ACCRETION KINEMATICS THROUGH THE WARPED TRANSITION DISK IN HD 142527 FROM RESOLVED CO(6–5) OBSERVATIONS

Image synthesis was performed with a non-parametric least-squares fit to the visibility data (see Appendix B); the resulting model images are labelled "MEM." These "deconvolved" images pick up finer details than the conventional "restored" maps, which are produced by convolving the MEM maps with an ellipical Gaussian called the "clean" beam, which is fit to the "dirty" beam (or point-spread function, PSF). With the addition of a dirty map of the model residuals, the restored maps allow a standard representation of the data, with a single and well defined angular resolution. However, the moments extracted on the "restored" maps (Appendix B) are affected by convolution with the clean beam, which enhances velocity dispersions by aligning different velocity components, with consequences on the intensity maps if extracting moments with Gaussian spectral fits (see Appendix B.3). We thus chose to base our study on the moment maps inferred from deconvolved (MEM) datacubes. A drawback of this choice is that since we are extrapolating power in the Fourier domain, the resolution of the MEM images is variable and depends on the image. Here the FWHM of the MEM PSF varies from 0062 × 0051 for a bright point source, up to ∼50% coarser for fainter extended emission (approximated by a collection of spikes).

The main properties of the continuum-subtracted CO(6–5) data are summarized by the moment maps shown in Figure 1. The CO(6–5) line intensity displays a central decrement so that the minimum intensity is a factor of $\sim 0.25\pm 0.03$ times lower than the average intensity in the brighter ring at a radius of 02. This central decrement is probably related to photodissociation of CO, so that the very central CO(6–5) could be rarefied and broad enough to be optically thin. The more extended emission in CO(6–5) seems to be ascribed to the dust-depleted cavity, with a sharp drop at ∼1 arcsec, corresponding to the radius of the Bright crescent-shaped outer ring seen in the continuum. This sharp drop is absent in CO(3-2), which extends well outside the cavity, so that the CO temperature outside the cavity is probably not high enough to excite J = 6.

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The disk position angle (PA) is defined as the intersection of the plane of a disk with the plane of the sky. For Keplerian rotation in disks with axial symmetry, the velocity centroid maps bear reflection symmetry about the disk PA, and the highest Doppler-shifted emission toward the blue and red are aligned along the PA. In Figure 1, the velocity centroid is more complex than the usual butterfly pattern. It is as if the velocity field had been "twisted" anti-clockwise, which would happen if the disk PA rotated with stellocentric radius r, from −20° east of north outside r ∼ 06, to ∼+60° at r ∼ 025, coincident with the extremes in velocity centroid. Inside 01, the PA appears to rotate further and reaches 110 ± 10°. However, the scattered light shadows from the inner disk show that its PA is −8 ± 5°(Marino et al. 2015).

The CO(6–5) velocity dispersion reaches very high values, especially near the star. Velocity dispersion values above 4 km s⁻¹ are found in the unresolved central beam; the bulk of this dispersion is probably due to flow kinematics. However, values of about 2 km s⁻¹ are also found away from the central beam, which persist after deconvolution. For instance, in Figure 1 the 1σ velocity dispersion in the restored maps, ${\sigma }_{\mathrm{rest}.}$, measured at an offset of ${\boldsymbol{P}}=(+0\buildrel{\prime\prime}\over{.} 2,+0\buildrel{\prime\prime}\over{.} 2)$, is 2.01 km s⁻¹, while the 1σ dispersion extracted from the deconvolved datacubes, ${\sigma }_{\mathrm{mem}}$, still shows a dispersion of 1.78 km s⁻¹. Further tests on the suitability of the deconvolved images as measures of the intrinsic line width are provided in Appendix C.

Beyond 01 from the nominal stellar position, the line profiles appear to be singly peaked, as illustrated in Figure 2. If due to thermal broadening, the CO velocity distribution corresponds to temperatures $T=28{m}_{p}{\sigma }^{2}/k$ in excess of 5000 K, as far out as 05 from the star. Another mechanism for producing the observed line widths is microscopic turbulence. There are, however, hints of line asymmetry, such as shoulders or lack of low-level Gaussian wings, which suggest the presence of multiple velocity flows stratified along the line of sight. However, the significance of these spectral features is not high enough to motivate detailed interpretation.

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Integrated line profiles for CO(6–5) are shown in Figure 3. The total line flux extracted from the restored datacube, using natural weights, and in a circular aperture with a radius of 25, is 70 Jy km s⁻¹. This value is fairly close to the flux density of 80 Jy km s⁻¹ reported by Casassus et al. (2013a) from APEX+CHAMP+ single-dish observations. The double-peaked CO(6–5) profiles obtained with ALMA are typical of Keplerian disks, and are also reminiscent of the CHAMP+ spectrum, given its noise level. However, here the blueshifted peak appears to be fainter than the redshifted peak by ∼20%. This line asymmetry is the opposite of that seen in ¹²CO(2-1) (Perez et al. 2015), but is similar to HCO⁺(4-3) (Casassus et al. 2013c) and the CO isotopologues (Perez et al. 2015). It is likely that the lower-J ¹²CO is absorbed by the diffuse screen at redshifted velocities (Casassus et al. 2013a). The origin of the blueshifted decrement in species not affected by the diffuse molecular screen is probably related to the anti-correlation with the continuum: in continuum-subtracted maps, the line emission appears to be quenched under the crescent-shaped continuum (Casassus et al. 2013c; van der Plas et al. 2014; Perez et al. 2015), at locations that correspond to blueshifted velocities. The pointing offset invoked by Casassus et al. (2013a) to account for the asymmetric CHAMP+ profile is probably unnecessary given the match in line flux with the interferometer CO(6–5) maps, and given the later finding of the molecular decrements at blueshifted velocities.

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As mentioned in Section 1 the HCO⁺(4-3) and CO(3-2) data previously described in the literature also display deviations from Keplerian rotation with a constant disk orientation. Although the outer disk follows Keplerian rotation with a PA of −20°, inside the cavity the PA joining regions of opposite velocities⁸ rotates with stellocentric distance resulting in "twisted" kinematics (Casassus et al. 2013b). The high velocity⁹ blue and redshifted HCO⁺ are offset by 0.2 arcsec, with a PA of ∼60° (Casassus et al. 2013c), while the outer disk PA is at approximately −20°. Low-velocity filamentary HCO⁺(4-3), within 0.8 km s⁻¹ of systemic, connects the outer disk to the east with the central broad-velocity HCO⁺ (Casassus et al. 2013c), along a PA that coincides with that of the blueshifted signal. A similar but fainter filament may connect with the western outer disk. Interestingly, the peak CO(3-2) intensity is offset from the star, again toward the same direction as the blueshifted HCO⁺. The PA joining the blue- and redshifted velocities is thus ∼60° and common for CO(3-2) and HCO⁺, and approximately orthogonal to the PA of the outer disk.

Such kinematic features, seen as extremes in HCO⁺, and probably also in CO(3-2), are expected in the framework of an additional radial velocity component directed toward the star. In order to impact the observed kinematics, the additional radial velocity component must be comparable in magnitude to the rotation velocity (Casassus et al. 2013b), so close to free-fall (Rosenfeld et al. 2014).

Figure 4 provides a summary of the data in each transition. It is apparent that the coarser beam in band 7, compared to band 9, prevents a detailed study of the kinematics in the central 03. We also see in the deconvolved maps that attempts to trace the CO(3-2) kinematics inside the cavity are thwarted by the absorption from the intervening diffuse cloud in the line of sight to HD 142527 (e.g., Casassus et al. 2013a). Once convolved with the clean beam, the regions affected by the intervening CO cloud are less conspicuous and may lead to an accidental interpolation of the velocity field (as in Rosenfeld et al. 2014). Due to this intervening absorption, the PA in CO(3-2) as a function of radius does not appear to rotate beyond 30°–40° east of north, or ≲60° relative to the outer disk. This shift is close to the value of 54° obtained when the radial velocity component scales as $\sqrt{2}$ times the azimuthal velocity component (i.e., for a radial component close to free-fall).

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In order to reproduce the intra-cavity kinematics, we developed on the accretion flows proposed to account for the HCO⁺ observations (Casassus et al. 2013c), while also taking into account the warp implied by the scattered-light shadows (Marino et al. 2015). We used a parametric model for HD 142527 that fits the spectral energy distribution (see Marino et al. 2015, for a detailed description), with the addition of a radial velocity component corresponding to stellocentric accretion. Emergent specific intensity fields were predicted by transferring the stellar radiation through the model circumstellar material with the radmc3d ¹⁰ package (version 0.39, Dullemond et al. 2015).

The essential elements of our model are depicted in Figure 5. The warp is implemented by rotating the disk as a function of stellocentric radius. The orientation of the outer disk, with a fixed inclination i = 160° and PA = −20° beyond ${r}_{\mathrm{orient}\_\mathrm{out}}=23\;\mathrm{AU}$ (in spherical coordinates), is linked linearly at ${r}_{\mathrm{orient}\_\mathrm{in}}=20\;\mathrm{AU}$ with a non-coplanar inner disk, at a relative inclination of 70° and at PA = −8° (absolute east of north). The orientation of the inner disk is such that its inclination relative to the plane of the sky is $i\sim 133\buildrel{\circ}\over{.} 3$, so that the eastern side is near, while east is far for the outer disk.¹¹ The inner disk probably contains the orbit of the low-mass companion reported by Biller et al. (2012) and Close et al. (2014).

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Radial cuts illustrating our choice of velocity and surface density profiles are shown in Figure 6 inside the cavity. We caution that this parametric model is meant to help the interpretation of the data, and is not derived from a systematic search in parameter space. It is not a dynamically consistent model. Along with the warp, we also add a radial velocity component that accounts for accretion. We connect zero accretion at ∼140 AU to free-fall at 30 AU, with a cubic profile. The free fall halts at 23.3 AU. The tilted inner disk is assumed to be in pure Keplerian rotation, so that inside 20 AU we set zero accretion (a build-up of accreted mass onto the inner disk could then trickle to feed pole-on stellar accretion). The total surface density profile in the gap follows from the assumption of steady-state accretion:

$$\begin{eqnarray*}&&{\rm{\Sigma }}(r)=\displaystyle \frac{{{dM}}_{\star }}{{dt}}/(2\pi {{rv}}_{r}),\end{eqnarray*}$$

as a function of spherical polar radius r, where v_r is the radial velocity component,

$$\begin{eqnarray}{v}_{r} & = & 0\;\mathrm{if}\;r\lt {r}_{g1},\;\mathrm{with}\;{r}_{g1}=20\;\mathrm{AU},\;\mathrm{or}\;\\ {v}_{r} & = & -0.1{v}_{\mathrm{ff}}\;\mathrm{if}\;r\lt {r}_{\mathrm{stop}},\;\mathrm{with}\;{r}_{\mathrm{stop}}=23.3\;\mathrm{AU},\;\mathrm{or}\;\\ {v}_{r} & = & -0.9{v}_{\mathrm{ff}}\;\mathrm{if}\;r\lt {r}_{\mathrm{ff}},\;\mathrm{with}\;{r}_{\mathrm{ff}}=30\;\mathrm{AU},\;\mathrm{or}\;\\ {v}_{r} & = & -0.9{v}_{\mathrm{ff}}\times {\left[\displaystyle \frac{(f\;{r}_{g2}-r)}{(f\;{r}_{g2}-{r}_{g1})}\right]}^{3}\mathrm{if}r\lt {r}_{g2},\end{eqnarray} \tag{ 1 }$$

with ${r}_{g2}=130\;\mathrm{AU}$, and where f = 1.1 is a factor to avoid divergence at r_g2, and

$$\begin{eqnarray*}&&{v}_{\mathrm{ff}}=\sqrt{2{{GM}}_{\star }\times \left(\displaystyle \frac{1}{r}-\displaystyle \frac{1}{f\;{r}_{g2}}\right)}.\end{eqnarray*}$$

We use a stellar accretion rate of ${{dM}}_{\star }/{dt}={10}^{-7}\;{M}_{\odot }$ (Garcia Lopez et al. 2006). The stellar mass is set at $1.8\;{M}_{\odot }$; higher masses produce higher velocities inside the cavity than observed.

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The orientation of the disk is parametrized in spherical coordinates, where the vertical axis ${\hat{z}}^{\prime }$ is the normal to the local disk plane, and where the origin of azimuth ${\phi }^{\prime }$ is the local line of nodes (i.e., the disk PA as a function ${\boldsymbol{r}}$). The azimuthal velocity ${v}_{{\phi }^{\prime }}$ is set to Keplerian rotation ${v}_{{\phi }^{\prime }}={v}_{{\rm{K}}}$, except in regions where $| {v}_{r}| \gt 0$, where we assumed that the specific energy density was close to 0, so that ${v}_{\phi }=\sqrt{{v}_{\mathrm{ff}}^{2}-{v}_{r}^{2}}$ (neglecting the internal energy).

In the warp itself, between ${r}_{\mathrm{orient}\_\mathrm{in}}=20\;\mathrm{AU}$ and ${r}_{\mathrm{orient}\_\mathrm{out}}=23\;\mathrm{AU}$, material continuously connects both orientations. We investigated a range of values for the vertical velocity component in the warp and obtained a closer match to the observations with relatively fast velocities, ${v}_{{\theta }^{\prime }}={v}_{\mathrm{warp}}={v}_{{\rm{K}}}\mathrm{sin}({\phi }^{\prime })$ (see Section 3.2.2).

The temperature profile we adopted is $T=70\;{\rm{K}}$ if $r\lt 30\;\mathrm{AU}$, or

$$\begin{eqnarray}&&T(r)=70{\left(\displaystyle \frac{r}{30\mathrm{AU}}\right)}^{-0.5}\;{\rm{K}},\;\mathrm{if}\;r\gt 30\;\mathrm{AU},\end{eqnarray} \tag{ 2 }$$

which allows us to approximately reproduce the CO(6–5) line profile. Equation (2) is probably not the best representation of the actual CO temperature field. It could be improved by adding structure, especially in the outer disk, where the gas temperatures probably flatten out. Equation (2) results in gas temperatures slightly lower than the dust temperatures in the outer disk, which leads to negatives in continuum-subtracted data. These absorption features appear to be necessary to account for the decrements seen in the molecular-line in the outer disk, and which are discussed in a companion paper (Casassus et al. 2015, see also Section 3.2.1). These temperatures are also well below the dust temperatures in the closer-in regions. If we impose thermal equilibrium between both solid and gas phases, the predicted flux densities soar an order of magnitude above the observations.

Close to the star, CO is probably photodissociated. The line intensity of CO(6–5) appears to display a decrement inside 02, which we accounted for with a Gaussian taper of the gas abundance inside 30 AU, with a $1\sigma$ width of 5 AU.

3.2.1. Adopted Abundance Fields and Depth of the Cavity

We adopted a nominal H₂/¹²CO ratio ${X}_{\mathrm{CO}}={10}^{-4}$, and the following molecular abundances relative to H₂ (no selective photodissociation was required). For ¹³CO, we used the ISM isotopic abundance for ¹²C/¹³C of 76 (Stahl et al. 2008), multiplied by ${X}_{\mathrm{CO}}$. For C¹⁸O, we proceeded as for ¹³CO, but with an ISM isotopologue abundance for C¹⁸O/¹²CO of 500 (Wilson & Rood 1994). For HCO⁺, we used a default value for the HCO⁺ abundance relative to H₂ of 10⁻⁹ (somewhat lower than observed in molecular cloud cores and comparable to values inferred in other disks, Wootten et al. 1979; Teague et al. 2015).

After smoothing to the resolution of the deconvolved models, Figure 7 shows that the accreting warped disk model qualitatively reproduces the basic properties of the cavity seen in the available molecular tracers. The model is in agreement with the non-detection of ¹³CO and C¹⁸O inside the gap. Both in band 6 (Perez et al. 2015) and band 7 (Fukagawa et al. 2013), the ¹³CO and C¹⁸O datacubes do not show any sign of either twisted kinematics, a central peak, or of the gap-crossing filaments. The CO isotopologue data display plain Keplerian rotation, without signal inside ∼90 AU.

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The decrements under the crescent-shaped continuum, previously reported by Casassus et al. (2013c), are a natural feature of the predictions. In continuum-subtracted images, and with our gas temperature prescription, the gas effectively acts as a cool foreground (Casassus et al. 2015).

3.2.2. Central Beam

The warp inside the cavity of HD 142527, i.e., the continuous change in inclination at some specific radius, should significantly impact the observed kinematics. For instance, given the orientation implied by the scattered light shadows (Marino et al. 2015), the blueshifted flows to the north should suddenly shift to red as the inclination changes sign, at the radius where the far side becomes the near side. Interestingly, as illustrated in finer detail in Figure 8(a), the observed centroid map indeed has structure very close to the central star, well inside the central beam. Within ∼025, the "twist" in PA, i.e., the rotation of the axis joining blue- and redshifted velocities, appears to dwell at ∼40°, and thus is offset by ∼60° from the outer disk PA, as expected for a radial velocity component that has reached close to free-fall values while also keeping in near-Keplerian rotation. Indeed, at a given stellocentric radius, in the presence of a radial velocity component that is $\sqrt{2}$ times the azimuthal component, the peak line-of-sight velocity is offset from the disk PA by ∼546. However, inside 01, the PA joining blue and redshifted velocities appears to reach 110 ± 10°.

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The extreme in PA rotation in the inner 01 cannot be accounted for by free-falling material that is also close to Keplerian rotation. This can instead be understood as the halt of free-fall inside a warped structure, as the blueshifted flows to the north–west (11 hr) suddenly Doppler-flip into red closer to the star, where the inclination crosses the plane of the sky (the far side turns near). After smoothing to the resolution of the deconvolved MEM datacubes, we obtain an approximate match to the velocity field for an abrupt warp connecting the inner disk at 20 AU with the orientation of the outer disk at 23 AU, as shown in Figure 8(b). The warp orientation must align to that of the inner disk as far out as 20 AU, to account for the shift in declination at systemic velocities, which covers almost 02 when crossing the stellar position.

In a continuous warp, material must flow from one plane to the other and be accelerated in the transition. Thus, inside a warp, there should be a velocity component orthogonal to the plane of the disk ${v}_{\mathrm{warp}}$. This component is probably limited by the Keplerian velocity v_K around the central star. For instance with ${v}_{r}=0.1\;{v}_{\mathrm{ff}}$ and ${v}_{\theta }={v}_{\mathrm{warp}}={v}_{{\rm{K}}}$ in spherical coordinates, the warp's radial width must be at least ∼3 AU to connect one orientation to the other. Interestingly, the inclusion of ${v}_{\mathrm{warp}}$ approximates better the observed velocity centroid, with fairly point-symmetric high velocity ridges connecting the cavity "twist" with the inner disk, corresponding to the loci of bluest and redest velocities in Figure 8(b). These ridges are missing in the model without ${v}_{\mathrm{warp}}$ (Figure 8(d)).

In order to further illustrate the model, we have included a radiative transfer prediction if the parametric model was viewed closer to edge-on, rather than face-on. Figure 9 shows the equivalent of Figure 8, for the case where the disk has an inclination of 66°. Since our adopted temperature field results in gas temperatures cooler than the continuum in the outer disk, in these edge-on predictions, the molecular line moments taken on the continuum-subtracted data are more strongly affected by extended negatives. Therefore, for the close to edge-on predictions, we have chosen not to subtract the continuum.

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The CRIRES observations by Pontoppidan et al. (2011) assign bright rovib CO to an inner disk, with similar inclination as the outer disk but offset in PA, at 61 ± 3°—thus, within uncertainties coincident with the direction of the high-velocity HCO⁺. The total line widths in CO(v = 1-0) at 4.67 μm, at zero-intensity, are close to ∼40 km s⁻¹ (Pontoppidan et al. 2011). With a spectroastrometric offset of only 0.2 AU, CO(v = 1-0) is either fairly uniform or else confined to the central few milliarcseconds.

We check the astrometric signal of a modified version of our disk model and find it to be in agreement with the spectro-astrometric CRIRES observations. We take the predicted CO(6–5) emission and transform the intensity with an $1/{r}^{\alpha }$ mask to mimic the CO ro-vibrational emission, which traces higher temperatures and emits closer to the star compared to the CO rotational lines. We manually add continuum emission scaled to reproduce a line to a continuum ratio of 1.1, as in the observed rovibrational CO, and convolve with a 0192 FWHM Gaussian to mimic the PSF of the AO-assisted CRIRES observations. After superimposing a 02 arcsec wide slit positioned at 150°, we recover a line profile and spectro-astrometric signal similar in shape and magnitude to that reported by Pontoppidan et al. (2011) when using $\alpha \sim 2.5$.

The orientation of the disk is well known. As explained in Sections 1 and 3.1, the shadows seen in scattered light imply that the inclination of the outer disk is such that the far side lies to the east. The eastern side being brighter in the mid-IR is also in support of this orientation (Fujiwara et al. 2006). In addition, several near-IR spirals have been found that are all consistently trailing (Fukagawa et al. 2006; Casassus et al. 2012; Canovas et al. 2013; Avenhaus et al. 2014), even in their radio extensions into the outer disk (Christiaens et al. 2014). Given this orientation, we can rule out an outflowing disk wind: the velocity component orthogonal to the disk would broaden the lines and preserve reflection symmetry about the outer disk PA, while the radial component in the plane of the disk would twist the kinematics in the opposite direction than observed.

The radial velocity in a warped viscous disk is predicted to be greater than in a flat disk (Pringle 1992), but is not expected to exceed the sound speed ${c}_{s}=(h/r){v}_{{\rm{K}}}$. Supersonic disk inflow is in principle possible in regions of the disk that lose angular momentum rapidly through a magnetized wind, rather than via internal viscous transport, though whether this can occur without equally rapid mass loss (for which there is no evidence in HD 142527) is not clear. Alternatively, the free-fall velocity signal could be a consequence of strong dynamical perturbations. If the low-mass companion detected in the system (Biller et al. 2012; Close et al. 2014) is misaligned to the outer disk in the same way as the inner disk, which is known to be inclined by 70° (Marino et al. 2015), then an observable dynamical impact is highly likely. The alignment of the companion in the plane of the inner disk seems like a natural way to explain the inclination of the inner disk itself. Miranda & Lai (2015) have recently shown that large offsets between the orbital planes of circumprimary disks and the plane of the binary can be stable for several megayears, longer than the expected lifetime of the disk. The origin of the companion and its possibly tilted orbit relative to the outer disk are to be searched for in the context of clustered star formation from a turbulent cloud, for instance through a late accretion episode (as investigated by Bate et al. 2010).

It has recently been shown that such strongly misaligned binary-disk systems can undergo a process dubbed disk tearing (Nixon et al. 2013; Doğan et al. 2015; Nealon et al. 2015), where nodal precession torques induced by the binary produce a warp at the inner edge of the disk. If the disk is unable to communicate the warp efficiently, then the disk will effectively break at some radius ${R}_{\mathrm{break}}$. Annuli of gas then begin to tear off of the inner edge and can precess freely, undergoing self-interaction and angular momentum cancellation causing a subsequent infall of gas driving very high accretion rates (Nixon et al. 2012). In the context of circumstellar disks, Facchini et al. (2013, 2014) show that in the thick-disk regime, where $\alpha \lt H/R$, an inner warp greater than ∼40° will break the disk into distinct planes.

To date, the process of disk tearing has primarily been studied in the thin-disk regime appropriate for black hole accretion, where the dimensionless viscosity parameter is larger than the disk aspect ratio, i.e., $\alpha \gt H/R$ (Nixon et al. 2012, 2013). Nevertheless, it has also been shown to work in the thick-disk regime where $\alpha \lt H/R$ (Nealon et al. 2015), which is more likely to hold true for circumstellar disks like HD 142527.

It is possible to estimate a value for the radius ${R}_{\mathrm{break}}$ at which disk tearing will occur (see Equation (A3) of Nixon et al. 2013) using the parameters of the disk and binary. With appropriate values for HD 142527, we expect that the disk could break at ${R}_{\mathrm{break}}\sim a$, where a is the binary semimajor axis. However, Nealon et al. (2015) found a consistent offset between the estimated minimum value and the true breaking radius in a series of smoothed particle hydrodynamics simulations, by a factor of two to three. Estimates of $a\sim 15\;\mathrm{AU}$ are therefore entirely consistent with a breaking radius of 30 AU, as demanded by our model. However, because this is likely very sensitive to the parameters of the system, a more quantitative comparison of this scenario with the observed data is out of the scope of this paper, requiring the development of targeted numerical simulations.

We also note that while this scenario seems to adequately explain both the inner warp and the free-falling velocities, it does not explain the presence of the ∼130 AU cavity in the system. This should not be surprising, given the large difference in scale between the warp and the cavity (and therefore different timescales associated with physical processes at these radii), but means that the model is not yet a complete description of the system.

The dynamical influence of the low-mass companion on its current orbit will not extend out to the 100 AU scale needed to explain the large extent of the cavity. It is possible, however, that its orbit may have changed over time. The highly inclined orbit of the companion relative to that of the massive outer disk could trigger Kozai oscillations (Teyssandier et al. 2013), with a period of the order of 10⁵ year if the outer disk has a mass of 0.1 M${}_{\odot }$. A Kozai cycle would result in (damped) oscillations between the current inclined circular orbit, and a highly eccentric coplanar orbit, which would perturb the disk out to greater radii. Numerical simulations are needed to determine if such a cycle is possible in HD 142527.

Observationally, we cannot test directly for past coplanar eccentric orbits, as in the Kozai oscillations, but we can instead look for other mechanisms that could account for the clearing, such as additional bodies at ∼100 AU. Stringent limits are available (Casassus et al. 2013c), ∼4 M_jup bodies should have been detected unless they are obscured.

An interesting feature of the Cycle 0 HCO⁺(4-3) data is the faint filament crossing the cavity to the east, at low velocites, with perhaps another filament to the west (see Figure 10 for a summary, Casassus et al. 2013c). It is tempting to associate these HCO⁺ features with planet-induced accretion flows, i.e., gaseous streamers due to obscured protoplanets inside the cavity, that feed the faster flows at the disk breaking radius. As the critical density for the excitation of HCO⁺(4-3) is ${n}_{{{\rm{H}}}_{2}}\sim {10}^{6}\;{\mathrm{cm}}^{-3}$, and higher than the CO(3-2) critical density of $\sim {10}^{3}\;{\mathrm{cm}}^{-3}$, in the streamer interpretation the HCO⁺ filaments and high-velocity flows would trace the densest regions of the general accretion flow across the gap, which is also reflected in the "twisted" CO kinematics. If the free-falling accretion is initially fed by planet accretion at $\sim 100\;\mathrm{AU}$, there should be corresponding azimuthal modulations of the H₂ density field. Perhaps this is reflected in the structure of the faint, low-velocity HCO⁺(4-3) inside the cavity.

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An alternative to azimuthal modulations of the H₂ density field in the cavity, is that only the abundance of HCO⁺ is modulated. The tilted inner disk is shadowing the UV radiation required to produce HCO⁺ in the cavity, resulting in HCO⁺ filaments with wide opening angles, as opposed to the thin protoplanetary streamers predicted in hydrodynamic simulations. A problem with this interpretation is that the outer ring is fairly round in HCO⁺, there are no obvious counterparts in HCO⁺ of the scattered-light shadows. Perhaps this reflects a different production chain for HCO⁺ in the outer disk, where it could be driven by charge-exchange with cosmic-ray induced ${{\rm{H}}}_{3}^{+}$.

Details on the instrumental setup are described in a companion article on the continuum emission (Casassus et al. 2015). We used self-calibration to improve the dynamic range of the continuum images. Applying the same gain corrections to the line data also resulted in an improved dynamic range. Before self calibration, the peak signal in the systemic velocity channel reached 0.42 Jy beam⁻¹, in natural weights (beam of $0\buildrel{\prime\prime}\over{.} 30\times 0\buildrel{\prime\prime}\over{.} 25$), with a noise level of 0.08 Jy beam⁻¹, which was clearly dominated by systematics rather than thermal noise. After self calibration, the peak signal increased to 0.67 Jy beam⁻¹, while the rms noise level decreased to 0.04 Jy beam⁻¹.

Continuum subtraction under CO(6–5) was performed with a first-order fit to the continuum in the visibility domain. The subset of channels neighboring the line was then split off into another datafile and subsequently re-sampled in frequency into the LSRK frame.

The CO(6–5) data set is presented in channel maps in Figures 11 and 12, with three-channel bins. We chose to present both the restored image and the underlying MEM model.

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The comparison of the band 9 and band 7 continua reveals a positional offset of ∼0.07 arcsec essentially in the east–west direction (precisely $[-0.063,-0.016]$ in arcsec, along R.A. and decl.). As detailed in a companion article devoted to a multi-frequency analysis of the continuum, including a detailed presentation of the band 9 continuum, this positional offset is measured by cross-correlating the visibilities, but it is also noticeable by visual inspection of the continuum maps (for instance, by blinking the images). With the 0.35 arcsec resolution provided by these Cycle 0 observations in band 7, the center of symmetry of the CO(3-2) velocity centroids coincide fairly well with the position of the central star at the epoch of observations. Hence for the multi-frequency continuum studies we chose to take the band 7 astrometry as reference.

However, at 0.02 arcsec resolutions the center of symmetry of the velocity centroid appears to be offset from the nominal stellar position as given by the default band 7 world-coordinate-system (WCS). This represents an opportunity to improve the astrometry by tying the stellar position with the center of symmetry. We aligned the velocity centroids by applying an offset of $[-0.109,-0.031]$ arcsec to the default band 9 WCS. As illustrated in Figures 1, 8 and 13, the center of symmetry of the velocity centroid coincides with the origin of coordinates, located at the stellar position. The peak velocity dispersion is also close to the origin, but in this case the exact location of the peak depends on the moment extraction algorithm because the signal is spread over a large range in velocity and includes low signal-to-noise channels.

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Details on our image synthesis algorithm uvmem are given in a companion paper on the continuum emission (Casassus et al. 2015). Here we exploit the finer angular resolutions provided by the MEM models, which requires an assessment of their statistical properties.

We start by scaling the observed visibility weights so that they correspond to the observed scatter. In order to preserve the relative values of the calibrated weights, a constant scale factor is applied to all visibilities. This factor is the median of the ratio between the original weights and the dispersion values.

Estimates of the angular resolution of the deconvolved images were obtained as follows. We selected a reference channel, at the systemic velocity and split off the corresponding visibilities into a reference visibility data set. We then estimated the PSF by simulating interferometer observations on a point source, with an identical $u,v$ coverage as the reference visibilities, and with the addition of Gaussian noise, with a dispersion given by the visibility weights. In practice, the point source is a spike, defined on the same canvas as used for the deconvolved images, and whose flux density corresponds to that of the whole observed image. A deconvolved model of these simulated point-source visibilities is then obtained using the same algorithm as for the observations (i.e., uvmem). This deconvolved model represents the PSF of the deconvolution algorithm, with a central source and secondary maxima fainter by a factor of at least 20. An elliptical Gaussian fit to the central peak defines the finest resolution achievable in the deconvolved images, of 0062 × 0051.

Since the maximum-entropy regularization is nonlinear, the uvmem PSF depends on the model. We approximate the case of extended emission by spreading the total flux in a collection of spikes. The "clean" beam in this case varies by up to 50%. So, for the purpose of comparing synthetic radiative transfer predictions with the uvmem model images, we chose a representative resolution of 30% times coarser than the finest PSF.

Monte-Carlo simulations provide estimates of the uncertainties associated with these MEM model datacubes. We added Gaussian noise to the observed visibilities, as given by the visibility weights, and obtained a deconvolved model image with uvmem, with the same settings as for the observations. We then took statistics on 120 realizations, checking that the average datacube satisfactorily converges on the original model datacube without the addition of noise.

In the case of noisy data, the standard approach to extract moment maps by collapsing the velocity axis injects unnecessary noise when the line-of-sight line profiles are much narrower than the spatially integrated line. Rather than collapse the datacubes with standard moments, we extracted moments by restricting the velocity range above a given threshold (which is set to 0 for the restored maps, with thermal noise). For each line of sight, we identify the position of the peak specific intensity. We then search for the first nulls, both toward the red and blue, and extract a spectrum leaving room for a few more channels (two in this case). Last, we take standard moments over this reduced velocity range, and also fit a Gaussian. The resulting moment maps are embellished by median-smoothing with a square 5 × 5 kernel.

In the case of the MEM deconvolved models, the strict positivity requirement forces an intensity floor ${I}_{\mathrm{min}}$, which we take at 1/100 the estimate noise level (in natural weights). We subtracted a posteriori ${I}_{\mathrm{min}}$ from the deconvolved maps. However, the positivity requirement biases the noise, so that velocity dispersions are artificially broad in regions of low signal (such as the outer ring in HD 142527 in CO(6–5)). To account for this, we applied the velocity restrictions described above, with a threshold defined by the rms dispersion of the noise in velocity channels devoid of signal.

The moments maps extracted on the clean, and uvmem datacubes are compared in Figure 13. The details of the centroid map do not depend on the reconstruction. However, the intensity and velocity dispersion maps inside the central beam (so within 02 of the star) result from the superposition of several velocity components.