ALMA Detection of Extended Millimeter Halos in the HD 32297 and HD 61005 Debris Disks

Figure 1 shows our new ALMA 1.3 mm continuum images of HD 32297 (left) and HD 61005 (right) overlaid as contours on the previous HST STIS coronagraphic images of optical scattered light from Schneider et al. (2014). With robust = 0.5 weighting, the synthesized beam size is 076 × 051 (100 au × 68 au at 133 pc, position angle = −65°) and the rms noise is 14 μJy beam⁻¹ for HD 32297. For HD 61005, the synthesized beam size is 049 × 043 (18 au × 16 au at 36.6 pc, position angle = −71°) and the rms is comparable, 13 μJy beam⁻¹.

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For both sources, the millimeter continuum emission aligns well with the orientation of the disk major axis seen in the scattered light images. The HST images for these two disks are characterized by broad, wing-like structures extending to the northwest and southeast of the disk major axis for HD 32297 and HD 61005, respectively. While we do not detect such large wing structures for either source in our ALMA images, both do show indications of some extended emission (seen in the 3σ–12σ contours) beyond the disk ansae (the bright peaks seen on either side of the star that are characteristic of limb brightening from an edge-on, optically thin disk), which we interpret as an outer halo.

The presence of significant millimeter emission at large stellocentric distances is atypical for debris disks, most of which appear sharply truncated at an outer radius. For HD 61005, the extended halo emission matches well with the outer scattered light that is along the disk midplane. The structure of the halo is somewhat less apparent by eye for HD 32297, given its much larger distance (113 pc compared to 36.6 pc for HD 61005) and thus lower resolution. Despite this, these new ALMA images indicate that both the HD 32297 and HD 61005 debris disks are best characterized by a two-component model with (1) a planetesimal belt characteristic of most millimeter observations of debris disks and (2) an additional outer halo extending ∼2''–4'' radially.

We model the ALMA 1.3 mm continuum observations of both HD 32297 and HD 61005 with an optically thin, geometrically flat, axisymmetric belt model. In order to draw comparisons between the two systems and because their scattered light and millimeter images show similar structures, we adopt the same model for both disks. Model fits with only a single power-law or Gaussian belt component (as we have used previously for other debris disks including AU Mic and Eridani; see MacGregor et al. 2013, 2015) left significant residuals, most notably in the outer regions of the disk beyond the ansae. We interpret these residuals as evidence for an outer halo component not accounted for by simple models with symmetric inner and outer edges. Motivated by this apparent two-component structure of the ALMA continuum images (Figure 1) of HD 32297 and HD 61005, we adopt a parametric model with a radial temperature profile, T ∝ r^−0.5, and a surface density profile described by a broken power law with ${\rm{\Sigma }}\propto {r}^{{x}_{1}}$ for ${R}_{\mathrm{in}}\lt r\lt {R}_{\mathrm{halo}}$ (within the planetesimal belt) and ${\rm{\Sigma }}\propto {r}^{{x}_{2}}$ for ${R}_{\mathrm{halo}}\lt r\lt {R}_{\mathrm{out}}$ (within the halo). A schematic of the model surface density distribution is shown in Figure 2.

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In our model fits, the inner radius of the planetesimal belt, R_in, the outer radius of the planetesimal belt or inner radius of the "halo," R_halo, and the outer radius of the halo, R_out, are all free parameters. We fit for the flux of the planetesimal belt, F_belt, and halo component, F_halo, independently, with the total flux density normalized to ${F}_{\mathrm{tot}}={F}_{\mathrm{belt}}+{F}_{\mathrm{halo}}=\int {I}_{\nu }d{\rm{\Omega }}$. We assume that the surface density profile of both components is continuous such that ${{\rm{\Sigma }}}_{\mathrm{belt}}={{\rm{\Sigma }}}_{\mathrm{halo}}$ at R_halo. It is possible that the surface density profile could instead be discontinuous, which we do not consider here. Adding a discontinuity introduces an additional model parameter, and the continuous model fits demonstrate that this is not necessary. In addition, we fit for the belt geometry, namely, the inclination, i, and the position angle, PA. Although we explored more complicated models that allowed for different surface density profiles, gaps between the belt and halo components, or multiple rings, they did not yield substantially different results. In principle, other two-component parametric profiles, such as an asymmetric Gaussian, could be fitted to these data. We choose a broken power law as the simplest model justified by the sensitivity and resolution of our current data set.

To obtain best-fit values and uncertainties for all parameters, we adopt our previously described approach (e.g., MacGregor et al. 2013) and fit directly to the millimeter visibilities within a Markov Chain Monte Carlo (MCMC) framework making use of the emcee package (Foreman-Mackey et al. 2013). We compute synthetic visibilities for each model using the Python package vis_sample⁹ and then calculate a χ² likelihood function, $\mathrm{ln}{ \mathcal L }=-{\chi }^{2}/2$, to compare with the data. In order to fully explore the posterior probability distribution of the data conditioned on the model, we use 10⁶ iterations (100 walkers and 10,000 steps each). To check for convergence, we compute the Gelman–Rubin statistic (Gelman & Rubin 1992) and ensure that $\hat{R}\lt 1.1$ for all model parameters. We assume uniform priors, with limits that ensure each model is physical: F_belt, F_halo, F_tot > 0 and 0 < R_in < R_halo < R_out.

The best-fit parameter values and uncertainties for our model fits to the ALMA data of both HD 32297 and HD 61005 are presented in Table 2. Both models provide reasonably good fits to the data with reduced χ² values of 1.32 and 1.61, respectively. Figure 2 shows the ALMA 1.3 mm continuum image, the best-fit model at full resolution (pixel scale of 003 = 4 au for HD 32297 and 1 au for HD 61005), the best-fit model imaged like the data with no noise, and the resulting imaged residual visibilities for HD 32297 (top) and HD 61005 (bottom). Although the best-fit models reproduce the bulk structure of both sources, some significant residuals are clearly seen. For HD 32297, a 4σ residual peak is present on the northwest side of the disk major axis, on the same side as the swept-back wings seen in scattered light images. We have chosen not to fit for vertical structure, given the moderate resolution of both data sets; there is no evidence that either disk is resolved in the vertical direction. However, we note that given this choice, the residual emission from HD 32297 probably biases our model fits, pulling the best-fit value for the outer radius farther away from the star (see Section 4.1.1 for further discussion). For HD 61005, residual emission (∼4σ) is evident along the disk major axis between the disk ansae and the central star, with an 8σ peak located ∼05 northeast of the stellar location (and present in all individual observations). We cannot yet confirm whether this peak is also evident in scattered light images, since it lies at the edge of the HST STIS inner working angle (∼04 ∼ 14 au). Both the Gemini Planet Imager (GPI) and SPHERE have a small-enough inner working angle to provide a direct comparison, and indeed, published SPHERE images show evidence for a brightness asymmetry (Olofsson et al. 2016). Since residual emission is seen on both sides of the disk, one possibility is that this system contains an inner ring at ∼18 au (05 at a distance of 36.6 pc) that remains unresolved in our observations. Multiple groups have modeled the spectral energy distribution (SED) of HD 61005 and concluded that there is strong evidence for an additional warm component in the system (e.g., Morales et al. 2011; Ballering et al. 2013; Ricarte et al. 2013; Chen et al. 2014; Olofsson et al. 2016). As yet, we do not have direct imaging evidence for this claimed inner belt. Additional observations with higher resolution at both millimeter and near-infrared wavelengths are needed to confirm the nature of this residual feature seen in our new ALMA image.

We can also examine the quality of our model fits by looking at the deprojected visibilities. Figure 3 shows the real (top) and imaginary (bottom) 1.3 mm visibilities deprojected using the disk geometry obtained from our model fits and averaged in concentric annular bins of 10 kλ in deprojected (u, v) distance (${{ \mathcal R }}_{{UV}}$) for HD 32297 (left) and HD 61005 (right). The best-fit broken power-law models (solid blue line) agree very well with the data for R_UV < 150 kλ, showing the characteristic peak and null of an annular belt of emission. The data diverge from the models slightly at larger (u, v) spacings, which could indicate the need for a more complicated, non-axisymmetric emission model. For comparison, a Gaussian model fit to the data is shown as the dashed red line. By eye, this simple model provides a poor fit to the real visibilities (especially in the first null and second peak of the visibility function from 50 to 250 kλ), further motivating the need to include an additional component. The imaginary visibilities provide the best probe of non-axisymmetric structure (see the discussion in MacGregor et al. 2015). In the case of an axisymmetric belt, the imaginary visibilities are expected to be uniformly zero. For both HD 32297 and HD 61005, the imaginary visibilities instead show some low-amplitude structure that again hints at a non-axisymmetric disk structure not resolved by our current observations.

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In addition to continuum dust emission, we also detect ¹²CO J = 2–1 gas emission from the HD 32297 system. Figure 4 displays the moment (left) and channel maps (right), both of which show a clear velocity gradient that is indicative of rotation around the central star. In the moment maps, the velocity-integrated intensity (zeroth moment) has been overlaid as contours on the intensity-weighted velocity (first moment). The central velocity in the barycentric frame is 20.6 ± 0.3 km s⁻¹, consistent with the measured stellar radial velocity of ∼23 km s⁻¹ (Torres et al. 2006). Converting to the LSRK frame, which accounts for the peculiar motion of the Sun, yields a central velocity of 5.3 ± 0.1 km s⁻¹. The channel maps show only the central nine channels in which emission is clearly detected above 3σ. The rms noise with robust = 0.5 weighting is 1.0 mJy beam⁻¹. The peak and integrated intensity are 0.28 ± 0.003 Jy beam⁻¹ and 1.02 ± 0.01 Jy km s⁻¹ = 7.91 ± 0.08 × 10⁻²¹ W m⁻², respectively, determined over the region above 3σ in the zeroth moment map. No ¹²CO emission was detected from HD 61005 in the earlier Cycle 1 data, and Olofsson et al. (2016) placed an upper limit on the CO gas mass assuming local thermodynamic equilibrium (LTE) of 7.7 × 10⁻⁷ M_⊕ (scaled to the new Gaia distance; see Section 1) for optically thin gas using these archival observations. In contrast, Kral et al. (2017) predicted a CO mass for HD 61005 in non-LTE of 1.8 × 10⁻⁶ M_⊕.

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For HD 32297, we can calculate the total mass of CO probed by the J = 2–1 line transition (denoted by the subscript "21" in the following equation) for optically thin line emission in LTE:

$$\begin{eqnarray}&&{M}_{\mathrm{CO}}=\displaystyle \frac{4\pi }{h{\nu }_{21}}\displaystyle \frac{{F}_{21}{{md}}^{2}}{{A}_{21}{x}_{2}}.\end{eqnarray} \tag{ 1 }$$

Here, F₂₁ = 7.91 × 10⁻²¹ W m² is the integrated flux density of the line, m is the mass of the CO molecule, d = 133 pc is the distance to the source, h is Planck's constant, ν₂₁ = 230.538 GHz is the rest frequency of the line, A₂₁ = 6.91 × 10⁻⁷ s⁻¹ is the Einstein A coefficient (Müller et al. 2005), and ${x}_{2}={N}_{2}/{N}_{{\rm{tot}}}$ is the fractional level population of the J = 2 rotational level (N₂) relative to the total CO population (N_tot) evaluated at a characteristic temperature of 30 K. This approach yields a total CO mass of M_CO = 4.32 × 10⁻⁴ M_⊕. If the CO were primordial and therefore accompanied by H₂, and assuming the canonical CO/H₂ ratio of 10⁻⁴ typical for the ISM, the total mass of molecular hydrogen in HD 32297 would be ∼4.3 M_⊕.

We have made two significant assumptions in our analysis of the ¹²CO emission from the HD 32297 debris disk, which may need to be reevaluated: (1) the gas is optically thin and (2) the disk is in LTE. We can estimate the optical depth of the J = 2–1 line from the 3D data cube following Matrà et al. (2017) and again assuming LTE:

$$\begin{eqnarray}&&{\tau }_{\nu }=\displaystyle \frac{{d}^{2}{F}_{21}}{{A}_{21}{\rm{\Delta }}\nu {\rm{\Delta }}A}\left(\displaystyle \frac{{x}_{1}}{{x}_{2}}{B}_{12}-{B}_{21}\right),\end{eqnarray} \tag{ 2 }$$

where d is the distance, F₂₁ is the same as above, Δν is the line width, ΔA is the area of the emission on the sky along the line of sight (equivalent to the area of the 076 × 051 synthesized beam), x₁ and x₂ are the fractional populations of the lower and upper transition levels, and A₂₁, B₁₂, and B₂₁ are the Einstein coefficients. To determine the fractional level populations, we assume a kinetic temperature of 30 K, appropriate for a belt at ∼80 au. From this calculation, we obtain a peak optical depth of 0.3, reasonably consistent with optically thin emission. However, previous observations of gas in debris disks derive low excitation temperatures (e.g., Kóspál et al. 2013; Flaherty et al. 2016; Hughes et al. 2017), suggesting that the assumption of LTE might not be appropriate. For non-LTE, a detailed radiative transfer model (e.g., the Line Modeling Engine or LIME; Brinch & Hogerheijde 2010) would be required to obtain accurate gas masses.

To place our new ALMA results into context, we compare our best-fit model structure and geometry for the HD 32297 and HD 61005 debris disks with previous imaging studies at shorter wavelengths. Optical scattered light observations trace small, micron-sized grains rather than the larger, millimeter-sized grains we expect to dominate emission at ALMA wavelengths. Comparing the disk geometry at these complementary wavelengths reveals the distribution of grain sizes within these disks. In all of our model fitting, we have adopted the new Gaia distances (discussed in Section 1). Thus, for the purposes of making a consistent comparison between our ALMA results and previous scattered light observations which assumed the Hipparcos distance, we have scaled all previous determinations of radii for both disks to the new Gaia distances.

4.1.1. HD 32297

4.1.2. HD 61005

Since the wing-like structures of the HD 32297 and HD 61005 debris disks have previously only been seen in scattered light images, discussions of their origin have centered on mechanisms that affect predominantly small, micron-sized grains. The millimeter-sized grains that dominate emission at ALMA wavelengths are expected to closely trace the location of the parent bodies in the disk. Thus, we have typically assumed that these large grains should not populate extended halos. Few previous observations have challenged this assumption, with the exception of Marino et al. (2016), who detected low-level extended emission from HD 181327, a face-on debris disk, which they interpreted as either a halo or unresolved second ring. If the population of larger grains in HD 32297 and HD 61005 can be more extended, as our new ALMA observations suggest, the mechanisms invoked to produce the morphology of these disks must be reevaluated. In this section, we present several potential mechanisms and discuss their applicability to millimeter grains.

It is possible that the millimeter emission detected in the halo components of HD 32297 and HD 61005 could result from an abundance of micron-sized grains instead of millimeter-sized grains. To assess the likelihood of this scenario, we can estimate the mass of small grains needed in the halo to account for the observed millimeter flux. For optically thin dust emission, the dust mass is ${M}_{\mathrm{dust}}={F}_{\nu }{D}^{2}/({\kappa }_{\nu }{B}_{\nu }({T}_{\mathrm{dust}}))$, where F_ν is the flux density, D is the distance (133 pc for HD 32297, 36.6 pc for HD 61005), κ_ν is the dust opacity, and B_ν is the Planck function at the dust temperature, T_dust. The main source of uncertainty in this calculation is the dust opacity. For millimeter-sized grains, a commonly used value in the literature is κ_ν = 2.3 cm² g⁻¹ at 1.3 mm (Beckwith et al. 1990). In comparison, Pollack et al. (1994) determined a dust opacity of 7.9 × 10⁻³ cm² g⁻¹ for their 300 μm radius composite (50%) grains and 4.4 × 10⁻³ cm² g⁻¹ for 3 μm grains with the same composition, several orders of magnitude smaller. In order to be able to compare to literature values for other debris disk systems, we adopt the typical value of 2.3 cm² g⁻¹ in our calculations for millimeter-sized grains in the planetesimal belt and 1.3 cm² g⁻¹ for micron-sized grains in the halo, determined using the same ratio between small and large grains as the Pollack et al. (1994) values. These values are similar to those shown in Andrews (2015) for grains that are a mixture of amorphous silicates, carbon, and vacuum with a filling factor of 0.5. We note, however, that if we instead used the Pollack et al. (1994) values, our calculated dust masses would be significantly higher.

To obtain an estimate for the dust temperature, we assume radiative equilibrium and use the radial location from our best-fit models. Since small grains are likely hotter than the blackbody equilibrium temperature, we adopt a simplified emission efficiency, ${Q}_{\lambda }=1-{e}^{-}{(\lambda /2\pi a)}^{-\beta }$, where a is the grain size and β is the power-law index of grain emission efficiency at long wavelengths, which we assume to be 0.7, comparable with measurements from other disks around main-sequence stars (Williams et al. 2004). For HD 32297, the best-fit inner edge of the planetesimal belt is 78.5 ± 8.1 au and the start of the halo component is 122 ± 3 au, which gives dust temperatures of ∼47 K and ∼38 K for each component, respectively. The total flux density of the HD 32297 planetesimal belt is 3.04 ± 0.21 mJy, which yields a total mass of millimeter-sized grains of 0.57 ± 0.07 M_⊕. The halo component has a total flux density of 0.63 ± 0.26 mJy and a total mass of micron-sized grains of 0.29 ± 0.06 M_⊕. For HD 61005, the planetesimal belt inner edge is at 41.9 ± 0.9 au and the halo component starts at 67.0 ± 0.5 au, implying dust temperatures of ∼37 K and ∼29 K, respectively. The total flux density of the planetesimal belt is 4.82 ± 0.29 mJy, yielding a total mass of millimeter-sized grains of 0.088 ± 0.010 M_⊕, and the total flux density of the halo is 1.54 ± 0.48 mJy for a mass of micron-sized grains of 0.070 ± 0.012 M_⊕. We can then calculate the ratio of halo dust mass to planetesimal belt dust mass to be 0.51 and 0.79 for HD 32297 and HD 61005, respectively, a significant fraction for both systems.

Recent work has shown that such high opacities may be unrealistic for micron-sized astro-silicate grains in the Rayleigh regime (Kataoka et al. 2014). If we assume a much lower opacity of 10⁻³ cm² g⁻¹, the implied mass fraction of the halo compared to the planetesimal belt is instead 800 and 500 for HD 32297 and HD 61005, respectively. Mass ratios of 0.5–800 (the full span of the opacity values we have considered here) are highly unphysical and inconsistent with collisional evolution models. Thus, it is unlikely that a large-enough mass of such grains will build up to explain the observed millimeter fluxes, disfavoring any proposed mechanisms that operate preferentially on small grains. A population of larger bodies with longer collisional lifetimes and higher opacities is needed in the halo of both disks.

One mechanism that operates predominantly on small grains and that has been discussed extensively in the literature (e.g., Artymowicz & Clampin 1997; Debes et al. 2009; Maness et al. 2009; Pástor 2017) is interactions with the local ISM, in which disk grains interact with gas in an ISM cloud and are subsequently blown out due to gas drag or ram pressure stripping. Millimeter grains are not expected to feel a significant effect from interactions with the ISM. If the grains are highly porous as indicated for some debris disks (e.g., AU Mic; Graham et al. 2007), it is possible that ISM interactions could still play a role, but further investigation would be required to better evaluate this scenario. It has also been suggested that the observed halos could result from a density enhancement of small grains due to a recent massive collision, as has been invoked previously to explain asymmetric structure in the HD 15115 (Mazoyer et al. 2014) and β Pictoris (Dent et al. 2014) debris disks. Such an event would likely produce an asymmetric distribution of small grains and is expected to be transient (lasting for ∼1000 orbits or a few Myr at a radius of ∼50 au; Jackson et al. 2014), neither of which is characteristic of the HD 32297 and HD 61005 systems.

Interactions with massive planets are often invoked to explain observed disk structures, including asymmetries, warps, and offsets, and are able to sculpt both small and large grains. To date, there are no detected planets in either the HD 32297 or HD 61005 systems. However, scattered light imaging of both disks shows brightness asymmetries that could be indicative of eccentric structure. Currie et al. (2012) reported that the southwest side of the HD 32297 debris disk is 50%–100% brighter than the northeast side in Keck/NIRC2 coronagraphic images, which is mirrored in the early CARMA image at 1.3 mm (Maness et al. 2008). HST NICMOS and ACS observations of HD 61005 also show a brightness asymmetry, with the northeast side of the disk nearly twice as bright as the southwest (Hines et al. 2007). VLT NaCo (Buenzli et al. 2010) and SPHERE (Olofsson et al. 2016) observations of HD 61005 show an offset of the disk center to the west of the stellar position along the disk major axis, giving an eccentricity for the disk of e = 0.045 ± 0.015 and e ∼ 0.1, respectively. The significant residuals that we see in our new ALMA observations (see Section 3.2 for discussion) further support the claim that the HD 61005 debris disk may be asymmetric. These ALMA observations do not detect the central star or any asymmetry between the two disk ansae for either HD 32297 and HD 61005, which would be required to place strong constraints on any disk eccentricity. Without detecting the star, we cannot determine whether there is an offset between the stellar position and the disk centroid. Without detecting a brightness asymmetry, we cannot make any claims of pericenter or apocenter glow. In an eccentric disk, the pericenter side of the disk is closer to the star and as a result glows more brightly at shorter wavelengths, producing pericenter glow. At longer (millimeter and radio) wavelengths, the apocenter side of the disk appears brighter due to a surface density enhancement (Pan et al. 2016; MacGregor et al. 2017). We did not attempt to model such a brightness asymmetry here, because it is not apparent in the residuals resulting from our simpler model. In principle, the argument of pericenter is unconstrained by these observations; the pericenter of the disk could be located along the observed disk major axis or be projected along the line of sight.

To date, multiple models of secular perturbation by a planet have been proposed to explain the unusual morphology of the HD 32297 and HD 61005 debris disks. Esposito et al. (2016) considered a planet interior to the HD 61005 disk with an eccentricity of at least 0.2 and were able to produce models that exhibit the same features as scattered light observations. A range of possible semimajor axes and masses are allowed, from an Earth-mass planet farther from the star at 35 au to a Jupiter-mass planet close-in at 5 au. Lee & Chiang (2016) constructed a more generalized debris disk model in which a possibly eccentric planet secularly perturbs a narrow ring of parent bodies, producing small dust grains that are thrown outwards via stellar radiation pressure. The resulting scattered light disk morphology depends on several factors, including the planet eccentricity, disk inclination, and whether or not the dust grains are on apsidally aligned orbits. By varying these parameters, they are able to qualitatively reproduce the observed morphologies of both HD 32297 and HD 61005. To produce the "moth"-like shape of HD 61005, a highly eccentric planet (e ∼ 0.7) is needed along with grains on orbits that are apsidally aligned with the parent ring and with their apoastra directed toward the observer. The double wings of HD 32297 can be produced by a similar model, but with dust grains only launched at the parent body periastra. Both of these models treat only the small grains that dominate scattered light images, but their results could be extended in order to compare to millimeter images. Maness et al. (2009) discussed a slightly different process by which a planet could perturb the orbits of disk grains over time, slowly forcing them to have high orbital eccentricities and inclinations. It is also possible that an exterior planet could be responsible for sculpting these systems. In the models of Thebault et al. (2014), a planet exterior to an initially narrow ring produces a population of large grains outside of the planet's orbit. Although these grains are eventually removed from the system, their lifetime is long enough to contribute to the optical depth of the disk at large radii.

Our new ALMA observations indicate that millimeter-sized grains are present in the halos of the HD 32297 and HD 61005 debris disks. Since many of the previously proposed mechanisms operate predominantly on small grains, it is likely that interactions with planetary perturbers play a role in generating the wing structures seen at both optical and millimeter wavelengths. In the case of HD 32297, the high mass of gas within the disk may also contribute to the dynamics of the system. Ultimately, observations with higher angular resolution will reveal any asymmetric structure or disk centroid offsets that might be indicative of planetary sculpting in these disks. If an eccentric interior planet really is responsible for shaping these systems, we would expect to see additional substructure in the inner regions of the disk as a result of its gravitational interaction with disk material.

Our model fits constrain the disk radial surface density profile, Σ ∝ r^x, with power-law index x₁ within the planetesimal belt and x₂ for the halo. Both HD 32297 and HD 61005 exhibit a rising surface density profile for the planetesimal belt with x₁ = 2.23 ± 0.61 and 2.87 ± 0.19, respectively. The surface density falls off steeply in the halo as x₂ = −6.20 ± 0.30 for HD 32297 and −5.52 ± 0.14 for HD 61005. Resolved millimeter observations have placed constraints on the surface density gradients of a handful of other debris disks. Notably, a growing population exhibit rising surface density gradients (e.g., AU Mic and Eridani; see MacGregor et al. 2015, 2013). Intriguingly, many of these disks appear radially broad like HD 32297 and HD 61005, which have fractional widths (ΔR/R) of 0.43 ± 0.04 and 0.46 ± 0.01, respectively. For AU Mic, ${\rm{\Delta }}R/R={1.28}_{-0.01}^{+0.13}$, and for Eridani, ${\rm{\Delta }}R/R={0.31}_{-0.13}^{+0.09}$. In comparison, the fractional width of the confined Fomalhaut debris disk is only 0.10 ± 0.01 (MacGregor et al. 2017). Some of these systems may in fact exhibit more complicated radial structures. ALMA observations of the HD 107146 debris disk also indicate a rising surface density gradient, but with multiple concentric rings (Ricci et al. 2015).

Measuring the surface density gradient of debris disks could provide a key observational constraint on the mechanisms operating in these systems to incite collisions. One possibility is that debris disks are "planet-stirred" through the gravitational influence of giant planets interior to the disk (Mustill & Wyatt 2009). Kenyon & Bromley (2002, 2008) discussed an alternative "self-stirred" model in which Pluto-sized bodies (radii ∼1000 km) are produced on the inner edge of the disk and trigger a collisional cascade. The growth time in a disk is proportional to P/Σ, where P ∝ r^3/2 and Σ is the initial surface density. If the initial surface density decreases with radius, as is expected in a primordial disk, the growth time is shorter on the inner edge of the disk. For a disk with total dust mass comparable to HD 32297 and HD 61005, these models predict timescales of tens of Myr to form large bodies on the inner edge of a disk at tens of astronomical units. On the outer edge of the disk (>100 au), the timescale is much longer, ≳1 Gyr. Kennedy & Wyatt (2010) predicted the resulting surface density profile in such a "self-stirred" disk, finding Σ ∝ r^+7/3. The ages of HD 32297 and HD 61005 are estimated to be ∼30–40 Myr. At face value, this could allow enough time for larger bodies to form near the inner edge of the HD 61005 disk at ∼42 au, but is not entirely consistent for HD 32297 with an inner edge nearly twice as far from the star at ∼79 au.

There a few ways to solve this slight discrepancy in timescales. The age of the HD 32297 system is not well constrained. Although stellar kinematics and the high disk luminosity suggest a young age (∼10–20 Myr), evolutionary tracks allow ages up to ∼500 Myr (Rodigas et al. 2014), which may provide more time to form large bodies on the inner edge of the disk. In addition, the recent work by Krivov & Booth (2018) considered the possibility that smaller (a few kilometers to ∼200 km in size) planetesimals could effectively stir debris disks. Such bodies form much more rapidly in protoplanetary disks through pebble concentration than larger Pluto-sized bodies. If large bodies are in fact not needed to incite collisions in debris disks, both the HD 32297 and HD 61005 debris disks could be self-stirred.

Of course, it is possible that an entirely different stirring mechanism may be at work in the gas-rich HD 32297 disk. There is some similarity between the surface density profile of this system and 49 Ceti, a comparable ∼40 Myr old gas-rich debris disk. Resolved ALMA observations of this disk are well fit with a surface density profile that rises with a power-law index of 1.44 in the inner part of the disk between 7 and 68 au, and then falls off with an index of −2.5 out to 215 au (Hughes et al. 2017). High-resolution (sub)millimeter observations of a larger population of gas-rich debris disks are needed to better understand the stirring mechanisms in these systems.

The HD 32297 system is one of three CO-rich debris disks around 30–40 Myr old A-type stars, a group that also includes HD 21997 (A3V, 69.6 pc) and 49 Ceti (A1V, 57.1 pc). Our measured ALMA flux density makes HD 32297 one of the most CO-rich debris disks observed, comparable in integrated line flux to HD 21997 (Kóspál et al. 2013) and 1.5× that of 49 Ceti (Hughes et al. 2017), after accounting for their different distances (see Moór et al. 2017). All three of these systems have a dust belt detected in addition to the observed gas emission. For HD 21997, however, the gas disk appears to have an inner radius closer to the central star than the dust. In HD 32297, the dust and gas seem to be co-located, implying that both are likely created through collisions between the same planetesimals. To illustrate this, Figure 5 (left) shows the ALMA ¹²CO J = 2–1 emission overlaid as contours on the 1.3 mm continuum emission. Unlike the other two systems, HD 32297 is the only one to display millimeter gas and dust emission from an extended halo component. HD 32297 also has the latest spectral type of the group at A5V–A6V (often misquoted in the literature as A0V, see Debes et al. 2009 for further discussion) with a mass of ∼1.7 M_⊙ and luminosity of ∼8 L_⊙, more comparable to the somewhat younger and more gas-poor β Pictoris system (A6V, 19.8 pc, 23 Myr).

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Figure 5 (right) shows the position–velocity diagram for the CO emission observed by ALMA. For reference, the expected Keplerian rotation curve is overlaid as a black dashed line, assuming a stellar mass of 1.7 M_⊙, typical for an A5V–A6V star, and an inclination of 836, the best fit from our continuum modeling. By eye, the rotation velocity of the gas at the peak locations appears to be ±2.5 km s⁻¹ from the systemic velocity, below the ±4.4 km s⁻¹ that is expected from Keplerian rotation for a ring at ∼80 au (using a higher inclination of ∼88°, as suggested by scattered light observations, makes the fit even worse). Although suggestive, this result is marginal given the low spectral resolution of our data. With a channel width of only 1.3 km s⁻¹, the observed velocity difference is only ∼2σ. Intriguingly, sub-Keplerian rotation is also seen in the β Pictoris debris disk. By modeling C i and C ii emission, Cataldi et al. (2018) derived a dynamical mass of 0.8 M_⊙, significantly below the assumed stellar mass of 1.75 M_⊙ (Crifo et al. 1997) but comparable to the dynamical mass derived from Na i emission (Olofsson et al. 2001).

One explanation for the sub-Keplerian rotation in debris disks could be radiation pressure, which acts opposite to a star's gravity, making the star appear less massive. Mid to late A-type stars like HD 32297, however, do not emit significant UV radiation at the absorption wavelengths of CO, so this effect is likely have a negligible direct effect on neutral molecules. In the β Pictoris disk, CO is quickly converted to C and O through photodissociation on timescales of ∼50 yr. Fernández et al. (2006) suggested that these ionized species, which are directly affected by radiation pressure, are coupled into a single fluid through Coulomb interactions. As a result, neutral molecules like CO could also become coupled and experience indirect braking due to radiation pressure. Given their similar spectral types, it is possible a similar explanation could be invoked in the case of HD 32297. An alternative explanation was originally presented in Weidenschilling (1977), where a pressure gradient in a gas disk causes the gas to rotate more slowly than the free orbital velocity. The deviation of the gas velocity from the Keplerian orbital velocity, v_k, is given by ${\rm{\Delta }}v={v}_{k}-{v}_{g}\approx -({\rm{\Delta }}g/2g){v}_{k}$, where $g={v}_{k}^{2}/r$ is the central gravity and ${\rm{\Delta }}g=-{nRT}/\mu r$ is the residual gravity in a reference frame rotating with the gas. Here, n is the power-law index of pressure, $P={P}_{0}{(r/{r}_{0})}^{-n}$, which we take to be 3, R is the gas constant, T is the gas temperature, and μ is the mean molecular weight. Given the expected stellar mass (1.7 M_⊙), gas temperature (30 K), and radius of the HD 32297 debris disk, we estimate the magnitude of this effect to be ∼0.1–0.5 km s⁻¹, which is not large enough to account for the ∼2 km s⁻¹ observed difference in orbital velocity. We note, however, that modifying the pressure gradient and mean molecular weight to account for a primordial or secondary origin of the gas could change this calculation significantly. Although we do not discuss them at length here, two other possible explanations for the observed sub-Keplerian rotation of the gas could include non-uniform self-absorption or a stellar dynamical mass that disagrees with pre-main-sequence models.

Circumstellar gas has been detected previously from the HD 32297 system. Redfield (2007) observed absorption from the Na i D doublet (5895.9242 and 5889.9510 Å) with a column density of log N_{Na i} ∼ 11.4, the strongest Na i absorption measured toward any nearby debris disk. A 3.7σ detection of [C ii] emission at 158 μm was also made with the Herschel PACS Spectrometer (Donaldson et al. 2013). Most recently, Greaves et al. (2016) detected ¹²CO J = 2–1 and tentatively J = 3–2 emission with JCMT SCUBA-2 (taken several years earlier in 2013). Their measured integrated intensity for ¹²CO J = 2–1 is 3.7 ± 0.4 × 10⁻²¹ W m⁻², giving a total CO mass of 1.3 × 10⁻³ M_⊕. This result is 5 × (7σ) higher than our measured ALMA integrated intensity for the same transition of 7.91 ± 0.08 × 10⁻²¹ W m⁻² with a corresponding CO mass of 4.32 × 10⁻⁴ M_⊕. The difference between these two measurements could easily stem from the lower signal-to-noise ratio and resolution of the earlier JCMT observations. However, Greaves et al. (2016) also found a higher velocity for the gas, which implies a 2× difference in the inner radius of the gas. Given this, the CO production rate and location in the HD 32297 disk could be variable on the ∼3 yr timescale between these two observations, with a higher production rate in 2013, although this would be challenging to explain given that the time between observations is much shorter than the orbital timescale for the system.

Given the relative wealth of gas detections from the HD 32297 debris disk, it is clear that this system offers us a unique opportunity to explore the properties of gas in main-sequence circumstellar disks. By combining our determinations of the total gas mass (4.3 × 10⁻³ M_⊕ for CO and 4.3 M_⊕ for H₂, calculated by assuming an ISM-like CO/H₂ ratio of 10⁻⁴ expected only for a primordial system; see Section 3.3) and the total dust mass (0.72 ± 0.13 M_⊕; Section 4.2), we can calculate the gas-to-dust ratio for the HD 32297 debris disk to be 6 × 10⁻⁴ if CO dominates the gas mass (possibly higher if the gas is non-LTE, but still <1) or 6 if H₂ is present in the disk. As expected for an evolved system, the result assuming a primordial disk is significantly below the canonical value for the ISM of ∼100 (Bohlin et al. 1978), but is comparable to recent values determined from surveys of protoplanetary disks in much younger star-forming regions (e.g., Ansdell et al. 2016; Miotello et al. 2017). Both results are also comparable to 49 Ceti, which has a gas-to-dust ratio of either 0.008 or 6, depending on whether CO or H₂ makes the largest contribution to the gas mass, respectively (Hughes et al. 2017). Kóspál et al. (2013) calculated a much higher gas-to-dust ratio for HD 21997 of 300–700. This difference points to a hybrid scenario for HD 21997, where some primordial gas remains in the system, but dust is generated through secondary collisions between planetesimals. For 49 Ceti and HD 32297, where the dust and gas are co-located, it seems more likely that both are created through secondary collisions between icy planetesimals. Indeed, Kral et al. (2017) showed that the mass of CO gas detected around HD 32297 is completely consistent with a secondary origin when considering non-LTE. If this is the case, it may be illustrative to compare the CO-to-dust ratio in HD 32297 with solar system comets; recent results from the Philae lander suggest that the comet 67P/Churyumov-Gerasimenko is more dust than ice with a volumetric ice-to-dust ratio of 0.4–2.6 (Kofman et al. 2015). Additional observations with higher spectral resolution will be critical to confirm the origin of the gas in the HD 32297 system, as well as to examine the somewhat confusing gas dynamics and whether or not the CO production rate is indeed variable.