ALMA Images the Eccentric HD 53143 Debris Disk

In order to quantify the significance of the brightness asymmetry of the HD 53143 disk, we fit both symmetric and eccentric disk models to the ALMA data. We follow the modeling approach first described in MacGregor et al. (2013) and updated for eccentric disks in MacGregor et al. (2017) in order to effectively constrain uncertainties and efficiently explore parameter space. Visibilities are sampled from models of the sky brightness using the galario package (Tazzari et al. 2018) and compared directly to the ALMA visibilities within a Markov Chain Monte Carlo (MCMC) framework using the emcee package (Foreman-Mackey et al. 2013). For the symmetric model, we assume that the disk is radially symmetric and the surface brightness is described by a power law between an inner radius R_in and an outer radius R_out: I_ν ∝ r^−0.5, where the power-law index describes the temperature profile and the surface density is assumed to be constant as a function of radius.

For the eccentric model, we first populate the complex eccentricity space defined by the forced eccentricity and argument of periastron (e_f and ω_f , respectively) and the proper eccentricity and argument of periastron (e_p and ω_p , respectively) following Wyatt et al. (1999). While ω_p is assumed to be randomly distributed from 0 to 2π, e_f , e_p , and ω_f are all left as free parameters. We then compute the true anomaly, f, using the kepler package (Foreman-Mackey et al. 2021), calculate the radial orbital position for each particle, and create a two-dimensional image by binning using the desired pixel scale (0.8 au). By assuming the same r^−0.5 temperature profile as for the symmetric model, we can then determine the flux in each pixel. In order to sample the eccentricity parameter space completely and avoid the impact of shot noise where too few particles can make model images with identical parameters have different χ² values (Kennedy 2020), we use a minimum of 10⁷ particles. Kennedy (2020) also includes a proper eccentricity dispersion in their model of the Fomalhaut disk to try to account for the fact that the apocenter side of the disk appears narrower than the pericenter side. Because the HD 53143 disk does not appear to have this feature, we exclude this extra parameter in our models for simplicity. Similarly, Lynch & Lovell (2022) allow the forced eccentricity to vary with the semimajor axis, which we also do not include here but could impact the derived parameter constraints.

In both models, the vertical density profile of the disk as a function of radius is Gaussian, and the standard deviation is given by the scale height H(r) = hr. Given the resolution of the data, we assume that the aspect ratio h is constant and fit for it as a free parameter. Both models are also normalized to a total flux F_disk = ∫I_ν dΩ and include a point source to describe the detected stellar flux, F_star, and offsets relative to the pointing position in RA and DEC, Δα and Δδ, respectively.

We assume uniform priors for all parameters, although some bounds are applied in order to ensure that the models are physical: F_disk > 0, F_star > 0, 0 < R_in < R_out. To fully explore the parameter space of each model and ensure that all parameters have converged, we use ∼10⁶ iterations (100 walkers, 11,450 and 12,750 steps for the eccentric and symmetric models, respectively). We consider the MCMC converged once the number of steps is more than 50 times greater than the autocorrelation function for each parameter. The one-dimensional marginalized probability distributions for all model parameters appear Gaussian. For the eccentric model, we do note a degeneracy between the forced (e_f , global orbital shape of the disk) and proper (e_p , intrinsic orbital scatter for individual particles) eccentricity.

Table 2 presents the best-fit model parameters for both the symmetric and eccentric models. The symmetric model is unable to reproduce the data without significant stellar offsets, which makes it clear that an eccentric model is required to describe the HD 53143 debris disk. Figure 2 shows the ALMA 1.3 mm data (left panel) along with the best-fit symmetric and eccentric models (top and bottom, respectively) displayed at full resolution (left center) and imaged like the ALMA data (right center). The residuals resulting from subtracting the best-fit model from the data are shown on the right. It is clear "by eye" that the eccentric model does a much better job fitting the structure of the outer debris disk. The symmetric model leaves >3σ residuals on the apocenter (northwest) side of the disk. Both models leave >6σ residuals interior to the disk. These significant residuals are clear evidence that there is an additional structure in this system that we are currently failing to resolve with our observations.

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HD 53143 is the most eccentric debris disk observed to date (e_f = 0.21 ± 0.02) and the second example of a disk in which we have detected apocenter glow. The first conclusive detection of this effect was made using ALMA observations of the Fomalhaut debris disk (e_f = 0.12 ± 0.01; MacGregor et al. 2017). These new observations of HD 53143 show that this effect can be expected in any eccentric debris disk. Because bodies on Keplerian orbits move more slowly at the apocenter than pericenter, theory predicts that we should see a surface density enhancement at this location in the disk (Pan et al. 2016). At shorter infrared wavelengths, grain temperature dominates, producing a brightness enhancement at the pericenter position closer to the star. At longer millimeter wavelengths, observations are more sensitive to surface density and apocenter glow can be seen. Lynch & Lovell (2022) argue that the interpretation from Pan et al. (2016) fails to account for the greater area over which dust is spread at the apocenter position and that debris disks might exhibit either pericenter or apocenter glow at longer wavelengths depending on the resolution of the observations. We note, however, that the spread in orbits at apocenter versus pericenter also depends on the free eccentricity, which is not included in these new models so further investigation is needed to fully explore this effect.

Unlike Fomalhaut, however, HD 53143 appears to have a high proper eccentricity with e_p = 0.11 ± 0.01 compared to e_p = 0.06 ± 0.04 (MacGregor et al. 2017). The proper eccentricity contributes to the overall width of the disk, so the high best-fit e_p of the HD 53143 debris disk could have interesting implications for the structure and dynamics of this system. Future observations with higher angular resolution would better resolve the disk width, confirm this result, and distinguish between different potential sculpting scenarios by searching for azimuthal variation in the disk width. Low e_p ( e _p ≪ e _f , not likely for this system but not completely ruled out by the current observations) generally indicates that particles are on apsidally aligned orbits (i.e., they share the same pericenter position) resulting in a disk that is narrower at pericenter than at apocenter. This "nesting" of orbits is frequently seen in other eccentric planetary systems. For example, the "hot classical" Kuiper Belt objects (KBOs) in our own solar system share a pericenter position determined by resonances with Neptune but with varying eccentricities (e.g., Malhotra 2019), and apsidal alignment is apparent in the Upsilon Andromeda planetary system potentially mediated by a circumstellar disk (Chiang et al. 2001). For HD 53143, our current observations support a scenario where the proper eccentricity is comparable to the forced eccentricity (e_p ∼ e_f ). In this case, the width should be more uniform azimuthally and higher-resolution observations would not see a difference between apocenter and pericenter. A more extreme and varied ratio of widths between apocenter and pericenter is possible if e_p > e_f . Dermott & Murray (1980) propose a combination of self-gravitation, particle collisions, and close packing to produce an extreme pinching of a belt at pericenter. The ring of Uranus has a width of ∼20 km at pericenter compared to ∼96 km at apocenter, implying a width ratio of ∼1:5 (Elliot & Nicholson 1984).

HD 53143 is also notable when compared with other eccentric disks because of its width. Our model fits yield Δa = 19.7 ± 2.5 au, which gives Δa/a ∼ 0.22. Other eccentric debris disks are significantly narrower with Δa/a values of ∼0.10 for Fomalhaut (MacGregor et al. 2017) and ∼0.14 for HD 202628 (Faramaz et al. 2019). Secular perturbations from an eccentric planet predict that the width of an eccentric debris disk should be 2ae_f , and both Fomalhaut and HD 202628 are far narrower than this (Kennedy 2020). Even though HD 53143 is comparably broader, it is still narrower than the theoretical prediction of ∼40 au given the best-fit semimajor axis and forced eccentricity. Kennedy (2020) proposed that narrower debris disks could be created if earlier planet perturbations during the gas-rich protoplanetary disk phase put planetesimals on initially eccentric orbits. This is an intriguing possibility to consider for the HD 53143 system given the presence of a potentially misaligned inner disk (Section 4.2) and vertically scattered small grains (Section 4.3), which both also suggest a previous scattering event or dynamical instability.

Given the significant excess of millimeter emission interior to the outer debris ring, it is clear that there is a source of dust in the inner part of the HD 53143 system. The two 6σ peaks on either side of the star are suggestive of limb brightening from an inclined inner disk. From the image, we can estimate the potential radius and width of this inner ring to be ∼25 au (14) and ∼5 au (03), respectively, given the separation of the two peaks, with a maximum flux density of ∼80 μJy. We attempted to include this inner component in our eccentric model, but results were limited by the data quality. By fixing the disk flux and radial position, we were able to return a fit on the inclination to be $85{^\circ }_{-15}^{+5}$, close to edge on. However, because the current ALMA observations only achieve a resolution of roughly 20 au, this potential inner disk is not well resolved and the geometry is not well constrained. Earlier HST observations detected a circularly symmetric excess, indicating the presence of an inner ring. The inferred geometry is quite different, however, with the inner disk extending from 5–55 au (03–31) and viewed face on (i.e., the inclination of 0°; Schneider et al. 2014). Interestingly, either a face-on or close to edge-on geometry would imply that the inner and outer rings are not aligned.

Another possibility is that dust from the outer ring is being passed inwards. The η Corvi system includes a hot inner dust ring and a cold outer belt that has been previously resolved by ALMA. In order to replenish the inner disk, the material must flow from the outer to the inner disk. Marino et al. (2017) suggest that a stable planetary system could scatter material and feed a close-in collisional cascade. They also discuss the possibility that grains could be scattered inwards by a planet and then transported through the Poynting–Robertson (PR) drag. PR drag generally affects small grains that do not emit efficiently at millimeter wavelengths. However, an abundance of micron-sized grains can still produce emission at longer wavelengths as has been discussed previously for the extended halos observed toward HD 32297 and HD 61005 (MacGregor et al. 2018b). Future observations with the higher spatial resolution are required to definitively show us what mechanism or structure is responsible for the observed inner excess emission in the HD 53143 system and, as a result, reveal the dynamical history of this planetary system.

As discussed above, previous HST coronagraphic imaging did not detect flux along the minor axis of the disk (Kalas et al. 2006; Schneider et al. 2014), which could suggest that the HD 53143 disk might be face on with resonant clumps of emission. New HST STIS observations from program GO-16202 (Ren et al., in prep.) show that this interpretation is not correct and confirm that the disk is in fact inclined relative to the line of sight. However, while the ALMA data are best fit by a thin (h < 0.04) disk, the HST data suggest a significant scale height of h ∼ 0.3. Unlike every other detected inclined debris disk, the HD 53143 disk shows no clear forward-scattering side in any of the previous HST images that match the minor axis of the ALMA observation at visible wavelengths. In fact, it shows the opposite—a likely absence of flux near the minor axes and an enhancement of flux near the ansae. Given the additional constraints from the ALMA observations, the two best physical explanations for this are a semi-inclined disk with either (1) a large scale height and isotropically scattering small grains or (2) a small scale height and density enhancements at the ansae. ALMA observations trace thermal emission from roughly millimeter-sized grains. HST observations trace scattered light from small, micron-sized grains. Thus, if the modeled difference in scale height between these two observations is real, then the dynamics of large versus small grains are different in the HD 53143 disk. One possible explanation is that the small grains are getting stirred and puffed up by a giant planet orbiting within the disk (e.g., Quillen & Faber 2006; Pan & Schlichting 2012). A significant scattering event, potentially involving the migration of giant planets, could also potentially puff up the disk and might also help explain the potential misalignment between an inner and outer disk (see Section 4.2).

The ALMA observations of HD 53143 were executed over eight nights in 2019 March. Although the sensitivity is not high enough to split the data up further, we are able to fit the flux of the star in each of these eight observations separately. The results are shown in Figure 3. Assuming that HD 53143 is a G9V star (temperature ∼5413 K, radius ∼0.86 R_⊙; Fuhrmann & Chini 2015) the expected photospheric flux at 1.3 mm is 33 μJy using a PHOENIX stellar atmosphere model (Husser et al. 2013). In observations 2 and 5–8, the best-fit flux for the star is significantly in excess of this value. The excess is most extreme in observation 6, when the star is >3× brighter than we would expect in quiescence. This transient behavior on roughly hour-long timescales is consistent with stellar flaring, which has been observed from several M dwarf stars (MacGregor et al. 2018a, 2020).

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Serendipitously, the Transiting Exoplanet Survey Satellite (TESS) observed HD 53143 simultaneously with our ALMA observations (the light curve is shown in gray in Figure 3). Although no significant flares are apparent, the periodic variations in brightness are indicative of spot modulation. We expect that millimeter emission is similar to FUV in that it traces particle acceleration in flares, while TESS traces the resulting photospheric heating (MacGregor et al. 2020). It is notable that stars observed to flare in the FUV (and therefore presumably in the millimeter) sometimes have no flares in the TESS bandpass (Loyd et al. 2020). Similarly, Williams et al. (2014) suggest that radio-loud dwarfs may be explained by constant low-level particle acceleration without producing heating in other bands. Because of its extreme southern decl., HD 53143 is actually near the continuous viewing zone for TESS and was observed in 14 additional sectors. We use a Lomb–Scargle periodogram to determine the rotation period for the star to be 9.6 ± 0.1 days. The rotation–age relation for a G9/K0 dwarf in Curtis et al. (2019) gives 10 days as the expected rotation period at 1 Gyr, although some K0 dwarfs with 10 day periods are as young as 670 Myr. This is now the best age determination for HD 53143. The previous estimate was slightly higher at 1.1 ± 0.13 Gyr derived using ROSAT X-ray observations and the stellar-activity–rotation relationship (Pizzolato et al. 2003).