A Close-up View of the Young Circumbinary Disk HD 142527

The map of the 342 GHz (λ = 0.88 mm) dust thermal emission is shown in Figure 1. It unveils a large eccentric crescent extending radially up to ∼300 au as previously observed by Fukagawa et al. (2013) and Casassus et al. (2015). The total flux density is about 3.31 Jy and is dominated by the emission coming from the northern side of the disk.

Zoom In Zoom Out Reset image size

The morphology of the dust crescent can be described by drawing the crest for the dust emission, defined as the line that connects the peaks of the flux density measured as a function of the position angle (P.A.; black dashed line  in the right panel). The radius of the crest is calculated by assuming that the center of the disk is pinpointed by the compact source detected inside the dust cavity, which is coincident with the Herbig star position and with the center of rotation of the disk (see Section 3.2). The crest has a maximum of ∼132 mJy beam⁻¹ at a P.A. of 30° and a minimum of ∼6 mJy beam⁻¹ at P.A. = 220°, resulting in a flux density contrast of 22 between the northern and southern sides of the disk and a peak-to-noise ratio in the image of 1150. The radial position of the azimuthal maximum is 165 au while the radial position of the azimuthal minimum is 205 au. Along the azimuthal direction that intersects the minimum and maximum of the crest, the radial profile of the continuum emission is in first approximation Gaussian with a width of 60–80 au. The radial profile of the dust emission is discussed in more detail in Section 4.2. The inner and outer radii of the circumbinary dust emission are measured based on the $5\sigma$ intensity contours (red solid lines in the top-right panel). The inner edge varies with the azimuth and is located between 80 and 155 au. The radius of the outer edge also depends on the azimuth and varies between 250 and 300 au.

In first approximation, the shape of the crest can be described by an ellipse characterized by a major axis of 185 au, an eccentricity of 0.11, and a P.A. of the major axis of $205^\circ$. Using the same P.A. for the major axis of the ellipse, the best fit gives a semimajor axis of 120 au along with an eccentricity of 0.29 for the inner edge and a semimajor axis of 300 au and an eccentricity of 0.050 for the outer edge. The eccentricity in the outer disk then decreases with the distance to the central stars. The periapsis and apoapsis P.A. of the cavity, crest, and outer edge are the same and are aligned with the dust peak emission on the dust crescent and with the dust minimum on the southeast side of the disk. As shown in the bottom panel of Figure 1, the crest also has two local minima of 97.2 and 7.8 mJy beam⁻¹ at P.A. = 340° and P.A. = 180°, respectively. These local minima are also visible in the CO moment 0 maps discussed in Section 3.1.2.

The observations also reveal a source of compact emission inside the dust cavity with a peak flux density of 4.1 mJy beam⁻¹. Its position corresponds to the center of rotation of the disk as measured by the CO observations discussed in Section 3.2. The emission is unresolved at the angular resolution of our observations, implying a radial extent less than 30 au in diameter. A flux density of 80 μJy beam⁻¹ was detected at 34 GHz at the same position by Casassus et al. (2015). At these frequencies, the signal might be contaminated by free–free emission. In order to estimate the amount of possible free–free emission in our ALMA data, we assume the emission observed at 34 GHz is entirely free–free and has a spectral index α (I_ν ∝ ${\nu }^{\alpha }$) equal to 0.4, this value being the steepest index predicted by theoretical models (see, e.g., Panagia & Felli 1975). Under these assumptions, we predict a maximum flux density for free–free emission of 0.2 mJy beam⁻¹ at 342 GHz. This value is 20 times less than that measured, implying therefore that the central continuum emission must come mostly from dust grains.

The brightness temperature of the central continuum emission is 5.3 K. This is much less than the physical dust temperature, which is expected to be ∼1000–100 K in the range 0.5–10 au. This suggests that the emission is either optically thin or it comes from an optically thick region much smaller than the synthesized beam. In order to have an idea of the extent of the inner disk, we performed a simple model assuming that the disk is optically thick, with an inclination of 70° (Marino et al. 2015), and that the surface density scales with the radius as ${r}^{-1}$ and Σ(1 au) = 3 g cm⁻². We calculated the temperature and emission at 342 GHz using the radiative code RADMC-3D (Dullemond et al. 2012). The method and the dust properties are detailed in Section 4.2. We found that a disk with a radius of 2–3 au reproduces the observed flux. If the inner disk is instead coplanar with the outer disk (i.e., with an inclination of 27°), its outer radius would be about 1 au. These disk sizes are in agreement, or smaller for the coplanar case, with the tidal truncation expected by the observed companion at ∼13 au (Papaloizou & Pringle 1977).

Finally, the continuum map reveals a faint compact source located at about 50 au north of the center (P.A. ∼ 5°). The flux density of this source, which is labeled in the figure with the letter c, is 0.80 mJy beam⁻¹, or 6.9 times the noise level. Its brightness temperature is 3.5 K, suggesting either a very small source or optically thin emission. At such distances from the star, the temperature due to stellar irradiation can be estimated to be ∼100 K, and the observed flux would be consistent with an optically thick clump of dust of about 1.6 au in size. If the emission is optically thin and the dust opacity is 2.9 cm² g⁻¹ as in Muto et al. (2015), the measured flux density corresponds to a mass of ∼1.5 × 10²⁴ kg, or about a quarter of the Earth mass. Despite the low signal-to-noise ratio of the continuum emission, the observations suggest that source c corresponds to a real structure in dust and gas. First, source c is detected with a signal-to-noise ratio of 6.9 while the second brightest peak emission inside the cavity has a signal-to-noise ratio of 3.5. Furthermore, the rms noise inside the cavity is the same as the noise in the outer parts of the map (130 μJy beam⁻¹ instead of 115 μJy beam⁻¹). Additionally, we verified that no negative components at the position of source c exist in the map of the residual obtained at the end of the deconvolution process. This suggests that source c is not a result of overcleaning the dirty map. Finally, we detected gas in non-Keplerian rotation at the position of source c in the ¹³CO map (see Figure 7). Deeper ALMA observations at higher angular resolution are required to assess the nature of source c.

No dust emission is detected somewhere else in the cavity, even when adopting natural weighting for the imaging, which delivers a sensitivity of 65 μJy beam⁻¹ and a beam of $0\buildrel{\prime\prime}\over{.} 36\times 0\buildrel{\prime\prime}\over{.} 31$. Using this weighting, the peak emission in the dust crescent is ∼240 mJy beam⁻¹. Considering we do not detect dust emission in the cavity above 3σ (195 μJy beam⁻¹), the dust emission at millimeter wavelengths has then dropped by a factor >1200 from the peak.

Figure 2 displays spectrally integrated (Moment 0) maps of the ¹³CO J = 3-2 and C¹⁸O J = 3-2 line emission, obtained after subtracting the dust-continuum emission. The rms noise in these maps is 7.2 Jy beam⁻¹ km s⁻¹ for ¹³CO J = 3-2 and 7.8 Jy beam⁻¹ km s⁻¹ for C¹⁸O J = 3-2.

Zoom In Zoom Out Reset image size

The ¹³CO and C¹⁸O emission extends to about 400 and 300 au from the center, respectively. By comparison, the outer radius of the dust emission is about 300 au, similar to C¹⁸O. In general, the azimuthal structure of the CO integrated emission differs substantially from that observed in the dust continuum. The CO emission is more azimuthally symmetric than the dust with only azimuthal variations by a factor of 1.5 for ¹³CO J = 3-2 and 1.4 for C¹⁸O J = 3-2. The maximum is located at P.A. = 0°–30° while the minimum is at P.A. ∼ 165°.

Furthermore, a few structures are visible. First, the CO emission presents an apparent decrement at a distance of 170–220 au from the star, on the north of the disk, corresponding with the continuum crescent. The interpretation of this feature is discussed in Section 4.1. Second, there are two local minima visible in both ¹³CO and C¹⁸O integrated maps, on the south side at P.A. = 130°–190° and more faintly, on the north side at P.A. ∼ 330°. They are at the same P.A. as the secondary minima observed in the dust emission, which were also previously seen in IR (Avenhaus et al. 2014). The local decrease is more pronounced in ¹³CO, the most optically thick molecule, and suggests that the decrease is in temperature and affects predominantly the upper layers, which are more sensitive to changes in stellar irradiation. This result supports the hypothesis of shadows cast by the inner circumprimary disk (Marino et al. 2015). Third, in the P.A. range 200°–250°, the radial profile of the ¹³CO emission shows two peaks at about 115 and 200 au from the star. This is characterized by the abrupt change of the crest radial position at P.A. = 230°, visible in the top-right panel of Figure 2.

Both the ¹³CO and C¹⁸O maps are characterized by much smaller central cavities than the cavity observed in the continuum. In C¹⁸O, the 3σ contours indicates an almost-circular cavity with radius between 60 and 70 au. In ¹³CO, the cavity size varies with the P.A. and measures ∼15 au at P.A = 75° and 35 au at P.A. = 250°. The minimum and maximum radii of the cavity in ¹³CO, dust, and at a smaller degree, C¹⁸O, are along the same azimuthal direction. As discussed in Section 5.1, this might suggest a common origin for their elliptical shape.

Figure 3 shows maps of the ¹³CO and C¹⁸O peak emission. The main advantage of using the peak intensity is that it probes the most optically thick part of the line emission and constrains the gas temperature if the line center is optically thick. The figure shows the line intensity in units of brightness temperature defined as the temperature of a black body covering the area of the synthesized beam and emitting the observed flux density. For the conversion of Jy beam⁻¹ to Kelvin, we used the inverse of the Planck function:

$$\begin{eqnarray}&&T=\displaystyle \frac{h\nu }{k}\,\displaystyle \frac{1}{\mathrm{ln}\left(\tfrac{2h{\nu }^{3}}{F{\rm{\Omega }}{c}^{2}}+1\right)},\end{eqnarray} \tag{ 1 }$$

with h the Planck constant, k the Boltzmann constant, ν the frequency, F the flux density, and Ω the beam solid angle defined by $(\pi {\theta }_{\max }{\theta }_{\min })/(4\mathrm{ln}(2))$, where ${\theta }_{\max }$ and ${\theta }_{\min }$ are the major and minor FWHMs of the synthesized beam.

Zoom In Zoom Out Reset image size

In the left column of Figure 3, we display the ¹³CO and C¹⁸O peak emission calculated after subtracting the continuum emission. They present a brightness temperature decrease at the position of the continuum crescent that is more pronounced than in the integrated intensity maps. Taken at face value, this might suggest a local decrease in either line optical depth or gas temperature. In the right column of the figure, we show brightness temperature maps obtained without subtracting the continuum. As expected, the brightness temperature increases to account for the extra emission previously attributed to the continuum, and the decrement observed at the position of the continuum crescent disappears. In Section 4.1, we claim that a peak intensity map obtained without subtracting the continuum emission is the best probe of the physical temperature of the gas if the emission at the line center is optically thick, as in the case of the ¹³CO J = 3-2 emission in the outer disk of HD 142527 (Muto et al. 2015). The map shown in the top-right panel of Figure 3 therefore unveils the thermal structure of the ¹³CO J = 3-2 emitting layer.

Figure 4 compares the peak emission coming from the crest of the two molecules with the dust-continuum. The peak emission of the molecules is warmer than the dust emission with differences between dust and ¹³CO J = 3-2 of ∼20 K on the dust crescent and 40 K on the opposite side. The horseshoe structure is more pronounced in the dust with brightness temperature varying between 30 K on the dust crescent to 5 K on the opposite side, but is also visible in C¹⁸O, with temperature varying from 47 to 31 K.

Zoom In Zoom Out Reset image size

The ¹³CO emission, which is more azimuthally symmetric, has a maximum brightness temperature of 54 K in the northeast part of the disk. In general, the eastern side of the disk is warmer than the western side, which is consistent with the east–west asymmetry observed in the mid-infrared thermal emission by Fujiwara et al. (2006). The temperature difference probably comes from the disk inclination as the inner wall of the outer ring on the east side is exposed to the observer at a more face-on inclination. Also, the ¹³CO peak emission map shows a local minimum at P.A. = 130°–180° with a local decrease of ∼10 K, corresponding to the larger azimuthal minimum observed in the integrated map, and due probably to the inner disk shadow. We nevertheless do not clearly see this feature in C¹⁸O or in the opposite side of the disk as in the integrated maps.

The bottom panel of Figure 4 shows the radial position of the crests, which are located at smaller radii for the CO molecules than for the dust. ¹³CO, the most optically thick molecule, generally has its crest at smaller radii than C¹⁸O. This suggests that the gas density at the cavity edge increases with radius on a spatial scale resolved by our observations. The smaller radius of the ¹³CO crest is then a result of the larger optical depth of this line. This is particularly visible at P.A. = 0°–160° and 250°–360°. Conversely, at the azimuthal angles between 160° and 250°, the ¹³CO and C¹⁸O crests are at the same distance from the star. As we will discuss later, in this region the emission of the lines are mostly optically thin and the crest likely indicates the peak of the gas surface density instead of the transition between the optically thin and optically thick regions.

Finally, the ¹³CO map in Figure 3 reveals a spiral structure starting form the west (at ∼2'') and propagating to the north of the disk up to 25. This structure is consistent with the S1 spiral arm observed by ALMA in the ¹²CO J = 3-2 and J = 2-1 lines by Christiaens et al. (2014). This spiral was also observed in the near-infrared H and K bands, implying that it entrains both molecular gas and small grains (see also Avenhaus et al. 2014).

As a first step, we compare our observations with the M15 model, rescaled to the distance of 156 pc, which is defined as follow. The dust surface density is expressed by a Gaussian law

$$\begin{eqnarray}&&{{\rm{\Sigma }}}_{d}(r)={{\rm{\Sigma }}}_{d,0}\,\exp \left[-{\left(\displaystyle \frac{r-{r}_{d}}{{w}_{d}}\right)}^{2}\right].\end{eqnarray} \tag{ 2 }$$

In the north direction, defined by P.A.s between 16° and 26°, the dust surface density has ${{\rm{\Sigma }}}_{d,0}$ = 0.6 g cm⁻², r_d = 193 au, and ${w}_{d}=30\,\mathrm{au}$. In the south direction, defined by P.A.s between 216° and 226°, the dust surface density has ${{\rm{\Sigma }}}_{d,0}$ = 8.45 × 10⁻³ g cm⁻², r_d = 218 au, and ${w}_{d}=38\,\mathrm{au}$.

The disk temperature is calculated with the radiative code RADMC-3D (Dullemond et al. 2012) assuming thermal equilibrium. The stellar irradiation comes from the central Herbig star of 2.4 solar masses, a luminosity of about 23 ${L}_{\odot }$, and a surface temperature of 6250 K. In this analysis, we neglect the irradiation coming from the stellar companion of ∼0.25 ${M}_{\odot }$. The dust and the gas have the same vertical distribution, which is assumed to be in hydrostatic equilibrium with the midplane temperature. A few iterations between the vertical distribution and the disk temperature are needed to find a stable solution.

The dust grain properties are chosen to have a dust opacity of 2.9 g cm⁻² at 0.88 mm, as in M15. This value corresponds to the mean opacity of porous grains made of silicates (25.7%), carbon (18%), and water ice (56.3%), with sizes a between 0.05 μm to 1 mm, and a grain size distribution proportional to ${a}^{-3.5}$. The observations are then simulated with RADMC-3D, performing ray tracing on the disk with the same inclination and P.A. as HD 142527 and smoothed via CASA at the same angular resolution as our observation.

The left panels of Figure 9 show the comparison between the M15 dust model and our observations. Overall, the model reproduces well the radial position of the peak but underestimates the observed flux. Differently from M15, we do not include dust scattering in calculating the disk emission. We made this choice because millimeter-wave dust-scattering opacities strongly depend on the composition and structure of (sub)millimeter particles, which are largely uncertain (see the Appendix).

Zoom In Zoom Out Reset image size

The gas surface density in M15 is parameterized using a broken power law:

$$\begin{eqnarray}{{\rm{\Sigma }}}_{g}(r)=\left\{\begin{array}{ll}{f}_{\mathrm{in}}\,{\sigma }_{g}({r}_{c})\,\left(\tfrac{r}{{r}_{c}}\right) & (r\lt {r}_{c})\\ {\sigma }_{g}(r) & ({r}_{c}\lt r\lt {r}_{\mathrm{out}})\\ {f}_{\mathrm{out}}\,{\sigma }_{g}({r}_{\mathrm{out}}) & (r\gt {r}_{\mathrm{out}})\end{array}\right.,\end{eqnarray} \tag{ 3 }$$

with ${\sigma }_{g}$(r) = ${\sigma }_{g,0}{\left(\tfrac{r}{200\mathrm{au}}\right)}^{-1}$, r_c the cavity radius, and r_out the outer edge of the dense disk. At these radii, the gas surface density decreases sharply by a factor of f_in and f_out, respectively. Inside the cavity, for $r\lt {r}_{c}$, the surface density increases linearly with radius, while for $r\gt {r}_{\mathrm{out}}$, the gas surface density is constant. The values for the north profile are ${\sigma }_{g,0}$ = 0.94 g cm⁻², r_c = 123 au, r_out = 279 au, f_in = 1/8, and f_out = 0.01. For the south profile, the values are ${\sigma }_{g,0}$ = 0.26 g cm⁻², r_c = 111 au, r_out = 279 au, f_in = 1/8, and f_out = 0.1. The fractional abundances of ¹³CO and C¹⁸O are 9 × 10⁻⁷ and 1.35 × 10⁻⁷, respectively. Finally, as in M15, the line profile is calculated accounting for the thermal broadening and Keplerian rotation but does not include any turbulence.

Figure 9 shows the comparison between the M15 model and our observations. Dust emission is shown in the left panels, while the spectrally integrated and peak CO emission are plotted in the central and right panels, respectively. In the right panel, we also plot the profile of the disk temperature in the disk midplane. As discussed below, the comparison between peak brightness temperature and physical disk temperature provides a rough idea of the optical depth for the CO line emission. In the north direction, the M15 model provides a good fit for both the integrated emission and the peak emission, even if the emission in the cavity is a little overestimated. The model also correctly reproduces the decrease in integrated line emission observed at the position of the dust crescent between 130 and 240 au from the star.

However, the M15 model fails to reproduce the observations along the south direction. In particular, it underpredicts the radius of the peak of CO intensity. In our observations, the highest peak is located at an orbital radius of about 200 au, while the model predicts the peak to be located about 150 au from the star. Additionally, the integrated CO emission presents a double-peaked structure, which is not captured by the model.

Whereas the M15 model provides an acceptable fit to our observations, at least along the north direction, the assumed profile for the gas surface density (Equation (3)) is not physically motivated. In particular, it is unclear why the dust and gas surface densities should have different shapes and what might be the origin of sharp edges in the gas distribution at r_c and r_out. In this section, we adopt a different approach and model the gas and dust radial distributions using Gaussian functions centered at the same radius r_r and characterized by different widths. This parametrization mimics the effect of the trapping of dust grains by a Gaussian gas surface density profile peaking at r_r (see, e.g., Pinilla et al. 2012b). Indeed, dust trapping causes the dust distribution to be more peaked toward the gas density maximum. To add an additional degree of freedom, we allow the width of the Gaussian distribution for $r\lt {r}_{r}$ to be different from the width for $r\gt {r}_{r}$. The dust distribution is therefore defined by

$$\begin{eqnarray}{{\rm{\Sigma }}}_{d}(r)=\left\{\begin{array}{ll}{{\rm{\Sigma }}}_{d,0}\,\exp \left[-{\left(\tfrac{r-{r}_{r}}{{w}_{d,\mathrm{in}}}\right)}^{2}\right] & (r\lt {r}_{r})\\ & \\ {{\rm{\Sigma }}}_{d,0}\,\exp \left[-{\left(\tfrac{r-{r}_{r}}{{w}_{d,\mathrm{out}}}\right)}^{2}\right] & (r\gt {r}_{r}).\end{array}\right.\end{eqnarray} \tag{ 4 }$$

The gas distribution is described by the same equation but with different values ${{\rm{\Sigma }}}_{g,0}$, ${w}_{g,\mathrm{in}}$, and ${w}_{g,\mathrm{out}}$. Using this parameterization for the gas and dust surface density, we repeat the calculation of the disk temperature, continuum, and line emission as discussed above. However, differently from M15 model, we calculate the line emission by adding a constant turbulence velocity of 0.2 km s⁻¹ across the disk.

In Figure 10, we present our best fit for the dust emission. The northern dust density profile has a maximum density of 0.65 g cm⁻² at ${r}_{r}=185\,\mathrm{au}$. The inner width is 28 au while the outer width is 50 au. The southern profile has a maximum surface density of 0.012 g cm⁻² at ${r}_{r}=205\,\mathrm{au}$ and inner and outer widths of 17 au and 43 au, respectively. This model provides a good fit to the observations between 25 and 230 au. Instead, the dust distribution at larger distances seems to deviate from a simple Gaussian profile. Within 25 au, the dust emission traces the compact source discussed above, which is not included in our model.

Zoom In Zoom Out Reset image size

The best-fit model for the CO emission is shown in Figure 11. Along the north direction, the gas surface density is ∼1.1 g cm⁻² at ${r}_{r}=185\,\mathrm{au}$ and has widths of 60 and 85 au inside and outside the peak, respectively. In the south profile, the gas surface density is 0.24 g cm⁻² at ${r}_{r}=205\,\mathrm{au}$ and the widths are 90 au for the inner side and 100 au for the outer side. Along the north direction, our model well reproduces all the main features of the observations. However, there is still a discrepancy in the south profile, where the model fails to reproduce the secondary maximum in the integrated emission and the shoulder in the peak emission.

Zoom In Zoom Out Reset image size

The comparison between the physical disk temperature and the brightness temperature of the line emission (see the right panel of Figure 11) indicates that both lines are optically thin for $r\leqslant 200\,\mathrm{au}$, as the brightness temperature of the emission is inferior to the disk midplane temperature. The secondary local maximum observed in the south profile at r = 115 au might then come from a local enhancement in the gas density. In order to reproduce it, we added a second Gaussian in the description of the gas surface density for the south profile, such that the gas surface density is now defined as

$$\begin{eqnarray}&&{\sigma }_{g}(r)={{\rm{\Sigma }}}_{g}(r)+{{\rm{\Sigma }}}_{g}^{\prime }(r),\end{eqnarray} \tag{ 5 }$$

where ${{\rm{\Sigma }}}_{g}(r)$ is as in Equation (4), and

$$\begin{eqnarray}&&{{\rm{\Sigma }}}_{g}^{\prime }(r)={{\rm{\Sigma }}}_{g,0}^{\prime }\,\exp \left[-{\left(\displaystyle \frac{r-{r}_{r}^{\prime }}{{w}_{g}^{\prime }}\right)}^{2}\right].\end{eqnarray} \tag{ 6 }$$

The best-fit model is shown in Figure 12. The surface density ${{\rm{\Sigma }}}_{g}(r)$ has a maximum at ${r}_{r}=205\,\mathrm{au}$, equal to that of the dust surface density, with values of ${{\rm{\Sigma }}}_{g,0}=0.30$ g cm⁻², ${w}_{g,\mathrm{in}}=30\,\mathrm{au}$, and ${w}_{g,\mathrm{out}}=100\,\mathrm{au}$. The second Gaussian ${{\rm{\Sigma }}}_{g}^{\prime }(r)$ is centered at 115 au, and is characterized by ${{\rm{\Sigma }}}_{g,0}^{\prime }=0.18$ g cm⁻² and ${w}_{g}^{\prime }=30\,\mathrm{au}$. This second Gaussian profile, while producing a visible CO emission, does not have a counterpart in the dust surface density. The summary of all the model parameters is shown in Table 1, and the surface densities as a function of the radius are shown in Figure 13.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

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

	${{\rm{\Sigma }}}_{0}$ (g cm−2)	rr (au)	win (au)	wout (au)
North (P.A. = 16''–26'')
Dust	0.65 ± 0.05	185 ± 2	28 ± 2	50 ± 2
Gas	1.125 ± 0.1	185 ± 2	60 ± 5	85 ± 5
South (P.A. = 216''–226'')
Dust	0.012 ± 0.001	205 ± 2	17 ± 2	43 ± 2
Gas	0.18 ± 0.02	115 ± 5	30 ± 5	30 ± 5
	0.30 ± 0.02	205 ± 2	30 ± 5	100 ± 5

Note. In the south profile, the gas surface density is described by two Gaussians.

Download table as:  ASCIITypeset image

In conclusion, our analysis indicates that the radial distribution of dust particles is well-reproduced by asymmetric Gaussians whose inner widths are 2–3 times smaller than the outer widths. The density contrast between the dust crescent and the south side at the maximum of the dust surface density is ∼54. This is larger than the flux density contrast of 22 measured in the continuum, and this is explained by the fact that the dust emission along the north profile is optically thick with a maximum optical depth ${\tau }_{d}=1.9$ compared to an optical depth of 0.035 along the south. The gas distribution is more complex. The north profile is well-reproduced by a single asymmetric Gaussian centered at the same radius as the dust density. However, the distribution along the south is the sum of two Gaussian profiles separated by 90 au. Similarly to the dust, the gas surface density is the highest along the north direction. At the location of the maxima, the ratio between the north and south gas surface densities is ${{\rm{\Sigma }}}_{0,g}^{\mathrm{north}}/{{\rm{\Sigma }}}_{0,g}^{\mathrm{south}}=3.75$, while the ratio between the dust surface densities is ${{\rm{\Sigma }}}_{0,d}^{\mathrm{north}}/{{\rm{\Sigma }}}_{0,d}^{\mathrm{south}}=54$. Furthermore, the gas-to-dust ratio at $r={r}_{r}$ is 1.7 in the north and about 25 in the south. Similarly to the dust distribution, the inner widths for the gas distribution are smaller than the outer widths. Finally, if we assume that the north and south profiles are representative of the two sides of the disk, the total dust mass is 1.5 × 10⁻³ ${M}_{\odot }$ and the total gas mass is 5.7 × 10⁻³ ${M}_{\odot }$. The disk mass is therefore about 7.2 × 10⁻³ ${M}_{\odot }$, or ∼0.3% of the mass of the binary system. The measured gas-to-dust ratio is about 3–5 in the circumbinary disk, largely inferior to the standard ratio of 100.

These results support the dust-trapping scenario where dust is located at the radial and azimuthal gas pressure/density maximum. The differences between the inner and outer widths suggest, in the context of dust trapping, that the gas pressure gradient in the inner side is larger than that in the outer side. As discussed in the next section, the gas pressure maximum might originate from the interaction between the disk and the stellar companion, if in a highly eccentric orbit, or a giant planet orbiting inside the inner cavity, perhaps located at the position of source c. Finally, the nature of the double-Gaussian profile along the south profile is unclear. We argue that the innermost Gaussian might be tracing the onset of a gas spiral. We note that this feature is located next to the shadow cast by the warped inner disk on the south side. Following Montesinos et al. (2016), such a shadow may decrease the local gas pressure and create trailing spirals.

HD 142527 has a very lopsided disk characterized by gas and dust surface density ratios of about 3.75 and 54, respectively, between the north and south sides of the disk (Table 1). The favored theory to produce such azimuthal asymmetries is the formation of a large vortex capable of concentrating dust grains. In a first step, small vortices can be triggered by the Rossby wave instability (Lovelace et al. 1999; Li et al. 2000) caused by radial variations in the gas density due to either a companion or, for example, a steep radial variation of the disk viscosity (Regály et al. 2012). Vortex formation might also result from hydrodynamic instabilities like the baroclinic instability (see, e.g., Owen & Kollmeier 2016). Then, in a second step, they grow or merge together to form larger vortices (Li et al. 2001), which usually are limited to sizes of about one or two scale heights.

Different works have recently focused on scenarios able to generate a larger vortex with mode m = 1 surviving for a sufficiently long time (i.e., ∼1000 orbits) to produce an azimuthal dust concentration similar to those observed in HD 142527 and Oph IRS 48. Mittal & Chiang (2015) proposed that a massive lopsided disk could displace the center of mass of the star+disk system, creating an indirect force onto the gas particles that increases the vortex dimension and life expectancy (see also Zhu & Baruteau 2016 for a model where the indirect force effect is reduced by the disk self-gravity). This hypothesis appears to be ruled out by our observations, which show that the center of mass, calculated as the center of rotation of the disk, is located at the same position as the central compact dust-continuum emission attributed to the circumprimary disk. In practice, our ALMA observations set an upper limit for the displacement between the primary star and the center of mass of about one-tenth of the angular resolution of the observations, i.e., about 003, or about 5 au at the distance of this system. Furthermore, contrary to the model prediction, the central star is located closer to the dust crescent (165 au) compared to the opposite side of the disk (180 au). Therefore, the indirect force is not the driving factor of the disk asymmetry, probably due to the low disk mass, which is less than 1% of  the mass of the central stars.

Large and long-lived vortices also require a low viscosity (Fu et al. 2014), which cannot be easily reconciled with the relatively large mass accretion rate measured for HD 142527. A possible solution has been recently proposed by Zhu & Baruteau (2016). They studied the case of a large vortex created by the interaction of a disk and a 9 M_J planet using a global MHD simulation. The vortex produces an azimuthal asymmetry of a factor of a few in the gas density and necessitates a low viscosity corresponding to an equivalent Shakura–Sunyaev parameter $\alpha \lt {10}^{-3}$. Such a low viscosity is obtained when ambipolar diffusion, the dominant non-ideal MHD term at large radii (i.e., 10s of au), is added in the simulations as demonstrated in Zhu & Stone (2014). Also, low viscosity helps trigger Rossby wave instabilities because the density perturbations induced by the planet are less smoothed out by diffusion. Following this model, ambipolar diffusion is less important in the innermost and more ionized regions of the disk. This leads to higher disk viscosity and consequently a larger mass accretion rate. Interestingly, the simulations of Zhu & Baruteau (2016) suggest that disk–planet interaction might create an elliptical cavity ($e\sim 0.1\mbox{--}0.2$) more easily seen in the dust than in the gas emission. Moreover, the vortex is located closer to the star compared to the other side of the ring. This scenario is consistent with our observations and might explain the cavity shape without placing the companion or a planet in an eccentric orbit.

Our analysis indicates that the gas-to-dust ratio at the center of the dust crescent is ∼1.7. This is very close to the minimum gas-to-dust ratio allowed by theoretical models, which account for the dust feedback on the gas dynamics. Indeed, as the gas-to-dust ratio approaches unity, the dust particles, which tend to move at Keplerian velocity, will accelerate the sub-Keplerian gas. As discussed in Fu et al. (2014), this generates an instability that brakes the vortex in smaller dust clumps.

Finally, we note that the concentration of dust particles toward an azimuthal gas pressure bump, e.g., a vortex, depends on the dust Stokes number ${\tau }_{s}$, which can be expressed as (Owen & Kollmeier 2016)

$$\begin{eqnarray}&&{\tau }_{s}\approx \left(\displaystyle \frac{a}{2\,\mathrm{mm}}\right)\left(\displaystyle \frac{1\,{\rm{g}}\,{\mathrm{cm}}^{-2}}{{{\rm{\Sigma }}}_{g}}\right)\left(\displaystyle \frac{\rho }{3\,{\rm{g}}\,{\mathrm{cm}}^{-3}}\right),\end{eqnarray} \tag{ 7 }$$

where a is the size of the dust grains and ρ is the dust density. If we assume $\rho =1.5$ g cm⁻³ and take for the gas density the value at the center of the dust crescent (Table 1), ${{\rm{\Sigma }}}_{g}=1.125$ g cm⁻², we obtain that the dust trapping is the most efficient (${\tau }_{s}=1$) for grains of ∼4.5 mm. Our observations probe the distribution of dust particles with size $a\sim \lambda /2\pi \sim 0.1\,\mathrm{mm}$, where λ is the wavelength of the observation. This implies that observations at longer wavelengths, such as at 3 mm with ALMA, in addition to being more optically thin and better probing the disk density, should show a more compact concentration of dust particles. They might also be able to tell if the dust crescent observed in the HD 142527 disk is a single coherent structure or consists instead of smaller clumps. An even higher dust concentration should be detected at centimeter wavelengths. So far, the only observations of HD 142527 at wavelengths longer than 0.8 mm is a 9 mm continuum image obtained with the Australian Compact Array (ATCA; Casassus et al. 2015). This image suggests indeed that millimeter-size particles are more concentrated than submillimeter dust grains, but the low sensitivity of ATCA observations does not allow the spatial distribution of the larger particles to be studied in detail.