 100. This standard ratio is being increasingly questioned, as the processes happening in disks (photoevaporation, planet formation, viscous evolution) are expected to affect the gas/dust ratio, including radial variations, now clearly exposed by the differences in dust-gaps and gas-gaps (Section 3). The mass of dust can be estimated from a continuum measurement and an adopted dust opacity, by assuming a mass-averaged dust temperature, often in the 20–30K range for TTS disks and somewhat higher for HAeBe disks (Andrews et al. Reference Andrews, Rosenfeld, Kraus and Wilner2013). The grain size distribution, porosity, and composition affect the dust opacity, considering that disk and ISM dust can be very different. This in turn affects the thermo-chemical models of the disks.

Dust grains are poor emitters of blackbody radiation above wavelengths ~ 2π × radius, so long wavelengths can be used to examine large particles to discern what systems look promising for planets. Finding radio emission with a dust-like spectral index is thus a clue to the presence of grains up to centimetre-sizes. This field of study was pioneered by Wilner et al. (Reference Wilner, D’Alessio, Calvet, Claussen and Hartmann2005), who detected dust at 3.5 cm in TW Hya, and similarly large grains have since then been found in many other objects (Rodmann et al. Reference Rodmann, Henning, Chandler, Mundy and Wilner2006; Ricci et al. Reference Ricci2010). Advances in sensitivity with instruments such as VLA and MERLIN make it possible to image cm-sized grains even at very low surface brightnesses. In the future, this science will be opened up with the Square Kilometre Array, especially in later phases when ~ 1000-km baselines at several-GHz frequencies could be used to obtain few-AU resolution at the distances of nearby star-forming regions.

For typical grain size distributions in disks, it is usually true that the mass is mostly in the large particles, while the emission comes mainly from the smaller grains (due to a more favourable surface-area to mass ratio). However, if extended up to the size of planetesimals, this means that most of the disk mass is unobservable by radiation signatures. Hence, where M _disk is deduced from data, it should strictly refer to a size of particles contributing significantly to the emission at the wavelength of observation. Where measured dust disk masses are below those required to build planetary cores, it may be that planet formation has already occurred, and what we observe is remnant material (Greaves & Rice Reference Greaves and Rice2011).

Very low-mass, anemic, or dust-depleted disks (Lada et al. Reference Lada2006; Currie et al. Reference Currie, Lada, Plavchan, Robitaille, Irwin and Kenyon2009) have low submillimetre and millimetre fluxes, which makes it hard to detect them at long wavelengths. In addition to evolved disks, other disks are intrinsically faint, such as disks around BD. For these cases, the mid- and far-IR data may be a good option to set strong constraints to the total dust content (Currie & Sicilia-Aguilar Reference Currie and Sicilia-Aguilar2011; Harvey et al. Reference Harvey2012a; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2011, Reference Sicilia-Aguilar2013a, Reference Sicilia-Aguilar2015a; Daemgen et al. Reference Daemgen2016), even though the degeneracy between disk scale height and total disk mass cannot be broken unless long-wavelength data is included.

4.2. The gas mass

Although molecular hydrogen is the main component of the disk mass, the total H₂ mass cannot be directly measured. H₂ does not emit at temperatures found in cold disk regions (T _gas < 100K) due to its lack of a permanent dipole moment, and alternatives such as vibrationally excited H₂ gas trace only the hottest part of the disk. Moreover, H₂ is optically thick in the parts of the disk where emission originates, not even allowing a regional mass determination (Carmona et al. Reference Carmona2008; Bitner et al. Reference Bitner2008). Line-of-sight absorption is another interesting, but poorly explored, method to trace a part of the H₂ mass, but difficult to apply in practise (e.g. France et al. Reference France, Herczeg, McJunkin and Penton2014; Martin-Zaïdi et al. Reference Martin-Zaïdi2008). This has led to great interest in alternative tracers of the gas mass, the main of which we review below.

Carbon monoxide (CO): The most commonly used cold gas tracer is rotational emission from the CO molecule, which in disks has an abundance of ¹²CO/H₂ ≈ 10⁻⁴ (Thi et al. Reference Thi2001; France et al. Reference France, Herczeg, McJunkin and Penton2014). The J _upper = 1, 2, and 3 transitions, as well as several higher lying ones, are observable from the ground with, for example, the ALMA, NOEMA, and SMA interferometers and the APEX, ASTE, and IRAM 30-m telescopes. Extensive archival data exist for JCMT, CSO, and Herschel. Optical depth effects can be corrected for by observing the less abundant isotopologues ¹³CO, C¹⁸O, and C¹⁷O. Modelling of these needs to include isotopologue-selective (photo)chemistry (Miotello et al. 2016; Miotello, Bruderer, & van Dishoeck Reference Miotello, Bruderer and van Dishoeck2014). Simpler models calibrated with detailed simulations can also yield good estimates of the gas mass, although with no provision for global carbon depletion (Williams & Best Reference Williams and Best2014; Kama et al. Reference Kama2016a, Reference Kama2016b). CO-based gas masses are often a factor of 10–1000 lower than expected from the interstellar standard gas-to-dust ratio of 100 (Dutrey, Guilloteau, & Guelin Reference Dutrey, Guilloteau and Guelin1997; Thi et al. Reference Thi2001). These low CO fluxes may signal the depletion of carbon and oxygen from the warm, UV-irradiated gas of the disk surface layers, and highlight the need for complementary tracers of the total gas mass (Bruderer et al. Reference Bruderer, van Dishoeck, Doty and Herczeg2012; Favre et al. Reference Favre, Cleeves, Bergin, Qi and Blake2013; Du, Bergin, & Hogerheijde Reference Du, Bergin and Hogerheijde2015; Kama et al. Reference Kama2016b).

Hydrogen deuteride (HD): The singly deuterated isotopologue of H₂ is a powerful probe of the total warm gas mass in a disk. The two lowest rotational lines of HD are at 112 and 56μm, and require space-based observations because of the high atmospheric opacity. The first and to-date only published detection of HD was obtained towards TW Hya by Bergin et al. (Reference Bergin2013), who found a total disk mass of ≈ 0.05M_⊙. McClure et al. (Reference McClure2016) expand the sample of 3σ detections with DM Tau (4.5 × 10⁻²M_⊙) and GM Aur (19.5 × 10⁻²M_⊙). The upper limits on HD lines towards HD 100546 constrain the gas-to-dust ratio in that system to ⩽ 300, equivalent to a gas mass of ⩽ 2.4 × 10⁻¹M_⊙ (Kama et al. Reference Kama2016b).

Atomic oxygen ([OI]): Neutral atomic oxygen traces warm-to-hot gas in the disk atmosphere, but the analysis can be thwarted by contamination issues. For late-type stars and disks with no residual envelope, the far-infrared 63 and 145μm lines of [OI] are in principle a clean probe of the warm oxygen or even total gas mass (Woitke et al. Reference Woitke2010; Kamp et al. Reference Kamp2011). However, this assumes a standard total gas-phase oxygen abundance. Depletion of volatile oxygen from the disk atmosphere by sequestration into planetesimals forming in the midplane can reduce the oxygen abundance globally by several orders of magnitude, making it impossible to derive the gas mass from [OI] alone (Du et al. Reference Du, Bergin and Hogerheijde2015; Kama et al. Reference Kama2016b). Many transitional TTS disks have [OI] fluxes approximately a factor of two lower than ‘full’ or ‘primordial’ disks with the same far-infrared continuum luminosity, while the transitional disk [OI] flux range also contains all ‘primordial’ disks (Keane et al. Reference Keane2014). The cause of this is not yet clear, but a low gas-to-dust ratio or overall oxygen depletion are potential explanations. For early-type stars, where the disks are warmer and depletion of volatiles may be less important, the [OI] flux sometimes carries a non-disk contribution (Dent et al. Reference Dent2013) and gives an upper limit on the warm gas mass. This is underlined by the case of HD 100546, where a circum-disk envelope adds to the 63μm line flux (Bruderer et al. Reference Bruderer, van Dishoeck, Doty and Herczeg2012; Kama et al. Reference Kama2016b).

Figure 4 offers a visualisation of the various uncertainties to which different disk mass tracers are subject. For this exercise, we take as a reference the mass derived for the disk around a 1 M_⊙ star at 140 pc distance with a 1.3-mm flux of 25 mJy, following the methods in Andrews et al. (Reference Andrews, Rosenfeld, Kraus and Wilner2013). This is roughly the mean value for solar-type stars in Andrews et al. (Reference Andrews, Rosenfeld, Kraus and Wilner2013). After deriving this dust-based total disk mass, we made the experiment of considering it as the ‘true mass’ of the disk, and calculate the mass values that other different methods would measure, based on their own uncertaintiesFootnote ⁶ . For dust-based estimates, we explored the effect of grain growth (Miyake & Nakagawa Reference Miyake and Nakagawa1993; Henning & Stognienko Reference Henning and Stognienko1996; Henning Reference Henning2010), dust temperature (Andrews et al. Reference Andrews, Rosenfeld, Kraus and Wilner2013), and of the gas/dust ratio (Riviere-Marichalar et al. Reference Riviere-Marichalar2013; Panić et al. Reference Panić, Hogerheijde, Wilner and Qi2009). As for gas-based measurements, we explored gas depletion (Thi et al. Reference Thi2001; Du et al. Reference Du, Bergin and Hogerheijde2015; Kama et al. Reference Kama2016a; Miotello et al. Reference Miotello, Bruderer and van Dishoeck2014) for several species and the mass values we would obtain accounting for the typical gas-phase C depletion, including freezing-out (Thi et al. Reference Thi2001), carbon depletion (Kama et al. Reference Kama2016a), and gas isotopologue relations (Miotello et al. Reference Miotello, Bruderer and van Dishoeck2014). The uncertainties in case the disk mass is estimated from an incomplete SED (lacking mm data) are also shown, as they are important to estimate the mass dispersal timescales, including low-mass and evolved disks (too faint for most mm-wavelength instrumentation). From this figure, the intrinsic uncertainties in all estimates of disk masses are revealed, as well as the importance of finding reliable gas tracers to estimate reliable disk masses is the main open problem regarding disk masses.

Figure 4. Ranges of disk masses resulting from the uncertainties in total masses derived from dust and gas and measured by various techniques. The dashed vertical line indicates our reference mass for this exercise, taken to be the mass estimate for a disk with 1.3 mm emission of 25 mJy around a 1 M_⊙ star (the median value in Andrews et al. Reference Andrews, Rosenfeld, Kraus and Wilner2013). The coloured bars mark how the mass estimate may change depending on the method. Using a gas tracer, depending on: C abundance (purple; Kama et al. Reference Kama2016a), CO depletion/freeze out (pink, Thi et al. Reference Thi2001; Du et al. Reference Du, Bergin and Hogerheijde2015), isotopologue relations (yellow; Miotello et al. Reference Miotello, Bruderer and van Dishoeck2014), and changing the gas/dust ratio between 10–200 (red; Panić et al. Reference Panić, Hogerheijde, Wilner and Qi2009; Riviere-Marichalar et al. Reference Riviere-Marichalar2013). Using a dust indicator: with a complete SED lacking the mm data but including mid-IR (light blue) and far-IR (dark blue; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2011; Sicilia-Aguilar et al. 2015a; Currie & Sicilia-Aguilar Reference Currie and Sicilia-Aguilar2011), varying the assumed dust temperature (green; Andrews et al. Reference Andrews, Rosenfeld, Kraus and Wilner2013), and changing the maximum grain size between 10 μm and 1 mm (black; Miyake & Nakagawa Reference Miyake and Nakagawa1993; Henning & Stognienko Reference Henning and Stognienko1996).

The possibility of high-sensitivity gas tracers with ALMA would be a key, both to obtain better mass estimates as well as to resolve the potential radial dependency of grain sizes and gas/dust ratios throughout the disk. A robust way to estimate gas masses would require simultaneous modeling of spatially resolved CO isotopologue data, together with sub-mm imaging, and also [O I] 63 μm and [C I] emission (Woitke et al. Reference Woitke2016; Kama et al. Reference Kama2016a, Reference Kama2016b). Building on these and other works, future ALMA observations together with a better understanding of the disk chemistry will be keys to determine the disk masses.

5.1. Accretion as a probe of the disk and the star

Accretion involves the whole disk, as transport through the disk is needed to maintain the accretion rate over time. Therefore, the presence (or lack) of accretion is a powerful tool to investigate disk structure and physical processes. Although it is possible to measure accretion rates down to 10⁻¹¹ M_⊙ yr⁻¹ for solar-type starsFootnote ⁷ , we find that only very few stars have such low rates, suggesting that accretion stops quickly after reaching levels below ~ 10⁻¹⁰ M_⊙ yr⁻¹ (Sicilia-Aguilar et al. Reference Sicilia-Aguilar, Henning and Hartmann2010). This is consistent with the predictions of photoevaporation as a process removing the inner gaseous disk in a relatively short time (Clarke et al. Reference Clarke, Gendrin and Sotomayor2001; Alexander, Clarke, & Pringle Reference Alexander, Clarke and Pringle2006; Gorti, Dullemond, & Hollenbach Reference Gorti, Dullemond and Hollenbach2009). For solar-type stars, stopping accretion seems very rare unless dramatic changes have occurred to the whole disk (such as strong mass depletion Sicilia-Aguilar et al. Reference Sicilia-Aguilar, Kim, Sobolev, Getman, Henning and Fang2013b, Reference Sicilia-Aguilar2015a). This is in agreement with accretion being a global process that connects the inner and the outer disk and can be used as an indicator of global disk evolution (Sicilia-Aguilar et al. Reference Sicilia-Aguilar2015a; Manara et al. Reference Manara2016).

The presence (or lack) of accretion in disks with inner holes (identified from SEDs) also clearly separates two classes amongst transition disks around TTS: accreting and non-accreting ones. While essentially all primordial or ‘full’ disks show signs of accretion (Sicilia-Aguilar et al. Reference Sicilia-Aguilar, Kim, Sobolev, Getman, Henning and Fang2013b), between 30–50% of transition disks show none (narrow emission lines, no UV excess, no veiling; Fang et al. Reference Fang, van Boekel, Wang, Carmona, Sicilia-Aguilar and Henning2009; Sicilia-Aguilar et al. Reference Sicilia-Aguilar, Henning, Juhász, Bouwman, Garmire and Garmire2008b, Reference Sicilia-Aguilar, Henning and Hartmann2010). Although less explored, differences in the accretion rate between primordial and transitional disks have also been observed for HAeBe stars (Mendigutía et al. Reference Mendigutía2012). Our understanding of the evolutionary stage of transition disks will improve with multi-wavelength data (see Section 7).

Accretion is also connected to the stellar properties, since the accreting matter is channelled onto the star by the stellar magnetic field (Koenigl Reference Königl1991). Therefore, studies of the properties and distribution of accretion columns can also help to study the magnetic field topology of the star, intimately related to the stellar structure and evolution (e.g. Donati et al. Reference Donati2011, Reference Donati2013; Gregory et al. Reference Gregory, Jardine, Cameron and Donati2006, Reference Gregory2014). Time-resolved Hα and metallic line emission spectroscopy are promising ways to study the presence, distribution, and evolution of accretion-related hot spots, which can be connected to the structure of the stellar magnetic field (Alencar et al. Reference Alencar2012; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2015b). Extension of these studies to other stars have the power to provide new information on stellar properties during a key time in their evolution.

5.2. Open problems for accretion: disk masses and accretion tracers

An outstanding problem regarding the disk’s gas content is that accretion rates and observed disk masses are often in conflict: Considering the measured disk masses (dust- or gas-based) and the observed accretion rates, a significant fraction of stars are expected to fully drain their disks in timescales shorter (sometimes, by several orders of magnitude) than the usual disk lifetimes. The situation can be extreme for some strong accretors with not-so-massive disks (Hartmann et al. Reference Hartmann, D’Alessio, Calvet and Muzerolle2006; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2008a; Sipos et al. Reference Sipos2009; Liu et al. Reference Liu2016; Kóspál et al. Reference Kóspál2016).

Figure 6 shows the extent of the problem: If we compare the observed disk masses (Andrews et al. Reference Andrews, Rosenfeld, Kraus and Wilner2013) with the mass ingested by the star during 2 Myr (which is shorter than the median disk lifetime of ~ 3 Myr; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2006a), there is a clear divergence. This is a problem that affects both TTS (Andrews & Williams Reference Andrews and Williams2007; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2011) and HAeBes (Mendigutía et al. Reference Mendigutía2012), although the difference is negligible for stellar masses M _* < 0.2 M_⊙ and increases with the mass of the star (see Figure 6). Assuming that stars have variable accretion and that they only spend a small part of their lives accreting at very high rates could help solving the problem, although there is no evidence of short-term strong accretion variability amongst most 1–10 Myr old stars (Sicilia-Aguilar et al. Reference Sicilia-Aguilar, Henning and Hartmann2010; Costigan et al. Reference Costigan2012, Reference Costigan, Vink, Scholz, Ray and Testi2014). Moreover, the problem still persits if the accretion rate is taken to be the median accretion rate observed for stars aged ~ 3–4 Myr (Sicilia-Aguilar et al. Reference Sicilia-Aguilar, Henning and Hartmann2010), scaling the results from solar-type stars to higher and lower masses following the usual Ṁ∝M ² _* relation (Natta et al. Reference Natta, Testi, Randich and Muzerolle2005). This points to an overestimation of the accretion rates (or the time stars spend accreting), or an underestimation of the disk masses, or both.

Figure 6. Disk masses as measured by observations, and as expected from the need to support the observed accretion rates during a lifetime of 2–3 Myr. The black dotted lines represent the usual limits of disk masses between 0.1–10% of the mass of the star. The yellow area displays the disk masses measured by (Andrews et al. Reference Andrews, Rosenfeld, Kraus and Wilner2013). The blue region represents the expected disk masses for the whole range of accretion rates observed, and a disk lifetime of 2 Myr (which is typically lower than the median disk lifetime of ~ 3 Myr). The dark blue line represents the expected disk masses considering the median accretion rate at 4 Myr and an accretion lifetime of 3 Myr (Sicilia-Aguilar et al. Reference Sicilia-Aguilar, Henning and Hartmann2010).

At present, the uncertainty in the accretion rates (especially if derived from UV or accretion luminosities for stars with well-known spectral types and extinctions) is smaller than the uncertainty in the total disk mass (or at least, in the part of gas mass that we can measure; see Figure 4). Freezing-out of gas tracers and the potential changes in the gas/dust ratio as the disk evolves are clear problems in the estimation of gas masses. We may be able to solve this mismatch as more detailed, spatially resolved gas observations become available. The problem could be solbed by assuming gas/dust ratio ~ 1 000, but current observations, including data from several Herschel Consortia, rather suggest that if any, the gas/dust ratios may be lower than in the ISM (e.g. Riviere-Marichalar et al. Reference Riviere-Marichalar2013).

Shorter disk and accretion lifetimes for HAeBe could contribute to solve the problem, and indeed accretion rates in HAeBe are expected to drop more abruptly than for TTS (Mendigutía et al. Reference Mendigutía2012). Changing the way the accreted matter reaches the star does not help: BL results in higher accretion rates than MA, making the problem worse. Considering that the correlations between the accretion rate and the disk mass expected from viscous accretion models (Hartmann et al. Reference Hartmann, Calvet, Gullbring and D’Alessio1998) often remain elusive, the mass/accretion disagreement may be a signature of our difficulties estimating total disk masses, where dust masses are by far better determined than gas masses—but they only trace a minimal part of the disk (Manara et al. Reference Manara2016).

Another open problem is whether all accretion tracers measure the same thing. The observed correlations between line and accretion luminosities do not necessarily indicate a physical relation between both (Mendigutía et al. Reference Mendigutía2015a). Spectro-interferometry of Hα, Brγ, and CO, with instruments on Keck-I, CHARA, and VLTI, shows that although the Hydrogen lines are often used as a proxy to estimate mass accretion rates, the bulk of the emission arises in regions more extended than expected from MA. Indeed, several observations reveal extended emission, consistent with the base of a disk wind (Kraus et al. Reference Kraus2008; Benisty et al. Reference Benisty2010c; Weigelt et al. Reference Weigelt2011; Garcia Lopez et al. Reference Lopez2015; Caratti o Garatti et al. Reference Caratti o Garatti2015). In the same objects, in particular, the most massive ones, the displacement of the photocentre is consistent with Keplerian motion (Ellerbroek et al. Reference Ellerbroek2014; Kraus et al. Reference Kraus2012; Mendigutía et al. Reference Mendigutía2015b), although it might be difficult to disentangle the emission from the disk from the emission from the base of the disk wind (Kurosawa et al. Reference Kurosawa2016).

Moreover, observed emission lines often suggest that accretion-related structures are not monolithic entities, but include gas with different physical conditions. Several stars (DR Tau, Petrov et al. Reference Petrov, Gahm, Stempels, Walter and Artemenko2011; S CrA, Gahm et al. Reference Gahm, Walter, Stempels, Petrov and Herczeg2008; EX Lupi, Sicilia-Aguilar et al. Reference Sicilia-Aguilar2012, Reference Sicilia-Aguilar2015b; RU Lupi, Dodin & Lamzin Reference Dodin and Lamzin2012, Reference Dipierro, Laibe, Price and Lodato2013) show evidence of line-dependent veiling or ‘veiling-by-lines.’ In these cases, part of the accretion luminosity is not emitted as continuum, but as spectral lines, filling in the stellar photospheric lines to different extents. The strength of the veiling on a given line depends on the physical conditions on the accretion structures (temperature, density) and the line formation conditions/atomic parameters of the given line. The properties and structure of the accretion column may vary, depending on their number and structure, resulting in strong line differences even in objects with similar accretion rates (Sicilia-Aguilar et al. Reference Sicilia-Aguilar2015b). Line-dependent veiling can dominate the spectrum during times of high accretion, resulting in strong, broad line emission (Kóspál et al. Reference Kóspál2008; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2012; Holoien et al. Reference Holoien2014). Line veiling has been poorly explored for the general population, and could potentially affect the estimates of accretion rates, especially for objects with very low accretion or in cases where the accretion columns are optically thin. Nevertheless, line-dependent veiling can be also used as a tool to estimate the physical conditions in the accretion columns and accreting material (Sicilia-Aguilar et al. Reference Sicilia-Aguilar2012, Reference Sicilia-Aguilar2015b) (see Section 6), although extracting broad, faint lines from the stellar spectrum can be hard.

6.1. Photometric and spectroscopic variability

Photometric and spectroscopic variability is a defining characteristic of pre-main sequence stars (PMS; Joy Reference Joy1945; Herbst et al. Reference Herbst, Herbst, Grossman and Weinstein1994; Briceño et al. Reference Briceño2001; Alencar, Johns-Krull, & Basri Reference Alencar, Johns-Krull and Basri2001). Photometric monitoring campaigns at optical wavelengths covering timescales of days to months reveal three main causes for the variations in low-mass TTS (Herbst et al. Reference Herbst, Herbst, Grossman and Weinstein1994): periodic, cold (chromospheric) spots on the stellar surface, non-periodic hot (accretion-related) spots, and more extreme dimmings (up to 3–4 mag in the optical on timescales of one week) accompanied by polarisation changes, caused by circumstellar material in the line of sight (UXOr-type variability; see e.g Grinin et al. Reference Grinin, Kiselev, Chernova, Minikulov and Voshchinnikov1991; Natta et al. Reference Natta, Grinin, Manings and Ungerechts1997; Rodgers Reference Rodgers2003). A sensitive photometric survey with CoRoT identified several common types of variability and was able to probe the presence of stable and unstable accretion, stellar hot spots, and common occultations by inner disk structures such as accretion columns and warps (McGinnis et al. Reference McGinnis2015). While hot and cold spots explain most of the variability observed in TTS, HAeBes, without cold spots, no chromospheres, and accretion shock temperatures comparable to their effective temperatures, are dominated by UXOr-type variability (Muzerolle et al. Reference Muzerolle, D’Alessio, Calvet and Hartmann2004; Mendigutía et al. Reference Mendigutía2011b, Reference Mendigutía2011a).

The Spitzer Space Telescope, especially during its warm mission, has been used to study infrared variability in a number of nearby clusters (Morales-Calderón et al. Reference Morales-Calderón2009; Poppenhaeger et al. Reference Poppenhaeger2015; Rebull et al. Reference Rebull2015; Morales-Calderón et al. Reference Morales-Calderón2011; Günther et al. Reference Günther2014; Wolk et al. Reference Wolk2015; Flaherty et al. Reference Flaherty2013; Cody et al. Reference Cody2014). These studies find that 60–90% of the young stellar objects are variable in the infrared, with variability being stronger and more common amongst Class I sources and weaker and less common amongst Class III sources, with typical fluctuations of a few tenths of a magnitude. While many of these studies are focussed on daily-to-weekly fluctuations, year-to-year fluctuations have been seen by both Spitzer (Rebull et al. Reference Rebull2014; Megeath et al. Reference Megeath2012) and ground-based NIR studies (Scholz Reference Scholz2012; Wolk, Rice, & Aspin Reference Wolk, Rice and Aspin2013; Parks et al. Reference Parks, Plavchan, White and Gee2014; Rice et al. Reference Rice, Reipurth, Wolk, Vaz and Cross2015). Full disks tend to show a flatter wavelength dependence of their variability over the 2–10 μm region (Megeath et al. Reference Megeath2012; Kóspál et al. Reference Kóspál2012), but some changes in colour have been seen. The 3–5 μm variability can be explained by a mix of extinction and disk variability (Poppenhaeger et al. Reference Poppenhaeger2015; Wolk et al. Reference Wolk2015), while ground-based NIR studies find similar results along with additional contributions from star spots (Carpenter, Hillenbrand, & Skrutskie Reference Carpenter, Hillenbrand and Skrutskie2001; Parks et al. Reference Parks, Plavchan, White and Gee2014), due to the larger fraction of stellar emission at shorter wavelengths.

Variability at different wavelengths (e.g. optical vs. IR) and spectroscopic variability (in emission and absorption lines, affecting the flux or the line profiles) can be very different for the same star. Campaigns to monitor variability at different wavelengths simultaneously provide information on the process that causes the variable events (e.g. extinction by disk material, compared to variations in the accretion rate/accretion luminosity; Eiroa et al. Reference Eiroa2000, Reference Eiroa2002; Morales-Calderón et al. Reference Morales-Calderón2009).

6.2. Stellar variability and variable accretion

Accretion variability is a highly debated topic, although part of the discussion depends on how one measures accretion: Using the UV-excess as tracer, the accretion rate variations over few-year timescales are small, typically less than 0.5 dex both in TTS (Sicilia-Aguilar et al. Reference Sicilia-Aguilar, Henning and Hartmann2010; Costigan et al. Reference Costigan2012; Venuti et al. Reference Venuti2015) and HAeBes (Mendigutía et al. Reference Mendigutía2011b, Reference Mendigutía2013). Line variability has been also used to study accretion variations, since accretion-related emission lines can change quite dramatically in flux and profile. However, these lines are affected by other physical processes, so even though the variations in line intensity and profile are stronger in stars with variable accretion (Alencar et al. Reference Alencar, Johns-Krull and Basri2001; Herbig Reference Herbig2008; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2012), rotational modulation of the line intensities, and/or profiles is also observed in stars with relatively constant accretion (Alencar et al. Reference Alencar2012; Costigan et al. Reference Costigan, Vink, Scholz, Ray and Testi2014; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2012, Reference Sicilia-Aguilar2015b). This effect has led to proposing stable and unstable accretion regimes, depending on whether accretion proceeds via well-defined channels (stable) vs. multiple, quickly changing fingers (unstable; Kurosawa & Romanova Reference Kurosawa and Romanova2013; Takami et al. Reference Takami2016).

Without detailed time-resolved data, it is often hard to determine whether accretion itself is variable, or whether there are rotational modulations due to an irregular distribution of accretion columns over the stellar surface (Alencar et al. Reference Alencar2012; Costigan et al. Reference Costigan2012, Reference Costigan, Vink, Scholz, Ray and Testi2014). Nevertheless, some objects (FUOr and EXOr) display dramatic accretion variations, with increases in the accretion rate up to a few orders of magnitude. Both classes were initially identified from optical variability, and their nature, evolutionary stage, and the link between them and the rest of PMS stars remains open to debate (e.g. review in Audard et al. Reference Audard, Beuther, Klessen, Dullemond and Henning2014, amongst others).

Besides their interest as part of the star-formation pathway and disk evolution, stars with variable accretion are key target to understand the physics of disks, by observing how the disk reacts to a sudden increase in the accretion rate. The luminosity variations associated to increased accretion episodes can dramatically affect the disk properties, processing the amorphous dust in the disk, and creating crystalline silicates (Ábrahám et al. Reference Ábrahám2009), and changing the gas composition in the planet-formation region by evaporating icy bodies and destroying organic molecules (Banzatti et al. Reference Banzatti2012). An increased disk heating can also shift the water snow line to much larger disk radii during an accretion outburst, as discovered in the FUor disk of V883 Ori (Cieza et al. Reference Cieza2016), producing ice evaporation and dust fragmentation over a disk region where planets would otherwise typically form (Banzatti et al. Reference Banzatti2015b). Subsequent evolution of the disk after outbursts reveals longer term processes happening in inner and out disk regions, such as the draining of inner disk gas by the central star (Banzatti et al. Reference Banzatti, Pontoppidan, Bruderer, Muzerolle and Meyer2015a; Goto et al. Reference Goto2011) and the redistribution of crystalline silicates to larger radial distances by disk winds (Juhász et al. Reference Juhász2012), allowing us to explore disk parameters that are otherwise hardly observable (disk mass budgets, disk viscosity, radial transport).

6.3. Time-resolved data as a means to trace disk and stellar properties

Time-resolved data allows to probe phenomena that involve variability, but they also allow us to access processes with well-defined timescales, such as stellar rotation, rotational modulation of accretion, companion orbits, and disk rotation. It is specially powerful to track relatively short timescales (hours–days), which typically correspond to spatial scales that are beyond the current direct resolution limits (e.g. stellar spots, accretion columns at few stellar radii, structures, and clumps on the inner disk rim at sub-AU scales).

The puffed-up inner rim may cause a radial part of the inner disk to be in shadow (Natta et al. Reference Natta2001; Dullemond et al. Reference Dullemond, Dominik and Natta2001; Dullemond & Dominik Reference Dullemond and Dominik2004; Isella & Natta Reference Isella and Natta2005). Although shadowing by features in the inner disk rim is more common amongst intermediate-mass stars, evidence for occultations by clumpy inner disks has been found for objects down to the BD regime (Scholz, Mužić, & Geers Reference Scholz, Mužić and Geers2015). One common subgroup are the ‘dippers’ or ‘AA-Tau’-like objects. The prototype is AA-Tau, which exhibits periodic extinction events that have been traced back to a warp at the interface of the disk and stellar magnetic field that periodically obscures they star as it rotates (e.g. Bouvier et al. Reference Bouvier2003). While this behavior is seen more often in the optical (where the extinction is stronger), it provides insight on the inner disk since it is the disk that is doing the obscuring. AA-Tau events occur in ~ 30% of the young stellar objects (Alencar et al. Reference Alencar2010; Cody et al. Reference Cody2014), with rapid extinction events associated with obscuration by material in the accretion flow (Stauffer et al. Reference Stauffer2014) and longer, quasi-periodic events associated with warps in the disk (McGinnis et al. Reference McGinnis2015).

Quasi-periodic dippers can be used to determine the height of the inner wall, which can vary by ~ 10% from one period to the next (McGinnis et al. Reference McGinnis2015). This is similar to the ‘seesaw’ behaviour seen in pre-transition disks, in which the short-wavelength flux increases (decreases) as the long-wavelength flux decreases (increases) (Muzerolle et al. Reference Muzerolle2009; Espaillat et al. Reference Espaillat2011; Flaherty et al. Reference Flaherty2011, Reference Flaherty2012), which has been successfully modelled by a variable inner disk height.

Azimuthally narrow shadowing structures at < 1AU in the optically thick inner disk height affect the illumination of part or all of the outer disk. They have orbital timescales comparable to the light travel time to the outer edge of the disk. As a result, the shadows cast by any such structures will be curved, and can take a range of shapes from nearly linear to strongly curved spirals (Kama, Pinilla, & Heays Reference Kama, Pinilla and Heays2016c). Fitting the shape of such features, we can constrain the orbital properties of spatially unresolved structures in the inner disk, as well as provide an independent constraint on the vertical structure and absolute radial size of the disk. The 1mag variability of the HD 163296 disk in scattered light imaging spanning 6 yrs may be direct evidence for time-variable shadowing (Sitko et al. Reference Sitko2008; Wisniewski et al. Reference Wisniewski2008). The systematic study of such variations could constrain the presence and properties of large-mass substellar companions and various instabilities (Sitko et al. Reference Sitko2008).

Polarisation, despite being a main technique to study the extended disk (see Section 3.2), can be also used to study variability of PMS and the innermost disk through unresolved photo-polarimetry. Unpolarised stellar light that scatters off dust grains in a circumstellar environment will become linearly polarised. The photometric signal from star and disk combined will be partially polarised when the emission from the stellar photosphere deviates from spherical symmetry (e.g. stellar spots), when part of the stellar surface is obscured by the disk (e.g. flaring inner disk), or the circumstellar disk is inclined or non-axisymmetric, producing polarisation levels of 0–2% (e.g Oudmaijer et al. Reference Oudmaijer2001). Photo-polarimetric variability can thus reveal changes in the stellar photosphere and the inner disk, for example, by a warped inner disk which is coupled to the stellar magnetic field leading to variable obscuration of the star (e.g. Manset et al. Reference Manset2009).

Time-resolved spectroscopy is a further tool to study the complexity of parts of the star-disk system that are beyond the possibilities of direct resolution. Applied to absorption lines, it can be used to track the orbits of atomic gas packages in the disk and to study atomic gas dynamics (Mora et al. Reference Mora2002, Reference Mora2004). Bright emission lines like Hα and Hβ can be used to study the stability of accretion (Alencar et al. Reference Alencar2012; Kurosawa & Romanova Reference Kurosawa and Romanova2013). Metallic emission lines (Fe I, Fe II, Ti II, Mg I, Ca II, etc.; Hamann & Persson Reference Hamann and Persson1992) are specially valuable, since they are simpler than Hydrogen and Helium emission lines and span a large range of critical densities and temperatures, which allows to probe different regions within the accretion structures. Time-resolved spectroscopy of the metallic emission lines thus provides a ‘tomographic’ 3D view of accretion, tracing the location, extent, and physical properties of the accretion columns and associated hot spots (Sicilia-Aguilar et al. Reference Sicilia-Aguilar2012, Reference Sicilia-Aguilar2015b).

Time-resolved radial velocity data is also a classical means to determine the presence of planetary and binary companions. Nevertheless, the signatures of companions in young stars can be mimicked/masked by the presence of periodic signatures associated to stable accretion columns or stellar spots (Kóspál et al. Reference Kóspál2014; Sicilia-Aguilar et al. Reference Sicilia-Aguilar2015b). This makes it hard, but not impossible (if the star properties are well-constrained), to detect young planets (Johns-Krull et al. Reference Johns-Krull2016; Donati et al. Reference Donati2016; David et al. Reference David2016). Companions embedded in the disk are a potential tool to study disk properties. Accretion rate variations are normally random, but the presence of close-in stellar companions embedded in the disk can cause pulsed accretion (in L54361; Muzerolle et al. Reference Muzerolle, Furlan, Flaherty, Balog and Gutermuth2013) and periodic perturbations to the accretion-related wind (in GW Ori; Fang et al. Reference Fang2014). A companion in the disk acts as a ‘disk scanner’: It moves through a well-defined orbit that crosses (and potentially perturbs) the material in the inner disk. This allows us to use its disturbances to estimate the location of the launching point of the disk wind and where the bulk of the matter flow runs through the inner disk.

6.4. Disk dynamics

Radio interferometers not only can trace the spatial distribution of gas within a disk, but also its kinematic profile. To zeroth order, the gas in a disk is moving in Keplerian orbits around the central star(s). With small corrections due to the pressure gradient and the height of gas above the midplane (Rosenfeld et al. Reference Rosenfeld, Andrews, Hughes, Wilner and Qi2013), this motion can be used to ‘weigh’ the central star(s), as has been done in the AK Sco (Czekala et al. Reference Czekala2015) and DQ Tau (Czekala et al. Reference Czekala2016) binary systems.

Beyond Keplerian rotation, turbulence plays a large role in e.g. setting the relative velocity of small dust grains (Testi et al. 2014), regulating the accretion flow through the disk (Turner et al. Reference Turner2014), setting the vertical chemical structure (e.g. Owen et al. 2014), setting the minimum mass of gap opening planets (e.g. Kley & Nelson Reference Kley and Nelson2012), amongst many other effects. In part because of its importance, turbulence has received a great deal of attention in theoretical studies (see recent reviews by Armitage Reference Armitage2011; Turner et al. Reference Turner2014). The predominant theory for turbulence, magneto-rotational instability (MRI) predicts motions of a few tenths of the local sound speed in the upper few pressure scale heights of the outer disk (Miller & Stone Reference Miller and Stone2000; Flock et al. Reference Flock, Dzyurkevich, Klahr, Turner and Henning2011; Simon et al. Reference Simon, Hughes, Flaherty, Bai and Armitage2015), which translates to tens to hundreds of metres per second in the outer disk.

Given the weakness of this effect and its degeneracy with thermal broadening, observations have been less common than theoretical studies. The high spatial and spectral resolution of radio interferometers can overcome many of these complications, making them a promising source of observational constraints. Simon et al. (Reference Simon, Hughes, Flaherty, Bai and Armitage2015) demonstrated, using simulated ALMA CO observations of their shearing-box MRI simulations, that turbulence can change the peak-to-trough ratio of the CO spectrum, as well as the broadening in the images, removing some of the degeneracy with thermal broadening. Guilloteau et al. (Reference Guilloteau, Dutrey, Wakelam, Hersant, Semenov, Chapillon, Henning and Piétu2012) used CS, whose relatively high mass reduces the contribution from thermal broadening, to measure turbulence of ~ 0.5 c _s in DM Tau. Flaherty et al. (Reference Flaherty2015) examined ALMA observations of HD 163296 and put an upper limit of only 0.03 c _s on the turbulence in the outer disk, well below theoretical predictions. Hughes et al. (Reference Hughes, Wilner, Andrews, Qi and Hogerheijde2011) used high spectral resolution SMA observations of CO to derive an upper limit ( < 40 m s⁻¹) in the TW Hya disk. Teague et al. (Reference Teague2016) examined ALMA data of TW Hya and tentatively detect turbulence at ~ 50–130 m s⁻¹, while emphasising that uncertainties in the absolute calibration are a substantial limiting factor in these types of observations.

Other non-Keplerian effects have also been examined in recent years, often in response to new ALMA observations. Rosenfeld, Chiang, & Andrews (Reference Rosenfeld, Chiang and Andrews2014) modelled the rapid radial inflow of gas that can arise in transition disk systems with heavily depleted inner gaps. Casassus et al. (Reference Casassus2015) considered a warped disk in which the inner disk is tilted with respect to the outer disk. Dong et al. (Reference Dong, Vorobyov, Pavlyuchenkov, Chiang and Liu2016) estimates that signatures of gravitational instability should be detectable by ALMA in the gas dynamics of disks up to 400 pc distance. All these situations generate velocity differences on the order of the Keplerian velocity, which can be easily resolved over much of the disk. Salyk et al. (Reference Salyk2014) find evidence for molecular winds in CO observations of the binary AS 205 based on the kinematics of the extended emission. Shocks associated with spiral arms can create velocity jumps that are multiples of the local sound speed (Zhu et al. Reference Zhu, Dong, Stone and Rafikov2015) and surface density differences across the spiral arms that are potentially observable (Dipierro et al. Reference Dipierro, Lodato, Testi and Monsalvo2014; Hall et al. Reference Hall, Forgan, Rice, Harries, Klaassen and Biller2015).

The dynamical timescale of the outer disk stretches from decades to thousands of years, while the surface layers can respond rapidly to changes in illumination (Chiang & Goldreich Reference Chiang and Goldreich1997). This time dependence means that synoptic observations over many years can trace changes in structure as well as the response of the upper disk layers to variable illumination. HH 30, a nearly edge-on disk, exhibits variable reflection from the dust surface layers that can be explained by a central beam of light sweeping through the outer disk (Stapelfeldt et al. Reference Stapelfeldt1999). Accretion bursts can modify the solid-state features in disks, producing crystalline silicates and cometary material (Ábrahám et al. Reference Ábrahám2009). These newly created crystals can be used as a ‘contrast’ to track the mass flow within the disk: Follow-up of these crystals over months/years can be used to trace transport, mixing, turbulence, and viscosity through the disk (Juhász et al. Reference Juhász2012), even though disentangling the various transport mechanisms (wind, viscous transport, mixing on the vertical direction, turbulence) is not easy.

As the optical and IR (and soon also longer wavelengths) temporal baseline of observations in public databases grow, a new door to exploring long-period variability opens, including studing accretion variability on half a century term, spectral type changes associated to activity cycles, and constraining the long-timescale variations in protostars and FUor objects.