The Big Sibling of AU Mic: A Cold Dust-rich Debris Disk around CP−72 2713 in the β Pic Moving Group

The star CP−72 2713 was observed with the Multiband Imaging Photometer for Spitzer (MIPS; Rieke et al. 2004) on board the Spitzer Space Telescope (Werner et al. 2004) at 24 and 70 μm on 2008 November 23 (PI: P. Plavchan). Photometry at 24 μm was taken from the Spitzer Enhanced Imaging Products (SEIP) catalog. The photometric uncertainty was computed as the quadratic sum of the instrumental noise listed by the catalog and the calibration error of 4% (MIPS Instrument Handbook¹⁰ ). The SEIP catalog does not include data from the 70 μm channel. Therefore, we downloaded the pipeline-reduced basic calibrated data images (version S18.13.0) from the Spitzer Heritage Archive and used MOsaicking and Point source Extraction (MOPEX; Makovoz & Marleau 2005) to coadd them and correct for array distortions. For further improvement prior to the coaddition, we applied column mean subtraction and time filtering for the images following Gordon et al. (2007). The final image shows a point source close to the Gaia DR2 position of CP−72 2713 (corrected for proper motion between the epochs of observations). The separation is only 09 (${\rm{\Delta }}{\rm{R}}.{\rm{A}}.\,=\,-0\buildrel{\prime\prime}\over{.} 86\pm 0\buildrel{\prime\prime}\over{.} 60$, ${\rm{\Delta }}\mathrm{decl}.\,=\,+0\buildrel{\prime\prime}\over{.} 16\pm 0\buildrel{\prime\prime}\over{.} 60$), that is, within the 1σ uncertainty (17) of the pointing reconstruction at 70 μm (MIPS Instrument Handbook). It is somewhat smaller than the typical angular offsets measured by Carpenter et al. (2008; see their Figure 5) and Moór et al. (2011; Figure 3) in MIPS 70 μm observations of debris disks with similar or higher signal-to-noise ratios (S/N > 25). Therefore, it can be concluded that the observed emission well matches the position of our target.

We performed aperture photometry for this source with a radius of 16'' and sky annulus between 39'' and 65''. We applied the proper aperture correction factor and adopted a calibration error of 7% (MIPS Instrument Handbook) that was added quadratically to the measured uncertainty. The MIPS flux densities are given in Table 1.

Table 1.  Measured Continuum Fluxes and Predicted Photospheric Fluxes for CP−72 2713

λ	Meas. Fluxa	Instrument	Photosph. Flux	Reference
(μm)	(mJy)		(mJy)
9.00	128.1 ± 12.3	IRC	105.2	Ishihara et al. (2010)
11.56	60.0 ± 2.8	WISE	65.0	Cutri et al. (2013)
22.09	18.9 ± 1.5	WISE	18.3	Cutri et al. (2013)
23.68	16.1 ± 0.6	MIPS	16.0	SEIP
71.42	71.1 ± 5.6	MIPS	1.8	This work
100b	110.6 ± 9.7	PACS	0.9	This work
160	103.9 ± 16.9	PACS	0.35	This work
1330b	3.80 ± 0.59	ALMA	0.005	This work
8820	0.096 ± 0.023	ATCA	$10.6\times {10}^{-5}$	Norfolk et al. (2020, in preparation)

Notes.

^aThe quoted flux densities are not color-corrected. ^bThe emission is marginally resolved at these wavelengths.

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We processed far-IR imaging observations of CP−72 2713 carried out with the Photodetector Array Camera and Spectrometer (PACS; Poglitsch et al. 2010) instrument of the Herschel Space Observatory on 2013 April 23 (PI: A. Tanner). These measurements were performed in mini scan map mode (PACS Observer's Manual v2.5.13) at 100 and 160 μm. The data reduction and calibration were done in the Herschel Interactive Processing Environment (Ott 2010) version 14.2 using the standard pipeline script optimized for mini scan map observations and applying the PACS calibration tree No. 78. To mitigate the low-frequency (1/f) noise present in the data, we applied high pass filtering with filter width parameters of 20 and 35 at 100 and 160 μm, respectively. Since this process introduces flux loss, the immediate vicinity of the target was excluded from the filtering using a 25'' radius circular mask positioned at the source's location. The final images were generated with pixel sizes of 1'' at 100 μm and 2'' at 160 μm.

In both PACS bands, CP−72 2713 was clearly detected. The 100 μm image is displayed in Figure 1(a). The positional offsets between the source's centroid and its proper motion–corrected Gaia DR2 position is 14 (ΔR.A. = −106 ± 007, ${\rm{\Delta }}\mathrm{decl}.=-0\buildrel{\prime\prime}\over{.} 84\pm 0\buildrel{\prime\prime}\over{.} 07$) and 16 (${\rm{\Delta }}{\rm{R}}.{\rm{A}}.\,=\,-1\buildrel{\prime\prime}\over{.} 35\,\pm 0\buildrel{\prime\prime}\over{.} 20$, ${\rm{\Delta }}\mathrm{decl}.\,=\,-0\buildrel{\prime\prime}\over{.} 76\pm 0\buildrel{\prime\prime}\over{.} 20$) at 100 and 160 μm, respectively. Sánchez-Portal et al. (2014) derived a typical absolute pointing accuracy of 09 for the phase of the Herschel mission when our target's observations were performed. Utilizing large number of PACS mini scan maps of standard stars, Marton et al. (2017) found a median positional difference of 15 for the blue PACS detector (70 and 100 μm filters) and 17 for the red PACS detector (160 μm). Our measured offsets correspond well to the latter values, implying their instrumental origin.

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We measured the source's flux by placing a 15'' radius aperture onto the centroid position and a sky annulus between 60'' and 70''. Aperture corrections were taken from the appropriate calibration files. To estimate the uncertainty of the measured flux densities, we placed 16 apertures with radii identical to the source aperture evenly along the sky annulus and carried out photometry without background subtraction in each of them. Then the uncertainty was derived as the standard deviation of these background flux values. The final photometric uncertainty was calculated as a quadratic sum of this and the absolute calibrational uncertainty of the PACS detector (7%; Balog et al. 2014). The resulting flux densities are in Table 1.

To evaluate whether the detected source is spatially extended, we fitted a two-dimensional Gaussian model to the images using the mpfit2dpeak IDL procedure (Markwardt 2009). At 100 μm, the best-fit Gaussian has an FWHM of 85 ± 03 × 81 ± 03, while the FWHM sizes of the point-spread function (PSF) in maps performed with a scan speed of 20'' s⁻¹ (as in our case) are 689 × 669 (PACS Observer's Manual). This implies that CP−72 2713 is marginally resolved at 100 μm. The fitted Gaussian at 160 μm is consistent with the PSF.

Assuming that the observed emission arises from a circumstellar dust ring, we fitted a grid of simple disk models to the 100 μm image. The models have three free parameters: the radius of the ring (R), the position angle (PA; measured east of north), and the inclination (i; angle of the disk plane with respect to the sky plane). Considering that the observation does not resolve the radial structure, we assumed a Gaussian radial surface brightness profile that peaks at R and has an FWHM fixed to 0.2R. Since at this wavelength, the stellar photosphere is predicted to be ∼100× fainter than the measured flux density (Section 3), we neglected its contribution in our modeling. Disk images constructed in this way were then convolved with a PSF model that we constructed from mini scan map observations of α Boo (ObsID 1342247702/1342247703), processed in the same way as that of our target. The wings of the PACS beam form a characteristic trilobe pattern whose orientation depends on the actual roll angle of the observation. To allow direct comparison, we rotated the image of α Boo to match the telescope's roll angle at the observation of CP−72 2713. In order to select the best-fitting model and estimate the uncertainties of the fitted parameters, we used Bayesian inference following Moór et al. (2015). The best-fitting model parameters are $R=2\buildrel{\prime\prime}\over{.} {7}_{-0\buildrel{\prime\prime}\over{.} 6}^{+0\buildrel{\prime\prime}\over{.} 7}$ (or 99${}_{-26}^{+22}$ au), $i=29{^\circ }_{-{21}^{^\circ }}^{+26^\circ }$, $\mathrm{PA}=153{{}^{^\circ }}_{-{64}^{^\circ }}^{+{60}^{^\circ }}$. This model and the residuals are displayed in Figures 1(b)–(c). As Figure 1(c) shows, toward the source, no residuals higher than 3σ were observed. The >3σ residuals at the edge of the displayed image are at an angular separation >15'' and may be related to background sources.

We observed CP−72 2713 with the ALMA 7 m array in the framework of a Cycle 4 project (2016.2.00200.S; PI: Á. Kóspál) that focused on the gas content of young dust-rich debris disks. Our Band 6 observations include two 1.875 GHz wide continuum spectral windows, each with 128 channels centered at 217.0 and 233.5 GHz and two additional windows that were designed to cover the J = 2–1 rotational lines of ¹²CO, ¹³CO, and C¹⁸O. The latter two lines were measured in a single window using a channel width of 428.28 kHz and thereby providing a bandwidth of 1.875 GHz with 4096 channels. In the case of ¹²CO, the channel width was set to 122.07 kHz; this band had a total width of 468.8 MHz. Two observations were performed, 1 day apart from each other, on 2017 July 25 and 26. In both cases, nine antennas were involved, providing projected baseline lengths ranging between 8.9 and 44.7 m (6.7–33.6 kλ). The obtained data were calibrated and flagged with the ALMA reduction tool Common Astronomy Software Applications (CASA v4.7.2; McMullin et al. 2007) utilizing the pipeline script delivered with the data.

Continuum emission—We used the tclean task in CASA (v5.6.2; McMullin et al. 2007) to construct the continuum image by applying Briggs weighting with a robustness parameter of 0.5. Since no line was detected (see below), we combined nonflagged data from all spectral windows achieving an rms noise level of 0.28 mJy beam⁻¹. The beam size is 74 × 55 with a PA of 63. The obtained 1.33 mm continuum image (Figure 1(d)) shows a moderately resolved source around CP−72 2713 with a peak S/N of 5.7. To determine the source's flux density and constrain the spatial distribution of emitting dust grains, we used the CASA-based uvmultifit tool (Martí-Vidal et al. 2014) that allows one to fit models to the measured visibilities. Prior to this running, the data weights were recomputed using the statwt task. Similarly to the case of PACS image analysis, we adopted a Gaussian ring model with a fixed FWHM width of 0.2R. The obtained best-fit solution has R = 140 ± 14 au (38 ± 04), $i=46^\circ \pm 12^\circ$, and PA = 130° ± 16° and yields a flux density of 3.8 ± 0.6 mJy (the quoted uncertainty includes a 10% calibration uncertainty). We used the tclean task to compile images of the best-fit model and the residuals (Figures 1(e)–(f)). No significant residual emission appears in the disk region. The fitted center of the model ring shows an offset of 13 from the stellar position (${\rm{\Delta }}{\rm{R}}.{\rm{A}}.\,=-0\buildrel{\prime\prime}\over{.} 3\pm 0\buildrel{\prime\prime}\over{.} 42$, ${\rm{\Delta }}\mathrm{decl}.\,=\,-1\buildrel{\prime\prime}\over{.} 22\pm 0\buildrel{\prime\prime}\over{.} 45$). The positional accuracy of an ALMA observation with normal calibration can be estimated as the ratio of the achieved resolution and S/N, i.e., ∼09 in our case; thus, the observed offset is not significant. The best-fitting disk parameters derived from the analysis of PACS and ALMA data are summarized in Table 2.

Table 2.  Best-fitting Dust Disk Parameters Derived from the Analysis of PACS and ALMA Data

Data Set	PA (deg)	i (deg)	R (au)
PACS 100 μm	${153}_{-64}^{+60}$	${29}_{-21}^{+26}$	${99}_{-26}^{+22}$
ALMA 1.33 mm	130 ± 16	46 ± 12	140 ± 14

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CO line data—We used CASA to compile the spectral line cubes. After the continuum emission was subtracted from the calibrated visibilities using the uvcontsub task, the imaging was done with the tclean task. In the latter step, we used Briggs weighting with a robustness parameter of 0.5, and the channel width was set to 0.4 km s⁻¹ for the ¹²CO line and 1.4 km s⁻¹ for data of the rarer ¹³CO and C¹⁸O isotopologues. Using the radial velocity data from Table 3, we derived a radial velocity of +0.4 km s⁻¹ for CP−72 2713 in the local standard of rest (LSR) frame. We found no significant emission at this velocity (or anywhere else) in the CO data cubes.

Table 3.  Stellar Parameters

Parameter	Data	References
Distance (pc)	36.62 ± 0.03 pc	Bailer-Jones et al. (2018)
Spectral type	K7Ve	Torres et al. (2006)
	K7IVe	Pecaut & Mamajek (2013)
	M0	Gaidos et al. (2014)
Teff (K)	3900 ± 70 K	This work
L* (L⊙)	0.18 ± 0.01	This work
R* (${R}_{\odot }$)	0.94 ± 0.04	This work
M* (M⊙)	${0.71}_{-0.05}^{+0.03}$	This work
${L}_{{\rm{X}}}/{L}_{\mathrm{bol}}$	−2.92	Kiraga (2012)
$v\sin {i}_{* }$ (km s−1)	7.1 ± 0.9a	Torres et al. (2006)
		Weise et al. (2010)
Prot (days)	4.437	This work
vrad (km s−1)	8.0 ± 0.4a	Torres et al. (2006)
		Lindegren et al. (2018)

Note.

^aWeighted average of the values reported by the cited papers.

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In order to estimate an upper limit for the ¹²CO (2–1) integrated line flux, we assumed that the possible CO gas is colocated with the dust material in the disk. We defined a disk mask considering those regions in the millimeter continuum image that are adjacent with the maximum brightness and having S/N > 2. Using the obtained mask, we constructed the spectrum and calculated its rms. To consider the correlation between the neighboring channels due to the applied weighting function, this rms was multiplied by $\sqrt{2.667}$ (see Matrà et al. 2019, and references therein). Since, based on our results, the bulk of the dust is located at radii ≳100 au and the disk inclination is ≲82° (3σ confidence interval), by adopting a stellar mass of 0.71 M_⊙ (see Section 3.1), we expect a maximum line width of 5 km s⁻¹. Using the corrected rms value and this line width, we derived a 3σ upper limit of 0.216 Jy km s⁻¹ for the ¹²CO (2–1) integrated line flux.

To estimate the basic stellar parameters of CP−72 2713 and provide photospheric flux predictions at IR and millimeter wavelengths, we modeled the stellar photosphere by fitting an ATLAS9 atmosphere model (Castelli & Kurucz 2004) to the photometric data of the star. An active star, CP−72 2713 exhibits variability due to spots (see Figure A1). Using photometric data from the ASAS survey, Kiraga (2012) analyzed 498 and 191 measurements in the V and I bands, respectively. They derived average magnitudes and inferred variability amplitudes of 0.16 and 0.017 mag in the V and I bands. We derived an amplitude of ∼0.04 mag in the Transiting Exoplanet Survey Satellite (TESS) band (Appendix). To reduce uncertainties stemming from the spot-induced variability in the optical regime, we limited our analysis to data that are based on longer-term monitoring observations taken from Kiraga (2012). This was further supplemented by near-IR (J, H, K_s) photometry from the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) and W1- and W2-band data from the AllWISE (Cutri et al. 2013) catalog. This longer-wavelength photometry is typically less susceptible to variations caused by spots (e.g., Goulding et al. 2012). Based on the recent three-dimensional reddening map of the local interstellar medium, which is available through the Stilism tool¹¹ (Capitanio et al. 2017; Lallement et al. 2018), the reddening toward our target is negligible. Thus, we assumed $E(B-V)=0$ in our fitting. By adopting solar metallicity and a log g of 4.5 dex, our χ² minimization yielded an effective temperature of 3900 ± 70 K for CP−72 2713. Using the inferred photosphere model and the Gaia DR2 distance of the object, we derived a luminosity of 0.18 ± 0.01 L${}_{\odot }$ and a stellar radius of 0.94 ± 0.04 R_⊙. To estimate the stellar mass and age, the effective temperature and obtained luminosity values were compared to the theoretical predictions of the MESA Isochrones and Stellar Tracks (Choi et al. 2016; Dotter 2016). In the course of isochrone fitting, we followed the method described by Pascucci et al. (2016), which yielded 0.71${}_{-0.05}^{+0.03}$ M_⊙ and 14${}_{-3}^{+5}$ Myr for the best-fit mass and age, respectively. Considering the uncertainties, the estimated age is satisfactorily consistent with that of the BPMG (24 ± 3 Myr; Bell et al. 2015). We note that the derived stellar mass and radius result in a log g of 4.34 dex, adequately confirming our a priori assumption. The stellar parameters are summarized in Table 3.

Similarly to other young late-type stars, CP−72 2713 shows strong stellar activity that manifests in various indicators. It has an X-ray counterpart in the ROSAT catalog implying a fractional X-ray luminosity of $\mathrm{log}{L}_{{\rm{X}}}/{L}_{\mathrm{bol}}=-2.92$ (Kiraga 2012). This is close to the saturation value of –3, indicating strong coronal activity. The star was also detected by the Galaxy Evolution Explorer satellite (Martin et al. 2005) in both the near-UV (NUV) and far-UV (FUV) bands. By combining these photometric data with 2MASS measurements and placing the object in the NUV − J versus J − K color–color diagram, compiled by Findeisen et al. (2011), we found that its position well matches the locus of other BPMG members. This implies significant excess at UV wavelengths, which is likely due to prominent chromospheric activity.

The star CP−72 2713 has already been observed by TESS (Ricker et al. 2015), providing a very precise, ∼52 day long photometric data set with a cadence of 2 minutes. The reduction and analysis of these TESS data are described in detail in the Appendix. As further signatures of activity, CP−72 2713 exhibits flares and rotational modulation due to stellar spots in its TESS light curve (Figure A1). Consistent with previous ASAS-based results of 4.456 (Kiraga 2012) and 4.48 (Messina et al. 2010) days, we obtained a rotation period of P = 4.437 days from a Fourier analysis of our light curve. In addition, we identified 51 flares or groups of flares. We found that the star spent about 936 minutes in a flaring state, which is 1.24% of the time covered by TESS.

To construct the spectral energy distribution (SED) of our target at λ > 5 μm, the already reported Spitzer, Herschel, and ALMA data were supplemented by additional space-based mid-IR photometry obtained by the AKARI and Wide-field Infrared Survey Explorer (WISE) satellites. The SED was further supplemented by a recent observation obtained with the ATCA at 9 mm (B. Norfolk et al. 2020, in preparation). The available photometric data, as well as the predicted photospheric flux densities in the specific bands, are given in Table 1. The uncertainty of the predicted photospheric fluxes is estimated to be 5%. The compiled SED, together with the photosphere model, is displayed in Figure 2. While at wavelengths shortward of 25 μm, the measured flux densities are consistent with the predicted photospheric contribution, in the far-IR and millimeter regime, CP−72 2713 exhibits significant excess emission that arises from an extended circumstellar dust disk (Section 2). To estimate the characteristic temperature (T_d) and fractional luminosity (f_d = L_disk / L_bol) of this disk, we fitted the excess emission by a single temperature-modified blackbody model where the emissivity is 1 at wavelengths shorter than ${\lambda }_{0}$ and varies as ${(\lambda /{\lambda }_{0})}^{-\beta }$ at longer wavelengths. This model accounts for the general observational results that the emission of debris disks exhibits a fall at wavelengths that are large relative to the typical size of the emitting grains. Because of the sparse wavelength coverage, the λ₀ parameter could not be adequately constrained in our case; thus, in the fitting, we fixed its value to 100 μm. We adopted a Levenberg–Marquardt approach (Markwardt 2009) in searching for the best-fitting model. During the fitting process, we used an iterative way to compute and apply color corrections for our photometric data. As a result, we derived a dust temperature of 43 ± 3 K and a β of 0.05 ± 0.08. The low β value indicates an excess spectrum that is almost identical to a pure blackbody; therefore, changing the λ₀ parameter has no effect on our results. We note that though most debris disks show considerably steeper millimeter slopes (Gáspár et al. 2012; MacGregor et al. 2016; Marshall et al. 2017), interestingly, the excess SED of AU Mic can also be well reproduced by a blackbody (Matthews et al. 2015). For the fractional luminosity, we obtained f_d = 1.1 × 10⁻³.

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3.3.1. The Dust Component

Using our ALMA millimeter measurement, we estimated the dust mass in grains of sizes smaller than a few millimeters (M_d). Assuming optically thin dust emission that can be characterized by a single dust temperature, the dust mass is

$$\begin{eqnarray}&&{M}_{d}=\displaystyle \frac{{F}_{\nu }{d}^{2}}{{B}_{\nu }({T}_{\mathrm{dust}}){\kappa }_{\nu }},\end{eqnarray} \tag{ 1 }$$

where d is the distance, B_ν(T_dust) is the Planck function at 1.33 mm for the characteristic dust temperature, and κ_ν is the dust opacity at the given frequency. Dust particles with sizes >100 μm, whose radiation dominates the emission at this wavelength (Hughes et al. 2018), are thought to behave like blackbodies. At a radial distance of 140 au from CP−72 2713, a star with a luminosity of 0.18 L_⊙ (Section 3.1), the temperature of such grains is ∼15 K. By adopting κ_ν = 2.3 cm² g⁻¹ for the dust opacity (Andrews et al. 2013), Equation (1) provides a dust mass estimate of 0.21 ± 0.03 M_⊕. The quoted uncertainty accounts for the errors of the measured flux density and the distance of the system. Note, however, that the potential systematic uncertainties of the dust opacity can introduce even a factor of 2–3 difference in the estimate (e.g., Miyake & Nakagawa 1993; Ossenkopf & Henning 1994), and the dust temperature may not be characterized by a single value. These factors were not considered in our error calculations.

3.3.2. The Gas Component

So far in our analysis, we have assumed that the observed excess emission solely originates from a circumstellar disk. Knowing the main properties of the source, at this point it is worth assessing the possibility of source confusion, as well as the potential influence of different kinds of contaminations.

First, we examine whether the excess could come from a background galaxy. Based on the recently derived double power-law model of the cumulative number counts of galaxies at millimeter wavelengths (González-López et al. 2020), we estimated a probability of ∼0.006 of the presence of a background galaxy brighter than 3.8 mJy within the primary beam of the ALMA 7 m array. If we consider only the interferometric synthesized beam, this value is reduced to ∼1.1 × 10⁻⁴. Besides the low probability of positional coincidence, there are other strong arguments against this scenario. We measured an angular size of ∼75 for the emitting structure at 1.3 mm. As interferometric observations show, galaxies are compact at (sub)millimetric wavelengths, with a typical size of 03 ± 01 (Franco et al. 2018, and references therein); i.e., they are significantly smaller than our source. The SED of the measured excess emission toward CP−72 2713 peaks at ∼120 μm and has a millimeter spectral index of ∼2. Although the SEDs of local (low-redshift) galaxies peak at a similar wavelength, their millimeter spectral slope is significantly steeper, with typical indices between 3.5 and 4.0 (Casey et al. 2014). Moreover, such low-redshift objects represent only a small fraction of known millimeter galaxies (Casey et al. 2014, and references therein).

Lensed galaxies deserve special attention, since the gravitational lensing effect can magnify distant background sources, thereby increasing both their fluxes and angular sizes. At the spatial resolution we achieved in our ALMA observation, multiple images of lensed galaxies can mimic a source having a more comparable size to that of our target than normal (unlensed) dusty galaxies. However, despite their significant contribution to the bright-end population of galaxies at submillimeter/millimeter wavelengths, lensed dusty star-forming galaxies are rare objects with a sky density of 0.1–0.2 deg⁻² (Negrello et al. 2010, 2017; Wardlow et al. 2013; Casey et al. 2014). Thus, the probability that such an object appears within the primary beam of our millimeter observation is less than 4 × 10⁻⁵. The shape of their SEDs also deviates from what we measured toward CP−72 2713: the redshifts of lensed galaxies are typically >2 (Vieira et al. 2013), and their long-wavelength emission peaks at ≳250 μm (Negrello et al. 2017).

Although it is very unlikely that all observed excess is coming from a background galaxy, owing to our coarse spatial resolution, positional coincidence with fainter extragalactic objects cannot be completely ruled out. Recent high spatial resolution millimeter images of several debris disks show compact sources—most likely background galaxies—colocated or located close to the dust ring (Chavez-Dagostino et al. 2016; Booth et al. 2017; Marino et al. 2017; Su et al. 2017; Faramaz et al. 2019). Such objects, if present, can contribute to the measured emission at far-IR and millimeter wavelengths and modify the derived millimeter spectral index of our target. Higher-resolution millimeter observations are needed to explore these possible contaminating sources and assess their role, e.g., in the observed unusually shallow millimeter slope.

In our analysis, the modeling of the stellar contribution to the measured emission was limited to the photospheric fluxes. However, at millimeter wavelengths, low-mass active stars can exhibit nonphotospheric emission (e.g., Liseau et al. 2015; MacGregor et al. 2015). Recent millimeter ALMA observations of AU Mic revealed a central point source at the star's position with a flux density ∼6× higher than predicted based on the pure photospheric model (MacGregor et al. 2013). The observed excess was attributed to either an inner dust belt (MacGregor et al. 2013) or coronal emission from the star itself (Cranmer et al. 2013). In the case of CP−72 2713, the 1σ measurement uncertainty (0.37 mJy) of the 1.33 mm observation is ∼80× higher than the predicted photospheric flux density. Supposing the nonphotospheric contribution at CP−72 2713 is not stronger than in the case of AU Mic (based on their fractional X-ray luminosity (see Kiraga 2012), the coronal activity levels of the two stars are similar), i.e., ≲6× the photospheric emission, the measurement uncertainty is significantly higher than the uncertainty of the stellar flux prediction. For shorter periods, however, a higher level of activity cannot be excluded. As was demonstrated in the cases of Proxima Cen and AU Mic, a strong flare can enhance a star's millimeter flux by orders of magnitudes for a few tens of s (MacGregor et al. 2018; Daley et al. 2019). White et al. (2018) also found significant variability in the 9 mm emission of the young M-type star HD 141569 B throughout its ∼1 hr observation. By examining the obtained ALMA data stream of CP−72 2713, we found no evidence for such flux enhancements. Actually, this meets our expectations: we identified only 51 flare events in the 52 day long TESS light curves (Section 3.2) and found that the star spends only ∼1.2% of the time in flare phase in the studied period (in fact, the peaks of the flares, which can substantially contribute to the millimeter emission, cover much less time). Based on all of this, we believe that most of the measured millimeter flux is due to the dust disk.

For the projected rotational velocity of the star, Torres et al. (2006) obtained a value of $v\sin {i}_{* }=7.5\pm 1.2$ km s⁻¹, while Weise et al. (2010) quoted $v\sin {i}_{* }=6.6\pm 1.4$ km s⁻¹ in their work. Computing the weighted mean of these $v\sin {i}_{* }$ measurements and using the rotational period (in days) and the stellar radius derived above (in solar radii), following Campbell & Garrison (1985) and Greaves et al. (2014), we estimated the inclination of the stellar pole with respect to the line of sight as

$$\begin{eqnarray}&&\sin {i}_{* }=0.0198\displaystyle \frac{{Pv}\sin {i}_{* }}{{R}_{* }}.\end{eqnarray} \tag{ 2 }$$

This yields an inclination of ${i}_{* }=42^\circ \pm 7^\circ$, which is in good agreement with the disk inclination obtained from the analysis of our ALMA data (Section 2.3). This finding coincides well with the conclusions made by Watson et al. (2011), Kennedy et al. (2013), and Greaves et al. (2014); by examining larger debris disk samples, these authors also found no evidence for significant misalignment between the stellar equator and the disk in the studied systems.

A noteworthy fraction of members in the ∼24 Myr old BPMG exhibit excess emission at IR wavelengths (Rebull et al. 2008; Riviere-Marichalar et al. 2014; Moór et al. 2016). While in most of these systems, the observed excess is likely attributed to thermal emission of tenuous circumstellar debris disks, at least one member of this group, the late-type close binary V4046 Sgr, harbors a long-lived gas-rich protoplanetary disk (e.g., Rosenfeld et al. 2013). Thus, the presence of a protoplanetary disk, even at the age of the BPMG, has previously been seen. Therefore, in the following, we will examine the nature of the CP−72 2713 disk.

Observationally, one of the most conspicuous differences between protoplanetary and debris disks is related to the amount of dust. While protoplanetary disks with their larger dust content are optically thick at most wavelengths, debris disks are optically thin across the spectrum. This is manifested in the fractional luminosities; the threshold between the two classes is typically set to f_d = 0.01, which is about 10× higher than that of CP−72 2713. The estimated dust mass of ∼0.2 M_⊕ in our target well matches those of other debris disks (Holland et al. 2017). Recent large surveys of protoplanetary disks implied a positive correlation between disk radius and millimeter continuum luminosity (e.g., Andrews et al. 2010; Tripathi et al. 2017; Hendler et al. 2020). The relationship between the effective disk radii (R_eff) and the millimeter continuum luminosity (L_mm) was studied in five nearby star-forming regions (Ophiuchus, Taurus-Auriga, Chameleon I, Lupus, and Upper Sco) by Hendler et al. (2020). In their work, R_eff was defined as the radius that encircles 68% of the continuum emission, while L_mm was the Band 7 flux density scaled to 140 pc. Using our SED model (Section 3.3), we estimated a flux density of 8.4 mJy at 890 μm for CP−72 2713, which results in ${L}_{\mathrm{mm}}\sim 6\times {10}^{-4}$ Jy. With its low luminosity and large size of the disk, CP−72 2713 deviates significantly from the observed relationships: protoplanetary disks with ${R}_{\mathrm{eff}}\gt 100\,\mathrm{au}$ have at least 2 orders of magnitude higher ${L}_{\mathrm{mm}}$. The dust properties of our target seem inconsistent with a protoplanetary nature.

The mass of protoplanetary disks is dominated by their gas component, which is no longer present in significant quantities in most debris disks (Wyatt et al. 2015; Kral et al. 2018). We observed no CO emission toward CP−72 2713. The obtained 3σ upper limit on the ¹²CO (2–1) line luminosity is about 3 orders of magnitude lower than that of the protoplanetary disk around V4046 Sgr (Rosenfeld et al. 2013). We note that ¹²CO in V4046 Sgr is optically thick, suggesting an even higher contrast in the gas mass ratio between the two systems. Even more indicatively, this upper limit also remains six times below the measured ¹²CO (2–1) line luminosity of the disk of β Pic, whose gas and dust components are attributed to collisional erosion of larger bodies thus found to be of second generation (Kral et al. 2016; Matrà et al. 2017; Cataldi et al. 2018). Torres et al. (2006) and Gaidos et al. (2014) found the Hα line in emission in CP−72 2713 with measured equivalent widths of 1.9 and 0.84 Å, respectively. Based on the criteria proposed by Barrado y Navascués & Martín (2003), these values can be explained with chromospheric activity and do not indicate ongoing accretion and thus the presence of an inner gas-rich disk.

These findings suggest that our target harbors a gas-poor disk and, together with the results on the dust component, favors the classification of CP−72 2713 as a debris disk.

Nevertheless, with its fractional luminosity of 1.1 × 10⁻³, this disk is considered as a very dust-rich system among debris disks. By comparing this value with that of other cold debris disks with late-type host stars in the BPMG, we can find that it is about 3× higher than that of the iconic disk of AU Mic (3.5 × 10⁻⁴; Matthews et al. 2015) and well matches the fractional luminosity of the debris disk around AG Tri (10⁻³; Riviere-Marichalar et al. 2014). Besides CP−72 2713, we know only four debris systems within 40 pc of the Sun that have well-established cold dust components and exhibit fractional luminosities higher than 10⁻³, namely, β Pic, HD 61005, TWA 7, and HD 107146.

Despite its large dust content and proximity, the disk of CP−72 2713 has remained undiscovered for a long time. This is largely due to the low luminosity of the host star: the system does not exhibit excess at the mid-IR wavelengths observed by the WISE satellite, and its far-IR emission falls below the detection limit of all-sky surveys performed by the IRAS and AKARI satellites.

In steady state, the production of dust particles by collisions in debris disks is balanced by grain removal processes through radiation and stellar wind forces. In most known debris disks around main-sequence stars, the stellar radiation pressure plays an important role in controlling the dust dynamics by driving particles on more eccentric orbits than those of their parent bodies and expelling small enough grains from the system (e.g., Krivov 2010). In lower-luminosity K- and M-type stars, however, the radiation pressure is not strong enough to remove grains (Plavchan et al. 2005; Reidemeister et al. 2011; Schüppler et al. 2015).

Figure 3 shows the ratio of radiation to gravitational force, ${\beta }_{\mathrm{rad}}=\tfrac{{F}_{\mathrm{rad}}}{{F}_{\mathrm{grav}}}=\tfrac{3{L}_{* }{Q}_{\mathrm{pr}}}{16\pi {{GM}}_{* }c\rho s}$ (Burns et al. 1979), for compact spherical dust grains with different ρ densities and s sizes in the CP−72 2713 system. We explored four different grain compositions for which the Q_pr radiation pressure efficiency was computed by means of Mie theory using the code developed by Bohren & Huffman (1983). Assuming parent bodies on a circular orbit, the released grains become unbound if their β_rad is >0.5. As Figure 3 demonstrates, β_rad remains below this critical value for each tested dust composition, i.e., none of the particles are expelled by the radiation pressure in the CP−72 2713 system. We note that as an active star, CP−72 2713 exhibits excess at UV wavelengths and shows strong coronal X-ray emission (Section 3.2), and during flares, its short-wavelength emission increases further. Our stellar model does not account for these effects; thus, we likely underestimate the strength of the radiation pressure. In the case of AU Mic, whose UV, EUV, and X-ray emission is better constrained by observations than that of our target, Augereau & Beust (2006) found that this excess radiation is most important in the flare state, when the β_rad value could even be a few times higher.

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The stellar wind mass loss of magnetically active late-type stars, as CP−72 2713 (Section 3.2), is thought to significantly exceed the solar value (e.g., Wargelin & Drake 2001; Wood et al. 2002). In such systems, wind forces can dominate the dust removal (Plavchan et al. 2005; Augereau & Beust 2006; Strubbe & Chiang 2006). Considering this corpuscular component as well, the ratio of the radiation and wind forces to gravitational force can be calculated following Strubbe & Chiang (2006),

$$\begin{eqnarray}&&{\beta }_{\mathrm{rad}}=\displaystyle \frac{{F}_{\mathrm{rad}}+{F}_{\mathrm{sw}}}{{F}_{\mathrm{grav}}}=\displaystyle \frac{3{L}_{* }{P}_{\mathrm{swr}}}{16\pi {{GM}}_{* }c\rho s},\end{eqnarray} \tag{ 3 }$$

where ${P}_{\mathrm{swr}}\equiv {Q}_{\mathrm{pr}}+{Q}_{\mathrm{sw}}\tfrac{{\dot{M}}_{* ,\mathrm{wind}}{v}_{\mathrm{wind}}c}{{L}_{* }}$. In this formula, Q_sw is the stellar wind coupling coefficient that gives the ratio of the effective to geometric cross section, ${\dot{M}}_{* ,\mathrm{wind}}$ is the stellar wind mass-loss rate, and v_wind is the stellar wind velocity. No data are available on the wind mass-loss rate of our target in the literature. For the similarly active AU Mic, Augereau & Beust (2006) derived mass-loss rates 50× and 300× higher than that of our Sun (${\dot{M}}_{\odot ,\mathrm{wind}}=2\times {10}^{-14}\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$) by taking its quiescent phase and considering the influence of episodic flare activity, respectively. Using these mass-loss rates and adopting Q_sw = 1 and a wind velocity of 400 km s⁻¹ (that corresponds to the average wind velocity of the Sun), we recomputed the β values for astrosilicate particles. As Figure 3 shows, particles with sizes smaller than ∼0.013 μm in the ${\dot{M}}_{* ,\mathrm{wind}}=50\,{\dot{M}}_{\odot ,\mathrm{wind}}$ scenario and ∼0.09 μm in the ${\dot{M}}_{* ,\mathrm{wind}}=300\,{\dot{M}}_{\odot ,\mathrm{wind}}$ scenario have a β value >0.5. Thus, by considering the possible wind pressure, these small grains are blown out from the system.

The Poynting–Robertson (P-R) and stellar wind drag also affect the dynamics of dust particles; producing effective forces opposite to the direction of the orbital motion, these drags result in a gradual loss of the grains' angular momentum and lead them to spiral into the star. Assuming a particle originally having a circular orbit, the time necessary to reach the central star from a radius R under the effect of P-R drag can be computed as ${t}_{{\rm{P}}-{\rm{R}}}(\mathrm{yr})=400\tfrac{R{\left(\mathrm{au}\right)}^{2}}{{M}_{* }({M}_{\odot })}\tfrac{1}{{\beta }_{\mathrm{rad}}}$ (Wyatt 2005). Taking the disk radius of 140 au (Section 2.3), during the lifetime of the system (∼24 Myr), only grains with ${\beta }_{\mathrm{rad}}\gt 0.45$ could have spiraled into the star. Since the collision cascade probably started well after the birth of the system (see Section 4.6), the available time is even shorter, and the threshold value for β is even larger. The stellar wind drag can work on a shorter timescale. According to Plavchan et al. (2005), $\tfrac{{t}_{{\rm{P}}-{\rm{R}}}}{{t}_{\mathrm{sw}}}=\tfrac{{Q}_{{\rm{P}}-{\rm{R}}}}{{Q}_{\mathrm{sw}}}\tfrac{{\dot{M}}_{* ,\mathrm{wind}}{c}^{2}}{{L}_{* }}$; thus, by assuming $\tfrac{{Q}_{{\rm{P}}-{\rm{R}}}}{{Q}_{\mathrm{sw}}}=1$ and using the adopted ${\dot{M}}_{* ,\mathrm{wind}}$ values of 50 or $300\,{\dot{M}}_{\odot ,\mathrm{wind}}$, the timescale of the wind drag could be ∼80 or ∼480 times shorter than the P-R timescale and can result in significant inward transport of larger dust particles as well. In the following, we will investigate how these effects, considering the influence of collisions, can affect the spatial distribution of grains.

We utilized the Analysis of Collisional Evolution (ACE; Krivov et al. 2006; Löhne et al. 2008) modeling code that can simulate the collisional evolution of the disk, as well as the impact of transport processes on the dust distribution. By numerically solving the Boltzmann–Smoluchowski kinetic equation, this code enables one to follow the evolution of a disk composed of subplanetary-sized bodies down to micron-sized dust particles, considering the outcomes of collisions between these solids and the influence of the stellar gravity force and stellar radiative/corpuscular forces on them. The ACE code has already been applied successfully to explore the long-term evolution of several debris disks (e.g., Reidemeister et al. 2011; Löhne et al. 2012; Schüppler et al. 2015; Geiler et al. 2019).

In our simulations, we used the stellar and disk parameters derived in this work. We adopted a stellar mass of 0.71 M_⊙ and a luminosity of 0.18 M_⊙, while for the stellar SED, we used the ATLAS9 atmosphere model compiled in Section 3. Based on the best-fit model of the millimeter emission (Section 2.3), the parent planetesimal belt was assumed to be located between 126 and 154 au, corresponding to a radial extent of 0.2R, with R = 140 au. We set a uniform surface density for this ring. For the initial mass distribution of the solids, we assumed a power law with an index of −1.88 (Gáspár et al. 2012; Krivov et al. 2018). The largest planetesimals were 10²¹ g (∼40 km in radius; note that this size is not constrained but was chosen to be sufficiently high to give a threshold for the collisional cascade), while the smallest particles were 10⁻¹³ g (submicron-sized). The average initial orbital eccentricity of the planetesimals was set to 0.03. Regarding the setup of the critical specific energy for disruption, we followed that described by Löhne et al. (2012). To explore the influence of the stellar wind, we performed simulations with three different wind mass-loss rates of ${\dot{M}}_{* ,\mathrm{wind}}=0$, $50\,{\dot{M}}_{\odot ,\mathrm{wind}}$, and $300\,{\dot{M}}_{\odot ,\mathrm{wind}}$. The wind velocity was set to 400 km s⁻¹ in all three models. We followed the disk evolution for 24 Myr. By assuming pure astronomical silicate (Draine 2003) as dust material, we calculated the SED of the simulated disks (for details, see Pawellek et al. 2019). We found that disk models with a mass of 50 ${M}_{\oplus }$—which include all solids up to the maximum size of 40 km—reproduce the measured SED at wavelengths ≤1.3 mm well, although they cannot account for the unusually shallow millimeter SED and thus substantially underestimate the observed flux at 9 mm (see Figure 2 for an example). It is yet unclear what may be the reason for the measured low millimeter spectral index, but several different factors, including external contamination (e.g., by galaxies; see Section 3.4), may play a role. To clarify these and refine the model further, higher spatial resolution images are needed.

Using the 50 M_⊕ models, we generated thermal maps at 100 μm and 1.3 mm. Figure 4 displays normalized surface brightness profiles as a function of radial distance at these two wavelengths after 1, 10, and 24 Myr of evolution of the disk. These profiles were compiled as the azimuthal average of the thermal maps. Assuming that the stellar wind is negligible (Figure 4(a)), we do not see significant differences between disks with different evolutionary states. This is consistent with the results of the above analytical calculations (Section 4.2): the stellar radiation force itself is too weak to substantially modify the grains' orbit. However, in models with stellar wind, the inward migration of dust particles becomes efficient due to the wind drag (Figures 4(b) and (c)). At 1.3 mm, this has no significant impact on the surface brightness distribution. The thermal emission peaks at the planetesimal belt, and the inner regions are 2 orders of magnitude fainter even in the ${\dot{M}}_{* ,\mathrm{wind}}=300\,{\dot{M}}_{\odot ,\mathrm{wind}}$ model. This finding is consistent with the results obtained by Pawellek et al. (2019) for debris disks around late-type stars with stellar wind. At 100 μm, where smaller grains dominate the emission, the influence of the wind drag is more visible; though the birth ring is still the brightest part of the disk, especially in the model with the strongest wind, the surface brightness inside the ring is only a few times lower.

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Interestingly, by analyzing the PACS image, we obtained a smaller disk radius (${99}_{-26}^{+22}$ au) than from the ALMA data (140 ± 14 au). Although the two estimated radii are consistent within the uncertainties, in light of the ACE results, it is worth examining whether it could be the effect of wind drag. We constructed simulated PACS images from the 100 μm thermal model maps by convolving them with our PSF model (Section 2.2). Then, using these simulated data, we derived the disk peak radius by fitting the same Gaussian ring model as we applied in the case of the real data (Section 2.2). For most simulations, the derived peak radii were around 140 au; i.e., the surface brightness distribution is dominated by the parent belt. However, for the most extreme model with ${\dot{M}}_{* ,\mathrm{wind}}\,=300\,{\dot{M}}_{\odot ,\mathrm{wind}}$ at 24 Myr, we obtained a peak radius of 114 au.

This result indicates that if the stellar wind is strong enough, it may be able to shape the spatial distribution of grains so that the belt appears smaller at 100 μm. We note, however, that taking into account that the formation of planetesimals and then the proper stirring of the disk (see Section 4.6) needs time, the evolutionary time is likely substantially shorter than 24 Myr. Thus, if the differences between the 100 μm and 1.3 mm measurements are real and related to transport processes, this simulation suggests a ${\dot{M}}_{* ,\mathrm{wind}}\gt 300\,{\dot{M}}_{\odot ,\mathrm{wind}}$ for this system.

Thanks to its large angular size and advantageous orientation, the disk around CP−72 2713 could be an ideal target to investigate the influence of wind-dominated transport in the future; however, it needs high-resolution multiwavelength observations that allow the study of the radial profile of the emitting regions.

Up to now, about two dozen debris disks have been spatially resolved at (sub)millimeter wavelengths, allowing one to constrain the location of the outer planetesimal belts in these systems. Using these data, Matrà et al. (2018) found a relationship between stellar luminosity L_* and disk radius in the form of $R{(\mathrm{au})={73}_{-6}^{+6}{L}_{* }({L}_{\odot })}^{{0.19}_{-0.04}^{+0.04}}$. This formula predicts a disk radius of 53 ± 6 au for CP−72 2713, which is significantly smaller than the measured size of 140 au. To further explore this aspect, in Figure 5, we display the outer radii¹² of six debris disks ( Eri, AU Mic, HD 61005, TWA 7, HD 92945, and HD 107146) hosted by stars with masses between 0.5 and $1.0\,{M}_{\odot }$ (similar to that of CP−72 2713) as a function of age. We have selected only objects that are younger than 1 Gyr and whose estimated radii are based on spatially resolved millimeter observations (Booth et al. 2017; MacGregor et al. 2018; Marino et al. 2018, 2019; Daley et al. 2019; Matrà et al. 2019) and thus thought to represent the outer edge of their planetesimal belts. The age estimates of these systems are taken from the literature (Williams et al. 2004; Mamajek & Hillenbrand 2008; Bell et al. 2015; Marino et al. 2019; Zuckerman 2019). Similarly to CP−72 2713, these objects represent the most dust-rich known debris disks hosted by late-type stars in our neighborhood. As Figure 5 demonstrates, the disk radius of our target is comparable to those of HD 92945 and HD 107146 and substantially larger than those of the other three debris systems. This is especially remarkable when considering that in the case of CP−72 2713, we displayed the estimated peak radius of the belt instead of the outer radius (because of the limited angular resolution, the disk width was fixed in our modeling). Thus, CP−72 2713 is not just very dust-rich; it is also unusually extended.

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Assuming that the planetesimal belt in the CP−72 2713 system is still close to its birthplace, we can expect that the predecessor protoplanetary disk must have contained a concentration of a large amount of material at the same radius. Thus, it is interesting to compare the size of our disk with the measured outer radii of protoplanetary disks around similar-mass (0.5–1.0 M_⊙) young stars. Thanks to recent ALMA observations, there is a growing sample of protoplanetary disks resolved at millimeter wavelengths in the continuum. In Figure 5, we plot the outer radii of 33 such protoplanetary disks belonging to the Lupus, Chamaeleon I, and Taurus star-forming regions. The ages of these groups range between 1 and 3  Myr. The disk size estimates of Lupus and Chamaeleon I objects were taken from Hendler et al. (2020). We used their R₉₀ radii, which are defined as radii containing 90% of the millimeter continuum flux. For disks in Taurus, we used the data from Long et al. (2018, 2019), who derived R₉₀ and R₉₅ radii, respectively. In Figure 5, the shaded orange box shows the 25%–75% quartiles of the size distribution, while the whiskers represent the 0%–25% and 75%–100% quartiles. The median disk radius is denoted by a horizontal black line. We note that due to observational biases toward brighter objects, the plotted disks likely represent the most massive/extended category of protoplanetary disks. Figure 5 shows that CP−72 2713 is not only the most extended debris disk but also its radius is comparable to the largest protoplanetary disks in the studied stellar mass range.

After the dispersal of the gas-rich protoplanetary disks, the leftover planetesimals are thought to have nearly circular orbits, likely resulting in nondestructive, low-velocity collisions between them. To ignite an effective collisional cascade that produces a continuous replenishment of dust particles observable at IR and millimeter wavelengths, the planetesimal disk needs to be dynamically excited. The possible reasons for this dynamical excitation are still debated in the literature. The most commonly invoked explanations require the existence of a giant planet or a stellar companion somewhere in the system (planetary or binary stirring; Mustill & Wyatt 2009) and/or the presence of large planetesimals embedded in the belt (self-stirring; Kenyon & Bromley 2008). In our solar system, both self-stirring and planetary stirring may contribute to the excitation of the Kuiper Belt, resulting in a high excitation level there (Matthews et al. 2014). However, our knowledge is limited on the origin of stirring in other debris disks (Moór et al. 2015; Krivov & Booth 2018). All proposed stirring mechanisms need time to be activated in a given part of the disk. Using the model predictions, we can thus examine their feasibility in the CP−72 2713 system.

According to the classical version of the self-stirring model (Kenyon & Bromley 2008), mutual low-velocity collisions between smaller bodies in a dynamically cold region of the disk lead to the formation of gradually larger planetesimals. Kenyon & Bromley (2008) found in their simulations that after reaching a radius of ∼1000 km, the largest planetesimals can stir their environment efficiently. It makes collisions between their smaller neighbors destructive and leads to the production of debris material through a collisional cascade. Adopting an initial protoplanetary disk with a surface density distribution of ${\rm{\Sigma }}{(a)=0.18({M}_{* }/{M}_{\odot }){x}_{{\rm{m}}}(r/30\mathrm{au})}^{-3/2}\,{\rm{g}}\,{\mathrm{cm}}^{-2},$ where ${x}_{{\rm{m}}}$ is a scaling factor (for the minimum-mass solar nebula x_m ≡ 1), Kenyon & Bromley (2008) provided an analytical formula for the formation time of 1000 km–sized planetesimals (the onset time of the stirring) at a stellocentric radius r:

$$\begin{eqnarray}&&{t}_{\mathrm{onset}}^{\mathrm{classical}}=145{x}_{{\rm{m}}}^{-1.15}{\left(\displaystyle \frac{r}{80\mathrm{au}}\right)}^{3}{\left(\displaystyle \frac{2{M}_{\odot }}{{M}_{* }}\right)}^{3/2}\mathrm{Myr}.\end{eqnarray} \tag{ 4 }$$

Realistically, the ${x}_{{\rm{m}}}$ factor could not be higher than 10 (Mustill & Wyatt 2009). Taking a disk with the above-described radial surface density profile with x_m = 10, and assuming that the location of the planetesimal belt at 140 au in the CP−72 2713 system corresponds to the outer edge of the initial protoplanetary disk, the total initial mass of solids would have been ∼1.2 × 10³ M${}_{\oplus }$. This hugely exceeds the measured dust masses of protoplanetary disks around similar-mass stars in the Lupus and Chameleon I star-forming regions (Ansdell et al. 2016; Pascucci et al. 2016), further confirming the usage of x_m = 10 as a strong upper limit.¹³ In Figure 6, we plot the onset time of the stirring at different radii for x_m = 1 and 10 (solid cyan lines). A comparison with the location of the planetesimal belt in the CP−72 2713 system (red circle) demonstrates that even with x_m = 10, the radius of the predicted stirring front is very far from the region of the observed planetesimal belt at the age of the system.

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The collisional coagulation model is not the sole feasible way for large planetesimals to form. Particle concentration models predict a significantly quicker formation of larger bodies even far from the star (at r > 100 au) through gravitational collapse of locally concentrated pebbles (Johansen et al. 2015; Krivov & Booth 2018, and references therein). According to these scenarios, large planetesimals are already present in the disk by the time of the dissipation of the gas-rich protoplanetary material. Due to the possibly smaller size of the largest bodies (a few hundred km; Simon et al. 2016; Schäfer et al. 2017) with respect to the classical model (where the 1000 km–sized planetesimals can stir the neighboring disk promptly), the excitation of the surrounding smaller bodies takes more time than in the previous scenario. According to Krivov & Booth (2018), in this scenario, the onset time of effective self-stirring at a radius r can be computed as

$$\begin{eqnarray}&&\begin{array}{l}{t}_{\mathrm{onset}}^{\mathrm{pebble}}=\left(\displaystyle \frac{129}{{x}_{{\rm{m}}}}\right)\left(\displaystyle \frac{1}{\gamma }\right){\left(\displaystyle \frac{\rho }{1{\rm{g}}{\mathrm{cm}}^{-3}}\right)}^{-1}{\left(\displaystyle \frac{{v}_{\mathrm{frag}}}{30{\mathrm{ms}}^{-1}}\right)}^{4}\\ {\left(\displaystyle \frac{{S}_{\max }}{200\mathrm{km}}\right)}^{-3}{\left(\displaystyle \frac{{M}_{* }}{{M}_{\odot }}\right)}^{-3/2}{\left(\displaystyle \frac{r}{100\mathrm{au}}\right)}^{3}(\mathrm{Myr}),\end{array}\end{eqnarray} \tag{ 5 }$$

where γ is a parameter in Equation (20) in Krivov & Booth (2018), ρ is the bulk density of planetesimals, v_frag is the minimum collisional velocity needed for fragmentation, and S_max is the size of the largest planetesimals. Figure 6 shows—by using the default values proposed by Krivov & Booth (2018) of γ = 1.5, $\rho =1\,{\rm{g}}\,{\mathrm{cm}}^{-3}$, ${v}_{\mathrm{frag}}=30\,{\mathrm{ms}}^{-1}$, and ${S}_{\max }=200\,\mathrm{km}$ —that the outer edge of the possibly stirred region (purple dashed–dotted line) is close to the position of the planetesimal belt in the CP−72 2713 system. Here we again adopted ${x}_{{\rm{m}}}=10$. Considering the caveats of the model and the uncertainties of the fundamental model parameters (Krivov & Booth 2018), this means that the excitation of the CP−72 2713 disk can be consistent with the pebble concentration stirring model. For instance, by adopting somewhat larger maximum planetesimal sizes of S_max = 230 km, the model would predict exactly 24 Myr for the onset of stirring at 140 au, the location of the belt.

Dynamical excitation of a planetesimal disk can also be caused by a planet via its secular perturbation (Wyatt 2005; Mustill & Wyatt 2009). Similar to the self-stirring scenario, the gravitational influence of a planet located within the planetesimal belt manifests in an outward propagating stirring front. Using the model developed by Mustill & Wyatt (2009) and assuming a Saturn-mass planet with an orbital radius of 65 au (roughly corresponding to the orbital radius of the outermost planet in the HR 8799 system) and a moderate eccentricity of 0.1, we found that the perturbation induced by such a planet could just reach the region of the belt by the age of the system (Figure 6). The same result can be obtained with a smaller planetary mass if the semimajor axis and/or the eccentricity of the orbit is larger. Thus, planetary stirring is a feasible model for the CP−72 2713 system.

Finally, we cannot exclude the possibility that the planetesimal belt is prestirred, i.e., born stirred (Wyatt 2008) because of some not-yet-specified physical mechanism. In this scenario, t_onset = 0 at all radii.