The Complex Morphology of the Young Disk MWC 758: Spirals and Dust Clumps around a Large Cavity

The image of the dust continuum emission is shown in Figure 1, and was obtained adopting a Briggs weight parameter equal to 0. The FWHM beam size is 016 × 014 (P.A. = 311). The rms noise level is 83 μJy beam⁻¹. The white cross pinpoints the center of rotation as measured from the ¹³CO emission (see Section 3.2) and is located at R.A. = 05^h30^m27536 and decl. = +25°19'5670, cospatial with the Herbig star position. In the same figure, the top right panel displays the deprojected intensity as a function of the distance from the disk center and the position angle (P.A.), defined as the angle east of north (i.e., toward the left). The orbital radius has been calculated by assuming an inclination of 21° and a P.A. of 62° for the disk. The black dashed line indicates the crest of the dust emission, which is defined as the line that connects the radial maximum of the emission for each position angle.

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The dust emission is characterized by a ring structure extending between roughly 40 and 100 au and two prominent azimuthal clumps. The brightest clump has a peak intensity of 17.2 mJy beam⁻¹, and is located in the northwest of the disk, at R = 81 au and P.A. = 335°. The second clump has a peak intensity of 13.7 mJy beam⁻¹, and is located on the southwest, at a radius of 46 au and P.A. = 209°. As shown by the deprojected flux map, the dust clumps correspond to the innermost and outermost radial positions of the dust crest, whose average radial distance from the disk center is 60 au. The brightness temperature of the north and south clumps, obtained by using the inverse of the Planck function, are 14.7 K and 12.9 K, respectively. These temperatures are lower by a factor ∼4 than the predicted physical temperatures of the dust at the location of the clumps (see Section 4.1), therefore suggesting that the dust emission is optically thin.

The bottom panel of Figure 1 indicates the intensity along the crest of the dust emission as well as the azimuthal profile of the dust emission at the radii of the two clumps. The contrast of the north and south dust clumps relative to the average emission at the same radial position is about 4 and 2.5, respectively.

Figure 2 shows the continuum map obtained with super-uniform weighting, which delivers a smaller beam size (012 × 011) but a higher noise of 115 μJy beam⁻¹, visible by dot-like features in the image. This new image better reveals the azimuthal morphology of the dust clumps. The peak emission is 12.3 and 10.2 mJy beam⁻¹ for the north and south clump, respectively. Converted in brightness temperature, the values are, 17.2 and 15.3 K, slightly larger than with the previous weighting parameter Briggs = 0, indicating a better resolution, mainly radially, of the dust clumps structure. Also, the dust clumps appear to be linked to a double-ring structure, located at the same radii. Finally, the continuum emission presents also substructures that may trace faint spirals in the dust. A detailed discussion of these features and a comparison with the ¹³CO peak emission line and previous IR observations are done in Section 4.2.

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On the right panel, an inset toward the disk center shows a non-resolved source of continuum emission detected inside the cavity. The peak emission of the signal is 0.83 mJy beam⁻¹, about 7.2 times the noise level in the outer regions of the map. Due to the close proximity with the center of rotation of the disk, this emission probably comes from an inner disk in rotation around the Herbig Ae star. This is consistent with the spectral energy distribution of the disk that present near-IR emission, and traces warm dust close to the star (Eisner et al. 2004; Isella et al. 2008). As the signal is not resolved, this implies an outer radius ≤ 8 au for the inner disk.

The ¹³CO and C¹⁸O emission lines were imaged using a Briggs factor of 2, to optimize the signal-to-noise ratio. The top and bottom left panels in Figure 3 show the moment 0 maps after continuum subtraction. The white cross represents the center of rotation of the disk, as derived from the ¹³CO velocity map, shown in Figure 5. The ¹³CO emission is more radially extended than the dust continuum, with signal detected up to about 140 au from the star. On the contrary, the radial extent of the C¹⁸O emission is about 100 au, similarly to the dust. This difference is likely due to the lower optical depth of C¹⁸O compared with ¹³CO.

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The right panels in Figure 3 present the emission, the crest, and the 3σ contours as a function of the position angle. The radius of the crest varies between 40 and 50 au for ¹³CO and from 50 to 60 au for C¹⁸O. This suggests that the gas surface density increases from the disk center to about 50–60 au. The crest radius for the two molecules is almost constant as a function of the azimuth, with variations no larger than 10 au. In particular, we do not observe any increase in the CO emission at the position of the two dust clumps.

The velocity map of ¹³CO is shown in Figure 5, in Section 3.3, and indicates a position angle of ∼62 ± 2°. Along the major axis, the northeast part (on the left) is blueshifted while the southwest part is redshifted. If the IR features observed in Grady et al. (2013) and Benisty et al. (2015) are trailing spirals, the disk is rotating clockwise and the northwest part of the disk is the closest to us. This seems confirmed by the position angle at which the emission of the two molecules reaches a maximum, between roughly 90° and 180°, with a value of 223 mJy beam⁻¹ km s⁻¹ at PA = 125° for ¹³CO, and 132 mJy beam⁻¹ km s⁻¹ at PA = 160° for C¹⁸O. If the southeast side is indeed the further half, the inner wall of the disk in this direction is directly exposed to the observer. The azimuthal minimum in gas is at a P.A. of about 240°, with a value 1.4 times lower than the maximum in ¹³CO and 1.9 times the maximum in C¹⁸O.

In Figure 4, we show the peak intensity maps of the ¹³CO and C¹⁸O emission lines. The ¹³CO peak emission is our most optically thick tracer and reveals a large spiral arm, as indicated by the increasing radius of the crest of the emission as a function of the position angle, between P.A. = 50° and 200°. A secondary spiral arm may also be visible at P.A. = 220°–360° but with less contrast with the surrounding disk. Along the crest, the brightness temperature of the emission varies between 40 and 60 K but shows little dependence on the orbital radius. In Section 4.1, we will show that these values of the brightness temperature are consistent with optically thick emission, with τ ∼ 3.7, and probably indicate variations in the temperature.

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In C¹⁸O, the observations present similar but less pronounced spirals. The crest of the emission, indicated by the black dashed line, is more centered at the position of 60 au, as for the integrated emission. This is probably due to the lower optical depth of this tracer, with a maximum optical depth of ∼0.6 according to our model in Section 4.1. It is then less sensitive to variation in the temperature than ¹³CO and better traces the gas surface density. This is similar to the integrated emission maps which are more optically thin than the peak emission maps, and do not present spirals.

As a note, the peak emission map was obtained without subtracting the continuum emission, that would have been resulted in underestimating the line peak brightness temperature (see the discussion in Boehler et al. 2017). However, the differences between the two methods are minor in MWC 758 due to the low optical depth of the dust.

We present in Figure 5 the kinematic of the disk. The major axis of the disk has a position angle of 62° ± 2° and the disk has a systemic velocity of 5.90 ± 0.05 km s⁻¹. The velocity map is globally consistent with a disk in Keplerian rotation around a central star of 1.4 ± 0.3 solar masses, considering an inclination of 21° (Isella et al. 2010). Inside the dust cavity, however, the gas presents hints of departure from Keplerian velocity. The twist of the iso-velocity curves might reveal radial inflow of the gas or a warp linking the outer disk with a non-coplanar inner disk, where a non-resolved source of dust emission is also observed.

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The panel in the right side of Figure 5 shows the ¹³CO velocity dispersion. The velocity dispersion usually decreases with the radius due mainly to lower temperatures. It can also vary azimuthally, with a larger range of projected velocities probed along the minor axis. We nevertheless also observe a minimum along the west side of the major axis, with values of 0.3 km s⁻¹ compared with 0.4 km s⁻¹ along the east side. We previously pointed out in the integrated ¹³CO and C¹⁸O emission maps an azimuthal minimum along this direction. Such diminution is consistent with an azimuthal dip of the temperature. However, it appears at a first glance surprising that the ¹³CO peak emission, which is our most optically thick tracer, shows a bright emission along this azimuthal direction, at ∼40 au, at the inner edge of the outer ring. This suggests that the azimuthal decrease in emission might be due to a shadow effect from the inner edge of the outer disk, where a spiral is present and might have a higher scale height, or from an inner warped disk.

To estimate qualitatively the hypothesis of an inner warped disk, we compared our observations with the simulations of Facchini et al. (2018). They performed synthetic images of disks having a relative inclination of 30° and 70°. The case with a moderate inclination predicts variations in the iso-velocity curves similar to what is observed in MWC 758 (i.e., their Figure 17). Also, an inner disk with a mild relative inclination will project a large shadow toward one side of the disk, but still letting an inner central region to be irradiated by the central star due to the relative geometry of the two disks (see Figures 9 and 11 in Facchini et al. 2018). Our ALMA data are then consistent with an inner mildly warped disk whose west side is the closer side. This is also supported by previous near-IR interferometric observations of Eisner et al. (2004) and Isella et al. (2008) that estimated the inclination of the inner regions to be in the range 30–40 degrees, instead of 21 ± 2 degrees for the outer regions (Isella et al. 2010). Future CO emission line observations with a better angular resolution and sensitivity, perhaps using higher rotational lines, will help to constrain precisely the velocity structure in the cavity. This case can be compared with the disk HD 135344B which also probably has a mildly inner warped disk (Stolker et al. 2016). It is different from the binary system HD 142527, which contains a strongly warped disk, by 70 degrees (Casassus et al. 2015a), and projects two shadows in the outer regions separated azimuthally by ∼180 degrees (Marino et al. 2015a; Casassus et al. 2015b; Boehler et al. 2017).

The disk around MWC 758 has a complex morphology, characterized by dust clumps and spirals surrounding a large cavity. A complete modeling of the 3D structure of the disk would be very difficult. We performed instead a study which focuses on three particular azimuthal directions, as shown in Figure 6. The emission coming from the red area, will be used to characterize the underlying rings, while we will study the variations in dust and gas surface densities along the north and south dust clumps, inside the blue and green areas, respectively.

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The model discussed below follows the analysis presented in Boehler et al. (2017). Following the observations of the dust with super-uniform weighting, we assume a surface density structure for the dust and the gas represented by the sum of two Gaussians, using the formula

$$\begin{eqnarray}{\rm{\Sigma }}(r) & = & {{\rm{\Sigma }}}_{1}\,\exp \left(-{\left(\displaystyle \frac{r-{R}_{1}}{{w}_{1}}\right)}^{2}\right)\\ & & +{{\rm{\Sigma }}}_{2}\,\exp \left(-{\left(\displaystyle \frac{r-{R}_{2}}{{w}_{2}}\right)}^{2}\right),\end{eqnarray} \tag{ 1 }$$

with R1 and R₂, the radial positions of the two Gaussians, ${{\rm{\Sigma }}}_{1}$ and ${{\rm{\Sigma }}}_{2}$ their surface density, and w1 and w₂, their half-widths. The dust surface density is then described by using 6 free parameters. For the gas, less spatially resolved, we generally only use 4 free parameters, fixing the radial location of the two Gaussians at the same position as for the dust. However, in one case, along the south clump, we had to modify the radial position of the inner Gaussian on a less eccentric position to better represent the gas emission. Vertically, the gas is assumed in hydrostatic equilibrium, at the midplane temperature, and the dust vertically mixed with the gas. We also tested two different degrees of dust settling, with the dust vertical scale height reduced by a factor of 5 and 10, but only negligible changes were observed between the models.

The temperature in the disk is determined by carrying out a two-dimensional (r, z) radiative transfer using the code RADMC-3D (Dullemond et al. 2012). The central star is an Herbig A5e star, with a temperature at the surface of 8130 K (van den Ancker & de Winter 1998). Taking into account the new estimated distance of 151 pc, the intrinsic luminosity is now 15.3 ${L}_{\odot }$ with a radius for the star of 2.0 ${R}_{\odot }$. The mass, deduced from Keplerian rotation, is 1.4 ± 0.3 ${M}_{\odot }$. The stellar emission is mainly absorbed in protoplanetary disks by μm-size grains, which are expected to be well coupled to the gas. We then assume for the radiative transfer the standard gas-to-dust ratio of 100, which corresponds to an opacity of about 6 cm² g⁻¹ of gas, in the frequency range 0.1–1 μm, at which most of the stellar energy is absorbed. The dust grains responsible of the dust emission at millimeter wavelength are represented by a grain size distribution following a power law of exponent −3.5 between 0.05 μm and 1 mm, and a chemical composition corresponding to the solar elemental abundance (Anders & Grevesse 1989). These dust properties were previously used in Boehler et al. (2017) and yields an opacity at 0.88 millimeter of 2.9 cm² g⁻¹. The fractional abundances of ¹³CO and C¹⁸O, with respect to molecular hydrogen, are assumed to be 9 × 10⁻⁷, and 1.35 × 10⁻⁷, respectively (Qi et al. 2011).

The radial profiles of the dust continuum emission are displayed in the left panels of Figure 7 and the integrated emission of the ¹³CO and C¹⁸O J = 3–2 in the right panels, from top to bottom for each of the three sectors presented in Figure 6. We use the integrated emission to fit the gas surface density distribution, as its optical depth is lower than for the peak emission, and less sensitive to variations at the disk surface, such than spirals, that are not taken into account in our modeling. At a first glance, we observe large azimuthal variations in the dust emission while the ¹³CO and C¹⁸O integrated emissions are more constant with the position angle.

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The models that best fit the data are represented by dotted lines and were found manually. They generally well recover the disk emission. A summary of the model parameters that give the dust and gas surface densities are provided in Table 1 and in Figure 8. Figure 8 also shows the radial evolution of the dust-to-gas ratio. On the left panels of Figure 7, the dust emission, optically thin, presents a double-ring structure. The two rings are located at 57 and 81 au and have a comparable surface density of ∼0.4 g cm⁻². In comparison, the two dust clumps are on more eccentric positions, with the south clump at 47 au and the north clump at 82 au, and have surface densities of about 2.5 and 6.5 times, respectively, the values encountered in the underlying rings.

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Table 1.  Density Prescription for the Gaussians Describing the Dust and Gas Surface Density

	${{\rm{\Sigma }}}_{1}$	R1	w1	${{\rm{\Sigma }}}_{2}$	R2	w2
	$({\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1})$	(au)	(au)	$({\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1})$	(au)	(au)
Ring (P.A. = 75°–150°)
Dust	0.040	57	8	0.036	81	12
Gas	1.3	57	17	0.9	81	30
South Clump (P.A. = 200°–220°)
Dust	0.102	47	5	0.030	78	18
Gas	0.9	53	17	0.9	78	24
North Clump (P.A. = 325°–345°)
Dust	0.027	56	12	0.24	82	9
Gas	1.3	56	18	1.0	82	28

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The gas has small azimuthal variations in the surface density structure. As we consider that the small grains follow the gas, the temperature of the disk is almost invariant azimuthally. The temperature along the double-ring structure is given in Figure 9. Only the gas surface density along the south dust clump appears slightly smaller. This area is located at the azimuthal minimum in the ¹³CO and C¹⁸O integrated emission. As mentioned in Section 3.3, this region might in fact be in the shadow projected by the inner regions of the disk. In this case, the temperature would be locally lower and inversely, the gas surface density higher, more similar to the value encountered at other polar angles.

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The gas distribution is also more extended radially than the large dust grains distribution, both in the cavity and in the outward direction. The lower resolution obtained for the gas of ∼02 about twice larger than in the dust, and its lower signal-to-noise, does not allow to probe as efficiently gas substructures. Therefore, we are not able to observe if the double-ring structure also exists in the gas distribution. We also do not find evidence of gas concentration cospatial with the dust clumps. This leads to an increase of the dust-to-gas ratio in the dust clumps to a value of about 0.1, shown in the bottom panel of Figure 8, 10 times the usual standard value. As a simple estimation of our precision, C¹⁸O, our best tracer of the gas density, has maximum values of about 100 mJy beam⁻¹ km s⁻¹, about 10 times larger than the rms noise. The precision for the gas density at 3σ is then known at best at ±30%.

Considering an average temperature of 60 K at a distance of 60 au, where the gas density reaches its maximum, we find optical depths of about ∼3.7 and 0.6 at the center of the ¹³CO and C¹⁸O J = 3–2 emission lines, respectively. By comparison, the dust has a maximum optical depth of about 0.12 in the underlying double disk structure, but which raises up to 0.7 in the north dust clump. Finally, if we consider that the gas and the dust distribution in the disk are represented azimuthally at 70% by the red sector, and at 15% each by the sectors along the dust clumps, the gas mass in the disk is about 1.3 × 10⁻³ ${M}_{\odot }$ and the dust mass about 3.0 × 10⁻⁵ ${M}_{\odot }$.

The near-IR emission is expected to be optically thick and to be scattered efficiently by small dust grains of a few μm in protoplanetary disks. The polarized emission therefore traces fluctuations of the disk surface and has been used in observations to detect spirals or gap structures. The observations were made by Grady et al. (2013) using the Subaru telescope in near-IR via the H Band (1.65 μm) in polarized emission and the Ks Band (2.15 μm) in direct imaging. They detected 2 spirals, but with a larger contrast for the spiral starting on the east side of the star, and wrapping around the disk toward the south (SE spiral). Benisty et al. (2015) redetected the spirals with VLT/SPHERE in scattered light in Y Band (1.04 μm) giving further insights on the disk surface. Here we propose to compare the observations of Benisty et al. (2015) with our ALMA data to have a 3D view, of the surface and midplane, of the disk around MWC 758.

In Figure 10, we compare the near-IR observations of Benisty et al. (2015) with the ¹³CO peak emission. The ¹³CO peak emission is optically thick in the outer disk, with τ ∼ 2.5 and therefore is particularly sensitive to the disk temperature. We observe a clear correlation between the ¹³CO peak emission and the near-IR features, especially for the southeast spiral, suggesting that the spirals observed in near-IR are coincident with a local increase in temperature. The correlation with the northwest spiral is less evident. The spiral is mainly located at a smaller radius of 40–50 au where the ¹³CO peak emission is more optically thin and depends also on the gas surface density, which increases up to 60 au. Also, in the previous IR observations of Grady et al. (2013) and Benisty et al. (2015), the northwest spiral was less pronounced or azimuthally extended, suggesting a spiral less irradiated by the central star due to shadows cast from the inner regions of the disk or a lower enhancement in density and/or vertical elevation. Using a linear regression method, we fitted the position of the IR radial maxima by spirals, with a constant pitch angle, described by the following equation:

$$\begin{eqnarray}&&R={R}_{0}\,\exp [\tan (\alpha )(\theta -{\theta }_{0})]\end{eqnarray} \tag{ 2 }$$

with α the pitch angle, and R₀ the radial distance of the spiral at the azimuthal angle ${\theta }_{0}$. These fits are represented by dashed black lines in the right panel of Figure 10. The southeast spiral, fit at P.A. between 50° and 200°, has a pitch angle of 127 and is located at R₀ = 43.0 au at P.A. = 50°. The northwest spiral, fit between 230° and 340°, features a similar pitch angle of 129, starting at the radial distance R₀ = 33.0 au at P.A. = 230°. The angular separation between the two spirals is of about 180°, only varying slightly in the outer disk. There is no similar spiral-like components in the integrated emission of ¹³CO and C¹⁸O, which are more optically thin and probe essentially the gas surface density.

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We also compared the position of the infrared spirals with the dust emission obtained using super-uniform weighting in Figure 11. The fit of the spirals in near-IR scattered light is represented in blue solid lines and their extrapolation toward larger radii in blue dotted lines. In addition to the double-ring structure, the dust emission reveals two faint spirals located at a slightly larger radius than the near-IR spirals (Shen et al. 2017, in preparation). Also, similarly to the near-IR observations, the pitch angle of the northwest spiral in the dust emission seems to increase at the proximity of the north dust clump.

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As already noticed by Benisty et al. (2015), and more recently by Reggiani et al. (2017) using the Keck telescope, the IR scattered light presents two other features in the outer ring, designated 3 and 4 in the right panel of Figure 11. They do not trace large spirals. The feature 3 has a negative pitch angle, and both have a very limited azimuthal extent. Reggiani et al. (2017) proposed that the north IR arc was possibly tracing the spiral 1, but in the bottom side of the disk. Our new observations show however that these two features are located at, and likely trace, the inner edge of the two dust clumps. Indeed, the local enhancement in dust surface density must increase locally the absorption and scattering of the stellar irradiation at the inner edge of the dust clumps. This may then also rise up the temperature and the disk scale height, unveiling even more the two near-IR features.

The disk around the Herbig star MWC 758 has a complex morphology which comprises a cavity, two rings, two large spirals and two dust clumps. According to our models, the disk, with a mass of about 1.3 × 10⁻³ ${M}_{\odot }$, is not massive enough to be gravitationally unstable (Kratter & Lodato 2016). One explanation for such a complex structure is the presence of planet(s) which can interact with the protoplanetary disk and create features (annuli, spirals, or vortices) which can be more easily detected than the planets themselves (Kley & Nelson 2012; Baruteau et al. 2014).

We observe in the continuum emission two large dust clumps which have an elongated structure and an azimuthal/radial aspect ratio of approximately five at our angular resolution. To our knowledge, MWC 758 is the only disk with V1247 Orionis, observed by Kraus et al. (2017), which features two dust clumps at two different radial distances. These structures are associated with azimuthal extensions dividing the disk in two rings, located at a distance from the star of about 57 and 81 au. By modeling the dust and gas emission, we conclude that the gas distribution is more diffused than the distribution of the large dust grains. Millimeter grains are gathered in compact regions with surface densities larger by a factor of 2.5 and 6.5 in the south and north dust clumps, respectively, compared with values encountered at other azimuthal angles. We do not detect increases of the gas surface density at the position of the dust clumps, what suggests a local augmentation of the dust-to-gas ratio, up to a value of ∼0.1.

The system MWC 758 is also famous for its two large and sharp spirals detected in near-IR scattered light by Grady et al. (2013), Benisty et al. (2015) and more recently by Reggiani et al. (2017). These spirals feature a large pitch angle of ∼13° and are also observed with ALMA using the optically thick ¹³CO J = 3–2 peak emission and the optically thin continuum dust emission. This is the first time that spirals in protoplanetary disks are visible with these three tracers. The bright southeast spiral is observed at the same radius in IR and in ¹³CO. The IR scattered light traces the inner side of the spiral shock front at the disk surface, where the stellar emission is absorbed and locally heats the disk. In comparison, the spirals observed with the dust emission show fainter spiral structures and are located at a slightly larger radius, by a few au. The difference in the radial location might come from the width of the spirals, as we expect that the dust emission traces mainly the central position of the spirals. It can also be caused by the vertical propagation of the spirals which is expected to curl toward the central star at the disk surface instead of being perpendicular to the disk midplane (Zhu et al. 2015).

The northeast spiral is less pronounced in the ¹³CO peak emission and (less extended azimuthally) in IR scattered light (Grady et al. 2013) than its southwest counterpart. It is possible that this spiral presents a lower scale height and/or density enhancement. We propose also that this might be due to a shadow cast by the inner regions of the disk. We detect a non-resolved source of continuum emission at the central star position, associated with a twist in the iso-velocity curves. Additionally, we detect an azimuthal minimum along the west direction in the ¹³CO and C¹⁸O integrated emission and in the velocity dispersion, which supports the hypothesis of a mildly warped inner disk.

The origin of the spirals in MWC 758 has been under debate since their discovery by Grady et al. (2013), and our ALMA observations also show the presence of two dust clumps and a dark ring, surrounding a large cavity. The south dust clump is located at the outer edge of the cavity, at 47 au, and the north dust clump, at the outer edge of the dark ring, at 82 au. These regions present large gas surface density gradients where Rossby-wave instabilities (RWIs) are thought to develop and trigger vortices. The two dust clumps are also cospatial with the two azimuthal maxima detected in the continuum emission by Marino et al. (2015b) with the VLA at 33 GHz. This suggests that large dust grains are trapped into gas pressure maxima through aerodynamical drag, as already proposed by Marino et al. (2015b) for the north dust clump. Small local variations of 20%–30% in the gas might not be visible in our observations but still be able to accrete efficiently dust particles (Pinilla et al. 2012).

Many disks, like IRS 48 (van der Marel et al. 2013), AB Aur (Tang et al. 2017), SAO 206462 and SR 21 (Pérez et al. 2014) among others, have shown large dust asymmetries that may also suit this scenario. As for MWC 758, most of these disks comprise a large cavity, which might be open by a stellar companion or planet(s). The probable detection by Reggiani et al. (2017) of a planet of 0.5−5 M_Jup inside the cavity supports this idea. If the companion is massive enough, simulations of Ragusa et al. (2017) have shown that it can also produce a large azimuthal variation of the gas surface density. This might be the case for the binary system HD 142527, which presents a stellar companion of about 0.25 ${M}_{\odot }$ and a large azimuthal ratio of ∼3.75 in the gas surface density (Muto et al. 2015; Boehler et al. 2017). This effect is however likely negligible in MWC 758 which has a low planet-to-star mass ratio, of about 0.001, and presents only moderate azimuthal variations of the gas surface density.

A scenario that might explain the complex structure of the outer regions of the MWC 758 system is the presence of a large planet at R $\geqslant$ 100 au. 3D hydrodynamical simulations of Zhu et al. (2015) and Dong et al. (2015) have shown that a massive planet of a few Jupiter mass in the outer regions would produce a pair of inner spiral arms, whose brightness and large pitch angle are compatible with the near-IR observations. Recent simulations of Bae et al. (2017) have also shown that, for a disk with low viscosity (i.e., α ∼ 10⁻⁴), a massive planet can also produce a secondary gap in the inner regions of the planet orbit. This gap is linked to the secondary spiral and is located at approximatively 0.5–0.6 the orbital radius of the planet. This is consistent with the observation of the dark ring located between the two dust clumps. Such planet can also produce a tertiary spiral that might have been observed in the cavity of the disk by Reggiani et al. (2017). However, this hypothetical massive planet has not been detected yet in the IR observations of Grady et al. (2013) and Reggiani et al. (2017).

There are also processes that can explain part of the observations without the need of a planet in the outer regions (at R ≥ 100 au.) A simple explanation for the dark ring is the presence of a supplementary planet of moderate mass inside the ring. It has also been proposed by Lobo Gomes et al. (2015) that a first vortex, formed at the edge of the central cavity, might accrete matter and cleans the orbit at a slightly larger radius. This process can then create a ring and be at the origin. Nevertheless, these hypotheses alone do not explain the presence of the spirals. Montesinos et al. (2016) suggested that spirals might be induced dynamically as a consequence of a different irradiation from the star due to a warp in the inner regions of the disc. With the possible presence of a warped inner disc in MWC 758 projecting shadows in the outer regions, this possibility has not to be discarded. Indeed, the two other disks known to feature an inner warped disk, HD 135344B and HD 142527, also have a large cavity and spirals (Casassus et al. 2015a; Stolker et al. 2016; Christiaens et al. 2014). It is also still unclear if a planet inside the cavity, with a non-coplanar or eccentric orbit, might produce such spirals.

Finally, if massive enough, dust clumps might interact with, or even produce, spirals (Baruteau & Zhu 2016; van der Marel et al. 2016b). The spiral propagating outwards in the north direction crosses, and maybe starts from, the south dust clump. We also observe that the pitch angle of this spiral increases in the vicinity of the north dust clump, both in near-IR and in the dust emission. However, this scenario is not able to produce the southeast spiral which is not cospatial with any of the two dust clumps. It would also be surprising that the south clump is able to produce a large spiral, while the north dust clump, about 3 times more massive, is not.