Taxonomy of protoplanetary discs observed with ALMA Free

ABSTRACT

Many observations of protoplanetary discs studied with ALMA have revealed the complex substructure present in the discs. Rings and gaps in the dust continuum are now a common sight in many discs; however, their origins still remain unknown. We look at all protoplanetary disc images taken with ALMA from cycles 0 to 5 and find that 56 discs show clear substructure. We further study the 56 discs and classify the morphology seen according to four categories: Rim, Ring, Horseshoe, and Spiral. We calculate the ages of the host stars using stellar isochrones and investigate the relation between the morphology of the substructure seen in the protoplanetary discs and the age of the host stars. We find that there is no clear evolutionary sequence in the protoplanetary discs as the stars increase in age, although there is a slight tendency for spirals to appear in younger systems and horseshoes to be seen in more evolved systems. We also show that majority of the images of protoplanetary discs made by ALMA may not have had a sufficiently high resolution or sensitivity to resolve substructure in the disc. We show that angular resolution is important in detecting substructure within protoplanetary discs, with sensitivity distinguishing between the different types of substructure. We compare the substructure seen in protoplanetary discs at sub-mm to those seen in scattered light. We find that cavities are a common substructure seen in discs at both sub-mm wavelengths and in scattered light.

1 INTRODUCTION

ALMA observations of protoplanetary discs have revealed a multitude of different complex substructures. These include horseshoe-like structures (Casassus et al. 2013), spiral arms (Pérez et al. 2016), inner cavities (van der Marel et al. 2015), and discs featuring bright, concentric dust rings (ALMA Partnership et al. 2015). There has also been an increase in the amount of theoretical work being undertaken in order to explain the origin of these substructures (Dong, Zhu & Whitney 2015a; Takahashi & Inutsuka 2016; Gonzalez, Laibe & Maddison 2017).

A common substructure seen in the protoplanetary discs observed with ALMA is a cavity of some sort. This could be in the form of the inner cavities seen in transition discs or the depletion of dust and gas in different regions of a protoplanetary disc. These cavities may be caused by photoevaporation (Hollenbach et al. 1994; Hardy et al. 2015), planet–disc interactions (Lin & Papaloizou 1979; Kley & Nelson 2012; Baruteau et al. 2014; Dong et al. 2015a), or gravitational instabilities (Lorén-Aguilar & Bate 2016; Takahashi & Inutsuka 2016). Comparisons between cavities seen in the dust and the gas may be used to determine if planets in the disc are responsible for the depletions (van der Marel et al. 2016a; Boehler et al. 2017, 2018; Dong et al. 2017; van der Marel, Williams & Bruderer 2018). Scattered light observations comparing the sizes of small and large grains may also be used to determine if planets are the origin of the inner cavities (de Juan Ovelar et al. 2013; Villenave et al. 2019). Dead zones may also be responsible for the inner cavities seen in transition discs (Pinilla et al. 2016).

Spiral density waves can also be seen in some protoplanetary discs at submillimetre wavelengths (Pérez et al. 2016). These structures are thought to be excited by either planet–disc interactions (Dong et al. 2015a; Zhu et al. 2015), gravitational instabilities (Dong et al. 2015b), or a combination of both (Pohl et al. 2015).

The interaction of a planet with a disc is commonly thought to be the origin mechanism for forming ring-like structures seen in protoplanetary discs. Fedele et al. (2018) were able to show that multiple gaps in a disc may be formed by single or multiple planets. Additional methods to explain the formation of dust rings in protoplanetary discs have also been theorized. Fast pebble growth near condensation fronts (Zhang, Blake & Bergin 2015), secular gravitational instability (Takahashi & Inutsuka 2016), and aggregate sintering (Okuzumi et al. 2016) are just some of the mechanisms proposed.

Submillimetre observations of the discs surrounding HD142527 and IRS48 have revealed azimuthal dust concentrations in the disc (Casassus et al. 2013; van der Marel et al. 2013). It is thought that these pile-ups of large dust grains are formed due to a pressure maximum at the edge of a gap in the disc. This pressure maximum can develop in a number of ways including the gas disc becoming unstable due to the Rossby Wave Instability (Baruteau & Zhu 2016) or due to a binary companion (Ragusa et al. 2017). Embedded young protoplanets could also cause a pressure maximum to form. These planets are able to carve out a gap in the dust and gas components of a protoplanetary disc (Paardekooper & Mellema 2006), developing the pressure maximum, and large dust grains, which would otherwise radially migrate inwards, are trapped.

Substructures have been observed in the protoplanetary discs surrounding stars with a wide range of different stellar parameters. Previous works have mostly focused on individual objects, or surveys have been conducted on specific regions (targeting both uniform and structured discs). More recently, van der Marel et al. (2019) focused solely on stars surrounded by protoplanetary discs featuring rings, while the Disk Substructures at High Angular Resolution Project (DSHARP) looked at 20 nearby discs to characterize the range of substructures seen in the dust spatial distribution (Andrews et al. 2018b). Long et al. (2018) have also recently focused on discs in Taurus featuring substructure.

In this work, we study the different substructures found in 56 protoplanetary discs observed with ALMA. There are a range of substructures seen in the discs and the stars studied cover a wide parameter range of both intermediate- and low-mass stars. Our 56 discs were chosen from the complete sample of discs observed by ALMA thus far. This is discussed further in Section 2, where we also present our sample. We discuss any biases in our sample in Section 3. This is followed by Section 6.1, where the properties of our sample are both derived here and obtained from literature. We present a new morphology scheme to classify the substructure seen in protoplanetary discs in Section 5. The main results of this paper are then presented in Section 6 and discussed in Section 7. We finally conclude in Section 8.

2 DATA

The ALMA archive has been searched to find protoplanetary discs that feature different morphological structures seen in the millimetre dust continuum. The continuum product images of 793 targets from cycles 0 to 5 were looked at. The full sample of images we have looked at is shown in Table A1 in Appendix  A. The project code for each observation can also be found in the table. The images obtained from the archive are of 793 unique systems, and feature both young pre-stellar discs and older debris discs.

Protoplanetary discs that are spatially resolved and show clear substructure in millimetre dust were chosen. We confirm that the discs are resolved by comparing the beam size of the observations to the disc size. In order to be classified as having substructure, the discs had to feature either a cavity or gap of some sort or a pile-up of dust grains. We are interested in asymmetric substructure that may be seen in the dust continuum of the mm-dust disc. We have chosen to exclude debris discs from our sample, including the well-studied discs surrounding HR4796A, HD107146, and HD181327. This was done as they are much older than the discs in our sample and the ALMA Archive is much less complete for these older discs (see Section 6.2). Similarly, we have excluded young, embedded discs such as Elias 2-24 and HL Tau as they may still be surrounded by an envelope. If no previous observations have found an object to be embedded, we discard it if its age is determined to be less than 0.5 Myr. These young objects are discarded as the ALMA Archive is much less complete for these discs. We have only obtained the final, calibrated continuum products of each observation and any images that have undergone further processing will be discussed in Section 5.1 below.

An absence of substructure may be seen in many of the discs due to a number of reasons. First, many objects observed by ALMA, unless explicitly targetted, have only been observed once. The detection of substructure can depend upon the observational waveband, resolution, and sensitivity. Therefore, many discs may feature substructure, but this has not been detected due to the incorrect conditions under which the observations were conducted. This is discussed further in Section 3.

Thus, we have a large sample of protoplanetary discs observed by ALMA, during cycles 0 to 5, that currently shows resolvable substructure. We acknowledge that our sample is not complete with regards to all protoplanetary discs featuring substructure, as some discs in the archive may have substructure that remains unresolved. It is, however, a large enough sample from which conclusions can be drawn.

The sample that we are left with consists of 56 protoplanetary discs across the first six cycles of ALMA observations. The observations for each disc were conducted at either Band 6 or Band 7 (1.3 or 0.8 mm, respectively) with three exceptions. Observations of 2MASS J16152023−3255051 (hereafter J16152023) and HD36112 were conducted at Band 9 (0.4 mm), while observations of HD163296 were conducted at Band 8 (0.6 mm). The complete sample of discs is shown in Table 1.

The continuum product files available on the ALMA Archive are often of a lower quality than the final published data. We compare the product files to the published data on each source and find that the quality of the data, with regards to the final rms and recovered total flux, improves by less than an order of magnitude. No additional substructure is revealed between the archive product files and the published data. Therefore, additional processing has not been done in order to improve the quality of the product files as this is not needed for the analysis conducted in this work.

The archival ALMA observations were taken at a range of resolutions; all sub-arcsecond. We further discuss the detectability of substructure in Section 3.1. The smallest angular scale we can resolve in our sample is in the DM Tau disc, with a resolution of 0.02 arcsec (2.9 au at 145 pc), while we can only resolve down to 0.77 arcsec (123.6 pc at 160 pc) in the disc of 2MASS J16230923−2417047. Also, the discs are located at a range of distances and the observations were conducted with varying sensitivities. As a result, any statement on the detectability of substructure based on flux would be meaningless.

3 OBSERVATIONAL BIASES OF ALMA

The analysis conducted in this work is subjected to several observational and selection biases. We discuss this further in the sections below.

3.1 Angular resolution

The angular resolutions of the discs studied in this work are shown in Table 2. These discs were observed with a higher resolution than the majority of the ALMA discs (see Table A1 for the angular resolution of all the ALMA protoplanetary discs observed during cycles 0–5). We have plotted a histogram of the angular resolutions with which the individual protoplanetary discs in our sample were observed (see Table A1). This is shown in Fig. 1.

We have looked at 793 protoplanetary discs, of which we have identified 56 that show substructure. As discussed above, we have omitted known young, embedded discs as well as debris discs. The majority of the discs we have classified here (46/56 ≃ 80 per cent) were observed with a resolution higher than 0.22 arcsec. This limit is indicated by the red dashed line on Fig. 1. From the complete sample of ALMA discs looked at, 171 discs were observed with a resolution of 0.22 arcsec or better. Therefore, ∼27 per cent of the discs observed with ALMA with a resolution 0.22 arcsec or greater have resolvable substructure.

Cieza et al. (2019) conduct a survey of the discs within Ophiuchus using ALMA at a resolution of 0.2 arcsec. Observations were able to resolve 60 protoplanetary discs, of which 12 showed substructure (eight clear, and four probable detections). This is 20 per cent of their resolved discs, which agrees with the finding here that ∼27 per cent of discs show substructure when observed at a resolution limit of 0.22 arcsec.

A resolution of 0.22 arcsec is still considered relatively moderate with ALMA. Studies explicitly targeting transition discs and discs with known substructure aim for resolutions of ≈0.1 arcsec or better. A total of 52 protoplanetary discs observed with ALMA at a resolution of 0.1 arcsec or better have been looked at in this work. This limit is shown as the green line on the histogram (Fig. 1). Of these 52 discs, 22 have been shown to have substructure and have been classified here. This is approximately 42 per cent of the discs.

Long et al. (2019) studied 32 protoplanetary discs in Taurus with ALMA using a resolution of ≈0.12 arcsec. They found that just under half of the discs showed dust gaps and rings. In agreement with the 42 per cent we have found here for the same resolution limit. The DSHARP project, however, has found that all the discs they observe at a very high resolution of ≈0.035 arcsec feature substructure. It should be noted, however, that the DSHARP project was a targeted survey and only looked at discs that had previously showed substructure. For a resolution limit of ≲0.04 arcsec, we find that the fraction of discs showing substructure increases to  60 per cent.

3.2 Sensitivity

The continuum sensitivities of the discs studied in this work are shown in Table 2, with Table A1 showing the sensitivity of all the ALMA protoplanetary discs observed during cycles 0–5. A histogram of the sensitivities used to observe the discs in this work has been plotted in Fig. 2.

The majority of our discs (53/56 ≃85 per cent) that show substructure were observed with a sensitivity greater than 140 |$\mu$|Jy beam⁻¹. A second histogram showing the discs with sensitivities greater than this can be seen in Fig. 2. From the complete sample of ALMA discs looked at, 308 discs were observed with a sensitivity of 140 |$\mu$|Jy beam⁻¹ or greater. Therefore, substructure can be seen in ∼17 per cent of the discs observed with ALMA when observed with a sensitivity of 140 |$\mu$|Jy beam⁻¹ or greater. This value agrees with the work of Cieza et al. (2019), who find that 20 per cent of their discs show substructure when observed with a sensitivity of 150 |$\mu$|Jy beam⁻¹.

The 32 protoplanetary discs observed by Long et al. (2019) had an average sensitivity of 50 |$\mu$|Jy beam⁻¹. We have indicated this sensitivity limit on Fig. 2 with a pink dashed line. The number of discs showing substructure below this limit is 31; this is ∼25 per cent out of a total of 126 discs observed by ALMA. Long et al. (2019) were able to detect substructure in just under half of their discs.

Similar to the effect of increasing the resolution, increasing the sensitivity limit to 20 |$\mu$|Jy beam⁻¹ results in 8 out of 23 discs featuring substructure (∼35 per cent). This limit is indicated by the blue, solid line on Fig. 2. At an average sensitivity limit of 17 |$\mu$|Jy beam⁻¹, the DSHARP project was able to detect substructure in all the discs they observed (Andrews et al. 2018b).

3.3 Selection biases

We have studied 56 protoplanetary discs that cover a wide parameter space. Both low- and intermediate-mass stars have been looked at, with a wide range of ages, temperatures, and luminosities. A plot of the relation between the stellar masses of our sample and their corresponding age has been made in order to determine if there are any observational biases in our sample (see Fig. 3).

There is a lack of old low-mass stars that show protoplanetary substructure as well as significantly fewer old high-mass stars. Although old low-mass stars have been previously observed (Barenfeld et al. 2016), deep, high-resolution observations have not been conducted with ALMA. This may indicate why there is a lack of old low-mass stars in our sample.

We also see that there are significantly fewer young, high-mass stars in our sample. This could be attributed to the fact that high-mass stars evolve on a much quicker time-scale than low-mass stars. They can evolve to the post pre-main-sequence (PMS) phase while still being embedded and actively accreting (Beuther et al. 2007). Therefore, imaging a protoplanetary disc around a high-mass star would be problematic.

Our sample contains more low-mass stars than intermediate-mass stars. However, it is known that low-mass stars are more common than intermediate- and high-mass stars, as would be expected from a standard Salpeter-like initial mass function (Salpeter 1955; Kroupa 2001; Chabrier 2003). Therefore, any results showing the commonalty of substructures around low-mass stars compared to high-mass stars may be a selection bias.

3.4 Comparison to full ALMA sample

A total of 793 protoplanetary discs were looked at in this work. Omitting young, embedded discs, as well as debris discs, we have identified 56 discs that show some kind of substructure, which is around 7 per cent of all discs. This is in contrast to Long et al. (2019) and work by the DSHARP project (Andrews et al. 2018b), who find that at least 50 per cent of the discs studied show substructure. As discussed in Section 3.1 above, this is due to the majority of ALMA observations being conducted at lower resolutions than studied in these works.

The 793 protoplanetary discs studied here mainly surround Class I, II, and III young stellar objects. However, the protoplanetary disc surveys conducted by ALMA thus far have focused mainly on Class II discs from several star-forming regions. These include Chamaeleon I (Pascucci et al. 2016), Lupus (Ansdell et al. 2016, 2018), Ophiuchus (Cox et al. 2017; Cieza et al. 2019), the Orion Nebula Cluster (Eisner et al. 2018), σ Ori (Ansdell et al. 2017), Taurus (Akeson & Jensen 2014; Akeson et al. 2019; Long et al. 2018, 2019), and Upper Scorpius (Barenfeld et al. 2016).

Although these surveys focused on Class II protoplanetary discs, the star-forming regions have a range of ages. Therefore, the Class II discs in the ALMA archive are at different evolutionary stages. The sample of 56 discs studied here is representative of that. We have young stellar objects from 11 different star-forming regions, with a range of ages (see Table A1 in Appendix  A). Also, there is a diverse range of calculated ages for the young stellar objects, the youngest being Wa Oph 6 (0.5 ± 0.1 Myr) and the oldest being J160230923 (30.0 ± 5.0 Myr). Therefore, we have studied systems with a comparable range of Class II evolutionary states as that found in the ALMA Archive.

4 PROPERTIES OF SAMPLE

A literature search has been conducted to obtain the temperature and luminosity of each host star. The luminosities have been scaled to the Gaia DR2 distances (Gaia Collaboration 2018). Where the error is not given in the literature for the temperature, we make an estimate of the uncertainty. The typical error on the quoted values is 6 per cent, therefore we use this and make a conservative estimated error of 10 per cent for temperatures without an uncertainty value. No Gaia DR2 distances were available for 2MASS J05052286+2531312. We make a distance estimate of 140.0 ± 14.0 pc for this object based on its location in the Taurus molecular cloud. We have assumed a conservative error estimate of 10 per cent for this distance.

An HR diagram of the sample has been plotted in Fig. 4. It is evident in the diagram that our sample uniformly covers both stellar luminosity and temperature. The zero-age main sequence (ZAMS) has also been plotted on the HR Diagram (ZAMS from Siess, Dufour & Forestini 2000). The discs have been plotting with different symbols according to the classification they have been given in this work. This will be discussed further in Section 5.

The 56 host stars have luminosities spanning from 0.1 to 90L_⊙ and temperatures from 3400 to 12 000 K, covering a wide parameter range of low- and intermediate-mass stars. We refer to host stars with mass M < 1.8M_⊙ as low-mass objects. Intermediate objects are defined as those with mass 1.8 < M_⊙ < 8, while objects with mass greater than 8M_⊙ are referred to as high-mass objects. The lower mass limit of 1.8M_⊙ for the intermediate stars comes from Simon et al. (2002). The lower mass limit for high-mass stars (8M_⊙) originates from the minimum mass required to produce a Type II supernova (Zinnecker & Yorke 2007). The stars in our sample are located in a number of different star-forming regions (SFR), at a range of distances.

The Gaia DR2 distances agree to within 20 per cent of the previous literature values for the majority of sources. The DR2 distance to HD169142 was determined to be 114.0 pc, compared to its previous distance of 145.0 pc (Manoj et al. 2006). Other examples include SZ111, which changed from 200.0 to 158.3 pc, and CQ Tau, 100 to 163 pc. The estimated distance to the Class II T-Tauri star RY Tau has changed drastically, from 140 pc (Agra-Amboage et al. 2009) to 177 pc in Gaia DR1 to 443.1 ± 47.0 pc in Gaia DR2 (Gaia Collaboration 2018). This discrepancy was discussed by Garufi et al. (2019). Therefore, we adopt their value of 133|$^{+55}_{-30}$| pc obtained from HIPPARCOS data (ESA 1997) The majority of the discs observed with ALMA are located in well-surveyed star-forming regions and have distances less than ∼200 pc.

All but eight systems in our sample are single-star systems. UX Tau A and HD100453 both have companions orbiting at a radius >100 au and are surrounded by a circumprimary disc (Tanii et al. 2012; Wagner et al. 2018). Circumbinary discs surround HD142527, CS Cha, DS Tau, V4046 Sgr, V892 Tau, and GG Tau (with GG Tau A being a triple-star system, Di Folco et al. 2014) (Smith et al. 2005; Fukagawa et al. 2006; Guenther et al. 2007; Rodriguez et al. 2010; Akeson & Jensen 2014). With such a limited sample of multiple star systems, we have not investigated trends relating to disc morphology and multiplicity.

4.1 Determining stellar ages and masses

Individual stellar ages and masses were determined for the host stars using the new luminosities and the models of Siess et al. (2000) and Baraffe et al. (2015). The models of Baraffe et al. (2015) are only applicable for stars <1.4 M_⊙, therefore we use the models of Siess et al. (2000) for any star with a mass larger than this. Evolutionary tracks were plotted on to the HR diagram (Fig. 4) and the stellar mass and ages were interpolated. Errors on the ages and masses are derived using the associated luminosity error for each star. For reference, we show the HR diagrams with plotted evolutionary tracks in Appendix  B.

The derived ages are given in Table 2. It should be noted that this method of determining the ages and masses of PMS stars is quite uncertain. This is due to the luminosities of some stars having large errors, resulting in a large uncertainty range for the ages and masses. Therefore, the derived values from this method are only an estimate and should be treated with caution. The estimates of the stellar ages are later used to order the protoplanetary discs according to age (see Section 6).

We compare the ages derived here to the estimated age of the star-forming region each star belongs to. We find that the ages we have derived generally agree with the estimated ages of the star-forming region within 3σ. The ages of the star-forming regions can be found in Table B1. We find that the derived ages of the objects that do not agree with the age of the star-forming region ar either very young or very old objects. Therefore, the stellar isochrones may be underestimating or overestimating the ages for these stars.

4.2 Determining disc radii

For a quantitative analysis of the structure of the protoplanetary discs, we calculate the dust disc radii. As the observations were taken with different resolutions and sensitivities, we calculate the radius containing 68 per cent of the total flux for each disc (see Tripathi et al. 2017 for a more detailed explanation of this method). The radius of each disc can be found in Table 2. This method for determining the effective radius of the disc has previously been utilized in a number of works. We compare our derived radii to literature values of the radii containing 68 per cent of the total flux for the discs where this has been calculated. We find that the radii calculated here agree with the literature values within 3σ (Tripathi et al. 2017; Ansdell et al. 2018; Long et al. 2019). We make use of the derived radii in Sections 6.2 and 6.3.

5 CLASSIFYING PROTOPLANETARY DISCS

Garufi et al. (2018) studied the appearance of protoplanetary discs (in morphology and spatial extent) in scattered light. Stellar and disc properties were calculated and related to seven categories defined in the study: Ring, Spiral, Giant, Rim, Inclined, Faint, and Small discs. Following a similar approach, we classify our discs into four categories based upon their appearance and morphology. The characteristics of the four categories are outlined below and summarized in Fig. 5.

Rings: Protoplanetary discs that feature bright, concentric rings have been classified as ringed discs. Between the rings are gaps devoid of gas and/or dust. A minimum of two concentric rings need to be seen in order for a disc to be classified as ringed. Examples of these discs that have been observed with ALMA include GM Auriga (Macías et al. 2018) and HD169142 (Fedele et al. 2017). These discs may also feature a central cavity, as can be seen in GM Auriga.

Rims: The majority of the discs that have been studied in this work feature a single bright rim at the edge of a large disc cavity. These rims have been seen in both intermediate-mass and low-mass young stellar objects including DM Tau, LkCa15, and 2MASS J16042165–2130284 – hereafter J16042165 (Pinilla et al. 2018). Disc rims can also be seen in protoplanetary discs that have been classified as ring or horseshoe. However since the rim is not the most prominent feature, these discs have been sorted in other categories. Furthermore, rims can be seen in some discs as such at the present angular resolution. As we will discuss later in the paper, further observation of rim discs may place them in alternate categories. Since we are only focusing on the continuum emission from the protoplanetary disc, the cavity needs to be void of only dust in order to be classified as a rim.

Horseshoe: Horseshoe-shaped discs are similar to rim discs; a single ring of dust surrounding a large cavity. However, the majority of the dust in horseshoe discs is located in a small region of one side of the disc. An example of a system containing a horseshoe-shaped protoplanetary disc is HD142527 (Casassus et al. 2015), where the dust in the protoplanetary disc resembles a crescent or horseshoe shape.

Spiral: Discs which feature spiral-like arms of continuum emission are classified as spiral discs. This structure has rarely been seen in protoplanetary discs as of yet, the first being Elias 2-27 (Pérez et al. 2016).

All of our chosen discs are resolved and show substructure, therefore we have omitted the Faint category of discs used by Garufi et al. (2018). We have also not used the Small disc category as all of our discs have a radius larger than 20 au. Garufi et al. (2018) define discs that show faint arm-like structures on large scales as Giant. These structures are only seen in discs with a radial extent ≫100 au. The structures seen in these discs are faint and could even be attributed to broken rings rather than spiral arms. Therefore, we have removed the Giant category and introduced the Horseshoe category which has been outlined above.

The discs have been classified based on the most prominent morphological feature seen in the sub-mm dust emission. Some discs like CQ Tau could be defined as either a horseshoe disc or a rim disc. We have chosen to classify this disc as a rim disc since this is the most prominent feature. RY Lup also appears to have a horseshoe-like morphology. However this disc is nearly edge on with an inclination angle of ≈70 deg (Langlois et al. 2018). Therefore, the horseshoe-like morphology may just be an observational effect. Therefore, we have placed this disc in the Rim category. We strongly acknowledge that some discs can fit into multiple classifications. The classification for each source can be found in Table 2.

5.1 Unsharp Masking Filtering

ALMA observations of Elias 2-27 by Pérez et al. (2016) revealed spiral density waves in the protoplanetary disc. The technique of Unsharp Masking Filtering was performed on the images in order to remove the large-scale disc emission and highlight the spiral structure of the disc. The observations of Elias 2-27 from Pérez et al. (2016) were obtained from the ALMA Archive and the original observation was smoothed with a 2D Gaussian of 0.33 arcsec full width at half-maximum (FWHM). This image was then scaled by a factor of 0.87 before subtracting it from the original image.

We applied a similar process to the ALMA observations of J16152023 and Wa Oph 6 as faint spiral substructure could be seen. The Filtering was applied to J16152023 and Wa Oph 6 in order to highlight the spiral structures that can be seen in the disc. These discs were smoothed with a Gaussian of FWHM 0.33 arcsec; J16152023 was scaled by a factor of 0.87, while Wa Oph 6 was scaled by 0.67. The Filtering was performed in order to bring out the fainter structures of the disc; this then allowed us to better classify these protoplanetary discs. No other science was performed using these filtered images

6 RESULTS

6.1 Prevalence of each substructure

The number of discs in each category can be seen in Fig. 6. Of the 56 discs studied in this sample, Rim discs appear to be the most populous category in our sample featuring 32 discs. 16 discs have been classified as having rings. Horseshoe and Spiral discs are least populous, with four discs in each category. Although the majority of our sample have been classified as a Rim disc, it should be noted that cavities are the easiest substructure to be detected with ALMA. And as a result, the large number of Rim discs may be a selection effect due to extensive interest in them. This is further discussed in Section 7.1.1 below. While horseshoe-shaped discs have been placed in their own category, they all feature a single ring of emission on the edge of a large cavity and could also be classified as Rim discs. This would increase the number of Rim discs to 36, more than 60 per cent of our sample, intensifying the notion that the presence of a Rim seems to be a common feature in the current population of protoplanetary discs observed at mm-wavelengths.

We now investigate the properties of the host stars of each disc category. From Fig. 4 we can see that Horseshoe-shaped discs are most commonly found around intermediate-mass stars. These stars are all Herbig Ae/Be type stars, with their high effective temperatures (T_eff > 6000 K). The lack of Horseshoe-shaped protoplanetary discs around low-mass stars may indicate that the formation mechanism responsible for forming a pile-up of dust grains on one side of the disc preferentially occurs in higher mass stars (van der Marel et al. 2021).

Spiral discs surround just four host stars in our sample. All systems in this category are single-star systems and are Class II T-Tauri-type stars with stellar masses ≤1.0M_⊙. Due to the small number of both Horseshoe and Spiral discs, we cannot make any real conclusions about the characteristics of the host stars that these discs surround.

6.2 Structure versus age

To study whether the morphological structures seen in protoplanetary discs evolve with age, we have ordered the discs studied in this work according to age. We have used the ages derived in Section 4.1 using the evolutionary tracks from Siess et al. (2000) and Baraffe et al. (2015). Figs C1, C2, C3, and C4 in Appendix  C show the Rim, Ring, Horseshoe, and Spiral discs ordered according to age. Images have been scaled to 500 × 500 au. Stars with a † symbol in the lower left corner have been scaled to 1000 × 1000 au. This has been done to enable us to compare the spatial extent of the discs.

6.2.1 Rims and ring

The Rim discs, ordered by age, can be seen in Fig. C1. The ages of the stars surrounded by a Rim protoplanetary disc vary quite widely. The youngest disc is a T-Tauri star with an age of 0.9 ± 0.2 Myr, while J16230923 is the oldest disc with an age of 30.0 ± 6.0 Myr. Furthermore, from Fig. 3, we can see that all of the discs with an age greater than 10 Myr (except one Horseshoe disc) are surrounded by a Rim. Therefore, a Rim appears to be a long-lasting structure of a protoplanetary disc, whereas a Spiral or Ring is a shorter lived structure. The intermediate-mass stars with Rims appear in the later stages of the evolutionary plot. However, this may simply be an observational bias as there are very little observations of old low-mass stars.

Fig. C2 shows the Ring discs ordered by age. There does not appear to be a correlation between the age of the system and the radial extent of the disc. RU Lup is the youngest Ring disc we have classified, while HD 142666 is the oldest. Each low-mass star is scaled to 500 × 500 au, therefore we can see that the radial extent of the disc does not depend on the age of the system.

The spatial extent of the Rim and Ring discs does not appear to be correlated with age. We test this quantitatively by plotting the disc radius against the derived stellar age (values in Table 2). This plot is shown in Fig. 7. The discs plotted do not feature a spiral or horseshoe morphology as we have a low number of these discs. We have also omitted the circumbinary discs.

We fit the relation of the disc radius to age using the Bayesian linear regression method of Kelly (2007), linmix. This method of regression takes into account errors on both axes, as well as intrinsic scatter.

We find a negative trend relating the disc radius to the age of the system with a slope of −1.3 ± 1.0 for the Rim discs. However, we have a large dispersion of 2.7 ± 2.3 dex, indicating that this relationship may not be significant. This high dispersion may be due to the large errors associated with the calculated ages. We confirm this by calculating a Pearson correlation coefficient for the trend. We find a slightly negative relationship with an R-value of −0.22. We measure a p-value of 0.24, indicating that this slight negative trend may not be statistically significant.

The same analysis is performed for the Ring discs and we find a slightly negative trend with a slope of −2.1 ± 4.0 and a high dispersion of 3.2 ± 3.0 dex. This negative correlation, however, has an R-value of −0.33, with a p-value of 0.21, thus indicating that this negative trend is not statistically significant. Therefore, we conclude that there is no correlation between the radial extent of the ring discs and the age of the system.

The results presented here agree with the work done by van der Marel et al. (2019) who showed that there was no correlation between the radius of the disc and the age of the system.

6.2.2 Horseshoe

Fig. C3 shows the Horseshoe discs arranged according to age. There is a wide range of ages for the protoplanetary discs that feature a Horseshoe morphology. AB Auriga, the youngest star, has an age of 3.0 ± 0.5 Myr, while the oldest disc, SAO 206462, is 14.0 ± 5.5 Myr old. Therefore, the horseshoe-like morphology may be caused by a mechanism that occurs in the later evolutionary stage of a protoplanetary disc. However, due to our small sample and a lack of young intermediate stars observed with ALMA at a high resolution, we cannot make any definitive conclusions about this.

There appears to be no variation in the morphological structure of the discs as they get older. It can be seen that the radius of the disc is not correlated with the age of the star. The radii of the discs surrounding the intermediate-mass stars AB Auriga, HD142527, HD34282, and SAO206462 are 163 ± 16, 186 ± 27, 187 ± 28, and 120 ± 62, respectively. However, our sample only features four protoplanetary discs with a horseshoe morphology, therefore any conclusions may be due to small number statistics.

We do not make use of the derived radii for the Horseshoe and Spiral discs as we only have four discs in each category; an insufficient sample to derive meaningful relationships.

6.3 Structure versus mass

We have also investigated whether the substructures seen in a protoplanetary disc are dependant on stellar mass. The stellar masses have been calculated in Section 4.1 and can be found in Table 1. Figs C5, C6, C7, and C8 can be found in Appendix  C and show the Rim, Ring, Horseshoe, and Spiral discs ordered according to stellar mass. The images of the low-mass stars have been scaled to 500 × 500 au, while the stars with a † symbol have been scaled to 1000 × 1000 au. This again was done to enable us to compare the spatial extents of the discs.

By looking at Figs C5, C6, C7, and C8, we can see that there is no correlation between the mass of the host star and the outer radius of the protoplanetary disc. This is true for both the low- and intermediate-mass stars of our sample. Our sample covers host stars with a wide range of stellar masses: from ∼0.3 to >3.0 M_⊙ for the stars surrounded by a rim disc, ∼0.3 to 4.0 M_⊙ for the Ring protoplanetary discs, ∼1.5 to 2.7M_⊙ for the horseshoe-shaped protoplanetary discs, and ∼0.5 to 1.0 M_⊙ for the stars surrounded by a spiral-shaped protoplanetary disc.

We confirm this by following the same method adopted when studying the relation between the radius of the disc and the age of the system in Section 6.2 above. A graph relating the mass of the star and the radius of the disc can be seen in Fig. 8. The values for the derived disc radii and stellar masses can be found in Tables 2 and 1, respectively. We have not examined trends for the Horseshoe and Spiral discs as we only have a small sample of discs. We have also omitted the circumbinary discs.

We find positive trends relating the mass of the star to the outer radius of the disc for both the Rim and Ring discs. However, the large errors associated with the determination of the stellar mass make these trends uncertain. The Rim discs have a slope of 5.3 ± 10.9 with a large dispersion of 2.8 ± 2.3 dex. We confirm that this is a weak relationship by calculating a correlation coefficient for the trend. We find an R-value of 0.24 with a p-value of 0.21 for the trend relating the stellar mass of the system to the radius of the disc. The trend relating the radius to the stellar mass of the Ring discs has a large dispersion of 3.2 ± 3.0 dex. We calculate a correlation coefficient of 0.03 for this trend with a p-value of 0.92. This is strong evidence for there being no correlation between the outer radius of the Ring discs and the stellar mass. This is in agreement with the result found by van der Marel et al. (2019).

7 DISCUSSION

7.1 The detectability of substructures

We previously introduced the resolution bias of our sample in Section 3.1. Our finding that ∼27 per cent of discs show substructure when observed with a resolution limit of 0.22 arcsec agrees with Cieza et al. (2019). These authors find that 20 per cent of their discs show substructure for the same resolution limit.

Furthermore, we were able to show that just less than half of the discs observed by ALMA show substructure when observed with a resolution limit of ≈0.12 arcsec, in agreement with Long et al. (2019). Higher resolution observations of protoplanetary discs are needed in order to bring the frequency of discs showing substructure in line with the results of the DSHARP project, where  60 per cent of discs showed substructure when observed with very high resolutions of ≈0.035 arcsec.

Similarly, only 25 per cent of discs observed by ALMA show substructure when observed with a sensitivity limit of 50 |$\mu$|Jy beam⁻¹ or greater. This increases to 35 per cent when the sensitivity increases to 20 |$\mu$|Jy beam⁻¹ or greater. Both Long et al. (2019) and Andrews et al. (2018b) were able to find a higher proportion of discs to show substructure when using these sensitivity limits (≤50 per cent and 100 per cent, respectively). Therefore, the fraction of discs showing substructure here is smaller than is expected for these sensitivity limits. This could imply that other factors, such as the resolution, may be affecting our ability to detect substructure in the discs even though our sensitivities are high enough.

We look at the 738 discs that do not show substructure – or showed substructure but were not included during our sample selection (see Section 2) – to determine the number of discs that are bright and extended enough to justify substructure that is undetected. We use our previous resolution and sensitivity limits of 0.1 arcsec and 50 |$\mu$|Jy beam⁻¹, where Long et al. (2019) were able to show that just under half of the discs in their sample show substructure. We find that 98 discs meet the sensitivity limit, while 30 discs meet the resolution limit. Of these objects, 16 discs are both bright and extended enough within our limits to show substructure. These discs are shown below in Table 3.

Six of these 16 discs showed substructure, but were removed from our sample due to having ages less than 0.5 Myr. These objects are V* HP Cha, V* GW Ori, IRAS 16285−2355, 2MASS J17112317−2724315, V* HL Tau, and Elias 2-20 (Welch et al. 2000; Brooke et al. 2007; Fang et al. 2014; Soderblom et al. 2014; Czekala et al. 2017; Segura-Cox et al. 2020). Furthermore, two discs were removed from our sample due to their large distances. Objects 2MASS J18191220−2047297 and IRAS 13481−6124 have distances of 1900 and 3600 pc, respectively (Busfield et al. 2006; Maud et al. 2015). Therefore, currently, no substructure can be detected in their discs regardless of how high the resolution and sensitivity are. The object V* V1213 Tau is an edge-on protoplanetary disc, therefore we are unable to detect substructure in the disc (Burrows et al. 1996; Stapelfeldt et al. 1999).

We show the continuum product images of the remaining seven discs that have been observed with a sufficiently high resolution and sensitivity to warrant substructure in Fig. 9. Reobservation of these discs at higher resolution and sensitivities may result in detection of substructure.

The resolution and sensitivity used to observe protoplanetary discs may also affect the type of substructure that is detected. We plot the resolution of the observations used to detect our sample against the sensitivities in Fig. 10. We find that the majority of discs featuring rings are detected when the sensitivity is below ∼60 |$\mu$|Jy beam⁻¹, regardless of the resolution used. Rim discs, on the other hand, span a wide resolution and sensitivity range. However, below 20 |$\mu$|Jy beam⁻¹, five ring discs are detected compared to only one rim disc. Thus, additionally, supporting the notion that increasing the resolution and sensitivity of observations may cause discs to be reclassified from Rim to Rings. Therefore, although angular resolution may play a vital role in detecting substructure in protoplanetary discs (as we have shown in Section 3.1), the sensitivity of the observations is key in determining the type of substructure present in the disc.

7.1.1 The observability of rims

32 discs in our sample have been classified as having a Rim; a single ring of dust surrounding a large cavity devoid of dust and/or gas. It is clear from Fig. 4 that the hosts stars that are surrounded by a Rim disc cover both stellar temperature and luminosity quite uniformly. There are somewhat more Rim discs around low-mass stars than around intermediate-mass stars (24 low-mass stars and eight intermediate-mass stars). However, due to the nature of our classification scheme, all four of the high-mass Horseshoe discs could also be classified as Rim discs. Therefore, a single ring of emission on the edge of a large cavity appears to be a very common feature seen in protoplanetary discs regardless of temperature or luminosity.

There are numerous ways to form a rim of dust around a star and this may explain why they are a frequent substructure seen in protoplanetary discs. A planet present in a disc would cause a pressure maximum to form. As dust radially migrates inwards from the outer regions of the disc it hits this pressure maximum. This would cause a pile-up of dust grains to form in a ring around the orbit of the forming protoplanet (Paardekooper & Mellema 2006; Fouchet et al.2007).

In order to detect if a rim has been formed due to a planetary companion, observations of CO isotopologues can be made. Gas gaps have previously been shown to have been carved out by a planetary or substellar companion (Bruderer et al. 2014; van der Marel et al. 2015, 2016b; Dong et al. 2017; Boehler et al. 2017, 2018) In recent work, Ubeira Gabellini et al. (2019) were able to show that depressions in both continuum and CO isotopologue ring maps could be caused by an embedded planet within the disc.

A rim can also form in the disc due to photoevaporation. UV radiation from the central star can heat up the surface of the disc. This can cause the dust to evaporate and eventually leave the disc as a photoevaporative wind, thus forming a cavity (Hollenbach et al. 1994; Hardy et al. 2015) A rim can then be seen at the outer edge of the cavity. A rim, as the outer edge of a cavity, can also form in a protoplanetary disc due to condensation fronts (Zhang et al. 2015), aggregate sintering (Okuzumi et al. 2016), and the inner edge of a dead zone (Flock et al. 2015; Béthune, Lesur & Ferreira 2016).

The populous nature of rings, however, may be due to a selection bias. Transition discs have explicitly been targeted by ALMA, both in individual projects as well as part of surveys (e.g. DSHARP, Andrews et al. 2018b). This is because rim discs are easily detected, even at the lower resolutions and sensitivities. More complex substructure, such as spiral and horseshoes, may only be detected at higher resolutions and sensitivities.

This resolution dependence has recently been demonstrated in ALMA observations of LkCa15 by Facchini et al. (2020). In previous works, and here, it has been classified as a rim surrounding a cavity. However, ALMA observations with a resolution ∼0.04 arcsec of were able to resolve multiple rings in the disc. In addition to this, Francis & van der Marel (2020) were able to show that the cavities of transition discs are often not void of dust. Therefore, there may be unresolved dust rings in some of the discs classified as being Rim discs in this work. Further high-resolution observations may reveal that Rings are the most populous substructure seen in protoplanetary discs and not a single rim of emission. Likewise, high-resolution observations would also increase the number of discs that are known to have resolvable substructure.

7.1.2 Observing horseshoes

Recent work by van der Marel et al. (2021) has shown that the diversity in asymmetric and non-asymmetric dust structures in protoplanetary discs is linked to the local gas surface density at the location of pressure bumps. Asymmetric structures such as horseshoes may only be detected if the local gas surface density is sufficiently low. The upcoming ngVLA may be able to trace the dust at these low gas density locations using centimetre wavelengths, thus increasing the population of discs showing asymmetric structures. The increased resolution capabilities of the ngVLA may also resolve new substructures and increase the population of discs showing substructures to greater than  60 per cent, as shown by the DSHARP project (Andrews et al. 2018b).

7.1.3 The observability of rings

The low-mass stars that feature protoplanetary rings have a wide range of ages; from 0.6 Myr for RU Lup to 10.3 Myr for HD 142666. The spread of ages imply that rings can form very early in the evolution of the disc and are long-lasting substructures or that they can form at a range of evolutionary stages.

Recent observations of HL Tau, Elias 2-24, and GY 91 revealed protoplanetary discs with multiple rings and gaps (ALMA Partnership et al. 2015; Dipierro et al. 2018; Sheehan & Eisner 2018). These young stellar objects all have ages less than 1 Myr. Therefore, planet formation is thought to begin very early in the evolution of the disc. As the protoplanets grow in mass and size, they are able to carve gaps in the dust and gas of the protoplanetary disc forming rings. Mamajek (2009) showed that planet formation could end between 2 and 3 Myr as half of the protoplanetary discs in their sample disappeared by this time. The majority of the low-mass discs in our sample have derived ages greater than 2 Myr (in part due to the removal of young, embedded discs from the sample), meaning that it is possible for their gaps and rings to have been formed by planets. In order to confirm this, similarly to rim discs, additional CO isotopologue observations could be carried out to determine the origin of the dust rings. However, the gas gaps in ring discs are harder to constrain, as discussed by Isella et al. (2016).

Other mechanisms, such as the accumulation and growth of material at various ice lines (Zhang et al. 2015), may be responsible for the ringed substructure. However, this method was recently put into question by Huang et al. (2018) and van der Marel et al. (2019) who showed that the gap radii in ringed protoplanetary discs do not correspond with common ice lines. The analysis conducted in this work cannot determine the precise origins of the protoplanetary rings seen.

7.2 Comparisons to scattered light observations

Observations of protoplanetary discs have previously been made at a number of different wavelengths, including optical, near-infrared, and sub-mm. These different wavelengths probe different regions of the protoplanetary disc. Observations at near-infrared wavelengths trace the smallest dust grains (typically |$\mu$|m-sized) in the innermost parts and surface of the protoplanetary disc. At these wavelengths the dust is optically thick. As the observing wavelength approaches mm/sub-mm, the dust in the mid-plane of the disc begins to become optically thin. The largest dust grains lie in the mid-plane of the disc and this is where the majority of the disc mass lies.

Substructures can be seen in protoplanetary discs in both mm and polarized scattered light observations. Garufi et al. (2018) studied the morphology of 58 protoplanetary discs in scattered light and classified them into the following categories: Rim, Rings, Spirals, Faint, Giant, Inclined, and Small. Our sample has 36 protoplanetary discs in common with the sample studied by Garufi et al. (2018). Five discs have been classified as Spiral, five discs as Giant, five as Faint, six as Rim, 11 as Rings, three as Inclined, and one as small.

We have discarded the Faint, Giant, Small, and Inclined categories as they are not morphological structures and have reclassified these discs according to our classification. The scattered light observation of RU Lup, Sz111, CI Tau, MWC 480, and GW Lup were classified as Faint in Garufi et al. (2018), while HD142666, T Cha, and RY Lup were classified as Inclined and CS Cha as Small. Since there is no clear substructure in the these discs and they do not fit in any of our classification categories, we have discarded them from the common sample, leaving 28 discs for comparison. Following the characteristics outlined in Section 5, three of the five discs classified as Giant by Garufi et al. (2018) have been classified as Spiral discs (AB Auriga, HD142527, and HD100546). These three discs are all intermediate-mass stars. The remaining two low-mass stars have been classified as Rim discs (GG Tau A and GM Auriga). The common sample and their classifications, including the newly reclassified Giant discs, can be found in Table 4.

Fig. 11 compares the morphology seen in scattered light with the morphology seen in sub-mm for the 27 protoplanetary discs. The columns indicate the morphology assigned by Garufi et al. (2018) and the rows indicate the morphologies assigned in this work.

All of the discs showing a Horseshoe-shaped morphology in sub-mm continuum emission have a Spiral morphology in scattered light. The disc surrounding SAO206462 was shown to have a mass of ∼0.002 M_⊙ (Pérez et al. 2014), while the disc masses of AB Auriga, HD142527, and HD100546 have been shown to be 0.01 M_⊙ (Tang et al. 2012), 0.1 M_⊙ (Perez et al. 2015), and ∼0.03 M_⊙ (Kama et al. 2016), respectively. The wide range of disc masses may indicate that disc mass plays little role in the type of morphology seen in discs in both sub-mm and scattered light.

Spiral substructure seen in scattered light observations has previously been seen in a number of protoplanetary discs (Grady et al. 2001, 2013; Fukagawa et al. 2004; Casassus et al. 2012; Muto et al. 2012; Wagner et al. 2015; Akiyama et al. 2016; Ohta et al. 2016; Canovas et al. 2018). The submillimetre counterpart observations to these discs, however, show large cavities and axisymmetric substructure (Isella et al. 2013; van der Marel et al. 2013; Ansdell et al. 2016; Kraus et al. 2017; Tang et al. 2017; Cazzoletti et al. 2018; Dong et al. 2018; Ohashi et al. 2018; Pineda et al. 2019). The mm images shown here of IM Lup and J16152023 both feature a spiral-like morphology, however rings were seen in scattered light observations rather than large cavities and axisymmetric substructures. This agrees with the results found by Avenhaus et al. (2018) and Huang et al. (2018) for these two discs.

The nine discs shown here with a spiral-like morphology in scattered light were found to be relatively old (Garufi et al. 2018). The host stars had ages between ≈3 and ≈12 Myr and are at the very late stage of their PMS lifetime. Also, the lack of young stars featuring a Spiral disc led to the conclusion that the formation of spiral arms in |$\mu$|m-sized dust discs may only occur in the latter phases of their PMS lifetime. This contrasts with the results found in this work. The four Spiral discs in this work are at an early stage of their PMS lifetime and have ages ≤6 Myr. Therefore, the mechanism responsible for forming spiral arms in the sub-mm dust of a protoplanetary disc happens during the earliest stages of its evolution around low-mass stars. This discrepancy may suggest that there are different mechanisms forming the spiral arms seen in scattered light and those seen in the sub-mm.

14 discs have been classified as Rim discs in the sub-mm, 10 of them being low-mass stars and four being intermediate-mass stars. Seven low-mass stars have been shown to have Rims in both sub-mm and scattered light. EM*SR21 and HD97048 are both intermediate-mass stars that show a Rim in sub-mm but have a ringed protoplanetary disc in scattered light. Both EM*SR21 and HD97048 have relatively young ages. Recent work by Muro-Arena et al. (2020) and van der Marel et al. (2021) has shown that the structure within these discs may be more complex and it may be possible for multiple rings to be present. Observations at a higher resolution would need to be conducted in order to confirm the structure within the disc.

All the discs in our sample (56 discs) show some sort of cavity or gap. 65 per cent of the discs studied by Garufi et al. (2018) showed some sort of cavity in scattered light indicating that they are a common occurrence in both sub-mm and scattered light. The discs that showed a cavity in sub-mm and not scattered light were classified by Garufi et al. (2018) as either Faint or Inclined. The lack of a cavity may contribute to the faintness of the discs in scattered light, while the absence of a cavity in the Inclined discs may be an observational bias (Garufi et al. 2018). The high number of discs that exhibit a cavity in both scattered light and sub-mm shows that cavities are a common feature found in protoplanetary discs across a range of star type and evolutionary stage. However, it should be noted that there may be a bias in both samples. The sample by Garufi et al. (2018) may contain many transition discs as they are bright due to their cavity wall. Likewise, the sample presented here may be biased towards transition discs as they are easiest to find at low resolution.

Eight discs classified as Rings in sub-mm have been studied in scattered light, six of which surround low-mass stars and two surrounding intermediate stars. Rings in scatted light are seen in six of the protoplanetary discs as well as in the sub-mm. The two systems that do not show rings in scattered light are GM Auriga and V1247 Ori, both low-mass stars. The discs around these stars were shown to have a Rim and Spiral morphology, respectively. The rings seen in protoplanetary discs in scattered light and in the sub-mm can form with similar mechanisms, such as the interaction of the disc with a companion (Lin & Papaloizou 1979; Kley & Nelson 2012; Pinilla, Benisty & Birnstiel 2012; de Juan Ovelar et al. 2013).

8 CONCLUSIONS

We have studied the morphology of the substructure seen in protoplanetary discs. We have classified 56 discs with visible structure in the ALMA Archive cycles 0 to 6. These discs, observed in the sub-mm continuum, were placed into four categories: Rim, Ring, Horseshoe, and Spiral. By calculating the age of the host stars we are able to study the evolution of the substructures seen in protoplanetary discs over a range of ages. The sub-mm images studied in this work were then compared to scattered light observations of protoplanetary discs studied by Garufi et al. (2018). We have reached the following conclusions in this work:

• We find that 27 per cent of 798 discs observed with ALMA during cycles 0–5 show substructure when observed with a moderate resolution of at least ∼0.22 arcsec. Using a higher resolution of ∼0.1 arcsec, 42 per cent of the discs observed show clear substructure. The fraction of discs showing substructure increases to  60 per cent when observed with a very high resolution of ≲0.04 arcsec. Therefore, many of the discs observed with ALMA thus far may have substructure that remains unresolved due to the relatively low resolutions used.

• When looking at the 798 discs observed with ALMA during cycles 0–5, we find that 31 (or 25 per cent) show substructure when observed with a moderate sensitivity of 50 |$\mu$|Jy beam⁻¹. A higher sensitivity of 20 |$\mu$|Jy beam⁻¹ results in 35 per cent of the discs showing substructure. This low proportion indicates that many of the discs observed by ALMA thus far may feature substructure that remains undetected due to relatively low sensitivities used.

• We have shown that angular resolution is key in detecting substructures within protoplanetary discs, with sensitivity playing a vital role in determining the type of substructure present in the disc.

• The protoplanetary discs studied here show substructure surrounds Class II young stellar objects with a range of ages. This is representative of the full sample of discs observed by ALMA thus far, where the majority of the systems observed have been Class II young stellar objects. The discs studied here, however, were observed with much higher resolutions than the majority of the discs in the ALMA Archive. Therefore, they are not representative of many discs which were observed at significantly lower resolutions.

• In our sample the most populous substructure seen is a rim of sub-mm dust surrounding a large cavity. A rim of some sort is found for over half of the discs in our sample and they appear around stars with a range of ages, temperatures, and luminosities. This type of substructure, however, is the easiest to detect and have been explicitly targeted by ALMA. None the less, it confirms that cavities and gaps are a common feature in protoplanetary discs.

• The second most common substructure seen in our protoplanetary discs is a ringed disc. As the majority of the discs observed with ALMA thus far were not observed using sufficiently high resolution, a Ring disc may be the most common substructure seen in protoplanetary discs.

• A distinctive horseshoe-shaped protoplanetary disc has only been seen in a few systems. These systems contain relatively old, intermediate-mass stars.

• All discs showing a horseshoe morphology in the sub-mm continuum images show a spiral-like morphology in scattered light.

• Low-mass stars that have been classified as Rim discs in the sub-mm have also been classified as Rim in scattered light. The occurrence of a single rim of emission around a large cavity seems to be a common substructure found in both scattered light and sub-mm continuum emission.

• The substructures seen in ALMA images of protoplanetary discs mostly do not seem to follow an evolutionary sequence nor do they depend on the mass of the star.

In future work we will compare the images with theoretical predictions.

SUPPORTING INFORMATION

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Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.

ACKNOWLEDGEMENTS

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2011.0.00724.S, ADS/JAO.ALMA#2012.1.00158.S, ADS/JAO.ALMA#2012.1.00182.S, ADS/JAO.ALMA#2012.1.00303.S, ADS/JAO.ALMA#2012.1.00631.S, ADS/JAO.ALMA#2012.1.00799.S, ADS/JAO.ALMA#2012.1.00870.S, ADS/JAO.ALMA#2013.1.00157.S, ADS/JAO.ALMA#2013.1.00091.S, ADS/JAO.ALMA#2013.1.00105.S ADS/JAO.ALMA#2013.1.00220.S, ADS/JAO.ALMA#2013.1.00226.S, ADS/JAO.ALMA#2013.1.00498.S, ADS/JAO.ALMA#2013.1.00658.S, ADS/JAO.ALMA#2013.1.00663.S, ADS/JAO.ALMA#2013.1.00355.S, ADS/JAO.ALMA#2015.1.00888.S, ADS/JAO.ALMA#2015.1.00486.S, ADS/JAO.ALMA#2015.1.00806.S, ADS/JAO.ALMA#2015.1.00847.S, ADS/JAO.ALMA#2015.1.00964.S, ADS/JAO.ALMA#2015.1.00986.S, ADS/JAO.ALMA#2015.1.01017.S, ADS/JAO.ALMA#2015.1.01083.S, ADS/JAO.ALMA#2015.1.01301.S, ADS/JAO.ALMA#2015.1.00480.S, ADS/JAO.ALMA#2015.1.01512.S, ADS/JAO.ALMA#2015.1.01268.S, ADS/JAO.ALMA#2015.1.01015.S, ADS/JAO.ALMA#2016.1.00484.L, ADS/JAO.ALMA#2016.1.00826.S, ADS/JAO.ALMA#2016.1.01042.S, ADS/JAO.ALMA#2016.1.01164.S, ADS/JAO.ALMA#2016.1.01239.S, ADS/JAO.ALMA#2016.1.00110.S, ADS/JAO.ALMA#2016.1.01504.S, ADS/JAO.ALMA#2016.1.01042.S, ADS/JAO.ALMA#2016.1.01186.S, ADS/JAO.ALMA#2017.1.00449.S, ADS/JAO.ALMA#2017.1.00520.S, ADS/JAO.ALMA#2017.1.00969.S, ADS/JAO.ALMA#2017.1.01151.S, ADS/JAO.ALMA#2017.1.01167.S, ADS/JAO.ALMA#2017.1.01424.S, ADS/JAO.ALMA#2017.1.01460.S, ADS/JAO.ALMA#2017.A.00006.S and ADS/JAO.ALMA#2017.A.00014.S, ADS/JAO.ALMA#2017.1.00286.S, ADS/JAO.ALMA#2017.1.01478.S, ADS/JAO.ALMA#2017.1.01701.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ.

DATA AVAILABILITY

The data underlying this article are available in the ALMA Archive, at https://almascience.nrao.edu/aq/. The project codes for the data have been provided in the Acknowledgements section above.

REFERENCES

APPENDIX A: COMPLETE LIST OF STUDIED PROTOPLANETARY DISCS

Table A1 shows the complete list of images we have looked at in our search for protoplanetary discs featuring substructure. Only continuum observations were looked at as we are interested in substructure present in the dust populations of the discs. The complete version of Table A1 can be found online.

APPENDIX B: STELLAR MASS AND AGE DETERMINATIONS

Figs B1 to B4 display the HR diagram shown in Fig. 4 with the addition of stellar tracks from the models of Baraffe et al. (2015) and Siess et al. (2000). These evolutionary diagrams have been used to determine the stellar masses and ages of the sources in our sample, the values of which can be found in Tables 1 and 2, respectively. The following plots and tables can be found online.

We compare the derived ages to the average age of the star-forming region each object belongs to. The ages of each star-forming region can be found online in Table B1.

APPENDIX C: CATALOGUE OF PROTOPLANETARY DISCS STUDIED

Figs C1 to C4 display the full catalogues of discs investigated in this work. Figs C1 to C4, respectively, show the rim, ring, horseshoe, and spiral class discs, with the discs within each class ordered by their stellar age. These images were discussed in Section 6.2. All figures in Appendix  C can be found online.

Figs C5 to C8, respectively, show the rim, ring, horseshoe, and spiral class discs, with the discs within each class ordered by their stellar mass.