A ~75\% Occurrence Rate of Debris Discs around F stars in the β Pic Moving Group
Nicole Pawellek, Mark Wyatt, Luca Matr?, Grant Kennedy, Ben Yelverton
MMNRAS , 1–26 (2021) Preprint 29th January 2021 Compiled using MNRAS L A TEX style file v3.0 A Occurrence Rate of Debris Discs around F stars in the 𝛽 PicMoving Group
Nicole Pawellek, , ★ Mark Wyatt, Luca Matrà, Grant Kennedy, Ben Yelverton, Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Konkoly-Thege Miklós út 15-17, H-1121 Budapest, Hungary School of Physics, National University of Ireland Galway, University Road, Galway, Ireland Department of Physics and Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Only 20% of old field stars have detectable debris discs, leaving open the question of what disc, if any, is present around theremaining 80%. Young moving groups allow to probe this population, since discs are expected to have been brighter early on.This paper considers the population of F stars in the 23 Myr-old BPMG where we find that 9/12 targets possess discs. We alsoanalyse archival ALMA data to derive radii for 4 of the discs, presenting the first image of the 63au radius disc of HD 164249.Comparing the BPMG results to disc samples from ∼
45 Myr and ∼
150 Myr-old moving groups, and to discs found around fieldstars, we find the disc incidence rate in young moving groups is comparable to that of the BPMG and significantly higher thanthat of field stars. The BPMG discs tend to be smaller than those around field stars. However, this difference is not statisticallysignificant due to the small number of targets. Yet, by analysing the fractional luminosity vs disc radius parameter space wefind that the fractional luminosities in the populations considered drop by two orders of magnitude within the first 100 Myr.This is much faster than expected by collisional evolution, implying a decay equivalent to 1 / age . We attribute this depletion toembedded planets which would be around 170 𝑀 earth to cause a depletion on the appropriate timescale. However, we cannot ruleout that different birth environments of nearby young clusters result in brighter debris discs than the progenitors of field starswhich likely formed in a more dense environment. Key words: infrared: planetary systems – planet-disc interactions – planets and satellites: dynamical evolution and stability
After its protoplanetary disc has dispersed, a star is left with - ifanything - a system of planets and debris belts. The dust in thosedebris belts is inferred to originate in the break-up of planetesimalsat least kilometres in size (e.g., Wyatt 2008; Krivov 2010; Hugheset al. 2018), and is seen in far-infrared (FIR) surveys towards ∼ 𝑛 ( 𝑟 ) ∝ 𝑟 − . distribution inthe range 1-1000 au (Sibthorpe et al. 2018).However, while this model makes accurate predictions for the 20% ★ E-mail: [email protected] of Gyr-old stars with detectable discs, it is almost completely uncon-strained for the 80% of stars without detectable discs for which modelpredictions rely on the log-normal or power law assumptions aboutthe underlying initial mass and radius distributions. For example,stars in the canonical model population without detectable discs arethe 80% with 1-10 au discs that are rapidly depleted and so neverseen, whereas it would be equally valid to put these undetected discsat 30-100 au with very low initial mass. A further challenge comesfrom the inference that planetesimal belt radii depend on stellar lu-minosity. Belts imaged at millimetre wavelengths are larger aroundhigher luminosity stars in a way that may be attributed to preferen-tial formation at protoplanetary disc ice-lines (Matrà et al. 2018), apossibility not currently included in the model.It is inevitably challenging to determine the properties of the plan-etesimal belts of the 80% of nearby stars without detectable dust.Our only hope is to probe these by studying stars that are young( (cid:28)
100 Myr when their discs are brightest) and nearby. Youngnearby moving groups are ideal for sample selection, having alsothe benefit of being co-eval. Given the stellar luminosity dependencementioned above, and that disc detection is maximised for higherluminosity stars, the optimal sample would include stars of similarearly spectral type in the nearest youngest moving group. The numberof A-type stars in nearby young moving groups for which the discdetection peaks is very limited while late-type stars are common. The © a r X i v : . [ a s t r o - ph . E P ] J a n N. Pawellek et al. best compromise between a high stellar luminosity and a reasonablylarge number of targets within the same moving group is given byF-type stars.An example fulfilling the aforementioned requirements is the 𝛽 Pictoris moving group (BPMG) which contains stars of ∼
23 Myrage (Bell et al. 2015). Based on a survey of 30 BPMG stars of dif-ferent spectral types, Rebull et al. (2008) found that more than 37%of the targets show evidence for a circumstellar disc. By consideringthe known F-type stars in the BPMG, Churcher et al. (2011) inferreda debris disc detection rate of 6/9 ( ∼ ∼
20 Myr and ∼ The BPMG is one of the nearest moving groups. Shkolnik et al.(2017) identified 146 objects belonging to this group, where fivestars are found to be A-type, eleven F-type, six G-type, 27 K-typeand 97 M- and L-type. Using data from the
Gaia data release 2 (GaiaCollaboration et al. 2018), several additional members of the BPMGwere found by Gagné & Faherty (2018). While the majority foundin that study are M- and L-type, one F-type star and one A-type starcould also be added to the sample given by Shkolnik et al. (2017).Thus, the sample of nine F-type members of the BPMG analysedby Churcher et al. (2011) is now increased to twelve by combiningthe samples of Shkolnik et al. (2017) and Gagné & Faherty (2018).These twelve targets will be the basis of our analysis. All of them liebetween 25 and 66 pc (Gaia Collaboration et al. 2018; Bailer-Joneset al. 2018), with stellar properties listed in Tab. 1.
Investigating the stellar multiplicity we found that our sample ofF stars possesses a 67% fraction of multiple systems (8/12) includingwide (separations > > In our sample of F stars only the most luminous star HD 29391, alsoknown as 51 Eridani, is known to possess a planetary companion(e.g., Macintosh et al. 2015; Nielsen et al. 2019). The system islocated at a distance of 29.8 pc and forms a multiple stellar systemwith the M-type binary star GJ 3305AB (e.g., Janson et al. 2014).The companion 51 Eri b was discovered by the Gemini Planet ImagerExoplanet Survey (GPIES, Patience et al. 2015; Nielsen et al. 2019)with a projected separation of 13 au. Depending on the formationmodel the estimated mass of the planet varies between 1. . . 2 𝑀 Jup for a so-called “hot start” model (Marley et al. 2007; Rajan et al.2017) and 2. . . 12 𝑀 Jup for a “cold start” model (Marley et al. 2007;Fortney et al. 2008).
We collected photometric data for all twelve targets in our samplefrom published catalogues, such as 2MASS (Cutri et al. 2003), theWISE All-Sky Release Catalog (Wright et al. 2010), the AKARI All-Sky Catalogue (Ishihara et al. 2010), the Spitzer Heritage Archive(Carpenter et al. 2008; Lebouteiller et al. 2011; Chen et al. 2014;Sierchio et al. 2014) and the Herschel Point Source Catalogue (Mar-ton et al. 2015). These data allowed us to analyse the spectral energydistributions (SEDs) and therefore the occurrence of infrared emis-sion in excess of that expected from the stellar photosphere. Mid-and far-infrared excesses are an indicator of the presence of a debrisdisc surrounding a host star.To find excesses we fit an SED model consisting of a star and a disc.We fit PHOENIX stellar photosphere models (Brott & Hauschildt2005) for each target using the stellar luminosity and the stellar tem-perature as model parameters. The resulting stellar luminosities andtemperatures are listed in Tab. 1. Knowing the stellar contributionto the mid- and far-infrared data we were able to derive the ex-cess emission in the appropriate wavelength bands between 22 and100 𝜇 m taking into account the uncertainties of the photometry andthe photospheric model (Yelverton et al. 2019). The results are givenin Tab. 2.After subtracting the stellar emission the disc is fitted with a mod-ified blackbody model (Backman & Paresce 1993) for which thethermal emission of the dust is described as 𝐹 𝜈 ∼ 𝐵 𝜈 ( 𝜆, 𝑇 dust ) (cid:34) 𝐻 ( 𝜆 − 𝜆 ) + 𝐻 ( 𝜆 − 𝜆 ) (cid:18) 𝜆𝜆 (cid:19) − 𝛽 (cid:35) , (1) MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic Table 1.
Stellar parameters of the sample of 12 F-type stars belonging to the 𝛽 Pic moving group.Multiplicity Planetary companionHD HIP SpT 𝐿 / 𝐿 sun 𝑇 eff d Companion SpT Separation Ref Separation Mass[K] [pc] [arcsec] [au] [au] [ 𝑀 Jup ]203 560 F2V 4 . ± .
03 6830 ±
30 40.0 . . . . . . . . . . . . . . . . . . . . .14082A 10680 F5V 2 . ± .
01 6170 ±
20 39.8 HD 14082B G2V 14 557 1, 4 . . . . . .15115 11360 F4V 3 . ± . ±
20 49.0 . . . . . . . . . . . . . . . . . . . . .29391 𝑎 . ± .
06 7330 ±
30 29.8 GJ 3305AB M1V 66 1957 1 13 1-1235850 25486 F8V 1 . ± .
01 6050 ±
20 26.9 HD 35850B . . . 7 . × − . ± .
03 6050 ±
40 65.7 . . . . . . . . . . . . . . . . . . . . .164249 88399 F5V 3 . ± .
04 6340 ±
40 49.6 HD 164249B M2V 6.5 323 1 . . . . . .2MASS J18011138-5125594 . . . . . . . . . 3 . . . . . .173167 - F5V 2 . ± . ±
90 50.6 TYC 9073-0762 M1V 571 28894 1, 2 . . . . . .181327 95270 F5V 2 . ± .
02 6480 ±
20 48.2 HD181296 A0V+M7/8V 416 20072 1 . . . . . .191089 99273 F5V 2 . ± .
02 6460 ±
30 50.1 . . . . . . . . . . . . . . . . . . . . .199143 103311 F8V 2 . ± .
02 5930 ±
20 45.7 HD 199143B M2V 1.1 50 4, 8 . . . . . .HD 358623 K7 325.0 14764 1, 8 . . . . . .213429 111170 F8V 1 . ± .
06 5970 ±
20 25.5 HD 213429B . . . ∼ . 𝑏 ∼ 𝑏
1, 5 . . . . . .
Notes: ( 𝑎 ) HD 29391 is also known as 51 Eridani. The references for the planetary companion are given in Section 2.3. ( 𝑏 ) The orbital period is 631 d. It isconverted to a separation assuming the mass of the binary companion to be equal to that of the primary HD 213429 with 1 . 𝑀 (cid:12) . References for multiplicity: [1] Elliott & Bayo (2016), [2] Moór et al. (2013), [3] Gagné et al. (2018a), [4] Mamajek & Bell (2014), [5] Kovaleva et al. (2015),[6] Eker et al. (2008), [7] Rodriguez & Zuckerman (2012), [8] Tokovinin (1997) where 𝐵 𝜈 is the Planck function and 𝐻 the Heaviside step function.The parameter 𝜆 represents the characteristic wavelength while 𝛽 isthe opacity index. From this model we derive the dust temperature, 𝑇 BB , and the resulting blackbody radius of the disc, 𝑅 BB , as well asthe fractional luminosity, 𝑓 d (see Tab. 3). Here, 𝑅 BB is the distancefrom the star that the temperature implies if the dust acted like black-bodies in equilibrium with the stellar radiation. In § 5 we apply adisc model including dust size distributions which do not exist in theframework of Yelverton et al. (2019).The uncertainties of the fit parameters were inferred in the follow-ing way. We start at the position of the minimum 𝜒 in parameterspace, i.e. from the best fitting 𝑓 d and 𝑅 BB . A set of new parametervalues is randomly generated from which we calculate the SED. Thisleads to a new 𝜒 value which is compared to the former minimumvalue. The 𝜒 parameter estimates how likely the set of parametervalues fits the SED. If the probability is larger than a certain thresholdvalue the set is saved. In the end, it is counted how often the codereaches a certain set of 𝑓 d and 𝑅 BB . The closer the parameters get tothe best fitting values the higher the probability. The resulting distri-bution in parameter space represents an estimate for the probabilitydistribution of the parameters and thus allows us to calculate theconfidence levels for the parameters assuming that the values followa normal distribution (simulated annealing; e.g., Pawellek 2017). We identified nine out of twelve stars (75%) that show infrared excessand therefore suggest the presence of a debris disc. Since we cannotdraw strong conclusions on HD 173167 (see § 3.3) we might evensay that nine out of eleven systems ( ∼ ∼
20% around FGK-stars for volume limitedsamples with older mean ages around Gyr (e.g., Su et al. 2006; Eiroaet al. 2013; Chen et al. 2014; Marshall et al. 2016; Sibthorpe et al.2018).The fractional luminosities of the excess emission lie between 1 . × − and 4 . × − , which are typical values for debris discs (e.g., Eiroa et al. 2013; Chen et al. 2014; Holland et al. 2017; Sibthorpeet al. 2018). The inferred blackbody temperatures lie between 51 and600 K corresponding to blackbody radii between 0.3 and 52 au.Pawellek & Krivov (2015) found a relation between the ratio of thespatially resolved disc radius seen at FIR wavelengths to blackbodyradius and the stellar luminosity of the form 𝑅 FIR 𝑅 BB = 𝐴 (cid:18) 𝐿𝐿 sun (cid:19) 𝐵 . (2)The disc radius seen at FIR wavelengths in this relation is that inferredfrom resolved Herschel /PACS imaging, and the blackbody radiusthat of a fit to the spectrum that is comparable with the modifiedblackbody fit used here. We use the updated values of 𝐴 and 𝐵 fromPawellek (2017) with 𝐴 = . ± .
86 and 𝐵 = − . ± .
05 assumingpure astronomical silicate (Draine 2003) for the dust material.Estimates of the FIR radii of the discs using eq. (2) give valuesbetween 1.5 and 215 au which are ∼ 𝑅 BB . In §4.4we compare those estimates to the observed disc radii of the spatiallyresolved discs. HD 14082A: For HD 14082A all WISE bands (3.4, 4.6, 12 and 22 𝜇 m,see WISE All-Sky Catalog, Wright et al. 2010) and Spitzer/MIPS(24 𝜇 m, Chen et al. 2014) exhibit significant excess emission, but noexcess was found with Spitzer/MIPS (70 𝜇 m) or Herschel/PACS. Thestar forms a binary system (Mamajek & Bell 2014; Elliott & Bayo2016) with its companion (HD 14082B) known to exhibit IR excessin the mid- and far-infrared (e.g., Riviere-Marichalar et al. 2014).After checking the WISE and MIPS data we found the photometryto be confused in all bands since those instruments were not able todifferentiate between the two stellar components. Thus, we assumeno significant excess emission for HD 14082A while the excess foundaround HD 14082B is real.HD 29391: The star HD 29391 (51 Eri) shows significant excess atMIPS24, MIPS70 and PACS100 providing a good constraint on thedisc as noted previously (Riviere-Marichalar et al. 2014). The targetpossesses the only planetary companion detected in our sample (see§2.3). The planet’s separation is ∼
13 au. With the disc’s 𝑅 BB = MNRAS000
13 au. With the disc’s 𝑅 BB = MNRAS000 , 1–26 (2021)
N. Pawellek et al. ± 𝑅 FIR = . ± . 𝜇 m so that we cannot draw any conclusions about a possiblefar-infrared excess. However, the mid-infrared data do not revealsignificant excess.HD 199143: Considering HD 199143, there are mid-infrared dataavailable as well as data from Herschel /PACS. The excess emissionis significant only for the MIPS24 band, but WISE data also show amarginal detection of excess emission at 22 𝜇 m. Despite the presenceof a close binary companion we could rule out confusion issuessince the companion is several orders of magnitude fainter than theprimary. Therefore, we assume that we detect emission from hot dustclose to the star. In our sample this is the only target with a close-indisc, with a dust temperature of 600 K and a blackbody radius of0.3 au. The FIR radius is estimated to be 1.5 au.While Tab. 2 gives the significance of the excess at 24 𝜇 m as 7 𝜎 this might be overestimated because of the SED fit being to bothstar and disc. Fitting the star without including the disc componentresults in a 24 𝜇 m excess of 3 𝜎 . Thus the excess is real, albeit at lowsignificance. We found that all four stars in our sample without a known stellarcompanion possess a debris disc (HD 203, HD 15115, HD 160305and HD 191089). Furthermore, three out of the five systems withcompanions at projected separations larger than 135 au (HD 14082A,HD 29391, HD 164249, HD 173167 and HD 181327) harbour a discas well. Two systems have companions at projected separations below25 au where one shows evidence of debris. (HD 35850 has debrisand a companion at a distance of 0.021 au, while HD 213429 has nodebris and a companion with an estimated separation of ∼ ∼
50 au (in addition to a wide separation component at ∼ 𝑅 BB = . ∼
25 and 135 auno discs could be detected. Since these values are comparable totypical debris disc radii (e.g., Booth et al. 2013; Pawellek et al. 2014;Matrà et al. 2018) it was suggested that the binaries are clearingthe primordial circumstellar or circumbinary material via dynamicalperturbation. While the detection rates for separations larger than135 au were found to be similar to the rates for single stars (at ∼ ∼
8% of binary systems with separations below 25 aushowed evidence for debris.Thus, considering the three aforementioned targets (HD 35850,HD 199143, HD 213429), we would expect a lower number of discdetections for these systems, but as they are only three in number wecannot draw any conclusions about detection rates.
Different observational wavelengths are sensitive to different sizes ofdust grains. While the emission seen by (sub-)mm telescopes suchas ALMA is expected to be dominated by thermal emission frommm-sized particles, near-infrared instruments such as VLT/SPHERE (Beuzit et al. 2019) are expected to trace scattered light from micron-sized grains. Particles as small as micron-size are significantly af-fected by radiation pressure and other transport processes (e.g., Burnset al. 1979) so that their distribution is expected to extend far bey-ond their birth environment. In contrast the large mm-sized grainsare expected to stay close to the parent belt. Hence, the disc sizeinferred in sub-mm observations is the best tracer of the locationof a system’s planetesimal belt, which might differ from the radialextent seen in near-infrared scattered light. Nevertheless, such shortwavelength observations can also be modelled to infer the planetes-imal belt location, and comparing the disc structure seen at differentwavelengths provides information on the physical mechanisms shap-ing debris discs.
Atacama Large Millimeter/submillimeter Array (ALMA) observa-tions of six out of the twelve stars in our sample were retrieved fromthe ALMA archive. Three of the analysed datasets have already beenpresented in literature work (HD 15115, HD 29391, HD 191089,MacGregor et al. 2019; Pérez et al. 2019; Kral et al. 2020), but arere-analysed here to maintain consistency across the sample. We alsopresent the first ALMA image of HD 164249 and new images ofthe disc around HD 181327. For the latter target another dataset waspublished by Marino et al. (2016), but due to their lower resolutionwe do not use those data here. In addition to that we present newconstraints for HD 14082A for which dust emission was not detected(as was also the case for HD 29391).The targets were observed as single pointings with the ALMA12 m array within the context of a variety of projects, over differentALMA Cycles, leading to inhomogeneous sensitivities, resolutions,and wavelengths (see Table 4). For each target, and each observingdate, we carried out standard calibration steps to obtain calibratedvisibility datasets; we used the same CASA and pipeline version asused in the original reduction delivered by the ALMA observatory.Later processing was carried out homogeneously in CASA v5.4.0.If available, for each target, we concatenated multiple datasets at sim-ilar frequencies to obtain a final combined visibility dataset. We alsoaveraged in time (to 30s integrations) and frequency (to 2 GHz-widechannels) to reduce the size of each dataset and speed up imagingand modelling.We then carried out continuum imaging using the CLEAN al-gorithm implemented through the tclean
CASA task. We usedmultiscale deconvolution (Cornwell 2008) in multi-frequency syn-thesis mode, adapting the choice of visibility weighting and/or taper-ing schemes to achieve a good trade-off between image sensitivityand resolution. The weighting choices, RMS noise levels (measuredin image regions free of source emission), and synthesised beamsizes achieved are listed in Table 4.Discs are detected and resolved around four out of the six BPMGF stars with existing ALMA observations. Fig. 2 shows the ALMAimages for the resolved discs, as well as the best-fit models, resid-uals, and deprojected visibilities. No detection was achieved near thelocation of HD 14082A and HD 29391 in the respective images. Weconservatively derive 3 𝜎 upper limits of < . < . (cid:48)(cid:48) radius circular region centered on the expectedstellar location. The high values for the upper limits are caused bythe relatively small beam used for the observation of HD 29391 andthe fact that HD 14082A is significantly offset from the phase center,increasing the already high RMS of that observation. For both targetsno (sub-)mm observations were reported in the literature before. MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic Table 2.
IR excesses. WISE22 MIPS24 MIPS70 PACS70 PACS100HD 𝐹 𝜈 𝐹 𝜈,★ Excess 𝐹 𝜈 𝐹 𝜈,★ Excess 𝐹 𝜈 𝐹 𝜈,★ Excess 𝐹 𝜈 𝐹 𝜈,★ Excess 𝐹 𝜈 𝐹 𝜈,★ Excess[mJy] [mJy] 𝜎 [mJy] [mJy] 𝜎 [mJy] [mJy] 𝜎 [mJy] [mJy] 𝜎 [mJy] [mJy] 𝜎
203 126.5 ± ± ± ± ± ± ∗ ± ∗ . . . 3.9 . . . <
13 4.1 . . . < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
249 3.3 5.9 . . . 3.5 . . . 1463 ±
47 1.7 31191089 192.8 ± ± ± ± ± ± < ± ± ± ± Notes:
Errors include both statistical and systematic uncertainties. WISE data from WISE All-Sky Catalog (Wright et al. 2010), MIPS24 and MIPS70 fromSpitzer Heritage Archive (Carpenter et al. 2008; Chen et al. 2014; Sierchio et al. 2014), PACS70 and PACS100 from Herschel Science Archive (Eiroa et al.2013). Upper limits stem from Riviere-Marichalar et al. (2014). The thermal emission caused by the dust material surrounding the star is given as excess fromthe stellar photosphere in units of 𝜎 and is considered to be significant if it reaches a value larger than 3. (∗) The WISE and MIPS data of HD 14082A werefound to be confused and thus, are not taken into account when checking the presence of IR excess.
Table 3.
SED fitting results.HD Resolved Modified blackbody model Grain size distribution model 𝑓 d 𝑇 bb 𝑅 bb 𝑅 est, sub-mm 𝑅 sub-mm 𝑠 blow 𝑠 min 𝑠 min / 𝑠 blow 𝑞 SED 𝑇 dust 𝑓 d [10 − ] [K] [au] [au] [au] [ 𝜇 m] [ 𝜇 m] [K] [10 − ]203 No 15 134 ± ± ± ± ± ±
27 93 ±
21 0.91 4.6 ± ± ± ± . . ±
20 18 ± ± . ± ± ± ±
10 32 ± ±
23 88 ± ± ± 𝑎 ± ± ± ±
15 63 ±
24 0.89 2.8 ± ± ± ± . ± ± ±
22 81 ±
16 1.02 1.1 ± ± ± ± ± ± ± ±
16 0.98 1.2 ± ± ± ± ±
100 0.2 ± ± Notes:
The blow-out limit is calculated assuming Mie theory and pure astronomical silicate (Draine 2003) with a bulk density of 3 . . The estimated discradius seen at sub-mm wavelengths, 𝑅 est, sub-mm , is calculated by eq. (2) using the parameters inferred in this work. A grain size distribution fit is done if thedisc is spatially resolved. 𝑎 The parameter 𝑞 SED was fixed due to a lack of photometric data in the far-infrared. Only HD 15115 shows evidence for a warm disccomponent.
Table 4.
BPMG F stars ALMA observations SummaryTarget Date Project ID Band Continuum Continuum Cont. Image Original ReferenceRMS Beam size weighting for Datasetdd-mm-yyyy 𝜇 Jy beam − HD14082A 31-08-2015 2013.1.01147 6 150 𝑎 (cid:48)(cid:48) × (cid:48)(cid:48) Natural This workHD15115 01-01-2016 2015.1.00633 6 15 0.6 (cid:48)(cid:48) × (cid:48)(cid:48) Briggs 0.5 MacGregor et al. (2019)09-06-2016 2015.1.00633 6 MacGregor et al. (2019)HD29391 13-10-2016 2016.1.00358 6 23 0.2 (cid:48)(cid:48) × (cid:48)(cid:48) Natural Pérez et al. (2019)HD164249 10-03-2014 2012.1.00437 6 45 1.1 (cid:48)(cid:48) × (cid:48)(cid:48) (cid:48)(cid:48) Taper This work11-08-2015 2013.1.01147 6 This workHD181327 25-07-2016 2015.1.00032 7 27 0.2 (cid:48)(cid:48) × (cid:48)(cid:48) Natural This workHD191089 23-03-2014 2012.1.00437 6 12 0.9 (cid:48)(cid:48) × (cid:48)(cid:48) Briggs 0.0 This work30-05-2018 2017.1.00704 6 Kral et al. (2020)14-09-2018 2017.1.00200 6 Matrà et al. (in prep.)
Notes: 𝑎 At field center. HD14082A is however ∼ (cid:48)(cid:48) from field center, where the primary beam level drops to 46%. The sensitivity per beam at that locationwould be 326 𝜇 Jy beam − . RMS noise levels, beam sizes and weightings of multiple datasets refer to imaging of the joint datasets.MNRAS000
Notes: 𝑎 At field center. HD14082A is however ∼ (cid:48)(cid:48) from field center, where the primary beam level drops to 46%. The sensitivity per beam at that locationwould be 326 𝜇 Jy beam − . RMS noise levels, beam sizes and weightings of multiple datasets refer to imaging of the joint datasets.MNRAS000 , 1–26 (2021) N. Pawellek et al.
Figure 1.
SEDs for the debris discs detected around F stars in the BPMG. Solid lines show the modified blackbody fit. For spatially resolved targets, dashedlines show the size distribution fit using Mie theory. Blue lines represent the outer ring, red lines the inner ring (if present). For the SED of HD 15115 both disccomponents were fitted with a modified blackbody model (solid line) and a size distribution model (dashed line).
For the visibility modelling, we follow the method described e.g.in Matrà et al. (2019), using RADMC-3D to calculate model imagesfrom a given density distribution, which we here assume to be a radialand vertical Gaussian described by 𝜌 = Σ 𝑒 − ( 𝑟 − 𝑟 c ) 𝜎 𝑒 − 𝑧 ( ℎ𝑟 ) √ 𝜋ℎ𝑟 , (3)with symbols having the same meaning as in Eq. 1 of (Matrà et al.2018). The vertical aspect ratio ℎ = 𝐻 / 𝑅 is radially constant andfixed to 0.03 for belts that are too face-on or too low S/N for it tobe meaningfully constrained. Additionally, rather than fitting for thenormalization factor Σ , we fit for the total flux density of the belt in the model images. When calculating model images, we also assumethe grains to act as blackbodies and therefore to have a temperaturescaling as 𝑟 − . .After producing a model image, we Fourier Transform it andsample the model visibility function at the same u-v locations asthe data using the GALARIO software package (Tazzari et al. 2018).This produces model visibilities that can be directly compared withthe observed ones. This process is then used to fit the model tothe data through a Markov Chain Monte Carlo (MCMC) implemen-ted using the EMCEE v3 software package (Foreman-Mackey et al.2013, 2019). This samples the posterior probability function of the n-dimensional parameter space of our model using the affine-invariantsampler of Goodman & Weare (2010). We use a likelihood function ∝ 𝑒 − 𝜒 and uniform priors on all model parameters. In addition tothe model parameters entering the equation describing the densitydistribution, we fit for RA and Dec offsets of the belt’s geometric MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic center from the phase center of the observations, and for a weightrescaling factor to account for the inaccurate data weights (and henceuncertainties) typically delivered by ALMA (e.g. Marino et al. 2018;Matrà et al. 2019). We fit these additional, nuisance parameters sep-arately to each observing date for any given target.Tab. 5 shows best-fit parameters and uncertainties derived foreach of the resolved belts, taken as the 50 + − th percentiles of themarginalised posterior probability distribution of each parameter.Fig. 2 shows full-resolution model images and residuals obtained bysubtracting the best fit visibility model from the data, and imagingwithout CLEAN deconvolution. The residual images look mostlyconsistent with noise, indicating that our models provide a verygood fit to the data. However, we note that some residual, extendedemission is detected 1) interior to the HD 181327 ring, to the SEof the star, and 2) at the SW ansa, and along the S side of theHD 191089 belt. While this could be due to true substructure in thedust morphology of these systems, this does not significantly affectthe measurement of the radius of the bulk of the planetesimal beltmaterial, which we are most interested in. The disc around HD 164249 was observed with ALMA at 1.35 mmand is spatially resolved for the first time increasing the number ofresolved debris discs reported in the literature to 153 according to thedatabase for resolved discs . It shows a face-on orientation with aninclination below 49 ◦ . The planetesimal belt is found at 63 au witha disc width of 24 au using a Gaussian disc model. The disc was notresolved at any other wavelength before. We re-analysed the data sets of two targets (HD 15115, HD 191089)presented in former studies to infer the system parameters, such asthe disc radius, in a consistent way and present the results of newhigh-resolution data for HD 181327.HD 15115: We find the edge-on disc of HD 15115 with an in-clination of 88 ◦ to be located at 93 . + . − . au with a disc width of21 + − au using a Gaussian ring model. The results from MacGregoret al. (2015, 2019) which are based on the same dataset as our studysuggest the disc to extend from 44 to 92 au with a 14 au wide gapat 59 au. MacGregor et al. (2019) suggests that a planet with a massof 0 . 𝑀 Jup is creating this gap, but so far no planet could be de-tected (see § 2.3). Our results do not show evidence for a gap inthe disc, which may be because of the different parameterisations ofthe two models; MacGregor et al. (2019) assumes a 2D disc modelusing a power law for the radial surface density distribution and aninfinitesimally small vertical scale height, whereas our disc modelassumes Gaussian radial and vertical density distributions (the latterwas found to be marginally resolved in our analysis).HD 181327: The face-on disc around HD 181327 was inferred tohave a radius of 81 . ± . + . − . au using a Gaussianring model. This is comparable with the 86 au radius and width of
23 au found by Marino et al. (2016) from lower resolution ALMABand 6 data.HD 191089. The debris disc around HD 191089 was observed at1.27 mm and formerly presented in Kral et al. (2020) which reporteda disc ring at 43 . ± . < . ∼ ◦ . With our Gaussian ring model we inferred an inclinationof 60 ◦ and a disc radius of 44 . ± . ± 𝜎 significance. We note that our data-set does not only contain thedata used in Kral et al. (2020), but a combination of those withdata from the “Resolved ALMA and SMA Observations of NearbyStars” (REASONS) programme (Sepulveda et al. 2019) which havea higher spatial resolution, as well as older observations from 2012(see Tab. 4). We visually checked the data cubes of the four ALMA resolvedtargets for CO gas emission, but did not detect any. HD 181327 is theonly target in our sample of F stars in the BMPG with a gas detectionpresented in Marino et al. (2016). That study found a significantamount of CO in its disc based on the J=2-1 excitation level andinferred a total CO-gas mass of 1 . . . . . × − 𝑀 ⊕ . The gas isconsistent with a secondary origin if the planetesimals in the discaround HD 181327 possess a similar volatile fraction compared toSolar system comets. Our observations included the J=3-2 excitationlevel. The non-detection could be consistent with the J=2-1 detectiondepending on excitation conditions, but a full gas analysis, includingoptimising detection, and considering the wide range of possibleexcitation conditions is needed to draw a definitive conclusion. Scattered light observations give us an additional opportunity to es-timate the planetesimal belt radii of discs especially if they werenot observed in thermal emission. Furthermore, observations atwavelengths shorter than sub-mm trace dust grain sizes smaller thanthose seen with ALMA and thus can help to investigate transport pro-cesses within the discs. While most of the spatially resolved discs inthe BPMG were observed with ALMA, there is one disc (HD 160305)only observed in scatterd light.HD 160305: The disc around HD 160305 was recently detectedwith VLT/SPHERE by Perrot et al. (2019) in scattered light. Thedebris dust is confined to a narrow ring between 86 and 90 au.It shows a near edge-on inclination and a brightness asymmetrybetween its western and eastern side. Perrot et al. (2019) suggestdifferent scenarios as the reason for this asymmetry, such as strongrecent collisions of planetesimals, interactions with massive com-panions, or pericentre glow effects, but was not able to differentiatebetween these scenarios.HD 15115: Scattered light observations of HD 15115 (e.g., Kalaset al. 2007; Engler et al. 2018) revealed a strong asymmetry of thedisc which is not seen in ALMA observations. Kalas et al. (2007) re-port a disc extent up to 580 au on the west side and 340 au on the eastside. MacGregor et al. (2019) concluded that the mechanism caus-ing the asymmetry is only affecting the smallest grains, suggestinginteraction with the local ISM as a likely reason for it. Engler et al.(2018) derived the maximum of polarised flux density at a location
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East offset (") N o r t h o ff s e t ( " )
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East offset (") R ea l ( m J y ) ModelData R uv (k ) I m a g i n a r y ( m J y ) Flux (mJy beam ) Flux ( Jy pix )
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East offset (") R ea l ( m J y ) ModelData R uv (k ) I m a g i n a r y ( m J y ) Flux (mJy beam ) Flux ( Jy pix )
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Flux ( Jy beam ) Figure 2.
ALMA models for four resolved debris discs. From top to bottom: HD 15115, HD 164249, HD 181327, HD 191089. of 94 ± HST /NICMOS observations of HD 181327 inscattered light presented by Schneider et al. (2006) derived a disc ra-dius of 86 au with a width of 36 au. While the radius is in agreementwith our ALMA-based results the disc width is broader in scatteredlight than at sub-mm wavelengths. We would expect a broader disc atshorter wavelengths since such observations trace smaller particles which are more susceptible to transport processes. Asymmetries werereported by Stark et al. (2014) which suggested a recent catastrophicdisruption or a warping of the disc by the ISM as probable causes.HD 191089: Churcher et al. (2011) observed HD 191089 at18.3 𝜇 m with T-ReCS on Gemini South and found excess emissionbetween 28 and 90 au. This is in agreement with the belt locationinferred from observations of the HD 191089 disc performed by HST /NICMOS and STIS and
Gemini /GPI (Ren et al. 2019). That
MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic Table 5.
Resolved discs and fitting parameters for ALMA models.HD 𝜆 𝐹 𝜈 ★ 𝐹 𝜈 belt 𝑅 Δ 𝑅 ℎ 𝑖 PA Δ RA Δ Dec[ 𝜇 m] [ 𝜇 Jy] [mJy] [au] [au] [ ◦ ] [ ◦ ] [ (cid:48)(cid:48) ] [ (cid:48)(cid:48) ]15115 1340 𝑎 + − . + . − . . + . − . 𝑎 + − 𝑎 . + . − . 𝑏 . + . − . . + . − . . + . − . − . + . − . − . + . − . + − 𝑎 + − − < 𝑐 − . + . − . − . + . − . ★ 𝑎 + − . + . − . . + . − . . + . − . < .
09 30 . + . − . . + . − . − . + . − . − . + . − . ★ 𝑎 + − . + . − . . + . − . + − 𝑎 . + . − . + − + − 𝑑 . + . − . 𝑑 − . + . − . Notes: ★ The model fit leaves significant residuals. 𝑎 Marginally resolved/detected, i.e. having a posterior probability distribution with a non-zero peak butconsistent with zero at the 3 𝜎 level. 𝑏 Inclination consistent with 90 ◦ (perfectly edge-on) at the 3 𝜎 level. 𝑐 Quantity unconstrained at the 3 𝜎 level, but with apronounced peak at the median value reported. 𝑑 Offsets refer to 2018 dataset. For 2014 dataset, offsets were Δ RA=0 . + . − . and Δ Dec=0 . + . − . . study detected scattered light between 26 and 78 au. In addition tothe dust ring a halo was found extending to ∼
640 au, but no bright-ness asymmetries were identified. However, similar to HD 181327the disc is broader in scattered light than at mm wavelengths.
Three discs in the BPMG sample were spatially resolved in the FIRwith
Herschel /PACS (HD 15115, HD 164249, and HD 181327). Toinfer their radii in a homogeneous way we apply the method describedin Yelverton et al. (2019) and Xuan et al. (2020). The PSF of the star isderived from observations of the
Herschel calibration star HD 164058and then rotated to the appropriate orientation and scaled to the stellarflux derived from the SED. Then we generate an axisymmetric,optically thin disc model and assume that the surface brightnessis proportional to 𝑟 − . with 𝑟 being the distance to the star. The dusttemperature at a distance 𝑟 is assumed to follow 𝑟 − . as for blackbodygrains. The free parameters of the model are the total disc flux density,the inner and outer edges of the disc, 𝑅 in and 𝑅 out , inclination, andposition angle. We also include a 2D offset to account for non-perfect Herschel pointing. The model disc is convolved with the PSFand then compared to the
Herschel /PACS image by calculating thegoodness of fit, 𝜒 . We estimate the parameters using the emceepackage. To get disc radii to be compared with those inferred fromALMA images that assumed a Gaussian radial profile, we derive aradius from Herschel /PACS, 𝑅 FIR = . × ( 𝑅 in + 𝑅 out ) . We note thatin some cases the inner and outer edge of a disc might be poorlyconstrained, and in any case 𝑅 FIR could differ from the location ofthe peak of the surface brightness that would have been inferred ifobserved at higher spatial resolution.The modelling results of the
Herschel /PACS images for the BPMGsample are listed in Tab. 6. In all cases the inclination and positionangle are in agreement with ALMA observations listed in Tab. 5. ForHD 15115 and HD 181327 the radii, 𝑅 FIR , are in agreement withvalues inferred from ALMA observations, but possess uncertaintiesof up to 25%. The disc widths seem to be larger compared to ALMA,but only show deviations within 2 𝜎 so that we assume the discs to besimilar in ALMA and Herschel . A broader extent in
Herschel mightindicate the presence of transport mechanisms altering the orbits ofsmaller dust particles towards larger eccentricities. For HD 164249the
Herschel results show large uncertainties due to the low spatialresolution. The
Herschel radius is a factor 2.2 smaller than that fromALMA, however the two radii are not significantly different ( ∼ 𝜎 )and the higher resolution ALMA result is a better estimate of theplanetesimal belt location. Figure 3.
Spatially resolved disc radius to blackbody radius ratio as a functionof stellar luminosity for NIR, FIR, and sub-mm wavlengths. Black circlesshow the ALMA sample from Matrà et al. (2018), red asterisks show theALMA-resolved F stars and the blue square the SPHERE-resolved F starHD 160305. The grey shaded areas depict the 1, 2, and 3 𝜎 levels of thecorrelation. The green dashed line shows the trend found in Pawellek (2017)from the Herschel resolved disc radius. We calculate the ratio of sub-mm radius to blackbody radius for thefour ALMA resolved discs in our sample. In addition, we infer theratio of the scattered light radius to blackbody radius for HD 160305.Given the knowledge that there is a potential trend in sub-mm discsizes with stellar luminosity (Matrà et al. 2018), and also a trend inthe far-infrared size to blackbody radius ratio with stellar luminosity(Booth et al. 2013; Pawellek & Krivov 2015), we compare the fivediscs to a sample of ALMA-resolved discs with a broader stellarluminosity range (Matrà et al. 2018). In Fig. 3 we plot the radius ratioas a function of stellar luminosity. The actual disc width inferred byALMA observations (see Tab. 5) is given by the error bars.For our sample of F stars the values of this ratio lie between 1.6 and3.4 where the system with the lowest stellar luminosity (HD 160305)possesses the highest value. Including the ALMA-sample of Matràet al. (2018) and fitting a trend of the form in eq. 2 for how the ratiodepends on stellar luminosity we infer a slight decrease of the ratiowith stellar luminosity finding parameter values of 𝐴 = . ± . 𝐵 = − . ± . Herschel images which showed parameter values of 𝐴 = . ± .
86 and 𝐵 = − . ± .
05 (see green dashed line in Fig. 3). For systemswith stellar luminosities larger than 5 𝐿 sun the radius ratio of the MNRAS000
05 (see green dashed line in Fig. 3). For systemswith stellar luminosities larger than 5 𝐿 sun the radius ratio of the MNRAS000 , 1–26 (2021) N. Pawellek et al.
Table 6.
Discs resolved with
Herschel /PACS.HD 𝑅 in 𝑅 out 𝑅 FIR Δ 𝑅 FIR 𝑖 PA[au] [au] [au] [au] [ ◦ ] [ ◦ ]15115 40 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . Notes: 𝑅 in and 𝑅 out give the inner and outer radii for Herschel /PACS inferred with the method described in § 4.3.2 following the procedure of Yelverton et al.(2019) and Xuan et al. (2020). 𝑅 FIR is the central radius defined as 𝑅 FIR = . ∗ ( 𝑅 in + 𝑅 out ) , Δ 𝑅 FIR gives the disc width. The parameters 𝑖 and PA give theinclination and position angle. ALMA sample is in agreement with Pawellek & Krivov (2015). Thedifferent fit is caused by a number of systems with lower luminositiesincluding our sample of ALMA resolved F stars that show relativelysmall ratios. Possible reasons for the different trends could be that
Herschel had a lower resolution and so there may be systematicuncertainties in the derived disc radii, or the discs could be largerwhen traced in the far-IR due to such wavelengths tracing small dustin the halo that extends beyond the planetesimal belt. However, ouranalysis of the
Herschel images of the BPMG F stars in § 4.3.2inferred radii that are consistent with those from ALMA images.Considering Pawellek & Krivov (2015), none of the BPMG targetswas used to derive the radius ratio vs luminosity trend, but the studyinferred radii between 93 and 112 au for HD 181327 dependingon the dust composition assumed which is in agreement with theresults of ALMA and
Herschel . A more detailed analysis is neededto investigate possible causes for the different outcomes between the
Herschel and ALMA samples. A systematic difference might indicatethe presence of dynamical processes affecting the size distribution ina way not considered before.
As mentioned before, five discs of our sample were spatially resolved(four with ALMA and one with SPHERE, see Tab. 5). This allowsus to apply a more detailed model to fit the SEDs of these fivediscs rather than using a simple modified blackbody model as in §3.In the following approach we model the dust size distribution andcomposition.
We use the SONATA code (Pawellek et al. 2014; Pawellek & Krivov2015) and apply the same PHOENIX-GAIA stellar photosphericmodels (Brott & Hauschildt 2005) to determine the host star contri-bution in a similar approach as for the modified blackbody fits (MBB,see §3). While for the MBB model we simply fitted a dust temperatureand a fractional luminosity without consideration of dust propertiesthe SONATA code calculates the temperature and the thermal emis-sion of dust particles at different distances to the star. It assumescompact spherical grains and uses Mie theory to derive the absorp-tion efficiencies (Bohren & Huffman 1983). The dust composition isassumed to be pure astronomical silicate (Draine 2003) with a bulkdensity of 3.3 g/cm . The code sums up the emission of particleswithin a range of sizes to generate the SED. The flux densities givenfor wavelengths shorter than 5 𝜇 m are not used to fit the dust discsince in this wavelength regime the stellar photosphere rather thanthe dust dominates the emission.We apply a power law for the size distribution and assume aGaussian radial distribution of the dust using the surface number density 𝑁 ( 𝑟, 𝑠 ) : 𝑁 SED ( 𝑟, 𝑠 ) ∼ 𝑠 − 𝑞 SED √ 𝜋 Δ 𝑅 disc exp (cid:34) − (cid:18) 𝑟 − 𝑅 disc Δ 𝑅 disc (cid:19) (cid:35) . (4)Here, 𝑟 represents the distance to the star, 𝑅 disc the peak and Δ 𝑅 disc the width of the radial distribution. The parameter 𝑠 is the grain radiusand 𝑞 SED is the SED power-law index for the size distribution. Thesurface number density is directly connected to the surface density, Σ , by Σ ( 𝑟, 𝑠 ) 𝑑𝑠 = 𝜋𝑠 𝑁 ( 𝑟, 𝑠 ) 𝑑𝑠 .The grain sizes lie between a minimum and a maximum value, 𝑠 min and 𝑠 max where we fix the maximum grain size to 10 cm. Largergrains do not contribute to the SED in the wavelength range observedfor the size distributions considered here with 𝑞 SED >
3. In addition,we fix the radial parameters to the values inferred from our resolvedimages (see Tab. 5). Therefore, we are left with three free parametersto fit: the minimum grain size, 𝑠 min , the size distribution index, 𝑞 SED ,and the amount of dust, 𝑀 dust , for particles between 𝑠 min and 𝑠 max assuming a bulk density 𝜚 .We follow the three criteria given in Ballering et al. (2013) andPawellek et al. (2014) to check for the presence of a warm com-ponent for the five discs. For us to consider a warm component tobe present, there has to be a significant excess ( ≥ 𝜎 ) in either theWISE/22 or MIPS/24 in excess of that which could originate in asingle ring fitted to longer wavelength data. Secondly, the fit of thetwo-component SED has to be much better than the one-componentfit. While the former studies assumed a better two-component fitwhen 𝜒 / 𝜒 > = 𝜒 + 𝐽 log 𝑒 ( 𝑁 ) , (5)where 𝐽 represents the number of free parameters and 𝑁 the numberof data points. We use the classification given in Kass & Raftery(1995) to infer whether a one- or a two-component model is morelikely. As a third criterion we require the inferred ring containingthe warm dust to be located outside the sublimation radius 𝑅 sub (assuming 1300 K as the sublimation temperature).If all three criteria are fulfilled we obtain the two-component modelin the following way. In a first step we assume the warm dust to bemodelled by a pure blackbody to infer its blackbody temperature andradius. We assume this radius to be the location of the warm dustbelt and fix the belt width to Δ 𝑅 disc / 𝑅 disc = ∼ . 𝑞 SED , to 3.5
MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic (the outcome of an ideal collisional cascade, Dohnanyi 1969) toreduce the number of free parameters. Following the criteria for two-component models we checked at firstthe SEDs of the four resolved discs around HD 15115, HD 164249,HD 181327 and HD 191089 for the presence of a warm inner com-ponent. Only HD 15115 fulfills all of them so that we fitted this discwith a two-component model. The SED fitting results of the wholesample are all summarised in Tab. 3 and the SEDs are depicted inFig. 1.Collisional evolution models show that grains smaller than a cer-tain blow-out size, 𝑠 blow , are expelled from the stellar system due toradiation pressure. The blow-out size depends on the optical paramet-ers of the dust material and increases with increasing stellar luminos-ity. We would expect the minimum grain size, 𝑠 min , to be comparableto 𝑠 blow . However, previous studies of grain size distributions (e.g.,Pawellek et al. 2014; Pawellek & Krivov 2015) found that 𝑠 min , isweakly connected to the stellar luminosity. It might also be consist-ent with being independent of stellar luminosity, since those studiesfound an average value of ∼ 𝜇 m to fit the majority of debris discsanalysed therein. It was also found that the ratio between 𝑠 min and 𝑠 blow is ∼ . . . 𝐿 sun (Pawellek et al. 2014). The 𝑠 min / 𝑠 blow ratio isthought to be connected to the dynamical excitation of the planetes-imals producing the visible dust (e.g., Krijt & Kama 2014; Thebault2016). Earlier studies, such as Krivov et al. (2006) or Thébault &Augereau (2007) suggest a value around 2 for collisionally activediscs.For three targets in our sample our modelling finds that 𝑠 min isclose to 𝑠 blow leading to a 𝑠 min / 𝑠 blow ratio of ∼
1. Only the resultsfor HD 15115 reveal a 𝑠 min close to 5 𝜇 m and a 𝑠 min / 𝑠 blow ratioof ∼
5. However, the difference in 𝑠 min of this disc to the othersin the sample should be treated with caution, since the minimumgrain size that we infer may be influenced by how we treated thewarm component that is only present in this system. Besides our fourtargets there is a range of different discs at the same stellar luminosityinvestigated by Pawellek & Krivov (2015) and Matrà et al. (2018)and shown as black dots in Fig. 3, most of which possess a larger 𝑠 min . The low 𝑠 min / 𝑠 blow ratio for F stars in the BPMG, which isreported for the first time, could indicate high levels of dynamicalexcitation similar to that found for discs around A-type stars (seeFig. 16 in Pawellek & Krivov 2015).The size distribution index, 𝑞 SED , lies between 3.4 and 3.8 for oursample. These values are consistent with collisional models (e.g.,Löhne et al. 2008; Gáspár et al. 2012; Kral et al. 2013; Löhne et al.2017).Overall, the results from our SED modelling suggest that all fourspatially resolved discs are in agreement with a stirred debris discscenario which means that the dust seen in the SED is consistent withbeing created by the collisional destruction of planetesimals in a belttraced by the ALMA images.
In the first part of this study we analysed the properties of the BPMGin detail. So far we do not know whether the high incidence rate ofdebris discs is a peculiarity of said moving group or whether we seemore discs due to the young age of the moving group. Therefore, wewill put the results of the BPMG into context with discs around other
Figure 4.
Stellar temperature as function of age. near-by F-type stars in the second part of this study. First we invest-igate the evolution of spectral type to ensure that we compare stellarpopulations with similar properties. Then we look at the appropriatesystems in samples of field stars and other young moving groups.
The stellar spectral type is determined by the effective temperatureof the star. Due to ongoing thermonuclear reactions, stars and theirphysical/chemical properties such as metallicity, stellar radius ortemperature, evolve over time so that the spectral type might change aswell. Therefore, it is not self-evident that comparing stars with similarspectral types but different ages show the same stellar population atvarying evolutionary phases.We use the "‘Modules for Experiments in Stellar Astrophysics"’(MESA, Paxton et al. 2011, 2013, 2015; Choi et al. 2016) to checkthe evolution of stellar temperature over time. MESA consists of aone-dimensional stellar evolution module simultaneously solving thefully coupled structure and composition equations. The results areshown in Fig. 4. We use the lowest (1 . 𝑀 sun ) and highest (1 . 𝑀 sun )stellar masses in our sample of F stars to analyse its parameter spaceand assume a stellar metallicity of [ Fe / H ] = . ∼
10 Myr andthen stays constant until ∼ Sibthorpe et al. (2018) analysed an unbiased sample of 275 FGK stars
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Table 7.
F stars in the DEBRIS sample with debris disc detections.
HD d SpT 𝐿 / 𝐿 sun 𝑓 d 𝑅 BB 𝑅 FIR Δ 𝑅 FIR [pc] [ − ] [au] [au] [au]1581 8.6 F9.5V 1.29 ± ±
45 . . . . . .7570 15.2 F9VFe+0.4 1.96 ± ±
10 . . . . . . ∗ ± ± . ± + . . ± . ± ±
17 . . . . . .16673 21.9 F8VFe-0.4 1.93 ± ±
23 . . . . . . ∗ ± ± . ± . . ± . ∗ ± ± . ± . . ± . ± ± ∗ ± ± . ± . . ± . ± ± 𝑎 ± ± ∗ ± ± . ± . . ± . ± ±
68 . . . . . . ∗ ± ± . ± . . ± . ∗ ± ± . ± . . ± . ± ±
22 . . . . . .160032 21.2 F4V 4.55 ± ±
35 . . . . . . ∗ ± ± . ± . . ± . ± ±
12 . . . . . . ∗ ± ± . ± . . ± . ± ± Notes: ∗ Target was reported in Sibthorpe et al. (2018) to possess extended disc emission. The radii, 𝑅 FIR , from
Herschel /PACS were derived from the model presented in Yelverton et al. (2019) and aredefined in the same way as described in §4.3.2. 𝑎 HD 56986 possesses a marginal excess at MIPS24.The image at PACS160 seems to be confused with a nearby background object making the SEDmodel very uncertain. including 92 F-type stars observed with
Herschel /PACS in theDEBRIS survey. None of the F-types belong to the BPMG, whichlie within 24 pc. All targets are older than 160 Myr following theage determination of Vican (2012) with the exception of the targetsHD 56986 with an age of ∼
20 Myr and HD 7788A where no age isgiven.Based on Sibthorpe et al. (2018), 22 of the 92 stars show evidencefor a debris disc. However, we note that the target HD 19994 (Wiegertet al. 2016) previously assumed to have spatially resolved IR emissionshows evidence of being confused rather than possessing an actualdisc (Yelverton et al. 2019). Thus, we update the number of detectionsfor F stars in the DEBRIS sample to 21 out of 92 targets leadingto a detection rate of 22 . + . − . %. Due to the large beam size of Herschel /PACS other targets might show confusion as well. However,after checking the PACS images available we did not identify morepotentially confused discs. The HR-diagram of the whole DEBRISsample is presented in Figs. 1 and 2 in Phillips et al. (2010) andshows that all F stars in the DEBRIS sample which possess debrisdiscs are compatible with belonging to the main sequence. Therefore,we assume that in the DEBRIS sample no debris discs around post-main sequence F stars are included.The SEDs are fitted using the same process outlined in § 4.3.2.The modelling results are listed in Tab. 7 and the SEDs are shown inFigs. A3 and A4. We find blackbody radii between 2 and 200 au forthe whole sample with the exception of HD 56986 with a blackbodyradius around 0.1 au based on a marginal mid-IR excess. The excessfound at PACS160 is confused by a nearby background object so thatthe SED model is very uncertain. We therefore exclude this targetfrom our further analysis.Ignoring HD 56986 due to the aforementioned reasons, we find nodiscs smaller than 1 au, one disc out of 92 targets with a blackbodyradius between 1 and 3 au (1.1%), three disc radii between 3 and10 au (3.3%), five discs between 10 and 30 au (5.4%), seven discsbetween 30 and 100 au (7.6%), and four discs larger than 100 au(4.3%). Nine targets were reported to be spatially resolved in theFIR (Sibthorpe et al. 2018) (excluding HD 19994). Only HD 10647and HD 109085 were observed with ALMA (see § B3). However,using the method of Yelverton et al. (2019) we infer radii and disc widths from
Herschel /PACS images in the same manner as describedin § 4.3.2 (see Tab. 7). The discs range from 20 au to more thanthan 150 au. The smallest discs are located around HD 22484 andHD 219482 with radii of 39.7 and 20.6 au respectively. The discwidths are uncertain because of the relatively poor spatial resolutionso that we cannot draw strong conclusions on them.
The question arises whether the high occurrence rate of debris discsaround F-type stars in BPMG is a singular phenomenon of this mov-ing group or if it is common in other associations with comparableproperties in age and distance as BPMG. Here we compare the BPMGdisc incidence rates with those of other clusters. When doing so weneed to recognise that some stars lack FIR data and so have limitedconstraints on the presence of circumstellar dust. We will considerdetection rates for the whole sample (e.g. the 9/12 rate from theBPMG) and separately we will consider the rate amongst those withFIR data (e.g. the 9/11 rate for the BPMG).Following studies of young associations (e.g., Fig. 7 in Gagnéet al. 2018c; Gagné & Faherty 2018) we identified five groups withsimilar peaks in their distance distributions around 50 pc comparableto the BPMG: the Tucana/Horologium association (THA), Columba(COL), Carina (CAR), AB Doradus (ABDMG) and Carina-Near(CARN). The groups THA, COL and CAR possess an age around ∼
45 Myr, the groups ABDMG and CARN an age around ∼
150 Myr.For the purpose of our analysis a differentiation between the singlemoving groups is not necessary. Indeed, Torres et al. (2008) andZuckerman et al. (2011) found that THA, COL and CAR are closelylocated making it difficult to place members in one or the other group.Therefore, we generated two samples, one referred to as 45 Myr groupsums up all F-type targets belonging to THA, COL and CAR, theother referred to as 150 Myr group combines the targets of ABDMGand CARN. Both samples are unbiased towards the presence of IR-excess.Using the studies of members of young moving groups (Zucker-man et al. 2011; Faherty et al. 2018; Gagné et al. 2018b; Gagné& Faherty 2018), we identified 29 F stars in Tab. 8 for the 45 Myrgroup and 13 for the 150 Myr group. For several targets only data upto mid-infrared wavelengths (WISE22) are available or upper limitsfrom IRAS at 25, 60 and 100 𝜇 m, but no Spitzer /MIPS or other far-infrared data. The presence of far-infrared emission for these targetscannot be ruled out, but none of their SEDs shows excess in the mid-infrared. The detection rates are listed in Tab. 9 and given for both thecomplete samples and the sub-samples only including targets withFIR data.We applied the same modified blackbody model to fit the SEDsof systems in the 45 Myr and 150 Myr groups (see Figs. A1and A2)and inferred stellar parameters, fractional luminosities and blackbodyradii using the same method as in § 3 (see Tab. 8). In the 45 Myrgroup we find no disc with a blackbody radius below 1 au. Two outof 29 targets possess belts with blackbody radii between 1 and 3 au(6.9%), five discs lie between 3 and 10 au (17.2%), two between 10and 30 au and two between 30 and 100 au (each 6.9%). There wereonly two discs detected within the 150 Myr group. One lies at 1 authe other at 17 au. We note that the disc around 1 au (HD 15407) isonly poorly fitted since a strong solid state feature is visible in theSED but that the conclusion of a small blackbody radius is reliable.Considering NIR, FIR or sub-mm disc radii, only HD 30447 wasreported as spatially resolved in scattered light (Soummer et al. 2014)with a detection between 60 and 200 au.
MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic Table 8.
F stars of the 45 and 150 Myr groups.
HD Group d SpT 𝐿 / 𝐿 sun Disc 𝑓 d 𝑅 BB [pc] excess [ − ] [au]984 45 Myr 45.9 F7V 2.04 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Notes:
The data are taken from Zuckerman et al. (2011); Faherty et al. (2018); Gagné et al. (2018b);Gagné & Faherty (2018). The excess emission is given for
Spitzer /MIPS at 24 𝜇 m and/or 𝜇 m. Theexcess emission for stars with only WISE22 data or upper limits from IRAS is shown as dots. Thefractional luminosities are inferred from a modified blackbody SED model. Table 9.
Detection rates for the different samples.Sample 𝑁 Discs 𝑁 total 𝑁 FIR
Rate total [%] Rate
FIR [%]BPMG 9 12 11 75 . + . − . . + . − .
45 Myr 11 29 20 37 . + . − . . + . − .
150 Myr 2 13 7 15 . + . − . . + . − . DEBRIS 21 92 92 22 . + . − . % 22 . + . − . % Notes: 𝑁 Discs gives the number of disc detections, 𝑁 total is the total numberof targets in the sample, 𝑁 FIR is the number of targets with FIR data. Thedetection rates are given for the complete samples and the sub-samplescomposed of targets with FIR data assuming the number of disc detections, 𝑁 Discs divided by the sample size. The uncertainties were calculated usingthe method of Gehrels (1986).
In Fig. 5 we compare the fractions of stars with debris disc detec-tions for each sample which suggests that there might be a decreaseof disc frequency with increasing age. Using the DEBRIS sampleas reference and Fisher’s exact test (Fisher 1956) we tested the hy-pothesis that the incidence rates for the BPMG, the 45 Myr groupand the 150 Myr group are similar to the DEBRIS sample. We foundthat for the BPMG the probability 𝑝 = . × − , for the 45 Myrgroup 𝑝 = .
013 and for the 150 Myr group 𝑝 = .
68. The hypo-
Figure 5.
Incidence rates for the different samples ordered by age: BPMG(23 Myr), 45 Myr group, 150 Myr group, DEBRIS ( >
160 Myr). The uncer-tainties are calculated using the method of Gehrels (1986). Only targets withFIR data are taken into account (see Tab. 9) Frequencies are not corrected forcompleteness. thesis is rejected if the 𝑝 -value is smaller than a chosen significancelevel, 𝛼 which we set to 0.05. Therefore, we can say that for BPMGand the 45 Myr group the detection rates are not similar to that ofthe DEBRIS sample. In addition, we tested whether the rates of theBPMG and the 45 Myr group are different from each other and found 𝑝 = .
45. This means that the BPMG and the 45 Myr group showsimilar detection rates. The result leads to the impression that a highfrequency of debris discs might be common for F stars younger than100 Myr.
Plotting detection rate versus age can be misleading, since differentsurveys reach different sensitivities to discs, for example due to thedifferent distance of the stars in their samples. This sensitivity can beunderstood within the context of a modified blackbody model, sincefor each star the region of fractional luminosity vs blackbody radiusfor which a disc detection would have been possible can be readilyquantified. Combining this information for all stars in a given sampleit is then possible to determine the fraction of stars for which discscould have been detected in different regions of parameter space.This is the basis of the approach taken in Fig. 6, which follows onfrom that used in Sibthorpe et al. (2018) and Wyatt (2018). Therewe plot the parameter space of fractional luminosity vs blackbodyradius for the four samples of F stars (BPMG, the 45 Myr group, the150 Myr group, and DEBRIS), noting that the sub-mm disc radius isexpected to be ∼ . − and 10 − we generated a grid of fiducial discsassuming a pure blackbody model. We inferred the flux density ofeach model disc at wavelengths corresponding to those of observa-tions of each star, e.g. with WISE, Spitzer /MIPS,
Herschel /PACS andALMA. If the total flux density of the fiducial model (star + disc)
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Figure 6.
Fractional luminosity as function of blackbody radius for the four samples (BMPG, 45 Myr group, 150 Myr group, and DEBRIS). The colour scaleshows the disc incidence, per log(au), per log(unit 𝑓 d ). The contour lines show the levels of completeness for 0.1, 0.3, 0.5, 0.7 and 1.0 starting from the bottomof the plot. satisfied 𝐹 𝜈 > 𝐹 star 𝜈 + √︂(cid:16) Δ 𝐹 obs 𝜈 (cid:17) + (cid:0) Δ 𝐹 star 𝜈 (cid:1) , (6)with 𝐹 star 𝜈 being the flux density of the stellar photosphere, Δ 𝐹 star 𝜈 itsuncertainty and Δ 𝐹 obs 𝜈 being the uncertainty of the observation, weassumed the model disc to be detected at the wavelength analysed. Amodel disc is counted as a detection as soon as one wavelength bandfulfills eq. (6). As a result we get the area of parameter space wherediscs around a certain host star can be detected. For a given samplewe calculate the number of stars for which discs could be detected foreach node of the grid generating the contour lines shown in Fig. 6.The contour lines are an estimate for the level of completeness of thedisc detections. For example, if 10 discs are found at a location wherediscs could have been detected towards 50% of stars, this suggeststhat the true number of discs at this location is 10*100/50, since forhalf of the stars the observations provide no information about thepresence of discs at this level.For the BPMG sample we find that discs with blackbody radii of ∼
20 au could be detected around 100% of the stars at fractionalluminosities of 1 × − . Discs around ∼
100 au could be detectedaround 10% of the stars for 𝑓 d = × − . For the 45 Myr group discsat 100 au could be detected around 10% of the stars for 𝑓 d = × − while for the 150 Myr group 𝑓 d = × − and for the DEBRIS 𝑓 d = × − . The reason for the different sensitivity limits is given by the observations themselves. Some targets have not been studiedin detail so that we do not have data longwards of 70 𝜇 m and onlyupper limits are available (e.g., from IRAS) which barely constrainthe sensitivity limits.A second aspect of Fig. 6 is the actual disc detections. They appearon the plot over the range of 𝑓 d and 𝑅 BB where they could appear ac-cording to their likelihood. The likelihood itself was inferred throughSED fitting as described in § 3. In Fig. 6 we use the colour scale toshow the fraction of stars for which discs are present. The scale givesthe incidence rate of a disc per log ( au ) , per log ( unit 𝑓 d ) , per num-ber of targets in the sample. The incidence rate has been correctedfor completeness by dividing the observed incidence rates by thesensitivity limits given by the contour lines and was then smoothedwith a Gaussian by one order of magnitude in blackbody radius andfractional luminosity.Although discs could have been detected down to fractional lu-minosities of ∼ − we find that the majority of discs in the BPMGsample is located around 𝑓 d = − , the area where 100% of fiducialdiscs can be detected. The 45 Myr group and DEBRIS discs arefound in areas closer to the sensitivity limits ( 𝑓 d = × − for the45 Myr group, 𝑓 d = × − for DEBRIS), some in areas whereless than 10% of the model discs are observable, which results in ahigher corrected incidence rate. For the 150 Myr group we only have MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic Figure 7.
Frequency of disc radii for different radius bins assuming the totalnumber of targets in each sample taken from Tab. 9. The uncertainties werecalculated using Gehrels (1986). two disc detections, one lying within the area of 100% completenessthe other close to the detection limit.Assuming that Fig. 6 shows comparable debris disc populationsat different ages starting from 23 Myr (BPMG) over 45 Myr to olderfield stars (DEBRIS) we see a decay of fractional luminosity withincreasing age which is in agreement with Fig. 5 where we see adecrease in detection rates. While we would expect such a decreasedue to collisional evolution it seems that the process takes place inthe first 100 Myr (see § 7.1). Furthermore, the blackbody radii seemto show a slight increase from the BPMG ( ∼
30 au) to DEBRIS( ∼
100 au). Possible reasons, besides observational biases, will bediscussed in § 6.6.
In this section we compare the radii of discs found in the BPMG withthose of other young moving groups and field stars. Since most of thetargets are not spatially resolved we will look at both blackbody andspatially resolved disc radii to identify possible differences betweenthe samples.
We focus on the SED results listed in Tabs. 3, 7, and 8 that wereused to produce Fig. 6. We compare the blackbody radius of eachsample in Fig. 7 applying four radius bins in logarithmic spacing: 𝑅 BB < −
10 au comparable to thewarm asteroid belt, 10 −
100 au comparable to the cold Kuiper belt,and (cid:62)
100 au for larger discs. The frequencies plotted are taken fromTab. 9 by comparing the number detected with the total number oftargets in each sample, noting that there could be more discs in eachradius bin that are below the detection threshold. Most of the discsare found with blackbody radii between 1 and 100 au. For the BPMGsample and the 45 Myr group the majority lies between 10 and 30 auand for the DEBRIS sample between 30 and 100 au.The latter is the only sample containing discs with blackbody radiilarger than 100 au. The DEBRIS sample has a detection limit forlarge discs down to 𝑓 d = × − (Fig. 6) where the 45 Myr grouponly shows discs when 𝑓 d > × − , while in the 150 Myr groupdiscs must be brighter than 𝑓 d = × − to be detected. Thus, it is possible that we miss those large and faint discs in the 45 Myrand 150 Myr group as they would lie below the respective detectionlimits. In the BPMG however, the detection limit lies at 6 × − andis lower than for the DEBRIS sample. Yet, we did not find any largediscs in the BPMG. This might be a result of the low number of targetscompared to the DEBRIS sample. For example, the probability ofdetecting one or more >
100 au disc in the BPMG sample of onlytwelve stars would be 41.3% if their incidence rate was the same asthat of the DEBRIS sample of 4/92.Nevertheless, it seems that the discs in moving groups (BPMG,45 Myr group) tend to be smaller compared to discs around fieldstars as seen in DEBRIS (see § 6.5). It could be a systematic increasein physical size with increasing age, or that discs in young movinggroups are hotter (and so appear smaller by the 𝑅 BB metric) thanaround older stars. Smaller discs in young moving groups might beexpected from collisional theory as those could have been depletedaround older field stars (see § 4.2.4 of Wyatt et al. 2007). On theother hand, the discs in the BPMG possess a high fraction of smallgrains (see § 5) while the particles around comparable field stars arefound to be larger (Pawellek & Krivov 2015). This might supportthe idea of hotter discs in young moving groups. Nevertheless, thenumber of targets in each sample is small and the uncertainties arelarge so that we cannot draw strong conclusions on the difference inthe radius distribution. We will consider the influence of collisionalevolution in more detail in § 7. In this section we compare the NIR, FIR, and sub-mm radii inferredfrom spatially resolved observations from ALMA,
Herschel /PACSand VLT/SPHERE data. Using ALMA, four targets were resolved inthe BPMG and two discs (HD 10647 and HD 109085, Tab. B1) inthe DEBRIS sample. With
Herschel /PACS three discs in the BPMGand nine discs in the DEBRIS sample were resolved (Tabs. 5, 7).Considering scattered light observations, four discs in the BPMGwere resolved. In the 45 Myr group only HD 30447 was reported asspatially resolved with SPHERE.In Fig. 8 we compare the ALMA radii to the
Herschel /PACS andVLT/SPHERE radii for the BPMG and DEBRIS to infer possiblebiases between the values from the different observations. In § 4.3.2we already found that the
Herschel and ALMA radii for the BPMGare in good agreement. This is also the case for HD 109085 fromthe DEBRIS sample, while for HD 10647 the
Herschel radius seemslarger compared to ALMA. Additionally, SPHERE data show broadextended discs for HD 15115, HD 181327, and HD 191089 with thelocation of the surface brightness peak being in good agreement withthe ALMA radii as well.Fig. 8 complements the results found in Pawellek et al. (2019).That study used collisional models and showed that at high resolutionthe peak of the discs’ surface brightness is at the same location insub-mm and far-infrared images (and is nearly coincident with theplanetesimal belt). However, the low surface brightness halo madeof small grains that extends beyond the belt gets brighter at shorterwavelengths. It is thus possible that due to the halo and the lowerresolution of
Herschel the radii inferred from
Herschel could appearlarger than ALMA radii, which might be the case for HD 10647.Based on Fig. 8 we assume that the disc radii inferred from differenttelescopes give comparable values.In Fig. 9 the FIR and sub-mm radii of the BPMG and DEBRISsample are shown as a function of stellar luminosity with error barsindicating the disc width. There are three discs in the DEBRIS samplewith FIR radii below 50 au, but the majority of targets (six) possesses
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Figure 8.
Resolved disc radii inferred from
Herschel/PACS andVLT/SPHERE compared to ALMA radii. The central radius of
Herschel is assumed to be 0 . × ( 𝑅 in, FIR + 𝑅 out, FIR ) . The error bars indicate the discwidth inferred from observations. Figure 9.
Resolved disc radii of the BPMG and DEBRIS as function ofstellar luminosity. The radii are inferred from Herschel and ALMA images.The error bars indicate the disc width. radii around ∼ −
150 au. All discs are found to be broad. Fiveof the discs with FIR radii between 100 and 150 au also possessblackbody radii larger than 50 au (Tab. 7) and are in agreement withan expected ratio of sub-mm to blackbody radius ratio of ∼ Herschel /PACS, but not with ALMA.
Herschel /PACS has alower spatial resolution and thus might bias the sample of resolveddiscs towards larger radii.
We found that the detection rate for debris discs around F-type starsis significantly higher in the BPMG than in the DEBRIS sample. In this section we investigate different scenarios which might explainthis phenomenon:(i) The BPMG is representative of the population of stars that becomefield stars. Hence, the discs seen in both the BPMG and DEBRISsamples are essentially the same population but seen at different ages.This is considered in § 7.1.(ii) The BPMG is representative of the population of stars that becomefield stars. However, the discs seen in BPMG and DEBRIS are not the same population seen at different ages. This is considered in § 7.2.(iii) The BPMG is not representative of the population of stars thatbecome field stars, since the environment of young moving groupsis different to that in which field stars formed, and more conduciveto the retention of bright discs. This is considered in § 7.3
In the first scenario we assume that the BPMG and DEBRIS samplespossess the same population of discs seen at different ages. There-fore, the discs in the BPMG should evolve into discs comparable tothe DEBRIS sample. To describe the evolution process we use thecollisional evolution model (§ B) and assume that the disc radiusstays constant while the fractional luminosity decreases over time.If the largest planetesimals are in collisional equilibrium at the ageof the BPMG then the fractional luminosity decreases with 𝑓 d ∝ / 𝑡 ,where 𝑡 is the time (see eq. B2). However, it could also have decreasedless than this or even stayed constant if the biggest bodies were notyet in collisional equilibrium. To predict the population that the BPMG would evolve into byDEBRIS ages, we make a generic model. We generate 100,000 arti-ficial samples of 92 targets similar to the size of the DEBRIS sample.Each target is randomly chosen from the 12 systems of the BPMGsample so that each artificial sample is completely made of BPMGtargets including those without a disc detection. We assume that thefractional luminosity follows 𝑓 d ( 𝑡 ) = 𝑓 d ( 𝑡 ) (cid:18) 𝑡𝑡 (cid:19) 𝛼 , (7)with 𝑓 d ( 𝑡 ) being the fractional luminosity at the time 𝑡 and 𝛼 beinga free parameter. DEBRIS is an unbiased sample of field stars and assuch its stars should possess random ages up to the main sequencelifetime. We therefore generate random ages ( 𝑡 ) for the 92 targets ineach of our artificial samples and calculate the fractional luminosity 𝑓 d ( 𝑡 ) using those inferred from SED modelling of the BPMG sampleas values for 𝑓 d ( 𝑡 ) . In the next step we consider the parameter space( 𝑅 BB , 𝑓 d ( 𝑡 ) ) as shown in Fig. 6. For each location we know theprobability that a star in the sample was observed with sufficientsensitivity to detect the disc. We generate a random number between0 and 1 for each target in the 100,000 samples and compare it to theprobability of detecting the disc at its location of parameter space. Ifthe probability is larger than this random number we count the discas a detection. For each of the 100,000 generated samples we assumethat the probability to detect a disc at a certain location ( 𝑅 BB , 𝑓 d ( 𝑡 ) )is comparable to that of the actually observed DEBRIS sample asshown in Fig. 6. As a result, we get a distribution of detection ratesfor the 100,000 artificial samples which is shown in Fig. 10.To test the model we considered what it would predict for theBPMG, i.e. for a set of 100,000 samples each containing 12 targetsrandomly taken from the actual BPMG sample with the same age MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic Figure 10.
Detection rates of a sample made of 92 discs around F-typestars similar to DEBRIS with disc properties similar to the discs in BPMG.The grey region shows the detection rate inferred from the DEBRIS sample(23 . + . − . % Sibthorpe et al. 2018). as the BPMG. We applied the disc detection probability distributioninferred for BPMG. In Fig. 10 the solid blue line shows the resultingdistribution of detection rates peaking around 75% similar to theactual BPMG sample. Given the derived age of the BPMG we set 𝑡 to 23 Myr and 𝛼 = − ±
10 % following Poissonstatistics with a 95% confidence level. This is incompatible with theobserved detection rate of 22 . + . − . % for the DEBRIS sample. Since 𝛼 = − The observed detection rate of the DEBRIS sample could be ex-plained if the cascade was initiated only recently, i.e., if the collisionage was closer to 𝑡 ∼ The other explanation that is compatible with the assumption of sim-ilar disc populations in the BPMG and DEBRIS samples is that theevolution is faster than 𝑡 − . The dash-dotted orange line in Fig. 10shows that 𝑡 − is in agreement with this hypothesis. However, suchrapid evolution is no longer consistent with simple collisional evolu-tion models. Collisional models might still be able to reproduce rapid evolution of disc luminosity if in addition to depletion of the largebodies there is also a change in the equilibrium dust size distribution,e.g., an over-abundance of small grains above steady state at BPMGages.There might be physical motivation for the dust size distributionto evolve, say if the quantity of sub-blowout grains destroying thelarger particles is changing or if there is gas preventing small dustbeing removed at young ages. Indeed, the collision model introducedby Löhne et al. (2017) shows an increase in particles slightly largerthan the blow-out size (e.g., Fig. 6 in Löhne et al. 2017). However,there is no evidence for a change in small dust properties in the SEDmodels’ 𝑠 min or 𝑞 , and there is not significant gas in these systems.The only target with a gas detection is HD 181327 (see § 4.2.3) forwhich Marino et al. (2016) found only low gas masses making thepresence of gas unlikely to influence the dust in this disc. Hence, gasis also unlikely to explain the fast depletion of the whole sample.This leads to the conclusion that something other than collisions isdepleting the BPMG discs.One potential problem with this scenario is that the evolution with 𝑡 − suggested by our model is not compatible with other studieswhich have shown that the discs of Sun-like stars evolve slowly onthe main sequence. While ages are hard to determine for those stars,there seems to be slow evolution ( ∼ 𝑡 − . ) beyond a few 100 Myr(e.g., Trilling et al. 2008; Holland et al. 2017). However, the 𝑡 − trendonly represents an average evolution. A solution to this problem isthus that there is a process that depletes the BPMG discs that acts evenfaster than 𝑡 − , but only on timescales of order 100 Myr followingwhich the slower collisional depletion resumes for any remainingplanetesimals that go on to supply the dust seen in the DEBRISpopulation.The Solar System’s Edgeworth-Kuiper belt underwent depletionby two orders of magnitude in mass on a timescale of 10-100 Myras a result of the dynamical instability in the planetary system, sothis is one possibility (Gomes et al. 2005). Others could be embed-ded planetary embryos, or planets that migrate into the discs (e.g.,Gomes et al. 2005; Levison et al. 2008; Izidoro et al. 2014; Nesvorný2015). Given the depletion timescale inferred above, we use eq. (3)of Shannon et al. (2016) to estimate the mass of potential planetaryperturbers by setting the timescale of such perturbers to clear theirsurrounding area from dust to 100 Myr. We find masses between 20and 170 earth masses (corresponding to 1 and 10 Neptune masses).With currently available telescopes such planets could very well beundetected within the discs in the BPMG. Based on results from dif-ferent observational instruments like Kepler or HARPS summarisedin the exoplanet database (Schneider 2011), ∼
260 close-in planetswere detected around F-type stars by radial velocity or transit obser-vations, ∼
50 of them possessing masses between 1 and 10 Neptunemasses. This is just an estimate, since in many cases the total massesof the planets could not be inferred. Furthermore, most of the planetsdetected are located close to the host star and are far away from thetypical debris discs investigated in our study. Suzuki et al. (2016)analysed data from the Microlensing Observations in Astrophysics(MOA) and estimates that cold Neptunes located beyond the snowline of stellar systems and thus, closer to debris discs might be morecommon than their close-in hot siblings.51 Eri is the only system with a planet detection in our sample.Due to a lack of spatially resolved images of the disc, we cannot ruleout that the Jupiter-mass planet might be located close to the disc andthus, accelerating its depletion. An indicator for this scenario could http://exoplanet.eu/ MNRAS000
50 of them possessing masses between 1 and 10 Neptunemasses. This is just an estimate, since in many cases the total massesof the planets could not be inferred. Furthermore, most of the planetsdetected are located close to the host star and are far away from thetypical debris discs investigated in our study. Suzuki et al. (2016)analysed data from the Microlensing Observations in Astrophysics(MOA) and estimates that cold Neptunes located beyond the snowline of stellar systems and thus, closer to debris discs might be morecommon than their close-in hot siblings.51 Eri is the only system with a planet detection in our sample.Due to a lack of spatially resolved images of the disc, we cannot ruleout that the Jupiter-mass planet might be located close to the disc andthus, accelerating its depletion. An indicator for this scenario could http://exoplanet.eu/ MNRAS000 , 1–26 (2021) N. Pawellek et al. be the already low disc’s fractional luminosity of 5 × − . Indeed, aJupiter-mass planet located within our BPMG discs would only need ∼
20 Myr to clear its surrounding area (eq. 3, Shannon et al. 2016).Another possible depletion mechanism is the disintegration ofplanetesimals due to heating. Lisse et al. (2020) showed that highenergy stellar flares are able to heat dust in close-in debris discs totemperatures of ∼ ∼
80 au) for this to be important. The close-indisc around HD 199143 might be a candidate for such a depletionmechanism though collisions would be expected to deplete this discby DEBRIS ages (Wyatt et al. 2007)Planetesimals could also be depleted by stellar radiation forcessuch as the YORP effect. However, the relatively slow evolution ofSolar system asteroids (Ďurech et al. 2018) suggests that this radiationeffect might be negligible, since it should be weaker for planetesimalsat several tens of au.
In § 7.1 we assumed that the discs seen in the BPMG and DEBRISsamples are the same population seen at different ages. While it ispossible that the BPMG is representative of the population of starsthat become field stars, comparable to the DEBRIS sample, it is alsopossible that the BPMG and DEBRIS samples do not show the samepopulation of discs.This could be the case for example if the discs in the DEBRISsample are belts of planetesimals like the Edgeworth-Kuiper beltthat formed as part of the planet formation process, whereas thosein BPMG are remnants of the primordial dust that is swept up intoa ring by the depleting gas that forms planetesimals by streaminginstability (e.g., Johansen et al. 2007, 2012; Carrera et al. 2015,2017; Schaffer et al. 2018). If that is the case the implication is thatBPMG stars would have two belts - the bright primordial dust beltand the DEBRIS-like belt with large planetesimals which may be toofaint to detect at this young age. This scenario may be supported bythe tentative outer belt found around HD 181327 (e.g., Marino et al.2017).However, the planetesimals in the two proposed belts in this scen-ario would deplete by collisions and thus by 𝑡 − as predicted by colli-sional models which is thus incompatible with the rate of 𝑡 − seen inFig. 10. Nevertheless, a key difference between the two populationsmight be that the DEBRIS belts would be planetesimals formed instable regions of the planetary system (like the Edgeworth-Kuiperbelt and Asteroid belt), whereas the BPMG belts could be depositedanywhere, since this would depend on how the gas disc depleteswhich could be driven by photo-evaporation processes. Thus, un-stable regions liable to dynamical depletion as discussed in § 7.1may be more likely for such BPMG belts.Another possibility is that the “planetesimals” formed in these un-stable regions could be more loosely bound and liable to disruption.To consider this, we compare the minimum sizes of planetesimalsinferred in § B3 of discs in both the BPMG and DEBRIS samples.Despite the large variation of the sizes, and the small number ofdiscs being compared, we see a similar range between both samples.This does not support the hypothesis of two belts with different plan-etesimal properties, but it should be noted that if planetesimals formdifferently then they may have different 𝑄 ∗ D and so different planetes-imal sizes would be inferred. Nevertheless, the small planetesimalsizes are in agreement with recent studies suggesting the absence oflarge planetesimals (Krivov & Wyatt 2020). Considering the disc radii inferred from spatially resolved images(§ 4) the radii of discs in the BPMG lie between 45 and 94 au.We might expect systematic differences in the disc radius betweenthe BPMG and DEBRIS samples for this scenario. This might besupported by the fact that the spatially resolved discs in DEBRIStend to be larger than those in the BPMG (see § 6.6.2). However,while the bright belts seen in the BPMG should be depleted and onlythe fainter DEBRIS belts remain detectable at DEBRIS ages bothplanetesimals rings should be present at BPMG ages.We investigated the possibility of detecting a DEBRIS-like outerplanetesimal belt around a BPMG star with a bright inner belt. Wetook HD 181327 with its bright ring at 80 au and considered anadditional fainter outer belt at 150 au with a width of 46 au similar tothat of HD 109085 from the DEBRIS sample. Originally, HD 109085was observed with ALMA at 880 𝜇 m and a sensitivity of 30 𝜇 Jy/beam(Marino et al. 2017) while HD 181327 was observed at a higherspatial resolution and a sensitivity of 27 𝜇 Jy/beam (see Tab. 5). Thesurface brightness of HD 109085 is ∼ 𝜇 Jy/beam (Fig. 1 in Marinoet al. 2017). If the disc was located around HD 181327 and observedwith the sensitivity of 27 𝜇 Jy/beam we would detect it at a 0.15 𝜎 level(in each beam). With azimuthal and radial averaging the detectionwould reach a 3 . 𝜎 level with ALMA band 7 for the whole disc.Applying an observational setting like that in Marino et al. (2016)with a lower spatial resolution we would even reach a level of ∼ 𝜎 .We do not detect such outer discs in the BPMG (the only exceptionbeing HD 181327 for which there is a tentative detection at ∼
200 au).This could either mean those outer belts do not exist or they are toofaint to detect at that age (e.g., because the collisional cascade hasyet to be fully initiated).
The third scenario to explain the higher detection rate supposes thatthe environment of young moving groups is different to that in whichfield stars form, such that these regions might be more conducive tothe retention of bright discs.Deacon & Kraus (2020) analysed the binary fraction of openclusters such as the Pleiades and compared it to less dense asso-ciations including the BPMG. That study found that the rate of widemultiples (between 300 and 3000 au) is higher in young movinggroups (14.6%) than in field stars (7.8%) or open clusters (Hyades,2.5%) which is in agreement with our results (see § 2.2). Deacon &Kraus (2020) concluded that the rate of multiple systems might beinfluenced more strongly by environmental factors than by age whichsupports the idea of different formation environments for young mov-ing groups and field stars. It seems that wide separation multiple sys-tems are more effectively formed in less dense regions such as youngmoving groups. However, as shown by Yelverton et al. (2019), aninfluence of wide-separation binaries on the detection rate of debrisdiscs could not be found so far (§ 2.2).Of greater importance might be the evolution of multiple stellarsystems. Reipurth & Mikkola (2012) and Elliott & Bayo (2016) sug-gested that the fraction of such systems might decrease over time asthe stellar systems become unstable and break-up within ∼
100 Myr.It is possible that firstly, the break-ups destroy the debris discs in thesystem, and secondly the break-ups lead to a higher rate of stellarflybys in the moving group which truncate and/or deplete the debrisdiscs. As a result, the radii of the discs in the field might be on averagesmaller and fainter than those in the BPMG.This idea however is not supported by our results on the radialdistribution in the BPMG and DEBRIS where the discs in DEBRIStend to be larger than in the BPMG (see § 6.6.2). Lestrade et al. (2011)
MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic investigated the depletion of debris discs due to flybys during the first100 Myr and found that only high-density regions like Orion withstar densities > ,
000 pc − have a significant impact on the discs.Similarly, Vincke & Pfalzner (2018) analysed the impact of the high-density environment found in open clusters, such as Trumpler 14, ondiscs and planetary systems. That study found that during the initialphase of evolution stellar flybys resulted in ∼
90% of discs havinga radial extent smaller than 50 au. For ∼
47% of the discs the radiiwere even smaller than 10 au. At later evolution stages of the clustersthe discs were barely influenced by stellar interactions. Assumingthat field stars formed in dense clusters (Eggen 1958) it is possiblethat stellar flybys truncated a number of their protoplanetary discsleading to a smaller fraction of debris discs with large radii and/or alower incidence of debris discs around field stars (Hands et al. 2019).Again, this is not supported by the radii of spatially resolved discs(see § 6.6.2), but since we analysed only a small number of themaround field stars these might be the ones which were not altered bystellar flybys.Nevertheless, it might be possible that the detection rate of debrisdiscs around field stars is low from an early phase, since their proto-planetary predecessors were already truncated. In contrast, the discswhich formed in less dense regions like the BPMG might retain theirhigh detection rates since stellar flybys are less frequent. This mightbe observationally testable by comparing disc incidences in § 6 fordifferent clusters with those of more dense clusters at a comparableage. Recently, Miret-Roig et al. (2020) derived a disc detection rateof 9 ±
9% for stars ranging from F5 to K5 in the 30 Myr old clusterIC 4665 based on Spitzer and WISE data. This is much lower com-pared to the rates we find for the BPMG and the 45 Myr group (75%and 38%, Tab. 9). However, we note that the cluster has a distanceof 350 pc in contrast to the close-by targets analysed in our study sothat many discs might be undetected. A more detailed analysis forexample repeating the analyses of the 𝑓 d vs 𝑅 BB parameter spacelike § 6.5 for IC 4665 would be needed to draw reliable conclusionson this scenario. In the first part of this study we analysed a sample of twelve F-type stars in the BPMG and investigated different properties of thesystems. In the second part we compared the results of the BPMGto those of other samples of young moving groups and field stars toanalyse possible disc evolution processes.We found that nine stars in the BPMG possess debris discs leadingto a detection rate of 75%. This is significantly higher than found inunbiased samples of field stars where only ∼
23% of the targets showevidence for debris discs (Sibthorpe et al. 2018).Five out of the nine discs were spatially resolved with either ALMAor VLT/SPHERE allowing us to study their radial and grain sizedistribution in more detail. The disc around HD 164249 was spatiallyresolved with ALMA for the first time. The disc radii lie between 45and 94 au and are comparable to the radii found for other debris discsand protoplanetary discs, but tend to be slightly smaller compared tospatially resolved discs found in the DEBRIS sample of field stars.We compared the disc radius to blackbody radius ratio derivedfrom SED modelling to the relation based on
Herschel data presentedin Pawellek & Krivov (2015) and found that the resolved discs inthe BPMG possess smaller radii than expected. Since ALMA has ahigher spatial resolution than
Herschel we inferred the sub-mm discto blackbody radius ratio - stellar luminosity relation from a sample of ALMA data (Matrà et al. 2018). The resulting relation shows aweaker decrease of the radius ratio with increasing stellar luminosity.The minimum grain sizes of the SED models are in agreementwith the blow-out grain sizes of the discs as we would expect fromcollisional evolution. The exception is HD 15115 with an 𝑠 min of ∼ 𝜇 m which is also the only disc showing the presence of a warminner component. This result is somewhat different to earlier studies(Pawellek et al. 2014) which found an average size of 5 𝜇 m for asample of 34 discs. A reason might be that 66% of those discs werefitted with a warm inner component, but nevertheless, the small 𝑠 min / 𝑠 blow ratio indicates that the discs are collisionally very activewith high levels of dynamical excitation. However, a more detailedanalysis is needed to draw strong conclusions.We compared the sample of BPMG stars to other young movinggroups and old field stars, finding that the detection rate of debrisdiscs is significantly higher in young moving groups than in the fieldstar sample. Furthermore, the discs in the BPMG possess a higherfractional luminosity. From collisional evolution models we wouldexpect the same discs around older stars to be fainter, which mightalso cause a lower detection rate. However, applying those modelswe found evolving the BPMG sample to DEBRIS ages results in apopulation with significantly higher detection rate than that observedfor the actual DEBRIS sample. We investigated different scenariosexplaining this.In the first scenario we assumed that the BPMG and the DEBRISsamples show the same disc population at different ages. We foundthat the observed detection rate could be explained by a delayed ig-nition of the collisional cascade, but that this option seems unlikelysince all discs would need to be delayed by the same ∼
20 Myr times-cale. A more likely scenario is that additional depleting processes areat work so that the disc evolution cannot be explained by collisionalprocesses alone. Depletion through gravitational interaction with un-seen planets is one possibility. We found that Neptune-sized planetsorbiting within discs can cause depletion on the required ∼
100 Myrtimescales, and are small enough to remain undetected in currentobservations. For discs close to the star high energy stellar flaresand other radiation effects (e.g., YORP) are also possible but lesslikely. Whatever the processes are they have to work between 10 and100 Myr since previous studies showed that disc evolution is slowerat older ages (e.g., Holland et al. 2017).The second scenario assumed that the discs in young movinggroups and around old field stars are not part of the same population.It is possible that discs in the BPMG possess two belts, one made oflarge planetesimals formed by planet formation processes compar-able to the Edgeworth-Kuiper belt, and another made of remnantsof the primordial dust that grow to planetesimal sizes during thedisc dispersal process. This might be supported by the different radiifound for the BPMG and DEBRIS samples, but since we studiedonly a small number of discs, the actual radius distribution is notwell characterised yet. However, while the two-population scenariois not impossible, we would still need to invoke a rapid depletion asproposed in the first scenario (§ 7.1).In the third scenario we assumed that the birth environment ofstars is different for young moving groups and field stars so thattheir respective discs might be different as well. The influence ofstellar flybys in circumstellar discs is significant at early stages ofthe evolution for dense stellar clusters like Orion (e.g., Lestradeet al. 2011; Vincke & Pfalzner 2018), but barely contributes to thedepletion of debris discs found in less dense associations like theBPMG. On the other hand, field stars are supposed to form in regionsof higher stellar density so that stellar flybys might truncate the discsat an early evolutionary stage. Therefore, a large fraction of discs
MNRAS , 1–26 (2021) N. Pawellek et al. around field stars might possess a radius too small to be detectedwhile discs with larger radii in moving groups remain detectable.This is not supported by the radii of spatially resolved discs in theBPMG and DEBRIS, but it is possible that we only see those discsaround field stars that were not truncated. A possibility to test thishypothesis is to analyse the detection rates of debris discs in youngdense clusters. Indeed, studies found lower disc detections for theclusters (e.g. IC 4665, Miret-Roig et al. 2020), but this might bebiased by the large distance of IC 4665 rather than an actual differencein the fraction of stars with discs.
ACKNOWLEDGEMENTS
NP thanks Alexander Krivov and Torsten Löhne for fruitful discus-sions. GMK was supported by the Royal Society as a Royal SocietyUniversity Research Fellow.The Combined Atlas of Sources with Spitzer/IRS Spectra (CAS-SIS) is a product of the Infrared Science Center at Cornell University,supported by NASA and JPL.ALMA is a partnership of ESO (representing its member states),NSF (USA) and NINS (Japan), together with NRC (Canada), MOSTand ASIAA (Taiwan), and KASI (Republic of Korea), in cooperationwith the Republic of Chile. The Joint ALMA Observatory is operatedby ESO, AUI/NRAO and NAOJ.
DATA AVAILABILITY
The data underlying this article will be shared on request to the corres-ponding author. The ALMA and
Herschel data are publicly availableand can be queried and downloaded directly from the ALMA archiveat https://almascience.nrao.edu/asax/ and from the
Herschel archiveat http://archives.esac.esa.int/hsa/whsa/.
References
Backman D., Paresce F., 1993, in Levy E. H., Lunine J. I., eds, Protostars andPlanets III. Univ. of Arizona Press, pp 1253–1304Bailer-Jones C. A. L., Rybizki J., Fouesneau M., Mantelet G., Andrae R.,2018, AJ, 156, 58Ballering N. P., Rieke G. H., Su K. Y. L., Montiel E., 2013, ApJ, 775, 55Bell C. P. M., Mamajek E. E., Naylor T., 2015, MNRAS, 454, 593Benz W., Asphaug E., 1999, Icarus, 142, 5Beuzit J.-L., et al., 2019, arXiv e-prints,Bohren C. F., Huffman D. R., 1983, Absorption and Scattering of Light bySmall Particles. Wiley and Sons: New York – Chichester – Brisbane –Toronto – SingaporeBooth M., et al., 2013, MNRAS, 428, 1263Brott I., Hauschildt P. H., 2005, in C. Turon, K. S. O’Flaherty, & M. A. C. Per-ryman ed., ESA SP Vol. 576, The Three-Dimensional Universe with Gaia.p. 565 ( arXiv:astro-ph/0503395 )Burns J. A., Lamy P. L., Soter S., 1979, Icarus, 40, 1Carpenter J. M., et al., 2008, ApJS, 179, 423Carrera D., Johansen A., Davies M. B., 2015, A& A, 579, A43Carrera D., Gorti U., Johansen A., Davies M. B., 2017, ApJ, 839, 16Chen C. H., Mittal T., Kuchner M., Forrest W. J., Lisse C. M., Manoj P.,Sargent B. A., Watson D. M., 2014, ApJS, 211, 25Choi J., Dotter A., Conroy C., Cantiello M., Paxton B., Johnson B. D., 2016,ApJ, 823, 102Churcher L., Wyatt M., Smith R., 2011, MNRAS, 410, 2Cornwell T. J., 2008, IEEE Journal of Selected Topics in Signal Processing,2, 793Cutri R. M., et al., 2003, 2MASS All Sky Catalog of point sources. Davenport J. R. A., 2016, ApJ, 829, 23Deacon N. R., Kraus A. L., 2020, MNRAS,Dohnanyi J. S., 1969, J. Geophys. Res., 74, 2531Draine B. T., 2003, ARA& A, 41, 241Eggen O. J., 1958, MNRAS, 118, 65Eiroa C., et al., 2013, A& A, 555, A11Eker Z., et al., 2008, MNRAS, 389, 1722Elliott P., Bayo A., 2016, MNRAS, 459, 4499Engler N., et al., 2018, arXiv e-prints,Faherty J. K., Bochanski J. J., Gagné J., Nelson O., Coker K., Smithka I.,Desir D., Vasquez C., 2018, ApJ, 863, 91Fisher S. R. A., 1956, The World of Mathematics, 3Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, PASP, 125,306Foreman-Mackey D., et al., 2019, The Journal of Open Source Software, 4,1864Fortney J. J., Marley M. S., Saumon D., Lodders K., 2008, ApJ, 683, 1104Gagné J., Faherty J. K., 2018, ApJ, 862, 138Gagné J., et al., 2018a, ApJ, 856, 23Gagné J., Roy-Loubier O., Faherty J. K., Doyon R., Malo L., 2018b, ApJ,860, 43Gagné J., Faherty J. K., Mamajek E. E., 2018c, ApJ, 865, 136Gaia Collaboration et al., 2018, A& A, 616, A1Gáspár A., Psaltis D., Rieke G. H., Özel F., 2012, ApJ, 754, 74Gáspár A., Rieke G. H., Balog Z., 2013, ApJ, 768, 25Gehrels N., 1986, ApJ, 303, 336Geiler F., Krivov A. V., Booth M., Löhne T., 2019, MNRAS, 483, 332Gomes R., Levison H. F., Tsiganis K., Morbidelli A., 2005, Nature, 435, 466Goodman J., Weare J., 2010, Commun. Appl. Math. Comput. Sci., 5, 65Hands T. O., Dehnen W., Gration A., Stadel J., Moore B., 2019, MNRAS,490, 21Holland W. S., et al., 2017, MNRAS, 470, 3606Hughes A. M., Duchêne G., Matthews B. C., 2018, ARA& A, 56, 541Ishihara D., et al., 2010, A& A, 514, A1Izidoro A., Morbidelli A., Raymond S. N., 2014, ApJ, 794, 11Janson M., et al., 2014, ApJS, 214, 17Johansen A., Oishi J. S., Low M.-M. M., Klahr H., Henning T., Youdin A.,2007, Nature, 448, 1022Johansen A., Youdin A. N., Lithwick Y., 2012, A& A, 537, A125Kalas P., Fitzgerald M. P., Graham J. R., 2007, ApJL, 661, L85Kass R. E., Raftery A. E., 1995, Journal of the American Statistical Associ-ation, 90, 773Kenyon S. J., Bromley B. C., 2008, ApJS, 179, 451Klahr H., Schreiber A., 2020, arXiv e-prints, p. arXiv:2007.10696Kovaleva D., Kaygorodov P., Malkov O., Debray B., Oblak E., 2015, Astro-nomy and Computing, 11, 119Kral Q., Thébault P., Charnoz S., 2013, A& A, 558, A121Kral Q., Matra L., Kennedy G., Marino S., Wyatt M., 2020, arXiv e-prints,p. arXiv:2005.05841Krijt S., Kama M., 2014, A& A, 566, L2Krivov A. V., 2010, Research in Astron. Astrophys., 10, 383Krivov A. V., Wyatt M. C., 2020, MNRAS,Krivov A. V., Löhne T., Sremčević M., 2006, A& A, 455, 509Krivov A. V., Ide A., Löhne T., Johansen A., Blum J., 2018, MNRAS, 474,2564Lebouteiller V., Barry D. J., Spoon H. W. W., Bernard-Salas J., Sloan G. C.,Houck J. R., Weedman D. W., 2011, ApJS, 196, 8Lestrade J. F., Morey E., Lassus A., Phou N., 2011, A& A, 532, A120Levison H. F., Morbidelli A., Vanlaerhoven C., Gomes R., Tsiganis K., 2008,Icarus, 196, 258Lisse C. M., et al., 2020, ApJ, 894, 116Löhne T., Krivov A. V., Rodmann J., 2008, ApJ, 673, 1123Löhne T., Krivov A. V., Kirchschlager F., Sende J. A., Wolf S., 2017, A& A,605, A7MacGregor M. A., Wilner D. J., Andrews S. M., Hughes A. M., 2015, ApJ,801, 59MacGregor M. A., et al., 2019, ApJL, 877, L32Macintosh B., et al., 2015, Science, 350, 64MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic Mamajek E. E., Bell C. P. M., 2014, MNRAS, 445, 2169Marino S., et al., 2016, MNRAS, 460, 2933Marino S., et al., 2017, MNRAS, 465, 2595Marino S., et al., 2018, MNRAS, 479, 5423Marley M. S., Fortney J. J., Hubickyj O., Bodenheimer P., Lissauer J. J., 2007,ApJ, 655, 541Marshall J. P., Booth M., Holland W., Matthews B. C., Greaves J. S., Zucker-man B., 2016, MNRAS,Marton G., et al., 2015, in IAU General Assembly. p. 2253107Matrà L., Marino S., Kennedy G. M., Wyatt M. C., Öberg K. I., Wilner D. J.,2018, ApJ, 859, 72Matrà L., Wyatt M. C., Wilner D. J., Dent W. R. F., Marino S., KennedyG. M., Milli J., 2019, AJ, 157, 135Miret-Roig N., Huélamo N., Bouy H., 2020, arXiv e-prints, p.arXiv:2007.04992Moór A., et al., 2013, ApJL, 775, L51Nesvorný D., 2015, AJ, 150, 73Nielsen E., et al., 2019, in AAS/Division for Extreme Solar Systems Abstracts.p. 100.02O’Brien D. P., Greenberg R., 2003, Icarus, 164, 334Pascucci I., et al., 2006, ApJ, 651, 1177Patience J., et al., 2015, in AAS/Division for Extreme Solar Systems Ab-stracts. p. 202.01Pawellek N., 2017, PhD thesis, Jena,
Pawellek N., Krivov A. V., 2015, MNRAS, 454, 3207Pawellek N., Krivov A. V., Marshall J. P., Montesinos B., Ábrahám P., MoórA., Bryden G., Eiroa C., 2014, ApJ, 792, 65Pawellek N., Moór A., Pascucci I., Krivov A. V., 2019, MNRAS, 487, 5874Paxton B., Bildsten L., Dotter A., Herwig F., Lesaffre P., Timmes F., 2011,ApJS, 192, 3Paxton B., et al., 2013, ApJS, 208, 4Paxton B., et al., 2015, ApJS, 220, 15Pérez S., Marino S., Casassus S., Baruteau C., Zurlo A., Flores C., ChauvinG., 2019, MNRAS, 488, 1005Perrot C., et al., 2019, A& A, 626, A95Phillips N. M., Greaves J. S., Dent W. R. F., Matthews B. C., Holland W. S.,Wyatt M. C., Sibthorpe B., 2010, MNRAS, 403, 1089Rajan A., et al., 2017, AJ, 154, 10Rebull L. M., et al., 2008, ApJ, 681, 1484Reipurth B., Mikkola S., 2012, Nature, 492, 221Ren B., et al., 2019, ApJ, 882, 64Riviere-Marichalar P., et al., 2014, A& A, 565, A68Rodriguez D. R., Zuckerman B., 2012, ApJ, 745, 147Schaffer N., Yang C.-C., Johansen A., 2018, A& A, 618, A75Schneider J., 2011, in EPSC-DPS Joint Meeting 2011. p. 3Schneider G., et al., 2006, ApJ, 650, 414Schüppler C., Löhne T., Krivov A. V., Ertel S., Marshall J. P., Eiroa C., 2014,ArXiv: 1404.6144,Sepulveda A. G., et al., 2019, ApJ, 881, 84Shannon A., Bonsor A., Kral Q., Matthews E., 2016, MNRAS, 462, L116Shkolnik E. L., Allers K. N., Kraus A. L., Liu M. C., Flagg L., 2017, AJ, 154,69Sibthorpe B., Kennedy G. M., Wyatt M. C., Lestrade J. F., Greaves J. S.,Matthews B. C., Duchêne G., 2018, MNRAS, 475, 3046Sierchio J. M., Rieke G. H., Su K. Y. L., Gaspar A., 2014, preprint,( arXiv:1402.6308 )Soummer R., et al., 2014, ApJL, 786, L23Stark C. C., Schneider G., Weinberger A. J., Debes J. H., Grady C. A., Jang-Condell H., Kuchner M. J., 2014, ApJ, 789, 58Stern S. A., et al., 2019, in Lunar and Planetary Science Conference. Lunarand Planetary Science Conference. p. 1742Stewart S. T., Leinhardt Z. M., 2009, ApJL, 691, L133Su K. Y. L., et al., 2006, ApJ, 653, 675Suzuki D., et al., 2016, ApJ, 833, 145Tazzari M., Beaujean F., Testi L., 2018, MNRAS, 476, 4527Thébault P., Augereau J.-C., 2007, A& A, 472, 169Thebault P., 2016, A& A, 587, A88 Tokovinin A. A., 1997, AApS, 124, 75Torres C. A. O., Quast G. R., Melo C. H. F., Sterzik M. F., 2008, YoungNearby Loose Associations. p. 757Trilling D. E., et al., 2008, ApJ, 674, 1086Van Doorsselaere T., Shariati H., Debosscher J., 2017, ApJS, 232, 26Vican L., 2012, AJ, 143, 135Vincke K., Pfalzner S., 2018, ApJ, 868, 1Wiegert J., Faramaz V., Cruz-Saenz de Miera F., 2016, MNRAS, 462, 1735Wright E. L., et al., 2010, AJ, 140, 1868Wyatt M. C., 2008, ARA& A, 46, 339Wyatt M. C., 2018, Debris Disks: Probing Planet Formation. p. 146,doi:10.1007/978-3-319-55333-7_146Wyatt M. C., Dent W. R. F., 2002, MNRAS, 334, 589Wyatt M. C., Smith R., Greaves J. S., Beichman C. A., Bryden G., LisseC. M., 2007, ApJ, 658, 569Xuan J. W., Kennedy G. M., Wyatt M. C., Yelverton B., 2020, MNRAS,Yelverton B., Kennedy G. M., Su K. Y. L., Wyatt M. C., 2019, MNRAS, 488,3588Zuckerman B., Rhee J. H., Song I., Bessell M. S., 2011, ApJ, 732, 61Ďurech J., et al., 2018, A& A, 609, A86
APPENDIX A: SEDS OF DEBRIS DISCS AROUNDNEARBY F STARSA1 45 Myr group
We analysed the sample of 29 F-type stars found in the 45 Myr group(see § 6.3) and found that eleven of them exhibit significant mid-infrared excess. We fitted the SEDs of these targets with a modifiedblackbody model which is described in detail in Section 3. The resultsare shown in Fig. A1.
A2 150 Myr group
We analysed the sample of 13 F-type stars found in the 150 Myrgroup (see § 6.3) and found that two of them exhibit significant mid-infrared excess. We fitted the SEDs of these targets with a modifiedblackbody model which is described in detail in Section 3. The resultsare shown in Fig. A2.
A3 DEBRIS
We analysed the sample of 92 F-type stars in DEBRIS (see § 6.2)and found that 21 of them exhibit significant mid-infrared excess.We fitted the SEDs of these targets with a modified blackbody modelwhich is described in detail in Section 3. The results are shown inFig. A3 and A4.
APPENDIX B: COLLISIONAL DISC EVOLUTION
While we inferred the minimum sizes of dust from SED modellingin § 5 we can further constrain the size distribution by inferringthe minimum size of the planetesimals that must be feeding thecollisional cascade, by extrapolating the size distribution of the dustup to the size at which the collisional lifetime is equal to the age of thestar, applying the lifetimes calculated using the analytical collisionevolution model introduced by Wyatt et al. (2007).
MNRAS000
MNRAS000 , 1–26 (2021) N. Pawellek et al.
Figure A1.
SEDs for the debris discs detected around F stars in the 45 Myr group.MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic Figure A2.
SEDs for the debris discs detected around F stars in the 150 Myr group.
B1 Collision model
The model uses a similar power law size distribution as the SEDmodel following 𝑁 coll ( 𝑠 ) ≈ 𝑠 − 𝑞 , (B1)with 𝑠 being the radius of a spherical body and 𝑁 ( 𝑠 ) 𝑑𝑠 the numberof bodies in the size range 𝑠 to 𝑠 + 𝑑𝑠 . We note that the parameter 𝑞 isdifferent from the size distribution index inferred by SED modelling(§ 5). They are related by 𝑞 SED = −( − 𝑞 ) leading to 𝑞 SED = . 𝑞 = .
83 for an ideal collisional cascade (Dohnanyi 1969).Following eqs. (12) from Wyatt et al. (2007) and (22) from Löhneet al. (2008) we get an equation for the collisional timescale, 𝑡 c as afunction of minimum size of the planetesimals necessary to feed tocollisional cascade, 𝑠 c : 𝑡 c = 𝑟 / 𝑑𝑟 𝑖 ( 𝛾𝑀 star ) / 𝑓 d (cid:16) 𝑒 + 𝑖 (cid:17) / (cid:18) 𝑠 c 𝑠 blow (cid:19) 𝑞 − (cid:26)(cid:104) 𝑋 − 𝑞 c − (cid:105) + 𝑞 − / 𝑞 − / (cid:104) 𝑋 − 𝑞 c − (cid:105) + 𝑞 − / 𝑞 − (cid:104) 𝑋 − 𝑞 c − (cid:105)(cid:27) − . (B2)The timescale depends on the fractional luminosity, 𝑓 d , the blow-outgrain size, 𝑠 blow , the stellar mass, 𝑀 star , the disc radius, 𝑟 , the discwidth, 𝑑𝑟 , the eccentricity, 𝑒 , the inclination, 𝑖 , and the parameter 𝑋 𝑐 which is defined as 𝑋 𝑐 = 𝑄 ∗ D 𝑣 / . (B3)Here, 𝑄 ∗ D the catastrophic disruption threshold and 𝑣 imp the impact velocity of the colliding bodies given as 𝑣 imp = √︁ 𝛾𝑀 star 𝑟 − ( / 𝑒 + 𝑖 ) with 𝛾 as gravitational constant.In the following section we fix both eccentricity and inclination to avalue of 0.1. B2 The catastrophic disruption threshold
The collisional timescale strongly depends on the catastrophic dis-ruption threshold, 𝑄 ∗ D of the planetesimals which is the specificenergy necessary to disperse a target (e.g., Benz & Asphaug 1999).The parameter can be described by a two-power law function taking into account the material strength, the self-gravity of particles andthe impact velocity (Stewart & Leinhardt 2009): 𝑄 ∗ D = (cid:20) 𝐴 (cid:16) 𝑠 (cid:17) 𝑎 + 𝐵 (cid:16) 𝑠 (cid:17) 𝑏 (cid:21) (cid:16) 𝑣 imp (cid:17) 𝑘 . (B4)The parameters 𝐴 , 𝐵 , 𝑎 , 𝑏 and 𝑘 are material constants. We found that 𝑣 imp is on average ∼ . 𝑒 = 𝑖 = .
1. Following O’Brien & Greenberg (2003), we caninfer the size distribution index, 𝑞 SED , from 𝑄 ∗ D using the parameter 𝑎 from eq. (B4): 𝑞 SED = + 𝑎 / + 𝑎 / . (B5)Hence, not only the collisional timescale but also the size distributionof planetesimals depends on 𝑄 ∗ D .Studies of the collisional evolution of debris discs (e.g., Wyatt &Dent 2002; Schüppler et al. 2014; Löhne et al. 2017; Krivov et al.2018; Geiler et al. 2019) often assume the materials “sand” (Stewart& Leinhardt 2009) and basalt (Benz & Asphaug 1999). In Fig. B1, 𝑄 ∗ D is depicted as a function of size for both materials. Using eq. (B4),we find that the values for basalt colliding at 0.4 km/s lie one orderof magnitude below those of Benz & Asphaug (1999) colliding at5 km/s.Another approach to infer values of 𝑄 ∗ D at the appropriate impactvelocity is given by Wyatt & Dent (2002) which introduced a scalingmethod where 𝑄 ∗ D ∝ 𝑣 𝛿 imp . Here, 𝛿 is found by comparing the twoimpact velocity curves given in Benz & Asphaug (1999). The methodgives values one order of magnitude below those from Stewart &Leinhardt (2009) for sizes smaller than ∼
100 m (strength regime).For larger sizes ( ∼ 𝑄 ∗ D to the impact velocity are both used inthe literature. Therefore, we emphasise that 𝑄 ∗ D strongly depends onthe method applied and shows variations of one order of magnitudeeven for the same material. Furthermore, 𝑄 ∗ D varies for the materialchosen. MNRAS000
100 m (strength regime).For larger sizes ( ∼ 𝑄 ∗ D to the impact velocity are both used inthe literature. Therefore, we emphasise that 𝑄 ∗ D strongly depends onthe method applied and shows variations of one order of magnitudeeven for the same material. Furthermore, 𝑄 ∗ D varies for the materialchosen. MNRAS000 , 1–26 (2021) N. Pawellek et al.
Figure A3.
SEDs for the debris discs detected around F stars in the DEBRIS sample.MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic Figure A4.
SEDs for the debris discs detected around F stars in the DEBRIS sample (continued). MNRAS000
SEDs for the debris discs detected around F stars in the DEBRIS sample (continued). MNRAS000 , 1–26 (2021) N. Pawellek et al.
Figure B1. 𝑄 ∗ D as function of size. The thin black dashed and dotted lineshow values for basalt at 3 and 5 km/s taken from Benz & Asphaug (1999).The parameters of the HD 109085 system are assumed. The thick blue dash-dotted line shows the scaling result taken for Wyatt & Dent (2002) and thethick green dashed line the lab results taken from Stewart & Leinhardt (2009)for basalt at 0.4 km/s. The thick solid red line shows the result for “sand” at0.4 km/s taken from Stewart & Leinhardt (2009). B3 Minimum sizes of planetesimals feeding the cascade
We calculate the minimum sizes of the planetesimals feeding the col-lisional cascade using eq. (B2) assuming that the collisional times-cale, 𝑡 c , is similar to the age of the system.Tab. B1 lists the planetesimal sizes and the corresponding min-imum disc masses (since the size distribution must extend up tothese sizes, and could extend further) assuming the two different ap-proaches to scale 𝑄 ∗ D to the impact velocity of the colliding bodiesas well as the two materials basalt and sand. We added the discsHD 10647 and HD 109085 from the DEBRIS sample to comparethe planetesimal sizes in systems of different age. Both discs werespatially resolved with ALMA.We find that the smallest planetesimals feeding the collisionalcascade show sizes from several metres up to ∼ 𝑄 ∗ D shown in Fig. B1. Considering the two scaling methods wefind a comparable trend – the method chosen to infer 𝑄 ∗ D becomesmore important for smaller sizes.The large variation in sizes leads to different disc masses dependingon the material applied. Again, discs for which the planetesimalsfeeding the dust belt are only required to be metre in size are moresensitive to the material and method used. The masses vary between2 𝑀 ⊕ (HD 160305) and 900 𝑀 ⊕ (HD 181327).Studies of planetesimal formation (e.g., Klahr & Schreiber 2020) found that typical planetesimal sizes tend to decrease with increasingdistance to the star and with the time of the formation of planetes-imals. While an early formation might lead to sizes of ∼
100 km,planetesimals formed at a later stage tend to be as small as ∼
10 km(e.g., Stern et al. 2019). This is still somewhat larger than the sizesof ∼ This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS , 1–26 (2021) ebris discs around F stars in 𝛽 Pic Table B1.
Sizes of planetesimals. System parameters Basalt (WD02) Basalt (SL09) Sand (SL09)HD r dr 𝑀 star 𝑠 blow 𝑓 d 𝑡 c 𝑠 c 𝑀 disc 𝑠 c 𝑀 disc 𝑠 c 𝑀 disc [au] [au] [ 𝑀 (cid:12) ] [ 𝜇 m ] [Myr] [m] [ 𝑀 earth ] [m] [ 𝑀 earth ] [m] [ 𝑀 earth ]15115 93 21 1.37 0.91 5 . × −
23 338 23 104 7.0 381 26160305 88 4 1.13 0.67 1 . × −
23 351 6.0 115 2.0 401 6.9164249 63 24 1.30 0.89 9 . × −
23 514 28 413 23 678 37181327 81 16 1.36 1.02 4 . × −
23 1417 562 1601 634 2188 867191089 45 16 1.36 0.98 1 . × −
23 1105 53 1310 63 1703 8110647 82 49 1.12 0.48 2 . × − . × − Notes:
The system data for HD 10647 were taken from Lovell et al. (in prep.), the data for HD 109085 from Matrà et al. (2018). The age estimates for both starsshow large uncertainties so that we fix the age to 1000 Myr for simplicity reasons. “Basalt (WD02)” refers to the scaling method of 𝑄 ∗ D used in Wyatt & Dent(2002) while “Basalt (SL09)” assumes the velocity dependence found in Stewart & Leinhardt (2009). “Sand (SL09)” refers to the weak rock materialintroduced in Stewart & Leinhardt (2009). MNRAS000